LMFDB - Embedded newform 220.3.s.a.31.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(31,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 6]))

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

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

chi := DirichletCharacter("220.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.s (of order $10$, degree $4$, 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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			31.15
Character	$\chi$	$=$	220.31
Dual form			220.3.s.a.71.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.445649 + 1.94972i) q^{2} +(2.29101 + 3.15331i) q^{3} +(-3.60279 + 1.73778i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-5.12707 + 5.87209i) q^{6} +(-5.93140 + 8.16388i) q^{7} +(-4.99376 - 6.24999i) q^{8} +(-1.91346 + 5.88902i) q^{9} +(-3.83838 + 2.29495i) q^{10} +(4.27229 - 10.1364i) q^{11} +(-13.7338 - 7.37944i) q^{12} +(4.43010 - 13.6344i) q^{13} +(-18.5606 - 7.92633i) q^{14} +(-5.12286 + 7.05101i) q^{15} +(9.96024 - 12.5217i) q^{16} +(4.83979 + 14.8953i) q^{17} +(-12.3347 - 1.10627i) q^{18} +(15.4818 + 21.3089i) q^{19} +(-6.18508 - 6.46102i) q^{20} -39.3321 q^{21} +(21.6671 + 3.81245i) q^{22} +31.4161i q^{23} +(8.26736 - 30.0657i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(28.5576 + 2.56126i) q^{26} +(10.4088 - 3.38201i) q^{27} +(7.18260 - 39.7202i) q^{28} +(-43.3341 - 31.4841i) q^{29} +(-16.0305 - 6.84585i) q^{30} +(-3.32552 - 1.08053i) q^{31} +(28.8526 + 13.8393i) q^{32} +(41.7512 - 9.75089i) q^{33} +(-26.8849 + 16.0743i) q^{34} +(-21.4600 - 6.97278i) q^{35} +(-3.34003 - 24.5421i) q^{36} +(18.1817 + 13.2098i) q^{37} +(-34.6469 + 39.6815i) q^{38} +(53.1430 - 17.2672i) q^{39} +(9.84079 - 14.9385i) q^{40} +(-26.5611 + 19.2978i) q^{41} +(-17.5283 - 76.6865i) q^{42} -14.5302i q^{43} +(2.22275 + 43.9438i) q^{44} -13.8459 q^{45} +(-61.2525 + 14.0006i) q^{46} +(29.1619 + 40.1379i) q^{47} +(62.3039 + 2.72027i) q^{48} +(-16.3255 - 50.2447i) q^{49} +(-7.53276 - 6.57704i) q^{50} +(-35.8816 + 49.3868i) q^{51} +(7.73293 + 56.8206i) q^{52} +(11.9385 - 36.7430i) q^{53} +(11.2326 + 18.7870i) q^{54} +(24.5085 + 2.08145i) q^{55} +(80.6441 - 3.69727i) q^{56} +(-31.7245 + 97.6379i) q^{57} +(42.0732 - 98.5201i) q^{58} +(22.5711 - 31.0665i) q^{59} +(6.20349 - 34.3057i) q^{60} +(16.8808 + 51.9537i) q^{61} +(0.624706 - 6.96536i) q^{62} +(-36.7277 - 50.5514i) q^{63} +(-14.1247 + 62.4219i) q^{64} +32.0565 q^{65} +(37.6179 + 77.0575i) q^{66} +57.3989i q^{67} +(-43.3216 - 45.2544i) q^{68} +(-99.0646 + 71.9747i) q^{69} +(4.03131 - 44.9484i) q^{70} +(22.4655 - 7.29949i) q^{71} +(46.3617 - 17.4493i) q^{72} +(-34.4852 - 25.0550i) q^{73} +(-17.6526 + 41.3360i) q^{74} +(-18.5347 - 6.02228i) q^{75} +(-92.8080 - 49.8676i) q^{76} +(57.4120 + 95.0018i) q^{77} +(57.3493 + 95.9187i) q^{78} +(-66.8614 - 21.7246i) q^{79} +(33.5114 + 12.5294i) q^{80} +(79.5966 + 57.8303i) q^{81} +(-49.4621 - 43.1866i) q^{82} +(118.311 - 38.4415i) q^{83} +(141.706 - 68.3506i) q^{84} +(-28.3326 + 20.5849i) q^{85} +(28.3297 - 6.47537i) q^{86} -208.776i q^{87} +(-84.6874 + 23.9173i) q^{88} +153.780 q^{89} +(-6.17043 - 26.9956i) q^{90} +(85.0332 + 117.038i) q^{91} +(-54.5943 - 113.186i) q^{92} +(-4.21157 - 12.9619i) q^{93} +(-65.2615 + 74.7448i) q^{94} +(-34.6184 + 47.6482i) q^{95} +(22.4619 + 122.687i) q^{96} +(35.4826 - 109.204i) q^{97} +(90.6875 - 54.2216i) q^{98} +(51.5189 + 44.5553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} - 4 q^{4} + 120 q^{5} + 20 q^{6} - 10 q^{8} + 64 q^{9} + 10 q^{10} + 70 q^{12} - 20 q^{13} - 37 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} + 5 q^{20} - 15 q^{22} - 62 q^{24} - 120 q^{25} + 12 q^{26}+ \cdots + 158 q^{98}+O(q^{100}) $ 96 * q + 2 * q^2 - 4 * q^4 + 120 * q^5 + 20 * q^6 - 10 * q^8 + 64 * q^9 + 10 * q^10 + 70 * q^12 - 20 * q^13 - 37 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 + 5 * q^20 - 15 * q^22 - 62 * q^24 - 120 * q^25 + 12 * q^26 - 200 * q^28 + 72 * q^29 + 40 * q^30 - 348 * q^32 - 60 * q^33 - 246 * q^34 + 26 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 - 25 * q^42 - 67 * q^44 - 40 * q^45 - 85 * q^46 + 213 * q^48 - 28 * q^49 + 10 * q^50 + 312 * q^52 - 224 * q^53 + 752 * q^54 + 660 * q^56 - 204 * q^57 + 88 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 + 44 * q^64 - 40 * q^65 + 75 * q^66 - 117 * q^68 + 32 * q^69 - 75 * q^70 - 198 * q^72 - 64 * q^73 - 672 * q^74 - 1280 * q^76 + 80 * q^77 - 1132 * q^78 - 125 * q^80 - 44 * q^81 - 301 * q^82 - 348 * q^84 - 60 * q^85 + 470 * q^86 + 5 * q^88 + 176 * q^89 - 162 * q^92 + 280 * q^93 + 394 * q^94 + 1143 * q^96 + 204 * q^97 + 158 * q^98

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

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 $

$2$	0.445649	+	1.94972i	0.222825	+	0.974859i
$2$	0.445649	+	1.94972i	0.222825	+	0.974859i
$3$	2.29101	+	3.15331i	0.763671	+	1.05110i	0.996900	+	0.0786807i	$0.0250708\pi$
$3$	2.29101	+	3.15331i	0.763671	+	1.05110i	−0.233229	+	0.972422i	$0.574929\pi$
$4$	−3.60279	+	1.73778i	−0.900698	+	0.434445i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$6$	−5.12707	+	5.87209i	−0.854512	+	0.978682i
$7$	−5.93140	+	8.16388i	−0.847343	+	1.16627i	0.137099	+	0.990557i	$0.456222\pi$
$7$	−5.93140	+	8.16388i	−0.847343	+	1.16627i	−0.984442	+	0.175711i	$0.943778\pi$
$8$	−4.99376	−	6.24999i	−0.624220	−	0.781248i
$9$	−1.91346	+	5.88902i	−0.212607	+	0.654336i
$10$	−3.83838	+	2.29495i	−0.383838	+	0.229495i
$11$	4.27229	−	10.1364i	0.388390	−	0.921495i
$11$	4.27229	−	10.1364i	0.388390	−	0.921495i
$12$	−13.7338	−	7.37944i	−1.14448	−	0.614953i
$13$	4.43010	−	13.6344i	0.340777	−	1.04880i	−0.623029	−	0.782199i	$-0.714098\pi$
$13$	4.43010	−	13.6344i	0.340777	−	1.04880i	0.963806	−	0.266604i	$-0.0859017\pi$
$14$	−18.5606	−	7.92633i	−1.32576	−	0.566167i
$15$	−5.12286	+	7.05101i	−0.341524	+	0.470067i
$16$	9.96024	−	12.5217i	0.622515	−	0.782608i
$17$	4.83979	+	14.8953i	0.284694	+	0.876197i	0.986490	+	0.163820i	$0.0523815\pi$
$17$	4.83979	+	14.8953i	0.284694	+	0.876197i	−0.701797	+	0.712377i	$0.747619\pi$
$18$	−12.3347	−	1.10627i	−0.685259	−	0.0614592i
$19$	15.4818	+	21.3089i	0.814833	+	1.12152i	0.990560	+	0.137082i	$0.0437725\pi$
$19$	15.4818	+	21.3089i	0.814833	+	1.12152i	−0.175727	+	0.984439i	$0.556228\pi$
$20$	−6.18508	−	6.46102i	−0.309254	−	0.323051i
$21$	−39.3321			−1.87296
$22$	21.6671	+	3.81245i	0.984870	+	0.173293i
$23$			31.4161i			1.36592i	0.730457	+	0.682959i	$0.239307\pi$
$23$			31.4161i			1.36592i	−0.730457	+	0.682959i	$0.760693\pi$
$24$	8.26736	−	30.0657i	0.344473	−	1.25274i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	28.5576	+	2.56126i	1.09837	+	0.0985099i
$27$	10.4088	−	3.38201i	0.385510	−	0.125260i
$28$	7.18260	−	39.7202i	0.256521	−	1.41858i
$29$	−43.3341	−	31.4841i	−1.49428	−	1.08566i	−0.972591	−	0.232522i	$-0.925302\pi$
$29$	−43.3341	−	31.4841i	−1.49428	−	1.08566i	−0.521689	−	0.853136i	$-0.674698\pi$
$30$	−16.0305	−	6.84585i	−0.534349	−	0.228195i
$31$	−3.32552	−	1.08053i	−0.107275	−	0.0348557i	0.254888	−	0.966971i	$-0.417961\pi$
$31$	−3.32552	−	1.08053i	−0.107275	−	0.0348557i	−0.362163	+	0.932115i	$0.617961\pi$
$32$	28.8526	+	13.8393i	0.901644	+	0.432480i
$33$	41.7512	−	9.75089i	1.26519	−	0.295481i
$34$	−26.8849	+	16.0743i	−0.790731	+	0.472774i
$35$	−21.4600	−	6.97278i	−0.613143	−	0.199222i
$36$	−3.34003	−	24.5421i	−0.0927786	−	0.681725i
$37$	18.1817	+	13.2098i	0.491397	+	0.357021i	0.805721	−	0.592295i	$-0.201778\pi$
$37$	18.1817	+	13.2098i	0.491397	+	0.357021i	−0.314325	+	0.949316i	$0.601778\pi$
$38$	−34.6469	+	39.6815i	−0.911760	+	1.04425i
$39$	53.1430	−	17.2672i	1.36264	−	0.442749i
$40$	9.84079	−	14.9385i	0.246020	−	0.373463i
$41$	−26.5611	+	19.2978i	−0.647831	+	0.470677i	−0.862532	−	0.506003i	$-0.831122\pi$
$41$	−26.5611	+	19.2978i	−0.647831	+	0.470677i	0.214701	+	0.976680i	$0.431122\pi$
$42$	−17.5283	−	76.6865i	−0.417341	−	1.82587i
$43$		−	14.5302i		−	0.337911i	−0.985624	−	0.168956i	$-0.945961\pi$
$43$		−	14.5302i		−	0.337911i	0.985624	−	0.168956i	$-0.0540394\pi$
$44$	2.22275	+	43.9438i	0.0505171	+	0.998723i
$45$	−13.8459			−0.307687
$46$	−61.2525	+	14.0006i	−1.33158	+	0.304360i
$47$	29.1619	+	40.1379i	0.620465	+	0.853997i	0.997387	−	0.0722482i	$-0.0230174\pi$
$47$	29.1619	+	40.1379i	0.620465	+	0.853997i	−0.376922	+	0.926245i	$0.623017\pi$
$48$	62.3039	+	2.72027i	1.29800	+	0.0566723i
$49$	−16.3255	−	50.2447i	−0.333173	−	1.02540i
$50$	−7.53276	−	6.57704i	−0.150655	−	0.131541i
$51$	−35.8816	+	49.3868i	−0.703561	+	0.968368i
$52$	7.73293	+	56.8206i	0.148710	+	1.09270i
$53$	11.9385	−	36.7430i	0.225255	−	0.693264i	−0.773010	−	0.634393i	$-0.781250\pi$
$53$	11.9385	−	36.7430i	0.225255	−	0.693264i	0.998266	−	0.0588709i	$-0.0187500\pi$
$54$	11.2326	+	18.7870i	0.208012	+	0.347907i
$55$	24.5085	+	2.08145i	0.445609	+	0.0378445i
$56$	80.6441	−	3.69727i	1.44007	−	0.0660226i
$57$	−31.7245	+	97.6379i	−0.556570	+	1.71295i
$58$	42.0732	−	98.5201i	0.725400	−	1.69862i
$59$	22.5711	−	31.0665i	0.382562	−	0.526551i	−0.573699	−	0.819066i	$-0.694492\pi$
$59$	22.5711	−	31.0665i	0.382562	−	0.526551i	0.956261	+	0.292515i	$0.0944922\pi$
$60$	6.20349	−	34.3057i	0.103392	−	0.571762i
$61$	16.8808	+	51.9537i	0.276734	+	0.851699i	0.988755	+	0.149542i	$0.0477798\pi$
$61$	16.8808	+	51.9537i	0.276734	+	0.851699i	−0.712022	+	0.702158i	$0.752220\pi$
$62$	0.624706	−	6.96536i	0.0100759	−	0.112345i
$63$	−36.7277	−	50.5514i	−0.582980	−	0.802403i
$64$	−14.1247	+	62.4219i	−0.220698	+	0.975342i
$65$	32.0565			0.493177
$66$	37.6179	+	77.0575i	0.569968	+	1.16754i
$67$			57.3989i			0.856700i	0.903613	+	0.428350i	$0.140905\pi$
$67$			57.3989i			0.856700i	−0.903613	+	0.428350i	$0.859095\pi$
$68$	−43.3216	−	45.2544i	−0.637083	−	0.665505i
$69$	−99.0646	+	71.9747i	−1.43572	+	1.04311i
$70$	4.03131	−	44.9484i	0.0575901	−	0.642120i
$71$	22.4655	−	7.29949i	0.316416	−	0.102810i	−0.146504	−	0.989210i	$-0.546802\pi$
$71$	22.4655	−	7.29949i	0.316416	−	0.102810i	0.462919	+	0.886400i	$0.346802\pi$
$72$	46.3617	−	17.4493i	0.643912	−	0.242351i
$73$	−34.4852	−	25.0550i	−0.472400	−	0.343219i	0.325976	−	0.945378i	$-0.394307\pi$
$73$	−34.4852	−	25.0550i	−0.472400	−	0.343219i	−0.798376	+	0.602159i	$0.794307\pi$
$74$	−17.6526	+	41.3360i	−0.238549	+	0.558595i
$75$	−18.5347	−	6.02228i	−0.247129	−	0.0802971i
$76$	−92.8080	−	49.8676i	−1.22116	−	0.656152i
$77$	57.4120	+	95.0018i	0.745611	+	1.23379i
$78$	57.3493	+	95.9187i	0.735247	+	1.22973i
$79$	−66.8614	−	21.7246i	−0.846347	−	0.274995i	−0.146432	−	0.989221i	$-0.546779\pi$
$79$	−66.8614	−	21.7246i	−0.846347	−	0.274995i	−0.699915	+	0.714226i	$0.746779\pi$
$80$	33.5114	+	12.5294i	0.418892	+	0.156618i
$81$	79.5966	+	57.8303i	0.982675	+	0.713955i
$82$	−49.4621	−	43.1866i	−0.603196	−	0.526665i
$83$	118.311	−	38.4415i	1.42543	−	0.463151i	0.508108	−	0.861293i	$-0.330345\pi$
$83$	118.311	−	38.4415i	1.42543	−	0.463151i	0.917324	+	0.398143i	$0.130345\pi$
$84$	141.706	−	68.3506i	1.68697	−	0.813698i
$85$	−28.3326	+	20.5849i	−0.333325	+	0.242175i
$86$	28.3297	−	6.47537i	0.329416	−	0.0752950i
$87$		−	208.776i		−	2.39973i
$88$	−84.6874	+	23.9173i	−0.962357	+	0.271787i
$89$	153.780			1.72787			0.863934	−	0.503605i	$-0.167993\pi$
$89$	153.780			1.72787			0.863934	+	0.503605i	$0.167993\pi$
$90$	−6.17043	−	26.9956i	−0.0685603	−	0.299951i
$91$	85.0332	+	117.038i	0.934431	+	1.28613i
$92$	−54.5943	−	113.186i	−0.593416	−	1.23028i
$93$	−4.21157	−	12.9619i	−0.0452857	−	0.139375i
$94$	−65.2615	+	74.7448i	−0.694271	+	0.795157i
$95$	−34.6184	+	47.6482i	−0.364404	+	0.501560i
$96$	22.4619	+	122.687i	0.233978	+	1.27799i
$97$	35.4826	−	109.204i	0.365800	−	1.12582i	−0.583679	−	0.811985i	$-0.698387\pi$
$97$	35.4826	−	109.204i	0.365800	−	1.12582i	0.949479	−	0.313831i	$-0.101613\pi$
$98$	90.6875	−	54.2216i	0.925383	−	0.553282i
$99$	51.5189	+	44.5553i	0.520393	+	0.450053i
$100$	9.46640	−	17.6178i	0.0946640	−	0.176178i
$101$	39.3577	−	121.130i	0.389680	−	1.19931i	−0.543348	−	0.839507i	$-0.682844\pi$
$101$	39.3577	−	121.130i	0.389680	−	1.19931i	0.933028	−	0.359804i	$-0.117156\pi$
$102$	−112.281	−	47.9498i	−1.10079	−	0.470096i
$103$	−35.3665	+	48.6778i	−0.343364	+	0.472600i	−0.945420	−	0.325853i	$-0.894348\pi$
$103$	−35.3665	+	48.6778i	−0.343364	+	0.472600i	0.602056	+	0.798454i	$0.294348\pi$
$104$	−107.338	+	40.3991i	−1.03210	+	0.388453i
$105$	−27.1778	−	83.6448i	−0.258836	−	0.796617i
$106$	76.9589	+	6.90225i	0.726027	+	0.0651156i
$107$	−34.2590	−	47.1535i	−0.320178	−	0.440687i	0.618344	−	0.785908i	$-0.287804\pi$
$107$	−34.2590	−	47.1535i	−0.320178	−	0.440687i	−0.938522	+	0.345221i	$0.887804\pi$
$108$	−31.6234	+	30.2728i	−0.292810	+	0.280304i
$109$	42.1557			0.386750			0.193375	−	0.981125i	$-0.438057\pi$
$109$	42.1557			0.386750			0.193375	+	0.981125i	$0.438057\pi$
$110$	6.86397	+	48.7123i	0.0623998	+	0.442839i
$111$			87.5961i			0.789154i
$112$	43.1476	+	155.586i	0.385247	+	1.38916i
$113$	164.771	−	119.713i	1.45815	−	1.05941i	0.474315	−	0.880355i	$-0.342696\pi$
$113$	164.771	−	119.713i	1.45815	−	1.05941i	0.983839	−	0.179056i	$-0.0573044\pi$
$114$	−204.504	−	18.3415i	−1.79390	−	0.160890i
$115$	−66.8103	+	21.7080i	−0.580959	+	0.188765i
$116$	210.836	+	38.1255i	1.81755	+	0.328668i
$117$	71.8167	+	52.1779i	0.613818	+	0.445965i
$118$	70.6297	+	30.1626i	0.598557	+	0.255615i
$119$	−150.311	−	48.8389i	−1.26311	−	0.410411i
$120$	69.6511	−	3.19327i	0.580425	−	0.0266106i
$121$	−84.4951	−	86.6116i	−0.698307	−	0.715799i
$122$	−93.7720	+	56.0658i	−0.768623	+	0.459556i
$123$	−121.703	−	39.5439i	−0.989459	−	0.321495i
$124$	13.8589	−	1.88611i	0.111765	−	0.0152106i
$125$	−9.04508	−	6.57164i	−0.0723607	−	0.0525731i
$126$	82.1932	−	94.1369i	0.652327	−	0.747118i
$127$	−46.6425	+	15.1551i	−0.367264	+	0.119331i	−0.486834	−	0.873494i	$-0.661848\pi$
$127$	−46.6425	+	15.1551i	−0.367264	+	0.119331i	0.119570	+	0.992826i	$0.461848\pi$
$128$	−128.000	+	0.279173i	−0.999998	+	0.00218104i
$129$	45.8181	−	33.2888i	0.355179	−	0.258053i
$130$	14.2860	+	62.5011i	0.109892	+	0.480778i
$131$			182.347i			1.39196i	0.718060	+	0.695981i	$0.245030\pi$
$131$			182.347i			1.39196i	−0.718060	+	0.695981i	$0.754970\pi$
$132$	−133.476	+	107.685i	−1.01118	+	0.815794i
$133$	−265.792			−1.99844
$134$	−111.912	+	25.5798i	−0.835161	+	0.190894i
$135$	14.3846	+	19.7986i	0.106552	+	0.146657i
$136$	68.9270	−	104.632i	0.506816	−	0.769356i
$137$	14.0829	+	43.3427i	0.102795	+	0.316370i	0.989207	−	0.146528i	$-0.0468097\pi$
$137$	14.0829	+	43.3427i	0.102795	+	0.316370i	−0.886412	+	0.462898i	$0.846810\pi$
$138$	−184.478	−	161.073i	−1.33680	−	1.16719i
$139$	107.375	−	147.790i	0.772485	−	1.06323i	−0.223587	−	0.974684i	$-0.571777\pi$
$139$	107.375	−	147.790i	0.772485	−	1.06323i	0.996072	−	0.0885501i	$-0.0282233\pi$
$140$	89.4332	−	12.1713i	0.638808	−	0.0869379i
$141$	−59.7568	+	183.913i	−0.423807	+	1.30434i
$142$	24.2437	+	40.5484i	0.170730	+	0.285552i
$143$	−119.278	−	103.156i	−0.834113	−	0.721368i
$144$	54.6822	+	82.6159i	0.379738	+	0.573721i
$145$	37.0118	−	113.910i	0.255253	−	0.785589i
$146$	33.4818	−	78.4021i	0.229327	−	0.537001i
$147$	121.035	−	166.591i	0.823368	−	1.13327i
$148$	−88.4605	−	15.9963i	−0.597706	−	0.108083i
$149$	5.08288	+	15.6435i	0.0341133	+	0.104990i	0.966663	−	0.256051i	$-0.0824215\pi$
$149$	5.08288	+	15.6435i	0.0341133	+	0.104990i	−0.932550	+	0.361041i	$0.882421\pi$
$150$	3.48178	−	38.8212i	0.0232119	−	0.258808i
$151$	−138.149	−	190.145i	−0.914891	−	1.25924i	−0.965469	−	0.260520i	$-0.916106\pi$
$151$	−138.149	−	190.145i	−0.914891	−	1.25924i	0.0505772	−	0.998720i	$-0.483894\pi$
$152$	55.8678	−	203.173i	0.367551	−	1.33666i
$153$	−96.9798			−0.633855
$154$	−159.641	+	154.275i	−1.03663	+	1.00178i
$155$		−	7.81877i		−	0.0504437i
$156$	−161.457	+	154.561i	−1.03498	+	0.990776i
$157$	−30.8588	+	22.4202i	−0.196553	+	0.142804i	−0.681709	−	0.731624i	$-0.738763\pi$
$157$	−30.8588	+	22.4202i	−0.196553	+	0.142804i	0.485156	+	0.874428i	$0.338763\pi$
$158$	12.5601	−	140.042i	0.0794941	−	0.886344i
$159$	143.213	−	46.5328i	0.900713	−	0.292659i
$160$	−9.49447	+	70.9215i	−0.0593405	+	0.443259i
$161$	−256.477	−	186.342i	−1.59303	−	1.15740i
$162$	−77.2806	+	180.963i	−0.477041	+	1.11706i
$163$	−142.320	−	46.2426i	−0.873129	−	0.283697i	−0.162028	−	0.986786i	$-0.551803\pi$
$163$	−142.320	−	46.2426i	−0.873129	−	0.283697i	−0.711102	+	0.703089i	$0.751803\pi$
$164$	62.1588	−	115.683i	0.379017	−	0.705385i
$165$	49.5859	+	82.0515i	0.300520	+	0.497282i
$166$	127.675	+	213.541i	0.769128	+	1.28639i
$167$	−15.8118	−	5.13756i	−0.0946814	−	0.0307638i	0.261293	−	0.965259i	$-0.415851\pi$
$167$	−15.8118	−	5.13756i	−0.0946814	−	0.0307638i	−0.355975	+	0.934496i	$0.615851\pi$
$168$	196.415	+	245.825i	1.16914	+	1.46325i
$169$	−29.5483	−	21.4681i	−0.174842	−	0.127030i
$170$	−52.7611	−	46.0670i	−0.310359	−	0.270982i
$171$	−155.112	+	50.3991i	−0.907090	+	0.294731i
$172$	25.2503	+	52.3492i	0.146804	+	0.304356i
$173$	178.159	−	129.440i	1.02982	−	0.748208i	0.0615472	−	0.998104i	$-0.480397\pi$
$173$	178.159	−	129.440i	1.02982	−	0.748208i	0.968273	+	0.249896i	$0.0803965\pi$
$174$	407.055	−	93.0410i	2.33939	−	0.534718i
$175$		−	50.4555i		−	0.288317i
$176$	−84.3728	−	154.458i	−0.479391	−	0.877601i
$177$	149.673			0.845610
$178$	68.5321	+	299.828i	0.385012	+	1.68443i
$179$	−26.8738	−	36.9886i	−0.150133	−	0.206640i	0.727326	−	0.686292i	$-0.240763\pi$
$179$	−26.8738	−	36.9886i	−0.150133	−	0.206640i	−0.877459	+	0.479652i	$0.840763\pi$
$180$	49.8840	−	24.0612i	0.277133	−	0.133673i
$181$	−9.53021	−	29.3310i	−0.0526531	−	0.162050i	0.921272	−	0.388918i	$-0.127151\pi$
$181$	−9.53021	−	29.3310i	−0.0526531	−	0.162050i	−0.973925	+	0.226869i	$0.927151\pi$
$182$	−190.296	+	217.949i	−1.04558	+	1.19752i
$183$	−125.152	+	172.257i	−0.683890	+	0.941293i
$184$	196.350	−	156.885i	1.06712	−	0.852633i
$185$	−15.5290	+	47.7934i	−0.0839406	+	0.258342i
$186$	23.3951	−	13.9878i	0.125780	−	0.0752034i
$187$	171.663	+	14.5789i	0.917983	+	0.0779620i
$188$	−174.815	−	93.9315i	−0.929867	−	0.499636i
$189$	−34.1282	+	105.036i	−0.180573	+	0.555746i
$190$	−108.328	−	46.2617i	−0.570148	−	0.243483i
$191$	40.1389	−	55.2465i	0.210152	−	0.289249i	−0.690909	−	0.722941i	$-0.742790\pi$
$191$	40.1389	−	55.2465i	0.210152	−	0.289249i	0.901061	+	0.433693i	$0.142790\pi$
$192$	−229.195	+	98.4699i	−1.19373	+	0.512864i
$193$	−1.87513	−	5.77106i	−0.00971570	−	0.0299019i	0.946081	−	0.323930i	$-0.105004\pi$
$193$	−1.87513	−	5.77106i	−0.00971570	−	0.0299019i	−0.955797	+	0.294028i	$0.905004\pi$
$194$	228.730	+	20.5142i	1.17902	+	0.105743i
$195$	73.4418	+	101.084i	0.376625	+	0.518379i
$196$	146.132	+	152.651i	0.745570	+	0.778833i
$197$	−299.121			−1.51838			−0.759191	−	0.650868i	$-0.774405\pi$
$197$	−299.121			−1.51838			−0.759191	+	0.650868i	$0.774405\pi$
$198$	−63.9108	+	120.303i	−0.322782	+	0.607593i
$199$			284.631i			1.43031i	0.698968	+	0.715153i	$0.253643\pi$
$199$			284.631i			1.43031i	−0.698968	+	0.715153i	$0.746357\pi$
$200$	38.5684	+	10.6054i	0.192842	+	0.0530271i
$201$	−180.996	+	131.502i	−0.900479	+	0.654237i
$202$	253.710	+	22.7546i	1.25599	+	0.112647i
$203$	514.064	−	167.030i	2.53234	−	0.822806i
$204$	43.4506	−	240.285i	0.212993	−	1.17787i
$205$	−59.3924	−	43.1511i	−0.289719	−	0.210493i
$206$	−110.669	−	47.2615i	−0.537229	−	0.229425i
$207$	−185.010	−	60.1134i	−0.893769	−	0.290403i
$208$	−126.602	−	191.275i	−0.608663	−	0.919590i
$209$	282.139	−	65.8930i	1.34995	−	0.315277i
$210$	150.972	−	90.2653i	0.718914	−	0.429835i
$211$	−120.100	−	39.0227i	−0.569192	−	0.184942i	0.0102608	−	0.999947i	$-0.496734\pi$
$211$	−120.100	−	39.0227i	−0.569192	−	0.184942i	−0.579453	+	0.815006i	$0.696734\pi$
$212$	20.8392	+	153.124i	0.0982983	+	0.722283i
$213$	74.4863	+	54.1175i	0.349701	+	0.254073i
$214$	76.6685	−	87.8094i	0.358264	−	0.410324i
$215$	30.9003	−	10.0401i	0.143722	−	0.0466982i
$216$	−73.1164	−	48.1657i	−0.338502	−	0.222989i
$217$	28.5463	−	20.7401i	0.131550	−	0.0955765i
$218$	18.7867	+	82.1917i	0.0861774	+	0.377026i
$219$		−	166.144i		−	0.758647i
$220$	−91.9162	+	35.0914i	−0.417801	+	0.159506i
$221$	224.530			1.01597
$222$	−170.788	+	39.0372i	−0.769314	+	0.175843i
$223$	−86.9465	−	119.672i	−0.389894	−	0.536644i	0.568277	−	0.822837i	$-0.307610\pi$
$223$	−86.9465	−	119.672i	−0.389894	−	0.536644i	−0.958172	+	0.286193i	$0.907610\pi$
$224$	−284.119	+	153.462i	−1.26839	+	0.685100i
$225$	−9.56730	−	29.4451i	−0.0425213	−	0.130867i
$226$	306.838	+	267.907i	1.35769	+	1.18543i
$227$	160.251	−	220.566i	0.705950	−	0.971657i	−0.293925	−	0.955829i	$-0.594961\pi$
$227$	160.251	−	220.566i	0.705950	−	0.971657i	0.999875	−	0.0158285i	$-0.00503857\pi$
$228$	−55.3765	−	406.899i	−0.242879	−	1.78465i
$229$	−17.6079	+	54.1915i	−0.0768903	+	0.236644i	−0.982113	−	0.188294i	$-0.939704\pi$
$229$	−17.6079	+	54.1915i	−0.0768903	+	0.236644i	0.905222	+	0.424938i	$0.139704\pi$
$230$	−72.0984	−	120.587i	−0.313471	−	0.524292i
$231$	−168.038	+	398.688i	−0.727438	+	1.72592i
$232$	19.6252	+	428.062i	0.0845915	+	1.84509i
$233$	−57.1928	+	176.021i	−0.245463	+	0.755457i	0.750097	+	0.661328i	$0.230007\pi$
$233$	−57.1928	+	176.021i	−0.245463	+	0.755457i	−0.995560	+	0.0941291i	$0.969993\pi$
$234$	−69.7270	+	163.275i	−0.297979	+	0.697758i
$235$	−65.2079	+	89.7510i	−0.277480	+	0.381919i
$236$	−27.3324	+	151.150i	−0.115815	+	0.640465i
$237$	−84.6760	−	260.606i	−0.357283	−	1.09960i
$238$	28.2361	−	314.828i	0.118639	−	1.32281i
$239$	−132.395	−	182.225i	−0.553952	−	0.762449i	0.436590	−	0.899661i	$-0.356186\pi$
$239$	−132.395	−	182.225i	−0.553952	−	0.762449i	−0.990542	+	0.137211i	$0.956186\pi$
$240$	37.2659	+	134.377i	0.155275	+	0.559903i
$241$	−454.253			−1.88487			−0.942433	−	0.334394i	$-0.891468\pi$
$241$	−454.253			−1.88487			−0.942433	+	0.334394i	$0.891468\pi$
$242$	131.213	−	203.340i	0.542202	−	0.840248i
$243$			284.983i			1.17277i
$244$	−151.102	−	157.843i	−0.619270	−	0.646898i
$245$	95.5711	−	69.4365i	0.390086	−	0.283414i
$246$	22.8623	−	254.910i	0.0929360	−	1.03622i
$247$	359.121	−	116.685i	1.45393	−	0.472411i
$248$	9.85358	+	26.1804i	0.0397322	+	0.105566i
$249$	392.269	+	285.000i	1.57538	+	1.14458i
$250$	8.78190	−	20.5640i	0.0351276	−	0.0822560i
$251$	−106.411	−	34.5752i	−0.423950	−	0.137750i	0.0892687	−	0.996008i	$-0.471547\pi$
$251$	−106.411	−	34.5752i	−0.423950	−	0.137750i	−0.513219	+	0.858258i	$0.671547\pi$
$252$	220.170	+	118.302i	0.873689	+	0.469450i
$253$	318.448	+	134.219i	1.25869	+	0.530508i
$254$	−50.3343	−	84.1859i	−0.198167	−	0.331441i
$255$	−129.821	−	42.1813i	−0.509101	−	0.165417i
$256$	−57.5873	−	249.439i	−0.224950	−	0.974370i
$257$	229.966	+	167.080i	0.894811	+	0.650118i	0.937128	−	0.348986i	$-0.113474\pi$
$257$	229.966	+	167.080i	0.894811	+	0.650118i	−0.0423168	+	0.999104i	$0.513474\pi$
$258$	85.3226	+	74.4972i	0.330708	+	0.288749i
$259$	−215.686	+	70.0805i	−0.832763	+	0.270581i
$260$	−115.493	+	55.7071i	−0.444203	+	0.214258i
$261$	268.328	−	194.952i	1.02808	−	0.746943i
$262$	−355.525	+	81.2629i	−1.35697	+	0.310164i
$263$			140.080i			0.532624i	0.963887	+	0.266312i	$0.0858052\pi$
$263$			140.080i			0.532624i	−0.963887	+	0.266312i	$0.914195\pi$
$264$	−269.438	−	212.251i	−1.02060	−	0.803980i
$265$	86.3880			0.325992
$266$	−118.450	−	518.220i	−0.445301	−	1.94819i
$267$	352.312	+	484.917i	1.31952	+	1.81617i
$268$	−99.7467	−	206.796i	−0.372189	−	0.771628i
$269$	57.8515	+	178.049i	0.215061	+	0.661891i	0.999149	+	0.0412410i	$0.0131311\pi$
$269$	57.8515	+	178.049i	0.215061	+	0.661891i	−0.784088	+	0.620650i	$0.786869\pi$
$270$	−32.1913	+	36.8691i	−0.119227	+	0.136552i
$271$	−224.294	+	308.714i	−0.827651	+	1.13916i	0.160704	+	0.987003i	$0.448623\pi$
$271$	−224.294	+	308.714i	−0.827651	+	1.13916i	−0.988356	+	0.152162i	$0.951377\pi$
$272$	234.721	+	87.7587i	0.862945	+	0.322642i
$273$	−174.245	+	536.271i	−0.638261	+	1.96436i
$274$	−78.2300	+	46.7733i	−0.285511	+	0.170706i
$275$	12.5085	+	53.5587i	0.0454855	+	0.194759i
$276$	231.833	−	431.462i	0.839975	−	1.56327i
$277$	109.054	−	335.633i	0.393696	−	1.21167i	−0.536277	−	0.844042i	$-0.680170\pi$
$277$	109.054	−	335.633i	0.393696	−	1.21167i	0.929973	−	0.367629i	$-0.119830\pi$
$278$	336.000	+	143.489i	1.20863	+	0.516149i
$279$	12.7265	−	17.5165i	0.0456147	−	0.0627832i
$280$	63.5864	+	168.945i	0.227094	+	0.603376i
$281$	−26.0818	−	80.2716i	−0.0928178	−	0.285664i	0.893861	−	0.448344i	$-0.147986\pi$
$281$	−26.0818	−	80.2716i	−0.0928178	−	0.285664i	−0.986679	+	0.162680i	$0.947986\pi$
$282$	−385.208	−	34.5484i	−1.36599	−	0.122512i
$283$	92.0563	+	126.705i	0.325287	+	0.447719i	0.940072	−	0.340975i	$-0.110757\pi$
$283$	92.0563	+	126.705i	0.325287	+	0.447719i	−0.614785	+	0.788695i	$0.710757\pi$
$284$	−68.2537	+	65.3387i	−0.240330	+	0.230066i
$285$	−229.560			−0.805475
$286$	147.968	−	278.530i	0.517371	−	0.973881i
$287$		−	331.304i		−	1.15437i
$288$	−136.708	+	143.433i	−0.474682	+	0.498030i
$289$	35.3581	−	25.6892i	0.122346	−	0.0888899i
$290$	238.587	+	21.3983i	0.822715	+	0.0737873i
$291$	425.645	−	138.301i	1.46270	−	0.475260i
$292$	167.783	+	30.3402i	0.574600	+	0.103905i
$293$	80.9237	+	58.7945i	0.276190	+	0.200664i	0.717254	−	0.696812i	$-0.245399\pi$
$293$	80.9237	+	58.7945i	0.276190	+	0.200664i	−0.441064	+	0.897476i	$0.645399\pi$
$294$	378.744	+	161.743i	1.28824	+	0.550147i
$295$	81.6631	+	26.5340i	0.276824	+	0.0899456i
$296$	−8.23414	−	179.602i	−0.0278181	−	0.606762i
$297$	10.1876	−	119.957i	0.0343018	−	0.403895i
$298$	−28.2352	+	16.8817i	−0.0947490	+	0.0566500i
$299$	428.341	+	139.176i	1.43258	+	0.465473i
$300$	77.2420	−	10.5122i	0.257473	−	0.0350405i
$301$	118.623	+	86.1844i	0.394095	+	0.286327i
$302$	309.164	−	354.089i	1.02372	−	1.17248i
$303$	472.130	−	153.404i	1.55819	−	0.506285i
$304$	421.027	+	18.3826i	1.38496	+	0.0604690i
$305$	−98.8217	+	71.7982i	−0.324006	+	0.235404i
$306$	−43.2190	−	189.083i	−0.141238	−	0.617919i
$307$		−	242.867i		−	0.791098i	−0.918445	−	0.395549i	$-0.870554\pi$
$307$		−	242.867i		−	0.791098i	0.918445	−	0.395549i	$-0.129446\pi$
$308$	−371.936	−	242.502i	−1.20758	−	0.787345i
$309$	−234.521			−0.758969
$310$	15.2444	−	3.48443i	0.0491754	−	0.0112401i
$311$	−131.087	−	180.426i	−0.421501	−	0.580147i	0.544475	−	0.838777i	$-0.316729\pi$
$311$	−131.087	−	180.426i	−0.421501	−	0.580147i	−0.965976	+	0.258630i	$0.916729\pi$
$312$	−373.303	−	245.915i	−1.19648	−	0.788188i
$313$	−59.1509	−	182.048i	−0.188981	−	0.581623i	0.811014	−	0.585027i	$-0.198916\pi$
$313$	−59.1509	−	182.048i	−0.188981	−	0.581623i	−0.999994	+	0.00340475i	$0.998916\pi$
$314$	−57.4652	−	50.1743i	−0.183010	−	0.159791i
$315$	82.1257	−	113.036i	0.260717	−	0.358846i
$316$	278.640	−	37.9213i	0.881774	−	0.120004i
$317$	38.2517	−	117.727i	0.120668	−	0.371378i	−0.872419	−	0.488759i	$-0.837450\pi$
$317$	38.2517	−	117.727i	0.120668	−	0.371378i	0.993087	+	0.117381i	$0.0374499\pi$
$318$	154.549	+	258.488i	0.486002	+	0.812856i
$319$	−504.273	+	304.745i	−1.58079	+	0.955313i
$320$	−142.508	+	13.0946i	−0.445338	+	0.0409205i
$321$	70.2017	−	216.059i	0.218697	−	0.673080i
$322$	249.014	−	583.101i	0.773337	−	1.81087i
$323$	−242.475	+	333.738i	−0.750696	+	1.03324i
$324$	−387.267	−	70.0293i	−1.19527	−	0.216140i
$325$	22.1505	+	68.1722i	0.0681553	+	0.209761i
$326$	26.7351	−	298.092i	0.0820096	−	0.914392i
$327$	96.5792	+	132.930i	0.295349	+	0.406514i
$328$	253.250	+	69.6380i	0.772105	+	0.212311i
$329$	−500.651			−1.52174
$330$	−137.879	+	133.245i	−0.417816	+	0.403772i
$331$		−	40.8096i		−	0.123292i	−0.998098	−	0.0616459i	$-0.980365\pi$
$331$		−	40.8096i		−	0.123292i	0.998098	−	0.0616459i	$-0.0196350\pi$
$332$	−359.446	+	344.095i	−1.08267	+	1.03643i
$333$	−112.582	+	81.7959i	−0.338085	+	0.245633i
$334$	2.97028	−	33.1181i	0.00889305	−	0.0991559i
$335$	−122.066	+	39.6617i	−0.364376	+	0.118393i
$336$	−391.757	+	492.506i	−1.16594	+	1.46579i
$337$	370.611	+	269.265i	1.09974	+	0.799005i	0.981017	−	0.193923i	$-0.0621212\pi$
$337$	370.611	+	269.265i	1.09974	+	0.799005i	0.118719	+	0.992928i	$0.462121\pi$
$338$	28.6885	−	67.1780i	0.0848773	−	0.198752i
$339$	754.987	+	245.310i	2.22710	+	0.723628i
$340$	66.3047	−	123.399i	0.195014	−	0.362938i
$341$	−25.1603	+	29.0926i	−0.0737838	+	0.0853157i
$342$	−167.390	−	279.965i	−0.489444	−	0.818611i
$343$	36.7614	+	11.9445i	0.107176	+	0.0348236i
$344$	−90.8134	+	72.5603i	−0.263993	+	0.210931i
$345$	−221.515	−	160.940i	−0.642073	−	0.466493i
$346$	331.768	+	289.674i	0.958866	+	0.837209i
$347$	−280.498	+	91.1393i	−0.808351	+	0.262649i	−0.683899	−	0.729576i	$-0.739717\pi$
$347$	−280.498	+	91.1393i	−0.808351	+	0.262649i	−0.124452	+	0.992226i	$0.539717\pi$
$348$	362.807	+	752.178i	1.04255	+	2.16143i
$349$	−265.125	+	192.625i	−0.759671	+	0.551933i	−0.898809	−	0.438340i	$-0.855567\pi$
$349$	−265.125	+	192.625i	−0.759671	+	0.551933i	0.139138	+	0.990273i	$0.455567\pi$
$350$	98.3740	−	22.4855i	0.281069	−	0.0642442i
$351$		−	156.900i		−	0.447009i
$352$	263.548	−	233.337i	0.748717	−	0.662890i
$353$	45.2529			0.128195			0.0640975	−	0.997944i	$-0.479583\pi$
$353$	45.2529			0.128195			0.0640975	+	0.997944i	$0.479583\pi$
$354$	66.7017	+	291.820i	0.188423	+	0.824350i
$355$	31.0466	+	42.7320i	0.0874552	+	0.120372i
$356$	−554.039	+	267.236i	−1.55629	+	0.750664i
$357$	−190.359	−	585.866i	−0.533219	−	1.64108i
$358$	60.1410	−	68.8803i	0.167992	−	0.192403i
$359$	87.1505	−	119.952i	0.242759	−	0.334129i	−0.670200	−	0.742181i	$-0.733792\pi$
$359$	87.1505	−	119.952i	0.242759	−	0.334129i	0.912959	+	0.408052i	$0.133792\pi$
$360$	69.1432	+	86.5368i	0.192065	+	0.240380i
$361$	−102.827	+	316.470i	−0.284840	+	0.876648i
$362$	52.9399	−	31.6525i	0.146243	−	0.0874379i
$363$	79.5337	−	464.867i	0.219101	−	1.28063i
$364$	−509.744	−	273.895i	−1.40039	−	0.752459i
$365$	29.4539	−	90.6497i	0.0806956	−	0.248355i
$366$	−391.626	−	167.245i	−1.07002	−	0.456952i
$367$	−226.710	+	312.039i	−0.617737	+	0.850243i	−0.997186	−	0.0749703i	$-0.976114\pi$
$367$	−226.710	+	312.039i	−0.617737	+	0.850243i	0.379448	+	0.925213i	$0.376114\pi$
$368$	393.384	+	312.912i	1.06898	+	0.850304i
$369$	−62.8213	−	193.344i	−0.170248	−	0.523968i
$370$	−100.104	−	8.97808i	−0.270551	−	0.0242651i
$371$	229.153	+	315.402i	0.617663	+	0.850141i
$372$	37.6983	+	39.3802i	0.101340	+	0.105861i
$373$	−303.778			−0.814418			−0.407209	−	0.913335i	$-0.633498\pi$
$373$	−303.778			−0.814418			−0.407209	+	0.913335i	$0.633498\pi$
$374$	48.0767	+	341.191i	0.128547	+	0.912276i
$375$		−	43.5776i		−	0.116207i
$376$	105.234	−	382.700i	0.279877	−	1.01782i
$377$	−621.242	+	451.359i	−1.64786	+	1.19724i
$378$	−220.000	−	19.7312i	−0.582010	−	0.0521990i
$379$	−288.379	+	93.7002i	−0.760896	+	0.247230i	−0.663663	−	0.748032i	$-0.730999\pi$
$379$	−288.379	+	93.7002i	−0.760896	+	0.247230i	−0.0972327	+	0.995262i	$0.530999\pi$
$380$	41.9210	−	231.826i	0.110318	−	0.610068i
$381$	−154.647	−	112.358i	−0.405898	−	0.294902i
$382$	125.603	+	53.6390i	0.328804	+	0.140416i
$383$	−61.1702	−	19.8754i	−0.159713	−	0.0518940i	0.228069	−	0.973645i	$-0.426759\pi$
$383$	−61.1702	−	19.8754i	−0.159713	−	0.0518940i	−0.387782	+	0.921751i	$0.626759\pi$
$384$	−294.129	−	402.983i	−0.765961	−	1.04943i
$385$	−162.363	+	187.739i	−0.421721	+	0.487633i
$386$	10.4163	−	6.22784i	0.0269852	−	0.0161343i
$387$	85.5685	+	27.8029i	0.221107	+	0.0718421i
$388$	61.9364	+	455.101i	0.159630	+	1.17294i
$389$	101.467	+	73.7198i	0.260840	+	0.189511i	0.710517	−	0.703680i	$-0.248461\pi$
$389$	101.467	+	73.7198i	0.260840	+	0.189511i	−0.449678	+	0.893191i	$0.648461\pi$
$390$	−164.356	+	188.239i	−0.421425	+	0.482663i
$391$	−467.954	+	152.047i	−1.19681	+	0.388868i
$392$	−232.503	+	352.944i	−0.593120	+	0.900368i
$393$	−574.996	+	417.759i	−1.46309	+	1.06300i
$394$	−133.303	−	583.202i	−0.338333	−	1.48021i
$395$		−	157.201i		−	0.397976i
$396$	−263.039	−	70.9949i	−0.664241	−	0.179280i
$397$	77.6330			0.195549			0.0977746	−	0.995209i	$-0.468828\pi$
$397$	77.6330			0.195549			0.0977746	+	0.995209i	$0.468828\pi$
$398$	−554.949	+	126.845i	−1.39435	+	0.318707i
$399$	−608.933	−	838.125i	−1.52615	−	2.10056i
$400$	−3.48958	+	79.9239i	−0.00872395	+	0.199810i
$401$	−225.616	−	694.376i	−0.562634	−	1.73161i	−0.674878	−	0.737930i	$-0.735804\pi$
$401$	−225.616	−	694.376i	−0.562634	−	1.73161i	0.112243	−	0.993681i	$-0.464196\pi$
$402$	−337.052	−	294.288i	−0.838437	−	0.732060i
$403$	−29.4648	+	40.5548i	−0.0731136	+	0.100632i
$404$	68.7006	+	504.803i	0.170051	+	1.24951i
$405$	−67.9836	+	209.232i	−0.167861	+	0.516623i
$406$	554.753	+	927.843i	1.36639	+	2.28533i
$407$	211.577	−	127.862i	0.519846	−	0.314157i
$408$	487.851	−	22.3664i	1.19571	−	0.0548195i
$409$	23.9146	−	73.6017i	0.0584710	−	0.179955i	−0.917555	−	0.397609i	$-0.869840\pi$
$409$	23.9146	−	73.6017i	0.0584710	−	0.179955i	0.976026	+	0.217653i	$0.0698402\pi$
$410$	57.6642	−	135.029i	0.140644	−	0.329338i
$411$	−104.409	+	143.706i	−0.254036	+	0.349651i
$412$	42.8269	−	236.835i	0.103949	−	0.574843i
$413$	119.745	+	368.536i	0.289938	+	0.892339i
$414$	34.7545	−	387.507i	0.0839482	−	0.936007i
$415$	163.502	+	225.041i	0.393980	+	0.542266i
$416$	316.512	−	332.079i	0.760845	−	0.798268i
$417$	712.024			1.70749
$418$	254.208	+	520.727i	0.608153	+	1.24576i
$419$			40.6843i			0.0970985i	0.998821	+	0.0485493i	$0.0154598\pi$
$419$			40.6843i			0.0970985i	−0.998821	+	0.0485493i	$0.984540\pi$
$420$	243.272	+	254.126i	0.579220	+	0.605061i
$421$	475.690	−	345.609i	1.12991	−	0.820924i	0.144224	−	0.989545i	$-0.453931\pi$
$421$	475.690	−	345.609i	1.12991	−	0.820924i	0.985681	+	0.168621i	$0.0539313\pi$
$422$	22.5610	−	251.551i	0.0534620	−	0.596092i
$423$	−292.173	+	94.9327i	−0.690716	+	0.224427i
$424$	−289.261	+	108.870i	−0.682220	+	0.256769i
$425$	−63.3537	−	46.0292i	−0.149068	−	0.108304i
$426$	−72.3190	+	169.345i	−0.169763	+	0.397523i
$427$	−524.270	−	170.346i	−1.22780	−	0.398936i
$428$	205.371	+	110.350i	0.479838	+	0.257826i
$429$	52.0140	−	612.452i	0.121245	−	1.42763i
$430$	33.3461	+	55.7724i	0.0775490	+	0.129703i
$431$	93.6683	+	30.4347i	0.217328	+	0.0706141i	0.415657	−	0.909521i	$-0.363552\pi$
$431$	93.6683	+	30.4347i	0.217328	+	0.0706141i	−0.198329	+	0.980135i	$0.563552\pi$
$432$	61.3251	−	164.021i	0.141956	−	0.379679i
$433$	256.526	+	186.377i	0.592440	+	0.430433i	0.843187	−	0.537620i	$-0.180676\pi$
$433$	256.526	+	186.377i	0.592440	+	0.430433i	−0.250748	+	0.968052i	$0.580676\pi$
$434$	53.1590	+	46.4144i	0.122486	+	0.106946i
$435$	443.989	−	144.261i	1.02066	−	0.331634i
$436$	−151.878	+	73.2574i	−0.348345	+	0.168021i
$437$	−669.443	+	486.379i	−1.53191	+	1.11299i
$438$	323.933	−	74.0418i	0.739573	−	0.169045i
$439$		−	142.749i		−	0.325168i	−0.986695	−	0.162584i	$-0.948017\pi$
$439$		−	142.749i		−	0.325168i	0.986695	−	0.162584i	$-0.0519828\pi$
$440$	−109.381	−	163.572i	−0.248593	−	0.371755i
$441$	327.130			0.741792
$442$	100.062	+	437.771i	0.226384	+	0.990432i
$443$	167.484	+	230.522i	0.378068	+	0.520365i	0.955071	−	0.296376i	$-0.0957782\pi$
$443$	167.484	+	230.522i	0.378068	+	0.520365i	−0.577004	+	0.816742i	$0.695778\pi$
$444$	−152.223	−	315.591i	−0.342844	−	0.710790i
$445$	106.260	+	327.033i	0.238786	+	0.734906i
$446$	194.578	−	222.853i	0.436274	−	0.499669i
$447$	−37.6838	+	51.8673i	−0.0843038	+	0.116034i
$448$	−425.826	−	485.562i	−0.950504	−	1.08384i
$449$	−128.570	+	395.697i	−0.286347	+	0.881285i	0.699645	+	0.714491i	$0.253342\pi$
$449$	−128.570	+	395.697i	−0.286347	+	0.881285i	−0.985992	+	0.166794i	$0.946658\pi$
$450$	53.1460	−	31.7757i	0.118102	−	0.0706127i
$451$	82.1341	+	351.680i	0.182116	+	0.779779i
$452$	−385.602	+	717.639i	−0.853101	+	1.58770i
$453$	283.086	−	871.250i	0.624914	−	1.92329i
$454$	501.457	+	214.148i	1.10453	+	0.471692i
$455$	−190.140	+	261.705i	−0.417890	+	0.575176i
$456$	768.660	−	289.303i	1.68566	−	0.634436i
$457$	62.0743	+	191.045i	0.135830	+	0.418042i	0.995718	−	0.0924406i	$-0.0294668\pi$
$457$	62.0743	+	191.045i	0.135830	+	0.418042i	−0.859888	+	0.510482i	$0.829467\pi$
$458$	−113.505	−	10.1800i	−0.247827	−	0.0222270i
$459$	100.753	+	138.674i	0.219504	+	0.302122i
$460$	202.980	−	194.311i	0.441261	−	0.422415i
$461$	853.193			1.85074			0.925372	−	0.379060i	$-0.123753\pi$
$461$	853.193			1.85074			0.925372	+	0.379060i	$0.123753\pi$
$462$	−852.215	−	149.952i	−1.84462	−	0.324571i
$463$			190.986i			0.412496i	0.978500	+	0.206248i	$0.0661254\pi$
$463$			190.986i			0.412496i	−0.978500	+	0.206248i	$0.933875\pi$
$464$	−825.853	+	229.029i	−1.77986	+	0.493597i
$465$	24.6550	−	17.9129i	0.0530215	−	0.0385223i
$466$	−368.680	−	33.0660i	−0.791159	−	0.0709571i
$467$	−598.229	+	194.376i	−1.28100	+	0.416223i	−0.868933	−	0.494929i	$-0.835194\pi$
$467$	−598.229	+	194.376i	−1.28100	+	0.416223i	−0.412070	+	0.911152i	$0.635194\pi$
$468$	−349.414	−	63.1845i	−0.746612	−	0.135010i
$469$	−468.597	−	340.456i	−0.999142	−	0.725919i
$470$	−204.049	−	87.1395i	−0.434147	−	0.185403i
$471$	−141.396	−	45.9422i	−0.300203	−	0.0975418i
$472$	−306.880	+	14.0694i	−0.650170	+	0.0298081i
$473$	−147.284	−	62.0771i	−0.311384	−	0.131241i
$474$	470.372	−	281.233i	0.992346	−	0.593319i
$475$	−125.251	−	40.6964i	−0.263685	−	0.0856766i
$476$	626.409	−	85.2504i	1.31599	−	0.179097i
$477$	193.536	+	140.612i	0.405737	+	0.294785i
$478$	296.286	−	339.340i	0.619846	−	0.709917i
$479$	679.143	−	220.667i	1.41784	−	0.460683i	0.502922	−	0.864332i	$-0.332258\pi$
$479$	679.143	−	220.667i	1.41784	−	0.460683i	0.914914	+	0.403649i	$0.132258\pi$
$480$	−245.389	+	132.543i	−0.511227	+	0.276131i
$481$	260.654	−	189.376i	0.541901	−	0.393714i
$482$	−202.438	−	885.665i	−0.419995	−	1.83748i
$483$		−	1235.66i		−	2.55831i
$484$	454.930	+	165.210i	0.939939	+	0.341343i
$485$	256.754			0.529390
$486$	−555.636	+	127.002i	−1.14328	+	0.261322i
$487$	−396.275	−	545.426i	−0.813706	−	1.11997i	−0.990741	−	0.135766i	$-0.956650\pi$
$487$	−396.275	−	545.426i	−0.813706	−	1.11997i	0.177035	−	0.984205i	$-0.443350\pi$
$488$	240.411	−	364.949i	0.492646	−	0.747846i
$489$	−180.240	−	554.721i	−0.368589	−	1.13440i
$490$	177.973	+	155.392i	0.363210	+	0.317127i
$491$	158.938	−	218.759i	0.323703	−	0.445539i	−0.615890	−	0.787832i	$-0.711204\pi$
$491$	158.938	−	218.759i	0.323703	−	0.445539i	0.939593	+	0.342293i	$0.111204\pi$
$492$	507.191	−	69.0256i	1.03088	−	0.140296i
$493$	259.238	−	797.853i	0.525838	−	1.61836i
$494$	387.546	+	648.183i	0.784505	+	1.31211i
$495$	−59.1537	+	140.348i	−0.119503	+	0.283532i
$496$	−46.6530	+	30.8790i	−0.0940586	+	0.0622560i
$497$	−73.6599	+	226.702i	−0.148209	+	0.456141i
$498$	−380.856	+	891.825i	−0.764770	+	1.79081i
$499$	−87.4694	+	120.391i	−0.175289	+	0.241265i	−0.887617	−	0.460582i	$-0.847641\pi$
$499$	−87.4694	+	120.391i	−0.175289	+	0.241265i	0.712328	+	0.701847i	$0.247641\pi$
$500$	44.0076	+	7.95789i	0.0880153	+	0.0159158i
$501$	−20.0247	−	61.6296i	−0.0399694	−	0.123013i
$502$	19.9896	−	222.881i	0.0398200	−	0.443985i
$503$	159.226	+	219.155i	0.316552	+	0.435697i	0.937411	−	0.348226i	$-0.113216\pi$
$503$	159.226	+	219.155i	0.316552	+	0.435697i	−0.620858	+	0.783923i	$0.713216\pi$
$504$	−132.536	+	481.990i	−0.262968	+	0.956329i
$505$	284.795			0.563950
$506$	−119.772	+	680.697i	−0.236704	+	1.34525i
$507$		−	142.358i		−	0.280786i
$508$	141.707	−	135.655i	0.278951	−	0.267038i
$509$	752.384	−	546.639i	1.47816	−	1.07395i	0.500018	−	0.866015i	$-0.333327\pi$
$509$	752.384	−	546.639i	1.47816	−	1.07395i	0.978143	−	0.207932i	$-0.0666733\pi$
$510$	24.3871	−	271.912i	0.0478179	−	0.533161i
$511$	409.091	−	132.922i	0.800570	−	0.260121i
$512$	460.671	−	223.441i	0.899749	−	0.436409i
$513$	233.214	+	169.440i	0.454607	+	0.330292i
$514$	−223.275	+	522.829i	−0.434387	+	1.01718i
$515$	−127.957	−	41.5758i	−0.248461	−	0.0807298i
$516$	−107.225	+	199.555i	−0.207800	+	0.386734i
$517$	531.443	−	124.117i	1.02794	−	0.240072i
$518$	−232.757	−	389.295i	−0.449339	−	0.751534i
$519$	816.328	+	265.241i	1.57289	+	0.511062i
$520$	−160.082	−	200.353i	−0.307851	−	0.385294i
$521$	−385.014	−	279.729i	−0.738990	−	0.536908i	0.153405	−	0.988163i	$-0.450976\pi$
$521$	−385.014	−	279.729i	−0.738990	−	0.536908i	−0.892395	+	0.451256i	$0.850976\pi$
$522$	499.682	+	436.284i	0.957245	+	0.835794i
$523$	121.680	−	39.5362i	0.232658	−	0.0755951i	−0.190368	−	0.981713i	$-0.560968\pi$
$523$	121.680	−	39.5362i	0.232658	−	0.0755951i	0.423026	+	0.906118i	$0.360968\pi$
$524$	−316.879	−	656.959i	−0.604731	−	1.25374i
$525$	159.102	−	115.594i	0.303051	−	0.220179i
$526$	−273.117	+	62.4266i	−0.519233	+	0.118682i
$527$		−	54.7643i		−	0.103917i
$528$	293.754	−	619.918i	0.556352	−	1.17409i
$529$	−457.972			−0.865731
$530$	38.4988	+	168.432i	0.0726392	+	0.317796i
$531$	139.762	+	192.366i	0.263206	+	0.362272i
$532$	957.594	−	461.888i	1.79999	−	0.868211i
$533$	145.446	+	447.636i	0.272882	+	0.839843i
$534$	−788.442	+	903.012i	−1.47648	+	1.69103i
$535$	76.6056	−	105.439i	0.143188	−	0.197081i
$536$	358.742	−	286.636i	0.669295	−	0.534770i
$537$	55.0683	−	169.483i	0.102548	−	0.315610i
$538$	−321.363	+	192.141i	−0.597329	+	0.357140i
$539$	−579.050	−	49.1773i	−1.07430	−	0.0912380i
$540$	−86.2303	−	46.3332i	−0.159686	−	0.0858023i
$541$	−127.830	+	393.421i	−0.236285	+	0.727211i	0.760663	+	0.649147i	$0.224874\pi$
$541$	−127.830	+	393.421i	−0.236285	+	0.727211i	−0.996948	+	0.0780645i	$0.975126\pi$
$542$	−701.860	−	299.731i	−1.29495	−	0.553009i
$543$	70.6557	−	97.2493i	0.130121	−	0.179096i
$544$	−66.5013	+	496.749i	−0.122245	+	0.913142i
$545$	29.1289	+	89.6495i	0.0534475	+	0.164494i
$546$	−1123.23	−	100.740i	−2.05720	−	0.184505i
$547$	227.278	+	312.821i	0.415499	+	0.571885i	0.964549	−	0.263904i	$-0.0850103\pi$
$547$	227.278	+	312.821i	0.415499	+	0.571885i	−0.549050	+	0.835790i	$0.685010\pi$
$548$	−126.058	−	131.682i	−0.230033	−	0.240295i
$549$	−338.257			−0.616133
$550$	−98.8500	+	48.2565i	−0.179727	+	0.0877390i
$551$		−	1410.83i		−	2.56050i
$552$	944.546	+	259.728i	1.71113	+	0.470522i
$553$	573.939	−	416.991i	1.03786	−	0.754053i
$554$	702.989	+	63.0493i	1.26893	+	0.113807i
$555$	−186.284	+	60.5274i	−0.335647	+	0.109058i
$556$	−130.026	+	719.050i	−0.233859	+	1.29326i
$557$	579.184	+	420.802i	1.03983	+	0.755479i	0.970252	−	0.242097i	$-0.0778353\pi$
$557$	579.184	+	420.802i	1.03983	+	0.755479i	0.0695761	+	0.997577i	$0.477835\pi$
$558$	39.8238	+	17.0068i	0.0713688	+	0.0304782i
$559$	−198.111	−	64.3701i	−0.354402	−	0.115152i
$560$	−301.058	+	199.266i	−0.537604	+	0.355832i
$561$	347.310	+	574.706i	0.619091	+	1.02443i
$562$	144.884	−	86.6251i	0.257800	−	0.154137i
$563$	909.437	+	295.494i	1.61534	+	0.524856i	0.970836	−	0.239744i	$-0.0770636\pi$
$563$	909.437	+	295.494i	1.61534	+	0.524856i	0.644505	+	0.764600i	$0.277064\pi$
$564$	−104.308	−	766.443i	−0.184944	−	1.35894i
$565$	368.440	+	267.687i	0.652106	+	0.473783i
$566$	−206.013	+	235.950i	−0.363981	+	0.416872i
$567$	−944.240	+	306.802i	−1.66533	+	0.541097i
$568$	−157.809	−	103.957i	−0.277833	−	0.183023i
$569$	247.679	−	179.950i	0.435289	−	0.316256i	−0.348471	−	0.937319i	$-0.613299\pi$
$569$	247.679	−	179.950i	0.435289	−	0.316256i	0.783760	+	0.621064i	$0.213299\pi$
$570$	−102.303	−	447.578i	−0.179480	−	0.785225i
$571$		−	17.5331i		−	0.0307059i	−0.999882	−	0.0153529i	$-0.995113\pi$
$571$		−	17.5331i		−	0.0307059i	0.999882	−	0.0153529i	$-0.00488718\pi$
$572$	608.996	+	164.369i	1.06468	+	0.287359i
$573$	266.168			0.464517
$574$	645.949	−	147.645i	1.12535	−	0.257222i
$575$	−92.3296	−	127.081i	−0.160573	−	0.221010i
$576$	−340.577	−	202.622i	−0.591279	−	0.351775i
$577$	−135.283	−	416.359i	−0.234460	−	0.721593i	−0.997193	−	0.0748790i	$-0.976143\pi$
$577$	−135.283	−	416.359i	−0.234460	−	0.721593i	0.762733	−	0.646714i	$-0.223857\pi$
$578$	65.8440	+	57.4900i	0.113917	+	0.0994636i
$579$	13.9020	−	19.1344i	0.0240103	−	0.0330474i
$580$	64.6057	+	474.714i	0.111389	+	0.818473i
$581$	−387.917	+	1193.89i	−0.667672	+	2.05488i
$582$	459.335	+	768.254i	0.789236	+	1.32002i
$583$	−321.439	−	277.991i	−0.551353	−	0.476828i
$584$	15.6177	+	340.651i	0.0267427	+	0.583306i
$585$	−61.3388	+	188.781i	−0.104853	+	0.322703i
$586$	−78.5691	+	183.980i	−0.134077	+	0.313959i
$587$	−572.907	+	788.538i	−0.975991	+	1.34334i	−0.0370295	+	0.999314i	$0.511790\pi$
$587$	−572.907	+	788.538i	−0.975991	+	1.34334i	−0.938962	+	0.344022i	$0.888210\pi$
$588$	−146.567	+	810.524i	−0.249263	+	1.37844i
$589$	−28.4603	−	87.5917i	−0.0483197	−	0.148713i
$590$	−15.3406	+	171.045i	−0.0260010	+	0.289907i
$591$	−685.290	−	943.221i	−1.15954	−	1.59598i
$592$	346.503	−	96.0936i	0.585309	−	0.162320i
$593$	−698.683			−1.17822			−0.589109	−	0.808054i	$-0.700521\pi$
$593$	−698.683			−1.17822			−0.589109	+	0.808054i	$0.700521\pi$
$594$	238.422	−	33.5957i	0.401384	−	0.0565584i
$595$		−	353.401i		−	0.593952i
$596$	−45.4975	−	47.5274i	−0.0763381	−	0.0797439i
$597$	−897.528	+	652.092i	−1.50340	+	1.09228i
$598$	−80.4647	+	897.167i	−0.134556	+	1.50028i
$599$	−591.792	+	192.285i	−0.987967	+	0.321010i	−0.758047	−	0.652199i	$-0.773846\pi$
$599$	−591.792	+	192.285i	−0.987967	+	0.321010i	−0.229920	+	0.973210i	$0.573846\pi$
$600$	54.9186	+	145.915i	0.0915310	+	0.243192i
$601$	−591.649	−	429.858i	−0.984441	−	0.715238i	−0.0257443	−	0.999669i	$-0.508196\pi$
$601$	−591.649	−	429.858i	−0.984441	−	0.715238i	−0.958697	+	0.284430i	$0.908196\pi$
$602$	−115.171	+	269.689i	−0.191314	+	0.447988i
$603$	−338.023	−	109.830i	−0.560569	−	0.182140i
$604$	828.151	+	444.982i	1.37111	+	0.736725i
$605$	125.806	−	239.537i	0.207944	−	0.395929i
$606$	509.500	+	852.156i	0.840759	+	1.40620i
$607$	−722.955	−	234.902i	−1.19103	−	0.386989i	−0.354576	−	0.935027i	$-0.615375\pi$
$607$	−722.955	−	234.902i	−1.19103	−	0.386989i	−0.836453	+	0.548038i	$0.815375\pi$
$608$	151.790	+	829.076i	0.249654	+	1.36361i
$609$	1704.42	+	1238.34i	2.79872	+	2.03339i
$610$	−184.026	−	160.678i	−0.301682	−	0.263406i
$611$	676.447	−	219.791i	1.10711	−	0.359723i
$612$	349.398	−	168.530i	0.570912	−	0.275375i
$613$	−505.486	+	367.257i	−0.824611	+	0.599115i	−0.918029	−	0.396512i	$-0.870220\pi$
$613$	−505.486	+	367.257i	−0.824611	+	0.599115i	0.0934189	+	0.995627i	$0.470220\pi$
$614$	473.522	−	108.234i	0.771209	−	0.176276i
$615$		−	286.142i		−	0.465272i
$616$	307.058	−	833.241i	0.498470	−	1.35266i
$617$	−11.7045			−0.0189700			−0.00948501	−	0.999955i	$-0.503019\pi$
$617$	−11.7045			−0.0189700			−0.00948501	+	0.999955i	$0.503019\pi$
$618$	−104.514	−	457.250i	−0.169117	−	0.739887i
$619$	−427.221	−	588.019i	−0.690179	−	0.949950i	0.309820	−	0.950795i	$-0.399731\pi$
$619$	−427.221	−	588.019i	−0.690179	−	0.949950i	−1.00000		0.000844784i	$0.999731\pi$
$620$	13.5873	+	28.1694i	0.0219150	+	0.0454345i
$621$	106.250	+	327.003i	0.171094	+	0.526575i
$622$	293.360	−	335.989i	0.471640	−	0.540175i
$623$	−912.133	+	1255.44i	−1.46410	+	2.01516i
$624$	313.102	−	837.427i	0.501765	−	1.34203i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$	328.581	−	196.457i	0.524890	−	0.313829i
$627$	854.165	+	738.711i	1.36231	+	1.17817i
$628$	72.2163	−	134.401i	0.114994	−	0.214014i
$629$	−108.768	+	334.755i	−0.172923	+	0.532202i
$630$	256.988	+	109.747i	0.407918	+	0.174202i
$631$	621.792	−	855.823i	0.985407	−	1.35630i	0.0515422	−	0.998671i	$-0.483586\pi$
$631$	621.792	−	855.823i	0.985407	−	1.35630i	0.933865	−	0.357626i	$-0.116414\pi$
$632$	198.112	+	526.371i	0.313468	+	0.832865i
$633$	−152.099	−	468.112i	−0.240283	−	0.739514i
$634$	246.581	+	22.1152i	0.388928	+	0.0348820i
$635$	−64.4584	−	88.7194i	−0.101509	−	0.139716i
$636$	−435.104	+	416.521i	−0.684126	+	0.654908i
$637$	−757.382			−1.18898
$638$	−818.895	−	847.379i	−1.28353	−	1.32818i
$639$			146.267i			0.228900i
$640$	−89.0393	−	272.015i	−0.139124	−	0.425023i
$641$	−352.881	+	256.383i	−0.550516	+	0.399973i	−0.827976	−	0.560764i	$-0.810507\pi$
$641$	−352.881	+	256.383i	−0.550516	+	0.399973i	0.277460	+	0.960737i	$0.410507\pi$
$642$	452.539	+	40.5871i	0.704889	+	0.0632197i
$643$	−541.940	+	176.087i	−0.842831	+	0.273852i	−0.698440	−	0.715668i	$-0.746122\pi$
$643$	−541.940	+	176.087i	−0.842831	+	0.273852i	−0.144391	+	0.989521i	$0.546122\pi$
$644$	1247.85	+	225.649i	1.93766	+	0.350387i
$645$	102.452	+	74.4361i	0.158841	+	0.115405i
$646$	−758.753	−	324.027i	−1.17454	−	0.501590i
$647$	1052.80	+	342.075i	1.62720	+	0.528710i	0.973626	−	0.228151i	$-0.0732679\pi$
$647$	1052.80	+	342.075i	1.62720	+	0.528710i	0.653576	+	0.756861i	$0.273268\pi$
$648$	−36.0478	−	786.269i	−0.0556294	−	1.21338i
$649$	−218.474	−	361.516i	−0.336631	−	0.557036i
$650$	−123.045	+	73.5681i	−0.189300	+	0.113182i
$651$	130.800	+	42.4994i	0.200921	+	0.0652833i
$652$	593.109	−	80.7185i	0.909677	−	0.123801i
$653$	−33.5591	−	24.3821i	−0.0513922	−	0.0373386i	0.561793	−	0.827278i	$-0.310112\pi$
$653$	−33.5591	−	24.3821i	−0.0513922	−	0.0373386i	−0.613185	+	0.789940i	$0.710112\pi$
$654$	−216.135	+	247.542i	−0.330482	+	0.378505i
$655$	−387.784	+	125.999i	−0.592037	+	0.192364i
$656$	−22.9135	+	524.801i	−0.0349291	+	0.800001i
$657$	213.535	−	155.142i	0.325016	−	0.236138i
$658$	−223.115	−	976.128i	−0.339080	−	1.48348i
$659$			125.542i			0.190504i	0.995453	+	0.0952518i	$0.0303656\pi$
$659$			125.542i			0.190504i	−0.995453	+	0.0952518i	$0.969634\pi$
$660$	−321.235	−	209.445i	−0.486720	−	0.317341i
$661$	−770.578			−1.16578			−0.582888	−	0.812553i	$-0.698077\pi$
$661$	−770.578			−1.16578			−0.582888	+	0.812553i	$0.698077\pi$
$662$	79.5672	−	18.1868i	0.120192	−	0.0274725i
$663$	514.402	+	708.014i	0.775870	+	1.06789i
$664$	−831.075	−	547.473i	−1.25162	−	0.824508i
$665$	−183.658	−	565.241i	−0.276177	−	0.849986i
$666$	−209.651	−	183.052i	−0.314792	−	0.274852i
$667$	989.107	−	1361.39i	1.48292	−	2.04106i
$668$	65.8946	−	8.96784i	0.0986445	−	0.0134249i
$669$	178.166	−	548.338i	0.266317	−	0.819638i
$670$	−131.728	−	220.319i	−0.196608	−	0.328834i
$671$	598.745	+	50.8499i	0.892317	+	0.0757823i
$672$	−1134.83	−	544.331i	−1.68874	−	0.810016i
$673$	150.772	−	464.028i	0.224029	−	0.689492i	−0.774359	−	0.632746i	$-0.781928\pi$
$673$	150.772	−	464.028i	0.224029	−	0.689492i	0.998389	−	0.0567455i	$-0.0180724\pi$
$674$	−359.827	+	842.584i	−0.533868	+	1.25012i
$675$	−32.1649	+	44.2711i	−0.0476516	+	0.0655868i
$676$	143.763	+	25.9966i	0.212667	+	0.0384566i
$677$	−328.420	−	1010.77i	−0.485111	−	1.49302i	−0.831820	−	0.555045i	$-0.812701\pi$
$677$	−328.420	−	1010.77i	−0.485111	−	1.49302i	0.346709	−	0.937973i	$-0.387299\pi$
$678$	−141.826	+	1581.33i	−0.209183	+	2.33235i
$679$	681.068	+	937.409i	1.00305	+	1.38057i
$680$	270.142	+	74.2827i	0.397267	+	0.109239i
$681$	1062.65			1.56042
$682$	−67.9351	−	36.0903i	−0.0996116	−	0.0529184i
$683$		−	632.151i		−	0.925551i	−0.886476	−	0.462775i	$-0.846854\pi$
$683$		−	632.151i		−	0.925551i	0.886476	−	0.462775i	$-0.153146\pi$
$684$	471.255	−	451.129i	0.688970	−	0.659545i
$685$	−82.4428	+	59.8982i	−0.120354	+	0.0874426i
$686$	−6.90570	+	76.9974i	−0.0100666	+	0.112241i
$687$	−211.222	+	68.6303i	−0.307456	+	0.0998985i
$688$	−181.943	−	144.724i	−0.264452	−	0.210355i
$689$	−448.081	−	325.550i	−0.650336	−	0.472497i
$690$	215.070	−	503.615i	0.311695	−	0.729877i
$691$	−595.551	−	193.506i	−0.861868	−	0.280038i	−0.155459	−	0.987842i	$-0.549686\pi$
$691$	−595.551	−	193.506i	−0.861868	−	0.280038i	−0.706408	+	0.707804i	$0.749686\pi$
$692$	−416.931	+	775.946i	−0.602502	+	1.12131i
$693$	−669.323	+	156.319i	−0.965834	+	0.225568i
$694$	−302.700	−	506.275i	−0.436166	−	0.729503i
$695$	388.488	+	126.227i	0.558975	+	0.181622i
$696$	−1304.85	+	1042.58i	−1.87478	+	1.49796i
$697$	−415.997	−	302.239i	−0.596839	−	0.433629i
$698$	−493.717	−	431.076i	−0.707330	−	0.617588i
$699$	−686.079	+	222.921i	−0.981515	+	0.318914i
$700$	87.6806	+	181.781i	0.125258	+	0.259687i
$701$	−1132.88	+	823.084i	−1.61609	+	1.17416i	−0.779230	+	0.626738i	$0.784390\pi$
$701$	−1132.88	+	823.084i	−1.61609	+	1.17416i	−0.836859	+	0.547419i	$0.815610\pi$
$702$	305.911	−	69.9225i	0.435771	−	0.0996047i
$703$			591.943i			0.842024i
$704$	572.392	+	409.858i	0.813056	+	0.582185i
$705$	−432.405			−0.613340
$706$	20.1669	+	88.2303i	0.0285650	+	0.124972i
$707$	755.448	+	1039.78i	1.06853	+	1.47070i
$708$	−539.241	+	260.099i	−0.761639	+	0.367371i
$709$	0.00587285	+	0.0180748i	8.28329e−6	+	2.54934e-5i	0.951061	−	0.309004i	$-0.0999957\pi$
$709$	0.00587285	+	0.0180748i	8.28329e−6	+	2.54934e-5i	−0.951052	+	0.309030i	$0.899996\pi$
$710$	−69.4793	+	79.5755i	−0.0978582	+	0.112078i
$711$	255.873	−	352.179i	0.359878	−	0.495330i
$712$	−767.942	−	961.125i	−1.07857	−	1.34989i
$713$	33.9460	−	104.475i	0.0476100	−	0.146529i
$714$	1057.44	−	632.237i	1.48101	−	0.885487i
$715$	136.955	−	324.939i	0.191545	−	0.454460i
$716$	161.099	+	86.5616i	0.224998	+	0.120896i
$717$	271.295	−	834.961i	0.378376	−	1.16452i
$718$	272.712	+	116.462i	0.379821	+	0.162203i
$719$	483.507	−	665.490i	0.672471	−	0.925577i	−0.327342	−	0.944906i	$-0.606153\pi$
$719$	483.507	−	665.490i	0.672471	−	0.925577i	0.999813	+	0.0193288i	$0.00615294\pi$
$720$	−137.909	+	173.375i	−0.191540	+	0.240798i
$721$	−187.627	−	577.456i	−0.260231	−	0.800910i
$722$	−662.852	−	59.4496i	−0.918077	−	0.0823401i
$723$	−1040.70	−	1432.40i	−1.43942	−	1.98119i
$724$	85.3061	+	89.1120i	0.117826	+	0.123083i
$725$	267.820			0.369406
$726$	941.804	−	52.0996i	1.29725	−	0.0717626i
$727$			839.149i			1.15426i	0.816651	+	0.577132i	$0.195828\pi$
$727$			839.149i			1.15426i	−0.816651	+	0.577132i	$0.804172\pi$
$728$	306.851	−	1115.92i	0.421499	−	1.53285i
$729$	−182.269	+	132.426i	−0.250026	+	0.181654i
$730$	189.867	+	17.0287i	0.260092	+	0.0233270i
$731$	216.432	−	70.3230i	0.296077	−	0.0962012i
$732$	151.552	−	838.092i	0.207038	−	1.14493i
$733$	−50.1402	−	36.4290i	−0.0684041	−	0.0496985i	0.553058	−	0.833143i	$-0.313461\pi$
$733$	−50.1402	−	36.4290i	−0.0684041	−	0.0496985i	−0.621462	+	0.783444i	$0.713461\pi$
$734$	−709.421	−	302.960i	−0.966513	−	0.412752i
$735$	437.909	+	142.285i	0.595795	+	0.193585i
$736$	−434.778	+	906.436i	−0.590731	+	1.23157i
$737$	581.821	+	245.225i	0.789445	+	0.332733i
$738$	348.970	−	208.648i	0.472859	−	0.282720i
$739$	1148.56	+	373.191i	1.55421	+	0.504995i	0.955254	−	0.295785i	$-0.0955813\pi$
$739$	1148.56	+	373.191i	1.55421	+	0.504995i	0.598959	+	0.800780i	$0.295581\pi$
$740$	−27.1066	−	199.176i	−0.0366305	−	0.269156i
$741$	1190.70	+	865.091i	1.60688	+	1.16746i
$742$	−512.823	+	587.343i	−0.691136	+	0.791567i
$743$	899.643	−	292.312i	1.21082	−	0.393421i	0.367092	−	0.930185i	$-0.380353\pi$
$743$	899.643	−	292.312i	1.21082	−	0.393421i	0.843732	+	0.536764i	$0.180353\pi$
$744$	−59.9800	+	91.0509i	−0.0806183	+	0.122380i
$745$	−29.7557	+	21.6188i	−0.0399405	+	0.0290185i
$746$	−135.379	−	592.281i	−0.181473	−	0.793943i
$747$			770.291i			1.03118i
$748$	−643.801	+	245.788i	−0.860696	+	0.328593i
$749$	588.160			0.785260
$750$	84.9641	−	19.4203i	0.113285	−	0.0258938i
$751$	−362.830	−	499.393i	−0.483130	−	0.664971i	0.495973	−	0.868338i	$-0.334812\pi$
$751$	−362.830	−	499.393i	−0.483130	−	0.664971i	−0.979103	+	0.203367i	$0.934812\pi$
$752$	793.054	+	34.6258i	1.05459	+	0.0460449i
$753$	−134.764	−	414.760i	−0.178969	−	0.550810i
$754$	−1156.88	−	1010.10i	−1.53432	−	1.33965i
$755$	308.910	−	425.178i	0.409152	−	0.563149i
$756$	−59.5724	−	437.730i	−0.0787995	−	0.579008i
$757$	−428.022	+	1317.32i	−0.565419	+	1.74018i	0.101286	+	0.994857i	$0.467704\pi$
$757$	−428.022	+	1317.32i	−0.565419	+	1.74018i	−0.666705	+	0.745322i	$0.732296\pi$
$758$	−311.205	−	520.501i	−0.410561	−	0.686677i
$759$	306.335	+	1311.66i	0.403603	+	1.72814i
$760$	470.676	−	21.5790i	0.619311	−	0.0283934i
$761$	333.154	−	1025.34i	0.437784	−	1.34736i	−0.452423	−	0.891804i	$-0.649440\pi$
$761$	333.154	−	1025.34i	0.437784	−	1.34736i	0.890207	−	0.455557i	$-0.150560\pi$
$762$	150.147	−	351.591i	0.197044	−	0.461405i
$763$	−250.043	+	344.154i	−0.327710	+	0.451054i
$764$	−48.6060	+	268.794i	−0.0636204	+	0.351825i
$765$	−67.0114	−	206.240i	−0.0875966	−	0.269594i
$766$	11.4910	−	128.122i	0.0150012	−	0.167261i
$767$	−323.582	−	445.372i	−0.421880	−	0.580668i
$768$	654.624	−	753.058i	0.852375	−	0.980544i
$769$	−259.985			−0.338081			−0.169041	−	0.985609i	$-0.554067\pi$
$769$	−259.985			−0.338081			−0.169041	+	0.985609i	$0.554067\pi$
$770$	−438.394	−	232.896i	−0.569343	−	0.302462i
$771$			1107.94i			1.43701i
$772$	16.7845	+	17.5334i	0.0217416	+	0.0227116i
$773$	−230.519	+	167.482i	−0.298213	+	0.216665i	−0.726823	−	0.686825i	$-0.759004\pi$
$773$	−230.519	+	167.482i	−0.298213	+	0.216665i	0.428609	+	0.903490i	$0.359004\pi$
$774$	−16.0742	+	179.225i	−0.0207677	+	0.231557i
$775$	16.6276	−	5.40264i	0.0214550	−	0.00697114i
$776$	−859.716	+	323.574i	−1.10788	+	0.416977i
$777$	−715.124	−	519.568i	−0.920365	−	0.668685i
$778$	−98.5142	+	230.684i	−0.126625	+	0.296509i
$779$	−822.428	−	267.223i	−1.05575	−	0.343033i
$780$	−440.257	−	236.559i	−0.564432	−	0.303281i
$781$	21.9882	−	258.906i	0.0281540	−	0.331506i
$782$	−504.993	−	844.618i	−0.645771	−	1.08007i
$783$	−557.534	−	181.154i	−0.712049	−	0.231359i
$784$	−791.757	−	296.026i	−1.00989	−	0.377584i
$785$	−69.0023	−	50.1331i	−0.0879010	−	0.0638638i
$786$	−1070.76	−	934.906i	−1.36229	−	1.18945i
$787$	−1171.33	+	380.588i	−1.48835	+	0.483594i	−0.936595	−	0.350413i	$-0.886041\pi$
$787$	−1171.33	+	380.588i	−1.48835	+	0.483594i	−0.551754	+	0.834007i	$0.686041\pi$
$788$	1077.67	−	519.807i	1.36760	−	0.659654i
$789$	−441.716	+	320.925i	−0.559843	+	0.406749i
$790$	306.497	−	70.0564i	0.387971	−	0.0886790i
$791$			2055.24i			2.59828i
$792$	21.1966	−	544.491i	0.0267634	−	0.687489i
$793$	783.142			0.987569
$794$	34.5971	+	151.362i	0.0435732	+	0.190633i
$795$	197.916	+	272.408i	0.248951	+	0.342651i
$796$	−494.626	−	1025.47i	−0.621389	−	1.28827i
$797$	−209.605	−	645.099i	−0.262993	−	0.809409i	−0.992149	−	0.125062i	$-0.960087\pi$
$797$	−209.605	−	645.099i	−0.262993	−	0.809409i	0.729156	−	0.684348i	$-0.239913\pi$
$798$	1362.74	−	1560.76i	1.70769	−	1.95584i
$799$	−456.730	+	628.635i	−0.571627	+	0.786777i
$800$	−157.384	+	28.8143i	−0.196730	+	0.0360179i
$801$	−294.252	+	905.615i	−0.367356	+	1.13061i
$802$	1253.29	−	749.336i	1.56271	−	0.934334i
$803$	−401.299	+	242.515i	−0.499750	+	0.302012i
$804$	423.572	−	788.305i	0.526830	−	0.980479i
$805$	219.058	−	674.190i	0.272121	−	0.837503i
$806$	−92.2013	−	39.3747i	−0.114394	−	0.0488520i
$807$	−428.904	+	590.335i	−0.531479	+	0.731518i
$808$	−953.606	+	358.912i	−1.18021	+	0.444198i
$809$	444.042	+	1366.62i	0.548878	+	1.68927i	0.711588	+	0.702597i	$0.247976\pi$
$809$	444.042	+	1366.62i	0.548878	+	1.68927i	−0.162710	+	0.986674i	$0.552024\pi$
$810$	−438.240	−	39.3047i	−0.541037	−	0.0485243i
$811$	112.426	+	154.741i	0.138627	+	0.190803i	0.872686	−	0.488283i	$-0.162376\pi$
$811$	112.426	+	154.741i	0.138627	+	0.190803i	−0.734059	+	0.679086i	$0.762376\pi$
$812$	−1561.81	+	1495.10i	−1.92341	+	1.84126i
$813$	−1487.33			−1.82943
$814$	343.583	+	355.534i	0.422093	+	0.436775i
$815$		−	334.615i		−	0.410570i
$816$	261.018	+	941.203i	0.319876	+	1.15344i
$817$	309.622	−	224.954i	0.378975	−	0.275341i
$818$	154.160	+	13.8262i	0.188460	+	0.0169025i
$819$	−851.948	+	276.815i	−1.04023	+	0.337991i
$820$	288.966	+	52.2535i	0.352397	+	0.0637238i
$821$	998.232	+	725.258i	1.21587	+	0.883384i	0.995751	−	0.0920884i	$-0.0293543\pi$
$821$	998.232	+	725.258i	1.21587	+	0.883384i	0.220123	+	0.975472i	$0.429354\pi$
$822$	−326.717	−	139.525i	−0.397466	−	0.169738i
$823$	660.377	+	214.570i	0.802403	+	0.260716i	0.681377	−	0.731933i	$-0.261382\pi$
$823$	660.377	+	214.570i	0.802403	+	0.260716i	0.121026	+	0.992649i	$0.461382\pi$
$824$	480.848	−	22.0453i	0.583553	−	0.0267540i
$825$	−140.230	+	162.147i	−0.169976	+	0.196542i
$826$	−665.177	+	397.706i	−0.805299	+	0.481484i
$827$	−183.354	−	59.5753i	−0.221710	−	0.0720379i	0.196056	−	0.980593i	$-0.437187\pi$
$827$	−183.354	−	59.5753i	−0.221710	−	0.0720379i	−0.417766	+	0.908555i	$0.637187\pi$
$828$	771.017	−	104.931i	0.931180	−	0.126728i
$829$	−661.852	−	480.864i	−0.798374	−	0.580053i	0.112062	−	0.993701i	$-0.464254\pi$
$829$	−661.852	−	480.864i	−0.798374	−	0.580053i	−0.910437	+	0.413648i	$0.864254\pi$
$830$	−365.901	+	419.071i	−0.440845	+	0.504905i
$831$	1308.20	−	425.059i	1.57424	−	0.511503i
$832$	788.514	+	469.117i	0.947733	+	0.563843i
$833$	669.401	−	486.348i	0.803602	−	0.583851i
$834$	317.313	+	1388.25i	0.380471	+	1.66456i
$835$		−	37.1757i		−	0.0445218i
$836$	−901.982	+	727.695i	−1.07893	+	0.870449i
$837$	−38.2689			−0.0457215
$838$	−79.3229	+	18.1309i	−0.0946573	+	0.0216360i
$839$	−853.898	−	1175.29i	−1.01776	−	1.40082i	−0.913765	−	0.406243i	$-0.866839\pi$
$839$	−853.898	−	1175.29i	−1.01776	−	1.40082i	−0.103991	−	0.994578i	$-0.533161\pi$
$840$	−387.059	+	587.563i	−0.460785	+	0.699480i
$841$	626.715	+	1928.83i	0.745202	+	2.29350i
$842$	885.831	+	773.441i	1.05206	+	0.918576i
$843$	193.367	−	266.147i	0.229380	−	0.315714i
$844$	500.507	−	68.1159i	0.593018	−	0.0807060i
$845$	25.2372	−	77.6723i	0.0298666	−	0.0919198i
$846$	−315.298	−	527.347i	−0.372693	−	0.623342i
$847$	1208.26	−	176.079i	1.42652	−	0.207886i
$848$	−341.175	−	515.460i	−0.402329	−	0.607854i
$849$	−188.637	+	580.564i	−0.222187	+	0.683820i
$850$	61.5103	−	144.035i	0.0723651	−	0.169453i
$851$	−414.999	+	571.197i	−0.487661	+	0.671207i
$852$	−362.403	−	65.5332i	−0.425356	−	0.0769169i
$853$	−268.775	−	827.205i	−0.315094	−	0.969760i	−0.975716	−	0.219041i	$-0.929707\pi$
$853$	−268.775	−	827.205i	−0.315094	−	0.969760i	0.660622	−	0.750719i	$-0.270293\pi$
$854$	98.4852	−	1098.09i	0.115322	−	1.28582i
$855$	−214.360	−	295.041i	−0.250714	−	0.345078i
$856$	−123.627	+	449.592i	−0.144425	+	0.525224i
$857$	−515.903			−0.601987			−0.300993	−	0.953626i	$-0.597318\pi$
$857$	−515.903			−0.601987			−0.300993	+	0.953626i	$0.597318\pi$
$858$	1217.29	−	171.526i	1.41875	−	0.199914i
$859$			1004.50i			1.16938i	0.811256	+	0.584691i	$0.198784\pi$
$859$			1004.50i			1.16938i	−0.811256	+	0.584691i	$0.801216\pi$
$860$	−93.8798	+	89.8703i	−0.109163	+	0.104500i
$861$	1044.70	−	759.022i	1.21336	−	0.881558i
$862$	−17.5958	+	196.190i	−0.0204127	+	0.227598i
$863$	−189.314	+	61.5119i	−0.219367	+	0.0712768i	−0.416639	−	0.909072i	$-0.636792\pi$
$863$	−189.314	+	61.5119i	−0.219367	+	0.0712768i	0.197271	+	0.980349i	$0.436792\pi$
$864$	347.125	+	46.4707i	0.401765	+	0.0537855i
$865$	398.375	+	289.437i	0.460549	+	0.334609i
$866$	−249.062	+	583.213i	−0.287601	+	0.673456i
$867$	162.012	+	52.6408i	0.186865	+	0.0607160i
$868$	−66.8047	+	124.329i	−0.0769639	+	0.143237i
$869$	−505.861	+	584.924i	−0.582119	+	0.673100i
$870$	479.131	+	801.363i	0.550726	+	0.921107i
$871$	782.602	+	254.283i	0.898509	+	0.291943i
$872$	−210.516	−	263.473i	−0.241417	−	0.302148i
$873$	575.211	+	417.915i	0.658890	+	0.478712i
$874$	−1246.64	−	1088.47i	−1.42636	−	1.24539i
$875$	107.300	−	34.8639i	0.122629	−	0.0398445i
$876$	288.721	+	598.581i	0.329590	+	0.683312i
$877$	264.570	−	192.222i	0.301677	−	0.219181i	−0.426640	−	0.904421i	$-0.640303\pi$
$877$	264.570	−	192.222i	0.301677	−	0.219181i	0.728317	+	0.685240i	$0.240303\pi$
$878$	278.319	−	63.6158i	0.316992	−	0.0724554i
$879$			389.876i			0.443545i
$880$	270.174	−	286.157i	0.307016	−	0.325179i
$881$	−1330.90			−1.51066			−0.755332	−	0.655342i	$-0.772524\pi$
$881$	−1330.90			−1.51066			−0.755332	+	0.655342i	$0.772524\pi$
$882$	145.785	+	637.812i	0.165290	+	0.723143i
$883$	43.4139	+	59.7541i	0.0491663	+	0.0676716i	0.832892	−	0.553435i	$-0.186683\pi$
$883$	43.4139	+	59.7541i	0.0491663	+	0.0676716i	−0.783726	+	0.621107i	$0.786683\pi$
$884$	−808.937	+	390.185i	−0.915087	+	0.441385i
$885$	103.421	+	318.299i	0.116860	+	0.359659i
$886$	−374.813	+	429.278i	−0.423040	+	0.484513i
$887$	−302.036	+	415.718i	−0.340515	+	0.468678i	−0.944592	−	0.328248i	$-0.893542\pi$
$887$	−302.036	+	415.718i	−0.340515	+	0.468678i	0.604077	+	0.796926i	$0.293542\pi$
$888$	547.475	−	437.434i	0.616525	−	0.492606i
$889$	152.932	−	470.675i	0.172026	−	0.529443i
$890$	−590.268	+	352.918i	−0.663222	+	0.396537i
$891$	926.254	−	559.759i	1.03957	−	0.628237i
$892$	521.213	+	280.058i	0.584319	+	0.313966i
$893$	−403.815	+	1242.81i	−0.452200	+	1.39173i
$894$	−117.920	−	50.3581i	−0.131902	−	0.0563290i
$895$	60.0917	−	82.7091i	0.0671415	−	0.0924124i
$896$	756.939	−	1046.63i	0.844798	−	1.16811i
$897$	542.468	+	1669.55i	0.604758	+	1.86125i
$898$	−828.794	−	74.3325i	−0.922933	−	0.0827756i
$899$	110.089	+	151.525i	0.122457	+	0.168548i
$900$	85.6381	+	89.4588i	0.0951535	+	0.0993986i
$901$	605.080			0.671565
$902$	−649.074	+	316.864i	−0.719595	+	0.351291i
$903$			571.503i			0.632894i
$904$	−1571.04	−	431.999i	−1.73787	−	0.477875i
$905$	55.7908	−	40.5344i	0.0616473	−	0.0447894i
$906$	1824.85	+	163.666i	2.01418	+	0.180647i
$907$	874.489	−	284.139i	0.964156	−	0.313273i	0.215701	−	0.976459i	$-0.430796\pi$
$907$	874.489	−	284.139i	0.964156	−	0.313273i	0.748454	+	0.663186i	$0.230796\pi$
$908$	−194.055	+	1073.13i	−0.213716	+	1.18187i
$909$	638.030	+	463.556i	0.701904	+	0.509963i
$910$	−594.987	−	254.090i	−0.653832	−	0.279220i
$911$	−288.635	−	93.7832i	−0.316833	−	0.102945i	0.146283	−	0.989243i	$-0.453269\pi$
$911$	−288.635	−	93.7832i	−0.316833	−	0.102945i	−0.463117	+	0.886297i	$0.653269\pi$
$912$	906.612	+	1369.74i	0.994092	+	1.50191i
$913$	115.797	−	1363.48i	0.126832	−	1.49341i
$914$	−344.821	+	206.167i	−0.377265	+	0.225565i
$915$	−452.804	−	147.125i	−0.494867	−	0.160792i
$916$	−30.7353	−	225.839i	−0.0335539	−	0.246549i
$917$	−1488.66	−	1081.57i	−1.62340	−	1.17947i
$918$	−225.475	+	258.239i	−0.245615	+	0.281306i
$919$	412.101	−	133.900i	0.448423	−	0.145701i	−0.0760956	−	0.997101i	$-0.524245\pi$
$919$	412.101	−	133.900i	0.448423	−	0.145701i	0.524518	+	0.851399i	$0.324245\pi$
$920$	469.310	+	309.159i	0.510119	+	0.336043i
$921$	765.835	−	556.412i	0.831525	−	0.604138i
$922$	380.225	+	1663.48i	0.412391	+	1.80421i
$923$		−	338.642i		−	0.366893i
$924$	−87.4256	−	1728.40i	−0.0946165	−	1.87057i
$925$	−112.369			−0.121480
$926$	−372.368	+	85.1127i	−0.402125	+	0.0919143i
$927$	−218.992	−	301.417i	−0.236238	−	0.325154i
$928$	−814.583	−	1508.11i	−0.877783	−	1.62512i
$929$	102.465	+	315.354i	0.110296	+	0.339455i	0.990937	−	0.134329i	$-0.0428877\pi$
$929$	102.465	+	315.354i	0.110296	+	0.339455i	−0.880641	+	0.473784i	$0.842888\pi$
$930$	45.9125	+	40.0874i	0.0493683	+	0.0431047i
$931$	817.911	−	1125.76i	0.878530	−	1.20919i
$932$	−99.8326	−	733.557i	−0.107117	−	0.787079i
$933$	268.616	−	826.715i	0.287906	−	0.886082i
$934$	−645.579	−	1079.75i	−0.691198	−	1.15605i
$935$	87.6122	+	375.137i	0.0937029	+	0.401216i
$936$	−32.5244	−	709.417i	−0.0347483	−	0.757924i
$937$	92.0134	−	283.188i	0.0982000	−	0.302229i	−0.889874	−	0.456206i	$-0.849208\pi$
$937$	92.0134	−	283.188i	0.0982000	−	0.302229i	0.988074	+	0.153977i	$0.0492082\pi$
$938$	454.963	−	1065.36i	0.485035	−	1.13577i
$939$	438.537	−	603.595i	0.467026	−	0.642806i
$940$	78.9631	−	436.671i	0.0840033	−	0.464544i
$941$	120.205	+	369.952i	0.127741	+	0.393148i	0.994391	−	0.105770i	$-0.0337308\pi$
$941$	120.205	+	369.952i	0.127741	+	0.393148i	−0.866649	+	0.498918i	$0.833731\pi$
$942$	26.5615	−	296.155i	0.0281969	−	0.314390i
$943$	−606.260	−	834.446i	−0.642906	−	0.884884i
$944$	−164.192	−	592.059i	−0.173933	−	0.627181i
$945$	−246.954			−0.261327
$946$	55.3956	−	314.828i	0.0585577	−	0.332799i
$947$		−	455.871i		−	0.481384i	−0.970602	−	0.240692i	$-0.922626\pi$
$947$		−	455.871i		−	0.481384i	0.970602	−	0.240692i	$-0.0773744\pi$
$948$	757.946	+	791.761i	0.799521	+	0.835191i
$949$	−494.383	+	359.190i	−0.520952	+	0.378494i
$950$	23.5286	−	262.340i	0.0247669	−	0.276147i
$951$	458.864	−	149.094i	0.482506	−	0.156776i
$952$	445.373	+	1183.33i	0.467829	+	1.24299i
$953$	1198.70	+	870.908i	1.25782	+	0.913859i	0.998649	−	0.0519722i	$-0.0165507\pi$
$953$	1198.70	+	870.908i	1.25782	+	0.913859i	0.259171	+	0.965831i	$0.416551\pi$
$954$	−187.905	+	440.005i	−0.196966	+	0.461221i
$955$	145.224	+	47.1862i	0.152067	+	0.0494096i
$956$	793.658	+	426.448i	0.830186	+	0.446075i
$957$	−2116.25	−	891.952i	−2.21134	−	0.932029i
$958$	732.898	+	1225.80i	0.765029	+	1.27954i
$959$	−437.376	−	142.112i	−0.456075	−	0.148188i
$960$	−367.779	−	419.372i	−0.383103	−	0.436846i
$961$	−767.574	−	557.675i	−0.798724	−	0.580307i
$962$	485.391	+	423.807i	0.504564	+	0.440547i
$963$	343.241	−	111.526i	0.356429	−	0.115811i
$964$	1636.58	−	789.392i	1.69770	−	0.818871i
$965$	10.9772	−	7.97541i	0.0113753	−	0.00826467i
$966$	2409.19	−	550.672i	2.49399	−	0.570054i
$967$		−	455.350i		−	0.470889i	−0.971888	−	0.235445i	$-0.924345\pi$
$967$		−	455.350i		−	0.470889i	0.971888	−	0.235445i	$-0.0756546\pi$
$968$	−119.373	+	960.611i	−0.123319	+	0.992367i
$969$	−1607.89			−1.65933
$970$	114.422	+	500.598i	0.117961	+	0.516081i
$971$	−954.786	−	1314.15i	−0.983301	−	1.35340i	−0.935032	−	0.354564i	$-0.884629\pi$
$971$	−954.786	−	1314.15i	−0.983301	−	1.35340i	−0.0482698	−	0.998834i	$-0.515371\pi$
$972$	−495.238	−	1026.73i	−0.509504	−	1.05631i
$973$	569.649	+	1753.20i	0.585456	+	1.80185i
$974$	886.826	−	1015.69i	0.910499	−	1.04281i
$975$	−164.221	+	226.031i	−0.168432	+	0.231826i
$976$	818.686	+	306.094i	0.838818	+	0.313621i
$977$	437.833	−	1347.51i	0.448140	−	1.37923i	−0.430862	−	0.902418i	$-0.641791\pi$
$977$	437.833	−	1347.51i	0.448140	−	1.37923i	0.879003	−	0.476817i	$-0.158209\pi$
$978$	1001.23	−	598.628i	1.02375	−	0.612094i
$979$	656.993	−	1558.79i	0.671086	−	1.59222i
$980$	−223.658	+	416.247i	−0.228222	+	0.424742i
$981$	−80.6632	+	248.256i	−0.0822255	+	0.253064i
$982$	497.350	+	212.394i	0.506466	+	0.216287i
$983$	241.022	−	331.739i	0.245191	−	0.337476i	−0.668629	−	0.743596i	$-0.733119\pi$
$983$	241.022	−	331.739i	0.245191	−	0.337476i	0.913820	+	0.406120i	$0.133119\pi$
$984$	360.610	+	958.118i	0.366473	+	0.973697i
$985$	−206.688	−	636.119i	−0.209835	−	0.645806i
$986$	1671.12	+	149.878i	1.69485	+	0.152006i
$987$	−1147.00	−	1578.71i	−1.16211	−	1.59950i
$988$	−1091.06	+	1044.47i	−1.10432	+	1.05715i
$989$	456.482			0.461559
$990$	−300.002	−	52.7869i	−0.303032	−	0.0533201i
$991$		−	1155.69i		−	1.16618i	−0.812407	−	0.583090i	$-0.801843\pi$
$991$		−	1155.69i		−	1.16618i	0.812407	−	0.583090i	$-0.198157\pi$
$992$	−80.9961	−	77.1991i	−0.0816493	−	0.0778216i
$993$	128.685	−	93.4953i	0.129592	−	0.0941544i
$994$	−474.831	−	42.5864i	−0.477697	−	0.0428435i
$995$	−605.303	+	196.675i	−0.608345	+	0.197663i
$996$	−1908.53	−	345.119i	−1.91620	−	0.346505i
$997$	890.773	+	647.184i	0.893453	+	0.649132i	0.936776	−	0.349929i	$-0.113794\pi$
$997$	890.773	+	647.184i	0.893453	+	0.649132i	−0.0433229	+	0.999061i	$0.513794\pi$
$998$	−273.710	−	116.888i	−0.274258	−	0.117123i
$999$	233.924	+	76.0066i	0.234158	+	0.0760827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.s.a.31.15	yes	96
4.3	odd	2	inner	220.3.s.a.31.5	✓	96
11.5	even	5	inner	220.3.s.a.71.5	yes	96
44.27	odd	10	inner	220.3.s.a.71.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.s.a.31.5	✓	96	4.3	odd	2	inner
220.3.s.a.31.15	yes	96	1.1	even	1	trivial
220.3.s.a.71.5	yes	96	11.5	even	5	inner
220.3.s.a.71.15	yes	96	44.27	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.445649 + 1.94972i) q^{2} +(2.29101 + 3.15331i) q^{3} +(-3.60279 + 1.73778i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-5.12707 + 5.87209i) q^{6} +(-5.93140 + 8.16388i) q^{7} +(-4.99376 - 6.24999i) q^{8} +(-1.91346 + 5.88902i) q^{9} +(-3.83838 + 2.29495i) q^{10} +(4.27229 - 10.1364i) q^{11} +(-13.7338 - 7.37944i) q^{12} +(4.43010 - 13.6344i) q^{13} +(-18.5606 - 7.92633i) q^{14} +(-5.12286 + 7.05101i) q^{15} +(9.96024 - 12.5217i) q^{16} +(4.83979 + 14.8953i) q^{17} +(-12.3347 - 1.10627i) q^{18} +(15.4818 + 21.3089i) q^{19} +(-6.18508 - 6.46102i) q^{20} -39.3321 q^{21} +(21.6671 + 3.81245i) q^{22} +31.4161i q^{23} +(8.26736 - 30.0657i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(28.5576 + 2.56126i) q^{26} +(10.4088 - 3.38201i) q^{27} +(7.18260 - 39.7202i) q^{28} +(-43.3341 - 31.4841i) q^{29} +(-16.0305 - 6.84585i) q^{30} +(-3.32552 - 1.08053i) q^{31} +(28.8526 + 13.8393i) q^{32} +(41.7512 - 9.75089i) q^{33} +(-26.8849 + 16.0743i) q^{34} +(-21.4600 - 6.97278i) q^{35} +(-3.34003 - 24.5421i) q^{36} +(18.1817 + 13.2098i) q^{37} +(-34.6469 + 39.6815i) q^{38} +(53.1430 - 17.2672i) q^{39} +(9.84079 - 14.9385i) q^{40} +(-26.5611 + 19.2978i) q^{41} +(-17.5283 - 76.6865i) q^{42} -14.5302i q^{43} +(2.22275 + 43.9438i) q^{44} -13.8459 q^{45} +(-61.2525 + 14.0006i) q^{46} +(29.1619 + 40.1379i) q^{47} +(62.3039 + 2.72027i) q^{48} +(-16.3255 - 50.2447i) q^{49} +(-7.53276 - 6.57704i) q^{50} +(-35.8816 + 49.3868i) q^{51} +(7.73293 + 56.8206i) q^{52} +(11.9385 - 36.7430i) q^{53} +(11.2326 + 18.7870i) q^{54} +(24.5085 + 2.08145i) q^{55} +(80.6441 - 3.69727i) q^{56} +(-31.7245 + 97.6379i) q^{57} +(42.0732 - 98.5201i) q^{58} +(22.5711 - 31.0665i) q^{59} +(6.20349 - 34.3057i) q^{60} +(16.8808 + 51.9537i) q^{61} +(0.624706 - 6.96536i) q^{62} +(-36.7277 - 50.5514i) q^{63} +(-14.1247 + 62.4219i) q^{64} +32.0565 q^{65} +(37.6179 + 77.0575i) q^{66} +57.3989i q^{67} +(-43.3216 - 45.2544i) q^{68} +(-99.0646 + 71.9747i) q^{69} +(4.03131 - 44.9484i) q^{70} +(22.4655 - 7.29949i) q^{71} +(46.3617 - 17.4493i) q^{72} +(-34.4852 - 25.0550i) q^{73} +(-17.6526 + 41.3360i) q^{74} +(-18.5347 - 6.02228i) q^{75} +(-92.8080 - 49.8676i) q^{76} +(57.4120 + 95.0018i) q^{77} +(57.3493 + 95.9187i) q^{78} +(-66.8614 - 21.7246i) q^{79} +(33.5114 + 12.5294i) q^{80} +(79.5966 + 57.8303i) q^{81} +(-49.4621 - 43.1866i) q^{82} +(118.311 - 38.4415i) q^{83} +(141.706 - 68.3506i) q^{84} +(-28.3326 + 20.5849i) q^{85} +(28.3297 - 6.47537i) q^{86} -208.776i q^{87} +(-84.6874 + 23.9173i) q^{88} +153.780 q^{89} +(-6.17043 - 26.9956i) q^{90} +(85.0332 + 117.038i) q^{91} +(-54.5943 - 113.186i) q^{92} +(-4.21157 - 12.9619i) q^{93} +(-65.2615 + 74.7448i) q^{94} +(-34.6184 + 47.6482i) q^{95} +(22.4619 + 122.687i) q^{96} +(35.4826 - 109.204i) q^{97} +(90.6875 - 54.2216i) q^{98} +(51.5189 + 44.5553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} - 4 q^{4} + 120 q^{5} + 20 q^{6} - 10 q^{8} + 64 q^{9} + 10 q^{10} + 70 q^{12} - 20 q^{13} - 37 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} + 5 q^{20} - 15 q^{22} - 62 q^{24} - 120 q^{25} + 12 q^{26}+ \cdots + 158 q^{98}+O(q^{100}) \) 96 * q + 2 * q^2 - 4 * q^4 + 120 * q^5 + 20 * q^6 - 10 * q^8 + 64 * q^9 + 10 * q^10 + 70 * q^12 - 20 * q^13 - 37 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 + 5 * q^20 - 15 * q^22 - 62 * q^24 - 120 * q^25 + 12 * q^26 - 200 * q^28 + 72 * q^29 + 40 * q^30 - 348 * q^32 - 60 * q^33 - 246 * q^34 + 26 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 - 25 * q^42 - 67 * q^44 - 40 * q^45 - 85 * q^46 + 213 * q^48 - 28 * q^49 + 10 * q^50 + 312 * q^52 - 224 * q^53 + 752 * q^54 + 660 * q^56 - 204 * q^57 + 88 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 + 44 * q^64 - 40 * q^65 + 75 * q^66 - 117 * q^68 + 32 * q^69 - 75 * q^70 - 198 * q^72 - 64 * q^73 - 672 * q^74 - 1280 * q^76 + 80 * q^77 - 1132 * q^78 - 125 * q^80 - 44 * q^81 - 301 * q^82 - 348 * q^84 - 60 * q^85 + 470 * q^86 + 5 * q^88 + 176 * q^89 - 162 * q^92 + 280 * q^93 + 394 * q^94 + 1143 * q^96 + 204 * q^97 + 158 * q^98

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