LMFDB - Embedded newform 220.3.s.b.71.19

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			71.19
Character	$\chi$	$=$	220.71
Dual form			220.3.s.b.31.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.56127 - 1.24997i) q^{2} +(3.38992 - 4.66582i) q^{3} +(0.875130 - 3.90309i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-0.539578 - 11.5219i) q^{6} +(3.89563 + 5.36188i) q^{7} +(-3.51245 - 7.18768i) q^{8} +(-7.49721 - 23.0740i) q^{9} +(1.57942 + 4.18395i) q^{10} +(-2.32357 + 10.7518i) q^{11} +(-15.2445 - 17.3144i) q^{12} +(4.33912 + 13.3544i) q^{13} +(12.7844 + 3.50190i) q^{14} +(7.58009 + 10.4331i) q^{15} +(-14.4683 - 6.83143i) q^{16} +(0.298562 - 0.918880i) q^{17} +(-40.5471 - 26.6535i) q^{18} +(11.1667 - 15.3697i) q^{19} +(7.69573 + 4.55805i) q^{20} +38.2235 q^{21} +(9.81174 + 19.6909i) q^{22} +38.7913i q^{23} +(-45.4434 - 7.97716i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(23.4672 + 15.4261i) q^{26} +(-83.7093 - 27.1988i) q^{27} +(24.3371 - 10.5127i) q^{28} +(-2.16652 + 1.57407i) q^{29} +(24.8757 + 6.81397i) q^{30} +(-32.0719 + 10.4208i) q^{31} +(-31.1280 + 7.41928i) q^{32} +(42.2893 + 47.2891i) q^{33} +(-0.682440 - 1.80781i) q^{34} +(-14.0945 + 4.57959i) q^{35} +(-96.6212 + 9.06954i) q^{36} +(17.4791 - 12.6993i) q^{37} +(-1.77742 - 37.9544i) q^{38} +(77.0187 + 25.0249i) q^{39} +(17.7125 - 2.50311i) q^{40} +(14.6436 + 10.6392i) q^{41} +(59.6772 - 47.7784i) q^{42} -63.8202i q^{43} +(39.9318 + 18.4783i) q^{44} +54.2503 q^{45} +(48.4881 + 60.5637i) q^{46} +(5.05424 - 6.95657i) q^{47} +(-80.9206 + 44.3485i) q^{48} +(1.56803 - 4.82591i) q^{49} +(-9.98905 + 0.467793i) q^{50} +(-3.27523 - 4.50797i) q^{51} +(55.9209 - 5.24913i) q^{52} +(-23.1315 - 71.1913i) q^{53} +(-164.691 + 62.1698i) q^{54} +(-21.2595 - 12.3707i) q^{55} +(24.8562 - 46.8339i) q^{56} +(-33.8580 - 104.204i) q^{57} +(-1.41498 + 5.16564i) q^{58} +(22.5173 + 30.9924i) q^{59} +(47.3549 - 20.4555i) q^{60} +(2.29515 - 7.06375i) q^{61} +(-37.0472 + 56.3588i) q^{62} +(94.5139 - 130.087i) q^{63} +(-39.3254 + 50.4927i) q^{64} -31.3982 q^{65} +(125.135 + 20.9706i) q^{66} +110.957i q^{67} +(-3.32519 - 1.96946i) q^{68} +(180.993 + 131.499i) q^{69} +(-16.2810 + 24.7678i) q^{70} +(14.9941 + 4.87187i) q^{71} +(-139.515 + 134.934i) q^{72} +(48.5079 - 35.2430i) q^{73} +(11.4158 - 41.6756i) q^{74} +(-27.4250 + 8.91093i) q^{75} +(-50.2170 - 57.0353i) q^{76} +(-66.7016 + 29.4263i) q^{77} +(151.527 - 57.2008i) q^{78} +(-72.5257 + 23.5650i) q^{79} +(24.5252 - 26.0483i) q^{80} +(-234.021 + 170.026i) q^{81} +(36.1612 - 1.69345i) q^{82} +(23.6466 + 7.68324i) q^{83} +(33.4505 - 149.190i) q^{84} +(1.74781 + 1.26986i) q^{85} +(-79.7736 - 99.6405i) q^{86} +15.4446i q^{87} +(85.4418 - 21.0641i) q^{88} -5.75178 q^{89} +(84.6994 - 67.8115i) q^{90} +(-54.7013 + 75.2898i) q^{91} +(151.406 + 33.9474i) q^{92} +(-60.0996 + 184.968i) q^{93} +(-0.804491 - 17.1788i) q^{94} +(24.9696 + 34.3677i) q^{95} +(-70.9044 + 170.389i) q^{96} +(-24.8791 - 76.5699i) q^{97} +(-3.58414 - 9.49455i) q^{98} +(265.508 - 26.9943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} + 16 q^{4} - 120 q^{5} - 20 q^{6} - 10 q^{8} + 64 q^{9} - 10 q^{10} - 70 q^{12} + 20 q^{13} + 83 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} - 25 q^{20} + 35 q^{22} - 62 q^{24} - 120 q^{25}+ \cdots - 1042 q^{98}+O(q^{100}) $ 96 * q + 2 * q^2 + 16 * q^4 - 120 * q^5 - 20 * q^6 - 10 * q^8 + 64 * q^9 - 10 * q^10 - 70 * q^12 + 20 * q^13 + 83 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 - 25 * q^20 + 35 * q^22 - 62 * q^24 - 120 * q^25 - 88 * q^26 - 130 * q^28 - 8 * q^29 + 40 * q^30 + 152 * q^32 + 180 * q^33 - 126 * q^34 - 394 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 + 275 * q^42 + 113 * q^44 + 40 * q^45 - 85 * q^46 + 353 * q^48 + 292 * q^49 + 10 * q^50 + 62 * q^52 - 224 * q^53 - 328 * q^54 + 380 * q^56 - 364 * q^57 + 598 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 - 356 * q^64 - 40 * q^65 - 65 * q^66 - 117 * q^68 + 32 * q^69 - 165 * q^70 - 28 * q^72 + 16 * q^73 - 72 * q^74 - 720 * q^77 - 752 * q^78 - 235 * q^80 - 44 * q^81 + 49 * q^82 - 348 * q^84 + 60 * q^85 + 70 * q^86 - 165 * q^88 - 144 * q^89 + 778 * q^92 + 40 * q^93 + 254 * q^94 + 243 * q^96 + 204 * q^97 - 1042 * q^98

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$1$

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 $

$2$	1.56127	−	1.24997i	0.780635	−	0.624987i
$2$	1.56127	−	1.24997i	0.780635	−	0.624987i
$3$	3.38992	−	4.66582i	1.12997	−	1.55527i	0.341853	−	0.939753i	$-0.388945\pi$
$3$	3.38992	−	4.66582i	1.12997	−	1.55527i	0.788120	−	0.615522i	$-0.211055\pi$
$4$	0.875130	−	3.90309i	0.218782	−	0.975774i
$5$	−0.690983	+	2.12663i	−0.138197	+	0.425325i
$5$	−0.690983	+	2.12663i	−0.138197	+	0.425325i
$6$	−0.539578	−	11.5219i	−0.0899297	−	1.92032i
$7$	3.89563	+	5.36188i	0.556519	+	0.765983i	0.990879	−	0.134757i	$-0.0430252\pi$
$7$	3.89563	+	5.36188i	0.556519	+	0.765983i	−0.434359	+	0.900740i	$0.643025\pi$
$8$	−3.51245	−	7.18768i	−0.439057	−	0.898459i
$9$	−7.49721	−	23.0740i	−0.833023	−	2.56378i
$10$	1.57942	+	4.18395i	0.157942	+	0.418395i
$11$	−2.32357	+	10.7518i	−0.211234	+	0.977436i
$11$	−2.32357	+	10.7518i	−0.211234	+	0.977436i
$12$	−15.2445	−	17.3144i	−1.27038	−	1.44287i
$13$	4.33912	+	13.3544i	0.333778	+	1.02726i	0.967321	+	0.253556i	$0.0816002\pi$
$13$	4.33912	+	13.3544i	0.333778	+	1.02726i	−0.633542	+	0.773708i	$0.718400\pi$
$14$	12.7844	+	3.50190i	0.913168	+	0.250136i
$15$	7.58009	+	10.4331i	0.505339	+	0.695540i
$16$	−14.4683	−	6.83143i	−0.904268	−	0.426964i
$17$	0.298562	−	0.918880i	0.0175625	−	0.0540517i	−0.941891	−	0.335918i	$-0.890953\pi$
$17$	0.298562	−	0.918880i	0.0175625	−	0.0540517i	0.959454	+	0.281866i	$0.0909535\pi$
$18$	−40.5471	−	26.6535i	−2.25262	−	1.48075i
$19$	11.1667	−	15.3697i	0.587723	−	0.808931i	−0.406792	−	0.913521i	$-0.633353\pi$
$19$	11.1667	−	15.3697i	0.587723	−	0.808931i	0.994516	+	0.104589i	$0.0333528\pi$
$20$	7.69573	+	4.55805i	0.384786	+	0.227902i
$21$	38.2235			1.82017
$22$	9.81174	+	19.6909i	0.445988	+	0.895039i
$23$			38.7913i			1.68658i	0.537459	+	0.843290i	$0.319384\pi$
$23$			38.7913i			1.68658i	−0.537459	+	0.843290i	$0.680616\pi$
$24$	−45.4434	−	7.97716i	−1.89347	−	0.332382i
$25$	−4.04508	−	2.93893i	−0.161803	−	0.117557i
$26$	23.4672	+	15.4261i	0.902586	+	0.593311i
$27$	−83.7093	−	27.1988i	−3.10034	−	1.00736i
$28$	24.3371	−	10.5127i	0.869183	−	0.375453i
$29$	−2.16652	+	1.57407i	−0.0747075	+	0.0542782i	−0.624512	−	0.781015i	$-0.714702\pi$
$29$	−2.16652	+	1.57407i	−0.0747075	+	0.0542782i	0.549805	+	0.835293i	$0.314702\pi$
$30$	24.8757	+	6.81397i	0.829189	+	0.227132i
$31$	−32.0719	+	10.4208i	−1.03458	+	0.336155i	−0.776599	−	0.629996i	$-0.783057\pi$
$31$	−32.0719	+	10.4208i	−1.03458	+	0.336155i	−0.257979	+	0.966150i	$0.583057\pi$
$32$	−31.1280	+	7.41928i	−0.972751	+	0.231853i
$33$	42.2893	+	47.2891i	1.28149	+	1.43300i
$34$	−0.682440	−	1.80781i	−0.0200718	−	0.0531710i
$35$	−14.0945	+	4.57959i	−0.402701	+	0.130846i
$36$	−96.6212	+	9.06954i	−2.68392	+	0.251932i
$37$	17.4791	−	12.6993i	0.472409	−	0.343225i	−0.325970	−	0.945380i	$-0.605691\pi$
$37$	17.4791	−	12.6993i	0.472409	−	0.343225i	0.798380	+	0.602155i	$0.205691\pi$
$38$	−1.77742	−	37.9544i	−0.0467743	−	0.998800i
$39$	77.0187	+	25.0249i	1.97484	+	0.641664i
$40$	17.7125	−	2.50311i	0.442814	−	0.0625779i
$41$	14.6436	+	10.6392i	0.357160	+	0.259492i	0.751866	−	0.659315i	$-0.229154\pi$
$41$	14.6436	+	10.6392i	0.357160	+	0.259492i	−0.394707	+	0.918807i	$0.629154\pi$
$42$	59.6772	−	47.7784i	1.42089	−	1.13758i
$43$		−	63.8202i		−	1.48419i	−0.670295	−	0.742095i	$-0.733832\pi$
$43$		−	63.8202i		−	1.48419i	0.670295	−	0.742095i	$-0.266168\pi$
$44$	39.9318	+	18.4783i	0.907542	+	0.419962i
$45$	54.2503			1.20556
$46$	48.4881	+	60.5637i	1.05409	+	1.31660i
$47$	5.05424	−	6.95657i	0.107537	−	0.148012i	−0.751856	−	0.659327i	$-0.770841\pi$
$47$	5.05424	−	6.95657i	0.107537	−	0.148012i	0.859394	+	0.511315i	$0.170841\pi$
$48$	−80.9206	+	44.3485i	−1.68585	+	0.923928i
$49$	1.56803	−	4.82591i	0.0320007	−	0.0984879i
$50$	−9.98905	+	0.467793i	−0.199781	+	0.00935586i
$51$	−3.27523	−	4.50797i	−0.0642202	−	0.0883915i
$52$	55.9209	−	5.24913i	1.07540	−	0.100945i
$53$	−23.1315	−	71.1913i	−0.436442	−	1.34323i	−0.891601	−	0.452821i	$-0.850417\pi$
$53$	−23.1315	−	71.1913i	−0.436442	−	1.34323i	0.455159	−	0.890410i	$-0.349583\pi$
$54$	−164.691	+	62.1698i	−3.04983	+	1.15129i
$55$	−21.2595	−	12.3707i	−0.386536	−	0.224921i
$56$	24.8562	−	46.8339i	0.443861	−	0.836320i
$57$	−33.8580	−	104.204i	−0.593999	−	1.82814i
$58$	−1.41498	+	5.16564i	−0.0243961	+	0.0890627i
$59$	22.5173	+	30.9924i	0.381649	+	0.525295i	0.956021	−	0.293300i	$-0.0947534\pi$
$59$	22.5173	+	30.9924i	0.381649	+	0.525295i	−0.574371	+	0.818595i	$0.694753\pi$
$60$	47.3549	−	20.4555i	0.789249	−	0.340925i
$61$	2.29515	−	7.06375i	0.0376254	−	0.115799i	−0.930480	−	0.366343i	$-0.880610\pi$
$61$	2.29515	−	7.06375i	0.0376254	−	0.115799i	0.968105	+	0.250544i	$0.0806096\pi$
$62$	−37.0472	+	56.3588i	−0.597536	+	0.909012i
$63$	94.5139	−	130.087i	1.50022	−	2.06488i
$64$	−39.3254	+	50.4927i	−0.614459	+	0.788949i
$65$	−31.3982			−0.483049
$66$	125.135	+	20.9706i	1.89599	+	0.317736i
$67$			110.957i			1.65608i	0.560670	+	0.828040i	$0.310544\pi$
$67$			110.957i			1.65608i	−0.560670	+	0.828040i	$0.689456\pi$
$68$	−3.32519	−	1.96946i	−0.0488999	−	0.0289626i
$69$	180.993	+	131.499i	2.62309	+	1.90579i
$70$	−16.2810	+	24.7678i	−0.232586	+	0.353826i
$71$	14.9941	+	4.87187i	0.211184	+	0.0686179i	0.412699	−	0.910868i	$-0.364586\pi$
$71$	14.9941	+	4.87187i	0.211184	+	0.0686179i	−0.201514	+	0.979486i	$0.564586\pi$
$72$	−139.515	+	134.934i	−1.93771	+	1.87408i
$73$	48.5079	−	35.2430i	0.664491	−	0.482781i	−0.203685	−	0.979036i	$-0.565292\pi$
$73$	48.5079	−	35.2430i	0.664491	−	0.482781i	0.868177	+	0.496255i	$0.165292\pi$
$74$	11.4158	−	41.6756i	0.154268	−	0.563184i
$75$	−27.4250	+	8.91093i	−0.365667	+	0.118812i
$76$	−50.2170	−	57.0353i	−0.660750	−	0.750465i
$77$	−66.7016	+	29.4263i	−0.866255	+	0.382160i
$78$	151.527	−	57.2008i	1.94266	−	0.733343i
$79$	−72.5257	+	23.5650i	−0.918046	+	0.298291i	−0.729665	−	0.683805i	$-0.760324\pi$
$79$	−72.5257	+	23.5650i	−0.918046	+	0.298291i	−0.188381	+	0.982096i	$0.560324\pi$
$80$	24.5252	−	26.0483i	0.306566	−	0.325603i
$81$	−234.021	+	170.026i	−2.88915	+	2.09909i
$82$	36.1612	−	1.69345i	0.440991	−	0.0206518i
$83$	23.6466	+	7.68324i	0.284898	+	0.0925691i	0.447980	−	0.894043i	$-0.352143\pi$
$83$	23.6466	+	7.68324i	0.284898	+	0.0925691i	−0.163082	+	0.986613i	$0.552143\pi$
$84$	33.4505	−	149.190i	0.398220	−	1.77607i
$85$	1.74781	+	1.26986i	0.0205625	+	0.0149395i
$86$	−79.7736	−	99.6405i	−0.927600	−	1.15861i
$87$			15.4446i			0.177524i
$88$	85.4418	−	21.0641i	0.970930	−	0.239365i
$89$	−5.75178			−0.0646268			−0.0323134	−	0.999478i	$-0.510287\pi$
$89$	−5.75178			−0.0646268			−0.0323134	+	0.999478i	$0.510287\pi$
$90$	84.6994	−	67.8115i	0.941104	−	0.753461i
$91$	−54.7013	+	75.2898i	−0.601113	+	0.827361i
$92$	151.406	+	33.9474i	1.64572	+	0.368994i
$93$	−60.0996	+	184.968i	−0.646233	+	1.98890i
$94$	−0.804491	−	17.1788i	−0.00855841	−	0.182753i
$95$	24.9696	+	34.3677i	0.262838	+	0.361765i
$96$	−70.9044	+	170.389i	−0.738588	+	1.77488i
$97$	−24.8791	−	76.5699i	−0.256485	−	0.789380i	−0.993533	−	0.113540i	$-0.963781\pi$
$97$	−24.8791	−	76.5699i	−0.256485	−	0.789380i	0.737048	−	0.675840i	$-0.236219\pi$
$98$	−3.58414	−	9.49455i	−0.0365728	−	0.0968831i
$99$	265.508	−	26.9943i	2.68189	−	0.272670i
$100$	−15.0109	+	13.2164i	−0.150109	+	0.132164i
$101$	−20.8659	−	64.2185i	−0.206593	−	0.635827i	−0.999644	−	0.0266722i	$-0.991509\pi$
$101$	−20.8659	−	64.2185i	−0.206593	−	0.635827i	0.793052	−	0.609154i	$-0.208491\pi$
$102$	−10.7484	−	2.94420i	−0.105376	−	0.0288647i
$103$	22.5458	+	31.0316i	0.218891	+	0.301278i	0.904314	−	0.426867i	$-0.140383\pi$
$103$	22.5458	+	31.0316i	0.218891	+	0.301278i	−0.685423	+	0.728145i	$0.740383\pi$
$104$	80.7464	−	78.0950i	0.776408	−	0.750913i
$105$	−26.4118	+	81.2871i	−0.251541	+	0.774163i
$106$	−125.102	−	82.2351i	−1.18020	−	0.775803i
$107$	−99.6165	+	137.110i	−0.930995	+	1.28141i	0.0284745	+	0.999595i	$0.490935\pi$
$107$	−99.6165	+	137.110i	−0.930995	+	1.28141i	−0.959470	+	0.281811i	$0.909065\pi$
$108$	−179.416	+	302.923i	−1.66126	+	2.80484i
$109$	31.4970			0.288963			0.144482	−	0.989507i	$-0.453849\pi$
$109$	31.4970			0.288963			0.144482	+	0.989507i	$0.453849\pi$
$110$	−48.6548	+	7.25987i	−0.442317	+	0.0659988i
$111$		−	124.604i		−	1.12256i
$112$	−19.7339	−	104.190i	−0.176195	−	0.930268i
$113$	−15.9626	−	11.5975i	−0.141262	−	0.102633i	0.514910	−	0.857244i	$-0.327825\pi$
$113$	−15.9626	−	11.5975i	−0.141262	−	0.102633i	−0.656172	+	0.754612i	$0.727825\pi$
$114$	−183.114	−	120.369i	−1.60626	−	1.05587i
$115$	−82.4947	−	26.8041i	−0.717345	−	0.233080i
$116$	4.24775	+	9.83364i	0.0366185	+	0.0847727i
$117$	275.609	−	200.242i	2.35564	−	1.71147i
$118$	73.8953	+	20.2415i	0.626232	+	0.171538i
$119$	6.09001	−	1.97876i	0.0511766	−	0.0166283i
$120$	48.3650	−	91.1290i	0.403042	−	0.759408i
$121$	−110.202	−	49.9651i	−0.910761	−	0.412934i
$122$	−5.24615	−	13.8973i	−0.0430012	−	0.113912i
$123$	99.2809	−	32.2583i	0.807162	−	0.262263i
$124$	12.6063	+	134.299i	0.101663	+	1.08306i
$125$	9.04508	−	6.57164i	0.0723607	−	0.0525731i
$126$	−15.0439	−	321.241i	−0.119396	−	2.54953i
$127$	−71.9285	−	23.3710i	−0.566366	−	0.184023i	0.0118176	−	0.999930i	$-0.496238\pi$
$127$	−71.9285	−	23.3710i	−0.566366	−	0.184023i	−0.578184	+	0.815907i	$0.696238\pi$
$128$	1.71710	+	127.988i	0.0134149	+	0.999910i
$129$	−297.774	−	216.345i	−2.30832	−	1.67710i
$130$	−49.0210	+	39.2469i	−0.377085	+	0.301899i
$131$			140.472i			1.07230i	0.844122	+	0.536152i	$0.180122\pi$
$131$			140.472i			1.07230i	−0.844122	+	0.536152i	$0.819878\pi$
$132$	221.582	−	123.675i	1.67865	−	0.936931i
$133$	125.912			0.946707
$134$	138.694	+	173.234i	1.03503	+	1.29279i
$135$	115.683	−	159.225i	0.856914	−	1.17944i
$136$	−7.65329	+	1.08155i	−0.0562742	+	0.00795260i
$137$	−20.5929	+	63.3784i	−0.150313	+	0.462616i	−0.997656	−	0.0684303i	$-0.978201\pi$
$137$	−20.5929	+	63.3784i	−0.150313	+	0.462616i	0.847343	+	0.531046i	$0.178201\pi$
$138$	446.951	−	20.9309i	3.23877	−	0.151674i
$139$	10.4486	+	14.3813i	0.0751698	+	0.103462i	0.844946	−	0.534851i	$-0.179632\pi$
$139$	10.4486	+	14.3813i	0.0751698	+	0.103462i	−0.769776	+	0.638314i	$0.779632\pi$
$140$	5.54003	+	59.0201i	0.0395717	+	0.421572i
$141$	−15.3247	−	47.1644i	−0.108685	−	0.334500i
$142$	29.4995	−	11.1359i	0.207743	−	0.0784218i
$143$	−153.666	+	15.6233i	−1.07459	+	0.109254i
$144$	−49.1568	+	385.059i	−0.341367	+	2.67402i
$145$	−1.85043	−	5.69503i	−0.0127616	−	0.0392761i
$146$	31.6810	−	115.657i	0.216993	−	0.792174i
$147$	−17.2013	−	23.6756i	−0.117016	−	0.161059i
$148$	−34.2702	−	79.3363i	−0.231555	−	0.536056i
$149$	−6.13795	+	18.8907i	−0.0411943	+	0.126783i	−0.969539	−	0.244938i	$-0.921232\pi$
$149$	−6.13795	+	18.8907i	−0.0411943	+	0.126783i	0.928344	+	0.371721i	$0.121232\pi$
$150$	−31.6794	+	48.1929i	−0.211196	+	0.321286i
$151$	84.5705	−	116.401i	0.560070	−	0.770870i	−0.431266	−	0.902225i	$-0.641933\pi$
$151$	84.5705	−	116.401i	0.560070	−	0.770870i	0.991335	+	0.131355i	$0.0419329\pi$
$152$	−149.695	−	26.2776i	−0.984836	−	0.172879i
$153$	−23.4406			−0.153207
$154$	−67.3571	+	129.318i	−0.437384	+	0.839726i
$155$		−	75.4056i		−	0.486488i
$156$	165.076	−	278.711i	1.05818	−	1.78661i
$157$	−165.663	−	120.361i	−1.05518	−	0.766632i	−0.0819879	−	0.996633i	$-0.526127\pi$
$157$	−165.663	−	120.361i	−1.05518	−	0.766632i	−0.973190	+	0.230002i	$0.926127\pi$
$158$	−83.7765	+	127.447i	−0.530231	+	0.806624i
$159$	−410.580	−	133.405i	−2.58226	−	0.839028i
$160$	5.73089	−	71.3243i	0.0358180	−	0.445777i
$161$	−207.994	+	151.117i	−1.29189	+	0.938614i
$162$	−152.842	+	557.977i	−0.943468	+	3.44430i
$163$	68.1503	−	22.1434i	0.418100	−	0.135849i	−0.0924094	−	0.995721i	$-0.529457\pi$
$163$	68.1503	−	22.1434i	0.418100	−	0.135849i	0.510509	+	0.859872i	$0.329457\pi$
$164$	54.3407	−	47.8445i	0.331346	−	0.291735i
$165$	−129.787	+	57.2575i	−0.786590	+	0.347015i
$166$	46.5225	−	17.5620i	0.280256	−	0.105795i
$167$	82.4307	−	26.7833i	0.493597	−	0.160379i	−0.0516327	−	0.998666i	$-0.516443\pi$
$167$	82.4307	−	26.7833i	0.493597	−	0.160379i	0.545229	+	0.838287i	$0.316443\pi$
$168$	−134.258	−	274.738i	−0.799156	−	1.63535i
$169$	−22.7891	+	16.5572i	−0.134847	+	0.0979718i
$170$	4.31610	−	0.202125i	0.0253888	−	0.00118897i
$171$	−438.360	−	142.432i	−2.56351	−	0.832935i
$172$	−249.096	−	55.8509i	−1.44823	−	0.324715i
$173$	121.777	+	88.4760i	0.703912	+	0.511422i	0.881204	−	0.472736i	$-0.156734\pi$
$173$	121.777	+	88.4760i	0.703912	+	0.511422i	−0.177292	+	0.984158i	$0.556734\pi$
$174$	19.3053	+	24.1131i	0.110950	+	0.138581i
$175$		−	33.1382i		−	0.189361i
$176$	107.068	−	139.687i	0.608342	−	0.793675i
$177$	220.937			1.24823
$178$	−8.98009	+	7.18958i	−0.0504499	+	0.0403909i
$179$	−149.343	+	205.552i	−0.834316	+	1.14834i	0.152789	+	0.988259i	$0.451175\pi$
$179$	−149.343	+	205.552i	−0.834316	+	1.14834i	−0.987104	+	0.160078i	$0.948825\pi$
$180$	47.4761	−	211.744i	0.263756	−	1.17636i
$181$	−43.9988	+	135.414i	−0.243087	+	0.748146i	0.752858	+	0.658183i	$0.228675\pi$
$181$	−43.9988	+	135.414i	−0.243087	+	0.748146i	−0.995945	+	0.0899626i	$0.971325\pi$
$182$	8.70687	+	185.923i	0.0478400	+	1.02155i
$183$	−25.1778	−	34.6543i	−0.137584	−	0.189368i
$184$	278.819	−	136.253i	1.51532	−	0.740504i
$185$	14.9290	+	45.9467i	0.0806971	+	0.248360i
$186$	137.373	+	363.907i	0.738564	+	1.95649i
$187$	9.18587	+	5.34516i	0.0491223	+	0.0285837i
$188$	−22.7290	−	25.8151i	−0.120899	−	0.137314i
$189$	−180.264	−	554.796i	−0.953778	−	2.93543i
$190$	81.9430	+	22.4459i	0.431279	+	0.118136i
$191$	−40.0789	−	55.1638i	−0.209837	−	0.288816i	0.691106	−	0.722753i	$-0.257124\pi$
$191$	−40.0789	−	55.1638i	−0.209837	−	0.288816i	−0.900943	+	0.433938i	$0.857124\pi$
$192$	102.280	+	354.652i	0.532711	+	1.84714i
$193$	80.1408	−	246.648i	0.415237	−	1.27797i	−0.496801	−	0.867864i	$-0.665492\pi$
$193$	80.1408	−	246.648i	0.415237	−	1.27797i	0.912039	−	0.410105i	$-0.134508\pi$
$194$	−134.553	−	88.4481i	−0.693574	−	0.455918i
$195$	−106.437	+	146.498i	−0.545832	+	0.751273i
$196$	−17.4637	−	10.3435i	−0.0891007	−	0.0527728i
$197$	46.5688			0.236390			0.118195	−	0.992990i	$-0.462289\pi$
$197$	46.5688			0.236390			0.118195	+	0.992990i	$0.462289\pi$
$198$	380.787	−	374.023i	1.92317	−	1.88900i
$199$		−	374.371i		−	1.88126i	−0.339433	−	0.940630i	$-0.610235\pi$
$199$		−	374.371i		−	1.88126i	0.339433	−	0.940630i	$-0.389765\pi$
$200$	−6.91588	+	39.3976i	−0.0345794	+	0.196988i
$201$	517.707	+	376.136i	2.57566	+	1.87133i
$202$	−112.849	−	74.1806i	−0.558657	−	0.367231i
$203$	−16.8799	−	5.48462i	−0.0831523	−	0.0270178i
$204$	−20.4613	+	8.83847i	−0.100300	+	0.0433259i
$205$	−32.7440	+	23.7899i	−0.159727	+	0.116048i
$206$	73.9888	+	20.2671i	0.359169	+	0.0983839i
$207$	895.072	−	290.827i	4.32402	−	1.40496i
$208$	28.4502	−	222.858i	0.136780	−	1.07143i
$209$	139.305	+	155.775i	0.666531	+	0.745335i
$210$	60.3708	+	159.925i	0.287480	+	0.761548i
$211$	137.129	−	44.5558i	0.649899	−	0.211165i	0.0345294	−	0.999404i	$-0.489007\pi$
$211$	137.129	−	44.5558i	0.649899	−	0.211165i	0.615370	+	0.788239i	$0.289007\pi$
$212$	−298.109	+	27.9826i	−1.40618	+	0.131993i
$213$	73.5600	−	53.4445i	0.345352	−	0.250913i
$214$	15.8561	+	338.584i	0.0740939	+	1.58217i
$215$	135.722	+	44.0987i	0.631264	+	0.205110i
$216$	98.5288	+	697.210i	0.456152	+	3.22782i
$217$	−180.816	−	131.370i	−0.833252	−	0.605393i
$218$	49.1753	−	39.3704i	0.225575	−	0.180598i
$219$		−	345.800i		−	1.57900i
$220$	−66.8887	+	72.1519i	−0.304040	+	0.327963i
$221$	13.5666			0.0613874
$222$	−155.752	−	194.541i	−0.701587	−	0.876311i
$223$	−91.8143	+	126.372i	−0.411723	+	0.566688i	−0.963638	−	0.267212i	$-0.913897\pi$
$223$	−91.8143	+	126.372i	−0.411723	+	0.566688i	0.551914	+	0.833901i	$0.313897\pi$
$224$	−161.045	−	138.002i	−0.718950	−	0.616080i
$225$	−37.4860	+	115.370i	−0.166605	+	0.512756i
$226$	−39.4185	+	1.84599i	−0.174418	+	0.00816809i
$227$	−41.3955	−	56.9760i	−0.182359	−	0.250996i	0.708044	−	0.706168i	$-0.249578\pi$
$227$	−41.3955	−	56.9760i	−0.182359	−	0.250996i	−0.890403	+	0.455172i	$0.849578\pi$
$228$	−436.348	+	40.9587i	−1.91381	+	0.179643i
$229$	2.37202	+	7.30031i	0.0103581	+	0.0318791i	0.956102	−	0.293034i	$-0.0946649\pi$
$229$	2.37202	+	7.30031i	0.0103581	+	0.0318791i	−0.945744	+	0.324913i	$0.894665\pi$
$230$	−162.301	+	61.2677i	−0.705656	+	0.266381i
$231$	−88.8149	+	410.971i	−0.384480	+	1.77910i
$232$	18.9237	+	10.0434i	0.0815676	+	0.0432905i
$233$	−104.167	−	320.595i	−0.447071	−	1.37594i	−0.880197	−	0.474609i	$-0.842589\pi$
$233$	−104.167	−	320.595i	−0.447071	−	1.37594i	0.433126	−	0.901333i	$-0.357411\pi$
$234$	180.004	−	657.136i	0.769246	−	2.80828i
$235$	11.3016	+	15.5554i	0.0480921	+	0.0661930i
$236$	140.672	−	60.7648i	0.596067	−	0.257478i
$237$	−135.906	+	418.276i	−0.573443	+	1.76488i
$238$	7.03475	−	10.7017i	0.0295578	−	0.0449653i
$239$	−232.624	+	320.180i	−0.973322	+	1.33966i	−0.0329718	+	0.999456i	$0.510497\pi$
$239$	−232.624	+	320.180i	−0.973322	+	1.33966i	−0.940351	+	0.340207i	$0.889503\pi$
$240$	−38.3980	−	202.732i	−0.159992	−	0.844717i
$241$	−273.414			−1.13450			−0.567250	−	0.823546i	$-0.691993\pi$
$241$	−273.414			−1.13450			−0.567250	+	0.823546i	$0.691993\pi$
$242$	−234.510	+	59.7407i	−0.969051	+	0.246862i
$243$			876.122i			3.60544i
$244$	−25.5619	−	15.1399i	−0.104762	−	0.0620487i
$245$	9.17942	+	6.66924i	0.0374670	+	0.0272214i
$246$	114.682	−	174.463i	0.466188	−	0.709197i
$247$	253.707	+	82.4345i	1.02716	+	0.333743i
$248$	187.552	+	193.920i	0.756260	+	0.781936i
$249$	116.009	−	84.2852i	0.465898	−	0.338495i
$250$	5.90744	−	21.5662i	0.0236298	−	0.0862649i
$251$	166.577	−	54.1240i	0.663651	−	0.215633i	0.0422276	−	0.999108i	$-0.486555\pi$
$251$	166.577	−	54.1240i	0.663651	−	0.215633i	0.621424	+	0.783475i	$0.286555\pi$
$252$	−425.031	−	482.740i	−1.68663	−	1.91563i
$253$	−417.076	−	90.1343i	−1.64852	−	0.356262i
$254$	−141.513	+	53.4203i	−0.557137	+	0.210316i
$255$	11.8499	−	3.85026i	0.0464702	−	0.0150991i
$256$	162.663	+	197.678i	0.635403	+	0.772181i
$257$	−127.701	+	92.7802i	−0.496891	+	0.361013i	−0.807828	−	0.589418i	$-0.799357\pi$
$257$	−127.701	+	92.7802i	−0.496891	+	0.361013i	0.310937	+	0.950430i	$0.399357\pi$
$258$	−735.331	+	34.4360i	−2.85012	+	0.133473i
$259$	136.185	+	44.2491i	0.525810	+	0.170846i
$260$	−27.4775	+	122.550i	−0.105683	+	0.471346i
$261$	52.5629	+	38.1892i	0.201390	+	0.146319i
$262$	175.586	+	219.314i	0.670176	+	0.837078i
$263$		−	351.128i		−	1.33509i	−0.744570	−	0.667545i	$-0.767345\pi$
$263$		−	351.128i		−	1.33509i	0.744570	−	0.667545i	$-0.232655\pi$
$264$	191.360	−	470.062i	0.724847	−	1.78054i
$265$	167.381			0.631625
$266$	196.583	−	157.387i	0.739033	−	0.591679i
$267$	−19.4981	+	26.8368i	−0.0730265	+	0.100512i
$268$	433.077	+	97.1021i	1.61596	+	0.362321i
$269$	−97.0167	+	298.587i	−0.360657	+	1.10999i	0.591999	+	0.805939i	$0.298339\pi$
$269$	−97.0167	+	298.587i	−0.360657	+	1.10999i	−0.952656	+	0.304050i	$0.901661\pi$
$270$	−18.4135	−	393.194i	−0.0681981	−	1.45627i
$271$	287.590	+	395.833i	1.06122	+	1.46064i	0.878662	+	0.477444i	$0.158437\pi$
$271$	287.590	+	395.833i	1.06122	+	1.46064i	0.182554	+	0.983196i	$0.441563\pi$
$272$	−10.5969	+	11.2550i	−0.0389594	+	0.0413787i
$273$	165.856	+	510.453i	0.607532	+	1.86979i
$274$	47.0703	+	124.691i	0.171789	+	0.455078i
$275$	40.9978	−	36.6631i	0.149083	−	0.133320i
$276$	671.648	−	591.356i	2.43351	−	2.14259i
$277$	71.6058	+	220.380i	0.258505	+	0.795595i	0.993119	+	0.117110i	$0.0373631\pi$
$277$	71.6058	+	220.380i	0.258505	+	0.795595i	−0.734614	+	0.678485i	$0.762637\pi$
$278$	34.2893	+	9.39256i	0.123343	+	0.0337862i
$279$	480.900	+	661.902i	1.72366	+	2.37241i
$280$	82.4230	+	85.2214i	0.294368	+	0.304362i
$281$	13.8962	−	42.7680i	0.0494525	−	0.152199i	−0.923281	−	0.384126i	$-0.874503\pi$
$281$	13.8962	−	42.7680i	0.0494525	−	0.152199i	0.972733	+	0.231927i	$0.0745029\pi$
$282$	−82.8802	−	54.4810i	−0.293902	−	0.193195i
$283$	119.917	−	165.051i	0.423734	−	0.583220i	−0.542767	−	0.839883i	$-0.682623\pi$
$283$	119.917	−	165.051i	0.423734	−	0.583220i	0.966501	+	0.256664i	$0.0826233\pi$
$284$	32.1371	−	54.2598i	0.113159	−	0.191056i
$285$	244.998			0.859644
$286$	−220.386	+	216.471i	−0.770580	+	0.756892i
$287$			119.963i			0.417991i
$288$	404.566	+	662.625i	1.40474	+	2.30078i
$289$	233.051	+	169.321i	0.806404	+	0.585887i
$290$	−10.0077	−	6.57849i	−0.0345092	−	0.0226845i
$291$	−441.600	−	143.484i	−1.51752	−	0.493074i
$292$	−95.1062	−	220.173i	−0.325706	−	0.754017i
$293$	−154.830	+	112.491i	−0.528430	+	0.383927i	−0.819770	−	0.572692i	$-0.805899\pi$
$293$	−154.830	+	112.491i	−0.528430	+	0.383927i	0.291340	+	0.956620i	$0.405899\pi$
$294$	−56.4498	−	15.4628i	−0.192006	−	0.0525946i
$295$	−81.4684	+	26.4707i	−0.276164	+	0.0897311i
$296$	−152.673	−	81.0286i	−0.515789	−	0.273745i
$297$	486.940	−	836.827i	1.63953	−	2.81760i
$298$	14.0299	+	37.1657i	0.0470800	+	0.124717i
$299$	−518.036	+	168.320i	−1.73256	+	0.562944i
$300$	10.7797	+	114.841i	0.0359325	+	0.382802i
$301$	342.196	−	248.620i	1.13686	−	0.825980i
$302$	−13.4612	−	287.445i	−0.0445735	−	0.951804i
$303$	−370.366	−	120.339i	−1.22233	−	0.397159i
$304$	−266.561	+	146.089i	−0.876844	+	0.480554i
$305$	13.4360	+	9.76186i	0.0440526	+	0.0320061i
$306$	−36.5972	+	29.3002i	−0.119599	+	0.0957523i
$307$		−	322.993i		−	1.05209i	−0.850456	−	0.526046i	$-0.823674\pi$
$307$		−	322.993i		−	1.05209i	0.850456	−	0.526046i	$-0.176326\pi$
$308$	56.4813	+	286.095i	0.183381	+	0.928878i
$309$	221.216			0.715911
$310$	−94.2551	−	117.729i	−0.304049	−	0.379770i
$311$	−79.7818	+	109.810i	−0.256533	+	0.353088i	−0.917786	−	0.397076i	$-0.870025\pi$
$311$	−79.7818	+	109.810i	−0.256533	+	0.353088i	0.661253	+	0.750163i	$0.270025\pi$
$312$	−90.6537	−	641.484i	−0.290557	−	2.05604i
$313$	121.940	−	375.291i	0.389583	−	1.19901i	−0.543517	−	0.839398i	$-0.682908\pi$
$313$	121.940	−	375.291i	0.389583	−	1.19901i	0.933100	−	0.359616i	$-0.117092\pi$
$314$	−409.093	+	19.1581i	−1.30284	+	0.0610129i
$315$	211.339	+	290.884i	0.670919	+	0.923440i
$316$	28.5071	+	303.697i	0.0902124	+	0.961066i
$317$	55.1546	+	169.748i	0.173989	+	0.535484i	0.999586	−	0.0287771i	$-0.00916131\pi$
$317$	55.1546	+	169.748i	0.173989	+	0.535484i	−0.825597	+	0.564261i	$0.809161\pi$
$318$	−807.779	+	304.932i	−2.54019	+	0.958906i
$319$	−11.8900	−	26.9514i	−0.0372727	−	0.0844872i
$320$	−80.2061	−	118.520i	−0.250644	−	0.370375i
$321$	302.041	+	929.586i	0.940937	+	2.89591i
$322$	−135.843	+	495.922i	−0.421874	+	1.54013i
$323$	−10.7889	−	14.8497i	−0.0334023	−	0.0459743i
$324$	458.830	+	1062.20i	1.41614	+	3.27840i
$325$	21.6956	−	66.7722i	0.0667557	−	0.205453i
$326$	78.7224	−	119.758i	0.241480	−	0.367355i
$327$	106.772	−	146.959i	0.326521	−	0.449417i
$328$	25.0361	−	142.623i	0.0763295	−	0.434825i
$329$	56.9898			0.173221
$330$	−131.063	+	251.625i	−0.397160	+	0.762501i
$331$			109.940i			0.332144i	0.986114	+	0.166072i	$0.0531084\pi$
$331$			109.940i			0.332144i	−0.986114	+	0.166072i	$0.946892\pi$
$332$	50.6822	−	85.5710i	0.152657	−	0.257744i
$333$	−424.070	−	308.105i	−1.27348	−	0.925240i
$334$	95.2181	−	144.852i	0.285084	−	0.433689i
$335$	−235.965	−	76.6696i	−0.704373	−	0.228865i
$336$	−553.029	−	261.121i	−1.64592	−	0.777146i
$337$	439.967	−	319.655i	1.30554	−	0.948531i	0.305548	−	0.952177i	$-0.401161\pi$
$337$	439.967	−	319.655i	1.30554	−	0.948531i	0.999993	+	0.00364587i	$0.00116052\pi$
$338$	−14.8838	+	54.3361i	−0.0440349	+	0.160758i
$339$	−108.224	+	35.1640i	−0.319244	+	0.103729i
$340$	6.48595	−	5.71059i	0.0190763	−	0.0167958i
$341$	−37.5209	−	369.044i	−0.110032	−	1.08224i
$342$	−862.435	+	325.564i	−2.52174	+	0.951942i
$343$	340.845	−	110.747i	0.993716	−	0.322878i
$344$	−458.719	+	224.165i	−1.33348	+	0.651643i
$345$	−404.714	+	294.042i	−1.17308	+	0.852295i
$346$	300.719	−	14.0828i	0.869130	−	0.0407019i
$347$	536.651	+	174.369i	1.54655	+	0.502503i	0.953173	−	0.302425i	$-0.0977960\pi$
$347$	536.651	+	174.369i	1.54655	+	0.502503i	0.593373	+	0.804928i	$0.297796\pi$
$348$	60.2816	+	13.5160i	0.173223	+	0.0388391i
$349$	155.114	+	112.697i	0.444452	+	0.322913i	0.787401	−	0.616441i	$-0.211426\pi$
$349$	155.114	+	112.697i	0.444452	+	0.322913i	−0.342949	+	0.939354i	$0.611426\pi$
$350$	−41.4219	−	51.7378i	−0.118348	−	0.147822i
$351$		−	1235.91i		−	3.52111i
$352$	−7.44246	−	351.921i	−0.0211434	−	0.999776i
$353$	−409.763			−1.16080			−0.580400	−	0.814331i	$-0.697104\pi$
$353$	−409.763			−1.16080			−0.580400	+	0.814331i	$0.697104\pi$
$354$	344.943	−	276.166i	0.974414	−	0.780129i
$355$	−20.7213	+	28.5204i	−0.0583699	+	0.0803392i
$356$	−5.03356	+	22.4497i	−0.0141392	+	0.0630611i
$357$	11.4121	−	35.1228i	0.0319666	−	0.0983831i
$358$	23.7710	+	507.597i	0.0663996	+	1.41787i
$359$	−247.736	−	340.980i	−0.690074	−	0.949805i	0.309926	−	0.950761i	$-0.399696\pi$
$359$	−247.736	−	340.980i	−0.690074	−	0.949805i	−1.00000		0.000955876i	$0.999696\pi$
$360$	−190.552	−	389.934i	−0.529310	−	1.08315i
$361$	0.0236123	+	0.0726710i	6.54079e−5	+	0.000201305i
$362$	100.570	+	266.416i	0.277819	+	0.735955i
$363$	−606.704	+	344.806i	−1.67136	+	0.949878i
$364$	245.993	+	279.393i	0.675804	+	0.767562i
$365$	41.4307	+	127.510i	0.113509	+	0.349344i
$366$	−82.6264	−	22.6331i	−0.225755	−	0.0618391i
$367$	−224.299	−	308.721i	−0.611168	−	0.841201i	0.385505	−	0.922706i	$-0.374027\pi$
$367$	−224.299	−	308.721i	−0.611168	−	0.841201i	−0.996673	+	0.0815052i	$0.974027\pi$
$368$	265.000	−	561.244i	0.720109	−	1.52512i
$369$	135.703	−	417.650i	0.367758	−	1.13184i
$370$	80.7403	+	53.0743i	0.218217	+	0.143444i
$371$	291.608	−	401.363i	0.786004	−	1.08184i
$372$	669.351	+	396.445i	1.79933	+	1.06571i
$373$	190.105			0.509665			0.254833	−	0.966985i	$-0.417980\pi$
$373$	190.105			0.509665			0.254833	+	0.966985i	$0.417980\pi$
$374$	21.0229	−	3.13687i	0.0562111	−	0.00838734i
$375$		−	64.4801i		−	0.171947i
$376$	−67.7544	−	11.8936i	−0.180198	−	0.0316320i
$377$	−30.4216	−	22.1026i	−0.0806938	−	0.0586275i
$378$	−974.921	−	640.861i	−2.57916	−	1.69540i
$379$	452.439	+	147.006i	1.19377	+	0.387879i	0.837465	−	0.546491i	$-0.184037\pi$
$379$	452.439	+	147.006i	1.19377	+	0.387879i	0.356304	+	0.934370i	$0.384037\pi$
$380$	155.992	−	67.3825i	0.410505	−	0.177322i
$381$	−352.877	+	256.380i	−0.926185	+	0.672913i
$382$	−131.527	−	36.0281i	−0.344312	−	0.0943144i
$383$	−166.773	+	54.1878i	−0.435438	+	0.141483i	−0.518530	−	0.855059i	$-0.673521\pi$
$383$	−166.773	+	54.1878i	−0.435438	+	0.141483i	0.0830917	+	0.996542i	$0.473521\pi$
$384$	602.993	+	425.859i	1.57029	+	1.10901i
$385$	−16.4892	−	162.183i	−0.0428291	−	0.421253i
$386$	−183.182	−	485.258i	−0.474565	−	1.25715i
$387$	−1472.59	+	478.473i	−3.80514	+	1.23636i
$388$	−320.632	+	30.0967i	−0.826371	+	0.0775689i
$389$	462.607	−	336.104i	1.18922	−	0.864020i	0.196040	−	0.980596i	$-0.437192\pi$
$389$	462.607	−	336.104i	1.18922	−	0.864020i	0.993182	+	0.116576i	$0.0371917\pi$
$390$	16.9418	+	361.767i	0.0434404	+	0.927608i
$391$	35.6446	+	11.5816i	0.0911625	+	0.0296205i
$392$	−40.1947	+	5.68026i	−0.102538	+	0.0144905i
$393$	655.417	+	476.188i	1.66773	+	1.21167i
$394$	72.7066	−	58.2098i	0.184534	−	0.147741i
$395$		−	170.518i		−	0.431691i
$396$	126.992	−	1059.92i	0.320688	−	2.67658i
$397$	−510.983			−1.28711			−0.643556	−	0.765399i	$-0.722542\pi$
$397$	−510.983			−1.28711			−0.643556	+	0.765399i	$0.722542\pi$
$398$	−467.954	−	584.494i	−1.17576	−	1.46858i
$399$	426.832	−	587.483i	1.06975	−	1.47239i
$400$	38.4484	+	70.1550i	0.0961210	+	0.175387i
$401$	8.52329	−	26.2320i	0.0212551	−	0.0654164i	−0.939866	−	0.341542i	$-0.889051\pi$
$401$	8.52329	−	26.2320i	0.0212551	−	0.0654164i	0.961121	+	0.276126i	$0.0890507\pi$
$402$	1278.44	−	59.8701i	3.18020	−	0.148931i
$403$	−278.328	−	383.085i	−0.690640	−	0.950584i
$404$	−268.911	+	25.2419i	−0.665622	+	0.0624799i
$405$	−199.878	−	615.161i	−0.493526	−	1.51892i
$406$	−33.2098	+	12.5365i	−0.0817974	+	0.0308781i
$407$	95.9267	+	217.440i	0.235692	+	0.534250i
$408$	−20.8977	+	39.3753i	−0.0512199	+	0.0965081i
$409$	−189.244	−	582.434i	−0.462700	−	1.42404i	−0.861852	−	0.507160i	$-0.830695\pi$
$409$	−189.244	−	582.434i	−0.462700	−	1.42404i	0.399152	−	0.916885i	$-0.369305\pi$
$410$	−21.3855	+	78.0716i	−0.0521596	+	0.190418i
$411$	225.904	+	310.930i	0.549645	+	0.756522i
$412$	140.850	−	60.8416i	0.341868	−	0.147674i
$413$	−78.4585	+	241.470i	−0.189972	+	0.584674i
$414$	1033.92	−	1572.88i	2.49740	−	3.79922i
$415$	−32.6788	+	44.9784i	−0.0787440	+	0.108382i
$416$	−234.149	−	383.504i	−0.562857	−	0.921885i
$417$	102.520			0.245852
$418$	412.208	+	69.0791i	0.986143	+	0.165261i
$419$			192.050i			0.458353i	0.973385	+	0.229177i	$0.0736033\pi$
$419$			192.050i			0.458353i	−0.973385	+	0.229177i	$0.926397\pi$
$420$	294.158	+	174.224i	0.700375	+	0.414820i
$421$	−245.399	−	178.293i	−0.582897	−	0.423499i	0.256871	−	0.966446i	$-0.417309\pi$
$421$	−245.399	−	178.293i	−0.582897	−	0.423499i	−0.839767	+	0.542947i	$0.817309\pi$
$422$	158.401	−	240.971i	0.375359	−	0.571021i
$423$	−198.409	−	64.4670i	−0.469052	−	0.152404i
$424$	−430.452	+	416.317i	−1.01522	+	0.981881i
$425$	−3.90823	+	2.83949i	−0.00919583	+	0.00668116i
$426$	48.0428	−	175.389i	0.112777	−	0.411712i
$427$	46.8160	−	15.2115i	0.109639	−	0.0356240i
$428$	447.977	+	508.802i	1.04668	+	1.18879i
$429$	−448.021	+	769.942i	−1.04434	+	1.79474i
$430$	267.020	−	100.799i	0.620978	−	0.234416i
$431$	704.763	−	228.991i	1.63518	−	0.531303i	0.659727	−	0.751505i	$-0.270672\pi$
$431$	704.763	−	228.991i	1.63518	−	0.531303i	0.975454	+	0.220203i	$0.0706719\pi$
$432$	1025.32	+	965.374i	2.37344	+	2.23466i
$433$	435.728	−	316.575i	1.00630	−	0.731120i	0.0428702	−	0.999081i	$-0.486350\pi$
$433$	435.728	−	316.575i	1.00630	−	0.731120i	0.963430	+	0.267961i	$0.0863498\pi$
$434$	−446.511	+	20.9104i	−1.02883	+	0.0481806i
$435$	−32.8448	−	10.6719i	−0.0755053	−	0.0245332i
$436$	27.5639	−	122.936i	0.0632201	−	0.281963i
$437$	596.211	+	433.172i	1.36433	+	0.991241i
$438$	−432.241	−	539.888i	−0.986852	−	1.23262i
$439$			48.3719i			0.110186i	0.998481	+	0.0550932i	$0.0175456\pi$
$439$			48.3719i			0.110186i	−0.998481	+	0.0550932i	$0.982454\pi$
$440$	−14.2434	+	196.258i	−0.0323713	+	0.446040i
$441$	−123.109			−0.279159
$442$	21.1812	−	16.9579i	0.0479212	−	0.0383663i
$443$	284.289	−	391.290i	0.641735	−	0.883273i	−0.356972	−	0.934115i	$-0.616191\pi$
$443$	284.289	−	391.290i	0.641735	−	0.883273i	0.998707	+	0.0508426i	$0.0161907\pi$
$444$	−486.343	−	109.045i	−1.09537	−	0.245597i
$445$	3.97438	−	12.2319i	0.00893120	−	0.0274874i
$446$	14.6142	+	312.066i	0.0327673	+	0.699699i
$447$	67.3334	+	92.6765i	0.150634	+	0.207330i
$448$	−423.933	−	14.1566i	−0.946280	−	0.0315996i
$449$	12.3343	+	37.9612i	0.0274707	+	0.0845460i	0.963852	−	0.266439i	$-0.0858469\pi$
$449$	12.3343	+	37.9612i	0.0274707	+	0.0845460i	−0.936381	+	0.350985i	$0.885847\pi$
$450$	85.6839	+	226.981i	0.190409	+	0.504401i
$451$	−148.415	+	132.724i	−0.329081	+	0.294287i
$452$	−59.2355	+	52.1542i	−0.131052	+	0.115385i
$453$	−256.421	−	789.182i	−0.566050	−	1.74212i
$454$	−135.848	−	37.2116i	−0.299225	−	0.0819640i
$455$	−122.316	−	168.353i	−0.268826	−	0.370007i
$456$	−630.061	+	609.372i	−1.38171	+	1.33634i
$457$	264.585	−	814.309i	0.578961	−	1.78186i	−0.0433179	−	0.999061i	$-0.513793\pi$
$457$	264.585	−	814.309i	0.578961	−	1.78186i	0.622278	−	0.782796i	$-0.286207\pi$
$458$	12.8286	+	8.43281i	0.0280100	+	0.0184122i
$459$	−49.9848	+	68.7982i	−0.108899	+	0.149887i
$460$	−176.813	+	298.527i	−0.384375	+	0.648973i
$461$	−167.149			−0.362579			−0.181290	−	0.983430i	$-0.558027\pi$
$461$	−167.149			−0.362579			−0.181290	+	0.983430i	$0.558027\pi$
$462$	375.039	+	752.653i	0.811773	+	1.62912i
$463$		−	422.251i		−	0.911990i	−0.889982	−	0.455995i	$-0.849284\pi$
$463$		−	422.251i		−	0.911990i	0.889982	−	0.455995i	$-0.150716\pi$
$464$	42.0989	−	7.97366i	0.0907305	−	0.0171846i
$465$	−351.829	−	255.619i	−0.756622	−	0.549718i
$466$	−563.368	−	370.328i	−1.20895	−	0.794696i
$467$	72.7949	+	23.6525i	0.155878	+	0.0506477i	0.385916	−	0.922534i	$-0.373885\pi$
$467$	72.7949	+	23.6525i	0.155878	+	0.0506477i	−0.230039	+	0.973181i	$0.573885\pi$
$468$	−540.369	−	1250.97i	−1.15464	−	2.67301i
$469$	−594.940	+	432.249i	−1.26853	+	0.921640i
$470$	37.0887	+	10.1594i	0.0789121	+	0.0216157i
$471$	−1123.17	+	364.940i	−2.38465	+	0.774819i
$472$	143.672	−	270.707i	0.304391	−	0.573531i
$473$	686.181	+	148.291i	1.45070	+	0.313511i
$474$	310.648	+	822.920i	0.655375	+	1.73612i
$475$	−90.3408	+	29.3535i	−0.190191	+	0.0617969i
$476$	−2.39375	−	25.5016i	−0.00502890	−	0.0535747i
$477$	−1469.25	+	1067.47i	−3.08019	+	2.23789i
$478$	37.0271	+	790.661i	0.0774625	+	1.65410i
$479$	601.535	+	195.450i	1.25581	+	0.408039i	0.860001	−	0.510293i	$-0.170463\pi$
$479$	601.535	+	195.450i	1.25581	+	0.408039i	0.395813	+	0.918331i	$0.370463\pi$
$480$	−313.359	−	268.523i	−0.652832	−	0.559423i
$481$	245.437	+	178.320i	0.510263	+	0.370728i
$482$	−426.874	+	341.761i	−0.885630	+	0.709047i
$483$			1482.74i			3.06985i
$484$	−291.460	+	386.403i	−0.602189	+	0.798354i
$485$	180.027			0.371189
$486$	1095.13	+	1367.86i	2.25335	+	2.81453i
$487$	−284.951	+	392.201i	−0.585114	+	0.805340i	−0.994244	−	0.107136i	$-0.965832\pi$
$487$	−284.951	+	392.201i	−0.585114	+	0.805340i	0.409130	+	0.912476i	$0.365832\pi$
$488$	−58.8335	+	8.31428i	−0.120561	+	0.0170375i
$489$	127.707	−	393.042i	0.261159	−	0.803766i
$490$	22.6679	−	1.06155i	0.0462611	−	0.00216643i
$491$	36.7564	+	50.5908i	0.0748602	+	0.103036i	0.844805	−	0.535074i	$-0.179716\pi$
$491$	36.7564	+	50.5908i	0.0748602	+	0.103036i	−0.769945	+	0.638110i	$0.779716\pi$
$492$	−39.0236	−	415.733i	−0.0793163	−	0.844986i
$493$	0.799538	+	2.46073i	0.00162178	+	0.00499133i
$494$	499.147	−	188.425i	1.01042	−	0.381427i
$495$	−126.054	+	583.288i	−0.254655	+	1.17836i
$496$	535.215	+	68.3259i	1.07906	+	0.137754i
$497$	32.2890	+	99.3755i	0.0649679	+	0.199951i
$498$	75.7665	−	276.600i	0.152142	−	0.555421i
$499$	288.046	+	396.462i	0.577247	+	0.794513i	0.993390	−	0.114786i	$-0.0366183\pi$
$499$	288.046	+	396.462i	0.577247	+	0.794513i	−0.416143	+	0.909299i	$0.636618\pi$
$500$	−17.7341	−	41.0549i	−0.0354682	−	0.0821097i
$501$	154.467	−	475.400i	0.308317	−	0.948903i
$502$	192.417	−	292.719i	0.383302	−	0.583105i
$503$	304.073	−	418.521i	0.604520	−	0.832050i	−0.391593	−	0.920139i	$-0.628076\pi$
$503$	304.073	−	418.521i	0.604520	−	0.832050i	0.996113	+	0.0880885i	$0.0280758\pi$
$504$	−1267.00	−	222.410i	−2.51389	−	0.441290i
$505$	150.987			0.298984
$506$	−763.834	+	380.610i	−1.50955	+	0.752194i
$507$			162.458i			0.320429i
$508$	−154.166	+	260.291i	−0.303476	+	0.512384i
$509$	155.607	+	113.055i	0.305711	+	0.222112i	0.730054	−	0.683389i	$-0.239495\pi$
$509$	155.607	+	113.055i	0.305711	+	0.222112i	−0.424343	+	0.905502i	$0.639495\pi$
$510$	13.6882	−	20.8234i	0.0268395	−	0.0408301i
$511$	377.938	+	122.799i	0.739604	+	0.240312i
$512$	501.054	+	105.305i	0.978621	+	0.205673i
$513$	−1352.80	+	982.864i	−2.63703	+	1.91592i
$514$	−83.4029	+	304.478i	−0.162263	+	0.592370i
$515$	−81.5714	+	26.5042i	−0.158391	+	0.0514644i
$516$	−1105.01	+	972.909i	−2.14149	+	1.88548i
$517$	63.0517	+	70.5063i	0.121957	+	0.136376i
$518$	267.931	−	101.143i	0.517242	−	0.195256i
$519$	825.627	−	268.262i	1.59080	−	0.516883i
$520$	110.285	+	225.680i	0.212086	+	0.434000i
$521$	−512.198	+	372.133i	−0.983105	+	0.714268i	−0.958400	−	0.285427i	$-0.907865\pi$
$521$	−512.198	+	372.133i	−0.983105	+	0.714268i	−0.0247046	+	0.999695i	$0.507865\pi$
$522$	129.800	−	6.07863i	0.248660	−	0.0116449i
$523$	214.583	+	69.7222i	0.410292	+	0.133312i	0.506889	−	0.862012i	$-0.330796\pi$
$523$	214.583	+	69.7222i	0.410292	+	0.133312i	−0.0965962	+	0.995324i	$0.530796\pi$
$524$	548.274	+	122.931i	1.04633	+	0.234601i
$525$	−154.617	−	112.336i	−0.294509	−	0.213973i
$526$	−438.901	−	548.206i	−0.834413	−	1.04222i
$527$			32.5815i			0.0618245i
$528$	−288.801	−	973.089i	−0.546972	−	1.84297i
$529$	−975.767			−1.84455
$530$	261.327	−	209.222i	0.493069	−	0.394758i
$531$	546.303	−	751.922i	1.02882	−	1.41605i
$532$	110.189	−	491.447i	0.207123	−	0.923772i
$533$	−78.5399	+	241.721i	−0.147354	+	0.453510i
$534$	3.10354	+	66.2716i	0.00581186	+	0.124104i
$535$	−222.749	−	306.588i	−0.416354	−	0.573062i
$536$	797.525	−	389.732i	1.48792	−	0.727112i
$537$	452.812	+	1393.61i	0.843225	+	2.59518i
$538$	221.756	+	587.443i	0.412187	+	1.09190i
$539$	48.2437	+	28.0725i	0.0895060	+	0.0520826i
$540$	−520.230	−	590.865i	−0.963390	−	1.09420i
$541$	−80.3047	−	247.152i	−0.148437	−	0.456844i	0.849000	−	0.528394i	$-0.177205\pi$
$541$	−80.3047	−	247.152i	−0.148437	−	0.456844i	−0.997437	+	0.0715500i	$0.977205\pi$
$542$	943.787	+	258.523i	1.74130	+	0.476980i
$543$	482.667	+	664.335i	0.888890	+	1.22345i
$544$	−2.47622	+	30.8180i	−0.00455187	+	0.0566508i
$545$	−21.7639	+	66.9823i	−0.0399337	+	0.122903i
$546$	896.999	+	589.639i	1.64286	+	1.07993i
$547$	186.485	−	256.675i	0.340923	−	0.469240i	−0.603788	−	0.797145i	$-0.706343\pi$
$547$	186.485	−	256.675i	0.340923	−	0.469240i	0.944711	+	0.327905i	$0.106343\pi$
$548$	229.350	+	135.840i	0.418523	+	0.247884i
$549$	−180.196			−0.328227
$550$	18.1806	−	108.487i	0.0330557	−	0.197249i
$551$			50.8759i			0.0923338i
$552$	309.444	−	1762.81i	0.560588	−	3.19349i
$553$	−408.886	−	297.073i	−0.739397	−	0.537203i
$554$	387.265	+	254.567i	0.699034	+	0.459508i
$555$	264.987	+	86.0995i	0.477454	+	0.155134i
$556$	65.2753	−	28.1964i	0.117402	−	0.0507129i
$557$	568.374	−	412.948i	1.02042	−	0.741378i	0.0540507	−	0.998538i	$-0.482787\pi$
$557$	568.374	−	412.948i	1.02042	−	0.741378i	0.966369	+	0.257160i	$0.0827867\pi$
$558$	1578.17	+	432.295i	2.82827	+	0.774723i
$559$	852.282	−	276.923i	1.52466	−	0.495391i
$560$	235.209	+	30.0269i	0.420016	+	0.0536195i
$561$	56.0789	−	24.7400i	0.0999625	−	0.0440998i
$562$	−31.7632	−	84.1422i	−0.0565181	−	0.149719i
$563$	−985.136	+	320.090i	−1.74980	+	0.568544i	−0.996064	−	0.0886373i	$-0.971749\pi$
$563$	−985.136	+	320.090i	−1.74980	+	0.568544i	−0.753733	+	0.657181i	$0.771749\pi$
$564$	−197.498	+	18.5386i	−0.350174	+	0.0328698i
$565$	35.6934	−	25.9328i	0.0631742	−	0.0458988i
$566$	−19.0873	−	407.582i	−0.0337231	−	0.720110i
$567$	−1823.32	−	592.433i	−3.21573	−	1.04486i
$568$	−17.6486	−	124.885i	−0.0310714	−	0.219868i
$569$	785.806	+	570.922i	1.38103	+	1.00338i	0.996783	+	0.0801467i	$0.0255389\pi$
$569$	785.806	+	570.922i	1.38103	+	1.00338i	0.384247	+	0.923230i	$0.374461\pi$
$570$	382.509	−	306.242i	0.671068	−	0.537266i
$571$			32.0587i			0.0561448i	0.999606	+	0.0280724i	$0.00893690\pi$
$571$			32.0587i			0.0561448i	−0.999606	+	0.0280724i	$0.991063\pi$
$572$	−73.4986	+	613.447i	−0.128494	+	1.07246i
$573$	−393.249			−0.686298
$574$	149.951	+	187.295i	0.261239	+	0.326298i
$575$	114.005	−	156.914i	0.198269	−	0.272894i
$576$	1459.90	+	528.840i	2.53455	+	0.918125i
$577$	98.1484	−	302.070i	0.170101	−	0.523518i	−0.829275	−	0.558841i	$-0.811246\pi$
$577$	98.1484	−	302.070i	0.170101	−	0.523518i	0.999376	+	0.0353235i	$0.0112462\pi$
$578$	575.502	−	26.9511i	0.995679	−	0.0466282i
$579$	−879.145	−	1210.04i	−1.51839	−	2.08988i
$580$	−23.8476	+	2.23850i	−0.0411166	+	0.00385949i
$581$	50.9218	+	156.721i	0.0876451	+	0.269744i
$582$	−868.808	+	327.970i	−1.49280	+	0.563523i
$583$	819.181	−	83.2866i	1.40511	−	0.142859i
$584$	−423.697	−	224.869i	−0.725509	−	0.385050i
$585$	235.399	+	724.482i	0.402391	+	1.23843i
$586$	−101.121	+	369.162i	−0.172562	+	0.629969i
$587$	−213.385	−	293.699i	−0.363518	−	0.500339i	0.587607	−	0.809147i	$-0.300070\pi$
$587$	−213.385	−	293.699i	−0.363518	−	0.500339i	−0.951125	+	0.308807i	$0.900070\pi$
$588$	−107.462	+	46.4192i	−0.182758	+	0.0789442i
$589$	−197.974	+	609.302i	−0.336119	+	1.03447i
$590$	−94.1065	+	143.161i	−0.159503	+	0.242646i
$591$	157.865	−	217.282i	0.267114	−	0.367652i
$592$	−339.648	+	64.3303i	−0.573730	+	0.108666i
$593$	−607.073			−1.02373			−0.511866	−	0.859065i	$-0.671046\pi$
$593$	−607.073			−1.02373			−0.511866	+	0.859065i	$0.671046\pi$
$594$	−285.766	−	1915.17i	−0.481088	−	3.22420i
$595$			14.3185i			0.0240647i
$596$	68.3606	+	40.4888i	0.114699	+	0.0679343i
$597$	−1746.75	−	1269.09i	−2.92588	−	2.12577i
$598$	−598.399	+	910.325i	−1.00067	+	1.52228i
$599$	−325.098	−	105.631i	−0.542735	−	0.176345i	0.0248033	−	0.999692i	$-0.492104\pi$
$599$	−325.098	−	105.631i	−0.542735	−	0.176345i	−0.567538	+	0.823347i	$0.692104\pi$
$600$	160.378	+	165.823i	0.267297	+	0.276372i
$601$	−34.4073	+	24.9984i	−0.0572501	+	0.0415947i	−0.616042	−	0.787713i	$-0.711265\pi$
$601$	−34.4073	+	24.9984i	−0.0572501	+	0.0415947i	0.558792	+	0.829308i	$0.311265\pi$
$602$	223.492	−	815.900i	0.371249	−	1.35531i
$603$	2560.23	−	831.870i	4.24583	−	1.37955i
$604$	−380.315	−	431.953i	−0.629661	−	0.715154i
$605$	182.405	−	199.834i	0.301496	−	0.330304i
$606$	−728.662	+	275.066i	−1.20241	+	0.453904i
$607$	−354.512	+	115.188i	−0.584040	+	0.189766i	−0.586110	−	0.810232i	$-0.699341\pi$
$607$	−354.512	+	115.188i	−0.584040	+	0.189766i	0.00206969	+	0.999998i	$0.499341\pi$
$608$	−233.566	+	561.278i	−0.384155	+	0.923154i
$609$	−82.8119	+	60.1663i	−0.135980	+	0.0987953i
$610$	33.1794	−	1.55381i	0.0543924	−	0.00254723i
$611$	114.832	+	37.3112i	0.187941	+	0.0610658i
$612$	−20.5136	+	91.4910i	−0.0335190	+	0.149495i
$613$	347.513	+	252.483i	0.566906	+	0.411881i	0.833980	−	0.551795i	$-0.186057\pi$
$613$	347.513	+	252.483i	0.566906	+	0.411881i	−0.267074	+	0.963676i	$0.586057\pi$
$614$	−403.732	−	504.279i	−0.657544	−	0.821301i
$615$			233.424i			0.379550i
$616$	445.793	+	376.071i	0.723690	+	0.610505i
$617$	185.357			0.300417			0.150209	−	0.988654i	$-0.452005\pi$
$617$	185.357			0.300417			0.150209	+	0.988654i	$0.452005\pi$
$618$	345.379	−	276.515i	0.558865	−	0.447435i
$619$	−686.557	+	944.965i	−1.10914	+	1.52660i	−0.286461	+	0.958092i	$0.592479\pi$
$619$	−686.557	+	944.965i	−1.10914	+	1.52660i	−0.822678	+	0.568507i	$0.807521\pi$
$620$	−294.315	−	65.9897i	−0.474702	−	0.106435i
$621$	1055.08	−	3247.19i	1.69900	−	5.22898i
$622$	12.6990	+	271.169i	0.0204164	+	0.435962i
$623$	−22.4068	−	30.8404i	−0.0359660	−	0.0495030i
$624$	−943.374	−	888.215i	−1.51182	−	1.42342i
$625$	7.72542	+	23.7764i	0.0123607	+	0.0380423i
$626$	−278.724	−	738.352i	−0.445246	−	1.17948i
$627$	1199.05	−	121.908i	1.91236	−	0.194431i
$628$	−614.758	+	541.267i	−0.978914	+	0.861889i
$629$	−6.45056	−	19.8528i	−0.0102553	−	0.0315624i
$630$	693.555	+	189.979i	1.10088	+	0.301555i
$631$	504.183	+	693.948i	0.799022	+	1.09976i	0.992926	+	0.118739i	$0.0378851\pi$
$631$	504.183	+	693.948i	0.799022	+	1.09976i	−0.193903	+	0.981021i	$0.562115\pi$
$632$	424.121	+	438.520i	0.671077	+	0.693861i
$633$	256.966	−	790.859i	0.405949	−	1.24938i
$634$	298.292	+	196.081i	0.470492	+	0.309276i
$635$	99.4027	−	136.816i	0.156540	−	0.215458i
$636$	−880.005	+	1485.78i	−1.38366	+	2.33614i
$637$	71.2512			0.111854
$638$	−52.2520	−	27.2162i	−0.0818997	−	0.0426587i
$639$		−	382.499i		−	0.598590i
$640$	−273.370	−	84.7862i	−0.427141	−	0.132478i
$641$	113.836	+	82.7064i	0.177591	+	0.129027i	0.673029	−	0.739616i	$-0.264993\pi$
$641$	113.836	+	82.7064i	0.177591	+	0.129027i	−0.495439	+	0.868643i	$0.664993\pi$
$642$	1633.53	+	1073.79i	2.54443	+	1.67257i
$643$	−1050.08	−	341.192i	−1.63310	−	0.530625i	−0.658115	−	0.752917i	$-0.728646\pi$
$643$	−1050.08	−	341.192i	−1.63310	−	0.530625i	−0.974980	+	0.222292i	$0.928646\pi$
$644$	407.801	+	944.069i	0.633231	+	1.46595i
$645$	665.842	−	483.763i	1.03231	−	0.750020i
$646$	−35.4062	−	9.69850i	−0.0548083	−	0.0150132i
$647$	−838.264	+	272.368i	−1.29562	+	0.420971i	−0.874054	−	0.485828i	$-0.838518\pi$
$647$	−838.264	+	272.368i	−1.29562	+	0.420971i	−0.421562	+	0.906799i	$0.638518\pi$
$648$	2044.08	+	1084.86i	3.15445	+	1.67416i
$649$	−385.545	+	170.088i	−0.594059	+	0.262078i
$650$	−49.5908	−	131.368i	−0.0762935	−	0.202105i
$651$	−1225.90	+	398.319i	−1.88310	+	0.611858i
$652$	−26.7873	−	285.375i	−0.0410848	−	0.437692i
$653$	572.084	−	415.644i	0.876086	−	0.636514i	−0.0561268	−	0.998424i	$-0.517875\pi$
$653$	572.084	−	415.644i	0.876086	−	0.636514i	0.932213	+	0.361910i	$0.117875\pi$
$654$	−16.9951	−	362.906i	−0.0259864	−	0.554902i
$655$	−298.731	−	97.0636i	−0.456078	−	0.148189i
$656$	−139.187	−	253.967i	−0.212175	−	0.387145i
$657$	−1176.87	−	855.048i	−1.79128	−	1.30144i
$658$	88.9765	−	71.2358i	0.135223	−	0.108261i
$659$		−	461.408i		−	0.700164i	−0.936719	−	0.350082i	$-0.886154\pi$
$659$		−	461.408i		−	0.700164i	0.936719	−	0.350082i	$-0.113846\pi$
$660$	109.901	+	556.680i	0.166516	+	0.843455i
$661$	607.649			0.919287			0.459644	−	0.888103i	$-0.347977\pi$
$661$	607.649			0.919287			0.459644	+	0.888103i	$0.347977\pi$
$662$	137.422	+	171.646i	0.207586	+	0.259283i
$663$	45.9897	−	63.2994i	0.0693661	−	0.0954743i
$664$	−27.8328	−	196.951i	−0.0419169	−	0.296613i
$665$	−87.0031	+	267.768i	−0.130832	+	0.402658i
$666$	−1047.21	+	49.0415i	−1.57239	+	0.0736358i
$667$	−61.0601	−	84.0421i	−0.0915444	−	0.126000i
$668$	−32.4004	−	345.174i	−0.0485036	−	0.516727i
$669$	278.384	+	856.779i	0.416120	+	1.28069i
$670$	−464.240	+	175.248i	−0.692895	+	0.261564i
$671$	70.6150	+	41.0901i	0.105238	+	0.0612371i
$672$	−1189.82	+	283.591i	−1.77057	+	0.422010i
$673$	372.581	+	1146.69i	0.553612	+	1.70384i	0.699580	+	0.714554i	$0.253370\pi$
$673$	372.581	+	1146.69i	0.553612	+	1.70384i	−0.145968	+	0.989289i	$0.546630\pi$
$674$	287.347	−	1049.02i	0.426332	−	1.55640i
$675$	258.676	+	356.037i	0.383224	+	0.527462i
$676$	44.6810	+	103.438i	0.0660962	+	0.153014i
$677$	−351.570	+	1082.02i	−0.519305	+	1.59826i	0.256004	+	0.966676i	$0.417594\pi$
$677$	−351.570	+	1082.02i	−0.519305	+	1.59826i	−0.775309	+	0.631582i	$0.782406\pi$
$678$	−125.012	+	190.178i	−0.184384	+	0.280498i
$679$	313.639	−	431.687i	0.461913	−	0.635769i
$680$	2.98823	−	17.0230i	0.00439446	−	0.0250339i
$681$	−406.167			−0.596428
$682$	−519.876	−	529.277i	−0.762281	−	0.776067i
$683$		−	1264.82i		−	1.85185i	−0.377705	−	0.925926i	$-0.623286\pi$
$683$		−	1264.82i		−	1.85185i	0.377705	−	0.925926i	$-0.376714\pi$
$684$	−939.547	+	1586.32i	−1.37361	+	2.31917i
$685$	−120.553	−	87.5868i	−0.175990	−	0.127864i
$686$	393.720	−	598.953i	0.573935	−	0.873110i
$687$	42.1029	+	13.6801i	0.0612852	+	0.0199128i
$688$	−435.983	+	923.369i	−0.633696	+	1.34211i
$689$	850.349	−	617.815i	1.23418	−	0.896683i
$690$	−264.323	+	964.960i	−0.383077	+	1.39849i
$691$	−307.133	+	99.7934i	−0.444476	+	0.144419i	−0.522700	−	0.852517i	$-0.675075\pi$
$691$	−307.133	+	99.7934i	−0.444476	+	0.144419i	0.0782240	+	0.996936i	$0.475075\pi$
$692$	451.901	−	397.878i	0.653036	−	0.574968i
$693$	1179.06	+	1318.46i	1.70139	+	1.90254i
$694$	1055.81	−	398.564i	1.52135	−	0.574299i
$695$	−37.8034	+	12.2831i	−0.0543933	+	0.0176735i
$696$	111.010	−	54.2483i	0.159498	−	0.0779429i
$697$	14.1481	−	10.2792i	0.0202986	−	0.0147478i
$698$	383.043	−	17.9381i	0.548772	−	0.0256993i
$699$	−1848.96	−	600.763i	−2.64515	−	0.859460i
$700$	−129.342	−	29.0003i	−0.184774	−	0.0414290i
$701$	428.481	+	311.310i	0.611243	+	0.444094i	0.849852	−	0.527022i	$-0.176691\pi$
$701$	428.481	+	311.310i	0.611243	+	0.444094i	−0.238609	+	0.971116i	$0.576691\pi$
$702$	−1544.85	−	1929.59i	−2.20065	−	2.74870i
$703$		−	410.459i		−	0.583868i
$704$	−451.512	−	540.141i	−0.641353	−	0.767246i
$705$	110.890			0.157291
$706$	−639.750	+	512.193i	−0.906162	+	0.725485i
$707$	263.046	−	362.052i	0.372060	−	0.512096i
$708$	193.349	−	862.338i	0.273091	−	1.21799i
$709$	−26.6196	+	81.9267i	−0.0375453	+	0.115552i	−0.968073	−	0.250670i	$-0.919349\pi$
$709$	−26.6196	+	81.9267i	−0.0375453	+	0.115552i	0.930527	+	0.366222i	$0.119349\pi$
$710$	3.29824	+	70.4292i	0.00464540	+	0.0991960i
$711$	1087.48	+	1496.79i	1.52951	+	2.10519i
$712$	20.2029	+	41.3419i	0.0283748	+	0.0580645i
$713$	−404.237	−	1244.11i	−0.566952	−	1.74490i
$714$	−26.0852	−	69.1010i	−0.0365339	−	0.0967801i
$715$	72.9558	−	337.586i	0.102036	−	0.472149i
$716$	671.596	+	762.783i	0.937983	+	1.06534i
$717$	705.325	+	2170.77i	0.983716	+	3.02757i
$718$	−813.000	−	222.698i	−1.13231	−	0.310164i
$719$	−112.526	−	154.879i	−0.156504	−	0.215409i	0.723564	−	0.690258i	$-0.242503\pi$
$719$	−112.526	−	154.879i	−0.156504	−	0.215409i	−0.880068	+	0.474849i	$0.842503\pi$
$720$	−784.910	−	370.607i	−1.09015	−	0.514732i
$721$	−78.5577	+	241.776i	−0.108957	+	0.335334i
$722$	0.127702	+	0.0839444i	0.000176873	+	0.000116267i
$723$	−926.853	+	1275.70i	−1.28195	+	1.76446i
$724$	490.030	+	290.237i	0.676838	+	0.400879i
$725$	13.3898			0.0184687
$726$	−516.231	+	1296.70i	−0.711062	+	1.78609i
$727$		−	211.060i		−	0.290317i	−0.989408	−	0.145159i	$-0.953631\pi$
$727$		−	211.060i		−	0.290317i	0.989408	−	0.145159i	$-0.0463692\pi$
$728$	733.294	+	128.723i	1.00727	+	0.176817i
$729$	1981.64	+	1439.75i	2.71830	+	1.97496i
$730$	224.069	+	147.291i	0.306944	+	0.201769i
$731$	−58.6431	−	19.0543i	−0.0802231	−	0.0260661i
$732$	−157.293	+	67.9444i	−0.214881	+	0.0928203i
$733$	−535.113	+	388.783i	−0.730032	+	0.530399i	−0.889573	−	0.456792i	$-0.848998\pi$
$733$	−535.113	+	388.783i	−0.730032	+	0.530399i	0.159542	+	0.987191i	$0.448998\pi$
$734$	−736.084	−	201.629i	−1.00284	−	0.274699i
$735$	62.2350	−	20.2214i	0.0846735	−	0.0275121i
$736$	−287.804	−	1207.50i	−0.391038	−	1.64062i
$737$	−1192.99	−	257.817i	−1.61871	−	0.349820i
$738$	−310.183	−	821.689i	−0.420302	−	1.11340i
$739$	−381.947	+	124.102i	−0.516843	+	0.167932i	−0.555812	−	0.831308i	$-0.687593\pi$
$739$	−381.947	+	124.102i	−0.516843	+	0.167932i	0.0389692	+	0.999240i	$0.487593\pi$
$740$	192.399	−	18.0599i	0.259999	−	0.0244053i
$741$	1244.67	−	904.308i	1.67972	−	1.22039i
$742$	−46.4156	−	991.138i	−0.0625547	−	1.33577i
$743$	−249.719	−	81.1387i	−0.336096	−	0.109204i	0.136107	−	0.990694i	$-0.456541\pi$
$743$	−249.719	−	81.1387i	−0.336096	−	0.109204i	−0.472203	+	0.881490i	$0.656541\pi$
$744$	1540.58	−	217.713i	2.07068	−	0.292626i
$745$	−35.9322	−	26.1063i	−0.0482312	−	0.0350420i
$746$	296.805	−	237.626i	0.397862	−	0.318534i
$747$		−	603.225i		−	0.807530i
$748$	28.9015	−	31.1756i	0.0386384	−	0.0416786i
$749$	−1123.24			−1.49965
$750$	−80.5985	−	100.671i	−0.107465	−	0.134228i
$751$	−128.891	+	177.403i	−0.171625	+	0.236222i	−0.886162	−	0.463376i	$-0.846638\pi$
$751$	−128.891	+	177.403i	−0.171625	+	0.236222i	0.714536	+	0.699599i	$0.246638\pi$
$752$	−120.650	+	66.1220i	−0.160438	+	0.0879282i
$753$	312.148	−	960.693i	0.414539	−	1.27582i
$754$	−75.1239	+	3.51809i	−0.0996338	+	0.00466591i
$755$	189.105	+	260.281i	0.250471	+	0.344743i
$756$	−2323.18	+	218.069i	−3.07298	+	0.288452i
$757$	34.6128	+	106.527i	0.0457236	+	0.140723i	0.971312	−	0.237809i	$-0.0764291\pi$
$757$	34.6128	+	106.527i	0.0457236	+	0.140723i	−0.925588	+	0.378532i	$0.876429\pi$
$758$	890.133	−	336.020i	1.17432	−	0.443298i
$759$	−1834.41	+	1640.46i	−2.41687	+	2.16134i
$760$	159.319	−	300.188i	0.209631	−	0.394984i
$761$	−398.783	−	1227.33i	−0.524025	−	1.61278i	−0.766235	−	0.642560i	$-0.777872\pi$
$761$	−398.783	−	1227.33i	−0.524025	−	1.61278i	0.242210	−	0.970224i	$-0.422128\pi$
$762$	−230.468	+	841.365i	−0.302451	+	1.10415i
$763$	122.701	+	168.883i	0.160814	+	0.221341i
$764$	−250.384	+	108.156i	−0.327728	+	0.141566i
$765$	16.1971	−	49.8495i	0.0211727	−	0.0651628i
$766$	−192.644	+	293.064i	−0.251494	+	0.382590i
$767$	−316.181	+	435.186i	−0.412231	+	0.567387i
$768$	1473.75	−	88.8441i	1.91894	−	0.115682i
$769$	−1162.42			−1.51160			−0.755800	−	0.654802i	$-0.772752\pi$
$769$	−1162.42			−1.51160			−0.755800	+	0.654802i	$0.772752\pi$
$770$	−228.468	−	232.600i	−0.296712	−	0.302078i
$771$			910.348i			1.18074i
$772$	−892.557	−	528.646i	−1.15616	−	0.684775i
$773$	666.838	+	484.486i	0.862663	+	0.626761i	0.928608	−	0.371062i	$-0.121006\pi$
$773$	666.838	+	484.486i	0.862663	+	0.626761i	−0.0659455	+	0.997823i	$0.521006\pi$
$774$	−1701.03	+	2587.72i	−2.19771	+	3.34331i
$775$	160.360	+	52.1040i	0.206916	+	0.0672310i
$776$	−462.973	+	447.771i	−0.596615	+	0.577024i
$777$	668.114	−	485.413i	0.859863	−	0.624727i
$778$	302.134	−	1103.00i	0.388347	−	1.41773i
$779$	327.041	−	106.262i	0.419822	−	0.136408i
$780$	478.650	+	543.640i	0.613654	+	0.696974i
$781$	−87.2211	+	149.893i	−0.111679	+	0.191925i
$782$	70.1275	−	26.4727i	0.0896771	−	0.0338526i
$783$	224.170	−	72.8374i	0.286297	−	0.0930235i
$784$	−55.6546	+	59.1108i	−0.0709880	+	0.0753964i
$785$	370.434	−	269.136i	0.471890	−	0.342848i
$786$	1618.50	−	75.7955i	2.05917	−	0.0964319i
$787$	484.851	+	157.538i	0.616075	+	0.200175i	0.600397	−	0.799702i	$-0.295009\pi$
$787$	484.851	+	157.538i	0.616075	+	0.200175i	0.0156779	+	0.999877i	$0.495009\pi$
$788$	40.7538	−	181.763i	0.0517180	−	0.230663i
$789$	−1638.30	−	1190.30i	−2.07643	−	1.50862i
$790$	−213.143	−	266.225i	−0.269801	−	0.336993i
$791$		−	130.769i		−	0.165321i
$792$	−1126.61	−	1813.57i	−1.42249	−	2.28986i
$793$	104.291			0.131515
$794$	−797.783	+	638.716i	−1.00476	+	0.804428i
$795$	567.407	−	780.969i	0.713720	−	0.982351i
$796$	−1461.20	−	327.623i	−1.83568	−	0.411587i
$797$	−67.4198	+	207.497i	−0.0845919	+	0.260347i	−0.984402	−	0.175935i	$-0.943705\pi$
$797$	−67.4198	+	207.497i	−0.0845919	+	0.260347i	0.899810	+	0.436282i	$0.143705\pi$
$798$	−67.9394	−	1450.75i	−0.0851370	−	1.81798i
$799$	−4.88324	−	6.72121i	−0.00611170	−	0.00841203i
$800$	147.720	+	61.4713i	0.184650	+	0.0768392i
$801$	43.1223	+	132.717i	0.0538356	+	0.165689i
$802$	−19.4821	−	51.6091i	−0.0242919	−	0.0643505i
$803$	266.214	+	603.436i	0.331525	+	0.751477i
$804$	1921.16	−	1691.49i	2.38950	−	2.10385i
$805$	−177.648	−	546.746i	−0.220681	−	0.679187i
$806$	−913.392	−	250.197i	−1.13324	−	0.310418i
$807$	1064.27	+	1464.85i	1.31880	+	1.81518i
$808$	−388.291	+	375.541i	−0.480559	+	0.464779i
$809$	88.1306	−	271.238i	0.108938	−	0.335276i	−0.881697	−	0.471817i	$-0.843598\pi$
$809$	88.1306	−	271.238i	0.108938	−	0.335276i	0.990634	+	0.136541i	$0.0435984\pi$
$810$	−1081.00	−	710.590i	−1.33457	−	0.877272i
$811$	−152.486	+	209.879i	−0.188022	+	0.258790i	−0.892613	−	0.450824i	$-0.851130\pi$
$811$	−152.486	+	209.879i	−0.188022	+	0.258790i	0.704591	+	0.709613i	$0.251130\pi$
$812$	−36.1791	+	61.0842i	−0.0445556	+	0.0752268i
$813$	2821.79			3.47084
$814$	421.562	+	219.577i	0.517889	+	0.269750i
$815$			160.231i			0.196602i
$816$	16.5911	+	87.5971i	0.0203323	+	0.107349i
$817$	−980.897	−	712.663i	−1.20061	−	0.872293i
$818$	−1023.49	−	672.787i	−1.25121	−	0.822478i
$819$	2147.35	+	697.715i	2.62191	+	0.851911i
$820$	64.1990	+	148.622i	0.0782914	+	0.181246i
$821$	−494.450	+	359.239i	−0.602253	+	0.437562i	−0.846678	−	0.532106i	$-0.821401\pi$
$821$	−494.450	+	359.239i	−0.602253	+	0.437562i	0.244425	+	0.969668i	$0.421401\pi$
$822$	741.352	+	203.072i	0.901889	+	0.247046i
$823$	−978.295	+	317.867i	−1.18869	+	0.386230i	−0.835590	−	0.549354i	$-0.814874\pi$
$823$	−978.295	+	317.867i	−1.18869	+	0.386230i	−0.353104	+	0.935584i	$0.614874\pi$
$824$	143.854	−	271.049i	0.174580	−	0.328943i
$825$	−32.0845	−	315.573i	−0.0388903	−	0.382513i
$826$	179.337	+	475.071i	0.217115	+	0.575147i
$827$	509.457	−	165.533i	0.616030	−	0.200160i	0.0156534	−	0.999877i	$-0.495017\pi$
$827$	509.457	−	165.533i	0.616030	−	0.200160i	0.600377	+	0.799717i	$0.295017\pi$
$828$	−351.819	−	3748.06i	−0.424903	−	4.52665i
$829$	1044.67	−	758.994i	1.26015	−	0.915553i	0.261386	−	0.965234i	$-0.415820\pi$
$829$	1044.67	−	758.994i	1.26015	−	0.915553i	0.998765	+	0.0496809i	$0.0158204\pi$
$830$	5.20152	+	111.071i	0.00626689	+	0.133821i
$831$	1270.99	+	412.970i	1.52947	+	0.496956i
$832$	−844.939	−	306.074i	−1.01555	−	0.367877i
$833$	−3.96627	−	2.88167i	−0.00476143	−	0.00345938i
$834$	160.062	−	128.148i	0.191921	−	0.153654i
$835$			193.806i			0.232103i
$836$	729.915	−	407.398i	0.873104	−	0.487318i
$837$	2968.15			3.54618
$838$	240.058	+	299.842i	0.286465	+	0.357807i
$839$	223.622	−	307.790i	0.266534	−	0.366853i	−0.654682	−	0.755905i	$-0.727197\pi$
$839$	223.622	−	307.790i	0.266534	−	0.366853i	0.921216	+	0.389052i	$0.127197\pi$
$840$	677.035	−	95.6778i	0.805995	−	0.113902i
$841$	−257.667	+	793.018i	−0.306382	+	0.942947i
$842$	−605.997	+	28.3792i	−0.719711	+	0.0337045i
$843$	−152.441	−	209.817i	−0.180831	−	0.248893i
$844$	−53.9001	−	574.218i	−0.0638627	−	0.680354i
$845$	−19.4642	−	59.9046i	−0.0230346	−	0.0708931i
$846$	−390.352	+	147.356i	−0.461409	+	0.174179i
$847$	−161.400	−	785.536i	−0.190555	−	0.927433i
$848$	−151.666	+	1188.04i	−0.178851	+	1.40099i
$849$	−363.592	−	1119.02i	−0.428259	−	1.31805i
$850$	−2.55251	+	9.31840i	−0.00300295	+	0.0109628i
$851$	492.624	+	678.039i	0.578877	+	0.796756i
$852$	−144.224	−	333.883i	−0.169277	−	0.391881i
$853$	126.168	−	388.305i	0.147911	−	0.455223i	−0.849463	−	0.527648i	$-0.823074\pi$
$853$	126.168	−	388.305i	0.147911	−	0.455223i	0.997374	+	0.0724255i	$0.0230739\pi$
$854$	54.0786	−	82.2680i	0.0633239	−	0.0963326i
$855$	605.799	−	833.811i	0.708537	−	0.975217i
$856$	1335.40	+	234.418i	1.56005	+	0.273852i
$857$	697.058			0.813370			0.406685	−	0.913568i	$-0.366685\pi$
$857$	697.058			0.813370			0.406685	+	0.913568i	$0.366685\pi$
$858$	262.926	+	1762.10i	0.306441	+	2.05373i
$859$			782.213i			0.910609i	0.890336	+	0.455305i	$0.150470\pi$
$859$			782.213i			0.910609i	−0.890336	+	0.455305i	$0.849530\pi$
$860$	290.895	−	491.143i	0.338250	−	0.571096i
$861$	559.728	+	406.666i	0.650090	+	0.472318i
$862$	814.092	−	1238.45i	0.944423	−	1.43672i
$863$	−1098.88	−	357.049i	−1.27333	−	0.413730i	−0.407103	−	0.913382i	$-0.633461\pi$
$863$	−1098.88	−	357.049i	−1.27333	−	0.413730i	−0.866226	+	0.499653i	$0.833461\pi$
$864$	2807.50	+	225.582i	3.24942	+	0.261090i
$865$	−272.301	+	197.838i	−0.314799	+	0.228715i
$866$	284.579	−	1038.91i	0.328613	−	1.19966i
$867$	1580.05	−	513.388i	1.82243	−	0.592143i
$868$	−670.988	+	590.774i	−0.773027	+	0.680616i
$869$	−84.8477	−	834.536i	−0.0976384	−	0.960340i
$870$	−64.6192	+	24.3934i	−0.0742750	+	0.0280384i
$871$	−1481.77	+	481.457i	−1.70123	+	0.552763i
$872$	−110.632	−	226.390i	−0.126871	−	0.259622i
$873$	−1580.25	+	1148.12i	−1.81014	+	1.31514i
$874$	1472.30	−	68.9486i	1.68455	−	0.0788886i
$875$	70.4727	+	22.8980i	0.0805402	+	0.0261691i
$876$	−1349.69	−	302.620i	−1.54074	−	0.345457i
$877$	920.419	+	668.723i	1.04951	+	0.762512i	0.972119	−	0.234488i	$-0.0753415\pi$
$877$	920.419	+	668.723i	1.04951	+	0.762512i	0.0773895	+	0.997001i	$0.475342\pi$
$878$	60.4636	+	75.5215i	0.0688651	+	0.0860154i
$879$			1103.74i			1.25568i
$880$	223.079	+	324.215i	0.253499	+	0.368427i
$881$	−720.052			−0.817312			−0.408656	−	0.912689i	$-0.634002\pi$
$881$	−720.052			−0.817312			−0.408656	+	0.912689i	$0.634002\pi$
$882$	−192.207	+	153.883i	−0.217921	+	0.174471i
$883$	−331.792	+	456.673i	−0.375756	+	0.517184i	−0.954454	−	0.298358i	$-0.903561\pi$
$883$	−331.792	+	456.673i	−0.375756	+	0.517184i	0.578698	+	0.815542i	$0.303561\pi$
$884$	11.8725	−	52.9518i	0.0134305	−	0.0599002i
$885$	−152.664	+	469.851i	−0.172501	+	0.530905i
$886$	−45.2506	−	966.263i	−0.0510729	−	1.09059i
$887$	955.306	+	1314.87i	1.07701	+	1.48237i	0.862773	+	0.505592i	$0.168726\pi$
$887$	955.306	+	1314.87i	1.07701	+	1.48237i	0.214235	+	0.976782i	$0.431274\pi$
$888$	−895.616	+	437.667i	−1.00858	+	0.492868i
$889$	−154.895	−	476.717i	−0.174235	−	0.536239i
$890$	−9.08446	−	24.0652i	−0.0102073	−	0.0270395i
$891$	−1284.32	−	2911.21i	−1.44144	−	3.26736i
$892$	412.891	+	468.951i	0.462882	+	0.525730i
$893$	−50.4810	−	155.364i	−0.0565296	−	0.173980i
$894$	220.969	+	60.5280i	0.247169	+	0.0677048i
$895$	−333.940	−	459.629i	−0.373117	−	0.513552i
$896$	−679.570	+	507.803i	−0.758448	+	0.566745i
$897$	−970.749	+	2987.66i	−1.08222	+	3.33072i
$898$	66.7077	+	43.8501i	0.0742848	+	0.0488308i
$899$	53.0814	−	73.0602i	0.0590449	−	0.0812683i
$900$	417.496	+	247.275i	0.463884	+	0.274751i
$901$	−72.3224			−0.0802690
$902$	−65.8155	+	392.733i	−0.0729662	+	0.435402i
$903$		−	2439.43i		−	2.70147i
$904$	−27.2912	+	155.470i	−0.0301894	+	0.171980i
$905$	−257.573	−	187.138i	−0.284612	−	0.206782i
$906$	−1386.80	−	911.607i	−1.53068	−	1.00619i
$907$	−952.079	−	309.349i	−1.04970	−	0.341069i	−0.267150	−	0.963655i	$-0.586082\pi$
$907$	−952.079	−	309.349i	−1.04970	−	0.341069i	−0.782551	+	0.622586i	$0.786082\pi$
$908$	−258.609	+	111.709i	−0.284812	+	0.123028i
$909$	−1325.34	+	962.919i	−1.45802	+	1.05932i
$910$	−401.405	−	109.953i	−0.441104	−	0.120828i
$911$	−933.302	+	303.248i	−1.02448	+	0.332874i	−0.772606	−	0.634886i	$-0.781047\pi$
$911$	−933.302	+	303.248i	−1.02448	+	0.332874i	−0.251875	+	0.967760i	$0.581047\pi$
$912$	−221.996	+	1738.95i	−0.243417	+	1.90675i
$913$	−137.553	+	236.390i	−0.150660	+	0.258916i
$914$	−604.776	−	1602.08i	−0.661681	−	1.75282i
$915$	91.0942	−	29.5983i	0.0995565	−	0.0323479i
$916$	30.5696	−	2.86948i	0.0333730	−	0.00313262i
$917$	−753.193	+	547.227i	−0.821366	+	0.596757i
$918$	7.95615	+	169.892i	0.00866683	+	0.185068i
$919$	206.474	+	67.0876i	0.224673	+	0.0730006i	0.419190	−	0.907898i	$-0.362314\pi$
$919$	206.474	+	67.0876i	0.224673	+	0.0730006i	−0.194517	+	0.980899i	$0.562314\pi$
$920$	97.0991	+	687.093i	0.105543	+	0.746840i
$921$	−1507.03	−	1094.92i	−1.63629	−	1.18884i
$922$	−260.965	+	208.932i	−0.283042	+	0.226607i
$923$			221.377i			0.239845i
$924$	1526.33	+	706.306i	1.65188	+	0.764401i
$925$	−108.027			−0.116786
$926$	−527.803	−	659.248i	−0.569982	−	0.711931i
$927$	546.994	−	752.873i	0.590069	−	0.812160i
$928$	55.7610	−	65.0716i	0.0600873	−	0.0701203i
$929$	−131.120	+	403.545i	−0.141141	+	0.434386i	−0.996495	−	0.0836580i	$-0.973340\pi$
$929$	−131.120	+	403.545i	−0.141141	+	0.434386i	0.855354	+	0.518044i	$0.173340\pi$
$930$	−868.818	+	40.6872i	−0.934213	+	0.0437497i
$931$	−56.6629	−	77.9898i	−0.0608625	−	0.0837700i
$932$	−1342.47	+	126.014i	−1.44042	+	0.135208i
$933$	241.901	+	744.496i	0.259273	+	0.797959i
$934$	143.218	−	54.0638i	0.153338	−	0.0578842i
$935$	−17.7144	+	15.8415i	−0.0189459	+	0.0169428i
$936$	−2407.34	−	1277.65i	−2.57194	−	1.36501i
$937$	287.645	+	885.281i	0.306985	+	0.944804i	0.978929	+	0.204201i	$0.0654597\pi$
$937$	287.645	+	885.281i	0.306985	+	0.944804i	−0.671944	+	0.740602i	$0.734540\pi$
$938$	−388.562	+	1418.52i	−0.414245	+	1.51228i
$939$	−1337.68	−	1841.16i	−1.42458	−	1.96076i
$940$	70.6045	−	30.4984i	0.0751111	−	0.0324451i
$941$	6.73493	−	20.7280i	0.00715721	−	0.0220276i	−0.947414	−	0.320010i	$-0.896314\pi$
$941$	6.73493	−	20.7280i	0.00715721	−	0.0220276i	0.954571	+	0.297982i	$0.0963137\pi$
$942$	−1297.40	+	1973.70i	−1.37729	+	2.09522i
$943$	−412.707	+	568.043i	−0.437653	+	0.602378i
$944$	−114.065	−	602.233i	−0.120831	−	0.637959i
$945$	1304.40			1.38032
$946$	1256.67	−	626.187i	1.32841	−	0.661931i
$947$			623.379i			0.658267i	0.944283	+	0.329134i	$0.106757\pi$
$947$			623.379i			0.658267i	−0.944283	+	0.329134i	$0.893243\pi$
$948$	1513.63	+	896.499i	1.59666	+	0.945674i
$949$	681.132	+	494.871i	0.717737	+	0.521466i
$950$	−104.355	+	158.752i	−0.109848	+	0.167108i
$951$	978.985	+	318.092i	1.02943	+	0.334481i
$952$	−35.6136	−	36.8227i	−0.0374092	−	0.0386793i
$953$	−82.3371	+	59.8214i	−0.0863978	+	0.0627717i	−0.630146	−	0.776477i	$-0.717005\pi$
$953$	−82.3371	+	59.8214i	−0.0863978	+	0.0627717i	0.543748	+	0.839249i	$0.317005\pi$
$954$	−959.583	+	3503.14i	−1.00585	+	3.67205i
$955$	145.007	−	47.1155i	0.151839	−	0.0493356i
$956$	1046.11	+	1188.15i	1.09426	+	1.24284i
$957$	−166.057	−	35.8865i	−0.173518	−	0.0374989i
$958$	1183.47	−	446.752i	1.23535	−	0.466338i
$959$	−420.050	+	136.482i	−0.438008	+	0.142317i
$960$	−824.886	−	27.5458i	−0.859256	−	0.0286936i
$961$	142.550	−	103.569i	0.148335	−	0.107772i
$962$	606.088	−	28.3835i	0.630030	−	0.0295046i
$963$	3910.54	+	1270.61i	4.06078	+	1.31943i
$964$	−239.273	+	1067.16i	−0.248209	+	1.10701i
$965$	469.152	+	340.859i	0.486168	+	0.353222i
$966$	1853.39	+	2314.96i	1.91862	+	2.39644i
$967$			1828.26i			1.89065i	0.326127	+	0.945326i	$0.394256\pi$
$967$			1828.26i			1.89065i	−0.326127	+	0.945326i	$0.605744\pi$
$968$	27.9468	+	967.596i	0.0288706	+	0.999583i
$969$	−105.860			−0.109246
$970$	281.070	−	225.029i	0.289763	−	0.231988i
$971$	229.352	−	315.676i	0.236202	−	0.325104i	−0.674418	−	0.738350i	$-0.735605\pi$
$971$	229.352	−	315.676i	0.236202	−	0.325104i	0.910619	+	0.413247i	$0.135605\pi$
$972$	3419.59	+	766.721i	3.51810	+	0.788808i
$973$	−36.4067	+	112.048i	−0.0374169	+	0.115158i
$974$	45.3560	+	968.512i	0.0465667	+	0.994366i
$975$	−238.001	−	327.580i	−0.244103	−	0.335980i
$976$	−81.4624	+	86.5212i	−0.0834656	+	0.0886488i
$977$	−238.210	−	733.134i	−0.243817	−	0.750393i	−0.995829	−	0.0912427i	$-0.970916\pi$
$977$	−238.210	−	733.134i	−0.243817	−	0.750393i	0.752011	−	0.659150i	$-0.229084\pi$
$978$	−291.907	−	773.275i	−0.298473	−	0.790669i
$979$	13.3647	−	61.8420i	0.0136513	−	0.0631685i
$980$	34.0639	−	29.9917i	0.0347591	−	0.0306038i
$981$	−236.139	−	726.762i	−0.240713	−	0.740838i
$982$	120.624	+	33.0414i	0.122835	+	0.0336471i
$983$	−977.073	−	1344.83i	−0.993971	−	1.36808i	−0.928952	−	0.370199i	$-0.879289\pi$
$983$	−977.073	−	1344.83i	−0.993971	−	1.36808i	−0.0650182	−	0.997884i	$-0.520711\pi$
$984$	−580.582	−	600.293i	−0.590022	−	0.610054i
$985$	−32.1783	+	99.0346i	−0.0326683	+	0.100543i
$986$	4.32414	+	2.84246i	0.00438554	+	0.00288282i
$987$	193.191	−	265.904i	0.195735	−	0.269407i
$988$	543.777	−	918.103i	0.550381	−	0.929254i
$989$	2475.67			2.50320
$990$	532.290	+	1068.23i	0.537667	+	1.07903i
$991$		−	1294.12i		−	1.30587i	−0.757412	−	0.652937i	$-0.773537\pi$
$991$		−	1294.12i		−	1.30587i	0.757412	−	0.652937i	$-0.226463\pi$
$992$	921.021	−	562.330i	0.928449	−	0.566865i
$993$	512.959	+	372.687i	0.516575	+	0.375314i
$994$	174.629	+	114.792i	0.175683	+	0.115484i
$995$	796.147	+	258.684i	0.800148	+	0.259984i
$996$	−227.450	−	526.553i	−0.228364	−	0.528668i
$997$	472.831	−	343.532i	0.474254	−	0.344566i	−0.324843	−	0.945768i	$-0.605311\pi$
$997$	472.831	−	343.532i	0.474254	−	0.344566i	0.799097	+	0.601202i	$0.205311\pi$
$998$	945.286	+	258.934i	0.947180	+	0.259453i
$999$	−1808.57	+	587.641i	−1.81038	+	0.588229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.s.b.71.19	yes	96
4.3	odd	2	inner	220.3.s.b.71.1	yes	96
11.9	even	5	inner	220.3.s.b.31.1	✓	96
44.31	odd	10	inner	220.3.s.b.31.19	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.s.b.31.1	✓	96	11.9	even	5	inner
220.3.s.b.31.19	yes	96	44.31	odd	10	inner
220.3.s.b.71.1	yes	96	4.3	odd	2	inner
220.3.s.b.71.19	yes	96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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+(1.56127 - 1.24997i) q^{2} +(3.38992 - 4.66582i) q^{3} +(0.875130 - 3.90309i) q^{4} +(-0.690983 + 2.12663i) q^{5} +(-0.539578 - 11.5219i) q^{6} +(3.89563 + 5.36188i) q^{7} +(-3.51245 - 7.18768i) q^{8} +(-7.49721 - 23.0740i) q^{9} +(1.57942 + 4.18395i) q^{10} +(-2.32357 + 10.7518i) q^{11} +(-15.2445 - 17.3144i) q^{12} +(4.33912 + 13.3544i) q^{13} +(12.7844 + 3.50190i) q^{14} +(7.58009 + 10.4331i) q^{15} +(-14.4683 - 6.83143i) q^{16} +(0.298562 - 0.918880i) q^{17} +(-40.5471 - 26.6535i) q^{18} +(11.1667 - 15.3697i) q^{19} +(7.69573 + 4.55805i) q^{20} +38.2235 q^{21} +(9.81174 + 19.6909i) q^{22} +38.7913i q^{23} +(-45.4434 - 7.97716i) q^{24} +(-4.04508 - 2.93893i) q^{25} +(23.4672 + 15.4261i) q^{26} +(-83.7093 - 27.1988i) q^{27} +(24.3371 - 10.5127i) q^{28} +(-2.16652 + 1.57407i) q^{29} +(24.8757 + 6.81397i) q^{30} +(-32.0719 + 10.4208i) q^{31} +(-31.1280 + 7.41928i) q^{32} +(42.2893 + 47.2891i) q^{33} +(-0.682440 - 1.80781i) q^{34} +(-14.0945 + 4.57959i) q^{35} +(-96.6212 + 9.06954i) q^{36} +(17.4791 - 12.6993i) q^{37} +(-1.77742 - 37.9544i) q^{38} +(77.0187 + 25.0249i) q^{39} +(17.7125 - 2.50311i) q^{40} +(14.6436 + 10.6392i) q^{41} +(59.6772 - 47.7784i) q^{42} -63.8202i q^{43} +(39.9318 + 18.4783i) q^{44} +54.2503 q^{45} +(48.4881 + 60.5637i) q^{46} +(5.05424 - 6.95657i) q^{47} +(-80.9206 + 44.3485i) q^{48} +(1.56803 - 4.82591i) q^{49} +(-9.98905 + 0.467793i) q^{50} +(-3.27523 - 4.50797i) q^{51} +(55.9209 - 5.24913i) q^{52} +(-23.1315 - 71.1913i) q^{53} +(-164.691 + 62.1698i) q^{54} +(-21.2595 - 12.3707i) q^{55} +(24.8562 - 46.8339i) q^{56} +(-33.8580 - 104.204i) q^{57} +(-1.41498 + 5.16564i) q^{58} +(22.5173 + 30.9924i) q^{59} +(47.3549 - 20.4555i) q^{60} +(2.29515 - 7.06375i) q^{61} +(-37.0472 + 56.3588i) q^{62} +(94.5139 - 130.087i) q^{63} +(-39.3254 + 50.4927i) q^{64} -31.3982 q^{65} +(125.135 + 20.9706i) q^{66} +110.957i q^{67} +(-3.32519 - 1.96946i) q^{68} +(180.993 + 131.499i) q^{69} +(-16.2810 + 24.7678i) q^{70} +(14.9941 + 4.87187i) q^{71} +(-139.515 + 134.934i) q^{72} +(48.5079 - 35.2430i) q^{73} +(11.4158 - 41.6756i) q^{74} +(-27.4250 + 8.91093i) q^{75} +(-50.2170 - 57.0353i) q^{76} +(-66.7016 + 29.4263i) q^{77} +(151.527 - 57.2008i) q^{78} +(-72.5257 + 23.5650i) q^{79} +(24.5252 - 26.0483i) q^{80} +(-234.021 + 170.026i) q^{81} +(36.1612 - 1.69345i) q^{82} +(23.6466 + 7.68324i) q^{83} +(33.4505 - 149.190i) q^{84} +(1.74781 + 1.26986i) q^{85} +(-79.7736 - 99.6405i) q^{86} +15.4446i q^{87} +(85.4418 - 21.0641i) q^{88} -5.75178 q^{89} +(84.6994 - 67.8115i) q^{90} +(-54.7013 + 75.2898i) q^{91} +(151.406 + 33.9474i) q^{92} +(-60.0996 + 184.968i) q^{93} +(-0.804491 - 17.1788i) q^{94} +(24.9696 + 34.3677i) q^{95} +(-70.9044 + 170.389i) q^{96} +(-24.8791 - 76.5699i) q^{97} +(-3.58414 - 9.49455i) q^{98} +(265.508 - 26.9943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} + 16 q^{4} - 120 q^{5} - 20 q^{6} - 10 q^{8} + 64 q^{9} - 10 q^{10} - 70 q^{12} + 20 q^{13} + 83 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} - 25 q^{20} + 35 q^{22} - 62 q^{24} - 120 q^{25}+ \cdots - 1042 q^{98}+O(q^{100}) \) 96 * q + 2 * q^2 + 16 * q^4 - 120 * q^5 - 20 * q^6 - 10 * q^8 + 64 * q^9 - 10 * q^10 - 70 * q^12 + 20 * q^13 + 83 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 - 25 * q^20 + 35 * q^22 - 62 * q^24 - 120 * q^25 - 88 * q^26 - 130 * q^28 - 8 * q^29 + 40 * q^30 + 152 * q^32 + 180 * q^33 - 126 * q^34 - 394 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 + 275 * q^42 + 113 * q^44 + 40 * q^45 - 85 * q^46 + 353 * q^48 + 292 * q^49 + 10 * q^50 + 62 * q^52 - 224 * q^53 - 328 * q^54 + 380 * q^56 - 364 * q^57 + 598 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 - 356 * q^64 - 40 * q^65 - 65 * q^66 - 117 * q^68 + 32 * q^69 - 165 * q^70 - 28 * q^72 + 16 * q^73 - 72 * q^74 - 720 * q^77 - 752 * q^78 - 235 * q^80 - 44 * q^81 + 49 * q^82 - 348 * q^84 + 60 * q^85 + 70 * q^86 - 165 * q^88 - 144 * q^89 + 778 * q^92 + 40 * q^93 + 254 * q^94 + 243 * q^96 + 204 * q^97 - 1042 * q^98

Introduction

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