LMFDB - Embedded newform 220.3.w.a.7.12

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			7.12
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74700 + 0.973643i) q^{2} +(-0.676076 + 0.344478i) q^{3} +(2.10404 - 3.40192i) q^{4} +(3.50937 + 3.56150i) q^{5} +(0.845708 - 1.26006i) q^{6} +(3.62504 - 7.11454i) q^{7} +(-0.363505 + 7.99174i) q^{8} +(-4.95165 + 6.81537i) q^{9} +(-9.59852 - 2.80508i) q^{10} +(8.53099 - 6.94422i) q^{11} +(-0.250604 + 3.02475i) q^{12} +(-2.75214 - 17.3763i) q^{13} +(0.594072 + 15.9586i) q^{14} +(-3.59946 - 1.19895i) q^{15} +(-7.14606 - 14.3155i) q^{16} +(0.282319 - 1.78249i) q^{17} +(2.01482 - 16.7276i) q^{18} +(29.4107 + 9.55611i) q^{19} +(19.4998 - 4.44505i) q^{20} +6.05871i q^{21} +(-8.14246 + 20.4377i) q^{22} +(10.0993 + 10.0993i) q^{23} +(-2.50722 - 5.52824i) q^{24} +(-0.368626 + 24.9973i) q^{25} +(21.7263 + 27.6768i) q^{26} +(2.06824 - 13.0584i) q^{27} +(-16.5758 - 27.3013i) q^{28} +(11.6683 + 35.9113i) q^{29} +(7.45561 - 1.41003i) q^{30} +(9.77073 - 13.4483i) q^{31} +(26.4224 + 18.0515i) q^{32} +(-3.37546 + 7.63356i) q^{33} +(1.24230 + 3.38889i) q^{34} +(38.0601 - 12.0570i) q^{35} +(12.7668 + 31.1849i) q^{36} +(4.52256 - 8.87603i) q^{37} +(-60.6848 + 11.9410i) q^{38} +(7.84640 + 10.7996i) q^{39} +(-29.7383 + 26.7513i) q^{40} +(70.5782 + 22.9322i) q^{41} +(-5.89903 - 10.5846i) q^{42} +(1.92568 - 1.92568i) q^{43} +(-5.67415 - 43.6326i) q^{44} +(-41.6501 + 6.28232i) q^{45} +(-27.4765 - 7.81035i) q^{46} +(-17.7547 - 34.8455i) q^{47} +(9.76265 + 7.21671i) q^{48} +(-8.67429 - 11.9391i) q^{49} +(-23.6945 - 44.0292i) q^{50} +(0.423159 + 1.30235i) q^{51} +(-64.9033 - 27.1978i) 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} +(-55.3494 - 51.3764i) q^{58} +(-8.73280 - 26.8768i) q^{59} +(-11.6521 + 9.72243i) q^{60} +(1.41349 + 1.94550i) q^{61} +(-3.97569 + 33.0073i) q^{62} +(30.5383 + 59.9347i) q^{63} +(-63.7357 - 5.81007i) q^{64} +(52.2275 - 70.7816i) q^{65} +(-1.53542 - 16.6223i) q^{66} +(-53.1731 + 53.1731i) q^{67} +(-5.46987 - 4.71085i) q^{68} +(-10.3068 - 3.34889i) q^{69} +(-54.7519 + 58.1205i) q^{70} +(-48.5363 - 66.8045i) q^{71} +(-52.6667 - 42.0497i) q^{72} +(9.19257 - 18.0414i) q^{73} +(0.741158 + 19.9098i) q^{74} +(-8.36179 - 17.0270i) q^{75} +(94.3902 - 79.9462i) q^{76} +(-18.4798 - 85.8671i) q^{77} +(-24.2227 - 11.2274i) q^{78} +(-27.3454 + 37.6377i) q^{79} +(25.9066 - 75.6892i) q^{80} +(-20.3291 - 62.5666i) q^{81} +(-145.628 + 28.6553i) q^{82} +(22.6709 - 143.139i) q^{83} +(20.6112 + 12.7478i) q^{84} +(7.33911 - 5.24994i) q^{85} +(-1.48925 + 5.23911i) q^{86} +(-20.2593 - 20.2593i) q^{87} +(52.3953 + 70.7017i) q^{88} -5.61342i q^{89} +(66.6462 - 51.5276i) q^{90} +(-133.601 - 43.4096i) q^{91} +(55.6060 - 13.1076i) q^{92} +(-1.97313 + 12.4578i) q^{93} +(64.9445 + 43.5885i) q^{94} +(69.1789 + 138.282i) q^{95} +(-24.0819 - 3.10227i) q^{96} +(-1.56473 - 9.87934i) q^{97} +(26.7785 + 12.4120i) 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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.74700	+	0.973643i	−0.873501	+	0.486822i
$2$	−1.74700	+	0.973643i	−0.873501	+	0.486822i
$3$	−0.676076	+	0.344478i	−0.225359	+	0.114826i	−0.563025	−	0.826440i	$-0.690362\pi$
$3$	−0.676076	+	0.344478i	−0.225359	+	0.114826i	0.337666	+	0.941266i	$0.390362\pi$
$4$	2.10404	−	3.40192i	0.526009	−	0.850479i
$5$	3.50937	+	3.56150i	0.701874	+	0.712301i
$5$	3.50937	+	3.56150i	0.701874	+	0.712301i
$6$	0.845708	−	1.26006i	0.140951	−	0.210010i
$7$	3.62504	−	7.11454i	0.517863	−	1.01636i	−0.472946	−	0.881091i	$-0.656809\pi$
$7$	3.62504	−	7.11454i	0.517863	−	1.01636i	0.990809	−	0.135271i	$-0.0431906\pi$
$8$	−0.363505	+	7.99174i	−0.0454381	+	0.998967i
$9$	−4.95165	+	6.81537i	−0.550184	+	0.757263i
$10$	−9.59852	−	2.80508i	−0.959852	−	0.280508i
$11$	8.53099	−	6.94422i	0.775544	−	0.631293i
$11$	8.53099	−	6.94422i	0.775544	−	0.631293i
$12$	−0.250604	+	3.02475i	−0.0208837	+	0.252062i
$13$	−2.75214	−	17.3763i	−0.211703	−	1.33664i	−0.833091	−	0.553136i	$-0.813431\pi$
$13$	−2.75214	−	17.3763i	−0.211703	−	1.33664i	0.621389	−	0.783503i	$-0.286569\pi$
$14$	0.594072	+	15.9586i	0.0424337	+	1.13990i
$15$	−3.59946	−	1.19895i	−0.239964	−	0.0799297i
$16$	−7.14606	−	14.3155i	−0.446629	−	0.894719i
$17$	0.282319	−	1.78249i	0.0166070	−	0.104852i	−0.977992	−	0.208640i	$-0.933096\pi$
$17$	0.282319	−	1.78249i	0.0166070	−	0.104852i	0.994599	+	0.103788i	$0.0330963\pi$
$18$	2.01482	−	16.7276i	0.111934	−	0.929312i
$19$	29.4107	+	9.55611i	1.54793	+	0.502953i	0.953551	−	0.301232i	$-0.0973978\pi$
$19$	29.4107	+	9.55611i	1.54793	+	0.502953i	0.594379	+	0.804185i	$0.297398\pi$
$20$	19.4998	−	4.44505i	0.974989	−	0.222252i
$21$			6.05871i			0.288510i
$22$	−8.14246	+	20.4377i	−0.370112	+	0.928987i
$23$	10.0993	+	10.0993i	0.439098	+	0.439098i	0.891708	−	0.452610i	$-0.149507\pi$
$23$	10.0993	+	10.0993i	0.439098	+	0.439098i	−0.452610	+	0.891708i	$0.649507\pi$
$24$	−2.50722	−	5.52824i	−0.104467	−	0.230343i
$25$	−0.368626	+	24.9973i	−0.0147450	+	0.999891i
$26$	21.7263	+	27.6768i	0.835627	+	1.06449i
$27$	2.06824	−	13.0584i	0.0766015	−	0.483643i
$28$	−16.5758	−	27.3013i	−0.591995	−	0.975048i
$29$	11.6683	+	35.9113i	0.402355	+	1.23832i	0.923084	+	0.384599i	$0.125660\pi$
$29$	11.6683	+	35.9113i	0.402355	+	1.23832i	−0.520729	+	0.853722i	$0.674340\pi$
$30$	7.45561	−	1.41003i	0.248520	−	0.0470010i
$31$	9.77073	−	13.4483i	0.315185	−	0.433815i	−0.621805	−	0.783172i	$-0.713600\pi$
$31$	9.77073	−	13.4483i	0.315185	−	0.433815i	0.936989	+	0.349358i	$0.113600\pi$
$32$	26.4224	+	18.0515i	0.825700	+	0.564110i
$33$	−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
$36$	12.7668	+	31.1849i	0.354634	+	0.866247i
$37$	4.52256	−	8.87603i	0.122231	−	0.239893i	−0.821780	−	0.569804i	$-0.807019\pi$
$37$	4.52256	−	8.87603i	0.122231	−	0.239893i	0.944012	+	0.329912i	$0.107019\pi$
$38$	−60.6848	+	11.9410i	−1.59697	+	0.314236i
$39$	7.84640	+	10.7996i	0.201190	+	0.276914i
$40$	−29.7383	+	26.7513i	−0.743457	+	0.668784i
$41$	70.5782	+	22.9322i	1.72142	+	0.559323i	0.992167	−	0.124922i	$-0.0398680\pi$
$41$	70.5782	+	22.9322i	1.72142	+	0.559323i	0.729252	+	0.684245i	$0.239868\pi$
$42$	−5.89903	−	10.5846i	−0.140453	−	0.252014i
$43$	1.92568	−	1.92568i	0.0447834	−	0.0447834i	−0.684360	−	0.729144i	$-0.739919\pi$
$43$	1.92568	−	1.92568i	0.0447834	−	0.0447834i	0.729144	+	0.684360i	$0.239919\pi$
$44$	−5.67415	−	43.6326i	−0.128958	−	0.991650i
$45$	−41.6501	+	6.28232i	−0.925559	+	0.139607i
$46$	−27.4765	−	7.81035i	−0.597315	−	0.169790i
$47$	−17.7547	−	34.8455i	−0.377759	−	0.741394i	0.621353	−	0.783531i	$-0.286583\pi$
$47$	−17.7547	−	34.8455i	−0.377759	−	0.741394i	−0.999112	+	0.0421373i	$0.986583\pi$
$48$	9.76265	+	7.21671i	0.203389	+	0.150348i
$49$	−8.67429	−	11.9391i	−0.177026	−	0.243656i
$50$	−23.6945	−	44.0292i	−0.473889	−	0.880585i
$51$	0.423159	+	1.30235i	0.00829724	+	0.0255363i
$52$	−64.9033	−	27.1978i	−1.24814	−	0.523035i
$53$	−14.3061	+	2.26586i	−0.269926	+	0.0427521i	−0.289930	−	0.957048i	$-0.593632\pi$
$53$	−14.3061	+	2.26586i	−0.269926	+	0.0427521i	0.0200041	+	0.999800i	$0.493632\pi$
$54$	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
$58$	−55.3494	−	51.3764i	−0.954299	−	0.885800i
$59$	−8.73280	−	26.8768i	−0.148014	−	0.455539i	0.849373	−	0.527794i	$-0.176981\pi$
$59$	−8.73280	−	26.8768i	−0.148014	−	0.455539i	−0.997386	+	0.0722546i	$0.976981\pi$
$60$	−11.6521	+	9.72243i	−0.194202	+	0.162041i
$61$	1.41349	+	1.94550i	0.0231719	+	0.0318934i	0.820446	−	0.571724i	$-0.193725\pi$
$61$	1.41349	+	1.94550i	0.0231719	+	0.0318934i	−0.797274	+	0.603618i	$0.793725\pi$
$62$	−3.97569	+	33.0073i	−0.0641240	+	0.532377i
$63$	30.5383	+	59.9347i	0.484734	+	0.951345i
$64$	−63.7357	−	5.81007i	−0.995871	−	0.0907824i
$65$	52.2275	−	70.7816i	0.803500	−	1.08895i
$66$	−1.53542	−	16.6223i	−0.0232639	−	0.251854i
$67$	−53.1731	+	53.1731i	−0.793628	+	0.793628i	−0.982082	−	0.188454i	$-0.939652\pi$
$67$	−53.1731	+	53.1731i	−0.793628	+	0.793628i	0.188454	+	0.982082i	$0.439652\pi$
$68$	−5.46987	−	4.71085i	−0.0804393	−	0.0692772i
$69$	−10.3068	−	3.34889i	−0.149374	−	0.0485347i
$70$	−54.7519	+	58.1205i	−0.782169	+	0.830293i
$71$	−48.5363	−	66.8045i	−0.683610	−	0.940908i	0.316360	−	0.948639i	$-0.397539\pi$
$71$	−48.5363	−	66.8045i	−0.683610	−	0.940908i	−0.999970	+	0.00773106i	$0.997539\pi$
$72$	−52.6667	−	42.0497i	−0.731482	−	0.584024i
$73$	9.19257	−	18.0414i	0.125926	−	0.247143i	−0.819433	−	0.573175i	$-0.805712\pi$
$73$	9.19257	−	18.0414i	0.125926	−	0.247143i	0.945359	+	0.326032i	$0.105712\pi$
$74$	0.741158	+	19.9098i	0.0100157	+	0.269051i
$75$	−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
$78$	−24.2227	−	11.2274i	−0.310547	−	0.143941i
$79$	−27.3454	+	37.6377i	−0.346144	+	0.476426i	−0.946223	−	0.323514i	$-0.895136\pi$
$79$	−27.3454	+	37.6377i	−0.346144	+	0.476426i	0.600079	+	0.799940i	$0.295136\pi$
$80$	25.9066	−	75.6892i	0.323832	−	0.946115i
$81$	−20.3291	−	62.5666i	−0.250977	−	0.772427i
$82$	−145.628	+	28.6553i	−1.77595	+	0.349455i
$83$	22.6709	−	143.139i	0.273144	−	1.72456i	−0.345092	−	0.938569i	$-0.612152\pi$
$83$	22.6709	−	143.139i	0.273144	−	1.72456i	0.618236	−	0.785993i	$-0.287848\pi$
$84$	20.6112	+	12.7478i	0.245372	+	0.151759i
$85$	7.33911	−	5.24994i	0.0863424	−	0.0617640i
$86$	−1.48925	+	5.23911i	−0.0173168	+	0.0609198i
$87$	−20.2593	−	20.2593i	−0.232866	−	0.232866i
$88$	52.3953	+	70.7017i	0.595402	+	0.803428i
$89$		−	5.61342i		−	0.0630721i	−0.999503	−	0.0315360i	$-0.989960\pi$
$89$		−	5.61342i		−	0.0630721i	0.999503	−	0.0315360i	$-0.0100399\pi$
$90$	66.6462	−	51.5276i	0.740513	−	0.572529i
$91$	−133.601	−	43.4096i	−1.46814	−	0.477028i
$92$	55.6060	−	13.1076i	0.604413	−	0.142474i
$93$	−1.97313	+	12.4578i	−0.0212164	+	0.133955i
$94$	64.9445	+	43.5885i	0.690899	+	0.463707i
$95$	69.1789	+	138.282i	0.728198	+	1.45560i
$96$	−24.0819	−	3.10227i	−0.250853	−	0.0323153i
$97$	−1.56473	−	9.87934i	−0.0161313	−	0.101849i	0.978309	−	0.207151i	$-0.0664191\pi$
$97$	−1.56473	−	9.87934i	−0.0161313	−	0.101849i	−0.994440	+	0.105302i	$0.966419\pi$
$98$	26.7785	+	12.4120i	0.273250	+	0.126653i
$99$	5.08492	+	92.5272i	0.0513629	+	0.934618i
$100$	84.2630	+	53.8492i	0.842630	+	0.538492i
$101$	−56.4692	+	77.7232i	−0.559101	+	0.769536i	−0.991212	−	0.132284i	$-0.957769\pi$
$101$	−56.4692	+	77.7232i	−0.559101	+	0.769536i	0.432111	+	0.901820i	$0.357769\pi$
$102$	−2.00729	−	1.86320i	−0.0196793	−	0.0182667i
$103$	−13.7955	+	27.0751i	−0.133937	+	0.262865i	−0.948228	−	0.317591i	$-0.897126\pi$
$103$	−13.7955	+	27.0751i	−0.133937	+	0.262865i	0.814291	+	0.580457i	$0.197126\pi$
$104$	139.867	−	15.6780i	1.34488	−	0.150750i
$105$	−21.5781	+	21.2623i	−0.205506	+	0.202498i
$106$	22.7866	−	17.8875i	0.214968	−	0.168750i
$107$	−143.834	+	73.2873i	−1.34425	+	0.684928i	−0.970160	−	0.242466i	$-0.922044\pi$
$107$	−143.834	+	73.2873i	−1.34425	+	0.684928i	−0.374087	+	0.927394i	$0.622044\pi$
$108$	−40.0718	−	34.5113i	−0.371035	−	0.319549i
$109$	−157.535			−1.44527			−0.722636	−	0.691229i	$-0.757069\pi$
$109$	−157.535			−1.44527			−0.722636	+	0.691229i	$0.757069\pi$
$110$	−101.364	+	42.7241i	−0.921490	+	0.388401i
$111$			7.55879i			0.0680972i
$112$	−127.753	−	1.05337i	−1.14065	−	0.00940507i
$113$	73.5546	+	144.359i	0.650926	+	1.27751i	0.946657	+	0.322243i	$0.104437\pi$
$113$	73.5546	+	144.359i	0.650926	+	1.27751i	−0.295731	+	0.955271i	$0.595563\pi$
$114$	36.9141	−	28.9776i	0.323808	−	0.254189i
$115$	−0.526504	+	71.4106i	−0.00457830	+	0.620962i
$116$	146.718	+	35.8642i	1.26481	+	0.309174i
$117$	132.053	+	67.2846i	1.12866	+	0.575082i
$118$	41.4247	+	38.4512i	0.351056	+	0.325858i
$119$	−11.6582	−	8.47016i	−0.0979679	−	0.0711778i
$120$	10.8901	−	28.3301i	0.0907507	−	0.236084i
$121$	24.5555	−	118.482i	0.202938	−	0.979192i
$122$	−4.36359	−	2.02256i	−0.0357671	−	0.0165783i
$123$	−55.6158	+	8.80868i	−0.452161	+	0.0716153i
$124$	−25.1919	−	61.5348i	−0.203160	−	0.496249i
$125$	−90.3216	+	86.4119i	−0.722573	+	0.691295i
$126$	−111.705	−	74.9727i	−0.886551	−	0.595022i
$127$	166.030	+	26.2966i	1.30732	+	0.207060i	0.770937	−	0.636912i	$-0.219789\pi$
$127$	166.030	+	26.2966i	1.30732	+	0.207060i	0.536388	+	0.843972i	$0.319789\pi$
$128$	117.003	−	51.9057i	0.914089	−	0.405513i
$129$	−0.638553	+	1.96526i	−0.00495002	+	0.0152346i
$130$	−22.3255	+	174.507i	−0.171735	+	1.34236i
$131$	165.619			1.26427			0.632135	−	0.774858i	$-0.282179\pi$
$131$	165.619			1.26427			0.632135	+	0.774858i	$0.282179\pi$
$132$	18.8666	+	27.5443i	0.142929	+	0.208669i
$133$	174.602	−	174.602i	1.31280	−	1.31280i
$134$	41.1219	−	144.665i	0.306880	−	1.07959i
$135$	53.7656	−	38.4606i	0.398264	−	0.284893i
$136$	14.1426	+	2.90416i	0.103989	+	0.0213541i
$137$	−113.597	−	17.9920i	−0.829177	−	0.131329i	−0.272603	−	0.962127i	$-0.587884\pi$
$137$	−113.597	−	17.9920i	−0.829177	−	0.131329i	−0.556574	+	0.830798i	$0.687884\pi$
$138$	21.2667	−	4.18465i	0.154106	−	0.0303236i
$139$	−194.379	+	63.1577i	−1.39841	+	0.454372i	−0.908677	−	0.417499i	$-0.862907\pi$
$139$	−194.379	+	63.1577i	−1.39841	+	0.454372i	−0.489735	+	0.871871i	$0.662907\pi$
$140$	39.0630	−	154.845i	0.279021	−	1.10604i
$141$	24.0070	+	17.4421i	0.170262	+	0.123703i
$142$	149.837	+	69.4505i	1.05519	+	0.489088i
$143$	−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
$146$	1.50648	+	40.4687i	0.0103184	+	0.277183i
$147$	9.97725	+	5.08366i	0.0678724	+	0.0345827i
$148$	−20.6799	−	34.0609i	−0.139729	−	0.230141i
$149$	128.941	−	93.6811i	0.865376	−	0.628732i	−0.0639665	−	0.997952i	$-0.520375\pi$
$149$	128.941	−	93.6811i	0.865376	−	0.628732i	0.929342	+	0.369220i	$0.120375\pi$
$150$	31.1863	+	21.6049i	0.207909	+	0.144033i
$151$	82.2950	−	253.278i	0.545000	−	1.67734i	−0.175989	−	0.984392i	$-0.556312\pi$
$151$	82.2950	−	253.278i	0.545000	−	1.67734i	0.720990	−	0.692946i	$-0.243688\pi$
$152$	−87.0608	+	231.569i	−0.572769	+	1.52348i
$153$	10.7504	+	10.7504i	0.0702639	+	0.0702639i
$154$	115.888	+	132.017i	0.752521	+	0.857256i
$155$	82.1851	−	12.3964i	0.530227	−	0.0799770i
$156$	53.2486	−	3.96994i	0.341337	−	0.0254484i
$157$	−20.0924	+	10.2376i	−0.127977	+	0.0652075i	−0.516807	−	0.856102i	$-0.672879\pi$
$157$	−20.0924	+	10.2376i	−0.127977	+	0.0652075i	0.388830	+	0.921310i	$0.372879\pi$
$158$	11.1268	−	92.3777i	0.0704225	−	0.584669i
$159$	8.89146	−	6.46002i	0.0559211	−	0.0406291i
$160$	28.4354	+	157.453i	0.177721	+	0.984081i
$161$	108.462	−	35.2414i	0.673676	−	0.218890i
$162$	96.4326	+	89.5107i	0.595263	+	0.552535i
$163$	−2.06309	−	13.0259i	−0.0126570	−	0.0799133i	0.980551	−	0.196263i	$-0.0628806\pi$
$163$	−2.06309	−	13.0259i	−0.0126570	−	0.0799133i	−0.993208	+	0.116350i	$0.962881\pi$
$164$	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	−0.815322	−	0.579008i	$-0.803440\pi$
$167$	−36.5443	−	230.731i	−0.218828	−	1.38162i	0.596494	−	0.802617i	$-0.296560\pi$
$168$	−48.4196	−	2.20237i	−0.288212	−	0.0131094i
$169$	−133.633	+	43.4200i	−0.790727	+	0.256923i
$170$	−7.70987	+	16.3173i	−0.0453522	+	0.0959843i
$171$	−210.760	+	153.126i	−1.23251	+	0.895474i
$172$	−2.49931	−	10.6027i	−0.0145308	−	0.0616438i
$173$	−19.1647	+	9.76490i	−0.110779	+	0.0564445i	−0.508502	−	0.861061i	$-0.669800\pi$
$173$	−19.1647	+	9.76490i	−0.110779	+	0.0564445i	0.397723	+	0.917505i	$0.369800\pi$
$174$	55.1184	+	15.6677i	0.316772	+	0.0900443i
$175$	176.508	+	93.2387i	1.00862	+	0.532793i
$176$	−160.373	−	72.5016i	−0.911210	−	0.411941i
$177$	15.1625	+	15.1625i	0.0856638	+	0.0856638i
$178$	5.46547	+	9.80665i	0.0307049	+	0.0550935i
$179$	−106.579	+	328.015i	−0.595411	+	1.83249i	−0.0427440	+	0.999086i	$0.513610\pi$
$179$	−106.579	+	328.015i	−0.595411	+	1.83249i	−0.552667	+	0.833402i	$0.686390\pi$
$180$	−66.2615	+	154.909i	−0.368120	+	0.860603i
$181$	44.7076	−	32.4820i	0.247004	−	0.179459i	−0.457394	−	0.889264i	$-0.651217\pi$
$181$	44.7076	−	32.4820i	0.247004	−	0.179459i	0.704398	+	0.709805i	$0.251217\pi$
$182$	275.667	−	54.2430i	1.51465	−	0.298039i
$183$	−1.62581	−	0.828389i	−0.00888418	−	0.00452672i
$184$	−84.3817	+	77.0395i	−0.458596	+	0.418693i
$185$	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
$188$	−155.898	−	12.9163i	−0.829244	−	0.0687039i
$189$	−85.4068	−	62.0517i	−0.451888	−	0.328316i
$190$	−255.493	−	174.224i	−1.34470	−	0.916967i
$191$	−122.340	+	39.7508i	−0.640526	+	0.208120i	−0.611232	−	0.791451i	$-0.709326\pi$
$191$	−122.340	+	39.7508i	−0.640526	+	0.208120i	−0.0292939	+	0.999571i	$0.509326\pi$
$192$	45.0916	−	18.0275i	0.234852	−	0.0938932i
$193$	−304.922	−	48.2950i	−1.57991	−	0.250233i	−0.696052	−	0.717991i	$-0.745062\pi$
$193$	−304.922	−	48.2950i	−1.57991	−	0.250233i	−0.883857	+	0.467758i	$0.845062\pi$
$194$	12.3526	+	15.7357i	0.0636730	+	0.0811121i
$195$	−10.9270	+	65.8449i	−0.0560361	+	0.337666i
$196$	−58.8670	+	4.38882i	−0.300342	+	0.0223920i
$197$	78.9040	−	78.9040i	0.400528	−	0.400528i	−0.477891	−	0.878419i	$-0.658599\pi$
$197$	78.9040	−	78.9040i	0.400528	−	0.400528i	0.878419	+	0.477891i	$0.158599\pi$
$198$	−98.9719	−	156.694i	−0.499858	−	0.791386i
$199$	−145.371			−0.730508			−0.365254	−	0.930908i	$-0.619018\pi$
$199$	−145.371			−0.730508			−0.365254	+	0.930908i	$0.619018\pi$
$200$	−199.638	−	12.0326i	−0.998189	−	0.0601630i
$201$	17.6321	−	54.2660i	0.0877218	−	0.269980i
$202$	22.9772	−	190.763i	0.113748	−	0.944374i
$203$	297.790	+	47.1654i	1.46695	+	0.232342i
$204$	5.32083	+	1.30064i	0.0260825	+	0.00637569i
$205$	166.012	+	331.842i	0.809814	+	1.61874i
$206$	−2.26080	−	60.7322i	−0.0109748	−	0.294817i
$207$	−118.838	+	18.8221i	−0.574097	+	0.0909281i
$208$	−229.084	+	163.570i	−1.10136	+	0.786395i
$209$	317.262	−	122.711i	1.51800	−	0.587135i
$210$	16.9952	−	58.1547i	0.0809294	−	0.276927i
$211$	−111.627	−	81.1020i	−0.529039	−	0.384370i	0.290959	−	0.956736i	$-0.406026\pi$
$211$	−111.627	−	81.1020i	−0.529039	−	0.384370i	−0.819998	+	0.572366i	$0.806026\pi$
$212$	−22.3923	+	53.4355i	−0.105624	+	0.252054i
$213$	55.8269	+	28.4452i	0.262098	+	0.133546i
$214$	179.923	−	268.077i	0.840764	−	1.25269i
$215$	13.6163	+	0.100392i	0.0633315	+	0.000466938i
$216$	103.607	+	21.2756i	0.479663	+	0.0984982i
$217$	−60.2589	−	118.265i	−0.277691	−	0.544999i
$218$	275.213	−	153.382i	1.26245	−	0.703589i
$219$			15.3640i			0.0701553i
$220$	135.485	−	173.332i	0.615841	−	0.787870i
$221$	−31.7501			−0.143665
$222$	−7.35957	−	13.2052i	−0.0331512	−	0.0594830i
$223$	77.6090	−	39.5438i	0.348022	−	0.177326i	−0.271237	−	0.962513i	$-0.587433\pi$
$223$	77.6090	−	39.5438i	0.348022	−	0.177326i	0.619260	+	0.785186i	$0.287433\pi$
$224$	224.210	−	122.546i	1.00094	−	0.547079i
$225$	−168.540	−	126.290i	−0.749068	−	0.561290i
$226$	−269.054	−	180.580i	−1.19051	−	0.799025i
$227$	−123.293	+	241.977i	−0.543143	+	1.06598i	0.442442	+	0.896797i	$0.354112\pi$
$227$	−123.293	+	241.977i	−0.543143	+	1.06598i	−0.985585	+	0.169181i	$0.945888\pi$
$228$	−36.2752	+	86.5650i	−0.159102	+	0.379671i
$229$	−23.4994	+	32.3442i	−0.102617	+	0.141241i	−0.857238	−	0.514921i	$-0.827821\pi$
$229$	−23.4994	+	32.3442i	−0.102617	+	0.141241i	0.754620	+	0.656162i	$0.227821\pi$
$230$	−68.6086	−	125.267i	−0.298298	−	0.544640i
$231$	42.0731	+	51.6868i	0.182134	+	0.223752i
$232$	−291.235	+	80.1960i	−1.25532	+	0.345672i
$233$	−21.4341	−	135.330i	−0.0919920	−	0.580814i	−0.990026	−	0.140888i	$-0.955004\pi$
$233$	−21.4341	−	135.330i	−0.0919920	−	0.580814i	0.898034	−	0.439927i	$-0.144996\pi$
$234$	−296.209	+	11.0266i	−1.26585	+	0.0471223i
$235$	61.7947	−	185.519i	0.262956	−	0.789443i
$236$	−109.807	−	26.8415i	−0.465283	−	0.113735i
$237$	5.52220	−	34.8658i	0.0233004	−	0.147113i
$238$	28.6138	+	3.44649i	0.120226	+	0.0144810i
$239$	−43.3398	−	14.0819i	−0.181338	−	0.0589203i	0.216941	−	0.976185i	$-0.430392\pi$
$239$	−43.3398	−	14.0819i	−0.181338	−	0.0589203i	−0.398278	+	0.917265i	$0.630392\pi$
$240$	8.55843	+	60.0958i	0.0356601	+	0.250399i
$241$			46.1322i			0.191420i	0.995409	+	0.0957100i	$0.0305121\pi$
$241$			46.1322i			0.191420i	−0.995409	+	0.0957100i	$0.969488\pi$
$242$	72.4608	+	230.897i	0.299425	+	0.954120i
$243$	119.436	+	119.436i	0.491505	+	0.491505i
$244$	9.59245	−	0.715164i	0.0393133	−	0.00293100i
$245$	12.0800	−	72.7924i	0.0493061	−	0.297112i
$246$	88.5845	−	69.5388i	0.360100	−	0.282678i
$247$	85.1076	−	537.348i	0.344565	−	2.17550i
$248$	103.923	+	82.9736i	0.419045	+	0.334571i
$249$	33.9808	+	104.582i	0.136469	+	0.420009i
$250$	73.6577	−	238.903i	0.294631	−	0.955611i
$251$	−192.816	+	265.388i	−0.768191	+	1.05732i	0.228297	+	0.973592i	$0.426684\pi$
$251$	−192.816	+	265.388i	−0.768191	+	1.05732i	−0.996488	+	0.0837328i	$0.973316\pi$
$252$	268.146	+	22.2163i	1.06407	+	0.0881597i
$253$	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
$256$	−153.868	+	204.599i	−0.601046	+	0.799215i
$257$	−135.201	+	265.347i	−0.526074	+	1.03248i	0.463179	+	0.886265i	$0.346709\pi$
$257$	−135.201	+	265.347i	−0.526074	+	1.03248i	−0.989253	+	0.146214i	$0.953291\pi$
$258$	−0.797913	−	4.05504i	−0.00309269	−	0.0157172i
$259$	−46.7544	−	64.3519i	−0.180519	−	0.248463i
$260$	−130.905	−	326.601i	−0.503479	−	1.25616i
$261$	−302.526	−	98.2967i	−1.15910	−	0.376616i
$262$	−289.337	+	161.254i	−1.10434	+	0.615474i
$263$	55.4741	−	55.4741i	0.210928	−	0.210928i	−0.593733	−	0.804662i	$-0.702347\pi$
$263$	55.4741	−	55.4741i	0.210928	−	0.210928i	0.804662	+	0.593733i	$0.202347\pi$
$264$	−59.7784	−	29.7507i	−0.226433	−	0.112692i
$265$	−58.2752	−	42.9994i	−0.219907	−	0.162262i
$266$	−135.030	+	475.031i	−0.507632	+	1.78583i
$267$	1.93370	+	3.79509i	0.00724231	+	0.0142138i
$268$	69.0122	+	292.769i	0.257508	+	1.09242i
$269$	−152.271	−	209.584i	−0.566065	−	0.779122i	0.426017	−	0.904715i	$-0.359916\pi$
$269$	−152.271	−	209.584i	−0.566065	−	0.779122i	−0.992082	+	0.125594i	$0.959916\pi$
$270$	−56.4818	+	119.539i	−0.209192	+	0.442738i
$271$	−90.2497	−	277.760i	−0.333025	−	1.02495i	−0.967687	−	0.252155i	$-0.918861\pi$
$271$	−90.2497	−	277.760i	−0.333025	−	1.02495i	0.634662	−	0.772790i	$-0.281139\pi$
$272$	−27.5347	+	8.69624i	−0.101231	+	0.0319715i
$273$	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	0.110554	−	0.993870i	$-0.464737\pi$
$277$	144.821	−	22.9374i	0.522821	−	0.0828067i	0.412266	+	0.911063i	$0.364737\pi$
$278$	278.088	−	299.593i	1.00032	−	1.07767i
$279$	43.2735	+	133.182i	0.155102	+	0.477356i
$280$	82.5211	+	308.549i	0.294718	+	1.10196i
$281$	4.99155	+	6.87029i	0.0177635	+	0.0244494i	0.817806	−	0.575493i	$-0.195190\pi$
$281$	4.99155	+	6.87029i	0.0177635	+	0.0244494i	−0.800043	+	0.599943i	$0.795190\pi$
$282$	−58.9227	−	7.09715i	−0.208946	−	0.0251672i
$283$	42.0181	+	82.4651i	0.148474	+	0.291396i	0.953250	−	0.302182i	$-0.0977149\pi$
$283$	42.0181	+	82.4651i	0.148474	+	0.291396i	−0.804777	+	0.593578i	$0.797715\pi$
$284$	−329.385	+	24.5573i	−1.15981	+	0.0864693i
$285$	−94.4053	−	69.6586i	−0.331247	−	0.244416i
$286$	377.541	+	85.2385i	1.32007	+	0.298037i
$287$	419.001	−	419.001i	1.45993	−	1.45993i
$288$	−253.862	+	90.6934i	−0.881466	+	0.314908i
$289$	271.758	+	88.2995i	0.940338	+	0.305534i
$290$	−11.2642	−	377.426i	−0.0388419	−	1.30147i
$291$	4.46109	+	6.14017i	0.0153302	+	0.0211002i
$292$	−42.0339	−	69.2322i	−0.143952	−	0.237097i
$293$	−235.210	+	461.626i	−0.802766	+	1.57552i	0.0149458	+	0.999888i	$0.495242\pi$
$293$	−235.210	+	461.626i	−0.802766	+	1.57552i	−0.817712	+	0.575628i	$0.804758\pi$
$294$	−22.3800	+	0.833112i	−0.0761223	+	0.00283371i
$295$	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
$298$	−134.048	+	289.204i	−0.449826	+	0.970482i
$299$	147.693	−	203.282i	0.493957	−	0.679874i
$300$	−75.5181	−	7.37941i	−0.251727	−	0.0245980i
$301$	−6.71968	−	20.6810i	−0.0223245	−	0.0687078i
$302$	102.833	+	522.603i	0.340506	+	1.73047i
$303$	11.4035	−	71.9991i	0.0376355	−	0.237621i
$304$	−73.3698	−	489.317i	−0.241348	−	1.60960i
$305$	−1.96845	+	11.8616i	−0.00645393	+	0.0388905i
$306$	−29.2480	−	8.31390i	−0.0955816	−	0.0271696i
$307$	−170.671	−	170.671i	−0.555933	−	0.555933i	0.372214	−	0.928147i	$-0.378599\pi$
$307$	−170.671	−	170.671i	−0.555933	−	0.555933i	−0.928147	+	0.372214i	$0.878599\pi$
$308$	−330.995	−	117.801i	−1.07466	−	0.382471i
$309$		−	23.0571i		−	0.0746184i
$310$	−131.508	+	101.676i	−0.424219	+	0.327986i
$311$	282.646	+	91.8372i	0.908829	+	0.295296i	0.725876	−	0.687825i	$-0.241435\pi$
$311$	282.646	+	91.8372i	0.908829	+	0.295296i	0.182953	+	0.983122i	$0.441435\pi$
$312$	−89.1601	+	58.7806i	−0.285770	+	0.188400i
$313$	−44.7144	+	282.315i	−0.142857	+	0.901966i	0.807288	+	0.590158i	$0.200935\pi$
$313$	−44.7144	+	282.315i	−0.142857	+	0.901966i	−0.950145	+	0.311808i	$0.899065\pi$
$314$	25.1337	−	37.4479i	0.0800436	−	0.119261i
$315$	−106.288	+	319.095i	−0.337421	+	1.01300i
$316$	70.5045	+	172.218i	0.223116	+	0.544993i
$317$	53.9840	+	340.841i	0.170296	+	1.07521i	0.913707	+	0.406374i	$0.133207\pi$
$317$	53.9840	+	340.841i	0.170296	+	1.07521i	−0.743410	+	0.668836i	$0.766793\pi$
$318$	−9.24364	+	19.9428i	−0.0290681	+	0.0627132i
$319$	348.918	+	225.332i	1.09379	+	0.706369i
$320$	−202.980	−	247.385i	−0.634312	−	0.773077i
$321$	71.9971	−	99.0955i	0.224290	−	0.308709i
$322$	−155.170	+	167.170i	−0.481896	+	0.519161i
$323$	25.3368	−	49.7264i	0.0784422	−	0.153952i
$324$	−255.619	−	62.4845i	−0.788949	−	0.192853i
$325$	435.375	−	62.3905i	1.33961	−	0.191971i
$326$	16.2868	+	20.7475i	0.0499595	+	0.0636427i
$327$	106.505	−	54.2672i	0.325704	−	0.165955i
$328$	−208.924	+	555.706i	−0.636963	+	1.69423i
$329$	−312.271			−0.949152
$330$	53.8122	−	63.8024i	0.163067	−	0.193341i
$331$		−	15.9005i		−	0.0480377i	−0.999712	−	0.0240188i	$-0.992354\pi$
$331$		−	15.9005i		−	0.0480377i	0.999712	−	0.0240188i	$-0.00764617\pi$
$332$	−439.245	−	378.293i	−1.32303	−	1.13944i
$333$	38.0992	+	74.7739i	0.114412	+	0.224546i
$334$	288.493	+	367.507i	0.863751	+	1.10032i
$335$	−375.980	−	2.77207i	−1.12233	−	0.00827484i
$336$	86.7336	−	43.2959i	0.258136	−	0.128857i
$337$	555.102	+	282.838i	1.64719	+	0.839283i	0.996822	+	0.0796602i	$0.0253835\pi$
$337$	555.102	+	282.838i	1.64719	+	0.839283i	0.650364	+	0.759623i	$0.274616\pi$
$338$	191.181	−	205.966i	0.565626	−	0.609366i
$339$	−99.4570	−	72.2597i	−0.293384	−	0.213156i
$340$	−2.41810	−	36.0131i	−0.00711206	−	0.105921i
$341$	−10.0337	−	182.577i	−0.0294243	−	0.535417i
$342$	219.108	−	472.716i	0.640666	−	1.38221i
$343$	270.054	−	42.7723i	0.787329	−	0.124701i
$344$	14.6896	+	16.0896i	0.0427022	+	0.0467720i
$345$	−24.2434	−	48.4603i	−0.0702707	−	0.140465i
$346$	23.9732	−	35.7189i	0.0692868	−	0.103234i
$347$	302.641	+	47.9336i	0.872164	+	0.138137i	0.576443	−	0.817137i	$-0.304440\pi$
$347$	302.641	+	47.9336i	0.872164	+	0.138137i	0.295721	+	0.955274i	$0.404440\pi$
$348$	−111.547	+	26.2941i	−0.320537	+	0.0755578i
$349$	107.776	−	331.701i	0.308814	−	0.950431i	−0.669413	−	0.742891i	$-0.733454\pi$
$349$	107.776	−	331.701i	0.308814	−	0.950431i	0.978226	−	0.207540i	$-0.0665459\pi$
$350$	−399.141	+	8.96744i	−1.14040	+	0.0256212i
$351$	−232.598			−0.662672
$352$	350.763	−	29.4856i	0.996485	−	0.0837660i
$353$	−7.94999	+	7.94999i	−0.0225212	+	0.0225212i	−0.718278	−	0.695757i	$-0.755069\pi$
$353$	−7.94999	+	7.94999i	−0.0225212	+	0.0225212i	0.695757	+	0.718278i	$0.255069\pi$
$354$	−41.2518	−	11.7261i	−0.116530	−	0.0331245i
$355$	67.5925	−	407.304i	0.190402	−	1.14733i
$356$	−19.0964	−	11.8108i	−0.0536415	−	0.0331765i
$357$	10.7996	+	1.71049i	0.0302510	+	0.00479128i
$358$	−133.177	−	676.813i	−0.372002	−	1.89054i
$359$	279.395	−	90.7810i	0.778259	−	0.252872i	0.107163	−	0.994242i	$-0.465823\pi$
$359$	279.395	−	90.7810i	0.778259	−	0.252872i	0.671097	+	0.741370i	$0.265823\pi$
$360$	−35.0666	−	335.141i	−0.0974072	−	0.930946i
$361$	481.613	+	349.913i	1.33411	+	0.969287i
$362$	−46.4785	+	100.275i	−0.128394	+	0.277004i
$363$	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
$366$	3.64684	−	0.135757i	0.00996405	−	0.000370920i
$367$	−7.96681	−	4.05929i	−0.0217079	−	0.0110607i	0.443103	−	0.896471i	$-0.353878\pi$
$367$	−7.96681	−	4.05929i	−0.0217079	−	0.0110607i	−0.464811	+	0.885410i	$0.653878\pi$
$368$	72.4061	−	216.746i	0.196756	−	0.588983i
$369$	−505.770	+	367.464i	−1.37065	+	0.995837i
$370$	−68.3079	+	72.5105i	−0.184616	+	0.195974i
$371$	−35.7396	+	109.995i	−0.0963330	+	0.296483i
$372$	38.2290	+	32.9242i	0.102766	+	0.0885058i
$373$	−177.519	−	177.519i	−0.475923	−	0.475923i	0.427902	−	0.903825i	$-0.359253\pi$
$373$	−177.519	−	177.519i	−0.475923	−	0.475923i	−0.903825	+	0.427902i	$0.859253\pi$
$374$	34.1313	+	20.2838i	0.0912600	+	0.0542348i
$375$	31.2972	−	89.5348i	0.0834593	−	0.238759i
$376$	284.930	−	129.224i	0.757792	−	0.343681i
$377$	591.893	−	301.584i	1.57001	−	0.799959i
$378$	209.622	+	25.2487i	0.554556	+	0.0667954i
$379$	−197.872	+	143.762i	−0.522089	+	0.379320i	−0.817390	−	0.576084i	$-0.804580\pi$
$379$	−197.872	+	143.762i	−0.522089	+	0.379320i	0.295301	+	0.955404i	$0.404580\pi$
$380$	615.979	+	55.6101i	1.62100	+	0.146342i
$381$	−121.308	+	39.4152i	−0.318393	+	0.103452i
$382$	175.026	−	188.561i	0.458183	−	0.493615i
$383$	106.222	+	670.661i	0.277343	+	1.75107i	0.595798	+	0.803135i	$0.296836\pi$
$383$	106.222	+	670.661i	0.277343	+	1.75107i	−0.318455	+	0.947938i	$0.603164\pi$
$384$	−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
$388$	−36.9010	−	15.4634i	−0.0951056	−	0.0398541i
$389$	−648.297	+	210.645i	−1.66657	+	0.541503i	−0.982234	−	0.187661i	$-0.939909\pi$
$389$	−648.297	+	210.645i	−1.66657	+	0.541503i	−0.684340	+	0.729163i	$0.739909\pi$
$390$	−45.0199	−	125.670i	−0.115436	−	0.322232i
$391$	20.8530	−	15.1506i	0.0533326	−	0.0387484i
$392$	98.5676	−	64.9827i	0.251448	−	0.165772i
$393$	−111.971	+	57.0522i	−0.284914	+	0.145171i
$394$	−61.0211	+	214.670i	−0.154876	+	0.544847i
$395$	−230.012	+	34.6939i	−0.582308	+	0.0878327i
$396$	325.469	+	177.382i	0.821890	+	0.447935i
$397$	−418.619	−	418.619i	−1.05446	−	1.05446i	−0.998429	−	0.0560277i	$-0.982156\pi$
$397$	−418.619	−	418.619i	−1.05446	−	1.05446i	−0.0560277	−	0.998429i	$-0.517844\pi$
$398$	253.964	−	141.540i	0.638100	−	0.355627i
$399$	−57.8977	+	178.191i	−0.145107	+	0.446594i
$400$	360.483	−	173.355i	0.901208	−	0.433387i
$401$	−485.852	+	352.992i	−1.21160	+	0.880280i	−0.995375	−	0.0960629i	$-0.969375\pi$
$401$	−485.852	+	352.992i	−1.21160	+	0.880280i	−0.216227	+	0.976343i	$0.569375\pi$
$402$	22.0324	+	111.970i	0.0548070	+	0.278533i
$403$	−260.571	−	132.768i	−0.646579	−	0.329448i
$404$	145.594	+	355.636i	0.360382	+	0.880287i
$405$	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
$408$	−10.5619	+	2.90837i	−0.0258869	+	0.00712835i
$409$	−58.5866	−	42.5657i	−0.143244	−	0.104073i	0.513856	−	0.857877i	$-0.328217\pi$
$409$	−58.5866	−	42.5657i	−0.143244	−	0.104073i	−0.657099	+	0.753804i	$0.728217\pi$
$410$	−613.119	−	418.093i	−1.49541	−	1.01974i
$411$	82.9982	−	26.9677i	0.201942	−	0.0656150i
$412$	63.0811	+	103.898i	0.153110	+	0.252180i
$413$	−222.873	−	35.2996i	−0.539644	−	0.0854712i
$414$	189.285	−	148.588i	0.457209	−	0.358909i
$415$	589.349	−	421.584i	1.42012	−	1.01586i
$416$	240.951	−	508.803i	0.579208	−	1.22309i
$417$	109.659	−	109.659i	0.262971	−	0.262971i
$418$	−434.780	+	523.277i	−1.04014	+	1.25186i
$419$	−540.520			−1.29002			−0.645012	−	0.764172i	$-0.723148\pi$
$419$	−540.520			−1.29002			−0.645012	+	0.764172i	$0.723148\pi$
$420$	26.9313	+	118.144i	0.0641221	+	0.281294i
$421$	4.20919	−	12.9546i	0.00999808	−	0.0307709i	−0.945933	−	0.324362i	$-0.894850\pi$
$421$	4.20919	−	12.9546i	0.00999808	−	0.0307709i	0.955931	+	0.293591i	$0.0948504\pi$
$422$	273.978	+	33.0002i	0.649236	+	0.0781995i
$423$	325.400	+	51.5383i	0.769267	+	0.121840i
$424$	−12.9078	−	115.154i	−0.0304430	−	0.271590i
$425$	44.4533	+	7.71427i	0.104596	+	0.0181512i
$426$	−125.225	+	4.66161i	−0.293956	+	0.0109427i
$427$	18.9653	−	3.00380i	0.0444152	−	0.00703467i
$428$	−53.3157	+	643.512i	−0.124569	+	1.50353i
$429$	141.933	+	37.6445i	0.330845	+	0.0877494i
$430$	−23.8854	+	13.0820i	−0.0555475	+	0.0304233i
$431$	108.092	+	78.5333i	0.250793	+	0.182212i	0.706078	−	0.708134i	$-0.250463\pi$
$431$	108.092	+	78.5333i	0.250793	+	0.182212i	−0.455285	+	0.890346i	$0.650463\pi$
$432$	−201.717	+	63.7079i	−0.466937	+	0.147472i
$433$	−103.112	−	52.5382i	−0.238134	−	0.121335i	0.330852	−	0.943683i	$-0.392664\pi$
$433$	−103.112	−	52.5382i	−0.238134	−	0.121335i	−0.568986	+	0.822347i	$0.692664\pi$
$434$	220.420	+	147.938i	0.507880	+	0.340871i
$435$	1.05618	−	143.251i	0.00242799	−	0.329313i
$436$	−331.458	+	535.919i	−0.760226	+	1.22917i
$437$	200.516	+	393.535i	0.458847	+	0.900539i
$438$	−14.9591	−	26.8410i	−0.0341531	−	0.0612808i
$439$			18.3830i			0.0418747i	0.999781	+	0.0209374i	$0.00666505\pi$
$439$			18.3830i			0.0418747i	−0.999781	+	0.0209374i	$0.993335\pi$
$440$	−67.9296	+	434.725i	−0.154385	+	0.988011i
$441$	124.322			0.281909
$442$	55.4674	−	30.9132i	0.125492	−	0.0699394i
$443$	−478.256	+	243.684i	−1.07958	+	0.550076i	−0.900987	−	0.433846i	$-0.857156\pi$
$443$	−478.256	+	243.684i	−1.07958	+	0.550076i	−0.178598	+	0.983922i	$0.557156\pi$
$444$	25.7144	+	15.9040i	0.0579152	+	0.0358198i
$445$	19.9922	−	19.6996i	0.0449263	−	0.0442687i
$446$	−97.0816	+	144.647i	−0.217672	+	0.324320i
$447$	−54.9028	+	107.753i	−0.122825	+	0.241058i
$448$	−272.381	+	432.389i	−0.607992	+	0.965153i
$449$	514.918	−	708.724i	1.14681	−	1.57845i	0.395551	−	0.918444i	$-0.370554\pi$
$449$	514.918	−	708.724i	1.14681	−	1.57845i	0.751260	−	0.660006i	$-0.229446\pi$
$450$	417.402	+	56.5311i	0.927560	+	0.125625i
$451$	761.348	−	294.476i	1.68813	−	0.652940i
$452$	645.859	+	53.5102i	1.42889	+	0.118385i
$453$	31.6110	+	199.584i	0.0697814	+	0.440583i
$454$	−20.2054	−	542.778i	−0.0445052	−	1.19555i
$455$	−314.252	−	628.161i	−0.690664	−	1.38057i
$456$	−20.9106	−	186.548i	−0.0458565	−	0.409098i
$457$	−83.1112	+	524.743i	−0.181863	+	1.14823i	0.712759	+	0.701409i	$0.247446\pi$
$457$	−83.1112	+	524.743i	−0.181863	+	1.14823i	−0.894621	+	0.446825i	$0.852554\pi$
$458$	9.56185	−	79.3854i	0.0208774	−	0.173331i
$459$	−22.6925	−	7.37324i	−0.0494390	−	0.0160637i
$460$	241.825	+	152.042i	0.525706	+	0.330525i
$461$			660.717i			1.43322i	0.697472	+	0.716612i	$0.254308\pi$
$461$			660.717i			1.43322i	−0.697472	+	0.716612i	$0.745692\pi$
$462$	−123.826	−	49.3328i	−0.268022	−	0.106781i
$463$	−66.4704	−	66.4704i	−0.143564	−	0.143564i	0.631672	−	0.775236i	$-0.282369\pi$
$463$	−66.4704	−	66.4704i	−0.143564	−	0.143564i	−0.775236	+	0.631672i	$0.782369\pi$
$464$	430.706	−	423.662i	0.928247	−	0.913064i
$465$	−51.2931	+	36.6919i	−0.110308	+	0.0789073i
$466$	169.208	+	215.552i	0.363108	+	0.462558i
$467$	−80.4077	+	507.674i	−0.172179	+	1.08710i	0.738582	+	0.674164i	$0.235496\pi$
$467$	−80.4077	+	507.674i	−0.172179	+	1.08710i	−0.910761	+	0.412933i	$0.864504\pi$
$468$	506.742	−	307.665i	1.08278	−	0.657405i
$469$	185.548	+	571.057i	0.395624	+	1.21760i
$470$	72.6740	+	384.268i	0.154626	+	0.817592i
$471$	10.0574	−	13.8428i	0.0213532	−	0.0293901i
$472$	217.967	−	60.0204i	0.461794	−	0.127162i
$473$	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
$476$	−53.3440	+	21.8386i	−0.112067	+	0.0458794i
$477$	55.3961	−	108.721i	0.116134	−	0.227927i
$478$	89.4255	−	17.5963i	0.187083	−	0.0368123i
$479$	−83.5926	−	115.055i	−0.174515	−	0.240199i	0.712795	−	0.701372i	$-0.247429\pi$
$479$	−83.5926	−	115.055i	−0.174515	−	0.240199i	−0.887310	+	0.461173i	$0.847429\pi$
$480$	−73.4635	−	96.6548i	−0.153049	−	0.201364i
$481$	−166.679	−	54.1573i	−0.346526	−	0.112593i
$482$	−44.9163	−	80.5931i	−0.0931874	−	0.167206i
$483$	−61.1885	+	61.1885i	−0.126684	+	0.126684i
$484$	−351.401	−	332.827i	−0.726034	−	0.687658i
$485$	29.6941	−	40.2431i	0.0612249	−	0.0829755i
$486$	−324.942	−	92.3666i	−0.668605	−	0.190055i
$487$	128.182	+	251.571i	0.263207	+	0.516573i	0.984352	−	0.176211i	$-0.0563840\pi$
$487$	128.182	+	251.571i	0.263207	+	0.516573i	−0.721145	+	0.692784i	$0.756384\pi$
$488$	−16.0617	+	10.5890i	−0.0329134	+	0.0216988i
$489$	5.88193	+	8.09578i	0.0120285	+	0.0165558i
$490$	49.7701	+	138.930i	0.101572	+	0.283531i
$491$	11.5819	+	35.6453i	0.0235883	+	0.0725974i	0.962158	−	0.272493i	$-0.0878482\pi$
$491$	11.5819	+	35.6453i	0.0235883	+	0.0725974i	−0.938569	+	0.345091i	$0.887848\pi$
$492$	−87.0514	+	207.734i	−0.176934	+	0.422224i
$493$	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
$498$	−161.190	−	149.620i	−0.323675	−	0.300442i
$499$	−81.6809	−	251.388i	−0.163689	−	0.503784i	0.835248	−	0.549873i	$-0.185324\pi$
$499$	−81.6809	−	251.388i	−0.163689	−	0.503784i	−0.998937	+	0.0460896i	$0.985324\pi$
$500$	103.926	+	489.080i	0.207852	+	0.978160i
$501$	104.189	+	143.403i	0.207961	+	0.286234i
$502$	78.4563	−	651.368i	0.156287	−	1.29755i
$503$	−252.204	−	494.978i	−0.501399	−	0.984052i	−0.993534	−	0.113533i	$-0.963783\pi$
$503$	−252.204	−	494.978i	−0.501399	−	0.984052i	0.492135	−	0.870519i	$-0.336217\pi$
$504$	−490.083	+	222.267i	−0.972387	+	0.441006i
$505$	−474.983	+	71.6442i	−0.940560	+	0.141870i
$506$	−288.639	+	124.173i	−0.570432	+	0.245401i
$507$	75.3887	−	75.3887i	0.148696	−	0.148696i
$508$	438.792	−	509.492i	0.863765	−	1.00294i
$509$	758.576	+	246.476i	1.49033	+	0.484236i	0.937180	−	0.348847i	$-0.113427\pi$
$509$	758.576	+	246.476i	1.49033	+	0.484236i	0.553147	+	0.833084i	$0.313427\pi$
$510$	−0.408503	−	13.6876i	−0.000800987	−	0.0268385i
$511$	−95.0331	−	130.802i	−0.185975	−	0.255972i
$512$	69.6008	−	507.247i	0.135939	−	0.990717i
$513$	185.615	−	364.291i	0.361823	−	0.710119i
$514$	−22.1568	−	595.200i	−0.0431066	−	1.15798i
$515$	−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
$518$	144.336	+	66.9008i	0.278641	+	0.129152i
$519$	9.59300	−	13.2036i	0.0184836	−	0.0254405i
$520$	546.683	+	443.118i	1.05131	+	0.852150i
$521$	−154.319	−	474.944i	−0.296197	−	0.911601i	−0.982817	−	0.184584i	$-0.940906\pi$
$521$	−154.319	−	474.944i	−0.296197	−	0.911601i	0.686619	−	0.727017i	$-0.259094\pi$
$522$	624.220	−	122.828i	1.19582	−	0.235303i
$523$	27.1497	−	171.416i	0.0519114	−	0.327756i	−0.948042	−	0.318144i	$-0.896940\pi$
$523$	27.1497	−	171.416i	0.0519114	−	0.327756i	0.999954	−	0.00961166i	$-0.00305953\pi$
$524$	348.469	−	563.423i	0.665018	−	1.07523i
$525$	−151.451	−	2.23340i	−0.288479	−	0.00425409i
$526$	−42.9014	+	150.925i	−0.0815617	+	0.286931i
$527$	−21.2129	−	21.2129i	−0.0402522	−	0.0402522i
$528$	133.400	−	6.22836i	0.252651	−	0.0117961i
$529$		−	325.010i		−	0.614386i
$530$	143.673	+	18.3808i	0.271081	+	0.0346808i
$531$	226.417	+	73.5674i	0.426398	+	0.138545i
$532$	−226.612	−	961.351i	−0.425963	−	1.80705i
$533$	204.237	−	1289.50i	0.383183	−	2.41932i
$534$	−7.07324	−	4.74731i	−0.0132458	−	0.00889009i
$535$	−765.781	−	255.075i	−1.43137	−	0.476775i
$536$	−405.617	−	444.274i	−0.756748	−	0.828870i
$537$	−40.9388	−	258.477i	−0.0762361	−	0.481336i
$538$	470.078	+	217.885i	0.873752	+	0.404991i
$539$	−156.908	−	41.6164i	−0.291110	−	0.0772105i
$540$	−17.7148	−	263.829i	−0.0328052	−	0.488572i
$541$	410.296	−	564.723i	0.758402	−	1.04385i	−0.238943	−	0.971034i	$-0.576801\pi$
$541$	410.296	−	564.723i	0.758402	−	1.04385i	0.997345	−	0.0728175i	$-0.0231991\pi$
$542$	428.106	+	397.377i	0.789863	+	0.733167i
$543$	−19.0364	+	37.3611i	−0.0350579	+	0.0688050i
$544$	39.6362	−	42.0014i	0.0728606	−	0.0772084i
$545$	−552.847	−	561.060i	−1.01440	−	1.02947i
$546$	−167.686	+	131.633i	−0.307117	+	0.241087i
$547$	−588.929	+	300.074i	−1.07665	+	0.548582i	−0.900088	−	0.435708i	$-0.856498\pi$
$547$	−588.929	+	300.074i	−1.07665	+	0.548582i	−0.176564	+	0.984289i	$0.556498\pi$
$548$	−300.220	+	348.592i	−0.547847	+	0.636117i
$549$	−20.2584			−0.0369005
$550$	−507.886	−	211.073i	−0.923429	−	0.383770i
$551$			1167.68i			2.11920i
$552$	30.5101	−	81.1521i	0.0552718	−	0.147015i
$553$	168.647	+	330.988i	0.304967	+	0.598531i
$554$	−230.670	+	181.076i	−0.416373	+	0.326852i
$555$	−26.9207	+	26.5266i	−0.0485057	+	0.0477957i
$556$	−194.124	+	794.148i	−0.349144	+	1.42832i
$557$	−23.0631	−	11.7512i	−0.0414059	−	0.0210974i	0.433165	−	0.901315i	$-0.357397\pi$
$557$	−23.0631	−	11.7512i	−0.0414059	−	0.0210974i	−0.474571	+	0.880217i	$0.657397\pi$
$558$	−205.271	−	190.537i	−0.367869	−	0.341464i
$559$	−38.7610	−	28.1615i	−0.0693399	−	0.0503784i
$560$	−444.581	−	458.690i	−0.793895	−	0.819089i
$561$	12.6538	+	8.17183i	0.0225558	+	0.0145665i
$562$	−15.4095	−	7.14241i	−0.0274190	−	0.0127089i
$563$	−568.005	+	89.9632i	−1.00889	+	0.159793i	−0.638938	−	0.769258i	$-0.720626\pi$
$563$	−568.005	+	89.9632i	−1.00889	+	0.159793i	−0.369952	+	0.929051i	$0.620626\pi$
$564$	109.848	−	44.9710i	0.194766	−	0.0797357i
$565$	−256.005	+	768.575i	−0.453106	+	1.36031i
$566$	−153.697	−	103.156i	−0.271550	−	0.182255i
$567$	−518.826	−	82.1740i	−0.915038	−	0.144928i
$568$	551.527	−	363.605i	0.970998	−	0.640151i
$569$	−58.4701	+	179.953i	−0.102759	+	0.316261i	−0.989198	−	0.146585i	$-0.953172\pi$
$569$	−58.4701	+	179.953i	−0.102759	+	0.316261i	0.886439	+	0.462846i	$0.153172\pi$
$570$	232.749	+	29.7767i	0.408332	+	0.0522399i
$571$	−668.647			−1.17101			−0.585505	−	0.810669i	$-0.699104\pi$
$571$	−668.647			−1.17101			−0.585505	+	0.810669i	$0.699104\pi$
$572$	−742.557	+	218.678i	−1.29818	+	0.382305i
$573$	69.0182	−	69.0182i	0.120451	−	0.120451i
$574$	−324.038	+	1139.95i	−0.564527	+	1.98598i
$575$	−256.177	+	248.731i	−0.445525	+	0.432576i
$576$	355.195	−	405.613i	0.616658	−	0.704189i
$577$	217.368	+	34.4277i	0.376721	+	0.0596668i	0.341924	−	0.939728i	$-0.388921\pi$
$577$	217.368	+	34.4277i	0.376721	+	0.0596668i	0.0347972	+	0.999394i	$0.488921\pi$
$578$	−560.734	+	110.336i	−0.970128	+	0.190892i
$579$	222.787	−	72.3879i	0.384779	−	0.125022i
$580$	387.157	+	648.397i	0.667512	+	1.11793i
$581$	−936.182	−	680.176i	−1.61133	−	1.17070i
$582$	−13.7719	−	6.38338i	−0.0236630	−	0.0109680i
$583$	−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
$586$	−38.5463	−	1035.47i	−0.0657787	−	1.76702i
$587$	50.1379	+	25.5466i	0.0854138	+	0.0435205i	0.496176	−	0.868222i	$-0.334737\pi$
$587$	50.1379	+	25.5466i	0.0854138	+	0.0435205i	−0.410762	+	0.911743i	$0.634737\pi$
$588$	38.2867	−	23.2455i	0.0651134	−	0.0395332i
$589$	415.877	−	302.152i	0.706073	−	0.512992i
$590$	8.43034	+	282.474i	0.0142887	+	0.478769i
$591$	−26.1644	+	80.5257i	−0.0442714	+	0.136253i
$592$	−159.383	−	1.31417i	−0.269229	−	0.00221988i
$593$	70.5152	+	70.5152i	0.118913	+	0.118913i	0.764059	−	0.645146i	$-0.223204\pi$
$593$	70.5152	+	70.5152i	0.118913	+	0.118913i	−0.645146	+	0.764059i	$0.723204\pi$
$594$	250.043	+	148.597i	0.420947	+	0.250164i
$595$	−10.7464	−	71.2456i	−0.0180611	−	0.119741i
$596$	−47.3986	−	635.755i	−0.0795279	−	1.06670i
$597$	98.2819	−	50.0771i	0.164626	−	0.0838813i
$598$	−60.0960	+	498.935i	−0.100495	+	0.834339i
$599$	−7.99488	+	5.80862i	−0.0133470	+	0.00969719i	−0.594439	−	0.804141i	$-0.702626\pi$
$599$	−7.99488	+	5.80862i	−0.0133470	+	0.00969719i	0.581092	+	0.813838i	$0.302626\pi$
$600$	139.115	−	60.6358i	0.231859	−	0.101060i
$601$	−318.990	+	103.646i	−0.530765	+	0.172456i	−0.562125	−	0.827052i	$-0.690016\pi$
$601$	−318.990	+	103.646i	−0.530765	+	0.172456i	0.0313600	+	0.999508i	$0.490016\pi$
$602$	31.8753	+	29.5873i	0.0529489	+	0.0491483i
$603$	−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	0.891462	+	0.453096i	$0.149680\pi$
$607$	111.473	+	703.812i	0.183646	+	1.15949i	−0.707816	+	0.706397i	$0.750320\pi$
$608$	604.598	+	783.403i	0.994404	+	1.28849i
$609$	−217.576	+	70.6948i	−0.357268	+	0.116083i
$610$	−8.11010	−	22.6388i	−0.0132952	−	0.0371129i
$611$	−556.622	+	404.410i	−0.911002	+	0.661882i
$612$	59.1911	−	13.9527i	0.0967174	−	0.0227985i
$613$	125.605	−	63.9988i	0.204902	−	0.104403i	−0.348528	−	0.937298i	$-0.613319\pi$
$613$	125.605	−	63.9988i	0.204902	−	0.104403i	0.553430	+	0.832896i	$0.313319\pi$
$614$	464.336	+	131.990i	0.756248	+	0.214968i
$615$	−226.549	−	167.163i	−0.368372	−	0.271810i
$616$	692.945	−	116.472i	1.12491	−	0.189079i
$617$	−837.199	−	837.199i	−1.35689	−	1.35689i	−0.877729	−	0.479157i	$-0.840942\pi$
$617$	−837.199	−	837.199i	−1.35689	−	1.35689i	−0.479157	−	0.877729i	$-0.659058\pi$
$618$	22.4494	+	40.2808i	0.0363258	+	0.0651792i
$619$	218.469	−	672.380i	0.352939	−	1.08624i	−0.604255	−	0.796791i	$-0.706529\pi$
$619$	218.469	−	672.380i	0.352939	−	1.08624i	0.957195	−	0.289445i	$-0.0934707\pi$
$620$	130.749	−	305.669i	0.210885	−	0.493015i
$621$	152.767	−	110.992i	0.246002	−	0.178731i
$622$	−583.200	+	114.756i	−0.937620	+	0.184496i
$623$	−39.9369	−	20.3489i	−0.0641041	−	0.0326627i
$624$	98.5316	−	189.500i	0.157903	−	0.303686i
$625$	−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
$628$	−7.44773	+	89.8928i	−0.0118594	+	0.143141i
$629$	−14.5446	−	10.5673i	−0.0231234	−	0.0168001i
$630$	−125.000	−	660.947i	−0.198413	−	1.04912i
$631$	373.554	−	121.375i	0.592003	−	0.192353i	0.00233239	−	0.999997i	$-0.499258\pi$
$631$	373.554	−	121.375i	0.592003	−	0.192353i	0.589671	+	0.807644i	$0.299258\pi$
$632$	−290.850	−	232.218i	−0.460206	−	0.367434i
$633$	103.406	+	16.3780i	0.163359	+	0.0258735i
$634$	−426.168	−	542.890i	−0.672190	−	0.856293i
$635$	489.006	+	683.602i	0.770088	+	1.07654i
$636$	−3.26850	−	43.8401i	−0.00513914	−	0.0689310i
$637$	−183.585	+	183.585i	−0.288203	+	0.288203i
$638$	−828.954	−	53.9333i	−1.29930	−	0.0845349i
$639$	695.632			1.08863
$640$	595.471	+	234.552i	0.930423	+	0.366487i
$641$	−114.059	+	351.038i	−0.177939	+	0.547641i	−0.999756	−	0.0221119i	$-0.992961\pi$
$641$	−114.059	+	351.038i	−0.177939	+	0.547641i	0.821816	+	0.569753i	$0.192961\pi$
$642$	−29.2954	+	243.220i	−0.0456315	+	0.378847i
$643$	248.142	+	39.3018i	0.385913	+	0.0611226i	0.346377	−	0.938096i	$-0.387412\pi$
$643$	248.142	+	39.3018i	0.385913	+	0.0611226i	0.0395362	+	0.999218i	$0.487412\pi$
$644$	108.319	−	443.127i	0.168198	−	0.688085i
$645$	−9.24022	+	4.62263i	−0.0143259	+	0.00716687i
$646$	4.15221	+	111.541i	0.00642757	+	0.172664i
$647$	675.080	−	106.922i	1.04340	−	0.165258i	0.388869	−	0.921293i	$-0.372866\pi$
$647$	675.080	−	106.922i	1.04340	−	0.165258i	0.654531	+	0.756035i	$0.272866\pi$
$648$	507.406	−	139.722i	0.783033	−	0.215620i
$649$	−261.138	−	168.643i	−0.402370	−	0.259851i
$650$	−699.855	+	532.896i	−1.07670	+	0.819840i
$651$	81.4791	+	59.1981i	0.125160	+	0.0909340i
$652$	−48.6537	−	20.3884i	−0.0746223	−	0.0312706i
$653$	−167.996	−	85.5984i	−0.257269	−	0.131085i	0.320600	−	0.947215i	$-0.396115\pi$
$653$	−167.996	−	85.5984i	−0.257269	−	0.131085i	−0.577869	+	0.816130i	$0.696115\pi$
$654$	−133.228	+	198.503i	−0.203713	+	0.303521i
$655$	581.220	+	589.854i	0.887359	+	0.900541i
$656$	−176.069	−	1174.24i	−0.268398	−	1.79000i
$657$	77.4406	+	151.986i	0.117870	+	0.231333i
$658$	545.538	−	304.041i	0.829086	−	0.462068i
$659$		−	943.001i		−	1.43096i	−0.698635	−	0.715479i	$-0.746209\pi$
$659$		−	943.001i		−	1.43096i	0.698635	−	0.715479i	$-0.253791\pi$
$660$	−31.8893	+	163.857i	−0.0483171	+	0.248268i
$661$	788.731			1.19324			0.596619	−	0.802524i	$-0.296510\pi$
$661$	788.731			1.19324			0.596619	+	0.802524i	$0.296510\pi$
$662$	15.4814	+	27.7782i	0.0233858	+	0.0419610i
$663$	21.4654	−	10.9372i	0.0323762	−	0.0164965i
$664$	1135.69	+	233.212i	1.71037	+	0.351222i
$665$	1234.59	+	9.10253i	1.85653	+	0.0136880i
$666$	−139.363	−	93.5352i	−0.209253	−	0.140443i
$667$	−244.836	+	480.519i	−0.367071	+	0.720418i
$668$	−861.819	−	361.147i	−1.29015	−	0.540639i
$669$	−38.8476	+	53.4692i	−0.0580682	+	0.0799240i
$670$	659.538	−	361.228i	0.984385	−	0.539146i
$671$	25.5684	+	6.78145i	0.0381049	+	0.0101065i
$672$	−109.369	+	160.086i	−0.162751	+	0.238223i
$673$	60.8690	+	384.311i	0.0904442	+	0.571042i	0.990741	+	0.135766i	$0.0433494\pi$
$673$	60.8690	+	384.311i	0.0904442	+	0.571042i	−0.900297	+	0.435277i	$0.856651\pi$
$674$	−1245.15	+	46.3516i	−1.84740	+	0.0687710i
$675$	325.661	+	56.5141i	0.482461	+	0.0837245i
$676$	−133.457	+	545.965i	−0.197422	+	0.807641i
$677$	−141.049	+	890.546i	−0.208344	+	1.31543i	0.632672	+	0.774420i	$0.281958\pi$
$677$	−141.049	+	890.546i	−0.208344	+	1.31543i	−0.841016	+	0.541010i	$0.818042\pi$
$678$	244.107	+	29.4023i	0.360040	+	0.0433662i
$679$	−75.9592	−	24.6806i	−0.111869	−	0.0363485i
$680$	39.2883	+	60.5606i	0.0577770	+	0.0890597i
$681$		−	206.067i		−	0.302594i
$682$	195.294	+	309.193i	0.286355	+	0.453363i
$683$	−165.942	−	165.942i	−0.242960	−	0.242960i	0.575113	−	0.818074i	$-0.304958\pi$
$683$	−165.942	−	165.942i	−0.242960	−	0.242960i	−0.818074	+	0.575113i	$0.804958\pi$
$684$	77.4752	+	1039.17i	0.113268	+	1.51925i
$685$	−334.576	−	467.718i	−0.488432	−	0.682800i
$686$	−430.140	+	337.659i	−0.627026	+	0.492215i
$687$	4.74553	−	29.9621i	0.00690762	−	0.0436130i
$688$	−41.3282	−	13.8061i	−0.0600701	−	0.0200670i
$689$	78.7446	+	242.351i	0.114288	+	0.351743i
$690$	89.5364	+	61.0559i	0.129763	+	0.0884868i
$691$	745.651	−	1026.30i	1.07909	−	1.48524i	0.218569	−	0.975821i	$-0.429861\pi$
$691$	745.651	−	1026.30i	1.07909	−	1.48524i	0.860520	−	0.509417i	$-0.170139\pi$
$692$	−7.10386	+	85.7424i	−0.0102657	+	0.123905i
$693$	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
$696$	169.271	−	154.543i	0.243206	−	0.222044i
$697$	60.8020	−	119.331i	0.0872339	−	0.171206i
$698$	134.673	+	684.417i	0.192941	+	0.980540i
$699$	61.1092	+	84.1096i	0.0874237	+	0.120328i
$700$	688.569	−	404.287i	0.983671	−	0.577553i
$701$	745.778	+	242.318i	1.06388	+	0.345675i	0.788100	−	0.615547i	$-0.211065\pi$
$701$	745.778	+	242.318i	1.06388	+	0.345675i	0.275777	+	0.961222i	$0.411065\pi$
$702$	406.349	−	226.468i	0.578845	−	0.322603i
$703$	217.832	−	217.832i	0.309860	−	0.309860i
$704$	−584.075	+	393.029i	−0.829652	+	0.558280i
$705$	22.1293	+	146.712i	0.0313891	+	0.208102i
$706$	6.14820	−	21.6291i	0.00870850	−	0.0306361i
$707$	348.262	+	683.502i	0.492591	+	0.966764i
$708$	83.4840	−	19.6791i	0.117915	−	0.0277953i
$709$	−9.63426	−	13.2604i	−0.0135885	−	0.0187030i	0.802169	−	0.597097i	$-0.203679\pi$
$709$	−9.63426	−	13.2604i	−0.0135885	−	0.0187030i	−0.815757	+	0.578394i	$0.803679\pi$
$710$	278.484	+	777.372i	0.392232	+	1.09489i
$711$	−121.110	−	372.737i	−0.170337	−	0.524244i
$712$	44.8609	+	2.04050i	0.0630069	+	0.00286588i
$713$	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
$718$	−399.716	+	430.626i	−0.556707	+	0.599757i
$719$	−92.3775	−	284.309i	−0.128481	−	0.395422i	0.866039	−	0.499977i	$-0.166658\pi$
$719$	−92.3775	−	284.309i	−0.128481	−	0.395422i	−0.994519	+	0.104555i	$0.966658\pi$
$720$	387.569	+	551.349i	0.538290	+	0.765763i
$721$	142.618	+	196.297i	0.197806	+	0.272256i
$722$	−1182.07	−	142.379i	−1.63722	−	0.197200i
$723$	−15.8915	−	31.1889i	−0.0219800	−	0.0431381i
$724$	−16.4345	−	220.435i	−0.0226996	−	0.304468i
$725$	−901.986	+	278.438i	−1.24412	+	0.384052i
$726$	−128.528	−	131.143i	−0.177036	−	0.180637i
$727$	555.190	−	555.190i	0.763673	−	0.763673i	−0.213311	−	0.976984i	$-0.568425\pi$
$727$	555.190	−	555.190i	0.763673	−	0.763673i	0.976984	+	0.213311i	$0.0684248\pi$
$728$	395.483	−	1051.92i	0.543245	−	1.44495i
$729$	441.209	+	143.357i	0.605225	+	0.196649i
$730$	−138.843	+	147.385i	−0.190196	+	0.201897i
$731$	−2.88886	−	3.97617i	−0.00395192	−	0.00543936i
$732$	−6.23886	+	3.78789i	−0.00852304	+	0.00517471i
$733$	−374.514	+	735.026i	−0.510934	+	1.00276i	0.481085	+	0.876674i	$0.340243\pi$
$733$	−374.514	+	735.026i	−0.510934	+	1.00276i	−0.992019	+	0.126090i	$0.959757\pi$
$734$	17.8703	−	0.665238i	0.0243465	−	0.000906318i
$735$	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
$738$	525.804	−	1134.40i	0.712471	−	1.53713i
$739$	646.145	−	889.342i	0.874350	−	1.20344i	−0.103604	−	0.994619i	$-0.533037\pi$
$739$	646.145	−	889.342i	0.874350	−	1.20344i	0.977954	−	0.208821i	$-0.0669625\pi$
$740$	48.7346	−	193.184i	0.0658576	−	0.261059i
$741$	127.565	+	392.606i	0.172153	+	0.529832i
$742$	−44.6589	−	226.959i	−0.0601871	−	0.305875i
$743$	36.4471	−	230.118i	0.0490540	−	0.309715i	−0.950946	−	0.309357i	$-0.899886\pi$
$743$	36.4471	−	230.118i	0.0490540	−	0.309715i	1.00000		0.000357556i	$-0.000113814\pi$
$744$	−98.8425	−	20.2972i	−0.132853	−	0.0272812i
$745$	786.147	+	130.462i	1.05523	+	0.175117i
$746$	482.968	+	137.286i	0.647410	+	0.184030i
$747$	863.284	+	863.284i	1.15567	+	1.15567i
$748$	−79.3766	−	2.20419i	−0.106118	−	0.00294678i
$749$			1288.99i			1.72094i
$750$	32.4986	+	186.890i	0.0433314	+	0.249186i
$751$	−214.087	−	69.5612i	−0.285070	−	0.0926247i	0.162992	−	0.986627i	$-0.447885\pi$
$751$	−214.087	−	69.5612i	−0.285070	−	0.0926247i	−0.448062	+	0.894003i	$0.647885\pi$
$752$	−371.955	+	503.175i	−0.494621	+	0.669116i
$753$	38.9378	−	245.843i	0.0517102	−	0.326485i
$754$	−740.403	+	1103.16i	−0.981966	+	1.46308i
$755$	1190.85	−	595.753i	1.57729	−	0.789076i
$756$	−390.793	+	159.988i	−0.516923	+	0.211624i
$757$	−161.749	−	1021.25i	−0.213672	−	1.34907i	−0.828314	−	0.560264i	$-0.810700\pi$
$757$	−161.749	−	1021.25i	−0.213672	−	1.34907i	0.614643	−	0.788806i	$-0.289300\pi$
$758$	205.709	−	443.810i	0.271385	−	0.585501i
$759$	−111.183	+	43.0036i	−0.146486	+	0.0566582i
$760$	−1130.26	+	502.593i	−1.48719	+	0.661307i
$761$	144.314	−	198.631i	0.189637	−	0.261013i	−0.703603	−	0.710593i	$-0.748427\pi$
$761$	144.314	−	198.631i	0.189637	−	0.261013i	0.893240	+	0.449581i	$0.148427\pi$
$762$	173.548	−	186.969i	0.227754	−	0.245366i
$763$	−571.069	+	1120.79i	−0.748452	+	1.46892i
$764$	−122.180	+	499.829i	−0.159921	+	0.654227i
$765$	−0.560449	+	76.0146i	−0.000732613	+	0.0993655i
$766$	−838.555	−	1068.22i	−1.09472	−	1.39455i
$767$	−442.985	+	225.712i	−0.577556	+	0.294280i
$768$	33.5464	−	191.328i	0.0436802	−	0.249126i
$769$	−140.854			−0.183165			−0.0915823

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+(-1.74700 + 0.973643i) q^{2} +(-0.676076 + 0.344478i) q^{3} +(2.10404 - 3.40192i) q^{4} +(3.50937 + 3.56150i) q^{5} +(0.845708 - 1.26006i) q^{6} +(3.62504 - 7.11454i) q^{7} +(-0.363505 + 7.99174i) q^{8} +(-4.95165 + 6.81537i) q^{9} +(-9.59852 - 2.80508i) q^{10} +(8.53099 - 6.94422i) q^{11} +(-0.250604 + 3.02475i) q^{12} +(-2.75214 - 17.3763i) q^{13} +(0.594072 + 15.9586i) q^{14} +(-3.59946 - 1.19895i) q^{15} +(-7.14606 - 14.3155i) q^{16} +(0.282319 - 1.78249i) q^{17} +(2.01482 - 16.7276i) q^{18} +(29.4107 + 9.55611i) q^{19} +(19.4998 - 4.44505i) q^{20} +6.05871i q^{21} +(-8.14246 + 20.4377i) q^{22} +(10.0993 + 10.0993i) q^{23} +(-2.50722 - 5.52824i) q^{24} +(-0.368626 + 24.9973i) q^{25} +(21.7263 + 27.6768i) q^{26} +(2.06824 - 13.0584i) q^{27} +(-16.5758 - 27.3013i) q^{28} +(11.6683 + 35.9113i) q^{29} +(7.45561 - 1.41003i) q^{30} +(9.77073 - 13.4483i) q^{31} +(26.4224 + 18.0515i) q^{32} +(-3.37546 + 7.63356i) q^{33} +(1.24230 + 3.38889i) q^{34} +(38.0601 - 12.0570i) q^{35} +(12.7668 + 31.1849i) q^{36} +(4.52256 - 8.87603i) q^{37} +(-60.6848 + 11.9410i) q^{38} +(7.84640 + 10.7996i) q^{39} +(-29.7383 + 26.7513i) q^{40} +(70.5782 + 22.9322i) q^{41} +(-5.89903 - 10.5846i) q^{42} +(1.92568 - 1.92568i) q^{43} +(-5.67415 - 43.6326i) q^{44} +(-41.6501 + 6.28232i) q^{45} +(-27.4765 - 7.81035i) q^{46} +(-17.7547 - 34.8455i) q^{47} +(9.76265 + 7.21671i) q^{48} +(-8.67429 - 11.9391i) q^{49} +(-23.6945 - 44.0292i) q^{50} +(0.423159 + 1.30235i) q^{51} +(-64.9033 - 27.1978i) 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} +(-55.3494 - 51.3764i) q^{58} +(-8.73280 - 26.8768i) q^{59} +(-11.6521 + 9.72243i) q^{60} +(1.41349 + 1.94550i) q^{61} +(-3.97569 + 33.0073i) q^{62} +(30.5383 + 59.9347i) q^{63} +(-63.7357 - 5.81007i) q^{64} +(52.2275 - 70.7816i) q^{65} +(-1.53542 - 16.6223i) q^{66} +(-53.1731 + 53.1731i) q^{67} +(-5.46987 - 4.71085i) q^{68} +(-10.3068 - 3.34889i) q^{69} +(-54.7519 + 58.1205i) q^{70} +(-48.5363 - 66.8045i) q^{71} +(-52.6667 - 42.0497i) q^{72} +(9.19257 - 18.0414i) q^{73} +(0.741158 + 19.9098i) q^{74} +(-8.36179 - 17.0270i) q^{75} +(94.3902 - 79.9462i) q^{76} +(-18.4798 - 85.8671i) q^{77} +(-24.2227 - 11.2274i) q^{78} +(-27.3454 + 37.6377i) q^{79} +(25.9066 - 75.6892i) q^{80} +(-20.3291 - 62.5666i) q^{81} +(-145.628 + 28.6553i) q^{82} +(22.6709 - 143.139i) q^{83} +(20.6112 + 12.7478i) q^{84} +(7.33911 - 5.24994i) q^{85} +(-1.48925 + 5.23911i) q^{86} +(-20.2593 - 20.2593i) q^{87} +(52.3953 + 70.7017i) q^{88} -5.61342i q^{89} +(66.6462 - 51.5276i) q^{90} +(-133.601 - 43.4096i) q^{91} +(55.6060 - 13.1076i) q^{92} +(-1.97313 + 12.4578i) q^{93} +(64.9445 + 43.5885i) q^{94} +(69.1789 + 138.282i) q^{95} +(-24.0819 - 3.10227i) q^{96} +(-1.56473 - 9.87934i) q^{97} +(26.7785 + 12.4120i) 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

L-functions

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