LMFDB - Embedded newform 220.3.w.a.7.17

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			7.17
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.49892 - 1.32409i) q^{2} +(0.172588 - 0.0879380i) q^{3} +(0.493549 + 3.96943i) q^{4} +(-2.34222 - 4.41746i) q^{5} +(-0.375135 - 0.0967104i) q^{6} +(-1.03219 + 2.02578i) q^{7} +(4.51611 - 6.60339i) q^{8} +(-5.26801 + 7.25080i) q^{9} +(-2.33832 + 9.72277i) q^{10} +(-0.824530 - 10.9691i) q^{11} +(0.434245 + 0.641675i) q^{12} +(1.11089 + 7.01390i) q^{13} +(4.22950 - 1.66978i) q^{14} +(-0.792703 - 0.556431i) q^{15} +(-15.5128 + 3.91822i) q^{16} +(-4.02299 + 25.4001i) q^{17} +(17.4971 - 3.89305i) q^{18} +(-29.6130 - 9.62185i) q^{19} +(16.3788 - 11.4775i) q^{20} +0.440395i q^{21} +(-13.2882 + 17.5335i) q^{22} +(11.3234 + 11.3234i) q^{23} +(0.198738 - 1.53680i) q^{24} +(-14.0280 + 20.6934i) q^{25} +(7.62192 - 11.9842i) q^{26} +(-0.544288 + 3.43650i) q^{27} +(-8.55065 - 3.09738i) q^{28} +(2.27903 + 7.01414i) q^{29} +(0.451435 + 1.88366i) q^{30} +(-22.1361 + 30.4677i) q^{31} +(28.4406 + 14.6673i) q^{32} +(-1.10690 - 1.82062i) q^{33} +(39.6623 - 32.7461i) q^{34} +(11.3664 - 0.185185i) q^{35} +(-31.3816 - 17.3324i) q^{36} +(-17.0916 + 33.5441i) q^{37} +(31.6474 + 53.6329i) q^{38} +(0.808515 + 1.11283i) q^{39} +(-39.7480 - 4.48314i) q^{40} +(11.0043 + 3.57551i) q^{41} +(0.583124 - 0.660118i) q^{42} +(28.1585 - 28.1585i) q^{43} +(43.1340 - 8.68669i) q^{44} +(44.3690 + 6.28826i) q^{45} +(-1.97967 - 31.9662i) q^{46} +(-2.31315 - 4.53981i) q^{47} +(-2.33277 + 2.04040i) q^{48} +(25.7631 + 35.4599i) q^{49} +(48.4269 - 12.4435i) q^{50} +(1.53932 + 4.73753i) q^{51} +(-27.2929 + 7.87132i) q^{52} +(-83.8731 + 13.2842i) q^{53} +(5.36609 - 4.43036i) q^{54} +(-46.5242 + 29.3343i) q^{55} +(8.71556 + 15.9646i) q^{56} +(-5.95698 + 0.943493i) q^{57} +(5.87128 - 13.5313i) q^{58} +(-20.2110 - 62.2032i) q^{59} +(1.81748 - 3.42121i) q^{60} +(-52.5800 - 72.3701i) q^{61} +(73.5225 - 16.3585i) q^{62} +(-9.25096 - 18.1560i) q^{63} +(-23.2095 - 59.6433i) q^{64} +(28.3817 - 21.3355i) q^{65} +(-0.751512 + 4.19461i) q^{66} +(-17.7580 + 17.7580i) q^{67} +(-102.810 - 3.43276i) q^{68} +(2.95004 + 0.958526i) q^{69} +(-17.2826 - 14.7727i) q^{70} +(-69.1875 - 95.2285i) q^{71} +(24.0889 + 67.5322i) q^{72} +(43.2254 - 84.8345i) q^{73} +(70.0346 - 27.6492i) q^{74} +(-0.601326 + 4.80502i) q^{75} +(23.5778 - 122.296i) q^{76} +(23.0720 + 9.65181i) q^{77} +(0.261583 - 2.73859i) q^{78} +(2.57463 - 3.54367i) q^{79} +(53.6431 + 59.3500i) q^{80} +(-24.7178 - 76.0735i) q^{81} +(-11.7603 - 19.9301i) q^{82} +(-1.42618 + 9.00452i) q^{83} +(-1.74812 + 0.217356i) q^{84} +(121.627 - 41.7214i) q^{85} +(-79.4920 + 4.92297i) q^{86} +(1.01014 + 1.01014i) q^{87} +(-76.1566 - 44.0928i) q^{88} +29.0201i q^{89} +(-58.1795 - 68.1744i) q^{90} +(-15.3553 - 4.98924i) q^{91} +(-39.3588 + 50.5361i) q^{92} +(-1.14115 + 7.20497i) q^{93} +(-2.54390 + 9.86767i) q^{94} +(26.8561 + 153.351i) q^{95} +(6.19833 + 0.0303891i) q^{96} +(-3.59532 - 22.7000i) q^{97} +(8.33525 - 87.2644i) q^{98} +(83.8780 + 51.8066i) 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 $

$2$	−1.49892	−	1.32409i	−0.749462	−	0.662047i
$2$	−1.49892	−	1.32409i	−0.749462	−	0.662047i
$3$	0.172588	−	0.0879380i	0.0575293	−	0.0293127i	−0.424989	−	0.905198i	$-0.639722\pi$
$3$	0.172588	−	0.0879380i	0.0575293	−	0.0293127i	0.482519	+	0.875886i	$0.339722\pi$
$4$	0.493549	+	3.96943i	0.123387	+	0.992359i
$5$	−2.34222	−	4.41746i	−0.468445	−	0.883493i
$5$	−2.34222	−	4.41746i	−0.468445	−	0.883493i
$6$	−0.375135	−	0.0967104i	−0.0625224	−	0.0161184i
$7$	−1.03219	+	2.02578i	−0.147455	+	0.289398i	−0.952906	−	0.303265i	$-0.901923\pi$
$7$	−1.03219	+	2.02578i	−0.147455	+	0.289398i	0.805451	+	0.592663i	$0.201923\pi$
$8$	4.51611	−	6.60339i	0.564514	−	0.825424i
$9$	−5.26801	+	7.25080i	−0.585335	+	0.805644i
$10$	−2.33832	+	9.72277i	−0.233832	+	0.972277i
$11$	−0.824530	−	10.9691i	−0.0749573	−	0.997187i
$11$	−0.824530	−	10.9691i	−0.0749573	−	0.997187i
$12$	0.434245	+	0.641675i	0.0361871	+	0.0534729i
$13$	1.11089	+	7.01390i	0.0854533	+	0.539531i	0.992861	+	0.119279i	$0.0380583\pi$
$13$	1.11089	+	7.01390i	0.0854533	+	0.539531i	−0.907407	+	0.420252i	$0.861942\pi$
$14$	4.22950	−	1.66978i	0.302107	−	0.119270i
$15$	−0.792703	−	0.556431i	−0.0528469	−	0.0370954i
$16$	−15.5128	+	3.91822i	−0.969551	+	0.244889i
$17$	−4.02299	+	25.4001i	−0.236646	+	1.49413i	0.527762	+	0.849393i	$0.323031\pi$
$17$	−4.02299	+	25.4001i	−0.236646	+	1.49413i	−0.764408	+	0.644733i	$0.776969\pi$
$18$	17.4971	−	3.89305i	0.972061	−	0.216281i
$19$	−29.6130	−	9.62185i	−1.55858	−	0.506413i	−0.602152	−	0.798381i	$-0.705690\pi$
$19$	−29.6130	−	9.62185i	−1.55858	−	0.506413i	−0.956428	+	0.291968i	$0.905690\pi$
$20$	16.3788	−	11.4775i	0.818941	−	0.573877i
$21$			0.440395i			0.0209712i
$22$	−13.2882	+	17.5335i	−0.604007	+	0.796979i
$23$	11.3234	+	11.3234i	0.492322	+	0.492322i	0.909037	−	0.416715i	$-0.136819\pi$
$23$	11.3234	+	11.3234i	0.492322	+	0.492322i	−0.416715	+	0.909037i	$0.636819\pi$
$24$	0.198738	−	1.53680i	0.00828075	−	0.0640335i
$25$	−14.0280	+	20.6934i	−0.561119	+	0.827735i
$26$	7.62192	−	11.9842i	0.293151	−	0.460932i
$27$	−0.544288	+	3.43650i	−0.0201588	+	0.127278i
$28$	−8.55065	−	3.09738i	−0.305380	−	0.110621i
$29$	2.27903	+	7.01414i	0.0785873	+	0.241867i	0.982630	−	0.185575i	$-0.0594148\pi$
$29$	2.27903	+	7.01414i	0.0785873	+	0.241867i	−0.904043	+	0.427442i	$0.859415\pi$
$30$	0.451435	+	1.88366i	0.0150478	+	0.0627887i
$31$	−22.1361	+	30.4677i	−0.714067	+	0.982830i	0.285633	+	0.958339i	$0.407796\pi$
$31$	−22.1361	+	30.4677i	−0.714067	+	0.982830i	−0.999700	+	0.0244904i	$0.992204\pi$
$32$	28.4406	+	14.6673i	0.888770	+	0.458353i
$33$	−1.10690	−	1.82062i	−0.0335424	−	0.0551703i
$34$	39.6623	−	32.7461i	1.16654	−	0.963120i
$35$	11.3664	−	0.185185i	0.324755	−	0.00529100i
$36$	−31.3816	−	17.3324i	−0.871711	−	0.481456i
$37$	−17.0916	+	33.5441i	−0.461935	+	0.906598i	0.536113	+	0.844146i	$0.319892\pi$
$37$	−17.0916	+	33.5441i	−0.461935	+	0.906598i	−0.998048	+	0.0624517i	$0.980108\pi$
$38$	31.6474	+	53.6329i	0.832828	+	1.41139i
$39$	0.808515	+	1.11283i	0.0207312	+	0.0285340i
$40$	−39.7480	−	4.48314i	−0.993699	−	0.112079i
$41$	11.0043	+	3.57551i	0.268397	+	0.0872076i	0.440124	−	0.897937i	$-0.354935\pi$
$41$	11.0043	+	3.57551i	0.268397	+	0.0872076i	−0.171726	+	0.985145i	$0.554935\pi$
$42$	0.583124	−	0.660118i	0.0138839	−	0.0157171i
$43$	28.1585	−	28.1585i	0.654849	−	0.654849i	−0.299307	−	0.954157i	$-0.596756\pi$
$43$	28.1585	−	28.1585i	0.654849	−	0.654849i	0.954157	+	0.299307i	$0.0967556\pi$
$44$	43.1340	−	8.68669i	0.980318	−	0.197425i
$45$	44.3690	+	6.28826i	0.985978	+	0.139739i
$46$	−1.97967	−	31.9662i	−0.0430364	−	0.694917i
$47$	−2.31315	−	4.53981i	−0.0492160	−	0.0965918i	0.865089	−	0.501619i	$-0.167262\pi$
$47$	−2.31315	−	4.53981i	−0.0492160	−	0.0965918i	−0.914305	+	0.405027i	$0.867262\pi$
$48$	−2.33277	+	2.04040i	−0.0485993	+	0.0425084i
$49$	25.7631	+	35.4599i	0.525777	+	0.723671i
$50$	48.4269	−	12.4435i	0.968537	−	0.248869i
$51$	1.53932	+	4.73753i	0.0301827	+	0.0928928i
$52$	−27.2929	+	7.87132i	−0.524864	+	0.151372i
$53$	−83.8731	+	13.2842i	−1.58251	+	0.250645i	−0.884883	−	0.465814i	$-0.845762\pi$
$53$	−83.8731	+	13.2842i	−1.58251	+	0.250645i	−0.697629	+	0.716459i	$0.745762\pi$
$54$	5.36609	−	4.43036i	0.0993721	−	0.0820438i
$55$	−46.5242	+	29.3343i	−0.845894	+	0.533351i
$56$	8.71556	+	15.9646i	0.155635	+	0.285082i
$57$	−5.95698	+	0.943493i	−0.104508	+	0.0165525i
$58$	5.87128	−	13.5313i	0.101229	−	0.233299i
$59$	−20.2110	−	62.2032i	−0.342560	−	1.05429i	−0.962877	−	0.269940i	$-0.912996\pi$
$59$	−20.2110	−	62.2032i	−0.342560	−	1.05429i	0.620317	−	0.784351i	$-0.287004\pi$
$60$	1.81748	−	3.42121i	0.0302913	−	0.0570201i
$61$	−52.5800	−	72.3701i	−0.861967	−	1.18640i	−0.981097	−	0.193517i	$-0.938011\pi$
$61$	−52.5800	−	72.3701i	−0.861967	−	1.18640i	0.119130	−	0.992879i	$-0.461989\pi$
$62$	73.5225	−	16.3585i	1.18585	−	0.263847i
$63$	−9.25096	−	18.1560i	−0.146841	−	0.288191i
$64$	−23.2095	−	59.6433i	−0.362648	−	0.931926i
$65$	28.3817	−	21.3355i	0.436641	−	0.328238i
$66$	−0.751512	+	4.19461i	−0.0113865	+	0.0635547i
$67$	−17.7580	+	17.7580i	−0.265045	+	0.265045i	−0.827100	−	0.562055i	$-0.810011\pi$
$67$	−17.7580	+	17.7580i	−0.265045	+	0.265045i	0.562055	+	0.827100i	$0.310011\pi$
$68$	−102.810	−	3.43276i	−1.51191	−	0.0504817i
$69$	2.95004	+	0.958526i	0.0427542	+	0.0138917i
$70$	−17.2826	−	14.7727i	−0.246895	−	0.211038i
$71$	−69.1875	−	95.2285i	−0.974472	−	1.34125i	−0.939755	−	0.341849i	$-0.888947\pi$
$71$	−69.1875	−	95.2285i	−0.974472	−	1.34125i	−0.0347175	−	0.999397i	$-0.511053\pi$
$72$	24.0889	+	67.5322i	0.334568	+	0.937947i
$73$	43.2254	−	84.8345i	0.592128	−	1.16212i	−0.379409	−	0.925229i	$-0.623873\pi$
$73$	43.2254	−	84.8345i	0.592128	−	1.16212i	0.971537	−	0.236888i	$-0.0761274\pi$
$74$	70.0346	−	27.6492i	0.946413	−	0.373638i
$75$	−0.601326	+	4.80502i	−0.00801768	+	0.0640670i
$76$	23.5778	−	122.296i	0.310235	−	1.60916i
$77$	23.0720	+	9.65181i	0.299636	+	0.125348i
$78$	0.261583	−	2.73859i	0.00335362	−	0.0351102i
$79$	2.57463	−	3.54367i	0.0325902	−	0.0448566i	−0.792411	−	0.609988i	$-0.791174\pi$
$79$	2.57463	−	3.54367i	0.0325902	−	0.0448566i	0.825001	+	0.565131i	$0.191174\pi$
$80$	53.6431	+	59.3500i	0.670539	+	0.741874i
$81$	−24.7178	−	76.0735i	−0.305158	−	0.939179i
$82$	−11.7603	−	19.9301i	−0.143418	−	0.243051i
$83$	−1.42618	+	9.00452i	−0.0171828	+	0.108488i	−0.994789	−	0.101954i	$-0.967490\pi$
$83$	−1.42618	+	9.00452i	−0.0171828	+	0.108488i	0.977606	+	0.210442i	$0.0674905\pi$
$84$	−1.74812	+	0.217356i	−0.0208109	+	0.00258758i
$85$	121.627	−	41.7214i	1.43090	−	0.490840i
$86$	−79.4920	+	4.92297i	−0.924326	+	0.0572438i
$87$	1.01014	+	1.01014i	0.0116108	+	0.0116108i
$88$	−76.1566	−	44.0928i	−0.865416	−	0.501054i
$89$			29.0201i			0.326068i	0.986620	+	0.163034i	$0.0521281\pi$
$89$			29.0201i			0.326068i	−0.986620	+	0.163034i	$0.947872\pi$
$90$	−58.1795	−	68.1744i	−0.646439	−	0.757493i
$91$	−15.3553	−	4.98924i	−0.168739	−	0.0548268i
$92$	−39.3588	+	50.5361i	−0.427813	+	0.549306i
$93$	−1.14115	+	7.20497i	−0.0122705	+	0.0774728i
$94$	−2.54390	+	9.86767i	−0.0270628	+	0.104975i
$95$	26.8561	+	153.351i	0.282696	+	1.61422i
$96$	6.19833	+	0.0303891i	0.0645659	+	0.000316553i
$97$	−3.59532	−	22.7000i	−0.0370652	−	0.234020i	0.962200	−	0.272343i	$-0.0877985\pi$
$97$	−3.59532	−	22.7000i	−0.0370652	−	0.234020i	−0.999265	+	0.0383226i	$0.987799\pi$
$98$	8.33525	−	87.2644i	0.0850536	−	0.890453i
$99$	83.8780	+	51.8066i	0.847253	+	0.523299i
$100$	−89.0645	−	45.4699i	−0.890645	−	0.454699i
$101$	−36.9391	+	50.8424i	−0.365734	+	0.503390i	−0.951735	−	0.306921i	$-0.900701\pi$
$101$	−36.9391	+	50.8424i	−0.365734	+	0.503390i	0.586001	+	0.810310i	$0.300701\pi$
$102$	3.96562	−	9.13941i	0.0388786	−	0.0896020i
$103$	−50.3030	+	98.7253i	−0.488379	+	0.958498i	0.506952	+	0.861974i	$0.330772\pi$
$103$	−50.3030	+	98.7253i	−0.488379	+	0.958498i	−0.995331	+	0.0965233i	$0.969228\pi$
$104$	51.3324	+	24.3399i	0.493581	+	0.234038i
$105$	1.94543	−	1.03150i	0.0185279	−	0.00982383i
$106$	143.309	+	91.1439i	1.35197	+	0.859848i
$107$	160.720	−	81.8908i	1.50205	−	0.765335i	0.506747	−	0.862095i	$-0.330848\pi$
$107$	160.720	−	81.8908i	1.50205	−	0.765335i	0.995308	+	0.0967601i	$0.0308480\pi$
$108$	−13.9096	−	0.464433i	−0.128792	−	0.00430031i
$109$	27.9859			0.256751			0.128375	−	0.991726i	$-0.459024\pi$
$109$	27.9859			0.256751			0.128375	+	0.991726i	$0.459024\pi$
$110$	108.578	+	17.6325i	0.987069	+	0.160295i
$111$			7.29231i			0.0656965i
$112$	8.07467	−	35.4699i	0.0720953	−	0.316696i
$113$	45.4229	+	89.1475i	0.401973	+	0.788916i	0.999920	−	0.0126195i	$-0.00401700\pi$
$113$	45.4229	+	89.1475i	0.401973	+	0.788916i	−0.597948	+	0.801535i	$0.704017\pi$
$114$	10.1783	+	6.47338i	0.0892837	+	0.0567840i
$115$	23.4988	−	76.5426i	0.204337	−	0.665588i
$116$	−26.7173	+	12.5083i	−0.230322	+	0.107830i
$117$	−56.7086	−	28.8945i	−0.484689	−	0.246961i
$118$	−52.0681	+	119.999i	−0.441255	+	1.01694i
$119$	−47.3027	−	34.3674i	−0.397502	−	0.288802i
$120$	−7.25426	+	2.72162i	−0.0604522	+	0.0226802i
$121$	−119.640	+	18.0886i	−0.988763	+	0.149493i
$122$	−17.0114	+	178.098i	−0.139438	+	1.45982i
$123$	2.21363	−	0.350605i	0.0179970	−	0.00285045i
$124$	−131.865	−	72.8304i	−1.06343	−	0.587342i
$125$	124.269	+	13.4995i	0.994151	+	0.107996i
$126$	−10.1738	+	39.4637i	−0.0807445	+	0.313204i
$127$	40.2329	+	6.37226i	0.316794	+	0.0501753i	0.312807	−	0.949817i	$-0.398731\pi$
$127$	40.2329	+	6.37226i	0.316794	+	0.0501753i	0.00398739	+	0.999992i	$0.498731\pi$
$128$	−44.1841	+	120.132i	−0.345188	+	0.938534i
$129$	2.38362	−	7.33603i	0.0184777	−	0.0568684i
$130$	−70.7922	−	5.59979i	−0.544555	−	0.0430753i
$131$	198.529			1.51549			0.757743	−	0.652553i	$-0.226302\pi$
$131$	198.529			1.51549			0.757743	+	0.652553i	$0.226302\pi$
$132$	6.68052	−	5.29234i	0.0506100	−	0.0400935i
$133$	50.0580	−	50.0580i	0.376376	−	0.376376i
$134$	50.1312	−	3.10464i	0.374113	−	0.0231689i
$135$	16.4554	−	5.64468i	0.121892	−	0.0418124i
$136$	149.559	+	141.275i	1.09970	+	1.03879i
$137$	−86.9465	−	13.7710i	−0.634646	−	0.100518i	−0.169182	−	0.985585i	$-0.554112\pi$
$137$	−86.9465	−	13.7710i	−0.634646	−	0.100518i	−0.465464	+	0.885067i	$0.654112\pi$
$138$	−3.15271	−	5.34289i	−0.0228457	−	0.0387166i
$139$	−210.433	+	68.3739i	−1.51391	+	0.491899i	−0.944038	−	0.329836i	$-0.893006\pi$
$139$	−210.433	+	68.3739i	−1.51391	+	0.491899i	−0.569870	+	0.821735i	$0.693006\pi$
$140$	6.34498	+	45.0269i	0.0453213	+	0.321621i
$141$	−0.798445	−	0.580104i	−0.00566273	−	0.00411421i
$142$	−22.3846	+	234.351i	−0.157638	+	1.65036i
$143$	76.0199	−	17.9686i	0.531608	−	0.125655i
$144$	53.3115	−	133.122i	0.370219	−	0.924455i
$145$	25.6467	−	26.4962i	0.176874	−	0.182733i
$146$	−177.120	+	69.9261i	−1.21315	+	0.478946i
$147$	7.56467	+	3.85439i	0.0514603	+	0.0262204i
$148$	−141.587	−	51.2882i	−0.956667	−	0.346542i
$149$	36.7563	−	26.7050i	0.246686	−	0.179228i	−0.457571	−	0.889173i	$-0.651280\pi$
$149$	36.7563	−	26.7050i	0.246686	−	0.179228i	0.704257	+	0.709945i	$0.251280\pi$
$150$	7.26364	−	6.40615i	0.0484243	−	0.0427077i
$151$	−22.8722	+	70.3933i	−0.151471	+	0.466181i	−0.997786	−	0.0665020i	$-0.978816\pi$
$151$	−22.8722	+	70.3933i	−0.151471	+	0.466181i	0.846315	+	0.532683i	$0.178816\pi$
$152$	−197.273	+	152.093i	−1.29785	+	1.00061i
$153$	−162.978	−	162.978i	−1.06522	−	1.06522i
$154$	−21.8033	−	45.0168i	−0.141580	−	0.292317i
$155$	186.438	+	26.4232i	1.20282	+	0.170472i
$156$	−4.01825	+	3.75858i	−0.0257580	+	0.0240935i
$157$	−204.405	+	104.150i	−1.30194	+	0.663373i	−0.960958	−	0.276695i	$-0.910761\pi$
$157$	−204.405	+	104.150i	−1.30194	+	0.663373i	−0.340986	+	0.940068i	$0.610761\pi$
$158$	−8.55133	+	1.90265i	−0.0541223	+	0.0120421i
$159$	−13.3073	+	9.66833i	−0.0836938	+	0.0608071i
$160$	−1.82205	−	159.990i	−0.0113878	−	0.999935i
$161$	−34.6266	+	11.2509i	−0.215072	+	0.0698812i
$162$	−63.6784	+	146.757i	−0.393076	+	0.905908i
$163$	26.0694	+	164.595i	0.159935	+	1.00979i	0.928855	+	0.370444i	$0.120794\pi$
$163$	26.0694	+	164.595i	0.159935	+	1.00979i	−0.768920	+	0.639345i	$0.779206\pi$
$164$	−8.76160	+	45.4455i	−0.0534244	+	0.277107i
$165$	−5.44991	+	9.15399i	−0.0330298	+	0.0554788i
$166$	14.0606	−	11.6087i	0.0847022	−	0.0699320i
$167$	−36.7704	−	232.159i	−0.220182	−	1.39018i	−0.811790	−	0.583950i	$-0.801507\pi$
$167$	−36.7704	−	232.159i	−0.220182	−	1.39018i	0.591608	−	0.806226i	$-0.298493\pi$
$168$	2.90810	+	1.98887i	0.0173101	+	0.0118385i
$169$	112.768	−	36.6405i	0.667265	−	0.216808i
$170$	−237.553	−	98.5082i	−1.39737	−	0.579460i
$171$	225.768	−	164.030i	1.32028	−	0.959240i
$172$	125.671	+	97.8758i	0.730646	+	0.569045i
$173$	−57.3448	+	29.2186i	−0.331473	+	0.168894i	−0.611804	−	0.791010i	$-0.709556\pi$
$173$	−57.3448	+	29.2186i	−0.331473	+	0.168894i	0.280331	+	0.959903i	$0.409556\pi$
$174$	−0.176604	−	2.85165i	−0.00101496	−	0.0163888i
$175$	−27.4408	−	49.7771i	−0.156805	−	0.284441i
$176$	55.7700	+	166.930i	0.316875	+	0.948467i
$177$	−8.95821	−	8.95821i	−0.0506114	−	0.0506114i
$178$	38.4253	−	43.4989i	0.215873	−	0.244376i
$179$	−68.1188	+	209.648i	−0.380552	+	1.17122i	0.559104	+	0.829098i	$0.311145\pi$
$179$	−68.1188	+	209.648i	−0.380552	+	1.17122i	−0.939656	+	0.342121i	$0.888855\pi$
$180$	−3.06255	+	179.223i	−0.0170142	+	0.995686i
$181$	21.0487	−	15.2928i	0.116291	−	0.0844906i	−0.528119	−	0.849170i	$-0.677103\pi$
$181$	21.0487	−	15.2928i	0.116291	−	0.0844906i	0.644411	+	0.764679i	$0.277103\pi$
$182$	16.4102	+	27.8103i	0.0901660	+	0.152804i
$183$	−15.4388	−	7.86644i	−0.0843648	−	0.0429860i
$184$	125.911	−	23.6351i	0.684296	−	0.128451i
$185$	188.212	−	3.06640i	1.01736	−	0.0165751i
$186$	11.2506	−	9.28871i	0.0604869	−	0.0499393i
$187$	281.933	+	23.1852i	1.50766	+	0.123985i
$188$	16.8788	−	11.4225i	0.0897811	−	0.0607581i
$189$	−6.39979	−	4.64972i	−0.0338613	−	0.0246017i
$190$	162.796	−	265.422i	0.856820	−	1.39696i
$191$	−106.200	+	34.5065i	−0.556022	+	0.180662i	−0.573530	−	0.819184i	$-0.694427\pi$
$191$	−106.200	+	34.5065i	−0.556022	+	0.180662i	0.0175087	+	0.999847i	$0.494427\pi$
$192$	−9.25059	−	8.25272i	−0.0481801	−	0.0429829i
$193$	276.471	+	43.7887i	1.43249	+	0.226884i	0.823961	−	0.566646i	$-0.191759\pi$
$193$	276.471	+	43.7887i	1.43249	+	0.226884i	0.608530	+	0.793531i	$0.291759\pi$
$194$	−24.6678	+	38.7861i	−0.127154	+	0.199928i
$195$	3.02214	−	6.17807i	0.0154982	−	0.0316824i
$196$	−128.040	+	119.766i	−0.653266	+	0.611052i
$197$	209.856	−	209.856i	1.06526	−	1.06526i	0.0675409	−	0.997717i	$-0.478485\pi$
$197$	209.856	−	209.856i	1.06526	−	1.06526i	0.997717	−	0.0675409i	$-0.0215153\pi$
$198$	−57.1300	−	188.717i	−0.288535	−	0.953114i
$199$	4.27386			0.0214767			0.0107383	−	0.999942i	$-0.496582\pi$
$199$	4.27386			0.0214767			0.0107383	+	0.999942i	$0.496582\pi$
$200$	73.2945	+	186.086i	0.366473	+	0.930429i
$201$	−1.50322	+	4.62642i	−0.00747869	+	0.0230170i
$202$	122.689	−	27.2980i	0.607372	−	0.135138i
$203$	−16.5615	−	2.62309i	−0.0815838	−	0.0129216i
$204$	−18.0456	+	8.44843i	−0.0884588	+	0.0414139i
$205$	−9.97983	−	56.9857i	−0.0486821	−	0.277979i
$206$	206.122	−	81.3758i	1.00059	−	0.395028i
$207$	−141.755	+	22.4519i	−0.684809	+	0.108463i
$208$	−44.7151	−	104.453i	−0.214976	−	0.502176i
$209$	−81.1258	+	332.760i	−0.388162	+	1.59215i
$210$	−4.28185	−	1.02978i	−0.0203898	−	0.00490373i
$211$	−237.152	−	172.301i	−1.12394	−	0.816591i	−0.139139	−	0.990273i	$-0.544434\pi$
$211$	−237.152	−	172.301i	−1.12394	−	0.816591i	−0.984802	+	0.173682i	$0.944434\pi$
$212$	−94.1263	−	326.373i	−0.443992	−	1.53949i
$213$	−20.3151	−	10.3511i	−0.0953763	−	0.0485966i
$214$	−349.338	−	90.0600i	−1.63242	−	0.420841i
$215$	−190.343	−	58.4357i	−0.885316	−	0.271794i
$216$	20.2345	+	19.1138i	0.0936781	+	0.0884896i
$217$	−38.8724	−	76.2913i	−0.179135	−	0.351573i
$218$	−41.9487	−	37.0559i	−0.192425	−	0.169981i
$219$		−	18.4426i		−	0.0842127i
$220$	−139.403	−	170.197i	−0.633648	−	0.773621i
$221$	−182.623			−0.826349
$222$	9.65571	−	10.9306i	0.0434942	−	0.0492371i
$223$	18.1478	−	9.24678i	0.0813804	−	0.0414654i	−0.412827	−	0.910810i	$-0.635458\pi$
$223$	18.1478	−	9.24678i	0.0813804	−	0.0414654i	0.494207	+	0.869344i	$0.335458\pi$
$224$	−59.0689	+	42.4751i	−0.263700	+	0.189621i
$225$	−76.1440	−	210.727i	−0.338418	−	0.936565i
$226$	49.9541	−	193.770i	0.221036	−	0.857387i
$227$	−119.684	+	234.893i	−0.527242	+	1.03477i	0.461779	+	0.886995i	$0.347211\pi$
$227$	−119.684	+	234.893i	−0.527242	+	1.03477i	−0.989021	+	0.147776i	$0.952789\pi$
$228$	−6.68520	−	23.1802i	−0.0293210	−	0.101667i
$229$	−178.446	+	245.610i	−0.779239	+	1.07253i	0.216126	+	0.976365i	$0.430658\pi$
$229$	−178.446	+	245.610i	−0.779239	+	1.07253i	−0.995365	+	0.0961655i	$0.969342\pi$
$230$	−136.573	+	83.6171i	−0.593794	+	0.363552i
$231$	4.83071	−	0.363118i	0.0209122	−	0.00157194i
$232$	56.6094	+	16.6273i	0.244006	+	0.0716694i
$233$	−10.6844	−	67.4588i	−0.0458559	−	0.289523i	0.954094	−	0.299506i	$-0.0968220\pi$
$233$	−10.6844	−	67.4588i	−0.0458559	−	0.289523i	−0.999950	+	0.00998374i	$0.996822\pi$
$234$	46.7429	+	118.398i	0.199756	+	0.505975i
$235$	−14.6365	+	20.8515i	−0.0622832	+	0.0887299i
$236$	236.936	−	110.927i	1.00397	−	0.470029i
$237$	0.132727	−	0.838003i	0.000560028	−	0.00353588i
$238$	25.3975	+	114.147i	0.106712	+	0.479611i
$239$	−119.116	−	38.7031i	−0.498393	−	0.161938i	0.0490240	−	0.998798i	$-0.484389\pi$
$239$	−119.116	−	38.7031i	−0.498393	−	0.161938i	−0.547417	+	0.836860i	$0.684389\pi$
$240$	14.4773	+	5.52582i	0.0603220	+	0.0230243i
$241$			158.784i			0.658853i	0.944181	+	0.329427i	$0.106855\pi$
$241$			158.784i			0.658853i	−0.944181	+	0.329427i	$0.893145\pi$
$242$	203.283	+	131.302i	0.840012	+	0.542568i
$243$	−33.0981	−	33.0981i	−0.136206	−	0.136206i
$244$	261.318	−	244.431i	1.07097	−	1.00177i
$245$	96.2997	−	196.862i	0.393060	−	0.803520i
$246$	−3.78230	−	2.40553i	−0.0153752	−	0.00977857i
$247$	34.5898	−	218.392i	0.140040	−	0.884177i
$248$	101.221	+	283.769i	0.408150	+	1.14423i
$249$	0.545699	+	1.67949i	0.00219156	+	0.00674493i
$250$	−168.395	−	184.778i	−0.673580	−	0.739114i
$251$	81.8983	−	112.723i	0.326288	−	0.449097i	−0.614086	−	0.789239i	$-0.710475\pi$
$251$	81.8983	−	112.723i	0.326288	−	0.449097i	0.940374	+	0.340142i	$0.110475\pi$
$252$	67.5034	−	45.6820i	0.267871	−	0.181278i
$253$	114.870	−	133.543i	0.454034	−	0.527840i
$254$	−51.8685	−	62.8236i	−0.204207	−	0.247337i
$255$	17.3225	−	17.8962i	0.0679312	−	0.0701813i
$256$	225.295	−	121.565i	0.880059	−	0.474865i
$257$	110.231	−	216.340i	0.428914	−	0.841791i	−0.570871	−	0.821040i	$-0.693394\pi$
$257$	110.231	−	216.340i	0.428914	−	0.841791i	0.999785	−	0.0207512i	$-0.00660577\pi$
$258$	−13.2865	+	7.84002i	−0.0514979	+	0.0303877i
$259$	−50.3114	−	69.2477i	−0.194252	−	0.267366i
$260$	98.6975	+	102.129i	0.379606	+	0.392804i
$261$	−62.8641	−	20.4258i	−0.240859	−	0.0782597i
$262$	−297.580	−	262.871i	−1.13580	−	1.00332i
$263$	−52.0148	+	52.0148i	−0.197775	+	0.197775i	−0.799045	−	0.601271i	$-0.794661\pi$
$263$	−52.0148	+	52.0148i	−0.197775	+	0.197775i	0.601271	+	0.799045i	$0.294661\pi$
$264$	−17.0211	−	0.912828i	−0.0644740	−	0.00345768i
$265$	255.132	+	339.392i	0.962763	+	1.28072i
$266$	−141.315	+	8.75166i	−0.531258	+	0.0329010i
$267$	2.55197	+	5.00852i	0.00955793	+	0.0187585i
$268$	−79.2537	−	61.7248i	−0.295723	−	0.230316i
$269$	180.786	+	248.831i	0.672067	+	0.925021i	0.999805	−	0.0197474i	$-0.00628619\pi$
$269$	180.786	+	248.831i	0.672067	+	0.925021i	−0.327738	+	0.944769i	$0.606286\pi$
$270$	−32.1396	−	13.3276i	−0.119035	−	0.0493615i
$271$	146.750	+	451.650i	0.541513	+	1.66661i	0.729140	+	0.684365i	$0.239920\pi$
$271$	146.750	+	451.650i	0.541513	+	1.66661i	−0.187627	+	0.982240i	$0.560080\pi$
$272$	−37.1156	−	409.791i	−0.136454	−	1.50658i
$273$	−3.08888	+	0.489231i	−0.0113146	+	0.00179206i
$274$	112.092	+	135.767i	0.409095	+	0.495500i
$275$	238.553	+	136.811i	0.867467	+	0.497496i
$276$	−2.34882	+	12.1831i	−0.00851020	+	0.0441416i
$277$	−38.6251	+	6.11761i	−0.139441	+	0.0220852i	−0.225765	−	0.974182i	$-0.572488\pi$
$277$	−38.6251	+	6.11761i	−0.139441	+	0.0220852i	0.0863239	+	0.996267i	$0.472488\pi$
$278$	405.957	+	176.146i	1.46028	+	0.633619i
$279$	−104.302	−	321.009i	−0.373842	−	1.15057i
$280$	50.1093	−	75.8933i	0.178962	−	0.271048i
$281$	−150.577	−	207.252i	−0.535862	−	0.737551i	0.452148	−	0.891943i	$-0.350658\pi$
$281$	−150.577	−	207.252i	−0.535862	−	0.737551i	−0.988010	+	0.154393i	$0.950658\pi$
$282$	0.428696	+	1.92675i	0.00152020	+	0.00683244i
$283$	91.4120	+	179.406i	0.323010	+	0.633944i	0.994225	−	0.107320i	$-0.0342269\pi$
$283$	91.4120	+	179.406i	0.323010	+	0.633944i	−0.671214	+	0.741264i	$0.734227\pi$
$284$	343.856	−	321.635i	1.21076	−	1.13252i
$285$	18.1204	+	24.1049i	0.0635805	+	0.0845785i
$286$	−137.740	−	73.7239i	−0.481609	−	0.257776i
$287$	−18.6017	+	18.6017i	−0.0648143	+	0.0648143i
$288$	−256.175	+	128.950i	−0.889498	+	0.447742i
$289$	−354.127	−	115.063i	−1.22535	−	0.398141i
$290$	−73.5260	+	5.75720i	−0.253538	+	0.0198524i
$291$	−2.61670	−	3.60158i	−0.00899210	−	0.0123766i
$292$	358.079	+	129.710i	1.22630	+	0.444213i
$293$	36.2179	−	71.0815i	0.123610	−	0.242599i	−0.820906	−	0.571063i	$-0.806531\pi$
$293$	36.2179	−	71.0815i	0.123610	−	0.242599i	0.944516	+	0.328464i	$0.106531\pi$
$294$	−6.23529	−	15.7938i	−0.0212085	−	0.0537203i
$295$	−227.442	+	234.975i	−0.770988	+	0.796527i
$296$	144.317	+	264.351i	0.487559	+	0.893079i
$297$	38.1439	+	3.13683i	0.128431	+	0.0105617i
$298$	−90.4548	−	8.63999i	−0.303540	−	0.0289933i
$299$	−66.8421	+	92.0003i	−0.223552	+	0.307693i
$300$	−19.3700	−	0.0154068i	−0.0645667	−	5.13561e-5i
$301$	27.9782	+	86.1080i	0.0929507	+	0.286073i
$302$	127.491	−	75.2293i	0.422156	−	0.249104i
$303$	−1.90428	+	12.0231i	−0.00628475	+	0.0396803i
$304$	497.082	+	33.2316i	1.63514	+	0.109315i
$305$	−196.538	+	401.777i	−0.644388	+	1.31730i
$306$	28.4935	+	460.090i	0.0931161	+	1.50356i
$307$	−157.349	−	157.349i	−0.512536	−	0.512536i	0.402767	−	0.915303i	$-0.368049\pi$
$307$	−157.349	−	157.349i	−0.512536	−	0.512536i	−0.915303	+	0.402767i	$0.868049\pi$
$308$	−26.9250	+	96.3464i	−0.0874190	+	0.312813i
$309$			21.4624i			0.0694574i
$310$	−244.469	−	286.467i	−0.788611	−	0.924088i
$311$	−230.927	−	75.0328i	−0.742531	−	0.241263i	−0.0867667	−	0.996229i	$-0.527653\pi$
$311$	−230.927	−	75.0328i	−0.742531	−	0.241263i	−0.655764	+	0.754966i	$0.727653\pi$
$312$	10.9998	−	0.313295i	0.0352557	−	0.00100415i
$313$	−50.2404	+	317.206i	−0.160513	+	1.01344i	0.767544	+	0.640997i	$0.221479\pi$
$313$	−50.2404	+	317.206i	−0.160513	+	1.01344i	−0.928056	+	0.372440i	$0.878521\pi$
$314$	444.292	+	114.539i	1.41494	+	0.364775i
$315$	−58.5358	+	83.3913i	−0.185828	+	0.264734i
$316$	15.3371	+	8.47084i	0.0485351	+	0.0268065i
$317$	17.2741	+	109.064i	0.0544924	+	0.344052i	0.999838	+	0.0179824i	$0.00572429\pi$
$317$	17.2741	+	109.064i	0.0544924	+	0.344052i	−0.945346	+	0.326069i	$0.894276\pi$
$318$	32.7484	+	3.12804i	0.102983	+	0.00983661i
$319$	75.0593	−	30.7822i	0.235296	−	0.0964959i
$320$	−209.110	+	242.225i	−0.653469	+	0.756953i
$321$	20.5370	−	28.2668i	0.0639782	−	0.0880584i
$322$	66.7999	+	28.9847i	0.207453	+	0.0900146i
$323$	363.529	−	713.466i	1.12548	−	2.20887i
$324$	289.769	−	135.662i	0.894349	−	0.418709i
$325$	−160.725	−	75.4027i	−0.494538	−	0.232008i
$326$	178.864	−	281.234i	0.548662	−	0.862683i
$327$	4.83002	−	2.46102i	0.0147707	−	0.00752606i
$328$	73.3071	−	56.5182i	0.223497	−	0.172312i
$329$	11.5843			0.0352106
$330$	20.2898	−	6.50495i	0.0614841	−	0.0197120i
$331$		−	461.485i		−	1.39422i	−0.716966	−	0.697108i	$-0.754470\pi$
$331$		−	461.485i		−	1.39422i	0.716966	−	0.697108i	$-0.245530\pi$
$332$	−36.4467	−	1.21694i	−0.109779	−	0.00366547i
$333$	−153.183	−	300.638i	−0.460009	−	0.902818i
$334$	−252.285	+	396.677i	−0.755344	+	1.18766i
$335$	120.039	+	36.8521i	0.358324	+	0.110006i
$336$	−1.72556	−	6.83176i	−0.00513561	−	0.0203326i
$337$	−331.851	−	169.087i	−0.984722	−	0.501741i	−0.113981	−	0.993483i	$-0.536360\pi$
$337$	−331.851	−	169.087i	−0.984722	−	0.501741i	−0.870741	+	0.491742i	$0.836360\pi$
$338$	−217.546	−	94.3939i	−0.643627	−	0.279272i
$339$	15.6789	+	11.3914i	0.0462504	+	0.0336029i
$340$	225.639	+	462.198i	0.663645	+	1.35941i
$341$	352.454	+	217.690i	1.03359	+	0.638388i
$342$	−555.600	−	53.0694i	−1.62456	−	0.155174i
$343$	−208.461	+	33.0169i	−0.607757	+	0.0962592i
$344$	−58.7746	−	313.109i	−0.170857	−	0.910200i
$345$	−2.67540	−	15.2768i	−0.00775478	−	0.0442805i
$346$	124.644	+	32.1334i	0.360242	+	0.0928710i
$347$	141.124	+	22.3518i	0.406696	+	0.0644143i	0.356431	−	0.934322i	$-0.383993\pi$
$347$	141.124	+	22.3518i	0.406696	+	0.0644143i	0.0502649	+	0.998736i	$0.483993\pi$
$348$	−3.51114	+	4.50825i	−0.0100895	+	0.0129547i
$349$	−25.4820	+	78.4255i	−0.0730143	+	0.224715i	−0.980903	−	0.194496i	$-0.937693\pi$
$349$	−25.4820	+	78.4255i	−0.0730143	+	0.224715i	0.907889	+	0.419210i	$0.137693\pi$
$350$	−24.7779	+	110.946i	−0.0707939	+	0.316989i
$351$	−24.7079			−0.0703929
$352$	137.436	−	324.061i	0.390444	−	0.920627i
$353$	−30.1338	+	30.1338i	−0.0853650	+	0.0853650i	−0.748500	−	0.663135i	$-0.769226\pi$
$353$	−30.1338	+	30.1338i	−0.0853650	+	0.0853650i	0.663135	+	0.748500i	$0.269226\pi$
$354$	1.56617	+	25.2892i	0.00442420	+	0.0714384i
$355$	−258.616	+	528.680i	−0.728495	+	1.48924i
$356$	−115.193	+	14.3228i	−0.323577	+	0.0402327i
$357$	−11.1861	−	1.77170i	−0.0313336	−	0.00496275i
$358$	379.699	−	224.051i	1.06061	−	0.625841i
$359$	−542.498	+	176.268i	−1.51114	+	0.490998i	−0.943243	−	0.332103i	$-0.892242\pi$
$359$	−542.498	+	176.268i	−1.51114	+	0.490998i	−0.567894	+	0.823101i	$0.692242\pi$
$360$	241.899	−	264.587i	0.671942	−	0.734965i
$361$	492.296	+	357.674i	1.36370	+	0.990787i
$362$	−51.7996	−	4.94775i	−0.143093	−	0.0136678i
$363$	−19.0578	+	13.6428i	−0.0525009	+	0.0375835i
$364$	12.2259	−	63.4143i	0.0335875	−	0.174215i
$365$	−475.997	+	7.75507i	−1.30410	+	0.0212468i
$366$	12.7256	+	32.2336i	0.0347695	+	0.0880699i
$367$	−534.380	−	272.280i	−1.45608	−	0.741907i	−0.466311	−	0.884621i	$-0.654417\pi$
$367$	−534.380	−	272.280i	−1.45608	−	0.741907i	−0.989764	+	0.142713i	$0.954417\pi$
$368$	−220.025	−	131.290i	−0.597895	−	0.356767i
$369$	−83.8961	+	60.9541i	−0.227361	+	0.165187i
$370$	−286.176	−	244.614i	−0.773449	−	0.661120i
$371$	59.6619	−	183.621i	0.160814	−	0.494934i
$372$	−29.1629	−	0.973731i	−0.0783948	−	0.00261756i
$373$	484.026	+	484.026i	1.29766	+	1.29766i	0.929937	+	0.367719i	$0.119861\pi$
$373$	484.026	+	484.026i	1.29766	+	1.29766i	0.367719	+	0.929937i	$0.380139\pi$
$374$	−391.896	−	408.058i	−1.04785	−	1.09106i
$375$	22.6345	−	8.59810i	0.0603585	−	0.0229283i
$376$	−40.4246	−	5.22767i	−0.107512	−	0.0139034i
$377$	−46.6647	+	23.7769i	−0.123779	+	0.0630686i
$378$	3.43614	+	15.4435i	0.00909031	+	0.0408558i
$379$	432.993	−	314.588i	1.14246	−	0.830048i	0.155002	−	0.987914i	$-0.450462\pi$
$379$	432.993	−	314.588i	1.14246	−	0.830048i	0.987460	+	0.157866i	$0.0504615\pi$
$380$	−595.462	+	182.290i	−1.56701	+	0.479711i
$381$	7.50407	−	2.43822i	0.0196957	−	0.00639953i
$382$	204.876	+	88.8963i	0.536324	+	0.232713i
$383$	44.8020	+	282.869i	0.116976	+	0.738561i	0.974545	+	0.224191i	$0.0719740\pi$
$383$	44.8020	+	282.869i	0.116976	+	0.738561i	−0.857569	+	0.514369i	$0.828026\pi$
$384$	2.93855	+	24.6189i	0.00765248	+	0.0641116i
$385$	−11.4033	−	124.526i	−0.0296189	−	0.323445i
$386$	−356.429	−	431.709i	−0.923390	−	1.11842i
$387$	55.8323	+	352.511i	0.144270	+	0.910882i
$388$	88.3316	−	25.4750i	0.227659	−	0.0656571i
$389$	−244.423	+	79.4180i	−0.628338	+	0.204159i	−0.605839	−	0.795588i	$-0.707162\pi$
$389$	−244.423	+	79.4180i	−0.628338	+	0.204159i	−0.0224991	+	0.999747i	$0.507162\pi$
$390$	−12.7103	+	5.25886i	−0.0325906	+	0.0134843i
$391$	−333.170	+	242.062i	−0.852096	+	0.619084i
$392$	350.504	−	9.98305i	0.894143	−	0.0254670i
$393$	34.2637	−	17.4582i	0.0871849	−	0.0444229i
$394$	−592.427	+	36.6892i	−1.50362	+	0.0931197i
$395$	−21.6844	−	3.07325i	−0.0548972	−	0.00778039i
$396$	−164.245	+	358.518i	−0.414760	+	0.905347i
$397$	161.098	+	161.098i	0.405788	+	0.405788i	0.880267	−	0.474479i	$-0.157364\pi$
$397$	161.098	+	161.098i	0.405788	+	0.405788i	−0.474479	+	0.880267i	$0.657364\pi$
$398$	−6.40619	−	5.65899i	−0.0160959	−	0.0142186i
$399$	4.23741	−	13.0414i	0.0106201	−	0.0326852i
$400$	136.532	−	375.977i	0.341330	−	0.939943i
$401$	265.228	−	192.699i	0.661416	−	0.480547i	−0.205725	−	0.978610i	$-0.565955\pi$
$401$	265.228	−	192.699i	0.661416	−	0.480547i	0.867141	+	0.498063i	$0.165955\pi$
$402$	8.37903	−	4.94426i	0.0208434	−	0.0122992i
$403$	−238.288	−	121.414i	−0.591286	−	0.301275i
$404$	−220.047	−	121.534i	−0.544670	−	0.300827i
$405$	−278.157	+	287.371i	−0.686808	+	0.709558i
$406$	21.3512	+	25.8608i	0.0525893	+	0.0636966i
$407$	382.040	+	159.820i	0.938673	+	0.392679i
$408$	38.2355	+	11.2305i	0.0937145	+	0.0275258i
$409$	285.176	+	207.193i	0.697252	+	0.506584i	0.879036	−	0.476755i	$-0.158187\pi$
$409$	285.176	+	207.193i	0.697252	+	0.506584i	−0.181784	+	0.983339i	$0.558187\pi$
$410$	−60.4955	+	98.6315i	−0.147550	+	0.240565i
$411$	−16.2169	+	5.26919i	−0.0394572	+	0.0128204i
$412$	−416.711	−	150.949i	−1.01143	−	0.366381i
$413$	146.872	+	23.2622i	0.355622	+	0.0563249i
$414$	242.209	+	154.044i	0.585046	+	0.372087i
$415$	43.1176	−	14.7905i	0.103898	−	0.0356398i
$416$	−71.2805	+	215.774i	−0.171347	+	0.518687i
$417$	−30.3056	+	30.3056i	−0.0726753	+	0.0726753i
$418$	562.208	−	391.364i	1.34499	−	0.936279i
$419$	381.222			0.909838			0.454919	−	0.890533i	$-0.349668\pi$
$419$	381.222			0.909838			0.454919	+	0.890533i	$0.349668\pi$
$420$	5.05465	+	7.21315i	0.0120349	+	0.0171742i
$421$	−104.947	+	322.995i	−0.249281	+	0.767209i	0.745621	+	0.666370i	$0.232153\pi$
$421$	−104.947	+	322.995i	−0.249281	+	0.767209i	−0.994903	+	0.100839i	$0.967847\pi$
$422$	127.330	+	572.277i	0.301730	+	1.35611i
$423$	45.1030	+	7.14361i	0.106626	+	0.0168880i
$424$	−291.060	+	613.840i	−0.686462	+	1.44774i
$425$	−469.180	−	439.562i	−1.10395	−	1.03426i
$426$	16.7451	+	42.4147i	0.0393077	+	0.0995649i
$427$	200.879	−	31.8160i	0.470442	−	0.0745106i
$428$	404.383	+	597.550i	0.944821	+	1.39614i
$429$	11.5400	−	9.78621i	0.0268998	−	0.0228117i
$430$	207.935	+	339.623i	0.483570	+	0.789820i
$431$	2.93712	+	2.13394i	0.00681467	+	0.00495115i	0.591187	−	0.806534i	$-0.298659\pi$
$431$	2.93712	+	2.13394i	0.00681467	+	0.00495115i	−0.584373	+	0.811485i	$0.698659\pi$
$432$	−5.02153	−	55.4424i	−0.0116239	−	0.128339i
$433$	389.083	+	198.248i	0.898575	+	0.457847i	0.841335	−	0.540513i	$-0.181770\pi$
$433$	389.083	+	198.248i	0.898575	+	0.457847i	0.0572401	+	0.998360i	$0.481770\pi$
$434$	−42.7501	+	165.826i	−0.0985026	+	0.382087i
$435$	2.09629	−	6.82825i	0.00481905	−	0.0156971i
$436$	13.8124	+	111.088i	0.0316798	+	0.254789i
$437$	−226.368	−	444.272i	−0.518004	−	1.01664i
$438$	−24.4197	+	27.6440i	−0.0557528	+	0.0631142i
$439$		−	39.9006i		−	0.0908899i	−0.998967	−	0.0454449i	$-0.985529\pi$
$439$		−	39.9006i		−	0.0908899i	0.998967	−	0.0454449i	$-0.0144706\pi$
$440$	−16.4024	+	439.694i	−0.0372783	+	0.999305i
$441$	−392.833			−0.890777
$442$	273.738	+	241.810i	0.619317	+	0.547082i
$443$	243.130	−	123.881i	0.548826	−	0.279641i	−0.157510	−	0.987517i	$-0.550347\pi$
$443$	243.130	−	123.881i	0.548826	−	0.279641i	0.706336	+	0.707876i	$0.250347\pi$
$444$	−28.9464	+	3.59912i	−0.0651945	+	0.00810612i
$445$	128.195	−	67.9715i	0.288079	−	0.152745i
$446$	−39.4458	−	10.1692i	−0.0884435	−	0.0228009i
$447$	3.99531	−	7.84124i	0.00893805	−	0.0175419i
$448$	144.781	+	14.5457i	0.323172	+	0.0324681i
$449$	253.396	−	348.770i	0.564356	−	0.776770i	−0.427516	−	0.904008i	$-0.640611\pi$
$449$	253.396	−	348.770i	0.564356	−	0.776770i	0.991872	+	0.127238i	$0.0406112\pi$
$450$	−164.888	+	416.686i	−0.366418	+	0.925968i
$451$	30.1466	−	123.655i	0.0668439	−	0.274179i
$452$	−331.447	+	224.302i	−0.733289	+	0.496243i
$453$	2.24278	+	14.1604i	0.00495096	+	0.0312591i
$454$	490.418	−	193.614i	1.08022	−	0.426463i
$455$	13.9258	+	79.5174i	0.0306061	+	0.174763i
$456$	−20.6721	+	43.5972i	−0.0453336	+	0.0956078i
$457$	−4.83879	+	30.5509i	−0.0105882	+	0.0668510i	−0.992417	−	0.122919i	$-0.960774\pi$
$457$	−4.83879	+	30.5509i	−0.0105882	+	0.0668510i	0.981829	+	0.189770i	$0.0607743\pi$
$458$	592.687	−	131.871i	1.29408	−	0.287928i
$459$	−85.0978	−	27.6500i	−0.185398	−	0.0602396i
$460$	315.429	+	55.4992i	0.685715	+	0.120650i
$461$		−	179.473i		−	0.389313i	−0.980871	−	0.194656i	$-0.937641\pi$
$461$		−	179.473i		−	0.389313i	0.980871	−	0.194656i	$-0.0623592\pi$
$462$	−7.72167	−	5.85203i	−0.0167136	−	0.0126667i
$463$	100.668	+	100.668i	0.217425	+	0.217425i	0.807412	−	0.589988i	$-0.200867\pi$
$463$	100.668	+	100.668i	0.217425	+	0.217425i	−0.589988	+	0.807412i	$0.700867\pi$
$464$	−62.8372	−	99.8793i	−0.135425	−	0.215257i
$465$	34.5005	−	11.8346i	0.0741947	−	0.0254508i
$466$	−73.3067	+	115.263i	−0.157310	+	0.247345i
$467$	−8.84081	+	55.8187i	−0.0189311	+	0.119526i	−0.995344	−	0.0963848i	$-0.969272\pi$
$467$	−8.84081	+	55.8187i	−0.0189311	+	0.119526i	0.976413	+	0.215911i	$0.0692721\pi$
$468$	86.7062	−	239.362i	0.185270	−	0.511457i
$469$	−17.6443	−	54.3035i	−0.0376210	−	0.115786i
$470$	49.5485	−	11.8747i	0.105422	−	0.0252653i
$471$	−26.1192	+	35.9500i	−0.0554547	+	0.0763269i
$472$	−502.027	−	147.455i	−1.06362	−	0.312405i
$473$	−332.090	−	285.655i	−0.702093	−	0.603921i
$474$	−1.30854	+	1.08036i	−0.00276064	+	0.00227924i
$475$	614.519	−	477.818i	1.29373	−	1.00593i
$476$	113.073	−	204.727i	0.237548	−	0.430099i
$477$	345.524	−	678.129i	0.724369	−	1.42165i
$478$	127.299	+	215.734i	0.266316	+	0.451326i
$479$	−81.5851	−	112.292i	−0.170324	−	0.234431i	0.715319	−	0.698798i	$-0.246282\pi$
$479$	−81.5851	−	112.292i	−0.170324	−	0.234431i	−0.885642	+	0.464368i	$0.846282\pi$
$480$	−14.3836	−	27.4521i	−0.0299659	−	0.0571918i
$481$	−254.262	−	82.6147i	−0.528611	−	0.171756i
$482$	210.244	−	238.005i	0.436192	−	0.493786i
$483$	−4.98676	+	4.98676i	−0.0103246	+	0.0103246i
$484$	−130.850	−	465.977i	−0.270351	−	0.962762i
$485$	−91.8553	+	69.0506i	−0.189392	+	0.142372i
$486$	5.78655	+	93.4365i	0.0119065	+	0.192256i
$487$	358.293	+	703.189i	0.735714	+	1.44392i	0.890031	+	0.455899i	$0.150682\pi$
$487$	358.293	+	703.189i	0.735714	+	1.44392i	−0.154317	+	0.988021i	$0.549318\pi$
$488$	−715.345	+	20.3744i	−1.46587	+	0.0417509i
$489$	18.9735	+	26.1147i	0.0388005	+	0.0534043i
$490$	−405.010	+	167.572i	−0.826552	+	0.341984i
$491$	102.689	+	316.043i	0.209142	+	0.643672i	0.999518	+	0.0310500i	$0.00988512\pi$
$491$	102.689	+	316.043i	0.209142	+	0.643672i	−0.790376	+	0.612622i	$0.790115\pi$
$492$	2.48424	+	8.61383i	0.00504927	+	0.0175078i
$493$	−187.329	+	29.6699i	−0.379977	+	0.0601824i
$494$	−341.019	+	281.552i	−0.690321	+	0.569944i
$495$	32.3927	−	491.871i	0.0654399	−	0.993679i
$496$	224.014	−	559.374i	0.451641	−	1.12777i
$497$	264.327	−	41.8653i	0.531845	−	0.0842359i
$498$	1.40584	−	3.23998i	0.00282297	−	0.00650599i
$499$	293.897	+	904.522i	0.588972	+	1.81267i	0.582697	+	0.812689i	$0.301997\pi$
$499$	293.897	+	904.522i	0.588972	+	1.81267i	0.00627467	+	0.999980i	$0.498003\pi$
$500$	7.74740	+	499.940i	0.0154948	+	0.999880i
$501$	−26.7618	−	36.8344i	−0.0534167	−	0.0735218i
$502$	−272.016	+	60.5227i	−0.541864	+	0.120563i
$503$	31.6543	+	62.1251i	0.0629310	+	0.123509i	0.920329	−	0.391144i	$-0.127921\pi$
$503$	31.6543	+	62.1251i	0.0629310	+	0.123509i	−0.857398	+	0.514653i	$0.827921\pi$
$504$	−161.670	−	20.9070i	−0.320773	−	0.0414821i
$505$	311.114	+	44.0931i	0.616067	+	0.0873131i
$506$	−349.006	+	48.0722i	−0.689736	+	0.0950044i
$507$	16.2403	−	16.2403i	0.0320321	−	0.0320321i
$508$	−5.43736	+	162.847i	−0.0107035	+	0.320564i
$509$	−563.435	−	183.071i	−1.10695	−	0.359668i	−0.302174	−	0.953253i	$-0.597712\pi$
$509$	−563.435	−	183.071i	−1.10695	−	0.359668i	−0.804772	+	0.593584i	$0.797712\pi$
$510$	−49.6614	+	3.88856i	−0.0973752	+	0.00762463i
$511$	127.240	+	175.130i	0.249001	+	0.342721i
$512$	−498.664	−	116.094i	−0.973954	−	0.226747i
$513$	49.1835	−	96.5280i	0.0958743	−	0.188164i
$514$	−451.683	+	178.322i	−0.878760	+	0.346929i
$515$	553.936	−	9.02487i	1.07560	−	0.0175240i
$516$	30.2963	+	5.84093i	0.0587138	+	0.0113196i
$517$	−47.8902	+	29.1163i	−0.0926310	+	0.0563178i
$518$	−16.2775	+	170.414i	−0.0314237	+	0.328985i
$519$	−7.32759	+	10.0856i	−0.0141187	+	0.0194327i
$520$	−12.7114	−	283.769i	−0.0244450	−	0.545709i
$521$	−15.6806	−	48.2599i	−0.0300971	−	0.0926294i	0.934880	−	0.354965i	$-0.115507\pi$
$521$	−15.6806	−	48.2599i	−0.0300971	−	0.0926294i	−0.964977	+	0.262336i	$0.915507\pi$
$522$	67.1829	+	113.855i	0.128703	+	0.218112i
$523$	3.90126	−	24.6316i	0.00745939	−	0.0470967i	−0.983678	−	0.179938i	$-0.942410\pi$
$523$	3.90126	−	24.6316i	0.00745939	−	0.0470967i	0.991137	+	0.132842i	$0.0424102\pi$
$524$	97.9837	+	788.047i	0.186992	+	1.50391i
$525$	−9.11325	−	6.17784i	−0.0173586	−	0.0117673i
$526$	146.839	−	9.09376i	0.279161	−	0.0172885i
$527$	−684.831	−	684.831i	−1.29949	−	1.29949i
$528$	24.3047	+	23.9059i	0.0460317	+	0.0452763i
$529$		−	272.561i		−	0.515239i
$530$	66.9631	−	846.542i	0.126345	−	1.59725i
$531$	557.495	+	181.141i	1.04990	+	0.341132i
$532$	223.408	+	173.996i	0.419940	+	0.327060i
$533$	−12.8537	+	81.1550i	−0.0241158	+	0.152261i
$534$	2.80654	−	10.8864i	0.00525570	−	0.0203866i
$535$	−738.192	−	518.167i	−1.37980	−	0.968537i
$536$	37.0659	+	197.460i	0.0691528	+	0.368396i
$537$	6.67955	+	42.1730i	0.0124386	+	0.0785344i
$538$	58.4906	−	612.356i	0.108719	−	1.13821i
$539$	367.719	−	311.834i	0.682224	−	0.578543i
$540$	30.5278	+	62.5329i	0.0565329	+	0.115802i
$541$	404.397	−	556.605i	0.747499	−	1.02884i	−0.250653	−	0.968077i	$-0.580645\pi$
$541$	404.397	−	556.605i	0.747499	−	1.02884i	0.998152	−	0.0607674i	$-0.0193548\pi$
$542$	378.060	−	871.300i	0.697528	−	1.60756i
$543$	2.28794	−	4.49034i	0.00421352	−	0.00826950i
$544$	−486.968	+	663.390i	−0.895162	+	1.21947i
$545$	−65.5491	−	123.626i	−0.120274	−	0.226838i
$546$	5.27779	+	3.35665i	0.00966628	+	0.00614771i
$547$	−41.6689	+	21.2314i	−0.0761771	+	0.0388142i	−0.491664	−	0.870785i	$-0.663611\pi$
$547$	−41.6689	+	21.2314i	−0.0761771	+	0.0388142i	0.415487	+	0.909599i	$0.363611\pi$
$548$	11.7506	−	351.925i	0.0214426	−	0.642199i
$549$	801.733			1.46035
$550$	−176.422	−	520.937i	−0.320768	−	0.947158i
$551$		−	229.638i		−	0.416767i
$552$	19.6522	−	15.1514i	0.0356019	−	0.0274483i
$553$	4.52121	+	8.87338i	0.00817579	+	0.0160459i
$554$	65.9964	+	41.9734i	0.119127	+	0.0757643i
$555$	32.2135	−	17.0802i	0.0580424	−	0.0307752i
$556$	−375.265	−	801.555i	−0.674937	−	1.44165i
$557$	−217.761	−	110.955i	−0.390954	−	0.199201i	0.247453	−	0.968900i	$-0.420406\pi$
$557$	−217.761	−	110.955i	−0.390954	−	0.199201i	−0.638407	+	0.769699i	$0.720406\pi$
$558$	−268.705	+	619.274i	−0.481550	+	1.10981i
$559$	228.782	+	166.220i	0.409270	+	0.297352i
$560$	−175.600	+	47.4090i	−0.313571	+	0.0846589i
$561$	50.6970	−	20.7911i	0.0903691	−	0.0370608i
$562$	−48.7169	+	510.033i	−0.0866849	+	0.907532i
$563$	−338.206	+	53.5666i	−0.600722	+	0.0951450i	−0.449386	−	0.893338i	$-0.648357\pi$
$563$	−338.206	+	53.5666i	−0.600722	+	0.0951450i	−0.151335	+	0.988482i	$0.548357\pi$
$564$	1.90861	−	3.45568i	0.00338406	−	0.00612710i
$565$	287.415	−	409.457i	0.508699	−	0.724703i
$566$	100.531	−	389.954i	0.177616	−	0.688965i
$567$	179.622	+	28.4493i	0.316793	+	0.0501751i
$568$	−941.289	+	26.8098i	−1.65720	+	0.0472003i
$569$	178.507	−	549.387i	0.313720	−	0.965532i	−0.662558	−	0.749011i	$-0.730529\pi$
$569$	178.507	−	549.387i	0.313720	−	0.965532i	0.976278	−	0.216521i	$-0.0694709\pi$
$570$	4.75596	−	60.1245i	0.00834380	−	0.105482i
$571$	−70.5079			−0.123482			−0.0617408	−	0.998092i	$-0.519665\pi$
$571$	−70.5079			−0.123482			−0.0617408	+	0.998092i	$0.519665\pi$
$572$	108.845	+	292.888i	0.190288	+	0.512041i
$573$	−15.2944	+	15.2944i	−0.0266919	+	0.0266919i
$574$	52.5130	−	3.25214i	0.0914860	−	0.00566576i
$575$	−393.164	+	75.4751i	−0.683763	+	0.131261i
$576$	554.729	+	145.914i	0.963072	+	0.253324i
$577$	345.481	+	54.7188i	0.598754	+	0.0948333i	0.448452	−	0.893807i	$-0.351976\pi$
$577$	345.481	+	54.7188i	0.598754	+	0.0948333i	0.150302	+	0.988640i	$0.451976\pi$
$578$	378.456	+	641.368i	0.654768	+	1.10963i
$579$	51.5663	−	16.7549i	0.0890609	−	0.0289376i
$580$	117.833	+	88.7257i	0.203160	+	0.152975i
$581$	−16.7691	−	12.1835i	−0.0288625	−	0.0209698i
$582$	−0.846593	+	8.86325i	−0.00145463	+	0.0152290i
$583$	214.871	+	909.056i	0.368561	+	1.55927i
$584$	−364.985	−	668.556i	−0.624974	−	1.14479i
$585$	5.18396	+	318.185i	0.00886147	+	0.543907i
$586$	−148.406	+	58.5900i	−0.253253	+	0.0999830i
$587$	−759.533	−	387.001i	−1.29392	−	0.659287i	−0.334803	−	0.942288i	$-0.608670\pi$
$587$	−759.533	−	387.001i	−1.29392	−	0.659287i	−0.959119	+	0.283002i	$0.908670\pi$
$588$	−11.5662	+	31.9298i	−0.0196704	+	0.0543024i
$589$	948.673	−	689.251i	1.61065	−	1.17021i
$590$	652.047	−	51.0563i	1.10516	−	0.0865361i
$591$	17.7643	−	54.6729i	0.0300580	−	0.0925091i
$592$	133.705	−	587.332i	0.225853	−	0.992116i
$593$	−451.636	−	451.636i	−0.761612	−	0.761612i	0.215002	−	0.976614i	$-0.431024\pi$
$593$	−451.636	−	451.636i	−0.761612	−	0.761612i	−0.976614	+	0.215002i	$0.931024\pi$
$594$	−53.0214	−	55.2080i	−0.0892616	−	0.0929428i
$595$	−41.0233	+	289.454i	−0.0689467	+	0.486477i
$596$	124.145	+	132.721i	0.208297	+	0.222687i
$597$	0.737616	−	0.375834i	0.00123554	−	0.000629538i
$598$	222.008	−	49.3962i	0.371251	−	0.0826024i
$599$	−327.810	+	238.168i	−0.547262	+	0.397609i	−0.826775	−	0.562533i	$-0.809827\pi$
$599$	−327.810	+	238.168i	−0.547262	+	0.397609i	0.279513	+	0.960142i	$0.409827\pi$
$600$	29.0138	+	25.6708i	0.0483563	+	0.0427847i
$601$	57.7582	−	18.7668i	0.0961035	−	0.0312259i	−0.260571	−	0.965455i	$-0.583911\pi$
$601$	57.7582	−	18.7668i	0.0961035	−	0.0312259i	0.356674	+	0.934229i	$0.383911\pi$
$602$	72.0779	−	166.115i	0.119731	−	0.275939i
$603$	−35.2103	−	222.309i	−0.0583919	−	0.368672i
$604$	−290.710	−	56.0470i	−0.481308	−	0.0927931i
$605$	360.130	+	486.139i	0.595257	+	0.803536i
$606$	18.7741	−	15.5003i	0.0309804	−	0.0255781i
$607$	51.9395	+	327.933i	0.0855675	+	0.540252i	0.992815	+	0.119656i	$0.0381791\pi$
$607$	51.9395	+	327.933i	0.0855675	+	0.540252i	−0.907248	+	0.420596i	$0.861821\pi$
$608$	−701.087	−	707.995i	−1.15310	−	1.16447i
$609$	−3.08899	+	1.00367i	−0.00507223	+	0.00164807i
$610$	826.587	−	341.998i	1.35506	−	0.560653i
$611$	29.2721	−	21.2675i	0.0479086	−	0.0348076i
$612$	566.493	−	727.369i	0.925642	−	1.18851i
$613$	323.421	−	164.791i	0.527604	−	0.268827i	−0.169834	−	0.985473i	$-0.554323\pi$
$613$	323.421	−	164.791i	0.527604	−	0.268827i	0.697438	+	0.716645i	$0.254323\pi$
$614$	27.5093	+	444.198i	0.0448034	+	0.723449i
$615$	−6.73361	−	8.95745i	−0.0109490	−	0.0145650i
$616$	167.930	−	108.765i	0.272614	−	0.176566i
$617$	618.571	+	618.571i	1.00255	+	1.00255i	0.999997	+	0.00254996i	$0.000811679\pi$
$617$	618.571	+	618.571i	1.00255	+	1.00255i	0.00254996	+	0.999997i	$0.499188\pi$
$618$	28.4182	−	32.1704i	0.0459841	−	0.0520557i
$619$	27.1161	−	83.4547i	0.0438063	−	0.134822i	−0.926761	−	0.375651i	$-0.877419\pi$
$619$	27.1161	−	83.4547i	0.0438063	−	0.134822i	0.970568	+	0.240829i	$0.0774193\pi$
$620$	−12.8688	+	753.093i	−0.0207561	+	1.21467i
$621$	−45.0760	+	32.7496i	−0.0725862	+	0.0527369i
$622$	246.792	+	418.238i	0.396772	+	0.672408i
$623$	−58.7884	−	29.9542i	−0.0943634	−	0.0480805i
$624$	−16.9026	−	14.0951i	−0.0270876	−	0.0225883i
$625$	−231.432	−	580.572i	−0.370291	−	0.928916i
$626$	495.317	−	408.944i	0.791241	−	0.653266i
$627$	15.2609	+	64.5645i	0.0243396	+	0.102974i
$628$	−514.299	−	759.970i	−0.818948	−	1.21014i
$629$	−783.266	−	569.076i	−1.24526	−	0.904731i
$630$	198.159	−	47.4904i	0.314538	−	0.0753815i
$631$	−248.719	+	80.8136i	−0.394166	+	0.128072i	−0.499392	−	0.866376i	$-0.666443\pi$
$631$	−248.719	+	80.8136i	−0.394166	+	0.128072i	0.105226	+	0.994448i	$0.466443\pi$
$632$	−11.7729	−	33.0049i	−0.0186281	−	0.0522229i
$633$	−56.0813	−	8.88241i	−0.0885961	−	0.0140322i
$634$	118.519	−	186.352i	0.186938	−	0.293930i
$635$	−66.0852	−	192.652i	−0.104071	−	0.303390i
$636$	−44.9456	−	48.0507i	−0.0706692	−	0.0755514i
$637$	−220.092	+	220.092i	−0.345513	+	0.345513i
$638$	−153.267	−	53.2455i	−0.240230	−	0.0834568i
$639$	1054.96			1.65096
$640$	634.169	−	86.1953i	0.990889	−	0.134680i
$641$	−82.0489	+	252.521i	−0.128001	+	0.393948i	−0.994436	−	0.105343i	$-0.966406\pi$
$641$	−82.0489	+	252.521i	−0.128001	+	0.393948i	0.866435	+	0.499291i	$0.166406\pi$
$642$	−68.2113	+	15.1768i	−0.106248	+	0.0236399i
$643$	−985.880	−	156.148i	−1.53325	−	0.242843i	−0.667992	−	0.744169i	$-0.732846\pi$
$643$	−985.880	−	156.148i	−1.53325	−	0.242843i	−0.865259	+	0.501326i	$0.832846\pi$
$644$	−61.7495	−	131.895i	−0.0958844	−	0.204806i
$645$	−37.9896	+	6.65307i	−0.0588986	+	0.0103148i
$646$	−1489.60	+	588.085i	−2.30588	+	0.910348i
$647$	1241.94	−	196.705i	1.91954	−	0.304026i	0.922841	−	0.385182i	$-0.125861\pi$
$647$	1241.94	−	196.705i	1.91954	−	0.304026i	0.996701	+	0.0811567i	$0.0258614\pi$
$648$	−613.971	−	180.335i	−0.947486	−	0.278295i
$649$	−665.646	+	272.984i	−1.02565	+	0.420623i
$650$	141.074	+	325.838i	0.217037	+	0.501289i
$651$	−13.4178	−	9.74861i	−0.0206111	−	0.0149748i
$652$	−640.484	+	184.717i	−0.982338	+	0.283308i
$653$	−687.479	−	350.288i	−1.05280	−	0.536429i	−0.160111	−	0.987099i	$-0.551185\pi$
$653$	−687.479	−	350.288i	−1.05280	−	0.536429i	−0.892691	+	0.450670i	$0.851185\pi$
$654$	−10.4985	−	2.70652i	−0.0160527	−	0.00413841i
$655$	−464.999	−	876.993i	−0.709922	−	1.33892i
$656$	−184.717	−	12.3490i	−0.281581	−	0.0188247i
$657$	387.406	+	760.328i	0.589660	+	1.15727i
$658$	−17.3640	−	15.3387i	−0.0263890	−	0.0233111i
$659$			28.3528i			0.0430239i	0.999769	+	0.0215120i	$0.00684800\pi$
$659$			28.3528i			0.0430239i	−0.999769	+	0.0215120i	$0.993152\pi$
$660$	−39.0260	−	17.1151i	−0.0591303	−	0.0259320i
$661$	−350.742			−0.530623			−0.265312	−	0.964163i	$-0.585475\pi$
$661$	−350.742			−0.530623			−0.265312	+	0.964163i	$0.585475\pi$
$662$	−611.050	+	691.732i	−0.923036	+	1.04491i
$663$	−31.5186	+	16.0595i	−0.0475393	+	0.0242225i
$664$	53.0196	+	50.0830i	0.0798488	+	0.0754262i
$665$	−338.376	−	103.882i	−0.508837	−	0.156214i
$666$	−168.464	+	653.463i	−0.252949	+	0.981176i
$667$	−53.6175	+	105.230i	−0.0803861	+	0.157767i
$668$	903.393	−	260.540i	1.35239	−	0.390030i
$669$	2.31895	−	3.19177i	0.00346630	−	0.00477095i
$670$	−131.133	−	214.181i	−0.195721	−	0.319673i
$671$	−750.478	+	636.424i	−1.11845	+	0.948471i
$672$	−6.45940	+	12.5251i	−0.00961221	+	0.0186385i
$673$	124.642	+	786.957i	0.185203	+	1.16933i	0.888653	+	0.458581i	$0.151642\pi$
$673$	124.642	+	786.957i	0.185203	+	1.16933i	−0.703450	+	0.710745i	$0.748358\pi$
$674$	273.533	+	692.851i	0.405836	+	1.02797i
$675$	−63.4775	−	59.4702i	−0.0940407	−	0.0881041i
$676$	201.099	+	429.541i	0.297483	+	0.635415i
$677$	−81.9369	+	517.329i	−0.121029	+	0.764149i	0.850280	+	0.526330i	$0.176432\pi$
$677$	−81.9369	+	517.329i	−0.121029	+	0.764149i	−0.971309	+	0.237819i	$0.923568\pi$
$678$	−8.41822	−	37.8352i	−0.0124163	−	0.0558041i
$679$	49.6963	+	16.1473i	0.0731904	+	0.0237810i
$680$	273.778	−	991.568i	0.402615	−	1.45819i
$681$			51.0645i			0.0749846i
$682$	−240.059	−	792.984i	−0.351993	−	1.16273i
$683$	−496.011	−	496.011i	−0.726223	−	0.726223i	0.243642	−	0.969865i	$-0.421658\pi$
$683$	−496.011	−	496.011i	−0.726223	−	0.726223i	−0.969865	+	0.243642i	$0.921658\pi$
$684$	762.534	+	815.214i	1.11482	+	1.19183i
$685$	142.815	+	416.337i	0.208490	+	0.607792i
$686$	356.184	+	226.532i	0.519219	+	0.330221i
$687$	−9.19920	+	58.0814i	−0.0133904	+	0.0845436i
$688$	−326.487	+	547.149i	−0.474545	+	0.795275i
$689$	−186.348	−	573.521i	−0.270462	−	0.832396i
$690$	−16.2177	+	26.4412i	−0.0235039	+	0.0383206i
$691$	311.925	−	429.328i	0.451411	−	0.621315i	−0.521289	−	0.853380i	$-0.674548\pi$
$691$	311.925	−	429.328i	0.451411	−	0.621315i	0.972700	+	0.232066i	$0.0745485\pi$
$692$	−144.284	−	213.205i	−0.208503	−	0.308100i
$693$	−191.527	+	116.445i	−0.276374	+	0.168030i
$694$	−181.938	−	220.364i	−0.262158	−	0.317528i
$695$	794.921	+	769.434i	1.14377	+	1.10710i
$696$	11.2323	−	2.10845i	0.0161383	−	0.00302938i
$697$	−135.089	+	265.126i	−0.193814	+	0.380382i
$698$	142.038	−	83.8133i	0.203493	−	0.120076i
$699$	−7.77620	−	10.7030i	−0.0111247	−	0.0153119i
$700$	184.043	−	133.492i	0.262919	−	0.190703i
$701$	1227.00	+	398.675i	1.75035	+	0.568724i	0.996130	−	0.0878958i	$-0.0280143\pi$
$701$	1227.00	+	398.675i	1.75035	+	0.568724i	0.754222	+	0.656620i	$0.228014\pi$
$702$	37.0353	+	32.7156i	0.0527568	+	0.0466034i
$703$	828.890	−	828.890i	1.17908	−	1.17908i
$704$	−635.093	+	303.764i	−0.902121	+	0.431482i
$705$	−0.692452	+	4.88583i	−0.000982201	+	0.00693026i
$706$	85.0684	−	5.26831i	0.120493	−	0.00746219i
$707$	−64.8675	−	127.310i	−0.0917503	−	0.180070i
$708$	31.1377	−	39.9803i	0.0439798	−	0.0564694i
$709$	−250.228	−	344.410i	−0.352932	−	0.485769i	0.595231	−	0.803555i	$-0.297061\pi$
$709$	−250.228	−	344.410i	−0.352932	−	0.485769i	−0.948162	+	0.317786i	$0.897061\pi$
$710$	1087.67	−	450.020i	1.53193	−	0.633831i
$711$	12.1313	+	37.3362i	0.0170623	+	0.0525123i
$712$	191.631	+	131.058i	0.269144	+	0.184070i
$713$	−595.654	+	94.3423i	−0.835419	+	0.132317i
$714$	14.4212	+	17.4671i	0.0201977	+	0.0244637i
$715$	−257.431	−	293.729i	−0.360044	−	0.410809i
$716$	−865.804	−	166.921i	−1.20922	−	0.233130i
$717$	−23.9615	+	3.79512i	−0.0334191	+	0.00529306i
$718$	1046.56	+	454.106i	1.45760	+	0.632459i
$719$	−256.842	−	790.478i	−0.357221	−	1.09941i	−0.954710	−	0.297536i	$-0.903835\pi$
$719$	−256.842	−	790.478i	−0.357221	−	1.09941i	0.597489	−	0.801877i	$-0.296165\pi$
$720$	−712.927	+	76.2990i	−0.990177	+	0.105971i
$721$	−148.074	−	203.806i	−0.205373	−	0.282671i
$722$	−264.321	−	1187.97i	−0.366095	−	1.64539i
$723$	13.9631	+	27.4042i	0.0193127	+	0.0379034i
$724$	71.0924	+	76.0038i	0.0981939	+	0.104978i
$725$	−177.116	−	51.2333i	−0.244299	−	0.0706666i
$726$	46.6306	+	4.78479i	0.0642295	+	0.00659062i
$727$	−982.763	+	982.763i	−1.35181	+	1.35181i	−0.468165	+	0.883641i	$0.655085\pi$
$727$	−982.763	+	982.763i	−1.35181	+	1.35181i	−0.883641	+	0.468165i	$0.844915\pi$
$728$	−102.292	+	78.8650i	−0.140511	+	0.108331i
$729$	676.038	+	219.658i	0.927350	+	0.301314i
$730$	723.752	+	618.641i	0.991441	+	0.847453i
$731$	601.949	+	828.512i	0.823460	+	1.13339i
$732$	23.6055	−	65.1656i	0.0322480	−	0.0890241i
$733$	−502.392	+	986.000i	−0.685392	+	1.34516i	0.241711	+	0.970348i	$0.422291\pi$
$733$	−502.392	+	986.000i	−0.685392	+	1.34516i	−0.927102	+	0.374808i	$0.877709\pi$
$734$	440.470	+	1115.70i	0.600096	+	1.52002i
$735$	−0.691517	−	42.4445i	−0.000940839	−	0.0577476i
$736$	155.961	+	488.128i	0.211903	+	0.663218i
$737$	209.431	+	180.147i	0.284166	+	0.244432i
$738$	206.463	+	19.7208i	0.279760	+	0.0267219i
$739$	−175.238	+	241.195i	−0.237129	+	0.326380i	−0.910952	−	0.412513i	$-0.864651\pi$
$739$	−175.238	+	241.195i	−0.237129	+	0.326380i	0.673823	+	0.738893i	$0.264651\pi$
$740$	105.064	+	745.583i	0.141978	+	1.00754i
$741$	−13.2351	−	40.7336i	−0.0178612	−	0.0549711i
$742$	−332.560	+	196.235i	−0.448194	+	0.264468i
$743$	−118.462	+	747.939i	−0.159437	+	1.00665i	0.770101	+	0.637922i	$0.220206\pi$
$743$	−118.462	+	747.939i	−0.159437	+	1.00665i	−0.929538	+	0.368725i	$0.879794\pi$
$744$	42.4236	+	40.0739i	0.0570210	+	0.0538628i
$745$	−204.060	−	99.8204i	−0.273906	−	0.133987i
$746$	−84.6224	−	1366.41i	−0.113435	−	1.83165i
$747$	−57.7769	−	57.7769i	−0.0773452	−	0.0773452i
$748$	47.1156	+	1130.56i	0.0629887	+	1.51144i
$749$			410.110i			0.547544i
$750$	−45.3120	−	17.0822i	−0.0604160	−	0.0227763i
$751$	1050.85	+	341.442i	1.39927	+	0.454649i	0.908954	−	0.416897i	$-0.136882\pi$
$751$	1050.85	+	341.442i	1.39927	+	0.454649i	0.490313	+	0.871546i	$0.336882\pi$
$752$	53.6715	+	61.3619i	0.0713717	+	0.0815982i
$753$	4.22200	−	26.6567i	0.00560691	−	0.0354006i
$754$	101.430	+	26.1488i	0.134522	+	0.0346800i
$755$	364.532	−	63.8399i	0.482823	−	0.0845562i
$756$	15.2981	−	27.6984i	0.0202356	−	0.0366381i
$757$	212.673	+	1342.77i	0.280942	+	1.77380i	0.575141	+	0.818054i	$0.304947\pi$
$757$	212.673	+	1342.77i	0.280942	+	1.77380i	−0.294199	+	0.955744i	$0.595053\pi$
$758$	−1065.57	−	101.780i	−1.40576	−	0.134275i
$759$	8.08173	−	33.1495i	0.0106479	−	0.0436752i
$760$	1133.92	+	515.209i	1.49200	+	0.677906i
$761$	−23.9787	+	33.0039i	−0.0315095	+	0.0433691i	−0.824481	−	0.565890i	$-0.808533\pi$
$761$	−23.9787	+	33.0039i	−0.0315095	+	0.0433691i	0.792972	+	0.609259i	$0.208533\pi$
$762$	−14.4765	−	6.28139i	−0.0189980	−	0.00824330i
$763$	−28.8867	+	56.6933i	−0.0378593	+	0.0743031i
$764$	−189.386	−	404.524i	−0.247888	−	0.529481i
$765$	−338.219	+	1101.68i	−0.442116	+	1.44011i
$766$	307.390	−	483.321i	0.401292	−	0.630967i
$767$	413.835	−	210.859i	0.539550	−	0.274914i
$768$	28.1930	−	40.7927i	0.0367097	−	0.0531155i
$769$	−1032.44			−1.34257

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+(-1.49892 - 1.32409i) q^{2} +(0.172588 - 0.0879380i) q^{3} +(0.493549 + 3.96943i) q^{4} +(-2.34222 - 4.41746i) q^{5} +(-0.375135 - 0.0967104i) q^{6} +(-1.03219 + 2.02578i) q^{7} +(4.51611 - 6.60339i) q^{8} +(-5.26801 + 7.25080i) q^{9} +(-2.33832 + 9.72277i) q^{10} +(-0.824530 - 10.9691i) q^{11} +(0.434245 + 0.641675i) q^{12} +(1.11089 + 7.01390i) q^{13} +(4.22950 - 1.66978i) q^{14} +(-0.792703 - 0.556431i) q^{15} +(-15.5128 + 3.91822i) q^{16} +(-4.02299 + 25.4001i) q^{17} +(17.4971 - 3.89305i) q^{18} +(-29.6130 - 9.62185i) q^{19} +(16.3788 - 11.4775i) q^{20} +0.440395i q^{21} +(-13.2882 + 17.5335i) q^{22} +(11.3234 + 11.3234i) q^{23} +(0.198738 - 1.53680i) q^{24} +(-14.0280 + 20.6934i) q^{25} +(7.62192 - 11.9842i) q^{26} +(-0.544288 + 3.43650i) q^{27} +(-8.55065 - 3.09738i) q^{28} +(2.27903 + 7.01414i) q^{29} +(0.451435 + 1.88366i) q^{30} +(-22.1361 + 30.4677i) q^{31} +(28.4406 + 14.6673i) q^{32} +(-1.10690 - 1.82062i) q^{33} +(39.6623 - 32.7461i) q^{34} +(11.3664 - 0.185185i) q^{35} +(-31.3816 - 17.3324i) q^{36} +(-17.0916 + 33.5441i) q^{37} +(31.6474 + 53.6329i) q^{38} +(0.808515 + 1.11283i) q^{39} +(-39.7480 - 4.48314i) q^{40} +(11.0043 + 3.57551i) q^{41} +(0.583124 - 0.660118i) q^{42} +(28.1585 - 28.1585i) q^{43} +(43.1340 - 8.68669i) q^{44} +(44.3690 + 6.28826i) q^{45} +(-1.97967 - 31.9662i) q^{46} +(-2.31315 - 4.53981i) q^{47} +(-2.33277 + 2.04040i) q^{48} +(25.7631 + 35.4599i) q^{49} +(48.4269 - 12.4435i) q^{50} +(1.53932 + 4.73753i) q^{51} +(-27.2929 + 7.87132i) q^{52} +(-83.8731 + 13.2842i) q^{53} +(5.36609 - 4.43036i) q^{54} +(-46.5242 + 29.3343i) q^{55} +(8.71556 + 15.9646i) q^{56} +(-5.95698 + 0.943493i) q^{57} +(5.87128 - 13.5313i) q^{58} +(-20.2110 - 62.2032i) q^{59} +(1.81748 - 3.42121i) q^{60} +(-52.5800 - 72.3701i) q^{61} +(73.5225 - 16.3585i) q^{62} +(-9.25096 - 18.1560i) q^{63} +(-23.2095 - 59.6433i) q^{64} +(28.3817 - 21.3355i) q^{65} +(-0.751512 + 4.19461i) q^{66} +(-17.7580 + 17.7580i) q^{67} +(-102.810 - 3.43276i) q^{68} +(2.95004 + 0.958526i) q^{69} +(-17.2826 - 14.7727i) q^{70} +(-69.1875 - 95.2285i) q^{71} +(24.0889 + 67.5322i) q^{72} +(43.2254 - 84.8345i) q^{73} +(70.0346 - 27.6492i) q^{74} +(-0.601326 + 4.80502i) q^{75} +(23.5778 - 122.296i) q^{76} +(23.0720 + 9.65181i) q^{77} +(0.261583 - 2.73859i) q^{78} +(2.57463 - 3.54367i) q^{79} +(53.6431 + 59.3500i) q^{80} +(-24.7178 - 76.0735i) q^{81} +(-11.7603 - 19.9301i) q^{82} +(-1.42618 + 9.00452i) q^{83} +(-1.74812 + 0.217356i) q^{84} +(121.627 - 41.7214i) q^{85} +(-79.4920 + 4.92297i) q^{86} +(1.01014 + 1.01014i) q^{87} +(-76.1566 - 44.0928i) q^{88} +29.0201i q^{89} +(-58.1795 - 68.1744i) q^{90} +(-15.3553 - 4.98924i) q^{91} +(-39.3588 + 50.5361i) q^{92} +(-1.14115 + 7.20497i) q^{93} +(-2.54390 + 9.86767i) q^{94} +(26.8561 + 153.351i) q^{95} +(6.19833 + 0.0303891i) q^{96} +(-3.59532 - 22.7000i) q^{97} +(8.33525 - 87.2644i) q^{98} +(83.8780 + 51.8066i) 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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