LMFDB - Embedded newform 220.3.w.a.63.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

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

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: 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:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			63.5
Character	$\chi$	$=$	220.63
Dual form			220.3.w.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96237 + 0.386136i) q^{2} +(0.676076 + 0.344478i) q^{3} +(3.70180 - 1.51549i) q^{4} +(3.50937 - 3.56150i) q^{5} +(-1.45973 - 0.414936i) q^{6} +(-3.62504 - 7.11454i) q^{7} +(-6.67911 + 4.40334i) q^{8} +(-4.95165 - 6.81537i) q^{9} +(-5.51146 + 8.34409i) q^{10} +(-8.53099 - 6.94422i) q^{11} +(3.02475 + 0.250604i) q^{12} +(-2.75214 + 17.3763i) q^{13} +(9.86085 + 12.5616i) q^{14} +(3.59946 - 1.19895i) q^{15} +(11.4066 - 11.2200i) q^{16} +(0.282319 + 1.78249i) q^{17} +(12.3486 + 11.4623i) q^{18} +(-29.4107 + 9.55611i) q^{19} +(7.59357 - 18.5024i) q^{20} -6.05871i q^{21} +(19.4224 + 10.3330i) q^{22} +(-10.0993 + 10.0993i) q^{23} +(-6.03244 + 0.676187i) q^{24} +(-0.368626 - 24.9973i) q^{25} +(-1.30891 - 35.1614i) q^{26} +(-2.06824 - 13.0584i) q^{27} +(-24.2011 - 20.8429i) q^{28} +(11.6683 - 35.9113i) q^{29} +(-6.60052 + 3.74266i) q^{30} +(-9.77073 - 13.4483i) q^{31} +(-18.0515 + 26.4224i) q^{32} +(-3.37546 - 7.63356i) q^{33} +(-1.24230 - 3.38889i) q^{34} +(-38.0601 - 12.0570i) q^{35} +(-28.6586 - 17.7249i) q^{36} +(4.52256 + 8.87603i) q^{37} +(54.0247 - 30.1092i) q^{38} +(-7.84640 + 10.7996i) q^{39} +(-7.75696 + 39.2407i) q^{40} +(70.5782 - 22.9322i) q^{41} +(2.33949 + 11.8894i) q^{42} +(-1.92568 - 1.92568i) q^{43} +(-42.1039 - 12.7775i) q^{44} +(-41.6501 - 6.28232i) q^{45} +(15.9188 - 23.7182i) q^{46} +(17.7547 - 34.8455i) q^{47} +(11.5768 - 3.65628i) q^{48} +(-8.67429 + 11.9391i) q^{49} +(10.3757 + 48.9116i) q^{50} +(-0.423159 + 1.30235i) q^{51} +(16.1457 + 68.4943i) q^{52} +(-14.3061 - 2.26586i) q^{53} +(9.10096 + 24.8267i) q^{54} +(-54.6703 + 6.01330i) q^{55} +(55.5398 + 31.5565i) q^{56} +(-23.1757 - 3.67067i) q^{57} +(-9.03085 + 74.9769i) q^{58} +(8.73280 - 26.8768i) q^{59} +(11.5075 - 9.89319i) q^{60} +(1.41349 - 1.94550i) q^{61} +(24.3667 + 22.6176i) q^{62} +(-30.5383 + 59.9347i) q^{63} +(25.2211 - 58.8209i) q^{64} +(52.2275 + 70.7816i) q^{65} +(9.57151 + 13.6765i) q^{66} +(53.1731 + 53.1731i) q^{67} +(3.74642 + 6.17057i) q^{68} +(-10.3068 + 3.34889i) q^{69} +(79.3436 + 8.96386i) q^{70} +(48.5363 - 66.8045i) q^{71} +(63.0831 + 23.7168i) q^{72} +(9.19257 + 18.0414i) q^{73} +(-12.3023 - 15.6717i) q^{74} +(8.36179 - 17.0270i) q^{75} +(-94.3902 + 79.9462i) q^{76} +(-18.4798 + 85.8671i) q^{77} +(11.2274 - 24.2227i) q^{78} +(27.3454 + 37.6377i) q^{79} +(0.0697902 - 80.0000i) q^{80} +(-20.3291 + 62.5666i) q^{81} +(-129.646 + 72.2544i) q^{82} +(-22.6709 - 143.139i) q^{83} +(-9.18189 - 22.4281i) q^{84} +(7.33911 + 5.24994i) q^{85} +(4.52248 + 3.03533i) q^{86} +(20.2593 - 20.2593i) q^{87} +(87.5572 + 8.81638i) q^{88} +5.61342i q^{89} +(84.1589 - 3.75441i) q^{90} +(133.601 - 43.4096i) q^{91} +(-22.0801 + 52.6907i) q^{92} +(-1.97313 - 12.4578i) q^{93} +(-21.3861 + 75.2355i) q^{94} +(-69.1789 + 138.282i) q^{95} +(-21.3061 + 11.6452i) q^{96} +(-1.56473 + 9.87934i) q^{97} +(12.4120 - 26.7785i) q^{98} +(-5.08492 + 92.5272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−1.96237	+	0.386136i	−0.981185	+	0.193068i
$2$	−1.96237	+	0.386136i	−0.981185	+	0.193068i
$3$	0.676076	+	0.344478i	0.225359	+	0.114826i	0.563025	−	0.826440i	$-0.309638\pi$
$3$	0.676076	+	0.344478i	0.225359	+	0.114826i	−0.337666	+	0.941266i	$0.609638\pi$
$4$	3.70180	−	1.51549i	0.925449	−	0.378871i
$5$	3.50937	−	3.56150i	0.701874	−	0.712301i
$5$	3.50937	−	3.56150i	0.701874	−	0.712301i
$6$	−1.45973	−	0.414936i	−0.243288	−	0.0691559i
$7$	−3.62504	−	7.11454i	−0.517863	−	1.01636i	−0.990809	−	0.135271i	$-0.956809\pi$
$7$	−3.62504	−	7.11454i	−0.517863	−	1.01636i	0.472946	−	0.881091i	$-0.343191\pi$
$8$	−6.67911	+	4.40334i	−0.834889	+	0.550418i
$9$	−4.95165	−	6.81537i	−0.550184	−	0.757263i
$10$	−5.51146	+	8.34409i	−0.551146	+	0.834409i
$11$	−8.53099	−	6.94422i	−0.775544	−	0.631293i
$11$	−8.53099	−	6.94422i	−0.775544	−	0.631293i
$12$	3.02475	+	0.250604i	0.252062	+	0.0208837i
$13$	−2.75214	+	17.3763i	−0.211703	+	1.33664i	0.621389	+	0.783503i	$0.286569\pi$
$13$	−2.75214	+	17.3763i	−0.211703	+	1.33664i	−0.833091	+	0.553136i	$0.813431\pi$
$14$	9.86085	+	12.5616i	0.704347	+	0.897257i
$15$	3.59946	−	1.19895i	0.239964	−	0.0799297i
$16$	11.4066	−	11.2200i	0.712913	−	0.701253i
$17$	0.282319	+	1.78249i	0.0166070	+	0.104852i	0.994599	−	0.103788i	$-0.0330963\pi$
$17$	0.282319	+	1.78249i	0.0166070	+	0.104852i	−0.977992	+	0.208640i	$0.933096\pi$
$18$	12.3486	+	11.4623i	0.686036	+	0.636792i
$19$	−29.4107	+	9.55611i	−1.54793	+	0.502953i	−0.953551	−	0.301232i	$-0.902602\pi$
$19$	−29.4107	+	9.55611i	−1.54793	+	0.502953i	−0.594379	+	0.804185i	$0.702602\pi$
$20$	7.59357	−	18.5024i	0.379679	−	0.925118i
$21$		−	6.05871i		−	0.288510i
$22$	19.4224	+	10.3330i	0.882835	+	0.469682i
$23$	−10.0993	+	10.0993i	−0.439098	+	0.439098i	−0.891708	−	0.452610i	$-0.850493\pi$
$23$	−10.0993	+	10.0993i	−0.439098	+	0.439098i	0.452610	+	0.891708i	$0.350493\pi$
$24$	−6.03244	+	0.676187i	−0.251352	+	0.0281745i
$25$	−0.368626	−	24.9973i	−0.0147450	−	0.999891i
$26$	−1.30891	−	35.1614i	−0.0503428	−	1.35236i
$27$	−2.06824	−	13.0584i	−0.0766015	−	0.483643i
$28$	−24.2011	−	20.8429i	−0.864327	−	0.744389i
$29$	11.6683	−	35.9113i	0.402355	−	1.23832i	−0.520729	−	0.853722i	$-0.674340\pi$
$29$	11.6683	−	35.9113i	0.402355	−	1.23832i	0.923084	−	0.384599i	$-0.125660\pi$
$30$	−6.60052	+	3.74266i	−0.220017	+	0.124755i
$31$	−9.77073	−	13.4483i	−0.315185	−	0.433815i	0.621805	−	0.783172i	$-0.286400\pi$
$31$	−9.77073	−	13.4483i	−0.315185	−	0.433815i	−0.936989	+	0.349358i	$0.886400\pi$
$32$	−18.0515	+	26.4224i	−0.564110	+	0.825700i
$33$	−3.37546	−	7.63356i	−0.102287	−	0.231320i
$34$	−1.24230	−	3.38889i	−0.0365382	−	0.0996733i
$35$	−38.0601	−	12.0570i	−1.08743	−	0.344485i
$36$	−28.6586	−	17.7249i	−0.796072	−	0.492360i
$37$	4.52256	+	8.87603i	0.122231	+	0.239893i	0.944012	−	0.329912i	$-0.107019\pi$
$37$	4.52256	+	8.87603i	0.122231	+	0.239893i	−0.821780	+	0.569804i	$0.807019\pi$
$38$	54.0247	−	30.1092i	1.42170	−	0.792346i
$39$	−7.84640	+	10.7996i	−0.201190	+	0.276914i
$40$	−7.75696	+	39.2407i	−0.193924	+	0.981017i
$41$	70.5782	−	22.9322i	1.72142	−	0.559323i	0.729252	−	0.684245i	$-0.239868\pi$
$41$	70.5782	−	22.9322i	1.72142	−	0.559323i	0.992167	+	0.124922i	$0.0398680\pi$
$42$	2.33949	+	11.8894i	0.0557021	+	0.283082i
$43$	−1.92568	−	1.92568i	−0.0447834	−	0.0447834i	0.684360	−	0.729144i	$-0.260081\pi$
$43$	−1.92568	−	1.92568i	−0.0447834	−	0.0447834i	−0.729144	+	0.684360i	$0.760081\pi$
$44$	−42.1039	−	12.7775i	−0.956906	−	0.290398i
$45$	−41.6501	−	6.28232i	−0.925559	−	0.139607i
$46$	15.9188	−	23.7182i	0.346061	−	0.515612i
$47$	17.7547	−	34.8455i	0.377759	−	0.741394i	−0.621353	−	0.783531i	$-0.713417\pi$
$47$	17.7547	−	34.8455i	0.377759	−	0.741394i	0.999112	+	0.0421373i	$0.0134167\pi$
$48$	11.5768	−	3.65628i	0.241183	−	0.0761724i
$49$	−8.67429	+	11.9391i	−0.177026	+	0.243656i
$50$	10.3757	+	48.9116i	0.207515	+	0.978232i
$51$	−0.423159	+	1.30235i	−0.00829724	+	0.0255363i
$52$	16.1457	+	68.4943i	0.310494	+	1.31720i
$53$	−14.3061	−	2.26586i	−0.269926	−	0.0427521i	0.0200041	−	0.999800i	$-0.493632\pi$
$53$	−14.3061	−	2.26586i	−0.269926	−	0.0427521i	−0.289930	+	0.957048i	$0.593632\pi$
$54$	9.10096	+	24.8267i	0.168536	+	0.459754i
$55$	−54.6703	+	6.01330i	−0.994005	+	0.109333i
$56$	55.5398	+	31.5565i	0.991782	+	0.563509i
$57$	−23.1757	−	3.67067i	−0.406591	−	0.0643978i
$58$	−9.03085	+	74.9769i	−0.155704	+	1.29270i
$59$	8.73280	−	26.8768i	0.148014	−	0.455539i	−0.849373	−	0.527794i	$-0.823019\pi$
$59$	8.73280	−	26.8768i	0.148014	−	0.455539i	0.997386	+	0.0722546i	$0.0230194\pi$
$60$	11.5075	−	9.89319i	0.191791	−	0.164886i
$61$	1.41349	−	1.94550i	0.0231719	−	0.0318934i	−0.797274	−	0.603618i	$-0.793725\pi$
$61$	1.41349	−	1.94550i	0.0231719	−	0.0318934i	0.820446	+	0.571724i	$0.193725\pi$
$62$	24.3667	+	22.6176i	0.393011	+	0.364800i
$63$	−30.5383	+	59.9347i	−0.484734	+	0.951345i
$64$	25.2211	−	58.8209i	0.394080	−	0.919076i
$65$	52.2275	+	70.7816i	0.803500	+	1.08895i
$66$	9.57151	+	13.6765i	0.145023	+	0.207219i
$67$	53.1731	+	53.1731i	0.793628	+	0.793628i	0.982082	−	0.188454i	$-0.0603475\pi$
$67$	53.1731	+	53.1731i	0.793628	+	0.793628i	−0.188454	+	0.982082i	$0.560348\pi$
$68$	3.74642	+	6.17057i	0.0550945	+	0.0907436i
$69$	−10.3068	+	3.34889i	−0.149374	+	0.0485347i
$70$	79.3436	+	8.96386i	1.13348	+	0.128055i
$71$	48.5363	−	66.8045i	0.683610	−	0.940908i	−0.316360	−	0.948639i	$-0.602461\pi$
$71$	48.5363	−	66.8045i	0.683610	−	0.940908i	0.999970	+	0.00773106i	$0.00246090\pi$
$72$	63.0831	+	23.7168i	0.876154	+	0.329400i
$73$	9.19257	+	18.0414i	0.125926	+	0.247143i	0.945359	−	0.326032i	$-0.105712\pi$
$73$	9.19257	+	18.0414i	0.125926	+	0.247143i	−0.819433	+	0.573175i	$0.805712\pi$
$74$	−12.3023	−	15.6717i	−0.166247	−	0.211780i
$75$	8.36179	−	17.0270i	0.111491	−	0.227027i
$76$	−94.3902	+	79.9462i	−1.24198	+	1.05192i
$77$	−18.4798	+	85.8671i	−0.239997	+	1.11516i
$78$	11.2274	−	24.2227i	0.143941	−	0.310547i
$79$	27.3454	+	37.6377i	0.346144	+	0.476426i	0.946223	−	0.323514i	$-0.104864\pi$
$79$	27.3454	+	37.6377i	0.346144	+	0.476426i	−0.600079	+	0.799940i	$0.704864\pi$
$80$	0.0697902	−	80.0000i	0.000872378	−	1.00000i
$81$	−20.3291	+	62.5666i	−0.250977	+	0.772427i
$82$	−129.646	+	72.2544i	−1.58104	+	0.881151i
$83$	−22.6709	−	143.139i	−0.273144	−	1.72456i	−0.618236	−	0.785993i	$-0.712152\pi$
$83$	−22.6709	−	143.139i	−0.273144	−	1.72456i	0.345092	−	0.938569i	$-0.387848\pi$
$84$	−9.18189	−	22.4281i	−0.109308	−	0.267002i
$85$	7.33911	+	5.24994i	0.0863424	+	0.0617640i
$86$	4.52248	+	3.03533i	0.0525870	+	0.0352945i
$87$	20.2593	−	20.2593i	0.232866	−	0.232866i
$88$	87.5572	+	8.81638i	0.994969	+	0.100186i
$89$			5.61342i			0.0630721i	0.999503	+	0.0315360i	$0.0100399\pi$
$89$			5.61342i			0.0630721i	−0.999503	+	0.0315360i	$0.989960\pi$
$90$	84.1589	−	3.75441i	0.935098	−	0.0417156i
$91$	133.601	−	43.4096i	1.46814	−	0.477028i
$92$	−22.0801	+	52.6907i	−0.240001	+	0.572725i
$93$	−1.97313	−	12.4578i	−0.0212164	−	0.133955i
$94$	−21.3861	+	75.2355i	−0.227512	+	0.800378i
$95$	−69.1789	+	138.282i	−0.728198	+	1.45560i
$96$	−21.3061	+	11.6452i	−0.221939	+	0.121304i
$97$	−1.56473	+	9.87934i	−0.0161313	+	0.101849i	−0.994440	−	0.105302i	$-0.966419\pi$
$97$	−1.56473	+	9.87934i	−0.0161313	+	0.101849i	0.978309	+	0.207151i	$0.0664191\pi$
$98$	12.4120	−	26.7785i	0.126653	−	0.273250i
$99$	−5.08492	+	92.5272i	−0.0513629	+	0.934618i
$100$	−39.2476	−	91.9762i	−0.392476	−	0.919762i
$101$	−56.4692	−	77.7232i	−0.559101	−	0.769536i	0.432111	−	0.901820i	$-0.357769\pi$
$101$	−56.4692	−	77.7232i	−0.559101	−	0.769536i	−0.991212	+	0.132284i	$0.957769\pi$
$102$	0.327510	−	2.71909i	0.00321089	−	0.0266578i
$103$	13.7955	+	27.0751i	0.133937	+	0.262865i	0.948228	−	0.317591i	$-0.102874\pi$
$103$	13.7955	+	27.0751i	0.133937	+	0.262865i	−0.814291	+	0.580457i	$0.802874\pi$
$104$	−58.1320	−	128.177i	−0.558961	−	1.23247i
$105$	−21.5781	−	21.2623i	−0.205506	−	0.202498i
$106$	28.9488	−	1.07764i	0.273102	−	0.0101664i
$107$	143.834	+	73.2873i	1.34425	+	0.684928i	0.970160	−	0.242466i	$-0.0779561\pi$
$107$	143.834	+	73.2873i	1.34425	+	0.684928i	0.374087	+	0.927394i	$0.377956\pi$
$108$	−27.4460	−	45.2050i	−0.254129	−	0.418565i
$109$	−157.535			−1.44527			−0.722636	−	0.691229i	$-0.757069\pi$
$109$	−157.535			−1.44527			−0.722636	+	0.691229i	$0.757069\pi$
$110$	104.961	−	32.9105i	0.954195	−	0.299186i
$111$			7.55879i			0.0680972i
$112$	−121.175	−	40.4797i	−1.08192	−	0.361426i
$113$	73.5546	−	144.359i	0.650926	−	1.27751i	−0.295731	−	0.955271i	$-0.595563\pi$
$113$	73.5546	−	144.359i	0.650926	−	1.27751i	0.946657	−	0.322243i	$-0.104437\pi$
$114$	46.8967	−	1.74577i	0.411375	−	0.0153138i
$115$	0.526504	+	71.4106i	0.00457830	+	0.620962i
$116$	−11.2294	−	150.620i	−0.0968054	−	1.29844i
$117$	132.053	−	67.2846i	1.12866	−	0.575082i
$118$	−6.75888	+	56.1143i	−0.0572787	+	0.475545i
$119$	11.6582	−	8.47016i	0.0979679	−	0.0711778i
$120$	−18.7618	+	23.8576i	−0.156349	+	0.198813i
$121$	24.5555	+	118.482i	0.202938	+	0.979192i
$122$	−2.02256	+	4.36359i	−0.0165783	+	0.0357671i
$123$	55.6158	+	8.80868i	0.452161	+	0.0716153i
$124$	−56.5499	−	34.9753i	−0.456048	−	0.282059i
$125$	−90.3216	−	86.4119i	−0.722573	−	0.691295i
$126$	36.7844	−	129.406i	0.291940	−	1.02703i
$127$	−166.030	+	26.2966i	−1.30732	+	0.207060i	−0.770937	−	0.636912i	$-0.780211\pi$
$127$	−166.030	+	26.2966i	−1.30732	+	0.207060i	−0.536388	+	0.843972i	$0.680211\pi$
$128$	−26.7803	+	125.167i	−0.209221	+	0.977868i
$129$	−0.638553	−	1.96526i	−0.00495002	−	0.0152346i
$130$	−129.821	−	118.733i	−0.998624	−	0.913329i
$131$	−165.619			−1.26427			−0.632135	−	0.774858i	$-0.717821\pi$
$131$	−165.619			−1.26427			−0.632135	+	0.774858i	$0.717821\pi$
$132$	−24.0638	−	23.1424i	−0.182302	−	0.175321i
$133$	174.602	+	174.602i	1.31280	+	1.31280i
$134$	−124.877	−	83.8133i	−0.931921	−	0.625472i
$135$	−53.7656	−	38.4606i	−0.398264	−	0.284893i
$136$	−9.73455	−	10.6623i	−0.0715776	−	0.0783993i
$137$	−113.597	+	17.9920i	−0.829177	+	0.131329i	−0.556574	−	0.830798i	$-0.687884\pi$
$137$	−113.597	+	17.9920i	−0.829177	+	0.131329i	−0.272603	+	0.962127i	$0.587884\pi$
$138$	18.9327	−	10.5516i	0.137193	−	0.0764610i
$139$	194.379	+	63.1577i	1.39841	+	0.454372i	0.908677	−	0.417499i	$-0.137093\pi$
$139$	194.379	+	63.1577i	1.39841	+	0.454372i	0.489735	+	0.871871i	$0.337093\pi$
$140$	−159.163	+	13.0470i	−1.13688	+	0.0931931i
$141$	24.0070	−	17.4421i	0.170262	−	0.123703i
$142$	−69.4505	+	149.837i	−0.489088	+	1.05519i
$143$	144.143	−	129.126i	1.00800	−	0.902976i
$144$	−132.950	−	22.1824i	−0.923266	−	0.154045i
$145$	−86.9499	−	167.583i	−0.599655	−	1.15574i
$146$	−25.0057	−	31.8544i	−0.171272	−	0.218181i
$147$	−9.97725	+	5.08366i	−0.0678724	+	0.0345827i
$148$	30.1931	+	26.0034i	0.204007	+	0.175698i
$149$	128.941	+	93.6811i	0.865376	+	0.628732i	0.929342	−	0.369220i	$-0.120375\pi$
$149$	128.941	+	93.6811i	0.865376	+	0.628732i	−0.0639665	+	0.997952i	$0.520375\pi$
$150$	−9.83417	+	36.6422i	−0.0655611	+	0.244281i
$151$	−82.2950	−	253.278i	−0.545000	−	1.67734i	−0.720990	−	0.692946i	$-0.756312\pi$
$151$	−82.2950	−	253.278i	−0.545000	−	1.67734i	0.175989	−	0.984392i	$-0.443688\pi$
$152$	154.358	−	193.332i	1.01552	−	1.27192i
$153$	10.7504	−	10.7504i	0.0702639	−	0.0702639i
$154$	3.10775	−	175.639i	0.0201802	−	1.14051i
$155$	−82.1851	−	12.3964i	−0.530227	−	0.0799770i
$156$	−12.6791	+	51.8692i	−0.0812761	+	0.332495i
$157$	−20.0924	−	10.2376i	−0.127977	−	0.0652075i	0.388830	−	0.921310i	$-0.372879\pi$
$157$	−20.0924	−	10.2376i	−0.127977	−	0.0652075i	−0.516807	+	0.856102i	$0.672879\pi$
$158$	−68.1950	−	63.3000i	−0.431614	−	0.400633i
$159$	−8.89146	−	6.46002i	−0.0559211	−	0.0406291i
$160$	30.7540	+	157.017i	0.192212	+	0.981353i
$161$	108.462	+	35.2414i	0.673676	+	0.218890i
$162$	15.7340	−	130.629i	0.0971236	−	0.806350i
$163$	2.06309	−	13.0259i	0.0126570	−	0.0799133i	−0.980551	−	0.196263i	$-0.937119\pi$
$163$	2.06309	−	13.0259i	0.0126570	−	0.0799133i	0.993208	+	0.116350i	$0.0371194\pi$
$164$	226.513	−	191.851i	1.38117	−	1.16982i
$165$	−39.0327	−	14.7673i	−0.236562	−	0.0894985i
$166$	99.7598	+	272.137i	0.600963	+	1.63938i
$167$	36.5443	−	230.731i	0.218828	−	1.38162i	−0.596494	−	0.802617i	$-0.703440\pi$
$167$	36.5443	−	230.731i	0.218828	−	1.38162i	0.815322	−	0.579008i	$-0.196560\pi$
$168$	26.6786	+	40.4668i	0.158801	+	0.240874i
$169$	−133.633	−	43.4200i	−0.790727	−	0.256923i
$170$	−16.4292	−	7.46843i	−0.0966426	−	0.0439319i
$171$	210.760	+	153.126i	1.23251	+	0.895474i
$172$	−10.0468	−	4.21015i	−0.0584119	−	0.0244776i
$173$	−19.1647	−	9.76490i	−0.110779	−	0.0564445i	0.397723	−	0.917505i	$-0.369800\pi$
$173$	−19.1647	−	9.76490i	−0.110779	−	0.0564445i	−0.508502	+	0.861061i	$0.669800\pi$
$174$	−31.9334	+	47.5791i	−0.183525	+	0.273443i
$175$	−176.508	+	93.2387i	−1.00862	+	0.532793i
$176$	−175.224	+	16.5080i	−0.995591	+	0.0937956i
$177$	15.1625	−	15.1625i	0.0856638	−	0.0856638i
$178$	−2.16754	−	11.0156i	−0.0121772	−	0.0618854i
$179$	106.579	+	328.015i	0.595411	+	1.83249i	0.552667	+	0.833402i	$0.313610\pi$
$179$	106.579	+	328.015i	0.595411	+	1.83249i	0.0427440	+	0.999086i	$0.486390\pi$
$180$	−163.701	+	39.8643i	−0.909451	+	0.221469i
$181$	44.7076	+	32.4820i	0.247004	+	0.179459i	0.704398	−	0.709805i	$-0.251217\pi$
$181$	44.7076	+	32.4820i	0.247004	+	0.179459i	−0.457394	+	0.889264i	$0.651217\pi$
$182$	−245.413	+	136.774i	−1.34842	+	0.751505i
$183$	1.62581	−	0.828389i	0.00888418	−	0.00452672i
$184$	22.9836	−	111.925i	0.124911	−	0.608286i
$185$	47.4834	+	15.0422i	0.256667	+	0.0813089i
$186$	8.68243	+	23.6850i	0.0466798	+	0.127339i
$187$	9.96955	−	17.1669i	0.0533131	−	0.0918015i
$188$	12.9163	−	155.898i	0.0687039	−	0.829244i
$189$	−85.4068	+	62.0517i	−0.451888	+	0.328316i
$190$	82.3588	−	298.073i	0.433467	−	1.56881i
$191$	122.340	+	39.7508i	0.640526	+	0.208120i	0.611232	−	0.791451i	$-0.290674\pi$
$191$	122.340	+	39.7508i	0.640526	+	0.208120i	0.0292939	+	0.999571i	$0.490674\pi$
$192$	37.3139	−	31.0792i	0.194343	−	0.161871i
$193$	−304.922	+	48.2950i	−1.57991	+	0.250233i	−0.883857	−	0.467758i	$-0.845062\pi$
$193$	−304.922	+	48.2950i	−1.57991	+	0.250233i	−0.696052	+	0.717991i	$0.745062\pi$
$194$	−0.744186	−	19.9911i	−0.00383601	−	0.103047i
$195$	10.9270	+	65.8449i	0.0560361	+	0.337666i
$196$	−14.0169	+	57.3420i	−0.0715147	+	0.292561i
$197$	78.9040	+	78.9040i	0.400528	+	0.400528i	0.878419	−	0.477891i	$-0.158599\pi$
$197$	78.9040	+	78.9040i	0.400528	+	0.400528i	−0.477891	+	0.878419i	$0.658599\pi$
$198$	−25.7496	−	183.536i	−0.130049	−	0.926950i
$199$	145.371			0.730508			0.365254	−	0.930908i	$-0.380982\pi$
$199$	145.371			0.730508			0.365254	+	0.930908i	$0.380982\pi$
$200$	112.534	+	165.337i	0.562669	+	0.826683i
$201$	17.6321	+	54.2660i	0.0877218	+	0.269980i
$202$	140.825	+	130.717i	0.697155	+	0.647113i
$203$	−297.790	+	47.1654i	−1.46695	+	0.232342i
$204$	0.407244	+	5.46233i	0.00199629	+	0.0267761i
$205$	166.012	−	331.842i	0.809814	−	1.61874i
$206$	−37.5265	−	47.8045i	−0.182168	−	0.232061i
$207$	118.838	+	18.8221i	0.574097	+	0.0909281i
$208$	163.570	+	229.084i	0.786395	+	1.10136i
$209$	317.262	+	122.711i	1.51800	+	0.587135i
$210$	50.5544	+	33.3924i	0.240735	+	0.159011i
$211$	111.627	−	81.1020i	0.529039	−	0.384370i	−0.290959	−	0.956736i	$-0.593974\pi$
$211$	111.627	−	81.1020i	0.529039	−	0.384370i	0.819998	+	0.572366i	$0.193974\pi$
$212$	−56.3921	+	13.2929i	−0.266000	+	0.0627024i
$213$	55.8269	−	28.4452i	0.262098	−	0.133546i
$214$	−310.555	−	88.2771i	−1.45119	−	0.412510i
$215$	−13.6163	+	0.100392i	−0.0633315	+	0.000466938i
$216$	71.3145	+	78.1111i	0.330160	+	0.361625i
$217$	−60.2589	+	118.265i	−0.277691	+	0.544999i
$218$	309.141	−	60.8298i	1.41808	−	0.279036i
$219$			15.3640i			0.0701553i
$220$	−193.265	+	105.112i	−0.878478	+	0.477782i
$221$	−31.7501			−0.143665
$222$	−2.91872	−	14.8331i	−0.0131474	−	0.0668160i
$223$	−77.6090	−	39.5438i	−0.348022	−	0.177326i	0.271237	−	0.962513i	$-0.412567\pi$
$223$	−77.6090	−	39.5438i	−0.348022	−	0.177326i	−0.619260	+	0.785186i	$0.712567\pi$
$224$	253.421	+	32.6461i	1.13134	+	0.145741i
$225$	−168.540	+	126.290i	−0.749068	+	0.561290i
$226$	−88.5991	+	311.688i	−0.392032	+	1.37915i
$227$	123.293	+	241.977i	0.543143	+	1.06598i	0.985585	+	0.169181i	$0.0541122\pi$
$227$	123.293	+	241.977i	0.543143	+	1.06598i	−0.442442	+	0.896797i	$0.645888\pi$
$228$	−91.3546	+	21.5344i	−0.400678	+	0.0944490i
$229$	−23.4994	−	32.3442i	−0.102617	−	0.141241i	0.754620	−	0.656162i	$-0.227821\pi$
$229$	−23.4994	−	32.3442i	−0.102617	−	0.141241i	−0.857238	+	0.514921i	$0.827821\pi$
$230$	−28.6074	−	139.931i	−0.124380	−	0.608394i
$231$	−42.0731	+	51.6868i	−0.182134	+	0.223752i
$232$	80.1960	+	291.235i	0.345672	+	1.25532i
$233$	−21.4341	+	135.330i	−0.0919920	+	0.580814i	0.898034	+	0.439927i	$0.144996\pi$
$233$	−21.4341	+	135.330i	−0.0919920	+	0.580814i	−0.990026	+	0.140888i	$0.955004\pi$
$234$	−233.157	+	183.028i	−0.996397	+	0.782171i
$235$	−61.7947	−	185.519i	−0.262956	−	0.789443i
$236$	−8.40435	−	112.727i	−0.0356116	−	0.477656i
$237$	5.52220	+	34.8658i	0.0233004	+	0.147113i
$238$	−19.6070	+	21.1232i	−0.0823825	+	0.0887531i
$239$	43.3398	−	14.0819i	0.181338	−	0.0589203i	−0.216941	−	0.976185i	$-0.569608\pi$
$239$	43.3398	−	14.0819i	0.181338	−	0.0589203i	0.398278	+	0.917265i	$0.369608\pi$
$240$	27.6054	−	54.0620i	0.115022	−	0.225258i
$241$		−	46.1322i		−	0.191420i	−0.995409	−	0.0957100i	$-0.969488\pi$
$241$		−	46.1322i		−	0.191420i	0.995409	−	0.0957100i	$-0.0305121\pi$
$242$	−93.9373	−	223.024i	−0.388171	−	0.921587i
$243$	−119.436	+	119.436i	−0.491505	+	0.491505i
$244$	2.28407	−	9.34396i	0.00936093	−	0.0382949i
$245$	12.0800	+	72.7924i	0.0493061	+	0.297112i
$246$	−112.540	+	4.18940i	−0.457481	+	0.0170301i
$247$	−85.1076	−	537.348i	−0.344565	−	2.17550i
$248$	124.477	+	46.7986i	0.501924	+	0.188704i
$249$	33.9808	−	104.582i	0.136469	−	0.420009i
$250$	210.611	+	134.696i	0.842445	+	0.538783i
$251$	192.816	+	265.388i	0.768191	+	1.05732i	0.996488	+	0.0837328i	$0.0266842\pi$
$251$	192.816	+	265.388i	0.768191	+	1.05732i	−0.228297	+	0.973592i	$0.573316\pi$
$252$	−22.2163	+	268.146i	−0.0881597	+	1.06407i
$253$	156.288	−	16.0252i	0.617740	−	0.0633405i
$254$	315.659	−	115.714i	1.24275	−	0.455567i
$255$	3.15330	+	6.07752i	0.0123659	+	0.0238334i
$256$	4.22133	−	255.965i	0.0164896	−	0.999864i
$257$	−135.201	−	265.347i	−0.526074	−	1.03248i	−0.989253	−	0.146214i	$-0.953291\pi$
$257$	−135.201	−	265.347i	−0.526074	−	1.03248i	0.463179	−	0.886265i	$-0.346709\pi$
$258$	2.01194	+	3.61001i	0.00779821	+	0.0139923i
$259$	46.7544	−	64.3519i	0.180519	−	0.248463i
$260$	300.604	+	182.869i	1.15617	+	0.703343i
$261$	−302.526	+	98.2967i	−1.15910	+	0.376616i
$262$	325.007	−	63.9517i	1.24048	−	0.244090i
$263$	−55.4741	−	55.4741i	−0.210928	−	0.210928i	0.593733	−	0.804662i	$-0.297653\pi$
$263$	−55.4741	−	55.4741i	−0.210928	−	0.210928i	−0.804662	+	0.593733i	$0.797653\pi$
$264$	56.1583	+	36.1221i	0.212721	+	0.136826i
$265$	−58.2752	+	42.9994i	−0.219907	+	0.162262i
$266$	−410.054	−	275.214i	−1.54156	−	1.03464i
$267$	−1.93370	+	3.79509i	−0.00724231	+	0.0142138i
$268$	277.419	+	116.253i	1.03515	+	0.433780i
$269$	−152.271	+	209.584i	−0.566065	+	0.779122i	−0.992082	−	0.125594i	$-0.959916\pi$
$269$	−152.271	+	209.584i	−0.566065	+	0.779122i	0.426017	+	0.904715i	$0.359916\pi$
$270$	120.359	+	54.7131i	0.445775	+	0.202641i
$271$	90.2497	−	277.760i	0.333025	−	1.02495i	−0.634662	−	0.772790i	$-0.718861\pi$
$271$	90.2497	−	277.760i	0.333025	−	1.02495i	0.967687	−	0.252155i	$-0.0811394\pi$
$272$	23.2199	+	17.1645i	0.0853673	+	0.0631049i
$273$	105.278	+	16.6744i	0.385634	+	0.0610784i
$274$	215.973	−	79.1711i	0.788221	−	0.288946i
$275$	−170.442	+	215.811i	−0.619789	+	0.784769i
$276$	−33.0786	+	28.0168i	−0.119850	+	0.101510i
$277$	144.821	+	22.9374i	0.522821	+	0.0828067i	0.412266	−	0.911063i	$-0.364737\pi$
$277$	144.821	+	22.9374i	0.522821	+	0.0828067i	0.110554	+	0.993870i	$0.464737\pi$
$278$	−405.832	−	48.8818i	−1.45983	−	0.175834i
$279$	−43.2735	+	133.182i	−0.155102	+	0.477356i
$280$	307.299	−	87.0617i	1.09749	−	0.310935i
$281$	4.99155	−	6.87029i	0.0177635	−	0.0244494i	−0.800043	−	0.599943i	$-0.795190\pi$
$281$	4.99155	−	6.87029i	0.0177635	−	0.0244494i	0.817806	+	0.575493i	$0.195190\pi$
$282$	−40.3756	+	43.4979i	−0.143176	+	0.154248i
$283$	−42.0181	+	82.4651i	−0.148474	+	0.291396i	−0.953250	−	0.302182i	$-0.902285\pi$
$283$	−42.0181	+	82.4651i	−0.148474	+	0.291396i	0.804777	+	0.593578i	$0.202285\pi$
$284$	78.4303	−	320.853i	0.276163	−	1.12976i
$285$	−94.4053	+	69.6586i	−0.331247	+	0.244416i
$286$	−233.003	+	309.051i	−0.814694	+	1.08060i
$287$	−419.001	−	419.001i	−1.45993	−	1.45993i
$288$	269.463	−	7.80677i	0.935636	−	0.0271068i
$289$	271.758	−	88.2995i	0.940338	−	0.305534i
$290$	235.338	+	295.285i	0.811510	+	1.01822i
$291$	−4.46109	+	6.14017i	−0.0153302	+	0.0211002i
$292$	61.3706	+	52.8545i	0.210173	+	0.181009i
$293$	−235.210	−	461.626i	−0.802766	−	1.57552i	−0.817712	−	0.575628i	$-0.804758\pi$
$293$	−235.210	−	461.626i	−0.802766	−	1.57552i	0.0149458	−	0.999888i	$-0.495242\pi$
$294$	17.6161	−	13.8286i	0.0599186	−	0.0470361i
$295$	−65.0752	−	125.423i	−0.220594	−	0.425161i
$296$	−69.2909	−	39.3696i	−0.234091	−	0.133005i
$297$	−73.0360	+	125.763i	−0.245913	+	0.423445i
$298$	−289.204	−	134.048i	−0.970482	−	0.449826i
$299$	−147.693	−	203.282i	−0.493957	−	0.679874i
$300$	5.14942	−	75.7028i	0.0171647	−	0.252343i
$301$	−6.71968	+	20.6810i	−0.0223245	+	0.0687078i
$302$	259.293	+	465.248i	0.858587	+	1.54056i
$303$	−11.4035	−	71.9991i	−0.0376355	−	0.237621i
$304$	−228.256	+	438.992i	−0.750842	+	1.44405i
$305$	−1.96845	−	11.8616i	−0.00645393	−	0.0388905i
$306$	−16.9451	+	25.2473i	−0.0553762	+	0.0825076i
$307$	170.671	−	170.671i	0.555933	−	0.555933i	−0.372214	−	0.928147i	$-0.621401\pi$
$307$	170.671	−	170.671i	0.555933	−	0.555933i	0.928147	+	0.372214i	$0.121401\pi$
$308$	61.7220	+	345.869i	0.200396	+	1.12295i
$309$			23.0571i			0.0746184i
$310$	166.064	−	7.40829i	0.535692	−	0.0238977i
$311$	−282.646	+	91.8372i	−0.908829	+	0.295296i	−0.725876	−	0.687825i	$-0.758565\pi$
$311$	−282.646	+	91.8372i	−0.908829	+	0.295296i	−0.182953	+	0.983122i	$0.558565\pi$
$312$	4.85246	−	106.682i	0.0155528	−	0.341931i
$313$	−44.7144	−	282.315i	−0.142857	−	0.901966i	−0.950145	−	0.311808i	$-0.899065\pi$
$313$	−44.7144	−	282.315i	−0.142857	−	0.901966i	0.807288	−	0.590158i	$-0.200935\pi$
$314$	43.3818	+	12.3315i	0.138159	+	0.0392724i
$315$	106.288	+	319.095i	0.337421	+	1.01300i
$316$	158.266	+	97.8855i	0.500843	+	0.309764i
$317$	53.9840	−	340.841i	0.170296	−	1.07521i	−0.743410	−	0.668836i	$-0.766793\pi$
$317$	53.9840	−	340.841i	0.170296	−	1.07521i	0.913707	−	0.406374i	$-0.133207\pi$
$318$	19.9428	+	9.24364i	0.0627132	+	0.0290681i
$319$	−348.918	+	225.332i	−1.09379	+	0.706369i
$320$	−120.980	−	296.249i	−0.378064	−	0.925779i
$321$	71.9971	+	99.0955i	0.224290	+	0.308709i
$322$	−226.450	−	27.2756i	−0.703261	−	0.0847068i
$323$	−25.3368	−	49.7264i	−0.0784422	−	0.153952i
$324$	19.5645	+	262.417i	0.0603843	+	0.809930i
$325$	435.375	+	62.3905i	1.33961	+	0.191971i
$326$	0.981206	+	26.3582i	0.00300983	+	0.0808534i
$327$	−106.505	−	54.2672i	−0.325704	−	0.165955i
$328$	−370.421	+	463.947i	−1.12933	+	1.41447i
$329$	−312.271			−0.949152
$330$	82.2988	+	13.9069i	0.249390	+	0.0421421i
$331$		−	15.9005i		−	0.0480377i	−0.999712	−	0.0240188i	$-0.992354\pi$
$331$		−	15.9005i		−	0.0480377i	0.999712	−	0.0240188i	$-0.00764617\pi$
$332$	−300.848	−	495.513i	−0.906168	−	1.49251i
$333$	38.0992	−	74.7739i	0.114412	−	0.224546i
$334$	17.3804	+	466.892i	0.0520372	+	1.39788i
$335$	375.980	−	2.77207i	1.12233	−	0.00827484i
$336$	−67.9790	−	69.1094i	−0.202319	−	0.205683i
$337$	555.102	−	282.838i	1.64719	−	0.839283i	0.650364	−	0.759623i	$-0.274616\pi$
$337$	555.102	−	282.838i	1.64719	−	0.839283i	0.996822	−	0.0796602i	$-0.0253835\pi$
$338$	279.003	+	33.6055i	0.825454	+	0.0994246i
$339$	99.4570	−	72.2597i	0.293384	−	0.213156i
$340$	35.1241	+	8.31190i	0.103306	+	0.0244468i
$341$	−10.0337	+	182.577i	−0.0294243	+	0.535417i
$342$	−472.716	−	219.108i	−1.38221	−	0.640666i
$343$	−270.054	−	42.7723i	−0.787329	−	0.124701i
$344$	21.3413	+	4.38242i	0.0620387	+	0.0127396i
$345$	−24.2434	+	48.4603i	−0.0702707	+	0.140465i
$346$	41.3788	+	11.7622i	0.119592	+	0.0339947i
$347$	−302.641	+	47.9336i	−0.872164	+	0.138137i	−0.576443	−	0.817137i	$-0.695560\pi$
$347$	−302.641	+	47.9336i	−0.872164	+	0.138137i	−0.295721	+	0.955274i	$0.595560\pi$
$348$	44.2931	−	105.698i	0.127279	−	0.303731i
$349$	107.776	+	331.701i	0.308814	+	0.950431i	0.978226	+	0.207540i	$0.0665459\pi$
$349$	107.776	+	331.701i	0.308814	+	0.950431i	−0.669413	+	0.742891i	$0.733454\pi$
$350$	310.371	−	251.125i	0.886774	−	0.717500i
$351$	232.598			0.662672
$352$	337.480	−	100.055i	0.958751	−	0.284248i
$353$	−7.94999	−	7.94999i	−0.0225212	−	0.0225212i	0.695757	−	0.718278i	$-0.255069\pi$
$353$	−7.94999	−	7.94999i	−0.0225212	−	0.0225212i	−0.718278	+	0.695757i	$0.755069\pi$
$354$	−23.8996	+	35.6092i	−0.0675131	+	0.100591i
$355$	−67.5925	−	407.304i	−0.190402	−	1.14733i
$356$	8.50705	+	20.7797i	0.0238962	+	0.0583700i
$357$	10.7996	−	1.71049i	0.0302510	−	0.00479128i
$358$	−335.805	−	602.534i	−0.938004	−	1.68306i
$359$	−279.395	−	90.7810i	−0.778259	−	0.252872i	−0.107163	−	0.994242i	$-0.534177\pi$
$359$	−279.395	−	90.7810i	−0.778259	−	0.252872i	−0.671097	+	0.741370i	$0.734177\pi$
$360$	305.849	−	141.440i	0.849581	−	0.392888i
$361$	481.613	−	349.913i	1.33411	−	0.969287i
$362$	−100.275	−	46.4785i	−0.277004	−	0.128394i
$363$	−24.2131	+	88.5618i	−0.0667027	+	0.243972i
$364$	428.777	−	363.164i	1.17796	−	0.997703i
$365$	96.5148	+	30.5747i	0.264424	+	0.0837664i
$366$	−2.87056	+	2.25339i	−0.00784306	+	0.00615680i
$367$	7.96681	−	4.05929i	0.0217079	−	0.0110607i	−0.443103	−	0.896471i	$-0.646122\pi$
$367$	7.96681	−	4.05929i	0.0217079	−	0.0110607i	0.464811	+	0.885410i	$0.346122\pi$
$368$	−1.88416	+	228.512i	−0.00512001	+	0.620957i
$369$	−505.770	−	367.464i	−1.37065	−	0.995837i
$370$	−98.9883	−	11.1832i	−0.267536	−	0.0302249i
$371$	35.7396	+	109.995i	0.0963330	+	0.296483i
$372$	−26.1838	−	43.1262i	−0.0703866	−	0.115931i
$373$	−177.519	+	177.519i	−0.475923	+	0.475923i	−0.903825	−	0.427902i	$-0.859253\pi$
$373$	−177.519	+	177.519i	−0.475923	+	0.475923i	0.427902	+	0.903825i	$0.359253\pi$
$374$	−12.9352	+	37.5374i	−0.0345861	+	0.100367i
$375$	−31.2972	−	89.5348i	−0.0834593	−	0.238759i
$376$	34.8512	+	310.917i	0.0926895	+	0.826907i
$377$	591.893	+	301.584i	1.57001	+	0.799959i
$378$	143.639	−	154.747i	0.379998	−	0.409384i
$379$	197.872	+	143.762i	0.522089	+	0.379320i	0.817390	−	0.576084i	$-0.195420\pi$
$379$	197.872	+	143.762i	0.522089	+	0.379320i	−0.295301	+	0.955404i	$0.595420\pi$
$380$	−46.5215	+	616.732i	−0.122425	+	1.62298i
$381$	−121.308	−	39.4152i	−0.318393	−	0.103452i
$382$	−255.427	−	30.7658i	−0.668656	−	0.0805386i
$383$	−106.222	+	670.661i	−0.277343	+	1.75107i	0.318455	+	0.947938i	$0.396836\pi$
$383$	−106.222	+	670.661i	−0.277343	+	1.75107i	−0.595798	+	0.803135i	$0.703164\pi$
$384$	−61.2228	+	75.3972i	−0.159434	+	0.196347i
$385$	240.964	+	367.156i	0.625880	+	0.953651i
$386$	579.722	−	212.514i	1.50187	−	0.550555i
$387$	−3.58892	+	22.6596i	−0.00927370	+	0.0585519i
$388$	9.17968	+	38.9427i	0.0236590	+	0.100368i
$389$	−648.297	−	210.645i	−1.66657	−	0.541503i	−0.684340	−	0.729163i	$-0.739909\pi$
$389$	−648.297	−	210.645i	−1.66657	−	0.541503i	−0.982234	+	0.187661i	$0.939909\pi$
$390$	−46.8680	−	124.993i	−0.120174	−	0.320495i
$391$	−20.8530	−	15.1506i	−0.0533326	−	0.0387484i
$392$	5.36446	−	117.939i	0.0136848	−	0.300864i
$393$	−111.971	−	57.0522i	−0.284914	−	0.145171i
$394$	−185.306	−	124.371i	−0.470321	−	0.315663i
$395$	230.012	+	34.6939i	0.582308	+	0.0878327i
$396$	121.400	+	350.223i	0.306566	+	0.884402i
$397$	−418.619	+	418.619i	−1.05446	+	1.05446i	−0.0560277	+	0.998429i	$0.517844\pi$
$397$	−418.619	+	418.619i	−1.05446	+	1.05446i	−0.998429	+	0.0560277i	$0.982156\pi$
$398$	−285.272	+	56.1331i	−0.716764	+	0.141038i
$399$	57.8977	+	178.191i	0.145107	+	0.446594i
$400$	−284.675	−	280.998i	−0.711688	−	0.702495i
$401$	−485.852	−	352.992i	−1.21160	−	0.880280i	−0.216227	−	0.976343i	$-0.569375\pi$
$401$	−485.852	−	352.992i	−1.21160	−	0.880280i	−0.995375	+	0.0960629i	$0.969375\pi$
$402$	−55.5548	−	99.6816i	−0.138196	−	0.247964i
$403$	260.571	−	132.768i	0.646579	−	0.329448i
$404$	−326.826	−	202.137i	−0.808975	−	0.500340i
$405$	151.489	+	291.972i	0.374046	+	0.720918i
$406$	566.163	−	207.544i	1.39449	−	0.511191i
$407$	23.0552	−	107.127i	0.0566467	−	0.263211i
$408$	−2.90837	−	10.5619i	−0.00712835	−	0.0258869i
$409$	−58.5866	+	42.5657i	−0.143244	+	0.104073i	−0.657099	−	0.753804i	$-0.728217\pi$
$409$	−58.5866	+	42.5657i	−0.143244	+	0.104073i	0.513856	+	0.857877i	$0.328217\pi$
$410$	−197.640	+	715.301i	−0.482049	+	1.74464i
$411$	−82.9982	−	26.9677i	−0.201942	−	0.0656150i
$412$	92.1000	+	79.3198i	0.223544	+	0.192524i
$413$	−222.873	+	35.2996i	−0.539644	+	0.0854712i
$414$	−240.472	+	8.95178i	−0.580851	+	0.0216227i
$415$	−589.349	−	421.584i	−1.42012	−	1.01586i
$416$	−409.443	−	386.387i	−0.984238	−	0.928814i
$417$	109.659	+	109.659i	0.262971	+	0.262971i
$418$	−669.969	−	118.299i	−1.60280	−	0.283011i
$419$	540.520			1.29002			0.645012	−	0.764172i	$-0.276852\pi$
$419$	540.520			1.29002			0.645012	+	0.764172i	$0.276852\pi$
$420$	−112.101	−	46.0073i	−0.266906	−	0.109541i
$421$	4.20919	+	12.9546i	0.00999808	+	0.0307709i	0.955931	−	0.293591i	$-0.0948504\pi$
$421$	4.20919	+	12.9546i	0.00999808	+	0.0307709i	−0.945933	+	0.324362i	$0.894850\pi$
$422$	−187.738	+	202.256i	−0.444876	+	0.479278i
$423$	−325.400	+	51.5383i	−0.769267	+	0.121840i
$424$	105.529	−	47.8607i	0.248890	−	0.112879i
$425$	44.4533	−	7.71427i	0.104596	−	0.0181512i
$426$	−98.5693	+	77.3768i	−0.231383	+	0.181636i
$427$	−18.9653	−	3.00380i	−0.0444152	−	0.00703467i
$428$	643.512	+	53.3157i	1.50353	+	0.124569i
$429$	141.933	−	37.6445i	0.330845	−	0.0877494i
$430$	26.6814	−	5.45475i	0.0620498	−	0.0126855i
$431$	−108.092	+	78.5333i	−0.250793	+	0.182212i	−0.706078	−	0.708134i	$-0.749537\pi$
$431$	−108.092	+	78.5333i	−0.250793	+	0.182212i	0.455285	+	0.890346i	$0.349537\pi$
$432$	−170.107	−	125.746i	−0.393766	−	0.291078i
$433$	−103.112	+	52.5382i	−0.238134	+	0.121335i	−0.568986	−	0.822347i	$-0.692664\pi$
$433$	−103.112	+	52.5382i	−0.238134	+	0.121335i	0.330852	+	0.943683i	$0.392664\pi$
$434$	72.5839	−	255.347i	0.167244	−	0.588358i
$435$	−1.05618	−	143.251i	−0.00242799	−	0.329313i
$436$	−583.161	+	238.741i	−1.33753	+	0.547572i
$437$	200.516	−	393.535i	0.458847	−	0.900539i
$438$	−5.93261	−	30.1499i	−0.0135448	−	0.0688354i
$439$			18.3830i			0.0418747i	0.999781	+	0.0209374i	$0.00666505\pi$
$439$			18.3830i			0.0418747i	−0.999781	+	0.0209374i	$0.993335\pi$
$440$	338.670	−	280.896i	0.769706	−	0.638399i
$441$	124.322			0.281909
$442$	62.3054	−	12.2599i	0.140962	−	0.0277372i
$443$	478.256	+	243.684i	1.07958	+	0.550076i	0.900987	−	0.433846i	$-0.142844\pi$
$443$	478.256	+	243.684i	1.07958	+	0.550076i	0.178598	+	0.983922i	$0.442844\pi$
$444$	11.4552	+	27.9811i	0.0258001	+	0.0630205i
$445$	19.9922	+	19.6996i	0.0449263	+	0.0442687i
$446$	167.567	+	47.6319i	0.375711	+	0.106798i
$447$	54.9028	+	107.753i	0.122825	+	0.241058i
$448$	−509.911	+	33.7912i	−1.13819	+	0.0754268i
$449$	514.918	+	708.724i	1.14681	+	1.57845i	0.751260	+	0.660006i	$0.229446\pi$
$449$	514.918	+	708.724i	1.14681	+	1.57845i	0.395551	+	0.918444i	$0.370554\pi$
$450$	281.973	−	312.908i	0.626607	−	0.695351i
$451$	−761.348	−	294.476i	−1.68813	−	0.652940i
$452$	53.5102	−	645.859i	0.118385	−	1.42889i
$453$	31.6110	−	199.584i	0.0697814	−	0.440583i
$454$	−335.384	−	427.240i	−0.738730	−	0.941058i
$455$	314.252	−	628.161i	0.690664	−	1.38057i
$456$	170.956	−	77.5338i	0.374904	−	0.170030i
$457$	−83.1112	−	524.743i	−0.181863	−	1.14823i	−0.894621	−	0.446825i	$-0.852554\pi$
$457$	−83.1112	−	524.743i	−0.181863	−	1.14823i	0.712759	−	0.701409i	$-0.247446\pi$
$458$	58.6038	+	54.3973i	0.127956	+	0.118771i
$459$	22.6925	−	7.37324i	0.0494390	−	0.0160637i
$460$	110.171	+	263.550i	0.239502	+	0.572934i
$461$		−	660.717i		−	1.43322i	−0.697472	−	0.716612i	$-0.745692\pi$
$461$		−	660.717i		−	1.43322i	0.697472	−	0.716612i	$-0.254308\pi$
$462$	62.6048	−	117.675i	0.135508	−	0.254707i
$463$	66.4704	−	66.4704i	0.143564	−	0.143564i	−0.631672	−	0.775236i	$-0.717631\pi$
$463$	66.4704	−	66.4704i	0.143564	−	0.143564i	0.775236	+	0.631672i	$0.217631\pi$
$464$	−269.831	−	540.545i	−0.581532	−	1.16497i
$465$	−51.2931	−	36.6919i	−0.110308	−	0.0789073i
$466$	−10.1940	−	273.844i	−0.0218756	−	0.587647i
$467$	80.4077	+	507.674i	0.172179	+	1.08710i	0.910761	+	0.412933i	$0.135496\pi$
$467$	80.4077	+	507.674i	0.172179	+	1.08710i	−0.738582	+	0.674164i	$0.764504\pi$
$468$	386.866	−	449.199i	0.826637	−	0.959827i
$469$	185.548	−	571.057i	0.395624	−	1.21760i
$470$	192.900	+	340.196i	0.410425	+	0.723821i
$471$	−10.0574	−	13.8428i	−0.0213532	−	0.0293901i
$472$	60.0204	+	217.967i	0.127162	+	0.461794i
$473$	3.05561	+	29.8004i	0.00646006	+	0.0630029i
$474$	−24.2995	−	66.2873i	−0.0512649	−	0.139847i
$475$	249.718	+	731.664i	0.525723	+	1.54035i
$476$	30.3198	−	49.0226i	0.0636971	−	0.102989i
$477$	55.3961	+	108.721i	0.116134	+	0.227927i
$478$	−79.6111	+	44.3691i	−0.166551	+	0.0928223i
$479$	83.5926	−	115.055i	0.174515	−	0.240199i	−0.712795	−	0.701372i	$-0.752571\pi$
$479$	83.5926	−	115.055i	0.174515	−	0.240199i	0.887310	+	0.461173i	$0.152571\pi$
$480$	−33.2967	+	116.749i	−0.0693682	+	0.243227i
$481$	−166.679	+	54.1573i	−0.346526	+	0.112593i
$482$	17.8133	+	90.5285i	0.0369571	+	0.187818i
$483$	61.1885	+	61.1885i	0.126684	+	0.126684i
$484$	270.458	+	401.383i	0.558797	+	0.829305i
$485$	29.6941	+	40.2431i	0.0612249	+	0.0829755i
$486$	188.258	−	280.495i	0.387363	−	0.577151i
$487$	−128.182	+	251.571i	−0.263207	+	0.516573i	−0.984352	−	0.176211i	$-0.943616\pi$
$487$	−128.182	+	251.571i	−0.263207	+	0.516573i	0.721145	+	0.692784i	$0.243616\pi$
$488$	−0.874145	+	19.2183i	−0.00179128	+	0.0393817i
$489$	5.88193	−	8.09578i	0.0120285	−	0.0165558i
$490$	−51.8132	−	138.181i	−0.105741	−	0.282002i
$491$	−11.5819	+	35.6453i	−0.0235883	+	0.0725974i	−0.962158	−	0.272493i	$-0.912152\pi$
$491$	−11.5819	+	35.6453i	−0.0235883	+	0.0725974i	0.938569	+	0.345091i	$0.112152\pi$
$492$	219.228	−	51.6771i	0.445585	−	0.105035i
$493$	67.3057	+	10.6602i	0.136523	+	0.0216231i
$494$	374.502	+	1021.61i	0.758102	+	2.06804i
$495$	311.691	+	342.822i	0.629679	+	0.692570i
$496$	−262.341	−	43.7710i	−0.528913	−	0.0882479i
$497$	−651.229	−	103.145i	−1.31032	−	0.207534i
$498$	−26.3000	+	218.350i	−0.0528111	+	0.438454i
$499$	81.6809	−	251.388i	0.163689	−	0.503784i	−0.835248	−	0.549873i	$-0.814676\pi$
$499$	81.6809	−	251.388i	0.163689	−	0.503784i	0.998937	+	0.0460896i	$0.0146760\pi$
$500$	−465.308	−	182.998i	−0.930616	−	0.365996i
$501$	104.189	−	143.403i	0.207961	−	0.286234i
$502$	−480.853	−	446.337i	−0.957874	−	0.889118i
$503$	252.204	−	494.978i	0.501399	−	0.984052i	−0.492135	−	0.870519i	$-0.663783\pi$
$503$	252.204	−	494.978i	0.501399	−	0.984052i	0.993534	−	0.113533i	$-0.0362167\pi$
$504$	−59.9446	−	534.781i	−0.118938	−	1.06107i
$505$	−474.983	−	71.6442i	−0.940560	−	0.141870i
$506$	−300.507	+	91.7958i	−0.593888	+	0.181415i
$507$	−75.3887	−	75.3887i	−0.148696	−	0.148696i
$508$	−574.758	+	348.961i	−1.13141	+	0.686931i
$509$	758.576	−	246.476i	1.49033	−	0.484236i	0.553147	−	0.833084i	$-0.313427\pi$
$509$	758.576	−	246.476i	1.49033	−	0.484236i	0.937180	+	0.348847i	$0.113427\pi$
$510$	−8.53470	−	10.7087i	−0.0167347	−	0.0209975i
$511$	95.0331	−	130.802i	0.185975	−	0.255972i
$512$	90.5537	+	503.929i	0.176863	+	0.984236i
$513$	185.615	+	364.291i	0.361823	+	0.710119i
$514$	367.775	+	468.503i	0.715515	+	0.911485i
$515$	144.842	+	45.8841i	0.281246	+	0.0890953i
$516$	−5.34212	−	6.30729i	−0.0103530	−	0.0122234i
$517$	−393.440	+	173.974i	−0.761005	+	0.336507i
$518$	−66.9008	+	144.336i	−0.129152	+	0.278641i
$519$	−9.59300	−	13.2036i	−0.0184836	−	0.0254405i
$520$	−660.509	−	242.783i	−1.27021	−	0.466890i
$521$	−154.319	+	474.944i	−0.296197	+	0.911601i	0.686619	+	0.727017i	$0.259094\pi$
$521$	−154.319	+	474.944i	−0.296197	+	0.911601i	−0.982817	+	0.184584i	$0.940906\pi$
$522$	555.712	−	309.711i	1.06458	−	0.593316i
$523$	−27.1497	−	171.416i	−0.0519114	−	0.327756i	−0.999954	−	0.00961166i	$-0.996940\pi$
$523$	−27.1497	−	171.416i	−0.0519114	−	0.327756i	0.948042	−	0.318144i	$-0.103060\pi$
$524$	−613.089	+	250.994i	−1.17002	+	0.478996i
$525$	−151.451	+	2.23340i	−0.288479	+	0.00425409i
$526$	130.281	+	87.4402i	0.247683	+	0.166236i
$527$	21.2129	−	21.2129i	0.0402522	−	0.0402522i
$528$	−124.151	−	49.2001i	−0.235135	−	0.0931821i
$529$			325.010i			0.614386i
$530$	97.7540	−	106.883i	0.184441	−	0.201666i
$531$	−226.417	+	73.5674i	−0.426398	+	0.138545i
$532$	910.949	+	381.735i	1.71231	+	0.717546i
$533$	204.237	+	1289.50i	0.383183	+	2.41932i
$534$	2.32921	−	8.19405i	0.00436181	−	0.0153447i
$535$	765.781	−	255.075i	1.43137	−	0.476775i
$536$	−589.289	−	121.010i	−1.09942	−	0.225765i
$537$	−40.9388	+	258.477i	−0.0762361	+	0.481336i
$538$	217.885	−	470.078i	0.404991	−	0.873752i
$539$	156.908	−	41.6164i	0.291110	−	0.0772105i
$540$	−257.316	−	60.8922i	−0.476511	−	0.112763i
$541$	410.296	+	564.723i	0.758402	+	1.04385i	0.997345	+	0.0728175i	$0.0231991\pi$
$541$	410.296	+	564.723i	0.758402	+	1.04385i	−0.238943	+	0.971034i	$0.576801\pi$
$542$	−69.8501	+	579.917i	−0.128875	+	1.06996i
$543$	19.0364	+	37.3611i	0.0350579	+	0.0688050i
$544$	−52.1939	−	24.7171i	−0.0959447	−	0.0454359i
$545$	−552.847	+	561.060i	−1.01440	+	1.02947i
$546$	−213.033	+	7.93033i	−0.390170	+	0.0145244i
$547$	588.929	+	300.074i	1.07665	+	0.548582i	0.900088	−	0.435708i	$-0.143502\pi$
$547$	588.929	+	300.074i	1.07665	+	0.548582i	0.176564	+	0.984289i	$0.443502\pi$
$548$	−393.247	+	238.758i	−0.717605	+	0.435690i
$549$	−20.2584			−0.0369005
$550$	251.138	−	489.316i	0.456614	−	0.889665i
$551$			1167.68i			2.11920i
$552$	54.0942	−	67.7522i	0.0979967	−	0.122739i
$553$	168.647	−	330.988i	0.304967	−	0.598531i
$554$	−293.050	+	10.9090i	−0.528971	+	0.0196914i
$555$	26.9207	+	26.5266i	0.0485057	+	0.0477957i
$556$	815.267	−	60.7822i	1.46631	−	0.109320i
$557$	−23.0631	+	11.7512i	−0.0414059	+	0.0210974i	−0.474571	−	0.880217i	$-0.657397\pi$
$557$	−23.0631	+	11.7512i	−0.0414059	+	0.0210974i	0.433165	+	0.901315i	$0.357397\pi$
$558$	33.4922	−	278.062i	0.0600218	−	0.498320i
$559$	38.7610	−	28.1615i	0.0693399	−	0.0503784i
$560$	−569.416	+	289.507i	−1.01681	+	0.516976i
$561$	12.6538	−	8.17183i	0.0225558	−	0.0145665i
$562$	−7.14241	+	15.4095i	−0.0127089	+	0.0274190i
$563$	568.005	+	89.9632i	1.00889	+	0.159793i	0.638938	−	0.769258i	$-0.279374\pi$
$563$	568.005	+	89.9632i	1.00889	+	0.159793i	0.369952	+	0.929051i	$0.379374\pi$
$564$	62.4358	−	100.949i	0.110702	−	0.178988i
$565$	−256.005	−	768.575i	−0.453106	−	1.36031i
$566$	50.6122	−	178.052i	0.0894209	−	0.314579i
$567$	518.826	−	82.1740i	0.915038	−	0.144928i
$568$	−30.0164	+	659.917i	−0.0528457	+	1.16183i
$569$	−58.4701	−	179.953i	−0.102759	−	0.316261i	0.886439	−	0.462846i	$-0.153172\pi$
$569$	−58.4701	−	179.953i	−0.102759	−	0.316261i	−0.989198	+	0.146585i	$0.953172\pi$
$570$	158.360	−	173.149i	0.277825	−	0.303771i
$571$	668.647			1.17101			0.585505	−	0.810669i	$-0.300896\pi$
$571$	668.647			1.17101			0.585505	+	0.810669i	$0.300896\pi$
$572$	337.901	−	696.444i	0.590737	−	1.21756i
$573$	69.0182	+	69.0182i	0.120451	+	0.120451i
$574$	984.027	+	660.444i	1.71433	+	1.15060i
$575$	256.177	+	248.731i	0.445525	+	0.432576i
$576$	−525.772	+	119.369i	−0.912799	+	0.207238i
$577$	217.368	−	34.4277i	0.376721	−	0.0596668i	0.0347972	−	0.999394i	$-0.488921\pi$
$577$	217.368	−	34.4277i	0.376721	−	0.0596668i	0.341924	+	0.939728i	$0.388921\pi$
$578$	−499.194	+	278.212i	−0.863657	+	0.481335i
$579$	−222.787	−	72.3879i	−0.384779	−	0.125022i
$580$	−575.840	−	488.586i	−0.992828	−	0.842390i
$581$	−936.182	+	680.176i	−1.61133	+	1.17070i
$582$	6.38338	−	13.7719i	0.0109680	−	0.0236630i
$583$	106.310	+	118.675i	0.182351	+	0.203559i
$584$	−140.841	−	80.0228i	−0.241166	−	0.137025i
$585$	223.790	−	706.436i	0.382547	−	1.20758i
$586$	639.821	+	815.059i	1.09184	+	1.39089i
$587$	−50.1379	+	25.5466i	−0.0854138	+	0.0435205i	−0.496176	−	0.868222i	$-0.665263\pi$
$587$	−50.1379	+	25.5466i	−0.0854138	+	0.0435205i	0.410762	+	0.911743i	$0.365263\pi$
$588$	−29.2295	+	33.9391i	−0.0497101	+	0.0577195i
$589$	415.877	+	302.152i	0.706073	+	0.512992i
$590$	176.132	+	220.998i	0.298529	+	0.374572i
$591$	26.1644	+	80.5257i	0.0442714	+	0.136253i
$592$	151.176	+	50.5020i	0.255366	+	0.0853075i
$593$	70.5152	−	70.5152i	0.118913	−	0.118913i	−0.645146	−	0.764059i	$-0.723204\pi$
$593$	70.5152	−	70.5152i	0.118913	−	0.118913i	0.764059	+	0.645146i	$0.223204\pi$
$594$	94.7621	−	274.996i	0.159532	−	0.462956i
$595$	10.7464	−	71.2456i	0.0180611	−	0.119741i
$596$	619.286	+	151.380i	1.03907	+	0.253994i
$597$	98.2819	+	50.0771i	0.164626	+	0.0838813i
$598$	368.323	+	341.885i	0.615925	+	0.571715i
$599$	7.99488	+	5.80862i	0.0133470	+	0.00969719i	0.594439	−	0.804141i	$-0.297374\pi$
$599$	7.99488	+	5.80862i	0.0133470	+	0.00969719i	−0.581092	+	0.813838i	$0.697374\pi$
$600$	19.1266	+	150.545i	0.0318776	+	0.250909i
$601$	−318.990	−	103.646i	−0.530765	−	0.172456i	0.0313600	−	0.999508i	$-0.490016\pi$
$601$	−318.990	−	103.646i	−0.530765	−	0.172456i	−0.562125	+	0.827052i	$0.690016\pi$
$602$	5.20079	−	43.1786i	0.00863919	−	0.0717252i
$603$	99.0994	−	625.689i	0.164344	−	1.03763i
$604$	−688.479	−	812.867i	−1.13987	−	1.34581i
$605$	508.149	+	328.343i	0.839916	+	0.542716i
$606$	50.1795	+	136.886i	0.0828044	+	0.225884i
$607$	−111.473	+	703.812i	−0.183646	+	1.15949i	0.707816	+	0.706397i	$0.249680\pi$
$607$	−111.473	+	703.812i	−0.183646	+	1.15949i	−0.891462	+	0.453096i	$0.850320\pi$
$608$	278.412	−	949.602i	0.457915	−	1.56185i
$609$	−217.576	−	70.6948i	−0.357268	−	0.116083i
$610$	8.44303	+	22.5168i	0.0138410	+	0.0369128i
$611$	556.622	+	404.410i	0.911002	+	0.661882i
$612$	23.5037	−	56.0878i	0.0384047	−	0.0916467i
$613$	125.605	+	63.9988i	0.204902	+	0.104403i	0.553430	−	0.832896i	$-0.313319\pi$
$613$	125.605	+	63.9988i	0.204902	+	0.104403i	−0.348528	+	0.937298i	$0.613319\pi$
$614$	−269.018	+	400.823i	−0.438140	+	0.652806i
$615$	226.549	−	167.163i	0.368372	−	0.271810i
$616$	−254.674	−	654.889i	−0.413432	−	1.06313i
$617$	−837.199	+	837.199i	−1.35689	+	1.35689i	−0.479157	+	0.877729i	$0.659058\pi$
$617$	−837.199	+	837.199i	−1.35689	+	1.35689i	−0.877729	+	0.479157i	$0.840942\pi$
$618$	−8.90318	−	45.2465i	−0.0144064	−	0.0732144i
$619$	−218.469	−	672.380i	−0.352939	−	1.08624i	−0.957195	−	0.289445i	$-0.906529\pi$
$619$	−218.469	−	672.380i	−0.352939	−	1.08624i	0.604255	−	0.796791i	$-0.293471\pi$
$620$	−323.019	+	78.6614i	−0.520999	+	0.126873i
$621$	152.767	+	110.992i	0.246002	+	0.178731i
$622$	519.194	−	289.358i	0.834717	−	0.465206i
$623$	39.9369	−	20.3489i	0.0641041	−	0.0326627i
$624$	31.6717	+	211.224i	0.0507559	+	0.338500i
$625$	−624.728	+	18.4293i	−0.999565	+	0.0294868i
$626$	196.758	+	536.742i	0.314311	+	0.857415i
$627$	172.222	+	192.252i	0.274676	+	0.306622i
$628$	−89.8928	−	7.44773i	−0.143141	−	0.0118594i
$629$	−14.5446	+	10.5673i	−0.0231234	+	0.0168001i
$630$	−331.790	−	585.142i	−0.526651	−	0.928796i
$631$	−373.554	−	121.375i	−0.592003	−	0.192353i	−0.00233239	−	0.999997i	$-0.500742\pi$
$631$	−373.554	−	121.375i	−0.592003	−	0.192353i	−0.589671	+	0.807644i	$0.700742\pi$
$632$	−348.374	−	130.975i	−0.551225	−	0.207239i
$633$	103.406	−	16.3780i	0.163359	−	0.0258735i
$634$	25.6747	+	689.703i	0.0404964	+	1.08786i
$635$	−489.006	+	683.602i	−0.770088	+	1.07654i
$636$	−42.7044	−	10.4388i	−0.0671454	−	0.0164132i
$637$	−183.585	−	183.585i	−0.288203	−	0.288203i
$638$	597.698	−	576.914i	0.936831	−	0.904255i
$639$	−695.632			−1.08863
$640$	351.801	+	534.636i	0.549689	+	0.835369i
$641$	−114.059	−	351.038i	−0.177939	−	0.547641i	0.821816	−	0.569753i	$-0.192961\pi$
$641$	−114.059	−	351.038i	−0.177939	−	0.547641i	−0.999756	+	0.0221119i	$0.992961\pi$
$642$	−179.549	−	166.661i	−0.279672	−	0.259597i
$643$	−248.142	+	39.3018i	−0.385913	+	0.0611226i	−0.346377	−	0.938096i	$-0.612588\pi$
$643$	−248.142	+	39.3018i	−0.385913	+	0.0611226i	−0.0395362	+	0.999218i	$0.512588\pi$
$644$	454.911	−	33.9159i	0.706384	−	0.0526644i
$645$	−9.24022	−	4.62263i	−0.0143259	−	0.00716687i
$646$	68.9214	+	87.7981i	0.106690	+	0.135910i
$647$	−675.080	−	106.922i	−1.04340	−	0.165258i	−0.388869	−	0.921293i	$-0.627134\pi$
$647$	−675.080	−	106.922i	−1.04340	−	0.165258i	−0.654531	+	0.756035i	$0.727134\pi$
$648$	−139.722	−	507.406i	−0.215620	−	0.783033i
$649$	−261.138	+	168.643i	−0.402370	+	0.259851i
$650$	−878.458	+	45.6807i	−1.35147	+	0.0702779i
$651$	−81.4791	+	59.1981i	−0.125160	+	0.0909340i
$652$	−12.1034	−	51.3457i	−0.0185634	−	0.0787511i
$653$	−167.996	+	85.5984i	−0.257269	+	0.131085i	−0.577869	−	0.816130i	$-0.696115\pi$
$653$	−167.996	+	85.5984i	−0.257269	+	0.131085i	0.320600	+	0.947215i	$0.396115\pi$
$654$	229.957	+	65.3667i	0.351617	+	0.0999491i
$655$	−581.220	+	589.854i	−0.887359	+	0.900541i
$656$	547.757	−	1053.47i	0.834995	−	1.60590i
$657$	77.4406	−	151.986i	0.117870	−	0.231333i
$658$	612.792	−	120.579i	0.931294	−	0.183251i
$659$		−	943.001i		−	1.43096i	−0.698635	−	0.715479i	$-0.746209\pi$
$659$		−	943.001i		−	1.43096i	0.698635	−	0.715479i	$-0.253791\pi$
$660$	−166.871	+	4.48811i	−0.252834	+	0.00680017i
$661$	788.731			1.19324			0.596619	−	0.802524i	$-0.296510\pi$
$661$	788.731			1.19324			0.596619	+	0.802524i	$0.296510\pi$
$662$	6.13975	+	31.2026i	0.00927455	+	0.0471339i
$663$	−21.4654	−	10.9372i	−0.0323762	−	0.0164965i
$664$	781.710	+	856.211i	1.17727	+	1.28947i
$665$	1234.59	−	9.10253i	1.85653	−	0.0136880i
$666$	−45.8919	+	161.446i	−0.0689067	+	0.242411i
$667$	244.836	+	480.519i	0.367071	+	0.720418i
$668$	−214.391	−	909.503i	−0.320944	−	1.36153i
$669$	−38.8476	−	53.4692i	−0.0580682	−	0.0799240i
$670$	−736.742	+	150.620i	−1.09962	+	0.224805i
$671$	−25.5684	+	6.78145i	−0.0381049	+	0.0101065i
$672$	160.086	+	109.369i	0.238223	+	0.162751i
$673$	60.8690	−	384.311i	0.0904442	−	0.571042i	−0.900297	−	0.435277i	$-0.856651\pi$
$673$	60.8690	−	384.311i	0.0904442	−	0.571042i	0.990741	−	0.135766i	$-0.0433494\pi$
$674$	−980.101	+	769.379i	−1.45416	+	1.14151i
$675$	−325.661	+	56.5141i	−0.482461	+	0.0837245i
$676$	−560.484	+	41.7869i	−0.829119	+	0.0618149i
$677$	−141.049	−	890.546i	−0.208344	−	1.31543i	−0.841016	−	0.541010i	$-0.818042\pi$
$677$	−141.049	−	890.546i	−0.208344	−	1.31543i	0.632672	−	0.774420i	$-0.281958\pi$
$678$	−167.269	+	180.204i	−0.246710	+	0.265788i
$679$	75.9592	−	24.6806i	0.111869	−	0.0363485i
$680$	−72.1360	−	2.74834i	−0.106082	−	0.00404168i
$681$			206.067i			0.302594i
$682$	−50.8098	−	362.158i	−0.0745012	−	0.531024i
$683$	165.942	−	165.942i	0.242960	−	0.242960i	−0.575113	−	0.818074i	$-0.695042\pi$
$683$	165.942	−	165.942i	0.242960	−	0.242960i	0.818074	+	0.575113i	$0.195042\pi$
$684$	1012.25	+	247.438i	1.47990	+	0.361751i
$685$	−334.576	+	467.718i	−0.488432	+	0.682800i
$686$	546.461	−	20.3425i	0.796591	−	0.0296537i
$687$	−4.74553	−	29.9621i	−0.00690762	−	0.0436130i
$688$	−43.5718	−	0.359264i	−0.0633311	−	0.000522187i
$689$	78.7446	−	242.351i	0.114288	−	0.351743i
$690$	28.8622	−	104.458i	0.0418293	−	0.151389i
$691$	−745.651	−	1026.30i	−1.07909	−	1.48524i	−0.860520	−	0.509417i	$-0.829861\pi$
$691$	−745.651	−	1026.30i	−1.07909	−	1.48524i	−0.218569	−	0.975821i	$-0.570139\pi$
$692$	−85.7424	−	7.10386i	−0.123905	−	0.0102657i
$693$	676.722	−	299.238i	0.976510	−	0.431801i
$694$	575.385	−	210.924i	0.829085	−	0.303925i
$695$	907.086	−	470.639i	1.30516	−	0.677179i
$696$	−46.1055	+	224.523i	−0.0662436	+	0.322590i
$697$	60.8020	+	119.331i	0.0872339	+	0.171206i
$698$	−339.578	−	609.303i	−0.486502	−	0.872927i
$699$	−61.1092	+	84.1096i	−0.0874237	+	0.120328i
$700$	−512.094	+	612.646i	−0.731563	+	0.875209i
$701$	745.778	−	242.318i	1.06388	−	0.345675i	0.275777	−	0.961222i	$-0.411065\pi$
$701$	745.778	−	242.318i	1.06388	−	0.345675i	0.788100	+	0.615547i	$0.211065\pi$
$702$	−456.444	+	89.8146i	−0.650204	+	0.127941i
$703$	−217.832	−	217.832i	−0.309860	−	0.309860i
$704$	−623.626	+	326.659i	−0.885833	+	0.464004i
$705$	22.1293	−	146.712i	0.0313891	−	0.208102i
$706$	18.6706	+	12.5310i	0.0264456	+	0.0177494i
$707$	−348.262	+	683.502i	−0.492591	+	0.966764i
$708$	33.1499	−	79.1070i	0.0468220	−	0.111733i
$709$	−9.63426	+	13.2604i	−0.0135885	+	0.0187030i	−0.815757	−	0.578394i	$-0.803679\pi$
$709$	−9.63426	+	13.2604i	−0.0135885	+	0.0187030i	0.802169	+	0.597097i	$0.203679\pi$
$710$	289.917	+	773.181i	0.408333	+	1.08899i
$711$	121.110	−	372.737i	0.170337	−	0.524244i
$712$	−24.7178	−	37.4926i	−0.0347160	−	0.0526582i
$713$	234.495	+	37.1403i	0.328884	+	0.0520902i
$714$	−20.5323	+	7.52673i	−0.0287568	+	0.0105416i
$715$	45.9712	−	966.517i	0.0642954	−	1.35177i
$716$	891.635	+	1052.73i	1.24530	+	1.47029i
$717$	34.1519	+	5.40913i	0.0476316	+	0.00754411i
$718$	583.331	+	70.2613i	0.812438	+	0.0978569i
$719$	92.3775	−	284.309i	0.128481	−	0.395422i	−0.866039	−	0.499977i	$-0.833342\pi$
$719$	92.3775	−	284.309i	0.128481	−	0.395422i	0.994519	+	0.104555i	$0.0333417\pi$
$720$	−545.575	+	395.657i	−0.757743	+	0.549523i
$721$	142.618	−	196.297i	0.197806	−	0.272256i
$722$	−809.990	+	872.627i	−1.12187	+	1.20862i
$723$	15.8915	−	31.1889i	0.0219800	−	0.0431381i
$724$	214.725	+	52.4880i	0.296581	+	0.0724972i
$725$	−901.986	−	278.438i	−1.24412	−	0.384052i
$726$	13.3181	−	183.141i	0.0183445	−	0.252260i
$727$	−555.190	−	555.190i	−0.763673	−	0.763673i	0.213311	−	0.976984i	$-0.431575\pi$
$727$	−555.190	−	555.190i	−0.763673	−	0.763673i	−0.976984	+	0.213311i	$0.931575\pi$
$728$	−701.189	+	878.228i	−0.963171	+	1.20636i
$729$	441.209	−	143.357i	0.605225	−	0.196649i
$730$	−201.204	−	22.7311i	−0.275622	−	0.0311384i
$731$	2.88886	−	3.97617i	0.00395192	−	0.00543936i
$732$	4.76299	−	5.53041i	0.00650682	−	0.00755521i
$733$	−374.514	−	735.026i	−0.510934	−	1.00276i	−0.992019	−	0.126090i	$-0.959757\pi$
$733$	−374.514	−	735.026i	−0.510934	−	1.00276i	0.481085	−	0.876674i	$-0.340243\pi$
$734$	−14.0664	+	11.0421i	−0.0191640	+	0.0150437i
$735$	−16.9084	+	53.3745i	−0.0230046	+	0.0726183i
$736$	−84.5395	−	449.153i	−0.114863	−	0.610263i
$737$	−84.3733	−	822.865i	−0.114482	−	1.11651i
$738$	1134.40	+	525.804i	1.53713	+	0.712471i
$739$	−646.145	−	889.342i	−0.874350	−	1.20344i	−0.977954	−	0.208821i	$-0.933037\pi$
$739$	−646.145	−	889.342i	−0.874350	−	1.20344i	0.103604	−	0.994619i	$-0.466963\pi$
$740$	198.570	−	16.2774i	0.268338	−	0.0219964i
$741$	127.565	−	392.606i	0.172153	−	0.529832i
$742$	−112.607	−	202.051i	−0.151762	−	0.272306i
$743$	−36.4471	−	230.118i	−0.0490540	−	0.309715i	−1.00000		0.000357556i	$-0.999886\pi$
$743$	−36.4471	−	230.118i	−0.0490540	−	0.309715i	0.950946	−	0.309357i	$-0.100114\pi$
$744$	68.0349	+	74.5190i	0.0914448	+	0.100160i
$745$	786.147	−	130.462i	1.05523	−	0.175117i
$746$	279.812	−	416.906i	0.375083	−	0.558855i
$747$	−863.284	+	863.284i	−1.15567	+	1.15567i
$748$	10.8891	−	78.6570i	0.0145576	−	0.105156i
$749$		−	1288.99i		−	1.72094i
$750$	95.9894	+	163.615i	0.127986	+	0.218154i
$751$	214.087	−	69.5612i	0.285070	−	0.0926247i	−0.162992	−	0.986627i	$-0.552115\pi$
$751$	214.087	−	69.5612i	0.285070	−	0.0926247i	0.448062	+	0.894003i	$0.352115\pi$
$752$	−188.447	−	596.677i	−0.250595	−	0.793453i
$753$	38.9378	+	245.843i	0.0517102	+	0.326485i
$754$	−1277.97	−	363.269i	−1.69492	−	0.481789i
$755$	−1190.85	−	595.753i	−1.57729	−	0.789076i
$756$	−222.120	+	359.135i	−0.293810	+	0.475047i
$757$	−161.749	+	1021.25i	−0.213672	+	1.34907i	0.614643	+	0.788806i	$0.289300\pi$
$757$	−161.749	+	1021.25i	−0.213672	+	1.34907i	−0.828314	+	0.560264i	$0.810700\pi$
$758$	−443.810	−	205.709i	−0.585501	−	0.271385i
$759$	111.183	+	43.0036i	0.146486	+	0.0566582i
$760$	−146.850	−	1228.22i	−0.193224	−	1.61608i
$761$	144.314	+	198.631i	0.189637	+	0.261013i	0.893240	−	0.449581i	$-0.148427\pi$
$761$	144.314	+	198.631i	0.189637	+	0.261013i	−0.703603	+	0.710593i	$0.748427\pi$
$762$	253.270	+	30.5060i	0.332375	+	0.0400341i
$763$	571.069	+	1120.79i	0.748452	+	1.46892i
$764$	513.122	−	38.2557i	0.671625	−	0.0500729i
$765$	−0.560449	−	76.0146i	−0.000732613	−	0.0993655i
$766$	−50.5192	−	1357.10i	−0.0659519	−	1.77167i
$767$	442.985	+	225.712i	0.577556	+	0.294280i
$768$	91.0283	−	171.598i	0.118526	−	0.223435i
$769$	−140.854			−0.183165			−0.0915823	−	0.995798i	$-0.529192\pi$
$769$	−140.854			−0.183165			−0.0915823	+	0.995798i	$0.529192\pi$
$770$	−614.632	−	627.450i	−0.798224	−	0.814871i
$771$		−	225.968i		−	0.293085i
$772$	−1055.57	+	640.884i	−1.36732	+	0.830160i
$773$	117.702	−	231.003i	0.152266	−	0.298840i	−0.802255	−	0.596981i	$-0.796367\pi$
$773$	117.702	−	231.003i	0.152266	−	0.298840i	0.954522	+	0.298141i	$0.0963667\pi$
$774$	−1.70689	−	45.8523i	−0.00220528	−	0.0592407i
$775$	−332.568	+	249.199i	−0.429120	+	0.321547i
$776$	−33.0511	−	72.8753i	−0.0425916	−	0.0939115i
$777$	53.7773	−	27.4009i	0.0692115	−	0.0352650i
$778$	1353.54	+	163.031i	1.73976	+	0.209552i
$779$	−1856.61	+	1348.91i	−2.38332	+	1.73159i
$780$	140.237	+	227.185i	0.179791	+	0.291263i
$781$	−877.968	+	232.861i	−1.12416	+	0.298158i
$782$	46.7716	+	21.6790i	0.0598102	+	0.0277225i
$783$	−493.076	−	78.0955i	−0.629726	−	0.0997388i
$784$	35.0134	+	233.511i	0.0446600	+	0.297846i
$785$	−106.973	+	35.6316i	−0.136271	+	0.0453906i
$786$	241.759	+	68.7214i	0.307581	+	0.0874318i
$787$	750.220	−	118.823i	0.953266	−	0.150982i	0.339619	−	0.940563i	$-0.389702\pi$
$787$	750.220	−	118.823i	0.953266	−	0.150982i	0.613647	+	0.789581i	$0.289702\pi$
$788$	411.664	+	172.509i	0.522417	+	0.218920i
$789$	−18.3951	−	56.6143i	−0.0233145	−	0.0717545i
$790$	−464.765	+	20.7336i	−0.588310	+	0.0262451i
$791$	−1293.69			−1.63551
$792$	−373.466	−	640.390i	−0.471548	−	0.808574i
$793$	29.9154	+	29.9154i	0.0377244	+	0.0377244i
$794$	659.842	−	983.131i	0.831036	−	1.23820i
$795$	−54.2108	+	8.99635i	−0.0681897	+	0.0113162i
$796$	538.135	−	220.308i	0.676048	−	0.276769i
$797$	−317.677	+	50.3151i	−0.398591	+	0.0631306i	−0.352512	−	0.935807i	$-0.614672\pi$
$797$	−317.677	+	50.3151i	−0.398591	+	0.0631306i	−0.0460786	+	0.998938i	$0.514672\pi$
$798$	−182.423	−	327.320i	−0.228600	−	0.410176i
$799$	67.1242	+	21.8100i	0.0840103	+	0.0272966i
$800$	667.142	+	441.499i	0.833928	+	0.551874i
$801$	38.2575	−	27.7957i	0.0477622	−	0.0347012i
$802$	1089.73	+	505.097i	1.35876	+	0.629796i
$803$	46.8620	−	217.747i	0.0583587	−	0.271166i
$804$	147.510	+	174.161i	0.183470	+	0.216618i
$805$	506.145	−	262.612i	0.628751	−	0.326226i
$806$	−460.071	+	361.156i	−0.570808	+	0.448084i
$807$	−175.144	+	89.2403i	−0.217031	+	0.110583i
$808$	719.406	+	270.469i	0.890354	+	0.334738i
$809$	118.187	+	85.8675i	0.146090	+	0.106140i	0.658429	−	0.752643i	$-0.271221\pi$
$809$	118.187	+	85.8675i	0.146090	+	0.106140i	−0.512340	+	0.858783i	$0.671221\pi$
$810$	−410.018	−	514.461i	−0.506195	−	0.635137i
$811$	79.6154	+	245.031i	0.0981694	+	0.302134i	0.988067	−	0.154027i	$-0.0492241\pi$
$811$	79.6154	+	245.031i	0.0981694	+	0.302134i	−0.889897	+	0.456161i	$0.849224\pi$
$812$	−1030.88	+	625.894i	−1.26956	+	0.770805i
$813$	156.698	−	156.698i	0.192740	−	0.192740i
$814$	−3.87720	+	219.125i	−0.00476314	+	0.269196i
$815$	−39.1515	−	53.0603i	−0.0480387	−	0.0651047i
$816$	9.78562	+	19.6033i	0.0119922	+	0.0240236i
$817$	75.0377	+	38.2336i	0.0918454	+	0.0467976i
$818$	98.5325	−	106.152i	0.120455	−	0.129770i
$819$	−957.398	−	695.590i	−1.16898	−	0.849317i
$820$	111.640	−	1480.00i	0.136146	−	1.80488i
$821$	−365.428	−	118.735i	−0.445101	−	0.144622i	0.0778867	−	0.996962i	$-0.475183\pi$
$821$	−365.428	−	118.735i	−0.445101	−	0.144622i	−0.522988	+	0.852340i	$0.675183\pi$
$822$	173.286	+	20.8721i	0.210811	+	0.0253918i
$823$	29.0149	−	183.193i	0.0352550	−	0.222591i	−0.963770	−	0.266734i	$-0.914056\pi$
$823$	29.0149	−	183.193i	0.0352550	−	0.222591i	0.999025	+	0.0441424i	$0.0140555\pi$
$824$	−211.363	−	120.092i	−0.256508	−	0.145742i
$825$	−189.574	+	87.1913i	−0.229787	+	0.105686i
$826$	423.729	−	155.330i	0.512989	−	0.188051i
$827$	103.675	−	654.578i	0.125363	−	0.791509i	−0.842253	−	0.539082i	$-0.818771\pi$
$827$	103.675	−	654.578i	0.125363	−	0.791509i	0.967616	−	0.252427i	$-0.0812287\pi$
$828$	468.439	−	110.422i	0.565748	−	0.133360i
$829$	−117.075	−	38.0400i	−0.141225	−	0.0458866i	0.237552	−	0.971375i	$-0.423655\pi$
$829$	−117.075	−	38.0400i	−0.141225	−	0.0458866i	−0.378776	+	0.925488i	$0.623655\pi$
$830$	1319.31	+	599.735i	1.58953	+	0.722572i
$831$	90.0088	+	65.3952i	0.108314	+	0.0786946i
$832$	952.677	+	600.133i	1.14504	+	0.721314i
$833$	−23.7303	−	12.0912i	−0.0284878	−	0.0145152i
$834$	−257.534	−	172.848i	−0.308794	−	0.207252i
$835$	−693.503	−	939.875i	−0.830543	−	1.12560i
$836$	1360.41	−	26.5537i	1.62728	−	0.0317628i
$837$	−155.404	+	155.404i	−0.185668	+	0.185668i
$838$	−1060.70	+	208.715i	−1.26575	+	0.249063i
$839$	−105.384	−	324.337i	−0.125606	−	0.386576i	0.868405	−	0.495856i	$-0.165146\pi$
$839$	−105.384	−	324.337i	−0.125606	−	0.386576i	−0.994011	+	0.109280i	$0.965146\pi$
$840$	237.748	+	46.9972i	0.283033	+	0.0559491i
$841$	−473.090	−	343.720i	−0.562533	−	0.408704i
$842$	−13.2622	−	23.7963i	−0.0157509	−	0.0282617i
$843$	5.74133	−	2.92535i	0.00681059	−	0.00347017i
$844$	290.313	−	469.393i	0.343972	−	0.556152i
$845$	−623.608	+	323.557i	−0.737997	+	0.382908i
$846$	618.654	−	226.786i	0.731270	−	0.268068i
$847$	753.931	−	604.204i	0.890120	−	0.713346i
$848$	−188.607	+	134.669i	−0.222414	+	0.158808i
$849$	−56.8148	+	41.2783i	−0.0669196	+	0.0486200i
$850$	−84.2552	+	32.3033i	−0.0991237	+	0.0380039i
$851$	−135.316	−	43.9668i	−0.159008	−	0.0516648i
$852$	163.551	−	189.903i	0.191962	−	0.222891i
$853$	−1091.95	+	172.948i	−1.28013	+	0.202752i	−0.759205	−	0.650852i	$-0.774412\pi$
$853$	−1091.95	+	172.948i	−1.28013	+	0.202752i	−0.520923	+	0.853604i	$0.674412\pi$
$854$	38.3768	−	1.42861i	0.0449377	−	0.00167284i
$855$	1284.99	−	213.246i	1.50292	−	0.249411i
$856$	−1283.40	+	143.858i	−1.49929	+	0.168059i
$857$	136.968	+	136.968i	0.159822	+	0.159822i	0.782488	−	0.622666i	$-0.213950\pi$
$857$	136.968	+	136.968i	0.159822	+	0.159822i	−0.622666	+	0.782488i	$0.713950\pi$
$858$	−263.989	+	128.678i	−0.307679	+	0.149974i
$859$	−453.245			−0.527643			−0.263821	−	0.964572i	$-0.584983\pi$
$859$	−453.245			−0.527643			−0.263821	+	0.964572i	$0.584983\pi$
$860$	−50.2526	+	21.0069i	−0.0584332	+	0.0244266i
$861$	−138.940	−	427.613i	−0.161370	−	0.496647i
$862$	181.792	−	195.850i	0.210895	−	0.227204i
$863$	527.066	−	83.4790i	0.610736	−	0.0967311i	0.156598	−	0.987662i	$-0.449947\pi$
$863$	527.066	−	83.4790i	0.610736	−	0.0967311i	0.454138	+	0.890931i	$0.349947\pi$
$864$	382.368	+	181.075i	0.442556	+	0.209578i
$865$	−102.034	+	33.9865i	−0.117958	+	0.0392907i
$866$	182.057	−	142.915i	0.210228	−	0.165029i
$867$	214.146	+	33.9174i	0.246997	+	0.0391204i
$868$	−43.8377	+	529.113i	−0.0505042	+	0.609578i
$869$	28.0813	−	510.979i	0.0323145	−	0.588008i
$870$	57.3870	+	280.704i	0.0659621	+	0.322648i
$871$	−1070.29	+	777.612i	−1.22881	+	0.892781i
$872$	1052.19	−	693.679i	1.20664	−	0.795503i
$873$	75.0794	−	38.2549i	0.0860016	−	0.0438200i
$874$	−241.529	+	849.689i	−0.276349	+	0.972184i
$875$	−287.362	+	955.843i	−0.328413	+	1.09239i
$876$	23.2839	+	56.8745i	0.0265798	+	0.0649252i
$877$	192.511	−	377.825i	0.219511	−	0.430815i	−0.754821	−	0.655931i	$-0.772276\pi$
$877$	192.511	−	377.825i	0.219511	−	0.430815i	0.974332	+	0.225116i	$0.0722762\pi$
$878$	−7.09835	−	36.0743i	−0.00808468	−	0.0410869i
$879$		−	393.119i		−	0.447234i
$880$	−556.133	+	681.994i	−0.631969	+	0.774993i
$881$	780.138			0.885514			0.442757	−	0.896642i	$-0.354001\pi$
$881$	780.138			0.885514			0.442757	+	0.896642i	$0.354001\pi$
$882$	−243.965	+	48.0051i	−0.276605	+	0.0544276i
$883$	903.368	+	460.289i	1.02307	+	0.521278i	0.883252	−	0.468899i	$-0.155349\pi$
$883$	903.368	+	460.289i	1.02307	+	0.521278i	0.139815	+	0.990178i	$0.455349\pi$
$884$	−117.532	+	48.1168i	−0.132955	+	0.0544307i
$885$	−0.790466	−	107.212i	−0.000893182	−	0.121144i
$886$	−1032.61	−	293.525i	−1.16547	−	0.331293i
$887$	80.3137	+	157.624i	0.0905453	+	0.177705i	0.931838	−	0.362875i	$-0.118205\pi$
$887$	80.3137	+	157.624i	0.0905453	+	0.177705i	−0.841293	+	0.540580i	$0.818205\pi$
$888$	−33.2839	−	50.4860i	−0.0374819	−	0.0568536i
$889$	788.954	+	1085.90i	0.887462	+	1.22149i
$890$	−46.8388	−	30.9381i	−0.0526279	−	0.0347619i
$891$	607.904	−	392.585i	0.682271	−	0.440612i
$892$	−347.221	−	28.7677i	−0.389261	−	0.0322507i
$893$	−189.189	+	1194.49i	−0.211858	+	1.33762i
$894$	−149.347	−	190.251i	−0.167055	−	0.212809i
$895$	1542.25	+	771.547i	1.72319	+	0.862064i
$896$	987.586	−	263.206i	1.10222	−	0.293757i
$897$	−29.8256	−	188.311i	−0.0332503	−	0.209934i
$898$	−1284.12	−	1191.95i	−1.42998	−	1.32734i
$899$	−596.952	+	193.962i	−0.664018	+	0.215753i
$900$	−432.511	+	722.921i	−0.480568	+	0.803246i
$901$		−	26.1401i		−	0.0290124i
$902$	1607.76	+	283.887i	1.78243	+	0.314730i
$903$	−11.6672	+	11.6672i	−0.0129205	+	0.0129205i
$904$	144.383	+	1288.08i	0.159716	+	1.42486i
$905$	272.581	−	45.2351i	0.301194	−	0.0499835i
$906$	15.0342	+	403.864i	0.0165940	+	0.445766i
$907$	224.487	+	1417.36i	0.247505	+	1.56269i	0.727931	+	0.685651i	$0.240482\pi$
$907$	224.487	+	1417.36i	0.247505	+	1.56269i	−0.480425	+	0.877036i	$0.659518\pi$
$908$	823.120	+	708.900i	0.906520	+	0.780727i
$909$	−250.096	+	769.716i	−0.275133	+	0.846773i
$910$	−374.123	+	1354.03i	−0.411124	+	1.48794i
$911$	−60.3878	−	83.1166i	−0.0662873	−	0.0912367i	0.774586	−	0.632468i	$-0.217958\pi$
$911$	−60.3878	−	83.1166i	−0.0662873	−	0.0912367i	−0.840873	+	0.541232i	$0.817958\pi$
$912$	−305.541	+	218.163i	−0.335023	+	0.239213i
$913$	−800.581	+	1378.55i	−0.876869	+	1.50991i
$914$	365.717	+	997.649i	0.400129	+	1.09152i
$915$	2.75524	−	8.69744i	0.00301119	−	0.00950540i
$916$	−136.007	−	84.1185i	−0.148479	−	0.0918324i
$917$	600.377	+	1178.31i	0.654718	+	1.28496i
$918$	−41.6840	+	23.2314i	−0.0454074	+	0.0253066i
$919$	607.208	−	835.750i	0.660727	−	0.909412i	−0.338779	−	0.940866i	$-0.610014\pi$
$919$	607.208	−	835.750i	0.660727	−	0.909412i	0.999505	+	0.0314539i	$0.0100137\pi$
$920$	−317.962	−	474.641i	−0.345611	−	0.515914i
$921$	174.179	−	56.5943i	0.189120	−	0.0614487i
$922$	255.127	+	1296.57i	0.276710	+	1.40626i
$923$	1027.24	+	1027.24i	1.11293	+	1.11293i
$924$	−77.4153	+	255.095i	−0.0837828	+	0.276077i
$925$	220.209	−	116.324i	0.238064	−	0.125755i
$926$	−104.773	+	156.106i	−0.113146	+	0.168581i
$927$	116.217	−	228.088i	0.125368	−	0.246049i
$928$	738.232	+	956.558i	0.795509	+	1.03077i
$929$	776.899	−	1069.31i	0.836275	−	1.15103i	−0.150447	−	0.988618i	$-0.548071\pi$
$929$	776.899	−	1069.31i	0.836275	−	1.15103i	0.986722	−	0.162416i	$-0.0519286\pi$
$930$	114.824	+	52.1969i	0.123467	+	0.0561257i
$931$	141.025	−	434.031i	0.151477	−	0.466198i
$932$	125.746	+	533.446i	0.134920	+	0.572367i
$933$	−222.726	−	35.2763i	−0.238720	−	0.0378095i
$934$	−353.821	−	965.197i	−0.378824	−	1.03340i
$935$	−26.1531	−	95.7516i	−0.0279712	−	0.102408i
$936$	−585.723	+	1030.88i	−0.625772	+	1.10137i
$937$	1663.61	+	263.491i	1.77547	+	0.281207i	0.956309	−	0.292359i	$-0.0944403\pi$
$937$	1663.61	+	263.491i	1.77547	+	0.281207i	0.819160	+	0.573566i	$0.194440\pi$
$938$	−143.607	+	1192.27i	−0.153099	+	1.27108i
$939$	67.0211	−	206.270i	0.0713749	−	0.219670i
$940$	−509.903	−	593.105i	−0.542450	−	0.630963i
$941$	411.553	−	566.454i	0.437357	−	0.601971i	−0.532265	−	0.846578i	$-0.678659\pi$
$941$	411.553	−	566.454i	0.437357	−	0.601971i	0.969622	+	0.244607i	$0.0786590\pi$
$942$	25.0814	+	23.2811i	0.0266257	+	0.0247146i
$943$	−481.189	+	944.386i	−0.510274	+	1.00147i
$944$	−201.947	−	404.556i	−0.213927	−	0.428555i
$945$	−78.7269	+	521.939i	−0.0833088	+	0.552316i
$946$	−17.5033	−	57.2995i	−0.0185024	−	0.0605703i
$947$	−119.933	−	119.933i	−0.126645	−	0.126645i	0.640943	−	0.767588i	$-0.278543\pi$
$947$	−119.933	−	119.933i	−0.126645	−	0.126645i	−0.767588	+	0.640943i	$0.778543\pi$
$948$	73.2806	+	120.697i	0.0773003	+	0.127318i
$949$	−338.793	+	110.080i	−0.357000	+	0.115996i
$950$	−772.562	−	1339.37i	−0.813223	−	1.40986i
$951$	153.910	−	211.838i	0.161840	−	0.222753i
$952$	−40.5693	+	107.908i	−0.0426148	+	0.113349i
$953$	404.438	+	793.755i	0.424384	+	0.832901i	0.999886	+	0.0151007i	$0.00480688\pi$
$953$	404.438	+	793.755i	0.424384	+	0.832901i	−0.575502	+	0.817801i	$0.695193\pi$
$954$	−150.689	−	191.960i	−0.157955	−	0.201216i
$955$	570.911	−	296.216i	0.597813	−	0.310174i
$956$	139.094	−	117.809i	0.145496	−	0.123232i
$957$	−313.517	+	32.1468i	−0.327604	+	0.0335912i
$958$	−119.613	+	258.059i	−0.124857	+	0.269373i
$959$	539.800	+	742.970i	0.562877	+	0.774734i
$960$	20.2594	−	241.962i	0.0211035	−	0.252044i
$961$	211.577	−	651.167i	0.220163	−	0.677593i
$962$	306.174	−	170.638i	0.318268	−	0.177378i
$963$	−212.738	−	1343.18i	−0.220912	−	1.39478i
$964$	−69.9127	−	170.772i	−0.0725235	−	0.177149i
$965$	−898.083	+	1255.47i	−0.930656	+	1.30100i
$966$	−143.702	−	96.4474i	−0.148759	−	0.0998420i
$967$	−319.296	+	319.296i	−0.330193	+	0.330193i	−0.852660	−	0.522467i	$-0.825012\pi$
$967$	−319.296	+	319.296i	−0.330193	+	0.330193i	0.522467	+	0.852660i	$0.325012\pi$
$968$	−685.727	−	683.230i	−0.708396	−	0.705816i
$969$		−	42.3468i		−	0.0437015i
$970$	−73.8101	−	67.5059i	−0.0760929	−	0.0695937i
$971$	509.320	−	165.488i	0.524531	−	0.170430i	−0.0347696	−	0.999395i	$-0.511070\pi$
$971$	509.320	−	165.488i	0.524531	−	0.170430i	0.559301	+	0.828965i	$0.311070\pi$
$972$	−261.123	+	623.129i	−0.268646	+	0.641080i
$973$	−255.295	−	1611.87i	−0.262379	−	1.65660i
$974$	154.400	−	543.172i	0.158521	−	0.557671i
$975$	272.854	+	192.158i	0.279850	+	0.197085i
$976$	−5.70548	−	38.0509i	−0.00584578	−	0.0389866i
$977$	75.5783	−	477.183i	0.0773576	−	0.488416i	−0.918343	−	0.395786i	$-0.870472\pi$
$977$	75.5783	−	477.183i	0.0773576	−	0.488416i	0.995701	−	0.0926309i	$-0.0295277\pi$
$978$	−8.41645	+	18.1582i	−0.00860578	+	0.0185666i
$979$	38.9808	−	47.8880i	0.0398170	−	0.0489152i
$980$	155.034	+	251.156i	0.158197	+	0.256281i
$981$	780.057	+	1073.66i	0.795165	+	1.09445i
$982$	8.96396	−	74.4215i	0.00912827	−	0.0757857i
$983$	−625.373	−	1227.36i	−0.636188	−	1.24859i	−0.953821	−	0.300376i	$-0.902888\pi$
$983$	−625.373	−	1227.36i	−0.636188	−	1.24859i	0.317633	−	0.948214i	$-0.397112\pi$
$984$	−410.252	+	186.061i	−0.416923	+	0.189087i
$985$	557.920	−	4.11350i	0.566416	−	0.00417614i
$986$	−136.195	+	5.06997i	−0.138129	+	0.00514196i
$987$	−211.119	−	107.570i	−0.213900	−	0.108987i
$988$	−1129.39	−	1860.18i	−1.14311	−	1.88277i
$989$	38.8960			0.0393286
$990$	−744.030	−	552.389i	−0.751545	−	0.557969i
$991$			1042.03i			1.05149i	0.850642	+	0.525745i	$0.176213\pi$
$991$			1042.03i			1.05149i	−0.850642	+	0.525745i	$0.823787\pi$
$992$	531.712	−	15.4045i	0.536000	−	0.0155287i
$993$	5.47736	−	10.7499i	0.00551597	−	0.0108257i
$994$	1317.78	−	49.0554i	1.32573	−	0.0493515i
$995$	510.161	−	517.740i	0.512725	−	0.520342i
$996$	−32.7027	−	438.639i	−0.0328341	−	0.440401i
$997$	−977.577	+	498.100i	−0.980518	+	0.499599i	−0.869347	−	0.494202i	$-0.835460\pi$
$997$	−977.577	+	498.100i	−0.980518	+	0.499599i	−0.111171	+	0.993801i	$0.535460\pi$
$998$	−63.2182	+	524.857i	−0.0633449	+	0.525908i
$999$	106.553	−	77.4150i	0.106659	−	0.0774925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.w.a.63.5	yes	544
4.3	odd	2	inner	220.3.w.a.63.12	yes	544
5.2	odd	4	inner	220.3.w.a.107.30	yes	544
11.7	odd	10	inner	220.3.w.a.183.44	yes	544
20.7	even	4	inner	220.3.w.a.107.44	yes	544
44.7	even	10	inner	220.3.w.a.183.30	yes	544
55.7	even	20	inner	220.3.w.a.7.12	yes	544
220.7	odd	20	inner	220.3.w.a.7.5	✓	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.5	✓	544	220.7	odd	20	inner
220.3.w.a.7.12	yes	544	55.7	even	20	inner
220.3.w.a.63.5	yes	544	1.1	even	1	trivial
220.3.w.a.63.12	yes	544	4.3	odd	2	inner
220.3.w.a.107.30	yes	544	5.2	odd	4	inner
220.3.w.a.107.44	yes	544	20.7	even	4	inner
220.3.w.a.183.30	yes	544	44.7	even	10	inner
220.3.w.a.183.44	yes	544	11.7	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96237 + 0.386136i) q^{2} +(0.676076 + 0.344478i) q^{3} +(3.70180 - 1.51549i) q^{4} +(3.50937 - 3.56150i) q^{5} +(-1.45973 - 0.414936i) q^{6} +(-3.62504 - 7.11454i) q^{7} +(-6.67911 + 4.40334i) q^{8} +(-4.95165 - 6.81537i) q^{9} +(-5.51146 + 8.34409i) q^{10} +(-8.53099 - 6.94422i) q^{11} +(3.02475 + 0.250604i) q^{12} +(-2.75214 + 17.3763i) q^{13} +(9.86085 + 12.5616i) q^{14} +(3.59946 - 1.19895i) q^{15} +(11.4066 - 11.2200i) q^{16} +(0.282319 + 1.78249i) q^{17} +(12.3486 + 11.4623i) q^{18} +(-29.4107 + 9.55611i) q^{19} +(7.59357 - 18.5024i) q^{20} -6.05871i q^{21} +(19.4224 + 10.3330i) q^{22} +(-10.0993 + 10.0993i) q^{23} +(-6.03244 + 0.676187i) q^{24} +(-0.368626 - 24.9973i) q^{25} +(-1.30891 - 35.1614i) q^{26} +(-2.06824 - 13.0584i) q^{27} +(-24.2011 - 20.8429i) q^{28} +(11.6683 - 35.9113i) q^{29} +(-6.60052 + 3.74266i) q^{30} +(-9.77073 - 13.4483i) q^{31} +(-18.0515 + 26.4224i) q^{32} +(-3.37546 - 7.63356i) q^{33} +(-1.24230 - 3.38889i) q^{34} +(-38.0601 - 12.0570i) q^{35} +(-28.6586 - 17.7249i) q^{36} +(4.52256 + 8.87603i) q^{37} +(54.0247 - 30.1092i) q^{38} +(-7.84640 + 10.7996i) q^{39} +(-7.75696 + 39.2407i) q^{40} +(70.5782 - 22.9322i) q^{41} +(2.33949 + 11.8894i) q^{42} +(-1.92568 - 1.92568i) q^{43} +(-42.1039 - 12.7775i) q^{44} +(-41.6501 - 6.28232i) q^{45} +(15.9188 - 23.7182i) q^{46} +(17.7547 - 34.8455i) q^{47} +(11.5768 - 3.65628i) q^{48} +(-8.67429 + 11.9391i) q^{49} +(10.3757 + 48.9116i) q^{50} +(-0.423159 + 1.30235i) q^{51} +(16.1457 + 68.4943i) q^{52} +(-14.3061 - 2.26586i) q^{53} +(9.10096 + 24.8267i) q^{54} +(-54.6703 + 6.01330i) q^{55} +(55.5398 + 31.5565i) q^{56} +(-23.1757 - 3.67067i) q^{57} +(-9.03085 + 74.9769i) q^{58} +(8.73280 - 26.8768i) q^{59} +(11.5075 - 9.89319i) q^{60} +(1.41349 - 1.94550i) q^{61} +(24.3667 + 22.6176i) q^{62} +(-30.5383 + 59.9347i) q^{63} +(25.2211 - 58.8209i) q^{64} +(52.2275 + 70.7816i) q^{65} +(9.57151 + 13.6765i) q^{66} +(53.1731 + 53.1731i) q^{67} +(3.74642 + 6.17057i) q^{68} +(-10.3068 + 3.34889i) q^{69} +(79.3436 + 8.96386i) q^{70} +(48.5363 - 66.8045i) q^{71} +(63.0831 + 23.7168i) q^{72} +(9.19257 + 18.0414i) q^{73} +(-12.3023 - 15.6717i) q^{74} +(8.36179 - 17.0270i) q^{75} +(-94.3902 + 79.9462i) q^{76} +(-18.4798 + 85.8671i) q^{77} +(11.2274 - 24.2227i) q^{78} +(27.3454 + 37.6377i) q^{79} +(0.0697902 - 80.0000i) q^{80} +(-20.3291 + 62.5666i) q^{81} +(-129.646 + 72.2544i) q^{82} +(-22.6709 - 143.139i) q^{83} +(-9.18189 - 22.4281i) q^{84} +(7.33911 + 5.24994i) q^{85} +(4.52248 + 3.03533i) q^{86} +(20.2593 - 20.2593i) q^{87} +(87.5572 + 8.81638i) q^{88} +5.61342i q^{89} +(84.1589 - 3.75441i) q^{90} +(133.601 - 43.4096i) q^{91} +(-22.0801 + 52.6907i) q^{92} +(-1.97313 - 12.4578i) q^{93} +(-21.3861 + 75.2355i) q^{94} +(-69.1789 + 138.282i) q^{95} +(-21.3061 + 11.6452i) q^{96} +(-1.56473 + 9.87934i) q^{97} +(12.4120 - 26.7785i) q^{98} +(-5.08492 + 92.5272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

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