LMFDB - Embedded newform 220.3.w.a.183.29

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			183.29
Character	$\chi$	$=$	220.183
Dual form			220.3.w.a.107.29

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.468777 + 1.94429i) q^{2} +(2.06150 + 4.04592i) q^{3} +(-3.56050 - 1.82287i) q^{4} +(-3.48586 - 3.58452i) q^{5} +(-8.83280 + 2.11151i) q^{6} +(-5.94803 - 3.03067i) q^{7} +(5.21327 - 6.06810i) q^{8} +(-6.82960 + 9.40014i) q^{9} +(8.60342 - 5.09717i) q^{10} +(2.74293 - 10.6525i) q^{11} +(0.0352426 - 18.1633i) q^{12} +(-24.4474 + 3.87209i) q^{13} +(8.68079 - 10.1440i) q^{14} +(7.31657 - 21.4930i) q^{15} +(9.35426 + 12.9807i) q^{16} +(-18.0163 - 2.85350i) q^{17} +(-15.0750 - 17.6853i) q^{18} +(10.7855 + 3.50442i) q^{19} +(5.87726 + 19.1169i) q^{20} -30.3129i q^{21} +(19.4257 + 10.3267i) q^{22} +(-20.8240 + 20.8240i) q^{23} +(35.2982 + 8.58307i) q^{24} +(-0.697556 + 24.9903i) q^{25} +(3.93194 - 49.3479i) q^{26} +(-11.7470 - 1.86054i) q^{27} +(15.6534 + 21.6332i) q^{28} +(9.88305 + 30.4169i) q^{29} +(38.3586 + 24.3009i) q^{30} +(8.80617 - 12.1207i) q^{31} +(-29.6232 + 12.1023i) q^{32} +(48.7538 - 10.8625i) q^{33} +(13.9936 - 33.6911i) q^{34} +(9.87049 + 31.8853i) q^{35} +(41.4520 - 21.0197i) q^{36} +(-13.6232 - 6.94136i) q^{37} +(-11.8696 + 19.3273i) q^{38} +(-66.0644 - 90.9299i) q^{39} +(-39.9239 + 2.46549i) q^{40} +(9.85319 + 3.20150i) q^{41} +(58.9370 + 14.2100i) 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} +(-15.9055 + 8.10427i) q^{47} +(-33.2349 + 64.6062i) q^{48} +(-2.60743 - 3.58882i) q^{49} +(-48.2612 - 13.0711i) q^{50} +(-25.5955 - 78.7748i) q^{51} +(94.1033 + 30.7780i) 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} +(-63.7721 + 4.95673i) q^{58} +(24.7682 + 76.2288i) q^{59} +(-65.2296 + 63.1885i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(19.4379 + 22.8036i) q^{62} +(69.1114 - 35.2140i) 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} +(58.9453 + 43.0012i) q^{68} +(-127.181 - 41.3235i) q^{69} +(-66.6212 + 4.24395i) q^{70} +(12.2736 + 16.8932i) q^{71} +(21.4365 + 90.4481i) q^{72} +(-71.1314 - 36.2433i) q^{73} +(19.8822 - 23.2334i) q^{74} +(-102.547 + 48.6951i) q^{75} +(-32.0136 - 32.1380i) q^{76} +(-48.5993 + 55.0486i) q^{77} +(207.763 - 85.8223i) q^{78} +(58.2496 - 80.1738i) q^{79} +(13.9218 - 78.7793i) q^{80} +(15.6260 + 48.0919i) q^{81} +(-10.8436 + 17.6566i) q^{82} +(-103.856 - 16.4491i) q^{83} +(-55.2567 + 107.929i) q^{84} +(52.5738 + 74.5265i) q^{85} +(34.3112 - 20.9802i) q^{86} +(-102.690 + 102.690i) q^{87} +(-50.3410 - 72.1788i) q^{88} +69.0839i q^{89} +(-10.8438 + 115.685i) q^{90} +(157.149 + 51.0608i) q^{91} +(112.103 - 36.1842i) q^{92} +(67.1931 + 10.6423i) q^{93} +(-8.30087 - 34.7240i) q^{94} +(-25.0350 - 50.8767i) q^{95} +(-110.033 - 94.9041i) q^{96} +(143.479 - 22.7249i) q^{97} +(8.20000 - 3.38724i) q^{98} +(81.4022 + 98.5364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

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

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

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 $

$2$	−0.468777	+	1.94429i	−0.234389	+	0.972143i
$2$	−0.468777	+	1.94429i	−0.234389	+	0.972143i
$3$	2.06150	+	4.04592i	0.687166	+	1.34864i	0.925980	+	0.377573i	$0.123241\pi$
$3$	2.06150	+	4.04592i	0.687166	+	1.34864i	−0.238814	+	0.971065i	$0.576759\pi$
$4$	−3.56050	−	1.82287i	−0.890124	−	0.455718i
$5$	−3.48586	−	3.58452i	−0.697172	−	0.716904i
$5$	−3.48586	−	3.58452i	−0.697172	−	0.716904i
$6$	−8.83280	+	2.11151i	−1.47213	+	0.351918i
$7$	−5.94803	−	3.03067i	−0.849718	−	0.432953i	−0.0258034	−	0.999667i	$-0.508214\pi$
$7$	−5.94803	−	3.03067i	−0.849718	−	0.432953i	−0.823914	+	0.566714i	$0.808214\pi$
$8$	5.21327	−	6.06810i	0.651658	−	0.758513i
$9$	−6.82960	+	9.40014i	−0.758845	+	1.04446i
$10$	8.60342	−	5.09717i	0.860342	−	0.509717i
$11$	2.74293	−	10.6525i	0.249357	−	0.968412i
$11$	2.74293	−	10.6525i	0.249357	−	0.968412i
$12$	0.0352426	−	18.1633i	0.00293689	−	1.51361i
$13$	−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	$0.850983\pi$
$14$	8.68079	−	10.1440i	0.620056	−	0.724568i
$15$	7.31657	−	21.4930i	0.487772	−	1.43287i
$16$	9.35426	+	12.9807i	0.584641	+	0.811292i
$17$	−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	$0.730252\pi$
$18$	−15.0750	−	17.6853i	−0.837500	−	0.982515i
$19$	10.7855	+	3.50442i	0.567657	+	0.184443i	0.578764	−	0.815495i	$-0.303535\pi$
$19$	10.7855	+	3.50442i	0.567657	+	0.184443i	−0.0111065	+	0.999938i	$0.503535\pi$
$20$	5.87726	+	19.1169i	0.293863	+	0.955847i
$21$		−	30.3129i		−	1.44347i
$22$	19.4257	+	10.3267i	0.882988	+	0.469395i
$23$	−20.8240	+	20.8240i	−0.905390	+	0.905390i	−0.995896	−	0.0905057i	$-0.971152\pi$
$23$	−20.8240	+	20.8240i	−0.905390	+	0.905390i	0.0905057	+	0.995896i	$0.471152\pi$
$24$	35.2982	+	8.58307i	1.47076	+	0.357628i
$25$	−0.697556	+	24.9903i	−0.0279022	+	0.999611i
$26$	3.93194	−	49.3479i	0.151228	−	1.89800i
$27$	−11.7470	−	1.86054i	−0.435073	−	0.0689089i
$28$	15.6534	+	21.6332i	0.559050	+	0.772614i
$29$	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	$0.714087\pi$
$30$	38.3586	+	24.3009i	1.27862	+	0.810031i
$31$	8.80617	−	12.1207i	0.284070	−	0.390989i	−0.643007	−	0.765861i	$-0.722313\pi$
$31$	8.80617	−	12.1207i	0.284070	−	0.390989i	0.927077	+	0.374872i	$0.122313\pi$
$32$	−29.6232	+	12.1023i	−0.925725	+	0.378197i
$33$	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
$36$	41.4520	−	21.0197i	1.15145	−	0.583879i
$37$	−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	$0.716245\pi$
$38$	−11.8696	+	19.3273i	−0.312357	+	0.508613i
$39$	−66.0644	−	90.9299i	−1.69396	−	2.33154i
$40$	−39.9239	+	2.46549i	−0.998099	+	0.0616373i
$41$	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	$0.559675\pi$
$42$	58.9370	+	14.2100i	1.40326	+	0.338334i
$43$	−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
$47$	−15.9055	+	8.10427i	−0.338415	+	0.172431i	−0.614937	−	0.788577i	$-0.710818\pi$
$47$	−15.9055	+	8.10427i	−0.338415	+	0.172431i	0.276521	+	0.961008i	$0.410818\pi$
$48$	−33.2349	+	64.6062i	−0.692394	+	1.34596i
$49$	−2.60743	−	3.58882i	−0.0532129	−	0.0732413i
$50$	−48.2612	−	13.0711i	−0.965225	−	0.261422i
$51$	−25.5955	−	78.7748i	−0.501872	−	1.54460i
$52$	94.1033	+	30.7780i	1.80968	+	0.591885i
$53$	−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
$58$	−63.7721	+	4.95673i	−1.09952	+	0.0854608i
$59$	24.7682	+	76.2288i	0.419801	+	1.29201i	0.907886	+	0.419218i	$0.137696\pi$
$59$	24.7682	+	76.2288i	0.419801	+	1.29201i	−0.488085	+	0.872796i	$0.662304\pi$
$60$	−65.2296	+	63.1885i	−1.08716	+	1.05314i
$61$	−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	$0.901043\pi$
$62$	19.4379	+	22.8036i	0.313514	+	0.367800i
$63$	69.1114	−	35.2140i	1.09701	−	0.558952i
$64$	−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	0.812019	−	0.583631i	$-0.198369\pi$
$67$	15.3020	+	15.3020i	0.228388	+	0.228388i	−0.583631	+	0.812019i	$0.698369\pi$
$68$	58.9453	+	43.0012i	0.866842	+	0.632371i
$69$	−127.181	−	41.3235i	−1.84320	−	0.598891i
$70$	−66.6212	+	4.24395i	−0.951732	+	0.0606279i
$71$	12.2736	+	16.8932i	0.172868	+	0.237932i	0.886656	−	0.462429i	$-0.153022\pi$
$71$	12.2736	+	16.8932i	0.172868	+	0.237932i	−0.713788	+	0.700362i	$0.753022\pi$
$72$	21.4365	+	90.4481i	0.297728	+	1.25622i
$73$	−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	$0.834154\pi$
$74$	19.8822	−	23.2334i	0.268679	−	0.313965i
$75$	−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
$78$	207.763	−	85.8223i	2.66363	−	1.10029i
$79$	58.2496	−	80.1738i	0.737337	−	1.01486i	−0.261430	−	0.965222i	$-0.584194\pi$
$79$	58.2496	−	80.1738i	0.737337	−	1.01486i	0.998767	−	0.0496354i	$-0.0158059\pi$
$80$	13.9218	−	78.7793i	0.174023	−	0.984742i
$81$	15.6260	+	48.0919i	0.192914	+	0.593727i
$82$	−10.8436	+	17.6566i	−0.132239	+	0.215325i
$83$	−103.856	−	16.4491i	−1.25127	−	0.198182i	−0.504587	−	0.863361i	$-0.668355\pi$
$83$	−103.856	−	16.4491i	−1.25127	−	0.198182i	−0.746684	+	0.665179i	$0.768355\pi$
$84$	−55.2567	+	107.929i	−0.657817	+	1.28487i
$85$	52.5738	+	74.5265i	0.618515	+	0.876783i
$86$	34.3112	−	20.9802i	0.398968	−	0.243956i
$87$	−102.690	+	102.690i	−1.18035	+	1.18035i
$88$	−50.3410	−	72.1788i	−0.572057	−	0.820214i
$89$			69.0839i			0.776223i	0.921612	+	0.388112i	$0.126872\pi$
$89$			69.0839i			0.776223i	−0.921612	+	0.388112i	$0.873128\pi$
$90$	−10.8438	+	115.685i	−0.120487	+	1.28539i
$91$	157.149	+	51.0608i	1.72691	+	0.561107i
$92$	112.103	−	36.1842i	1.21851	−	0.393306i
$93$	67.1931	+	10.6423i	0.722506	+	0.114434i
$94$	−8.30087	−	34.7240i	−0.0883071	−	0.369404i
$95$	−25.0350	−	50.8767i	−0.263527	−	0.535544i
$96$	−110.033	−	94.9041i	−1.14618	−	0.988584i
$97$	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	$0.180629\pi$
$98$	8.20000	−	3.38724i	0.0836735	−	0.0345636i
$99$	81.4022	+	98.5364i	0.822244	+	0.995317i
$100$	48.0377	−	87.7062i	0.480377	−	0.877062i
$101$	−73.0522	+	100.548i	−0.723289	+	0.995522i	0.276119	+	0.961123i	$0.410952\pi$
$101$	−73.0522	+	100.548i	−0.723289	+	0.995522i	−0.999408	+	0.0343985i	$0.989048\pi$
$102$	165.159	−	12.8371i	1.61921	−	0.125854i
$103$	−6.32402	−	3.22225i	−0.0613982	−	0.0312840i	0.423022	−	0.906119i	$-0.360969\pi$
$103$	−6.32402	−	3.22225i	−0.0613982	−	0.0312840i	−0.484420	+	0.874836i	$0.660969\pi$
$104$	−103.955	+	168.536i	−0.999564	+	1.62053i
$105$	−108.657	+	105.667i	−1.03483	+	1.00635i
$106$	140.834	+	11.2213i	1.32862	+	0.105862i
$107$	−0.400378	−	0.785785i	−0.00374185	−	0.00734379i	0.889128	−	0.457659i	$-0.151312\pi$
$107$	−0.400378	−	0.785785i	−0.00374185	−	0.00734379i	−0.892870	+	0.450315i	$0.851312\pi$
$108$	38.4336	+	28.0377i	0.355866	+	0.259608i
$109$	−187.495			−1.72014			−0.860068	−	0.510179i	$-0.829579\pi$
$109$	−187.495			−1.72014			−0.860068	+	0.510179i	$0.829579\pi$
$110$	−30.6992	−	105.629i	−0.279083	−	0.960267i
$111$		−	69.4279i		−	0.625477i
$112$	−16.2993	−	105.559i	−0.145529	−	0.942491i
$113$	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	$0.289178\pi$
$114$	−102.666	−	8.18019i	−0.900576	−	0.0717560i
$115$	147.233	+	2.05447i	1.28029	+	0.0178650i
$116$	20.2576	−	126.315i	0.174635	−	1.08892i
$117$	130.568	−	256.254i	1.11597	−	2.19020i
$118$	−159.821	+	12.4222i	−1.35442	+	0.105273i
$119$	98.5132	+	71.5740i	0.827842	+	0.601462i
$120$	−92.2783	−	156.446i	−0.768986	−	1.30372i
$121$	−105.953	−	58.4382i	−0.875642	−	0.482960i
$122$	70.3913	−	29.0770i	0.576978	−	0.238336i
$123$	7.35934	+	46.4651i	0.0598321	+	0.377765i
$124$	−53.4488	+	27.1030i	−0.431038	+	0.218573i
$125$	92.0097	−	84.6122i	0.736077	−	0.676897i
$126$	36.0682	+	150.880i	0.286256	+	1.19746i
$127$	1.31526	−	8.30422i	0.0103564	−	0.0653876i	−0.981969	−	0.189043i	$-0.939462\pi$
$127$	1.31526	−	8.30422i	0.0103564	−	0.0653876i	0.992325	+	0.123655i	$0.0394616\pi$
$128$	127.534	+	10.9091i	0.996362	+	0.0852274i
$129$	28.2164	−	86.8411i	0.218732	−	0.673187i
$130$	−190.595	+	157.926i	−1.46611	+	1.21481i
$131$	−160.641			−1.22627			−0.613134	−	0.789979i	$-0.710091\pi$
$131$	−160.641			−1.22627			−0.613134	+	0.789979i	$0.710091\pi$
$132$	−193.389	−	50.1961i	−1.46507	−	0.380273i
$133$	−53.5316	−	53.5316i	−0.402493	−	0.402493i
$134$	−36.9246	+	22.5782i	−0.275557	+	0.168494i
$135$	34.2792	+	48.5929i	0.253920	+	0.359947i
$136$	−111.239	+	94.4484i	−0.817933	+	0.694474i
$137$	−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	$0.957542\pi$
$138$	139.964	−	227.904i	1.01423	−	1.65148i
$139$	49.9473	−	16.2289i	0.359333	−	0.116754i	−0.123786	−	0.992309i	$-0.539504\pi$
$139$	49.9473	−	16.2289i	0.359333	−	0.116754i	0.483119	+	0.875554i	$0.339504\pi$
$140$	22.9791	−	131.520i	0.164136	−	0.939430i
$141$	−65.5784	−	47.6455i	−0.465095	−	0.337911i
$142$	−38.5988	+	15.9443i	−0.271822	+	0.112284i
$143$	−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
$146$	103.812	−	121.310i	0.711042	−	0.830889i
$147$	9.14486	−	17.9478i	0.0622100	−	0.122094i
$148$	35.8521	+	49.5481i	0.242244	+	0.334784i
$149$	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	$0.280435\pi$
$150$	−46.6057	−	222.207i	−0.310705	−	1.48138i
$151$	63.1157	−	194.250i	0.417984	−	1.28642i	−0.491570	−	0.870838i	$-0.663577\pi$
$151$	63.1157	−	194.250i	0.417984	−	1.28642i	0.909554	−	0.415586i	$-0.136423\pi$
$152$	77.4928	−	47.1779i	0.509821	−	0.310381i
$153$	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
$157$	−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	$0.869514\pi$
$158$	128.575	+	150.838i	0.813763	+	0.954668i
$159$	259.504	−	188.541i	1.63210	−	1.18579i
$160$	146.643	+	63.9979i	0.916521	+	0.399987i
$161$	186.972	−	60.7509i	1.16132	−	0.377335i
$162$	−100.830	+	7.83704i	−0.622405	+	0.0483768i
$163$	192.335	−	30.4629i	1.17997	−	0.186889i	0.464526	−	0.885560i	$-0.346225\pi$
$163$	192.335	−	30.4629i	1.17997	−	0.186889i	0.715443	+	0.698671i	$0.246225\pi$
$164$	−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	0.557352	−	0.830276i	$-0.311817\pi$
$167$	224.447	−	35.5489i	1.34400	−	0.212868i	0.786643	+	0.617408i	$0.211817\pi$
$168$	−183.942	−	158.029i	−1.09489	−	0.940651i
$169$	421.955	−	137.101i	2.49677	−	0.811251i
$170$	−169.546	+	67.2821i	−0.997331	+	0.395777i
$171$	−106.603	+	77.4513i	−0.623407	+	0.452932i
$172$	24.7072	+	76.5459i	0.143646	+	0.445034i
$173$	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	$0.777755\pi$
$174$	−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
$178$	−134.319	−	32.3849i	−0.754600	−	0.181938i
$179$	−51.6714	+	159.028i	−0.288667	+	0.888426i	0.696608	+	0.717452i	$0.254692\pi$
$179$	−51.6714	+	159.028i	−0.288667	+	0.888426i	−0.985275	+	0.170975i	$0.945308\pi$
$180$	−219.841	−	75.3140i	−1.22134	−	0.418411i
$181$	−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	$0.985861\pi$
$182$	−172.945	+	281.606i	−0.950245	+	1.54729i
$183$	78.5022	−	154.069i	0.428974	−	0.841909i
$184$	17.8010	+	234.923i	0.0967447	+	1.27676i
$185$	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
$188$	71.4046	+	0.138548i	0.379812	+	0.000736956i
$189$	64.2327	+	46.6678i	0.339855	+	0.246919i
$190$	110.655	−	24.8255i	0.582393	−	0.130660i
$191$	123.363	−	40.0830i	0.645878	−	0.209859i	0.0322823	−	0.999479i	$-0.489722\pi$
$191$	123.363	−	40.0830i	0.645878	−	0.209859i	0.613596	+	0.789620i	$0.289722\pi$
$192$	236.102	−	169.447i	1.22970	−	0.882536i
$193$	−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	$0.992923\pi$
$194$	−23.0762	+	289.618i	−0.118949	+	1.49288i
$195$	−95.6486	+	553.778i	−0.490505	+	2.83989i
$196$	2.74178	+	17.5310i	0.0139887	+	0.0894439i
$197$	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	$0.672426\pi$
$198$	−229.742	+	112.077i	−1.16032	+	0.566048i
$199$	−56.9753			−0.286308			−0.143154	−	0.989700i	$-0.545724\pi$
$199$	−56.9753			−0.286308			−0.143154	+	0.989700i	$0.545724\pi$
$200$	148.007	+	134.514i	0.740034	+	0.672569i
$201$	−30.3655	+	93.4554i	−0.151072	+	0.464952i
$202$	−161.248	−	189.169i	−0.798259	−	0.936479i
$203$	33.3990	−	210.873i	0.164527	−	1.03878i
$204$	−52.4639	+	327.134i	−0.257176	+	1.60360i
$205$	−22.8710	−	46.4789i	−0.111566	−	0.226726i
$206$	9.22953	−	10.7852i	0.0448035	−	0.0523553i
$207$	−53.5288	−	337.968i	−0.258593	−	1.63269i
$208$	−278.950	−	281.123i	−1.34111	−	1.35155i
$209$	66.9147	−	105.280i	0.320166	−	0.503734i
$210$	−154.510	−	260.795i	−0.735762	−	1.24188i
$211$	−225.181	−	163.604i	−1.06721	−	0.775373i	−0.0918009	−	0.995777i	$-0.529262\pi$
$211$	−225.181	−	163.604i	−1.06721	−	0.775373i	−0.975409	+	0.220404i	$0.929262\pi$
$212$	−87.8371	+	268.561i	−0.414326	+	1.26680i
$213$	−43.0464	+	84.4833i	−0.202096	+	0.396635i
$214$	1.71548	−	0.410090i	0.00801626	−	0.00191631i
$215$	−1.40283	+	100.533i	−0.00652478	+	0.467597i
$216$	−72.5301	+	61.5824i	−0.335788	+	0.285104i
$217$	−89.1131	+	45.4054i	−0.410659	+	0.209241i
$218$	87.8933	−	364.544i	0.403180	−	1.67222i
$219$		−	362.507i		−	1.65528i
$220$	219.765	−	10.1713i	0.998931	−	0.0462334i
$221$	451.500			2.04299
$222$	134.988	+	32.5462i	0.608053	+	0.146605i
$223$	88.8904	+	174.457i	0.398612	+	0.782319i	0.999860	−	0.0167431i	$-0.00532975\pi$
$223$	88.8904	+	174.457i	0.398612	+	0.782319i	−0.601248	+	0.799062i	$0.705330\pi$
$224$	212.878	+	17.7933i	0.950347	+	0.0794342i
$225$	−230.148	−	177.231i	−1.02288	−	0.787692i
$226$	19.9585	+	83.4900i	0.0883121	+	0.369425i
$227$	−101.029	−	51.4767i	−0.445061	−	0.226770i	0.217073	−	0.976155i	$-0.430349\pi$
$227$	−101.029	−	51.4767i	−0.445061	−	0.226770i	−0.662134	+	0.749386i	$0.730349\pi$
$228$	64.0319	−	195.777i	0.280842	−	0.858670i
$229$	−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	$0.282844\pi$
$230$	−73.0141	+	285.301i	−0.317453	+	1.24044i
$231$	−322.909	−	83.1461i	−1.39788	−	0.359940i
$232$	236.096	+	98.6001i	1.01765	+	0.425000i
$233$	−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	$0.669618\pi$
$234$	437.024	+	373.987i	1.86762	+	1.59824i
$235$	84.4943	+	28.7633i	0.359550	+	0.122397i
$236$	50.7683	−	316.562i	0.215120	−	1.34136i
$237$	444.458	+	70.3952i	1.87535	+	0.297026i
$238$	−185.341	+	157.986i	−0.778744	+	0.663805i
$239$	−163.096	−	52.9932i	−0.682412	−	0.221729i	−0.0527607	−	0.998607i	$-0.516802\pi$
$239$	−163.096	−	52.9932i	−0.682412	−	0.221729i	−0.629651	+	0.776878i	$0.716802\pi$
$240$	347.434	−	106.077i	1.44764	−	0.441987i
$241$		−	132.086i		−	0.548074i	−0.961719	−	0.274037i	$-0.911641\pi$
$241$		−	132.086i		−	0.548074i	0.961719	−	0.274037i	$-0.0883591\pi$
$242$	163.289	−	178.608i	0.674747	−	0.738049i
$243$	−238.052	+	238.052i	−0.979638	+	0.979638i
$244$	23.5363	+	150.491i	0.0964601	+	0.616768i
$245$	−3.77506	+	21.8565i	−0.0154084	+	0.0892103i
$246$	−93.7913	−	7.47310i	−0.381265	−	0.0303784i
$247$	−277.247	−	43.9116i	−1.12246	−	0.177780i
$248$	−27.6404	−	116.625i	−0.111453	−	0.470262i
$249$	−147.546	−	454.101i	−0.592555	−	1.82370i
$250$	121.378	+	218.557i	0.485513	+	0.874230i
$251$	15.5316	−	21.3775i	0.0618791	−	0.0851692i	−0.776956	−	0.629555i	$-0.783237\pi$
$251$	15.5316	−	21.3775i	0.0618791	−	0.0851692i	0.838835	+	0.544386i	$0.183237\pi$
$252$	−310.261	−	0.602006i	−1.23120	−	0.00238891i
$253$	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
$256$	−80.9956	+	242.849i	−0.316389	+	0.948630i
$257$	−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	$0.924781\pi$
$258$	155.617	+	95.5698i	0.603165	+	0.370426i
$259$	59.9941	+	82.5748i	0.231638	+	0.318822i
$260$	−217.706	−	444.603i	−0.837333	−	1.71001i
$261$	−353.420	−	114.833i	−1.35410	−	0.439974i
$262$	75.3048	−	312.332i	0.287423	−	1.19211i
$263$	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
$267$	−279.507	+	142.416i	−1.04684	+	0.533394i
$268$	−26.5890	−	82.3761i	−0.0992128	−	0.307374i
$269$	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	$0.709861\pi$
$270$	−110.548	+	43.8693i	−0.409436	+	0.162479i
$271$	−10.1507	−	31.2405i	−0.0374563	−	0.115279i	0.930580	−	0.366088i	$-0.119303\pi$
$271$	−10.1507	−	31.2405i	−0.0374563	−	0.115279i	−0.968036	+	0.250810i	$0.919303\pi$
$272$	−131.489	−	260.555i	−0.483414	−	0.957924i
$273$	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	$0.920219\pi$
$278$	8.13939	+	104.720i	0.0292784	+	0.376689i
$279$	53.7932	+	165.558i	0.192807	+	0.593400i
$280$	244.941	+	106.332i	0.874788	+	0.379755i
$281$	−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	$0.823751\pi$
$282$	123.378	−	105.168i	0.437511	−	0.372936i
$283$	−11.6374	+	5.92958i	−0.0411217	+	0.0209526i	−0.474430	−	0.880293i	$-0.657346\pi$
$283$	−11.6374	+	5.92958i	−0.0411217	+	0.0209526i	0.433309	+	0.901246i	$0.357346\pi$
$284$	−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
$288$	88.5512	−	361.116i	0.307469	−	1.25388i
$289$	41.5878	+	13.5127i	0.143903	+	0.0467568i
$290$	240.068	+	211.314i	0.827821	+	0.728668i
$291$	387.725	+	533.658i	1.33239	+	1.83388i
$292$	187.196	+	258.708i	0.641083	+	0.885985i
$293$	−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	$0.687885\pi$
$294$	30.6088	+	26.1938i	0.104111	+	0.0890944i
$295$	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
$298$	13.9774	+	33.8372i	0.0469039	+	0.113548i
$299$	428.460	−	589.725i	1.43298	−	1.97232i
$300$	453.882	+	13.5507i	1.51294	+	0.0451688i
$301$	41.4818	+	127.668i	0.137813	+	0.424145i
$302$	348.090	+	213.775i	1.15262	+	0.707864i
$303$	−557.405	−	88.2842i	−1.83962	−	0.291367i
$304$	55.4006	+	172.784i	0.182239	+	0.568369i
$305$	−32.4062	+	187.623i	−0.106250	+	0.615157i
$306$	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	$0.239915\pi$
$308$	273.384	−	107.410i	0.887611	−	0.348734i
$309$		−	32.2291i		−	0.104301i
$310$	13.9822	−	149.166i	0.0451039	−	0.481180i
$311$	−313.415	−	101.835i	−1.00776	−	0.327442i	−0.241800	−	0.970326i	$-0.577738\pi$
$311$	−313.415	−	101.835i	−1.00776	−	0.327442i	−0.765964	+	0.642884i	$0.777738\pi$
$312$	−896.183	−	73.1562i	−2.87238	−	0.234475i
$313$	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	$0.527339\pi$
$314$	37.4220	−	8.94583i	0.119178	−	0.0284899i
$315$	−367.138	−	124.980i	−1.16552	−	0.396762i
$316$	−353.544	+	179.277i	−1.11881	+	0.567331i
$317$	−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	$0.455856\pi$
$318$	244.928	+	592.934i	0.770213	+	1.86457i
$319$	351.125	−	21.8482i	1.10071	−	0.0684895i
$320$	−193.173	+	255.116i	−0.603667	+	0.797237i
$321$	2.35384	−	3.23979i	0.00733285	−	0.0100928i
$322$	30.4689	+	392.006i	0.0946239	+	1.21741i
$323$	−184.314	−	93.9128i	−0.570632	−	0.290752i
$324$	32.0292	−	199.715i	0.0988554	−	0.616405i
$325$	−79.7111	−	613.648i	−0.245265	−	1.88815i
$326$	−30.9337	+	388.234i	−0.0948887	+	1.19090i
$327$	−386.520	−	758.589i	−1.18202	−	2.31984i
$328$	70.7943	−	43.0999i	0.215836	−	0.131402i
$329$	119.168			0.362212
$330$	364.081	−	341.961i	1.10328	−	1.03625i
$331$		−	389.384i		−	1.17639i	−0.808720	−	0.588194i	$-0.799839\pi$
$331$		−	389.384i		−	1.17639i	0.808720	−	0.588194i	$-0.200161\pi$
$332$	339.793	+	247.882i	1.02347	+	0.746634i
$333$	158.291	−	80.6532i	0.475348	−	0.242202i
$334$	−36.0984	+	453.054i	−0.108079	+	1.35645i
$335$	1.50968	−	108.191i	0.00450649	−	0.322957i
$336$	393.482	−	283.555i	1.17108	−	0.843914i
$337$	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	$-0.0659691\pi$
$338$	68.7615	+	884.670i	0.203437	+	2.61737i
$339$	157.676	+	114.558i	0.465121	+	0.337930i
$340$	−51.3362	−	361.187i	−0.150989	−	1.06231i
$341$	−104.961	−	127.054i	−0.307803	−	0.372593i
$342$	−100.615	−	243.573i	−0.294195	−	0.712203i
$343$	55.8031	+	352.327i	0.162691	+	1.02719i
$344$	−160.409	+	12.1548i	−0.466306	+	0.0353338i
$345$	295.209	+	599.929i	0.855678	+	1.73893i
$346$	−151.448	+	36.2041i	−0.437711	+	0.104636i
$347$	−9.59150	+	60.5584i	−0.0276412	+	0.174520i	−0.997647	−	0.0685629i	$-0.978159\pi$
$347$	−9.59150	+	60.5584i	−0.0276412	+	0.174520i	0.970006	+	0.243083i	$0.0781586\pi$
$348$	552.820	−	178.437i	1.58856	−	0.512750i
$349$	−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	$0.118225\pi$
$350$	247.445	+	224.011i	0.706985	+	0.640032i
$351$	294.388			0.838711
$352$	47.6660	+	348.758i	0.135415	+	0.990789i
$353$	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
$355$	17.7698	−	102.882i	0.0500559	−	0.289809i
$356$	125.931	−	245.973i	0.353739	−	0.690935i
$357$	−86.4978	+	546.126i	−0.242291	+	1.52976i
$358$	−284.974	−	175.013i	−0.796017	−	0.488863i
$359$	−489.097	+	158.917i	−1.36239	+	0.442667i	−0.896840	−	0.442356i	$-0.854143\pi$
$359$	−489.097	+	158.917i	−1.36239	+	0.442667i	−0.465548	+	0.885022i	$0.654143\pi$
$360$	249.489	−	392.129i	0.693024	−	1.08925i
$361$	−188.009	−	136.597i	−0.520802	−	0.378385i
$362$	−230.618	−	558.291i	−0.637065	−	1.54224i
$363$	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
$366$	262.755	+	224.855i	0.717909	+	0.614358i
$367$	313.674	−	615.620i	0.854697	−	1.67744i	0.126611	−	0.991952i	$-0.459590\pi$
$367$	313.674	−	615.620i	0.854697	−	1.67744i	0.728086	−	0.685485i	$-0.240410\pi$
$368$	−465.102	−	75.5162i	−1.26386	−	0.205207i
$369$	−97.3879	+	70.7564i	−0.263924	+	0.191752i
$370$	−152.587	+	9.72023i	−0.412398	+	0.0262709i
$371$	−145.722	+	448.486i	−0.392782	+	1.20886i
$372$	−219.841	−	160.376i	−0.590970	−	0.431120i
$373$	−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	$0.371393\pi$
$374$	−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
$377$	−359.392	−	705.347i	−0.953294	−	1.87095i
$378$	−120.846	+	103.010i	−0.319699	+	0.272513i
$379$	−520.868	+	378.433i	−1.37432	+	0.998503i	−0.376936	+	0.926239i	$0.623022\pi$
$379$	−520.868	+	378.433i	−1.37432	+	0.998503i	−0.997386	+	0.0722642i	$0.976978\pi$
$380$	−3.60461	+	226.782i	−0.00948580	+	0.596795i
$381$	36.3096	−	11.7977i	0.0953008	−	0.0309651i
$382$	20.1031	+	258.642i	0.0526260	+	0.677074i
$383$	−384.380	+	60.8799i	−1.00360	+	0.158955i	−0.636543	−	0.771241i	$-0.719636\pi$
$383$	−384.380	+	60.8799i	−1.00360	+	0.158955i	−0.367061	+	0.930197i	$0.619636\pi$
$384$	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
$388$	−552.282	−	180.633i	−1.42341	−	0.465549i
$389$	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	$0.187169\pi$
$390$	−1031.87	−	445.567i	−2.64581	−	1.14248i
$391$	434.591	−	315.749i	1.11149	−	0.807542i
$392$	−35.3706	−	2.88733i	−0.0902311	−	0.00736564i
$393$	−331.161	−	649.940i	−0.842649	−	1.65379i
$394$	−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	$0.396221\pi$
$398$	26.7087	−	110.776i	0.0671074	−	0.278333i
$399$	106.229	−	326.940i	0.266238	−	0.819398i
$400$	−330.916	+	224.711i	−0.827289	+	0.561777i
$401$	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	$0.149649\pi$
$402$	−167.469	−	102.849i	−0.416591	−	0.255843i
$403$	−168.356	+	330.417i	−0.417757	+	0.819893i
$404$	443.388	−	224.835i	1.09749	−	0.556522i
$405$	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
$408$	−611.449	−	255.358i	−1.49865	−	0.625877i
$409$	−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	$0.858794\pi$
$410$	101.090	−	22.6796i	0.246560	−	0.0553160i
$411$	−338.892	+	110.113i	−0.824554	+	0.267914i
$412$	16.6429	+	23.0007i	0.0403954	+	0.0558269i
$413$	83.7023	−	528.475i	0.202669	−	1.27960i
$414$	682.199	+	54.3562i	1.64782	+	0.131295i
$415$	303.064	+	429.611i	0.730274	+	1.03521i
$416$	677.349	−	410.574i	1.62824	−	0.986957i
$417$	168.627	+	168.627i	0.404381	+	0.404381i
$418$	173.327	+	179.454i	0.414658	+	0.429317i
$419$	−312.635			−0.746145			−0.373072	−	0.927802i	$-0.621696\pi$
$419$	−312.635			−0.746145			−0.373072	+	0.927802i	$0.621696\pi$
$420$	579.491	−	178.157i	1.37974	−	0.424184i
$421$	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	$0.0603787\pi$
$422$	423.652	−	361.123i	1.00392	−	0.855742i
$423$	32.4471	−	204.863i	0.0767071	−	0.484310i
$424$	−480.983	−	296.676i	−1.13439	−	0.699707i
$425$	83.8770	−	448.241i	0.197358	−	1.05468i
$426$	−144.081	−	123.298i	−0.338217	−	0.289433i
$427$	39.7671	+	251.079i	0.0931313	+	0.588008i
$428$	−0.00684471	+	3.52762i	−1.59923e−5	+	0.00824211i
$429$	−1149.84	+	454.339i	−2.68029	+	1.05907i
$430$	−194.808	−	49.8553i	−0.453042	−	0.115943i
$431$	47.3487	+	34.4008i	0.109858	+	0.0798164i	0.641358	−	0.767242i	$-0.278371\pi$
$431$	47.3487	+	34.4008i	0.109858	+	0.0798164i	−0.531500	+	0.847058i	$0.678371\pi$
$432$	−85.7333	−	169.888i	−0.198457	−	0.393259i
$433$	−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	$0.249333\pi$
$434$	−46.5069	−	194.546i	−0.107159	−	0.448263i
$435$	726.060	+	10.1313i	1.66910	+	0.0232904i
$436$	667.575	+	341.780i	1.53114	+	0.783898i
$437$	−297.573	+	151.621i	−0.680944	+	0.346958i
$438$	704.818	+	169.935i	1.60917	+	0.387980i
$439$		−	132.823i		−	0.302557i	−0.988491	−	0.151279i	$-0.951661\pi$
$439$		−	132.823i		−	0.302557i	0.988491	−	0.151279i	$-0.0483391\pi$
$440$	−83.2447	+	432.054i	−0.189193	+	0.981940i
$441$	51.5432			0.116878
$442$	−211.653	+	877.845i	−0.478853	+	1.98607i
$443$	−2.05716	−	4.03740i	−0.00464370	−	0.00911378i	0.888673	−	0.458541i	$-0.151628\pi$
$443$	−2.05716	−	4.03740i	−0.00464370	−	0.00911378i	−0.893317	+	0.449428i	$0.851628\pi$
$444$	−126.558	+	247.198i	−0.285041	+	0.556752i
$445$	247.632	−	240.817i	0.556477	−	0.541161i
$446$	−380.864	+	91.0467i	−0.853956	+	0.204141i
$447$	74.0613	+	37.7361i	0.165685	+	0.0844208i
$448$	−134.387	+	405.554i	−0.299972	+	0.905254i
$449$	−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	$0.280524\pi$
$450$	452.475	−	364.392i	1.00550	−	0.809759i
$451$	61.1306	−	96.1800i	0.135545	−	0.213259i
$452$	−171.685	−	0.333123i	−0.379833	−	0.000736998i
$453$	916.032	−	145.085i	2.02215	−	0.320276i
$454$	147.445	−	172.298i	0.324770	−	0.379510i
$455$	−364.771	−	741.294i	−0.801694	−	1.62922i
$456$	350.629	+	216.272i	0.768924	+	0.474281i
$457$	−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	$0.684825\pi$
$458$	−152.912	−	179.389i	−0.333869	−	0.391679i
$459$	206.328	+	67.0399i	0.449516	+	0.146056i
$460$	−520.479	−	275.703i	−1.13148	−	0.599354i
$461$			886.126i			1.92218i	0.276232	+	0.961091i	$0.410914\pi$
$461$			886.126i			1.92218i	−0.276232	+	0.961091i	$0.589086\pi$
$462$	313.032	−	588.851i	0.677559	−	1.27457i
$463$	425.628	−	425.628i	0.919284	−	0.919284i	−0.0776934	−	0.996977i	$-0.524756\pi$
$463$	425.628	−	425.628i	0.919284	−	0.919284i	0.996977	+	0.0776934i	$0.0247555\pi$
$464$	−302.383	+	412.816i	−0.651688	+	0.889690i
$465$	−196.078	−	277.953i	−0.421673	−	0.597747i
$466$	47.1169	−	591.342i	0.101109	−	1.26897i
$467$	−216.913	−	34.3556i	−0.464481	−	0.0735666i	−0.0801922	−	0.996779i	$-0.525553\pi$
$467$	−216.913	−	34.3556i	−0.464481	−	0.0735666i	−0.384289	+	0.923213i	$0.625553\pi$
$468$	−932.005	+	674.382i	−1.99146	+	1.44099i
$469$	−44.6413	−	137.392i	−0.0951839	−	0.292946i
$470$	−95.5331	+	150.798i	−0.203262	+	0.320846i
$471$	51.3474	−	70.6737i	0.109018	−	0.150050i
$472$	591.687	+	247.105i	1.25358	+	0.523528i
$473$	−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
$476$	−220.285	−	434.416i	−0.462784	−	0.912639i
$477$	731.321	+	372.627i	1.53317	+	0.781188i
$478$	179.490	−	292.264i	0.375502	−	0.611431i
$479$	414.922	+	571.091i	0.866226	+	1.19226i	0.980049	+	0.198756i	$0.0636902\pi$
$479$	414.922	+	571.091i	0.866226	+	1.19226i	−0.113823	+	0.993501i	$0.536310\pi$
$480$	43.3745	+	725.238i	0.0903635	+	1.51091i
$481$	359.930	+	116.948i	0.748294	+	0.243136i
$482$	256.813	+	61.9188i	0.532806	+	0.128462i
$483$	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
$487$	308.957	−	157.422i	0.634410	−	0.323248i	−0.107042	−	0.994255i	$-0.534138\pi$
$487$	308.957	−	157.422i	0.634410	−	0.323248i	0.741451	+	0.671007i	$0.234138\pi$
$488$	−303.632	−	24.7857i	−0.622196	−	0.0507904i
$489$	519.748	+	715.372i	1.06288	+	1.46293i
$490$	−40.7257	−	17.5856i	−0.0831136	−	0.0358891i
$491$	125.437	+	386.055i	0.255472	+	0.786263i	0.993736	+	0.111751i	$0.0356459\pi$
$491$	125.437	+	386.055i	0.255472	+	0.786263i	−0.738264	+	0.674512i	$0.764354\pi$
$492$	58.4971	−	178.854i	0.118896	−	0.363524i
$493$	−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
$498$	952.068	−	74.0000i	1.91178	−	0.148594i
$499$	232.643	+	716.002i	0.466219	+	1.43487i	0.857443	+	0.514578i	$0.172052\pi$
$499$	232.643	+	716.002i	0.466219	+	1.43487i	−0.391225	+	0.920295i	$0.627948\pi$
$500$	−481.837	+	133.539i	−0.963675	+	0.267079i
$501$	606.525	+	834.811i	1.21063	+	1.66629i
$502$	34.2830	+	40.2192i	0.0682929	+	0.0801180i
$503$	773.978	−	394.361i	1.53872	−	0.784019i	0.540372	−	0.841426i	$-0.318283\pi$
$503$	773.978	−	394.361i	1.53872	−	0.784019i	0.998351	+	0.0574073i	$0.0182834\pi$
$504$	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
$508$	−19.8205	+	27.1696i	−0.0390168	+	0.0534835i
$509$	−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	$0.922165\pi$
$510$	−621.737	−	547.268i	−1.21909	−	1.07307i
$511$	313.250	+	431.152i	0.613014	+	0.843741i
$512$	−434.199	−	271.321i	−0.848046	−	0.529923i
$513$	−120.177	−	61.2331i	−0.234263	−	0.119363i
$514$	507.950	−	593.566i	0.988229	−	1.15480i
$515$	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
$518$	−188.673	+	77.9365i	−0.364234	+	0.150457i
$519$	−207.805	+	286.019i	−0.400395	+	0.551097i
$520$	966.491	−	214.864i	1.85864	−	0.413200i
$521$	−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	$-0.313969\pi$
$522$	388.944	−	633.319i	0.745104	−	1.21325i
$523$	−288.493	−	45.6928i	−0.551612	−	0.0873667i	−0.125594	−	0.992082i	$-0.540084\pi$
$523$	−288.493	−	45.6928i	−0.551612	−	0.0873667i	−0.426017	+	0.904715i	$0.640084\pi$
$524$	571.962	+	292.828i	1.09153	+	0.558833i
$525$	757.528	+	21.1450i	1.44291	+	0.0402761i
$526$	−570.124	+	348.612i	−1.08389	+	0.662761i
$527$	−193.241	+	193.241i	−0.366680	+	0.366680i
$528$	597.058	+	531.246i	1.13079	+	1.00615i
$529$		−	338.276i		−	0.639463i
$530$	−450.703	−	543.937i	−0.850384	−	1.02630i
$531$	−885.719	−	287.787i	−1.66802	−	0.541973i
$532$	93.0177	+	288.180i	0.174845	+	0.541693i
$533$	−253.282	−	40.1159i	−0.475200	−	0.0752643i
$534$	−145.871	−	610.204i	−0.273167	−	1.14270i
$535$	−1.42100	+	4.17430i	−0.00265608	+	0.00780243i
$536$	172.627	−	13.0806i	0.322065	−	0.0244041i
$537$	−749.936	+	118.778i	−1.39653	+	0.221188i
$538$	−277.872	+	114.782i	−0.516490	+	0.213350i
$539$	−45.3820	+	17.9319i	−0.0841967	+	0.0332688i
$540$	−33.4723	−	235.501i	−0.0619857	−	0.436114i
$541$	258.288	−	355.504i	0.477428	−	0.657123i	−0.500580	−	0.865690i	$-0.666880\pi$
$541$	258.288	−	355.504i	0.477428	−	0.657123i	0.978008	+	0.208567i	$0.0668799\pi$
$542$	65.4989	−	5.09094i	0.120847	−	0.00939289i
$543$	−1221.96	−	622.621i	−2.25039	−	1.14663i
$544$	568.233	−	133.509i	1.04455	−	0.245421i
$545$	653.581	+	672.079i	1.19923	+	1.23317i
$546$	−1495.88	−	119.189i	−2.73971	−	0.218294i
$547$	202.691	+	397.803i	0.370549	+	0.727244i	0.998707	−	0.0508421i	$-0.0161905\pi$
$547$	202.691	+	397.803i	0.370549	+	0.727244i	−0.628157	+	0.778086i	$0.716191\pi$
$548$	184.993	−	253.585i	0.337578	−	0.462745i
$549$	442.462			0.805942
$550$	−271.617	+	478.251i	−0.493850	+	0.869547i
$551$			362.695i			0.658249i
$552$	−913.782	+	556.314i	−1.65540	+	1.00782i
$553$	−589.451	+	300.340i	−1.06591	+	0.543111i
$554$	−103.187	−	8.22174i	−0.186258	−	0.0148407i
$555$	−248.866	+	242.016i	−0.448407	+	0.436065i
$556$	−207.420	−	33.2648i	−0.373058	−	0.0598289i
$557$	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	$0.0225224\pi$
$558$	−347.110	+	26.9793i	−0.622061	+	0.0483501i
$559$	402.674	+	292.560i	0.720347	+	0.523363i
$560$	−321.561	+	426.389i	−0.574217	+	0.761409i
$561$	−909.357	+	56.5831i	−1.62096	+	0.100861i
$562$	77.4448	−	31.9907i	0.137802	−	0.0569229i
$563$	42.1135	+	265.894i	0.0748019	+	0.472280i	0.996445	+	0.0842425i	$0.0268470\pi$
$563$	42.1135	+	265.894i	0.0748019	+	0.472280i	−0.921643	+	0.388038i	$0.873153\pi$
$564$	146.640	+	289.183i	0.260000	+	0.512735i
$565$	−203.157	−	69.1582i	−0.359571	−	0.122404i
$566$	−6.07342	−	25.4062i	−0.0107304	−	0.0448872i
$567$	52.8068	−	333.409i	0.0931338	−	0.588023i
$568$	166.495	+	13.5912i	0.293125	+	0.0239281i
$569$	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	$0.0915099\pi$
$570$	328.556	+	396.522i	0.576414	+	0.695653i
$571$	9.82448			0.0172057			0.00860287	−	0.999963i	$-0.497262\pi$
$571$	9.82448			0.0172057			0.00860287	+	0.999963i	$0.497262\pi$
$572$	585.982	−	918.016i	1.02444	−	1.60492i
$573$	416.484	+	416.484i	0.726849	+	0.726849i
$574$	118.009	−	72.1588i	0.205591	−	0.125712i
$575$	−505.871	−	534.923i	−0.879775	−	0.930300i
$576$	660.602	+	341.452i	1.14688	+	0.592798i
$577$	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	$0.00485791\pi$
$578$	−45.7680	+	74.5242i	−0.0791834	+	0.128935i
$579$	−297.310	+	96.6018i	−0.513488	+	0.166842i
$580$	−523.393	+	367.702i	−0.902402	+	0.633969i
$581$	567.883	+	412.591i	0.977424	+	0.710140i
$582$	−1219.34	+	503.682i	−2.09509	+	0.865433i
$583$	−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
$586$	90.4797	−	105.730i	0.154402	−	0.180427i
$587$	−251.807	+	494.198i	−0.428972	+	0.841905i	0.570811	+	0.821081i	$0.306629\pi$
$587$	−251.807	+	494.198i	−0.428972	+	0.841905i	−0.999783	+	0.0208237i	$0.993371\pi$
$588$	−65.2768	+	47.2332i	−0.111015	+	0.0803285i
$589$	137.455	−	99.8667i	0.233370	−	0.169553i
$590$	601.643	+	529.581i	1.01973	+	0.897594i
$591$	−133.406	+	410.580i	−0.225729	+	0.694721i
$592$	−37.3314	−	241.770i	−0.0630597	−	0.408395i
$593$	−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	$0.283064\pi$
$594$	−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
$597$	−117.455	−	230.517i	−0.196741	−	0.386126i
$598$	945.741	+	1109.50i	1.58151	+	1.85535i
$599$	2.16024	−	1.56951i	0.00360641	−	0.00262021i	−0.585981	−	0.810325i	$-0.699291\pi$
$599$	2.16024	−	1.56951i	0.00360641	−	0.00262021i	0.589587	+	0.807705i	$0.299291\pi$
$600$	−239.116	+	876.123i	−0.398526	+	1.46021i
$601$	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	$0.322953\pi$
$602$	−267.668	+	20.8047i	−0.444632	+	0.0345593i
$603$	−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	−0.829479	−	0.558538i	$-0.811363\pi$
$607$	−877.578	+	138.995i	−1.44576	+	0.228986i	−0.616284	+	0.787524i	$0.711363\pi$
$608$	−361.912	+	26.7173i	−0.595250	+	0.0439430i
$609$	922.025	−	299.584i	1.51400	−	0.491928i
$610$	−349.601	−	150.960i	−0.573117	−	0.247476i
$611$	357.468	−	259.716i	0.585055	−	0.425067i
$612$	−806.790	+	260.412i	−1.31828	+	0.425510i
$613$	−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	$0.894053\pi$
$614$	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	$0.158750\pi$
$618$	62.6626	+	15.1083i	0.101396	+	0.0244470i
$619$	146.025	−	449.420i	0.235905	−	0.726041i	−0.761095	−	0.648641i	$-0.775338\pi$
$619$	146.025	−	449.420i	0.235905	−	0.726041i	0.997000	−	0.0774008i	$-0.0246621\pi$
$620$	283.466	+	97.1109i	0.457204	+	0.156630i
$621$	283.363	−	205.875i	0.456301	−	0.331522i
$622$	344.917	−	561.630i	0.554529	−	0.902942i
$623$	209.370	−	410.913i	0.336068	−	0.659571i
$624$	562.347	−	1708.14i	0.901197	−	2.73741i
$625$	−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
$628$	−0.149313	+	76.9526i	−0.000237759	+	0.122536i
$629$	225.632	+	163.931i	0.358715	+	0.260622i
$630$	415.103	−	655.233i	0.658893	−	1.04005i
$631$	868.165	−	282.084i	1.37586	−	0.447042i	0.474550	−	0.880228i	$-0.342611\pi$
$631$	868.165	−	282.084i	1.37586	−	0.447042i	0.901305	+	0.433186i	$0.142611\pi$
$632$	−182.831	−	771.432i	−0.289290	−	1.22062i
$633$	197.717	−	1248.33i	0.312348	−	1.97209i
$634$	1.85264	−	23.2516i	0.00292215	−	0.0366745i
$635$	−34.3515	+	24.2328i	−0.0540968	+	0.0381619i
$636$	−1267.65	+	198.255i	−1.99316	+	0.311722i
$637$	77.6412	+	77.6412i	0.121886	+	0.121886i
$638$	−122.120	+	692.930i	−0.191411	+	1.08610i
$639$	−242.622			−0.379691
$640$	−405.463	−	495.177i	−0.633536	−	0.773714i
$641$	−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	$0.996067\pi$
$642$	5.19565	+	6.09529i	0.00809291	+	0.00949421i
$643$	154.130	−	973.141i	0.239705	−	1.51344i	−0.514894	−	0.857254i	$-0.672169\pi$
$643$	154.130	−	973.141i	0.239705	−	1.51344i	0.754600	−	0.656186i	$-0.227831\pi$
$644$	−776.455	−	124.523i	−1.20568	−	0.193359i
$645$	−409.642	+	201.574i	−0.635104	+	0.312517i
$646$	268.996	−	314.335i	0.416402	−	0.486587i
$647$	140.616	+	887.815i	0.217336	+	1.37220i	0.819156	+	0.573571i	$0.194442\pi$
$647$	140.616	+	887.815i	0.217336	+	1.37220i	−0.601820	+	0.798632i	$0.705558\pi$
$648$	373.289	+	155.896i	0.576064	+	0.240580i
$649$	879.967	−	54.7544i	1.35588	−	0.0843673i
$650$	1230.47	+	132.683i	1.89304	+	0.204128i
$651$	−367.413	−	266.941i	−0.564382	−	0.410048i
$652$	−740.338	−	242.139i	−1.13549	−	0.371380i
$653$	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	$0.137148\pi$
$654$	1656.11	−	395.897i	2.53227	−	0.605347i
$655$	559.972	+	575.821i	0.854919	+	0.879116i
$656$	50.6118	+	157.849i	0.0771521	+	0.240623i
$657$	826.491	−	421.118i	1.25798	−	0.640971i
$658$	−55.8632	+	231.696i	−0.0848984	+	0.352122i
$659$		−	741.252i		−	1.12481i	−0.826861	−	0.562407i	$-0.809875\pi$
$659$		−	741.252i		−	1.12481i	0.826861	−	0.562407i	$-0.190125\pi$
$660$	494.197	+	868.182i	0.748783	+	1.31543i
$661$	−747.326			−1.13060			−0.565299	−	0.824886i	$-0.691239\pi$
$661$	−747.326			−1.13060			−0.565299	+	0.824886i	$0.691239\pi$
$662$	757.074	+	182.534i	1.14362	+	0.275732i
$663$	930.766	+	1826.73i	1.40387	+	2.75525i
$664$	−641.241	+	544.452i	−0.965725	+	0.819958i
$665$	−5.28137	+	378.489i	−0.00794191	+	0.569156i
$666$	82.6097	+	345.571i	0.124039	+	0.518875i
$667$	−839.205	−	427.596i	−1.25818	−	0.641074i
$668$	−863.945	−	282.567i	−1.29333	−	0.423005i
$669$	−522.592	+	719.286i	−0.781154	+	1.07517i
$670$	209.646	+	53.6526i	0.312904	+	0.0800785i
$671$	−389.573	+	153.933i	−0.580586	+	0.229408i
$672$	366.857	+	897.966i	0.545918	+	1.33626i
$673$	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	$0.155218\pi$
$674$	642.790	+	550.074i	0.953694	+	0.816133i
$675$	54.6896	−	292.262i	0.0810216	−	0.432981i
$676$	−1752.29	−	281.021i	−2.59214	−	0.415712i
$677$	−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	$0.644439\pi$
$678$	−296.649	+	252.865i	−0.437536	+	0.372957i
$679$	−922.291	−	299.670i	−1.35831	−	0.441341i
$680$	726.315	+	69.5038i	1.06811	+	0.102212i
$681$		−	514.873i		−	0.756054i
$682$	296.233	−	144.514i	0.434359	−	0.211897i
$683$	544.013	−	544.013i	0.796506	−	0.796506i	−0.186037	−	0.982543i	$-0.559564\pi$
$683$	544.013	−	544.013i	0.796506	−	0.796506i	0.982543	+	0.186037i	$0.0595645\pi$
$684$	520.742	−	81.4420i	0.761319	−	0.119067i
$685$	320.616	−	226.174i	0.468052	−	0.330181i
$686$	−711.184	−	56.6657i	−1.03671	−	0.0826030i
$687$	−528.587	−	83.7200i	−0.769414	−	0.121863i
$688$	51.5638	−	317.579i	0.0749473	−	0.461598i
$689$	540.314	+	1662.92i	0.784200	+	2.41352i
$690$	−1304.82	+	292.738i	−1.89105	+	0.424257i
$691$	−152.782	+	210.287i	−0.221103	+	0.304323i	−0.905130	−	0.425134i	$-0.860227\pi$
$691$	−152.782	+	210.287i	−0.221103	+	0.304323i	0.684027	+	0.729457i	$0.260227\pi$
$692$	0.604274	−	311.430i	0.000873228	−	0.450043i
$693$	−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
$696$	87.7831	+	1158.49i	0.126125	+	1.66449i
$697$	−168.382	−	85.7950i	−0.241581	−	0.123092i
$698$	−68.0713	−	41.8051i	−0.0975234	−	0.0598926i
$699$	−791.658	−	1089.62i	−1.13256	−	1.55883i
$700$	−551.538	+	376.092i	−0.787912	+	0.537274i
$701$	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	$0.444308\pi$
$702$	−138.002	+	572.374i	−0.196584	+	0.815347i
$703$	−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
$707$	739.243	−	376.663i	1.04561	−	0.532763i
$708$	1385.44	−	447.187i	1.95684	−	0.631620i
$709$	−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	$0.919318\pi$
$710$	191.703	+	82.7785i	0.270004	+	0.116589i
$711$	355.823	+	1095.11i	0.500454	+	1.54024i
$712$	419.208	+	360.153i	0.588775	+	0.505832i
$713$	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
$718$	−79.7031	−	1025.44i	−0.111007	−	1.42819i
$719$	−363.969	−	1120.18i	−0.506216	−	1.55797i	−0.798717	−	0.601706i	$-0.794488\pi$
$719$	−363.969	−	1120.18i	−0.506216	−	1.55797i	0.292502	−	0.956265i	$-0.405512\pi$
$720$	645.456	+	668.898i	0.896467	+	0.929025i
$721$	27.8498	+	38.3320i	0.0386267	+	0.0531651i
$722$	353.718	−	301.511i	0.489914	−	0.417605i
$723$	534.408	−	272.295i	0.739154	−	0.376618i
$724$	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	0.989890	−	0.141839i	$-0.0453015\pi$
$727$	616.533	+	616.533i	0.848051	+	0.848051i	−0.141839	+	0.989890i	$0.545302\pi$
$728$	1129.10	−	687.402i	1.55096	−	0.944233i
$729$	−1021.06	−	331.761i	−1.40062	−	0.455091i
$730$	−796.712	+	50.7527i	−1.09139	+	0.0695242i
$731$	215.599	+	296.746i	0.294937	+	0.405946i
$732$	−560.356	+	405.463i	−0.765513	+	0.553912i
$733$	−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	$0.827236\pi$
$734$	1049.90	+	898.460i	1.43038	+	1.22406i
$735$	−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
$738$	−91.9175	−	222.519i	−0.124550	−	0.301516i
$739$	−401.252	+	552.275i	−0.542966	+	0.747328i	−0.989037	−	0.147669i	$-0.952823\pi$
$739$	−401.252	+	552.275i	−0.542966	+	0.747328i	0.446071	+	0.894997i	$0.352823\pi$
$740$	52.6306	−	301.230i	0.0711224	−	0.407068i
$741$	−393.881	−	1212.24i	−0.531553	−	1.63595i
$742$	−803.674	−	493.565i	−1.08312	−	0.665182i
$743$	1002.39	+	158.762i	1.34911	+	0.213677i	0.788822	−	0.614622i	$-0.210692\pi$
$743$	1002.39	+	158.762i	1.34911	+	0.213677i	0.560285	+	0.828300i	$0.310692\pi$
$744$	414.874	−	352.253i	0.557627	−	0.473458i
$745$	−90.1905	−	15.5777i	−0.121061	−	0.0209097i
$746$	−289.687	−	473.758i	−0.388321	−	0.635064i
$747$	863.916	−	863.916i	1.15651	−	1.15651i
$748$	619.754	−	509.967i	0.828548	−	0.681774i
$749$			5.88728i			0.00786019i
$750$	−634.044	+	941.642i	−0.845392	+	1.25552i
$751$	486.255	+	157.994i	0.647477	+	0.210378i	0.614301	−	0.789071i	$-0.289438\pi$
$751$	486.255	+	157.994i	0.647477	+	0.210378i	0.0331758	+	0.999450i	$0.489438\pi$
$752$	−253.983	−	130.655i	−0.337744	−	0.173743i
$753$	118.510	+	18.7701i	0.157384	+	0.0249271i
$754$	1539.87	−	368.110i	2.04227	−	0.488210i
$755$	−916.305	+	450.889i	−1.21365	+	0.597204i
$756$	−143.631	−	283.248i	−0.189988	−	0.374667i
$757$	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	$0.184552\pi$
$758$	−491.610	−	1190.12i	−0.648563	−	1.57008i
$759$	−789.047	+	1241.45i	−1.03959	+	1.63564i
$760$	−439.239	−	113.319i	−0.577946	−	0.149103i
$761$	−69.5768	+	95.7643i	−0.0914282	+	0.125840i	−0.852281	−	0.523085i	$-0.824781\pi$
$761$	−69.5768	+	95.7643i	−0.0914282	+	0.125840i	0.760852	+	0.648925i	$0.224781\pi$
$762$	5.91700	+	76.1267i	0.00776509	+	0.0999039i
$763$	1115.22	+	568.235i	1.46163	+	0.744738i
$764$	−512.299	−	82.1594i	−0.670548	−	0.107538i
$765$	−1059.62	−	14.7857i	−1.38512	−	0.0193277i
$766$	61.8209	−	775.884i	0.0807061	−	1.01290i
$767$	−900.684	−	1767.69i	−1.17430	−	2.30468i
$768$	−1149.52	+	172.932i	−1.49677	+	0.225171i
$769$	904.162			1.17576			0.587882	−	0.808947i	$-0.299962\pi$
$769$	904.162			1.17576			0.587882	+	0.808947i	$0.299962\pi$
$770$	−137.528	+	721.325i	−0.178608	+	0.936786i
$771$		−	1773.74i		−	2.30057i
$772$	162.294	−	222.470i	0.210226	−	0.288173i
$773$	−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	$0.553241\pi$
$774$	−37.1153	+	465.817i	−0.0479526	+	0.601831i
$775$	296.756	+	228.523i	0.382911	+	0.294869i
$776$	610.099	−	989.118i	0.786210	−	1.27464i
$777$	−210.413	+	412.959i	−0.270802	+	0.531479i
$778$	74.7473	+	961.681i	0.0960762	+	1.23609i
$779$	95.0521	+	69.0594i	0.122018	+	0.0886513i
$780$	1350.02	−	1797.37i	1.73080	−	2.30432i
$781$	213.621	−	84.4083i	0.273522	−	0.108077i
$782$	410.180	+	992.986i	0.524527	+	1.26980i
$783$	−59.5042	−	375.695i	−0.0759951	−	0.479814i
$784$	22.1947	−	67.4170i	0.0283096	−	0.0859911i
$785$	−30.9981	+	91.0593i	−0.0394881	+	0.115999i
$786$	1418.91	−	339.195i	1.80523	−	0.431545i
$787$	−46.8059	+	295.521i	−0.0594738	+	0.375503i	0.939942	+	0.341333i	$0.110879\pi$
$787$	−46.8059	+	295.521i	−0.0594738	+	0.375503i	−0.999416	+	0.0341693i	$0.989121\pi$
$788$	−116.814	−	361.905i	−0.148241	−	0.459270i
$789$	−468.850	+	1442.97i	−0.594234	+	1.82886i
$790$	92.4872	−	986.677i	0.117072	−	1.24896i
$791$	−286.526			−0.362233
$792$	1022.30	+	19.7402i	1.29078	+	0.0249245i
$793$	666.496	+	666.496i	0.840474	+	0.840474i
$794$	−367.304	−	600.692i	−0.462599	−	0.756540i
$795$	−1580.42	−	272.971i	−1.98795	−	0.343359i
$796$	202.860	+	103.859i	0.254850	+	0.130476i
$797$	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	$-0.0606580\pi$
$798$	585.866	+	359.802i	0.734168	+	0.450879i
$799$	309.684	−	100.622i	0.387589	−	0.125935i
$800$	−281.776	−	748.734i	−0.352220	−	0.935917i
$801$	−649.398	−	471.815i	−0.810734	−	0.589033i
$802$	278.620	+	674.498i	0.347406	+	0.841019i
$803$	−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
$806$	−563.504	−	482.224i	−0.699136	−	0.598293i
$807$	−309.890	+	608.193i	−0.384002	+	0.753647i
$808$	229.293	+	967.470i	0.283778	+	1.19736i
$809$	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	$0.201010\pi$
$810$	379.570	+	334.107i	0.468605	+	0.412477i
$811$	164.577	−	506.515i	0.202930	−	0.624556i	−0.796862	−	0.604162i	$-0.793508\pi$
$811$	164.577	−	506.515i	0.202930	−	0.624556i	0.999792	−	0.0203937i	$-0.00649198\pi$
$812$	−503.311	+	689.929i	−0.619842	+	0.849667i
$813$	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
$817$	−103.529	−	203.188i	−0.126719	−	0.248700i
$818$	595.670	−	507.752i	0.728203	−	0.620724i
$819$	−1553.24	+	1128.50i	−1.89651	+	1.37790i
$820$	−3.29303	+	207.179i	−0.00401588	+	0.252657i
$821$	−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	$0.531899\pi$
$822$	−55.2257	−	710.521i	−0.0671845	−	0.864380i
$823$	−1160.18	+	183.754i	−1.40969	+	0.223274i	−0.814433	−	0.580258i	$-0.802952\pi$
$823$	−1160.18	+	183.754i	−1.40969	+	0.223274i	−0.595262	+	0.803532i	$0.702952\pi$
$824$	−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	0.761462	−	0.648209i	$-0.224482\pi$
$827$	1394.29	−	220.834i	1.68596	−	0.267030i	0.924501	+	0.381179i	$0.124482\pi$
$828$	−425.483	+	1300.91i	−0.513869	+	1.57115i
$829$	−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	$0.470461\pi$
$830$	−977.357	+	387.851i	−1.17754	+	0.467290i
$831$	−190.136	+	138.142i	−0.228803	+	0.166235i
$832$	480.747	+	1509.43i	0.577821	+	1.81422i
$833$	36.7355	+	72.0975i	0.0441002	+	0.0865516i
$834$	−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
$838$	146.556	−	607.851i	0.174888	−	0.725359i
$839$	−206.240	+	634.743i	−0.245817	+	0.756547i	0.749684	+	0.661796i	$0.230205\pi$
$839$	−206.240	+	634.743i	−0.245817	+	0.756547i	−0.995501	+	0.0947510i	$0.969795\pi$
$840$	74.7363	+	1210.21i	0.0889718	+	1.44073i
$841$	−147.130	+	106.896i	−0.174946	+	0.127106i
$842$	178.158	+	109.413i	0.211589	+	0.129945i
$843$	86.3685	−	169.508i	0.102454	−	0.201077i
$844$	503.528	+	992.987i	0.596597	+	1.17653i
$845$	−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
$848$	802.296	−	796.093i	0.946104	−	0.938789i
$849$	−47.9811	−	34.8603i	−0.0565149	−	0.0410605i
$850$	832.188	+	373.206i	0.979045	+	0.439066i
$851$	428.236	−	139.142i	0.503215	−	0.163504i
$852$	307.269	−	222.334i	0.360644	−	0.260956i
$853$	−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	$0.725066\pi$
$854$	−506.812	−	40.3817i	−0.593457	−	0.0472854i
$855$	649.227	+	112.135i	0.759330	+	0.131152i
$856$	−6.85550	−	1.66698i	−0.00800876	−	0.00194740i
$857$	−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	$0.840618\pi$
$858$	−344.345	−	2448.61i	−0.401335	−	2.85386i
$859$	−1427.20			−1.66147			−0.830734	−	0.556670i	$-0.812079\pi$
$859$	−1427.20			−1.66147			−0.830734	+	0.556670i	$0.812079\pi$
$860$	188.255	−	355.392i	0.218901	−	0.413246i
$861$	97.0468	−	298.679i	0.112714	−	0.346898i
$862$	−89.0811	+	75.9331i	−0.103342	+	0.0880894i
$863$	244.584	−	1544.24i	0.283411	−	1.78939i	−0.276683	−	0.960961i	$-0.589235\pi$
$863$	244.584	−	1544.24i	0.283411	−	1.78939i	0.560095	−	0.828428i	$-0.310765\pi$
$864$	370.500	−	87.0506i	0.428820	−	0.100753i
$865$	125.451	−	368.521i	0.145030	−	0.426036i
$866$	−404.020	−	345.744i	−0.466536	−	0.399243i
$867$	31.0619	+	196.117i	0.0358269	+	0.226202i
$868$	400.055	+	0.776234i	0.460893	+	0.000894279i
$869$	−694.279	−	840.417i	−0.798940	−	0.967108i
$870$	−360.058	+	1406.92i	−0.413860	+	1.61715i
$871$	−433.344	−	314.843i	−0.497525	−	0.361473i
$872$	−977.461	+	1137.74i	−1.12094	+	1.30475i
$873$	−766.289	+	1503.93i	−0.877766	+	1.72271i
$874$	−155.299	−	649.643i	−0.177688	−	0.743298i
$875$	−803.707	+	224.424i	−0.918523	+	0.256485i
$876$	−660.805	+	1290.71i	−0.754344	+	1.47341i
$877$	−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	$0.520781\pi$
$878$	258.245	+	62.2643i	0.294129	+	0.0709160i
$879$		−	315.951i		−	0.359444i
$880$	−801.013	−	364.388i	−0.910242	−	0.414078i
$881$	−1402.92			−1.59241			−0.796206	−	0.605025i	$-0.793163\pi$
$881$	−1402.92			−1.59241			−0.796206	+	0.605025i	$0.793163\pi$
$882$	−24.1623	+	100.215i	−0.0273949	+	0.113622i
$883$	110.999	+	217.848i	0.125707	+	0.246713i	0.945279	−	0.326262i	$-0.105789\pi$
$883$	110.999	+	217.848i	0.125707	+	0.246713i	−0.819573	+	0.572975i	$0.805789\pi$
$884$	−1607.56	−	823.028i	−1.81851	−	0.931027i
$885$	1819.60	+	25.3904i	2.05605	+	0.0286898i
$886$	8.81422	−	2.10706i	0.00994833	−	0.00237818i
$887$	996.336	+	507.659i	1.12326	+	0.572332i	0.914076	−	0.405543i	$-0.132918\pi$
$887$	996.336	+	507.659i	1.12326	+	0.572332i	0.209189	+	0.977875i	$0.432918\pi$
$888$	−421.296	−	361.946i	−0.474432	−	0.407597i
$889$	−32.9906	+	45.4076i	−0.0371097	+	0.0510772i
$890$	352.132	+	594.358i	0.395654	+	0.667817i
$891$	555.162	−	34.5439i	0.623077	−	0.0387699i
$892$	1.51964	−	783.190i	0.00170363	−	0.878016i
$893$	−199.950	+	31.6689i	−0.223908	+	0.0354635i
$894$	−108.088	+	126.306i	−0.120904	+	0.141282i
$895$	750.159	−	369.133i	0.838167	−	0.412439i
$896$	−725.515	−	451.402i	−0.809727	−	0.503797i
$897$	3269.25	+	517.798i	3.64464	+	0.577255i
$898$	−291.601	−	342.092i	−0.324722	−	0.380949i
$899$	455.705	+	148.067i	0.506902	+	0.164702i
$900$	496.372	+	1050.56i	0.551524	+	1.16729i
$901$			1288.53i			1.43011i
$902$	158.345	+	163.942i	0.175548	+	0.181754i
$903$	−431.018	+	431.018i	−0.477318	+	0.477318i
$904$	81.1295	−	333.648i	0.0897450	−	0.369079i
$905$	1488.09	+	257.022i	1.64429	+	0.284002i
$906$	−147.328	+	1849.04i	−0.162613	+	2.04088i
$907$	877.167	+	138.930i	0.967109	+	0.153175i	0.619958	−	0.784635i	$-0.287149\pi$
$907$	877.167	+	138.930i	0.967109	+	0.153175i	0.347150	+	0.937810i	$0.387149\pi$
$908$	265.877	+	367.445i	0.292816	+	0.404675i
$909$	−446.245	−	1373.40i	−0.490919	−	1.51089i
$910$	1612.28	−	361.717i	1.77174	−	0.397491i
$911$	−900.848	+	1239.91i	−0.988856	+	1.36104i	−0.0569372	+	0.998378i	$0.518133\pi$
$911$	−900.848	+	1239.91i	−0.988856	+	1.36104i	−0.931919	+	0.362666i	$0.881867\pi$
$912$	−584.862	+	580.340i	−0.641296	+	0.636338i
$913$	−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
$916$	420.465	−	213.211i	0.459023	−	0.232763i
$917$	955.497	+	486.850i	1.04198	+	0.530916i
$918$	−227.066	+	369.733i	−0.247349	+	0.402759i
$919$	−282.703	−	389.108i	−0.307621	−	0.423403i	0.627017	−	0.779006i	$-0.284276\pi$
$919$	−282.703	−	389.108i	−0.307621	−	0.423403i	−0.934637	+	0.355602i	$0.884276\pi$
$920$	780.034	−	882.717i	0.847863	−	0.959475i
$921$	83.9950	+	27.2916i	0.0911998	+	0.0296326i
$922$	−1722.88	−	415.396i	−1.86864	−	0.450538i
$923$	−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
$927$	73.4801	−	37.4400i	0.0792666	−	0.0403883i
$928$	−660.882	−	781.438i	−0.712158	−	0.842067i
$929$	−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	$0.884712\pi$
$930$	632.336	−	250.934i	0.679931	−	0.269821i
$931$	−15.5457	−	47.8447i	−0.0166978	−	0.0513907i
$932$	1127.65	+	368.816i	1.20993	+	0.395726i
$933$	−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	$0.655485\pi$
$938$	288.056	−	22.3893i	0.307095	−	0.0238692i
$939$	62.4822	+	192.300i	0.0665412	+	0.204793i
$940$	−248.410	−	256.434i	−0.264266	−	0.272802i
$941$	−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	$0.943378\pi$
$942$	113.339	+	132.964i	0.120318	+	0.141151i
$943$	−271.851	+	138.515i	−0.288283	+	0.146887i
$944$	−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	$-0.825700\pi$
$947$	−1301.57	−	1301.57i	−1.37441	−	1.37441i	−0.520622	−	0.853787i	$-0.674300\pi$
$948$	−1454.17	−	1060.83i	−1.53393	−	1.11902i
$949$	1879.32	+	610.627i	1.98031	+	0.643443i
$950$	−474.714	−	310.106i	−0.499699	−	0.326427i
$951$	−31.1281	−	42.8442i	−0.0327320	−	0.0450517i
$952$	947.894	−	224.653i	0.995687	−	0.235980i
$953$	−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	$0.729121\pi$
$954$	−1067.32	+	1247.22i	−1.11878	+	1.30736i
$955$	−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
$958$	−1304.87	+	539.013i	−1.36208	+	0.562644i
$959$	307.914	−	423.807i	0.321078	−	0.441926i
$960$	−1430.40	−	255.643i	−1.49000	−	0.266294i
$961$	227.604	+	700.492i	0.236840	+	0.728920i
$962$	−396.107	+	644.983i	−0.411754	+	0.670461i
$963$	10.1209	+	1.60299i	0.0105098	+	0.00166458i
$964$	−240.776	+	470.291i	−0.249768	+	0.487854i
$965$	281.276	−	198.423i	0.291478	−	0.205619i
$966$	−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	$0.980303\pi$
$968$	−906.969	+	338.278i	−0.936951	+	0.349460i
$969$		−	939.321i		−	0.969372i
$970$	1118.58	−	926.850i	1.15318	−	0.955516i
$971$	478.302	+	155.410i	0.492587	+	0.160051i	0.544768	−	0.838586i	$-0.316618\pi$
$971$	478.302	+	155.410i	0.492587	+	0.160051i	−0.0521818	+	0.998638i	$0.516618\pi$
$972$	1281.52	−	413.645i	1.31844	−	0.425560i
$973$	−346.272	−	54.8441i	−0.355881	−	0.0563660i
$974$	161.241	+	674.497i	0.165545	+	0.692502i
$975$	2318.45	−	1587.54i	2.37789	−	1.62825i
$976$	190.526	−	578.728i	0.195211	−	0.592959i
$977$	−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	$0.640400\pi$
$978$	−1634.53	+	675.189i	−1.67130	+	0.690377i
$979$	735.918	+	189.492i	0.751703	+	0.193557i
$980$	53.2828	−	70.9386i	0.0543702	−	0.0723864i
$981$	1280.52	−	1762.48i	1.30532	−	1.79661i
$982$	−809.403	+	62.9114i	−0.824240	+	0.0640645i
$983$	1057.58	+	538.862i	1.07587	+	0.548181i	0.899847	−	0.436206i	$-0.143678\pi$
$983$	1057.58	+	538.862i	1.07587	+	0.548181i	0.176019	+	0.984387i	$0.443678\pi$
$984$	320.321	+	197.578i	0.325529	+	0.200790i
$985$	6.63249	−	475.317i	0.00673350	−	0.482555i
$986$	1163.08	+	92.6717i	1.17959	+	0.0939875i
$987$	245.664	+	482.143i	0.248900	+	0.488493i
$988$	907.090	+	661.733i	0.918108	+	0.669770i
$989$	592.190			0.598777
$990$	1202.59	+	432.830i	1.21474	+	0.437202i
$991$			388.087i			0.391612i	0.980643	+	0.195806i	$0.0627322\pi$
$991$			388.087i			0.391612i	−0.980643	+	0.195806i	$0.937268\pi$
$992$	−114.179	+	465.628i	−0.115100	+	0.469383i
$993$	1575.42	−	802.714i	1.58652	−	0.808373i
$994$	277.908	+	22.1432i	0.279586	+	0.0222768i
$995$	198.608	+	204.229i	0.199606	+	0.205255i
$996$	−302.430	+	1885.78i	−0.303645	+	1.89335i
$997$	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	$-0.155686\pi$
$998$	−1501.17	+	116.679i	−1.50418	+	0.116913i
$999$	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.183.29	yes	544
4.3	odd	2	inner	220.3.w.a.183.45	yes	544
5.2	odd	4	inner	220.3.w.a.7.6	✓	544
11.8	odd	10	inner	220.3.w.a.63.13	yes	544
20.7	even	4	inner	220.3.w.a.7.13	yes	544
44.19	even	10	inner	220.3.w.a.63.6	yes	544
55.52	even	20	inner	220.3.w.a.107.45	yes	544
220.107	odd	20	inner	220.3.w.a.107.29	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.6	✓	544	5.2	odd	4	inner
220.3.w.a.7.13	yes	544	20.7	even	4	inner
220.3.w.a.63.6	yes	544	44.19	even	10	inner
220.3.w.a.63.13	yes	544	11.8	odd	10	inner
220.3.w.a.107.29	yes	544	220.107	odd	20	inner
220.3.w.a.107.45	yes	544	55.52	even	20	inner
220.3.w.a.183.29	yes	544	1.1	even	1	trivial
220.3.w.a.183.45	yes	544	4.3	odd	2	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+(-0.468777 + 1.94429i) q^{2} +(2.06150 + 4.04592i) q^{3} +(-3.56050 - 1.82287i) q^{4} +(-3.48586 - 3.58452i) q^{5} +(-8.83280 + 2.11151i) q^{6} +(-5.94803 - 3.03067i) q^{7} +(5.21327 - 6.06810i) q^{8} +(-6.82960 + 9.40014i) q^{9} +(8.60342 - 5.09717i) q^{10} +(2.74293 - 10.6525i) q^{11} +(0.0352426 - 18.1633i) q^{12} +(-24.4474 + 3.87209i) q^{13} +(8.68079 - 10.1440i) q^{14} +(7.31657 - 21.4930i) q^{15} +(9.35426 + 12.9807i) q^{16} +(-18.0163 - 2.85350i) q^{17} +(-15.0750 - 17.6853i) q^{18} +(10.7855 + 3.50442i) q^{19} +(5.87726 + 19.1169i) q^{20} -30.3129i q^{21} +(19.4257 + 10.3267i) q^{22} +(-20.8240 + 20.8240i) q^{23} +(35.2982 + 8.58307i) q^{24} +(-0.697556 + 24.9903i) q^{25} +(3.93194 - 49.3479i) q^{26} +(-11.7470 - 1.86054i) q^{27} +(15.6534 + 21.6332i) q^{28} +(9.88305 + 30.4169i) q^{29} +(38.3586 + 24.3009i) q^{30} +(8.80617 - 12.1207i) q^{31} +(-29.6232 + 12.1023i) q^{32} +(48.7538 - 10.8625i) q^{33} +(13.9936 - 33.6911i) q^{34} +(9.87049 + 31.8853i) q^{35} +(41.4520 - 21.0197i) q^{36} +(-13.6232 - 6.94136i) q^{37} +(-11.8696 + 19.3273i) q^{38} +(-66.0644 - 90.9299i) q^{39} +(-39.9239 + 2.46549i) q^{40} +(9.85319 + 3.20150i) q^{41} +(58.9370 + 14.2100i) 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} +(-15.9055 + 8.10427i) q^{47} +(-33.2349 + 64.6062i) q^{48} +(-2.60743 - 3.58882i) q^{49} +(-48.2612 - 13.0711i) q^{50} +(-25.5955 - 78.7748i) q^{51} +(94.1033 + 30.7780i) 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} +(-63.7721 + 4.95673i) q^{58} +(24.7682 + 76.2288i) q^{59} +(-65.2296 + 63.1885i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(19.4379 + 22.8036i) q^{62} +(69.1114 - 35.2140i) 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} +(58.9453 + 43.0012i) q^{68} +(-127.181 - 41.3235i) q^{69} +(-66.6212 + 4.24395i) q^{70} +(12.2736 + 16.8932i) q^{71} +(21.4365 + 90.4481i) q^{72} +(-71.1314 - 36.2433i) q^{73} +(19.8822 - 23.2334i) q^{74} +(-102.547 + 48.6951i) q^{75} +(-32.0136 - 32.1380i) q^{76} +(-48.5993 + 55.0486i) q^{77} +(207.763 - 85.8223i) q^{78} +(58.2496 - 80.1738i) q^{79} +(13.9218 - 78.7793i) q^{80} +(15.6260 + 48.0919i) q^{81} +(-10.8436 + 17.6566i) q^{82} +(-103.856 - 16.4491i) q^{83} +(-55.2567 + 107.929i) q^{84} +(52.5738 + 74.5265i) q^{85} +(34.3112 - 20.9802i) q^{86} +(-102.690 + 102.690i) q^{87} +(-50.3410 - 72.1788i) q^{88} +69.0839i q^{89} +(-10.8438 + 115.685i) q^{90} +(157.149 + 51.0608i) q^{91} +(112.103 - 36.1842i) q^{92} +(67.1931 + 10.6423i) q^{93} +(-8.30087 - 34.7240i) q^{94} +(-25.0350 - 50.8767i) q^{95} +(-110.033 - 94.9041i) q^{96} +(143.479 - 22.7249i) q^{97} +(8.20000 - 3.38724i) q^{98} +(81.4022 + 98.5364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

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