LMFDB - Embedded newform 220.3.i.a.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(43,220)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("220.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	220.43
Dual form			220.3.i.a.87.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67372 - 1.09483i) q^{2} +(0.0944542 - 0.0944542i) q^{3} +(1.60268 + 3.66489i) q^{4} +(1.01027 - 4.89687i) q^{5} +(-0.261502 + 0.0546783i) q^{6} +(-6.56836 + 6.56836i) q^{7} +(1.33000 - 7.88867i) q^{8} +8.98216i q^{9} +(-7.05216 + 7.08992i) q^{10} +(-7.97654 - 7.57461i) q^{11} +(0.497544 + 0.194784i) q^{12} +(1.42743 - 1.42743i) q^{13} +(18.1848 - 3.80234i) q^{14} +(-0.367106 - 0.557954i) q^{15} +(-10.8628 + 11.7473i) q^{16} +(-14.5542 - 14.5542i) q^{17} +(9.83396 - 15.0336i) q^{18} +23.8822i q^{19} +(19.5656 - 4.14560i) q^{20} +1.24082i q^{21} +(5.05756 + 21.4108i) q^{22} +(-21.6435 + 21.6435i) q^{23} +(-0.619494 - 0.870742i) q^{24} +(-22.9587 - 9.89431i) q^{25} +(-3.95191 + 0.826319i) q^{26} +(1.69849 + 1.69849i) q^{27} +(-34.5993 - 13.5453i) q^{28} -0.979541 q^{29} +(0.00356623 + 1.33578i) q^{30} +42.2531i q^{31} +(31.0427 - 7.76870i) q^{32} +(-1.46887 + 0.0379638i) q^{33} +(8.42525 + 40.2941i) q^{34} +(25.5286 + 38.8002i) q^{35} +(-32.9186 + 14.3955i) q^{36} +(-7.62919 + 7.62919i) q^{37} +(26.1470 - 39.9721i) q^{38} -0.269653i q^{39} +(-37.2861 - 14.4825i) q^{40} +61.1443i q^{41} +(1.35849 - 2.07678i) q^{42} +(15.4025 + 15.4025i) q^{43} +(14.9763 - 41.3728i) q^{44} +(43.9845 + 9.07438i) q^{45} +(59.9213 - 12.5292i) q^{46} +(-62.3568 - 62.3568i) q^{47} +(0.0835414 + 2.13562i) q^{48} -37.2866i q^{49} +(27.5939 + 41.6963i) q^{50} -2.74942 q^{51} +(7.51907 + 2.94365i) q^{52} +(0.0107926 + 0.0107926i) q^{53} +(-0.983235 - 4.70236i) q^{54} +(-45.1504 + 31.4077i) q^{55} +(43.0796 + 60.5515i) q^{56} +(2.25577 + 2.25577i) q^{57} +(1.63948 + 1.07243i) q^{58} +26.3743 q^{59} +(1.45649 - 2.23963i) q^{60} -98.1345i q^{61} +(46.2601 - 70.7199i) q^{62} +(-58.9980 - 58.9980i) q^{63} +(-60.4622 - 20.9839i) q^{64} +(-5.54784 - 8.43201i) q^{65} +(2.50005 + 1.54463i) q^{66} +(-57.0549 - 57.0549i) q^{67} +(30.0138 - 76.6654i) q^{68} +4.08864i q^{69} +(-0.247996 - 92.8902i) q^{70} -30.7914i q^{71} +(70.8573 + 11.9463i) q^{72} +(17.1139 - 17.1139i) q^{73} +(21.1218 - 4.41644i) q^{74} +(-3.10311 + 1.23399i) q^{75} +(-87.5256 + 38.2755i) q^{76} +(102.146 - 2.64000i) q^{77} +(-0.295225 + 0.451324i) q^{78} -81.1764i q^{79} +(46.5506 + 65.0618i) q^{80} -80.5186 q^{81} +(66.9428 - 102.339i) q^{82} +(37.6780 + 37.6780i) q^{83} +(-4.54746 + 1.98863i) q^{84} +(-85.9738 + 56.5665i) q^{85} +(-8.91634 - 42.6428i) q^{86} +(-0.0925218 + 0.0925218i) q^{87} +(-70.3624 + 52.8500i) q^{88} +95.2458i q^{89} +(-63.6828 - 63.3436i) q^{90} +18.7517i q^{91} +(-114.009 - 44.6335i) q^{92} +(3.99099 + 3.99099i) q^{93} +(36.0976 + 172.638i) q^{94} +(116.948 + 24.1274i) q^{95} +(2.19832 - 3.66590i) q^{96} +(61.7662 - 61.7662i) q^{97} +(-40.8226 + 62.4073i) q^{98} +(68.0364 - 71.6465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) $ 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−1.67372	−	1.09483i	−0.836860	−	0.547417i
$2$	−1.67372	−	1.09483i	−0.836860	−	0.547417i
$3$	0.0944542	−	0.0944542i	0.0314847	−	0.0314847i	−0.691189	−	0.722674i	$-0.742913\pi$
$3$	0.0944542	−	0.0944542i	0.0314847	−	0.0314847i	0.722674	+	0.691189i	$0.242913\pi$
$4$	1.60268	+	3.66489i	0.400670	+	0.916222i
$5$	1.01027	−	4.89687i	0.202054	−	0.979374i
$5$	1.01027	−	4.89687i	0.202054	−	0.979374i
$6$	−0.261502	+	0.0546783i	−0.0435836	+	0.00911306i
$7$	−6.56836	+	6.56836i	−0.938336	+	0.938336i	−0.998206	−	0.0598697i	$-0.980931\pi$
$7$	−6.56836	+	6.56836i	−0.938336	+	0.938336i	0.0598697	+	0.998206i	$0.480931\pi$
$8$	1.33000	−	7.88867i	0.166250	−	0.986084i
$9$			8.98216i			0.998017i
$10$	−7.05216	+	7.08992i	−0.705216	+	0.708992i
$11$	−7.97654	−	7.57461i	−0.725140	−	0.688601i
$11$	−7.97654	−	7.57461i	−0.725140	−	0.688601i
$12$	0.497544	+	0.194784i	0.0414620	+	0.0162320i
$13$	1.42743	−	1.42743i	0.109802	−	0.109802i	−0.650071	−	0.759873i	$-0.725261\pi$
$13$	1.42743	−	1.42743i	0.109802	−	0.109802i	0.759873	+	0.650071i	$0.225261\pi$
$14$	18.1848	−	3.80234i	1.29892	−	0.271596i
$15$	−0.367106	−	0.557954i	−0.0244737	−	0.0371970i
$16$	−10.8628	+	11.7473i	−0.678927	+	0.734206i
$17$	−14.5542	−	14.5542i	−0.856131	−	0.856131i	0.134749	−	0.990880i	$-0.456977\pi$
$17$	−14.5542	−	14.5542i	−0.856131	−	0.856131i	−0.990880	+	0.134749i	$0.956977\pi$
$18$	9.83396	−	15.0336i	0.546331	−	0.835201i
$19$			23.8822i			1.25696i	0.777827	+	0.628479i	$0.216322\pi$
$19$			23.8822i			1.25696i	−0.777827	+	0.628479i	$0.783678\pi$
$20$	19.5656	−	4.14560i	0.978282	−	0.207280i
$21$			1.24082i			0.0590866i
$22$	5.05756	+	21.4108i	0.229889	+	0.973217i
$23$	−21.6435	+	21.6435i	−0.941023	+	0.941023i	−0.998355	−	0.0573324i	$-0.981741\pi$
$23$	−21.6435	+	21.6435i	−0.941023	+	0.941023i	0.0573324	+	0.998355i	$0.481741\pi$
$24$	−0.619494	−	0.870742i	−0.0258122	−	0.0362809i
$25$	−22.9587	−	9.89431i	−0.918349	−	0.395772i
$26$	−3.95191	+	0.826319i	−0.151996	+	0.0317815i
$27$	1.69849	+	1.69849i	0.0629071	+	0.0629071i
$28$	−34.5993	−	13.5453i	−1.23569	−	0.483761i
$29$	−0.979541			−0.0337773			−0.0168886	−	0.999857i	$-0.505376\pi$
$29$	−0.979541			−0.0337773			−0.0168886	+	0.999857i	$0.505376\pi$
$30$	0.00356623	+	1.33578i	0.000118874	+	0.0445260i
$31$			42.2531i			1.36300i	0.731816	+	0.681502i	$0.238673\pi$
$31$			42.2531i			1.36300i	−0.731816	+	0.681502i	$0.761327\pi$
$32$	31.0427	−	7.76870i	0.970083	−	0.242772i
$33$	−1.46887	+	0.0379638i	−0.0445113	+	0.00115042i
$34$	8.42525	+	40.2941i	0.247802	+	1.18512i
$35$	25.5286	+	38.8002i	0.729389	+	1.10858i
$36$	−32.9186	+	14.3955i	−0.914406	+	0.399876i
$37$	−7.62919	+	7.62919i	−0.206194	+	0.206194i	−0.802648	−	0.596453i	$-0.796576\pi$
$37$	−7.62919	+	7.62919i	−0.206194	+	0.206194i	0.596453	+	0.802648i	$0.296576\pi$
$38$	26.1470	−	39.9721i	0.688079	−	1.05190i
$39$		−	0.269653i		−	0.00691418i
$40$	−37.2861	−	14.4825i	−0.932154	−	0.362063i
$41$			61.1443i			1.49133i	0.666324	+	0.745663i	$0.267867\pi$
$41$			61.1443i			1.49133i	−0.666324	+	0.745663i	$0.732133\pi$
$42$	1.35849	−	2.07678i	0.0323450	−	0.0494472i
$43$	15.4025	+	15.4025i	0.358199	+	0.358199i	0.863149	−	0.504950i	$-0.168489\pi$
$43$	15.4025	+	15.4025i	0.358199	+	0.358199i	−0.504950	+	0.863149i	$0.668489\pi$
$44$	14.9763	−	41.3728i	0.340370	−	0.940292i
$45$	43.9845	+	9.07438i	0.977433	+	0.201653i
$46$	59.9213	−	12.5292i	1.30264	−	0.272373i
$47$	−62.3568	−	62.3568i	−1.32674	−	1.32674i	−0.908196	−	0.418544i	$-0.862540\pi$
$47$	−62.3568	−	62.3568i	−1.32674	−	1.32674i	−0.418544	−	0.908196i	$-0.637460\pi$
$48$	0.0835414	+	2.13562i	0.00174045	+	0.0444921i
$49$		−	37.2866i		−	0.760951i
$50$	27.5939	+	41.6963i	0.551877	+	0.833925i
$51$	−2.74942			−0.0539101
$52$	7.51907	+	2.94365i	0.144598	+	0.0566087i
$53$	0.0107926	+	0.0107926i	0.000203633	+	0.000203633i	0.707209	−	0.707005i	$-0.249954\pi$
$53$	0.0107926	+	0.0107926i	0.000203633	+	0.000203633i	−0.707005	+	0.707209i	$0.749954\pi$
$54$	−0.983235	−	4.70236i	−0.0182080	−	0.0870808i
$55$	−45.1504	+	31.4077i	−0.820916	+	0.571049i
$56$	43.0796	+	60.5515i	0.769279	+	1.08128i
$57$	2.25577	+	2.25577i	0.0395750	+	0.0395750i
$58$	1.63948	+	1.07243i	0.0282669	+	0.0184902i
$59$	26.3743			0.447022			0.223511	−	0.974701i	$-0.428248\pi$
$59$	26.3743			0.447022			0.223511	+	0.974701i	$0.428248\pi$
$60$	1.45649	−	2.23963i	0.0242748	−	0.0373271i
$61$		−	98.1345i		−	1.60876i	−0.594113	−	0.804382i	$-0.702497\pi$
$61$		−	98.1345i		−	1.60876i	0.594113	−	0.804382i	$-0.297503\pi$
$62$	46.2601	−	70.7199i	0.746131	−	1.14064i
$63$	−58.9980	−	58.9980i	−0.936476	−	0.936476i
$64$	−60.4622	−	20.9839i	−0.944722	−	0.327874i
$65$	−5.54784	−	8.43201i	−0.0853515	−	0.129723i
$66$	2.50005	+	1.54463i	0.0378795	+	0.0234035i
$67$	−57.0549	−	57.0549i	−0.851565	−	0.851565i	0.138761	−	0.990326i	$-0.455688\pi$
$67$	−57.0549	−	57.0549i	−0.851565	−	0.851565i	−0.990326	+	0.138761i	$0.955688\pi$
$68$	30.0138	−	76.6654i	0.441380	−	1.12743i
$69$			4.08864i			0.0592557i
$70$	−0.247996	−	92.8902i	−0.00354280	−	1.32700i
$71$		−	30.7914i		−	0.433682i	−0.976207	−	0.216841i	$-0.930425\pi$
$71$		−	30.7914i		−	0.433682i	0.976207	−	0.216841i	$-0.0695753\pi$
$72$	70.8573	+	11.9463i	0.984129	+	0.165921i
$73$	17.1139	−	17.1139i	0.234437	−	0.234437i	−0.580105	−	0.814542i	$-0.696988\pi$
$73$	17.1139	−	17.1139i	0.234437	−	0.234437i	0.814542	+	0.580105i	$0.196988\pi$
$74$	21.1218	−	4.41644i	0.285430	−	0.0596816i
$75$	−3.10311	+	1.23399i	−0.0413748	+	0.0164532i
$76$	−87.5256	+	38.2755i	−1.15165	+	0.503625i
$77$	102.146	−	2.64000i	1.32657	−	0.0342858i
$78$	−0.295225	+	0.451324i	−0.00378494	+	0.00578620i
$79$		−	81.1764i		−	1.02755i	−0.857925	−	0.513775i	$-0.828247\pi$
$79$		−	81.1764i		−	1.02755i	0.857925	−	0.513775i	$-0.171753\pi$
$80$	46.5506	+	65.0618i	0.581883	+	0.813273i
$81$	−80.5186			−0.994056
$82$	66.9428	−	102.339i	0.816376	−	1.24803i
$83$	37.6780	+	37.6780i	0.453951	+	0.453951i	0.896664	−	0.442712i	$-0.145984\pi$
$83$	37.6780	+	37.6780i	0.453951	+	0.453951i	−0.442712	+	0.896664i	$0.645984\pi$
$84$	−4.54746	+	1.98863i	−0.0541364	+	0.0236742i
$85$	−85.9738	+	56.5665i	−1.01146	+	0.665488i
$86$	−8.91634	−	42.6428i	−0.103678	−	0.495846i
$87$	−0.0925218	+	0.0925218i	−0.00106347	+	0.00106347i
$88$	−70.3624	+	52.8500i	−0.799573	+	0.600569i
$89$			95.2458i			1.07018i	0.844796	+	0.535089i	$0.179722\pi$
$89$			95.2458i			1.07018i	−0.844796	+	0.535089i	$0.820278\pi$
$90$	−63.6828	−	63.3436i	−0.707586	−	0.703818i
$91$			18.7517i			0.206063i
$92$	−114.009	−	44.6335i	−1.23923	−	0.485146i
$93$	3.99099	+	3.99099i	0.0429138	+	0.0429138i
$94$	36.0976	+	172.638i	0.384017	+	1.83658i
$95$	116.948	+	24.1274i	1.23103	+	0.253973i
$96$	2.19832	−	3.66590i	0.0228992	−	0.0381864i
$97$	61.7662	−	61.7662i	0.636765	−	0.636765i	−0.312991	−	0.949756i	$-0.601331\pi$
$97$	61.7662	−	61.7662i	0.636765	−	0.636765i	0.949756	+	0.312991i	$0.101331\pi$
$98$	−40.8226	+	62.4073i	−0.416557	+	0.636809i
$99$	68.0364	−	71.6465i	0.687236	−	0.723703i
$100$	−0.533951	−	99.9986i	−0.00533951	−	0.999986i
$101$		−	46.9259i		−	0.464612i	−0.972643	−	0.232306i	$-0.925373\pi$
$101$		−	46.9259i		−	0.464612i	0.972643	−	0.232306i	$-0.0746271\pi$
$102$	4.60175	+	3.01015i	0.0451152	+	0.0295113i
$103$	−18.0637	+	18.0637i	−0.175375	+	0.175375i	−0.789336	−	0.613961i	$-0.789575\pi$
$103$	−18.0637	+	18.0637i	−0.175375	+	0.175375i	0.613961	+	0.789336i	$0.289575\pi$
$104$	−9.36202	−	13.1590i	−0.0900194	−	0.126529i
$105$	6.07613	+	1.25356i	0.0578679	+	0.0119387i
$106$	−0.00624768	−	0.0298798i	−5.89404e−5	−	0.000281885i
$107$	−2.66110	+	2.66110i	−0.0248701	+	0.0248701i	−0.719432	−	0.694562i	$-0.755598\pi$
$107$	−2.66110	+	2.66110i	−0.0248701	+	0.0248701i	0.694562	+	0.719432i	$0.255598\pi$
$108$	−3.50264	+	8.94692i	−0.0324319	+	0.0828418i
$109$	82.5586			0.757419			0.378709	−	0.925516i	$-0.376368\pi$
$109$	82.5586			0.757419			0.378709	+	0.925516i	$0.376368\pi$
$110$	109.955	−	3.13562i	0.999594	−	0.0285057i
$111$			1.44122i			0.0129839i
$112$	−5.80947	−	148.511i	−0.0518703	−	1.32599i
$113$	56.9536	+	56.9536i	0.504014	+	0.504014i	0.912683	−	0.408668i	$-0.134007\pi$
$113$	56.9536	+	56.9536i	0.504014	+	0.504014i	−0.408668	+	0.912683i	$0.634007\pi$
$114$	−1.30584	−	6.24523i	−0.0114547	−	0.0547827i
$115$	84.1198	+	127.851i	0.731477	+	1.11175i
$116$	−1.56989	−	3.58991i	−0.0135335	−	0.0309475i
$117$	12.8214	+	12.8214i	0.109584	+	0.109584i
$118$	−44.1432	−	28.8755i	−0.374095	−	0.244708i
$119$	191.195			1.60668
$120$	−4.88977	+	2.15390i	−0.0407481	+	0.0179491i
$121$	6.25044	+	120.838i	0.0516565	+	0.998665i
$122$	−107.441	+	164.250i	−0.880664	+	1.34631i
$123$	5.77534	+	5.77534i	0.0469540	+	0.0469540i
$124$	−154.853	+	67.7183i	−1.24882	+	0.546115i
$125$	−71.6456	+	102.430i	−0.573165	+	0.819440i
$126$	34.1532	+	163.339i	0.271057	+	1.29634i
$127$	94.2281	−	94.2281i	0.741954	−	0.741954i	−0.231000	−	0.972954i	$-0.574200\pi$
$127$	94.2281	−	94.2281i	0.741954	−	0.741954i	0.972954	+	0.231000i	$0.0741997\pi$
$128$	78.2229	+	101.317i	0.611116	+	0.791541i
$129$	2.90967			0.0225556
$130$	0.0538942	+	20.1868i	0.000414571	+	0.155283i
$131$	−238.314			−1.81919			−0.909594	−	0.415498i	$-0.863607\pi$
$131$	−238.314			−1.81919			−0.909594	+	0.415498i	$0.863607\pi$
$132$	−2.49327	−	5.32241i	−0.0188884	−	0.0403213i
$133$	−156.867	−	156.867i	−1.17945	−	1.17945i
$134$	33.0283	+	157.959i	0.246480	+	1.17880i
$135$	10.0332	−	6.60136i	0.0743202	−	0.0488990i
$136$	−134.171	+	95.4563i	−0.986549	+	0.701884i
$137$	56.7371	−	56.7371i	0.414139	−	0.414139i	−0.469039	−	0.883178i	$-0.655399\pi$
$137$	56.7371	−	56.7371i	0.414139	−	0.414139i	0.883178	+	0.469039i	$0.155399\pi$
$138$	4.47638	−	6.84325i	0.0324376	−	0.0495887i
$139$		−	63.3949i		−	0.456079i	−0.973652	−	0.228039i	$-0.926769\pi$
$139$		−	63.3949i		−	0.456079i	0.973652	−	0.228039i	$-0.0732315\pi$
$140$	−101.284	+	155.744i	−0.723459	+	1.11246i
$141$	−11.7797			−0.0835442
$142$	−33.7115	+	51.5362i	−0.237405	+	0.362931i
$143$	−22.1981	+	0.573723i	−0.155232	+	0.00401205i
$144$	−105.516	−	97.5716i	−0.732750	−	0.677581i
$145$	−0.989599	+	4.79669i	−0.00682482	+	0.0330806i
$146$	−47.3808	+	9.90703i	−0.324526	+	0.0678564i
$147$	−3.52188	−	3.52188i	−0.0239583	−	0.0239583i
$148$	−40.1873	−	15.7330i	−0.271536	−	0.106304i
$149$	−167.364			−1.12325			−0.561623	−	0.827393i	$-0.689823\pi$
$149$	−167.364			−1.12325			−0.561623	+	0.827393i	$0.689823\pi$
$150$	6.54475	+	1.33203i	0.0436316	+	0.00888021i
$151$	−34.8292			−0.230657			−0.115328	−	0.993327i	$-0.536792\pi$
$151$	−34.8292			−0.230657			−0.115328	+	0.993327i	$0.536792\pi$
$152$	188.399	+	31.7634i	1.23947	+	0.208970i
$153$	130.728	−	130.728i	0.854433	−	0.854433i
$154$	−173.853	−	107.414i	−1.12892	−	0.697491i
$155$	206.908	+	42.6870i	1.33489	+	0.275400i
$156$	0.988249	−	0.432168i	0.00633493	−	0.00277031i
$157$	−174.574	+	174.574i	−1.11193	+	1.11193i	−0.119044	+	0.992889i	$0.537983\pi$
$157$	−174.574	+	174.574i	−1.11193	+	1.11193i	−0.992889	+	0.119044i	$0.962017\pi$
$158$	−88.8746	+	135.867i	−0.562498	+	0.859915i
$159$	0.00203881			1.28227e−5
$160$	−6.68092	−	159.860i	−0.0417557	−	0.999128i
$161$		−	284.325i		−	1.76599i
$162$	134.766	+	88.1544i	0.831886	+	0.544163i
$163$	−88.4587	+	88.4587i	−0.542691	+	0.542691i	−0.924317	−	0.381626i	$-0.875364\pi$
$163$	−88.4587	+	88.4587i	−0.542691	+	0.542691i	0.381626	+	0.924317i	$0.375364\pi$
$164$	−224.087	+	97.9948i	−1.36639	+	0.597529i
$165$	−1.29805	+	7.23123i	−0.00786698	+	0.0438257i
$166$	−21.8113	−	104.313i	−0.131393	−	0.628394i
$167$	−14.1920	+	14.1920i	−0.0849821	+	0.0849821i	−0.748320	−	0.663338i	$-0.769139\pi$
$167$	−14.1920	+	14.1920i	−0.0849821	+	0.0849821i	0.663338	+	0.748320i	$0.269139\pi$
$168$	9.78840	+	1.65029i	0.0582643	+	0.00982317i
$169$			164.925i			0.975887i
$170$	205.827	−	0.549512i	1.21075	−	0.00323242i
$171$	−214.514			−1.25447
$172$	−31.7633	+	81.1340i	−0.184670	+	0.471709i
$173$	−100.457	+	100.457i	−0.580679	+	0.580679i	−0.935090	−	0.354411i	$-0.884681\pi$
$173$	−100.457	+	100.457i	−0.580679	+	0.580679i	0.354411	+	0.935090i	$0.384681\pi$
$174$	0.256152	−	0.0535597i	0.00147214	−	0.000307814i
$175$	215.790	−	85.8117i	1.23309	−	0.490353i
$176$	175.629	−	11.4210i	0.997892	−	0.0648923i
$177$	2.49117	−	2.49117i	0.0140744	−	0.0140744i
$178$	104.278	−	159.415i	0.585833	−	0.895589i
$179$	176.489			0.985970			0.492985	−	0.870038i	$-0.335906\pi$
$179$	176.489			0.985970			0.492985	+	0.870038i	$0.335906\pi$
$180$	37.2364	+	175.742i	0.206869	+	0.976342i
$181$	317.980			1.75679			0.878396	−	0.477933i	$-0.158614\pi$
$181$	317.980			1.75679			0.878396	+	0.477933i	$0.158614\pi$
$182$	20.5300	−	31.3851i	0.112802	−	0.172446i
$183$	−9.26922	−	9.26922i	−0.0506515	−	0.0506515i
$184$	141.953	+	199.525i	0.771482	+	1.08437i
$185$	29.6516	+	45.0667i	0.160279	+	0.243604i
$186$	−2.31033	−	11.0493i	−0.0124211	−	0.0594046i
$187$	5.84975	+	226.335i	0.0312821	+	1.21035i
$188$	128.593	−	328.469i	0.684004	−	1.74718i
$189$	−22.3126			−0.118056
$190$	−169.323	−	168.421i	−0.891173	−	0.886427i
$191$		−	364.294i		−	1.90730i	−0.300919	−	0.953650i	$-0.597293\pi$
$191$		−	364.294i		−	1.90730i	0.300919	−	0.953650i	$-0.402707\pi$
$192$	−7.69293	+	3.72889i	−0.0400673	+	0.0194213i
$193$	−157.496	+	157.496i	−0.816041	+	0.816041i	−0.985532	−	0.169490i	$-0.945788\pi$
$193$	−157.496	+	157.496i	−0.816041	+	0.816041i	0.169490	+	0.985532i	$0.445788\pi$
$194$	−171.003	+	35.7557i	−0.881460	+	0.184308i
$195$	−1.32046	−	0.272422i	−0.00677157	−	0.00139704i
$196$	136.651	−	59.7585i	0.697200	−	0.304890i
$197$	111.489	+	111.489i	0.565933	+	0.565933i	0.930987	−	0.365054i	$-0.118949\pi$
$197$	111.489	+	111.489i	0.565933	+	0.565933i	−0.365054	+	0.930987i	$0.618949\pi$
$198$	−192.315	+	45.4278i	−0.971287	+	0.229433i
$199$	120.649			0.606275			0.303138	−	0.952947i	$-0.401966\pi$
$199$	120.649			0.606275			0.303138	+	0.952947i	$0.401966\pi$
$200$	−108.588	+	167.954i	−0.542940	+	0.839771i
$201$	−10.7781			−0.0536226
$202$	−51.3760	+	78.5408i	−0.254337	+	0.388816i
$203$	6.43397	−	6.43397i	0.0316944	−	0.0316944i
$204$	−4.40643	−	10.0763i	−0.0216002	−	0.0493936i
$205$	299.416	+	61.7722i	1.46057	+	0.301328i
$206$	50.0102	−	10.4568i	0.242768	−	0.0507613i
$207$	−194.406	−	194.406i	−0.939157	−	0.939157i
$208$	1.26251	+	32.2743i	0.00606975	+	0.155165i
$209$	180.898	−	190.497i	0.865543	−	0.911470i
$210$	−8.79730	−	8.75045i	−0.0418919	−	0.0416688i
$211$	121.309			0.574926			0.287463	−	0.957792i	$-0.407188\pi$
$211$	121.309			0.574926			0.287463	+	0.957792i	$0.407188\pi$
$212$	−0.0222565	+	0.0568506i	−0.000104984	+	0.000268163i
$213$	−2.90838	−	2.90838i	−0.0136544	−	0.0136544i
$214$	7.36739	−	1.54048i	0.0344271	−	0.00719848i
$215$	90.9850	−	59.8636i	0.423186	−	0.278435i
$216$	15.6578	−	11.1398i	0.0724899	−	0.0515733i
$217$	−277.534	−	277.534i	−1.27896	−	1.27896i
$218$	−138.180	−	90.3879i	−0.633853	−	0.414623i
$219$		−	3.23296i		−	0.0147624i
$220$	−187.467	−	115.135i	−0.852125	−	0.523339i
$221$	−41.5502			−0.188010
$222$	1.57789	−	2.41220i	0.00710763	−	0.0108657i
$223$	−151.819	+	151.819i	−0.680801	+	0.680801i	−0.960181	−	0.279380i	$-0.909871\pi$
$223$	−151.819	+	151.819i	−0.680801	+	0.680801i	0.279380	+	0.960181i	$0.409871\pi$
$224$	−152.872	+	254.927i	−0.682463	+	1.13807i
$225$	88.8722	−	206.219i	0.394988	−	0.916528i
$226$	−32.9697	−	157.679i	−0.145884	−	0.697696i
$227$	−102.712	+	102.712i	−0.452478	+	0.452478i	−0.896176	−	0.443698i	$-0.853666\pi$
$227$	−102.712	+	102.712i	−0.452478	+	0.452478i	0.443698	+	0.896176i	$0.353666\pi$
$228$	−4.65188	+	11.8824i	−0.0204030	+	0.0521160i
$229$		−	157.627i		−	0.688329i	−0.938909	−	0.344164i	$-0.888162\pi$
$229$		−	157.627i		−	0.688329i	0.938909	−	0.344164i	$-0.111838\pi$
$230$	−0.817177	−	306.085i	−0.00355294	−	1.33080i
$231$	9.39872	−	9.89744i	0.0406871	−	0.0428460i
$232$	−1.30279	+	7.72727i	−0.00561549	+	0.0333072i
$233$	−18.2635	+	18.2635i	−0.0783843	+	0.0783843i	−0.745212	−	0.666828i	$-0.767652\pi$
$233$	−18.2635	+	18.2635i	−0.0783843	+	0.0783843i	0.666828	+	0.745212i	$0.267652\pi$
$234$	−7.42213	−	35.4967i	−0.0317185	−	0.151695i
$235$	−368.350	+	242.356i	−1.56745	+	1.03130i
$236$	42.2696	+	96.6590i	0.179109	+	0.409572i
$237$	−7.66745	−	7.66745i	−0.0323521	−	0.0323521i
$238$	−320.006	−	209.326i	−1.34456	−	0.879522i
$239$		−	251.776i		−	1.05346i	−0.850033	−	0.526729i	$-0.823418\pi$
$239$		−	251.776i		−	1.05346i	0.850033	−	0.526729i	$-0.176582\pi$
$240$	10.5423	+	1.74846i	0.0439261	+	0.00728524i
$241$			292.983i			1.21570i	0.794053	+	0.607848i	$0.207967\pi$
$241$			292.983i			1.21570i	−0.794053	+	0.607848i	$0.792033\pi$
$242$	121.836	−	209.093i	0.503456	−	0.864021i
$243$	−22.8917	+	22.8917i	−0.0942047	+	0.0942047i
$244$	359.652	−	157.278i	1.47398	−	0.644583i
$245$	−182.588	−	37.6694i	−0.745256	−	0.153753i
$246$	−3.34327	−	15.9893i	−0.0135905	−	0.0649973i
$247$	34.0901	+	34.0901i	0.138017	+	0.138017i
$248$	333.321	+	56.1968i	1.34404	+	0.226600i
$249$	7.11769			0.0285851
$250$	232.058	−	92.9992i	0.928234	−	0.371997i
$251$		−	115.798i		−	0.461347i	−0.973031	−	0.230673i	$-0.925907\pi$
$251$		−	115.798i		−	0.461347i	0.973031	−	0.230673i	$-0.0740929\pi$
$252$	121.666	−	310.776i	0.482802	−	1.23324i
$253$	336.582	−	8.69913i	1.33036	−	0.0343839i
$254$	−260.876	+	54.5475i	−1.02707	+	0.214754i
$255$	−2.77765	+	13.4635i	−0.0108927	+	0.0527982i
$256$	−19.9978	−	255.218i	−0.0781166	−	0.996944i
$257$	−140.617	+	140.617i	−0.547146	+	0.547146i	−0.925614	−	0.378468i	$-0.876451\pi$
$257$	−140.617	+	140.617i	−0.547146	+	0.547146i	0.378468	+	0.925614i	$0.376451\pi$
$258$	−4.86997	−	3.18560i	−0.0188759	−	0.0123473i
$259$		−	100.222i		−	0.386959i
$260$	22.0110	−	33.8461i	0.0846576	−	0.130177i
$261$		−	8.79839i		−	0.0337103i
$262$	398.870	+	260.914i	1.52241	+	0.995854i
$263$	245.123	+	245.123i	0.932027	+	0.932027i	0.997832	−	0.0658056i	$-0.0209617\pi$
$263$	245.123	+	245.123i	0.932027	+	0.932027i	−0.0658056	+	0.997832i	$0.520962\pi$
$264$	−1.65412	+	11.6379i	−0.00626561	+	0.0440831i
$265$	0.0637532	−	0.0419464i	0.000240578	−	0.000158288i
$266$	90.8082	+	434.294i	0.341384	+	1.63268i
$267$	8.99637	+	8.99637i	0.0336943	+	0.0336943i
$268$	117.659	−	300.541i	0.439026	−	1.12142i
$269$			35.8456i			0.133255i	0.997778	+	0.0666276i	$0.0212239\pi$
$269$			35.8456i			0.133255i	−0.997778	+	0.0666276i	$0.978776\pi$
$270$	−24.0202	+	0.0641286i	−0.0889637	+	0.000237513i
$271$	129.306			0.477145			0.238573	−	0.971125i	$-0.423320\pi$
$271$	129.306			0.477145			0.238573	+	0.971125i	$0.423320\pi$
$272$	329.073	−	12.8727i	1.20983	−	0.0473261i
$273$	1.77118	+	1.77118i	0.00648783	+	0.00648783i
$274$	−157.080	+	32.8444i	−0.573283	+	0.119870i
$275$	108.186	+	252.826i	0.393402	+	0.919366i
$276$	−14.9844	+	6.55279i	−0.0542914	+	0.0237420i
$277$	−92.4412	−	92.4412i	−0.333723	−	0.333723i	0.520276	−	0.853998i	$-0.325829\pi$
$277$	−92.4412	−	92.4412i	−0.333723	−	0.333723i	−0.853998	+	0.520276i	$0.825829\pi$
$278$	−69.4069	+	106.105i	−0.249665	+	0.381674i
$279$	−379.524			−1.36030
$280$	340.035	−	149.782i	1.21441	−	0.534937i
$281$			148.143i			0.527199i	0.964632	+	0.263599i	$0.0849097\pi$
$281$			148.143i			0.527199i	−0.964632	+	0.263599i	$0.915090\pi$
$282$	19.7160	+	12.8968i	0.0699148	+	0.0457335i
$283$	198.091	+	198.091i	0.699969	+	0.699969i	0.964404	−	0.264435i	$-0.0851853\pi$
$283$	198.091	+	198.091i	0.699969	+	0.699969i	−0.264435	+	0.964404i	$0.585185\pi$
$284$	112.847	−	49.3488i	0.397349	−	0.173763i
$285$	13.3252	−	8.76730i	0.0467550	−	0.0307625i
$286$	37.7816	+	23.3430i	0.132104	+	0.0816189i
$287$	−401.618	−	401.618i	−1.39936	−	1.39936i
$288$	69.7797	+	278.830i	0.242291	+	0.968160i
$289$			134.651i			0.465920i
$290$	6.90788	−	6.94487i	0.0238203	−	0.0239478i
$291$		−	11.6682i		−	0.0400968i
$292$	90.1488	+	35.2925i	0.308729	+	0.120865i
$293$	−257.992	+	257.992i	−0.880517	+	0.880517i	−0.993587	−	0.113070i	$-0.963932\pi$
$293$	−257.992	+	257.992i	−0.880517	+	0.880517i	0.113070	+	0.993587i	$0.463932\pi$
$294$	2.03877	+	9.75050i	0.00693459	+	0.0331650i
$295$	26.6451	−	129.152i	0.0903225	−	0.437802i
$296$	50.0373	+	70.3310i	0.169045	+	0.237605i
$297$	−0.682670	−	26.4135i	−0.00229855	−	0.0889343i
$298$	280.120	+	183.235i	0.940000	+	0.614883i
$299$			61.7891i			0.206653i
$300$	−9.49572	−	9.39485i	−0.0316524	−	0.0313162i
$301$	−202.339			−0.672222
$302$	58.2943	+	38.1322i	0.193028	+	0.126265i
$303$	−4.43235	−	4.43235i	−0.0146282	−	0.0146282i
$304$	−280.551	−	259.428i	−0.922866	−	0.853382i
$305$	−480.552	−	99.1422i	−1.57558	−	0.325056i
$306$	−361.928	+	75.6770i	−1.18277	+	0.247310i
$307$	−175.702	+	175.702i	−0.572318	+	0.572318i	−0.932776	−	0.360457i	$-0.882621\pi$
$307$	−175.702	+	175.702i	−0.572318	+	0.572318i	0.360457	+	0.932776i	$0.382621\pi$
$308$	173.382	+	370.121i	0.562928	+	1.20169i
$309$			3.41238i			0.0110433i
$310$	−299.571	−	297.976i	−0.966359	−	0.961213i
$311$		−	254.241i		−	0.817497i	−0.912647	−	0.408748i	$-0.865965\pi$
$311$		−	254.241i		−	0.817497i	0.912647	−	0.408748i	$-0.134035\pi$
$312$	−2.12720	−	0.358639i	−0.00681796	−	0.00114949i
$313$	−213.752	−	213.752i	−0.682912	−	0.682912i	0.277743	−	0.960655i	$-0.410414\pi$
$313$	−213.752	−	213.752i	−0.682912	−	0.682912i	−0.960655	+	0.277743i	$0.910414\pi$
$314$	483.316	−	101.058i	1.53922	−	0.321842i
$315$	−348.509	+	229.302i	−1.10638	+	0.727942i
$316$	297.503	−	130.100i	0.941464	−	0.411708i
$317$	393.139	−	393.139i	1.24019	−	1.24019i	0.280263	−	0.959923i	$-0.409578\pi$
$317$	393.139	−	393.139i	1.24019	−	1.24019i	0.959923	−	0.280263i	$-0.0904217\pi$
$318$	−0.00341239	−	0.00223215i	−1.07308e−5	−	7.01935e-6i
$319$	7.81335	+	7.41964i	0.0244933	+	0.0232591i
$320$	−163.839	+	274.876i	−0.511995	+	0.858988i
$321$			0.502704i			0.00156605i
$322$	−311.288	+	475.880i	−0.966733	+	1.47789i
$323$	347.587	−	347.587i	1.07612	−	1.07612i
$324$	−129.046	−	295.092i	−0.398289	−	0.910777i
$325$	−46.8953	+	18.6485i	−0.144293	+	0.0573800i
$326$	244.903	−	51.2076i	0.751235	−	0.157079i
$327$	7.79801	−	7.79801i	0.0238471	−	0.0238471i
$328$	482.347	+	81.3222i	1.47057	+	0.247933i
$329$	819.163			2.48986
$330$	10.0896	−	10.6819i	0.0305745	−	0.0323694i
$331$			482.147i			1.45664i	0.685239	+	0.728319i	$0.259698\pi$
$331$			482.147i			1.45664i	−0.685239	+	0.728319i	$0.740302\pi$
$332$	−77.6998	+	198.471i	−0.234036	+	0.597805i
$333$	−68.5266	−	68.5266i	−0.205785	−	0.205785i
$334$	39.2913	−	8.21557i	0.117639	−	0.0245975i
$335$	−337.031	+	221.750i	−1.00606	+	0.661939i
$336$	−14.5763	−	13.4788i	−0.0433817	−	0.0401155i
$337$	314.946	+	314.946i	0.934557	+	0.934557i	0.997986	−	0.0634292i	$-0.0202037\pi$
$337$	314.946	+	314.946i	0.934557	+	0.934557i	−0.0634292	+	0.997986i	$0.520204\pi$
$338$	180.565	−	276.038i	0.534217	−	0.816681i
$339$	10.7590			0.0317375
$340$	−345.099	−	224.427i	−1.01500	−	0.660078i
$341$	320.051	−	337.034i	0.938566	−	0.988369i
$342$	359.036	+	234.857i	1.04981	+	0.686715i
$343$	−76.9379	−	76.9379i	−0.224309	−	0.224309i
$344$	141.991	−	101.020i	0.412764	−	0.293663i
$345$	20.0216	+	4.13063i	0.0580335	+	0.0119728i
$346$	278.122	−	58.1536i	0.803821	−	0.168074i
$347$	−461.603	+	461.603i	−1.33027	+	1.33027i	−0.425141	+	0.905127i	$0.639775\pi$
$347$	−461.603	+	461.603i	−1.33027	+	1.33027i	−0.905127	+	0.425141i	$0.860225\pi$
$348$	−0.487365	−	0.190799i	−0.00140047	−	0.000548274i
$349$	−373.881			−1.07129			−0.535646	−	0.844443i	$-0.679932\pi$
$349$	−373.881			−1.07129			−0.535646	+	0.844443i	$0.679932\pi$
$350$	−455.122	−	92.6296i	−1.30035	−	0.264656i
$351$	4.84894			0.0138147
$352$	−306.458	−	173.169i	−0.870619	−	0.491957i
$353$	343.128	+	343.128i	0.972033	+	0.972033i	0.999619	−	0.0275863i	$-0.00878211\pi$
$353$	343.128	+	343.128i	0.972033	+	0.972033i	−0.0275863	+	0.999619i	$0.508782\pi$
$354$	−6.89693	+	1.44210i	−0.0194828	+	0.00407374i
$355$	−150.782	−	31.1076i	−0.424737	−	0.0876270i
$356$	−349.065	+	152.649i	−0.980521	+	0.428788i
$357$	18.0591	−	18.0591i	0.0505858	−	0.0505858i
$358$	−295.393	−	193.226i	−0.825119	−	0.539737i
$359$		−	169.984i		−	0.473493i	−0.971572	−	0.236746i	$-0.923919\pi$
$359$		−	169.984i		−	0.473493i	0.971572	−	0.236746i	$-0.0760810\pi$
$360$	130.084	−	334.910i	0.361345	−	0.930306i
$361$	−209.359			−0.579942
$362$	−532.209	−	348.135i	−1.47019	−	0.961698i
$363$	12.0041	+	10.8233i	0.0330691	+	0.0298163i
$364$	−68.7229	+	30.0530i	−0.188799	+	0.0825631i
$365$	−66.5150	−	101.094i	−0.182233	−	0.276971i
$366$	5.36583	+	25.6623i	0.0146608	+	0.0701157i
$367$	260.278	+	260.278i	0.709204	+	0.709204i	0.966368	−	0.257164i	$-0.0827880\pi$
$367$	260.278	+	260.278i	0.709204	+	0.709204i	−0.257164	+	0.966368i	$0.582788\pi$
$368$	−19.1429	−	489.363i	−0.0520188	−	1.32979i
$369$	−549.208			−1.48837
$370$	−0.288049	−	107.893i	−0.000778511	−	0.291602i
$371$	−0.141779			−0.000382153
$372$	−8.23025	+	21.0228i	−0.0221243	+	0.0565129i
$373$	339.419	−	339.419i	0.909971	−	0.909971i	−0.0862979	−	0.996269i	$-0.527504\pi$
$373$	339.419	−	339.419i	0.909971	−	0.909971i	0.996269	+	0.0862979i	$0.0275037\pi$
$374$	238.008	−	385.226i	0.636386	−	1.03002i
$375$	2.90772	+	16.4422i	0.00775391	+	0.0438458i
$376$	−574.847	+	408.977i	−1.52885	+	1.08771i
$377$	−1.39822	+	1.39822i	−0.00370882	+	0.00370882i
$378$	37.3450	+	24.4286i	0.0987964	+	0.0646258i
$379$	116.272			0.306786			0.153393	−	0.988165i	$-0.450980\pi$
$379$	116.272			0.306786			0.153393	+	0.988165i	$0.450980\pi$
$380$	99.0061	+	467.270i	0.260542	+	1.22966i
$381$		−	17.8005i		−	0.0467204i
$382$	−398.841	+	609.727i	−1.04409	+	1.59614i
$383$	−316.783	+	316.783i	−0.827109	+	0.827109i	−0.987116	−	0.160007i	$-0.948848\pi$
$383$	−316.783	+	316.783i	−0.827109	+	0.827109i	0.160007	+	0.987116i	$0.448848\pi$
$384$	16.9583	+	2.18135i	0.0441623	+	0.00568061i
$385$	90.2666	−	502.861i	0.234459	−	1.30613i
$386$	436.036	−	91.1724i	1.12963	−	0.236198i
$387$	−138.348	+	138.348i	−0.357488	+	0.357488i
$388$	325.358	+	127.375i	0.838552	+	0.328286i
$389$			99.0400i			0.254601i	0.991864	+	0.127301i	$0.0406313\pi$
$389$			99.0400i			0.254601i	−0.991864	+	0.127301i	$0.959369\pi$
$390$	1.91182	+	1.90164i	0.00490210	+	0.00487599i
$391$	630.009			1.61128
$392$	−294.142	−	49.5913i	−0.750361	−	0.126508i
$393$	−22.5097	+	22.5097i	−0.0572767	+	0.0572767i
$394$	−64.5394	−	308.663i	−0.163806	−	0.783408i
$395$	−397.510	−	82.0099i	−1.00636	−	0.207620i
$396$	371.617	+	134.519i	0.938427	+	0.339695i
$397$	−210.268	+	210.268i	−0.529643	+	0.529643i	−0.920466	−	0.390823i	$-0.872191\pi$
$397$	−210.268	+	210.268i	−0.529643	+	0.529643i	0.390823	+	0.920466i	$0.372191\pi$
$398$	−201.932	−	132.090i	−0.507368	−	0.331885i
$399$	−29.6335			−0.0742693
$400$	365.628	−	162.223i	0.914070	−	0.405557i
$401$	−343.983			−0.857812			−0.428906	−	0.903349i	$-0.641101\pi$
$401$	−343.983			−0.857812			−0.428906	+	0.903349i	$0.641101\pi$
$402$	18.0396	+	11.8003i	0.0448746	+	0.0293539i
$403$	60.3133	+	60.3133i	0.149661	+	0.149661i
$404$	171.978	−	75.2072i	0.425688	−	0.186156i
$405$	−81.3453	+	394.289i	−0.200853	+	0.973553i
$406$	−17.8128	+	3.72455i	−0.0438739	+	0.00917376i
$407$	118.643	−	3.06638i	0.291505	−	0.00753411i
$408$	−3.65673	+	21.6892i	−0.00896258	+	0.0531599i
$409$	−326.947			−0.799381			−0.399690	−	0.916650i	$-0.630882\pi$
$409$	−326.947			−0.799381			−0.399690	+	0.916650i	$0.630882\pi$
$410$	−433.508	−	431.200i	−1.05734	−	1.05171i
$411$		−	10.7181i		−	0.0260781i
$412$	−95.1516	−	37.2510i	−0.230950	−	0.0904151i
$413$	−173.236	+	173.236i	−0.419457	+	0.419457i
$414$	112.539	+	538.222i	0.271833	+	1.30005i
$415$	222.569	−	146.439i	0.536311	−	0.352866i
$416$	33.2219	−	55.4004i	0.0798603	−	0.133174i
$417$	−5.98792	−	5.98792i	−0.0143595	−	0.0143595i
$418$	−511.336	+	120.786i	−1.22329	+	0.288961i
$419$	32.6169			0.0778446			0.0389223	−	0.999242i	$-0.487608\pi$
$419$	32.6169			0.0778446			0.0389223	+	0.999242i	$0.487608\pi$
$420$	5.14394	+	24.2774i	0.0122475	+	0.0578033i
$421$	−55.1991			−0.131114			−0.0655572	−	0.997849i	$-0.520882\pi$
$421$	−55.1991			−0.131114			−0.0655572	+	0.997849i	$0.520882\pi$
$422$	−203.038	−	132.813i	−0.481132	−	0.314724i
$423$	560.099	−	560.099i	1.32411	−	1.32411i
$424$	0.0994931	−	0.0707848i	0.000234654	−	0.000166945i
$425$	190.142	+	478.150i	0.447394	+	1.12506i
$426$	1.68362	+	8.05201i	0.00395217	+	0.0189014i
$427$	644.583	+	644.583i	1.50956	+	1.50956i
$428$	−14.0175	−	5.48774i	−0.0327512	−	0.0128218i
$429$	−2.04252	+	2.15090i	−0.00476111	+	0.00501375i
$430$	−217.824	+	0.581542i	−0.506568	+	0.00135242i
$431$	−691.489			−1.60438			−0.802191	−	0.597068i	$-0.796332\pi$
$431$	−691.489			−1.60438			−0.802191	+	0.597068i	$0.796332\pi$
$432$	−38.4031	+	1.50225i	−0.0888960	+	0.00347744i
$433$	−149.026	−	149.026i	−0.344170	−	0.344170i	0.513762	−	0.857933i	$-0.328251\pi$
$433$	−149.026	−	149.026i	−0.344170	−	0.344170i	−0.857933	+	0.513762i	$0.828251\pi$
$434$	160.661	+	768.367i	0.370186	+	1.77043i
$435$	0.359596	+	0.546539i	0.000826656	+	0.00125641i
$436$	132.315	+	302.568i	0.303475	+	0.693964i
$437$	−516.895	−	516.895i	−1.18283	−	1.18283i
$438$	−3.53956	+	5.41108i	−0.00808118	+	0.0123541i
$439$			327.610i			0.746265i	0.927778	+	0.373133i	$0.121716\pi$
$439$			327.610i			0.746265i	−0.927778	+	0.373133i	$0.878284\pi$
$440$	187.715	+	397.949i	0.426625	+	0.904429i
$441$	334.914			0.759442
$442$	69.5434	+	45.4905i	0.157338	+	0.102920i
$443$	−7.21361	+	7.21361i	−0.0162835	+	0.0162835i	−0.715202	−	0.698918i	$-0.753665\pi$
$443$	−7.21361	+	7.21361i	−0.0162835	+	0.0162835i	0.698918	+	0.715202i	$0.253665\pi$
$444$	−5.28191	+	2.30981i	−0.0118962	+	0.00520228i
$445$	466.407	+	96.2238i	1.04810	+	0.216233i
$446$	420.318	−	87.8859i	0.942417	−	0.197053i
$447$	−15.8082	+	15.8082i	−0.0353651	+	0.0353651i
$448$	534.967	−	259.307i	1.19412	−	0.578811i
$449$			343.710i			0.765502i	0.923852	+	0.382751i	$0.125023\pi$
$449$			343.710i			0.765502i	−0.923852	+	0.382751i	$0.874977\pi$
$450$	−374.522	+	247.852i	−0.832272	+	0.550783i
$451$	463.145	−	487.720i	1.02693	−	1.08142i
$452$	−117.450	+	300.007i	−0.259846	+	0.663733i
$453$	−3.28976	+	3.28976i	−0.00726217	+	0.00726217i
$454$	284.365	−	59.4590i	0.626355	−	0.130967i
$455$	91.8247	+	18.9442i	0.201812	+	0.0416357i
$456$	20.7952	−	14.7949i	0.0456036	−	0.0324449i
$457$	−139.720	−	139.720i	−0.305733	−	0.305733i	0.537519	−	0.843252i	$-0.319362\pi$
$457$	−139.720	−	139.720i	−0.305733	−	0.305733i	−0.843252	+	0.537519i	$0.819362\pi$
$458$	−172.576	+	263.824i	−0.376803	+	0.576035i
$459$		−	49.4404i		−	0.107713i
$460$	−333.744	+	513.195i	−0.725530	+	1.11564i
$461$			276.382i			0.599528i	0.954013	+	0.299764i	$0.0969079\pi$
$461$			276.382i			0.599528i	−0.954013	+	0.299764i	$0.903092\pi$
$462$	−26.5669	+	6.27551i	−0.0575040	+	0.0135834i
$463$	−120.737	+	120.737i	−0.260771	+	0.260771i	−0.825367	−	0.564596i	$-0.809032\pi$
$463$	−120.737	+	120.737i	−0.260771	+	0.260771i	0.564596	+	0.825367i	$0.309032\pi$
$464$	10.6406	−	11.5070i	0.0229323	−	0.0247995i
$465$	23.5753	−	15.5114i	0.0506996	−	0.0333578i
$466$	50.5636	−	10.5725i	0.108506	−	0.0226878i
$467$	129.275	+	129.275i	0.276821	+	0.276821i	0.831838	−	0.555018i	$-0.187289\pi$
$467$	129.275	+	129.275i	0.276821	+	0.276821i	−0.555018	+	0.831838i	$0.687289\pi$
$468$	−26.4404	+	67.5375i	−0.0564965	+	0.144311i
$469$	749.513			1.59811
$470$	881.855	−	2.35436i	1.87629	−	0.00500927i
$471$			32.9784i			0.0700179i
$472$	35.0779	−	208.058i	0.0743177	−	0.440801i
$473$	−6.19071	−	239.527i	−0.0130882	−	0.506400i
$474$	4.43859	+	21.2278i	0.00936412	+	0.0447843i
$475$	236.298	−	548.305i	0.497469	−	1.15433i
$476$	306.424	+	700.707i	0.643748	+	1.47207i
$477$	−0.0969405	+	0.0969405i	−0.000203230	+	0.000203230i
$478$	−275.653	+	421.403i	−0.576680	+	0.881597i
$479$		−	520.551i		−	1.08674i	−0.839492	−	0.543372i	$-0.817147\pi$
$479$		−	520.551i		−	1.08674i	0.839492	−	0.543372i	$-0.182853\pi$
$480$	−15.7305	−	14.4685i	−0.0327720	−	0.0301426i
$481$			21.7802i			0.0452811i
$482$	320.767	−	490.371i	0.665492	−	1.01737i
$483$	−26.8557	−	26.8557i	−0.0556018	−	0.0556018i
$484$	−432.842	+	216.573i	−0.894302	+	0.447464i
$485$	−240.061	−	364.862i	−0.494971	−	0.752293i
$486$	63.3770	−	13.2517i	0.130405	−	0.0272669i
$487$	−266.299	−	266.299i	−0.546816	−	0.546816i	0.378703	−	0.925518i	$-0.376370\pi$
$487$	−266.299	−	266.299i	−0.546816	−	0.546816i	−0.925518	+	0.378703i	$0.876370\pi$
$488$	−774.151	−	130.519i	−1.58637	−	0.267458i
$489$			16.7106i			0.0341730i
$490$	264.359	+	262.951i	0.539508	+	0.536635i
$491$	115.652			0.235544			0.117772	−	0.993041i	$-0.462425\pi$
$491$	115.652			0.235544			0.117772	+	0.993041i	$0.462425\pi$
$492$	−11.9100	+	30.4220i	−0.0242072	+	0.0618334i
$493$	14.2565	+	14.2565i	0.0289178	+	0.0289178i
$494$	−19.7343	−	94.3802i	−0.0399480	−	0.191053i
$495$	−282.109	−	405.548i	−0.569917	−	0.819288i
$496$	−496.360	−	458.989i	−1.00073	−	0.925380i
$497$	202.249	+	202.249i	0.406940	+	0.406940i
$498$	−11.9130	−	7.79268i	−0.0239217	−	0.0156479i
$499$	408.511			0.818659			0.409330	−	0.912387i	$-0.365763\pi$
$499$	408.511			0.818659			0.409330	+	0.912387i	$0.365763\pi$
$500$	−490.220	−	98.4107i	−0.980439	−	0.196821i
$501$			2.68099i			0.00535128i
$502$	−126.779	+	193.813i	−0.252549	+	0.386083i
$503$	−181.279	−	181.279i	−0.360396	−	0.360396i	0.503563	−	0.863959i	$-0.332022\pi$
$503$	−181.279	−	181.279i	−0.360396	−	0.360396i	−0.863959	+	0.503563i	$0.832022\pi$
$504$	−543.883	+	386.948i	−1.07913	+	0.767754i
$505$	−229.790	−	47.4077i	−0.455030	−	0.0938766i
$506$	−572.868	−	353.941i	−1.13215	−	0.699488i
$507$	15.5779	+	15.5779i	0.0307255	+	0.0307255i
$508$	496.353	+	194.318i	0.977073	+	0.382516i
$509$		−	411.402i		−	0.808256i	−0.914702	−	0.404128i	$-0.867575\pi$
$509$		−	411.402i		−	0.808256i	0.914702	−	0.404128i	$-0.132425\pi$
$510$	19.3893	−	19.4931i	0.0380183	−	0.0382218i
$511$			224.821i			0.439962i
$512$	−245.950	+	449.057i	−0.480371	+	0.877065i
$513$	−40.5637	+	40.5637i	−0.0790715	+	0.0790715i
$514$	389.305	−	81.4011i	0.757402	−	0.158368i
$515$	70.2063	+	106.705i	0.136323	+	0.207193i
$516$	4.66327	+	10.6636i	0.00903735	+	0.0206659i
$517$	25.0629	+	969.721i	0.0484776	+	1.87567i
$518$	−109.727	+	167.744i	−0.211828	+	0.323831i
$519$			18.9773i			0.0365651i
$520$	−73.8960	+	32.5505i	−0.142108	+	0.0625971i
$521$	261.653			0.502213			0.251106	−	0.967960i	$-0.419206\pi$
$521$	261.653			0.502213			0.251106	+	0.967960i	$0.419206\pi$
$522$	−9.63277	+	14.7260i	−0.0184536	+	0.0282108i
$523$	−615.582	−	615.582i	−1.17702	−	1.17702i	−0.980500	−	0.196521i	$-0.937036\pi$
$523$	−615.582	−	615.582i	−1.17702	−	1.17702i	−0.196521	−	0.980500i	$-0.562964\pi$
$524$	−381.941	−	873.393i	−0.728894	−	1.66678i
$525$	12.2770	−	28.4876i	0.0233848	−	0.0542621i
$526$	−141.899	−	678.636i	−0.269769	−	1.29018i
$527$	614.961	−	614.961i	1.16691	−	1.16691i
$528$	15.5101	−	17.6677i	0.0293753	−	0.0334615i
$529$		−	407.884i		−	0.771047i
$530$	−0.152629		0.000407486i	−0.000287980		7.68842e-7i
$531$			236.898i			0.446136i
$532$	323.492	−	826.306i	0.608068	−	1.55321i
$533$	87.2791	+	87.2791i	0.163751	+	0.163751i
$534$	−5.20788	−	24.9069i	−0.00975259	−	0.0466422i
$535$	10.3426	+	15.7195i	0.0193320	+	0.0293822i
$536$	−525.970	+	374.204i	−0.981288	+	0.698141i
$537$	16.6701	−	16.6701i	0.0310430	−	0.0310430i
$538$	39.2450	−	59.9956i	0.0729461	−	0.111516i
$539$	−282.431	+	297.418i	−0.523992	+	0.551796i
$540$	40.2733	+	26.1908i	0.0745802	+	0.0485014i
$541$			887.533i			1.64054i	0.571976	+	0.820270i	$0.306177\pi$
$541$			887.533i			1.64054i	−0.571976	+	0.820270i	$0.693823\pi$
$542$	−216.423	−	141.569i	−0.399304	−	0.261197i
$543$	30.0345	−	30.0345i	0.0553122	−	0.0553122i
$544$	−564.869	−	338.735i	−1.03836	−	0.622674i
$545$	83.4063	−	404.279i	0.153039	−	0.741796i
$546$	−1.02531	−	4.90360i	−0.00187786	−	0.00898095i
$547$	282.555	−	282.555i	0.516553	−	0.516553i	−0.399973	−	0.916527i	$-0.630981\pi$
$547$	282.555	−	282.555i	0.516553	−	0.516553i	0.916527	+	0.399973i	$0.130981\pi$
$548$	298.866	+	117.004i	0.545377	+	0.213510i
$549$	881.460			1.60557
$550$	95.7296	−	541.605i	0.174054	−	0.984736i
$551$		−	23.3936i		−	0.0424566i
$552$	32.2540	+	5.43791i	0.0584311	+	0.00985129i
$553$	533.195	+	533.195i	0.964187	+	0.964187i
$554$	53.5130	+	255.928i	0.0965939	+	0.461965i
$555$	7.05746	+	1.45602i	0.0127161	+	0.00262345i
$556$	232.335	−	101.602i	0.417869	−	0.182737i
$557$	−346.067	−	346.067i	−0.621305	−	0.621305i	0.324560	−	0.945865i	$-0.394784\pi$
$557$	−346.067	−	346.067i	−0.621305	−	0.621305i	−0.945865	+	0.324560i	$0.894784\pi$
$558$	635.218	+	415.516i	1.13838	+	0.744652i
$559$	43.9720			0.0786619
$560$	−733.110	−	121.588i	−1.30913	−	0.217121i
$561$	21.9308	+	20.8258i	0.0390924	+	0.0371226i
$562$	162.192	−	247.950i	0.288597	−	0.441192i
$563$	468.360	+	468.360i	0.831900	+	0.831900i	0.987777	−	0.155877i	$-0.0498203\pi$
$563$	468.360	+	468.360i	0.831900	+	0.831900i	−0.155877	+	0.987777i	$0.549820\pi$
$564$	−18.8791	−	43.1714i	−0.0334737	−	0.0765450i
$565$	336.433	−	221.356i	0.595457	−	0.391781i
$566$	−114.672	−	548.426i	−0.202602	−	0.968951i
$567$	528.874	−	528.874i	0.932759	−	0.932759i
$568$	−242.903	−	40.9527i	−0.427647	−	0.0720998i
$569$	−556.715			−0.978410			−0.489205	−	0.872169i	$-0.662713\pi$
$569$	−556.715			−0.978410			−0.489205	+	0.872169i	$0.662713\pi$
$570$	−31.9013	+	0.0851695i	−0.0559673	+	0.000149420i
$571$	396.901			0.695098			0.347549	−	0.937662i	$-0.387014\pi$
$571$	396.901			0.695098			0.347549	+	0.937662i	$0.387014\pi$
$572$	−37.6792	−	80.4342i	−0.0658727	−	0.140619i
$573$	−34.4091	−	34.4091i	−0.0600508	−	0.0600508i
$574$	232.491	+	1111.90i	0.405037	+	1.93711i
$575$	711.055	−	282.760i	1.23662	−	0.491756i
$576$	188.481	−	543.081i	0.327224	−	0.942849i
$577$	−8.74062	+	8.74062i	−0.0151484	+	0.0151484i	−0.714640	−	0.699492i	$-0.753410\pi$
$577$	−8.74062	+	8.74062i	−0.0151484	+	0.0151484i	0.699492	+	0.714640i	$0.253410\pi$
$578$	147.420	−	225.368i	0.255052	−	0.389910i
$579$			29.7523i			0.0513857i
$580$	−19.1653	+	4.06079i	−0.0330437	+	0.00700136i
$581$	−494.964			−0.851918
$582$	−12.7747	+	19.5292i	−0.0219496	+	0.0335554i
$583$	−0.00433783	−	0.167837i	−7.44053e−6	−	0.000287885i
$584$	−112.244	−	157.768i	−0.192199	−	0.270150i
$585$	75.7377	−	49.8316i	0.129466	−	0.0851822i
$586$	714.264	−	149.348i	1.21888	−	0.254860i
$587$	306.743	+	306.743i	0.522560	+	0.522560i	0.918344	−	0.395783i	$-0.129527\pi$
$587$	306.743	+	306.743i	0.522560	+	0.522560i	−0.395783	+	0.918344i	$0.629527\pi$
$588$	7.26284	−	18.5517i	0.0123518	−	0.0315506i
$589$	−1009.10			−1.71324
$590$	−185.996	+	186.992i	−0.315248	+	0.316935i
$591$	21.0612			0.0356365
$592$	−6.74774	−	172.497i	−0.0113982	−	0.291380i
$593$	519.759	−	519.759i	0.876490	−	0.876490i	−0.116680	−	0.993170i	$-0.537225\pi$
$593$	519.759	−	519.759i	0.876490	−	0.876490i	0.993170	+	0.116680i	$0.0372251\pi$
$594$	−27.7758	+	44.9562i	−0.0467606	+	0.0756839i
$595$	193.158	−	936.256i	0.324635	−	1.57354i
$596$	−268.230	−	613.369i	−0.450051	−	1.02914i
$597$	11.3958	−	11.3958i	0.0190884	−	0.0190884i
$598$	67.6488	−	103.418i	0.113125	−	0.172939i
$599$	−727.843			−1.21510			−0.607548	−	0.794283i	$-0.707847\pi$
$599$	−727.843			−1.21510			−0.607548	+	0.794283i	$0.707847\pi$
$600$	5.60739	+	26.1206i	0.00934564	+	0.0435343i
$601$		−	870.044i		−	1.44766i	−0.689978	−	0.723830i	$-0.742380\pi$
$601$		−	870.044i		−	1.44766i	0.689978	−	0.723830i	$-0.257620\pi$
$602$	338.658	+	221.527i	0.562556	+	0.367985i
$603$	512.476	−	512.476i	0.849877	−	0.849877i
$604$	−55.8201	−	127.645i	−0.0924173	−	0.211333i
$605$	598.045	+	91.4716i	0.988504	+	0.151193i
$606$	2.56583	+	12.2712i	0.00423404	+	0.0202495i
$607$	251.374	−	251.374i	0.414126	−	0.414126i	−0.469047	−	0.883173i	$-0.655403\pi$
$607$	251.374	−	251.374i	0.414126	−	0.414126i	0.883173	+	0.469047i	$0.155403\pi$
$608$	185.534	+	741.367i	0.305154	+	1.21935i
$609$		−	1.21543i		−	0.00199578i
$610$	695.766	+	692.061i	1.14060	+	1.13453i
$611$	−178.020			−0.291358
$612$	688.621	+	269.589i	1.12520	+	0.440505i
$613$	−571.963	+	571.963i	−0.933055	+	0.933055i	−0.997896	−	0.0648405i	$-0.979346\pi$
$613$	−571.963	+	571.963i	−0.933055	+	0.933055i	0.0648405	+	0.997896i	$0.479346\pi$
$614$	486.440	−	101.712i	0.792247	−	0.165654i
$615$	34.1157	−	22.4465i	0.0554728	−	0.0364983i
$616$	115.028	−	809.303i	0.186733	−	1.31380i
$617$	−99.1961	+	99.1961i	−0.160772	+	0.160772i	−0.782908	−	0.622137i	$-0.786265\pi$
$617$	−99.1961	+	99.1961i	−0.160772	+	0.160772i	0.622137	+	0.782908i	$0.286265\pi$
$618$	3.73598	−	5.71136i	0.00604528	−	0.00924169i
$619$	−481.347			−0.777620			−0.388810	−	0.921318i	$-0.627114\pi$
$619$	−481.347			−0.777620			−0.388810	+	0.921318i	$0.627114\pi$
$620$	175.165	+	826.709i	0.282524	+	1.33340i
$621$	−73.5226			−0.118394
$622$	−278.352	+	425.529i	−0.447511	+	0.684130i
$623$	−625.608	−	625.608i	−1.00419	−	1.00419i
$624$	3.16769	+	2.92920i	0.00507643	+	0.00469422i
$625$	429.205	+	454.321i	0.686729	+	0.726914i
$626$	123.738	+	591.783i	0.197665	+	0.945340i
$627$	−0.906658	−	35.0799i	−0.00144603	−	0.0559488i
$628$	−919.578	−	360.007i	−1.46430	−	0.573260i
$629$	222.074			0.353059
$630$	834.355	−	2.22754i	1.32437	−	0.00353578i
$631$			385.380i			0.610744i	0.952233	+	0.305372i	$0.0987808\pi$
$631$			385.380i			0.610744i	−0.952233	+	0.305372i	$0.901219\pi$
$632$	−640.374	−	107.965i	−1.01325	−	0.170831i
$633$	11.4582	−	11.4582i	0.0181014	−	0.0181014i
$634$	−1088.43	+	227.583i	−1.71676	+	0.358964i
$635$	−366.227	−	556.619i	−0.576736	−	0.876565i
$636$	0.00326756	+	0.00747200i	5.13767e−6	+	1.17484e-5i
$637$	−53.2239	−	53.2239i	−0.0835540	−	0.0835540i
$638$	−4.95409	−	20.9727i	−0.00776503	−	0.0328726i
$639$	276.573			0.432822
$640$	575.164	−	280.690i	0.898693	−	0.438578i
$641$	897.824			1.40066			0.700331	−	0.713819i	$-0.253036\pi$
$641$	897.824			1.40066			0.700331	+	0.713819i	$0.253036\pi$
$642$	0.550377	−	0.841385i	0.000857284	−	0.00131057i
$643$	−320.216	+	320.216i	−0.498003	+	0.498003i	−0.910816	−	0.412813i	$-0.864546\pi$
$643$	−320.216	+	320.216i	−0.498003	+	0.498003i	0.412813	+	0.910816i	$0.364546\pi$
$644$	1042.02	−	455.682i	1.61804	−	0.707580i
$645$	2.93955	−	14.2483i	0.00455744	−	0.0220904i
$646$	−962.313	+	201.214i	−1.48965	+	0.311476i
$647$	−497.330	−	497.330i	−0.768670	−	0.768670i	0.209202	−	0.977872i	$-0.432913\pi$
$647$	−497.330	−	497.330i	−0.768670	−	0.768670i	−0.977872	+	0.209202i	$0.932913\pi$
$648$	−107.090	+	635.184i	−0.165262	+	0.980222i
$649$	−210.376	−	199.775i	−0.324154	−	0.307820i
$650$	98.9066	+	20.1302i	0.152164	+	0.0309695i
$651$	−52.4284			−0.0805352
$652$	−465.962	−	182.420i	−0.714666	−	0.279786i
$653$	−357.269	−	357.269i	−0.547119	−	0.547119i	0.378487	−	0.925606i	$-0.376444\pi$
$653$	−357.269	−	357.269i	−0.547119	−	0.547119i	−0.925606	+	0.378487i	$0.876444\pi$
$654$	−21.5892	+	4.51417i	−0.0330110	+	0.00690240i
$655$	−240.761	+	1166.99i	−0.367574	+	1.78167i
$656$	−718.280	−	664.200i	−1.09494	−	1.01250i
$657$	153.720	+	153.720i	0.233972	+	0.233972i
$658$	−1371.05	−	896.847i	−2.08366	−	1.36299i
$659$			794.549i			1.20569i	0.797859	+	0.602844i	$0.205966\pi$
$659$			794.549i			1.20569i	−0.797859	+	0.602844i	$0.794034\pi$
$660$	−28.5820	+	6.83215i	−0.0433061	+	0.0103517i
$661$	−201.089			−0.304220			−0.152110	−	0.988364i	$-0.548607\pi$
$661$	−201.089			−0.304220			−0.152110	+	0.988364i	$0.548607\pi$
$662$	527.870	−	806.979i	0.797387	−	1.21900i
$663$	−3.92459	+	3.92459i	−0.00591944	+	0.00591944i
$664$	347.341	−	247.117i	0.523104	−	0.372164i
$665$	−926.634	+	609.679i	−1.39343	+	0.916810i
$666$	39.6692	+	189.719i	0.0595633	+	0.284864i
$667$	21.2007	−	21.2007i	0.0317852	−	0.0317852i
$668$	−74.7574	−	29.2669i	−0.111912	−	0.0438127i
$669$			28.6798i			0.0428697i
$670$	806.875	−	2.15418i	1.20429	−	0.00321519i
$671$	−743.331	+	782.774i	−1.10780	+	1.16658i
$672$	9.63954	+	38.5183i	0.0143446	+	0.0573189i
$673$	−19.0447	+	19.0447i	−0.0282983	+	0.0282983i	−0.721114	−	0.692816i	$-0.756370\pi$
$673$	−19.0447	+	19.0447i	−0.0282983	+	0.0282983i	0.692816	+	0.721114i	$0.256370\pi$
$674$	−182.318	−	871.944i	−0.270502	−	1.29369i
$675$	−22.1898	−	55.8006i	−0.0328737	−	0.0826675i
$676$	−604.432	+	264.322i	−0.894130	+	0.391009i
$677$	289.484	+	289.484i	0.427599	+	0.427599i	0.887810	−	0.460211i	$-0.152226\pi$
$677$	289.484	+	289.484i	0.427599	+	0.427599i	−0.460211	+	0.887810i	$0.652226\pi$
$678$	−18.0076	−	11.7793i	−0.0265599	−	0.0173737i
$679$			811.405i			1.19500i
$680$	331.889	+	753.453i	0.488072	+	1.10802i
$681$			19.4033i			0.0284923i
$682$	−904.672	+	213.698i	−1.32650	+	0.313340i
$683$	−104.564	+	104.564i	−0.153095	+	0.153095i	−0.779499	−	0.626404i	$-0.784526\pi$
$683$	−104.564	+	104.564i	−0.153095	+	0.153095i	0.626404	+	0.779499i	$0.284526\pi$
$684$	−343.797	−	786.169i	−0.502627	−	1.14937i
$685$	−220.515	−	335.154i	−0.321919	−	0.489276i
$686$	44.5384	+	213.007i	0.0649247	+	0.310505i
$687$	−14.8886	−	14.8886i	−0.0216719	−	0.0216719i
$688$	−348.253	+	13.6230i	−0.506182	+	0.0198009i
$689$	0.0308112			4.47187e−5
$690$	−28.9882	−	28.8338i	−0.0420118	−	0.0417881i
$691$		−	251.878i		−	0.364512i	−0.983251	−	0.182256i	$-0.941660\pi$
$691$		−	251.878i		−	0.364512i	0.983251	−	0.182256i	$-0.0583400\pi$
$692$	−529.167	−	207.164i	−0.764692	−	0.299370i
$693$	23.7129	+	917.487i	0.0342178	+	1.32394i
$694$	1277.97	−	267.216i	1.84146	−	0.385038i
$695$	−310.437	−	64.0458i	−0.446672	−	0.0921523i
$696$	0.606819	+	0.852928i	0.000871867	+	0.00122547i
$697$	889.908	−	889.908i	1.27677	−	1.27677i
$698$	625.772	+	409.337i	0.896522	+	0.586443i
$699$			3.45014i			0.00493582i
$700$	660.333	+	653.319i	0.943333	+	0.933313i
$701$		−	646.696i		−	0.922533i	−0.887262	−	0.461267i	$-0.847395\pi$
$701$		−	646.696i		−	0.922533i	0.887262	−	0.461267i	$-0.152605\pi$
$702$	−8.11578	−	5.30878i	−0.0115609	−	0.00756237i
$703$	−182.202	−	182.202i	−0.259177	−	0.259177i
$704$	323.334	+	625.357i	0.459281	+	0.888291i
$705$	−11.9007	+	57.6838i	−0.0168804	+	0.0818210i
$706$	−198.632	−	949.967i	−0.281349	−	1.34556i
$707$	308.226	+	308.226i	0.435963	+	0.435963i
$708$	13.1224	+	5.13731i	0.0185345	+	0.00725608i
$709$			956.497i			1.34908i	0.738238	+	0.674540i	$0.235658\pi$
$709$			956.497i			1.34908i	−0.738238	+	0.674540i	$0.764342\pi$
$710$	218.309	+	217.146i	0.307477	+	0.305840i
$711$	729.139			1.02551
$712$	751.363	+	126.677i	1.05528	+	0.177918i
$713$	−914.507	−	914.507i	−1.28262	−	1.28262i
$714$	−49.9977	+	10.4542i	−0.0700248	+	0.0146417i
$715$	−19.6166	+	109.281i	−0.0274358	+	0.152841i
$716$	282.855	+	646.812i	0.395049	+	0.903368i
$717$	−23.7814	−	23.7814i	−0.0331679	−	0.0331679i
$718$	−186.104	+	284.505i	−0.259198	+	0.396247i
$719$	−715.042			−0.994495			−0.497248	−	0.867609i	$-0.665656\pi$
$719$	−715.042			−0.994495			−0.497248	+	0.867609i	$0.665656\pi$
$720$	−584.395	+	418.125i	−0.811660	+	0.580729i
$721$		−	237.297i		−	0.329122i
$722$	350.409	+	229.213i	0.485331	+	0.317470i
$723$	27.6735	+	27.6735i	0.0382759	+	0.0382759i
$724$	509.620	+	1165.36i	0.703894	+	1.60961i
$725$	22.4890	+	9.69188i	0.0310193	+	0.0133681i
$726$	−8.24175	−	31.2577i	−0.0113523	−	0.0430547i
$727$	330.247	+	330.247i	0.454260	+	0.454260i	0.896766	−	0.442506i	$-0.145910\pi$
$727$	330.247	+	330.247i	0.454260	+	0.454260i	−0.442506	+	0.896766i	$0.645910\pi$
$728$	147.926	+	24.9398i	0.203195	+	0.0342580i
$729$		−	720.343i		−	0.988124i
$730$	0.646157	+	242.026i	0.000885146	+	0.331543i
$731$		−	448.344i		−	0.613330i
$732$	19.1151	−	48.8263i	0.0261135	−	0.0667026i
$733$	397.903	−	397.903i	0.542841	−	0.542841i	−0.381519	−	0.924361i	$-0.624599\pi$
$733$	397.903	−	397.903i	0.542841	−	0.542841i	0.924361	+	0.381519i	$0.124599\pi$
$734$	−150.672	−	720.593i	−0.205275	−	0.981735i
$735$	−20.8042	+	13.6881i	−0.0283051	+	0.0186233i
$736$	−503.731	+	840.015i	−0.684417	+	1.14132i
$737$	22.9319	+	887.269i	0.0311152	+	1.20389i
$738$	919.221	+	601.291i	1.24556	+	0.814758i
$739$			785.106i			1.06239i	0.847250	+	0.531195i	$0.178257\pi$
$739$			785.106i			1.06239i	−0.847250	+	0.531195i	$0.821743\pi$
$740$	−117.642	+	180.897i	−0.158976	+	0.244456i
$741$	6.43991			0.00869083
$742$	0.237298	+	0.155224i	0.000319809	+	0.000209197i
$743$	756.814	+	756.814i	1.01859	+	1.01859i	0.999824	+	0.0187678i	$0.00597433\pi$
$743$	756.814	+	756.814i	1.01859	+	1.01859i	0.0187678	+	0.999824i	$0.494026\pi$
$744$	36.7916	−	26.1755i	0.0494511	−	0.0351822i
$745$	−169.082	+	819.558i	−0.226956	+	1.10008i
$746$	−939.701	+	196.486i	−1.25965	+	0.263385i
$747$	−338.429	+	338.429i	−0.453051	+	0.453051i
$748$	−820.117	+	384.181i	−1.09641	+	0.513611i
$749$		−	34.9581i		−	0.0466730i
$750$	13.1347	−	30.7031i	0.0175130	−	0.0409374i
$751$			1381.45i			1.83948i	0.392526	+	0.919741i	$0.371601\pi$
$751$			1381.45i			1.83948i	−0.392526	+	0.919741i	$0.628399\pi$
$752$	1409.90	−	55.1524i	1.87486	−	0.0733409i
$753$	−10.9376	−	10.9376i	−0.0145254	−	0.0145254i
$754$	3.87106	−	0.809414i	0.00513403	−	0.00107349i
$755$	−35.1868	+	170.554i	−0.0466051	+	0.225899i
$756$	−35.7599	−	81.7731i	−0.0473015	−	0.108166i
$757$	467.852	−	467.852i	0.618034	−	0.618034i	−0.326993	−	0.945027i	$-0.606035\pi$
$757$	467.852	−	467.852i	0.618034	−	0.618034i	0.945027	+	0.326993i	$0.106035\pi$
$758$	−194.606	−	127.298i	−0.256737	−	0.167940i
$759$	30.9699	−	32.6132i	0.0408036	−	0.0429687i
$760$	345.874	−	890.475i	0.455098	−	1.17168i
$761$		−	10.2127i		−	0.0134201i	−0.999977	−	0.00671003i	$-0.997864\pi$
$761$		−	10.2127i		−	0.0134201i	0.999977	−	0.00671003i	$-0.00213589\pi$
$762$	−19.4886	+	29.7930i	−0.0255755	+	0.0390985i
$763$	−542.274	+	542.274i	−0.710713	+	0.710713i
$764$	1335.10	−	583.847i	1.74751	−	0.764198i
$765$	−508.089	−	772.230i	−0.664169	−	1.00945i
$766$	877.030	−	183.382i	1.14495	−	0.239401i
$767$	37.6474	−	37.6474i	0.0490840	−	0.0490840i
$768$	−25.9953	−	22.2175i	−0.0338480	−	0.0289291i
$769$	−319.451			−0.415411			−0.207705	−	0.978191i	$-0.566600\pi$
$769$	−319.451			−0.415411			−0.207705	+	0.978191i	$0.566600\pi$
$770$	−701.630	+	742.821i	−0.911207	+	0.964703i
$771$			26.5637i			0.0344535i
$772$	−829.621	−	324.790i

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.67372 - 1.09483i) q^{2} +(0.0944542 - 0.0944542i) q^{3} +(1.60268 + 3.66489i) q^{4} +(1.01027 - 4.89687i) q^{5} +(-0.261502 + 0.0546783i) q^{6} +(-6.56836 + 6.56836i) q^{7} +(1.33000 - 7.88867i) q^{8} +8.98216i q^{9} +(-7.05216 + 7.08992i) q^{10} +(-7.97654 - 7.57461i) q^{11} +(0.497544 + 0.194784i) q^{12} +(1.42743 - 1.42743i) q^{13} +(18.1848 - 3.80234i) q^{14} +(-0.367106 - 0.557954i) q^{15} +(-10.8628 + 11.7473i) q^{16} +(-14.5542 - 14.5542i) q^{17} +(9.83396 - 15.0336i) q^{18} +23.8822i q^{19} +(19.5656 - 4.14560i) q^{20} +1.24082i q^{21} +(5.05756 + 21.4108i) q^{22} +(-21.6435 + 21.6435i) q^{23} +(-0.619494 - 0.870742i) q^{24} +(-22.9587 - 9.89431i) q^{25} +(-3.95191 + 0.826319i) q^{26} +(1.69849 + 1.69849i) q^{27} +(-34.5993 - 13.5453i) q^{28} -0.979541 q^{29} +(0.00356623 + 1.33578i) q^{30} +42.2531i q^{31} +(31.0427 - 7.76870i) q^{32} +(-1.46887 + 0.0379638i) q^{33} +(8.42525 + 40.2941i) q^{34} +(25.5286 + 38.8002i) q^{35} +(-32.9186 + 14.3955i) q^{36} +(-7.62919 + 7.62919i) q^{37} +(26.1470 - 39.9721i) q^{38} -0.269653i q^{39} +(-37.2861 - 14.4825i) q^{40} +61.1443i q^{41} +(1.35849 - 2.07678i) q^{42} +(15.4025 + 15.4025i) q^{43} +(14.9763 - 41.3728i) q^{44} +(43.9845 + 9.07438i) q^{45} +(59.9213 - 12.5292i) q^{46} +(-62.3568 - 62.3568i) q^{47} +(0.0835414 + 2.13562i) q^{48} -37.2866i q^{49} +(27.5939 + 41.6963i) q^{50} -2.74942 q^{51} +(7.51907 + 2.94365i) q^{52} +(0.0107926 + 0.0107926i) q^{53} +(-0.983235 - 4.70236i) q^{54} +(-45.1504 + 31.4077i) q^{55} +(43.0796 + 60.5515i) q^{56} +(2.25577 + 2.25577i) q^{57} +(1.63948 + 1.07243i) q^{58} +26.3743 q^{59} +(1.45649 - 2.23963i) q^{60} -98.1345i q^{61} +(46.2601 - 70.7199i) q^{62} +(-58.9980 - 58.9980i) q^{63} +(-60.4622 - 20.9839i) q^{64} +(-5.54784 - 8.43201i) q^{65} +(2.50005 + 1.54463i) q^{66} +(-57.0549 - 57.0549i) q^{67} +(30.0138 - 76.6654i) q^{68} +4.08864i q^{69} +(-0.247996 - 92.8902i) q^{70} -30.7914i q^{71} +(70.8573 + 11.9463i) q^{72} +(17.1139 - 17.1139i) q^{73} +(21.1218 - 4.41644i) q^{74} +(-3.10311 + 1.23399i) q^{75} +(-87.5256 + 38.2755i) q^{76} +(102.146 - 2.64000i) q^{77} +(-0.295225 + 0.451324i) q^{78} -81.1764i q^{79} +(46.5506 + 65.0618i) q^{80} -80.5186 q^{81} +(66.9428 - 102.339i) q^{82} +(37.6780 + 37.6780i) q^{83} +(-4.54746 + 1.98863i) q^{84} +(-85.9738 + 56.5665i) q^{85} +(-8.91634 - 42.6428i) q^{86} +(-0.0925218 + 0.0925218i) q^{87} +(-70.3624 + 52.8500i) q^{88} +95.2458i q^{89} +(-63.6828 - 63.3436i) q^{90} +18.7517i q^{91} +(-114.009 - 44.6335i) q^{92} +(3.99099 + 3.99099i) q^{93} +(36.0976 + 172.638i) q^{94} +(116.948 + 24.1274i) q^{95} +(2.19832 - 3.66590i) q^{96} +(61.7662 - 61.7662i) q^{97} +(-40.8226 + 62.4073i) q^{98} +(68.0364 - 71.6465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 8 q^{5} + 8 q^{12} + 16 q^{16} + 80 q^{20} - 96 q^{22} - 8 q^{25} - 160 q^{26} + 80 q^{33} - 104 q^{36} - 8 q^{37} - 16 q^{38} - 168 q^{42} + 192 q^{45} + 32 q^{48} + 136 q^{53} + 264 q^{56} - 248 q^{58}+ \cdots - 168 q^{97}+O(q^{100}) \) 136 * q - 8 * q^5 + 8 * q^12 + 16 * q^16 + 80 * q^20 - 96 * q^22 - 8 * q^25 - 160 * q^26 + 80 * q^33 - 104 * q^36 - 8 * q^37 - 16 * q^38 - 168 * q^42 + 192 * q^45 + 32 * q^48 + 136 * q^53 + 264 * q^56 - 248 * q^58 - 128 * q^60 + 328 * q^66 + 96 * q^70 - 152 * q^77 - 24 * q^78 - 624 * q^80 - 664 * q^81 - 200 * q^82 + 752 * q^86 - 296 * q^88 - 776 * q^92 + 592 * q^93 - 168 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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