LMFDB - Embedded newform 153.3.t.a.7.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(7,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([32, 33])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.t (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$34$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	153.7
Dual form			153.3.t.a.22.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.30425 - 3.00295i) q^{2} +(1.06273 + 2.80546i) q^{3} +(-2.67290 + 9.97539i) q^{4} +(1.79172 - 1.57130i) q^{5} +(5.97588 - 9.65580i) q^{6} +(-7.21963 - 6.33144i) q^{7} +(22.1266 - 9.16514i) q^{8} +(-6.74122 + 5.96288i) q^{9} +(-8.84710 - 1.75980i) q^{10} +(0.768195 + 11.7204i) q^{11} +(-30.8261 + 3.10242i) q^{12} +(-15.8817 - 4.25549i) q^{13} +(-2.37722 + 36.2694i) q^{14} +(6.31232 + 3.35674i) q^{15} +(-42.7329 - 24.6719i) q^{16} +(-16.1465 - 5.31879i) q^{17} +(33.4397 + 6.50361i) q^{18} +(-10.8319 + 26.1505i) q^{19} +(10.8852 + 22.0730i) q^{20} +(10.0901 - 26.9830i) q^{21} +(33.4257 - 29.3135i) q^{22} +(3.65244 - 7.40642i) q^{23} +(49.2270 + 52.3353i) q^{24} +(-2.52187 + 19.1555i) q^{25} +(23.8163 + 57.4977i) q^{26} +(-23.8927 - 12.5753i) q^{27} +(82.4560 - 55.0953i) q^{28} +(6.77629 - 19.9623i) q^{29} +(-4.46501 - 26.6904i) q^{30} +(-0.305293 + 4.65787i) q^{31} +(11.8745 + 90.1959i) q^{32} +(-32.0647 + 14.6107i) q^{33} +(21.2335 + 60.7431i) q^{34} -22.8841 q^{35} +(-41.4635 - 83.1845i) q^{36} +(-15.7423 + 23.5601i) q^{37} +(103.488 - 27.7296i) q^{38} +(-4.93932 - 49.0779i) q^{39} +(25.2435 - 51.1888i) q^{40} +(-10.7980 + 3.66544i) q^{41} +(-104.279 + 31.8753i) q^{42} +(-43.7884 - 5.76485i) q^{43} +(-118.969 - 23.6644i) q^{44} +(-2.70892 + 21.2763i) q^{45} +(-30.6573 + 6.09811i) q^{46} +(-7.30979 - 27.2805i) q^{47} +(23.8025 - 146.105i) q^{48} +(5.64006 + 42.8405i) q^{49} +(63.3340 - 36.5659i) q^{50} +(-2.23772 - 50.9509i) q^{51} +(84.9003 - 147.052i) q^{52} +(-9.88153 + 23.8561i) q^{53} +(17.2917 + 100.725i) q^{54} +(19.7926 + 19.7926i) q^{55} +(-217.774 - 73.9245i) q^{56} +(-84.8756 - 2.59758i) q^{57} +(-75.5601 + 25.6492i) q^{58} +(90.8149 + 69.6848i) q^{59} +(-50.3570 + 53.9956i) q^{60} +(35.5239 - 40.5073i) q^{61} +(14.6908 - 9.81610i) q^{62} +(86.4227 - 0.368141i) q^{63} +(103.927 - 103.927i) q^{64} +(-35.1422 + 17.3302i) q^{65} +(117.760 + 62.6221i) q^{66} +(41.4543 - 23.9337i) q^{67} +(96.2151 - 146.851i) q^{68} +(24.6600 + 2.37577i) q^{69} +(52.7307 + 68.7200i) q^{70} +(11.7384 - 17.5678i) q^{71} +(-94.5097 + 193.723i) q^{72} +(-0.366976 - 1.84491i) q^{73} +(107.024 - 7.01472i) q^{74} +(-56.4200 + 13.2821i) q^{75} +(-231.909 - 177.950i) q^{76} +(68.6609 - 89.4807i) q^{77} +(-135.997 + 127.920i) q^{78} +(-5.03772 - 76.8607i) q^{79} +(-115.332 + 22.9410i) q^{80} +(9.88807 - 80.3942i) q^{81} +(35.8885 + 23.9799i) q^{82} +(37.3887 - 28.6893i) q^{83} +(242.196 + 172.776i) q^{84} +(-37.2875 + 15.8412i) q^{85} +(83.5877 + 144.778i) q^{86} +(63.2048 - 2.20388i) q^{87} +(124.417 + 252.292i) q^{88} +(-104.951 - 104.951i) q^{89} +(70.1337 - 40.8910i) q^{90} +(87.7165 + 131.277i) q^{91} +(64.1193 + 56.2311i) q^{92} +(-13.3919 + 4.09356i) q^{93} +(-65.0785 + 84.8120i) q^{94} +(21.6825 + 63.8745i) q^{95} +(-240.422 + 129.167i) q^{96} +(-36.8553 + 108.572i) q^{97} +(115.652 - 115.652i) q^{98} +(-75.0659 - 74.4291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) $ 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.30425	−	3.00295i	−1.15212	−	1.50148i	−0.832580	−	0.553905i	$-0.813137\pi$
$2$	−2.30425	−	3.00295i	−1.15212	−	1.50148i	−0.319544	−	0.947571i	$-0.603530\pi$
$3$	1.06273	+	2.80546i	0.354243	+	0.935154i
$3$	1.06273	+	2.80546i	0.354243	+	0.935154i
$4$	−2.67290	+	9.97539i	−0.668225	+	2.49385i
$5$	1.79172	−	1.57130i	0.358344	−	0.314259i	−0.461177	−	0.887308i	$-0.652573\pi$
$5$	1.79172	−	1.57130i	0.358344	−	0.314259i	0.819521	+	0.573049i	$0.194239\pi$
$6$	5.97588	−	9.65580i	0.995980	−	1.60930i
$7$	−7.21963	−	6.33144i	−1.03138	−	0.904492i	−0.0358852	−	0.999356i	$-0.511425\pi$
$7$	−7.21963	−	6.33144i	−1.03138	−	0.904492i	−0.995490	+	0.0948640i	$0.969758\pi$
$8$	22.1266	−	9.16514i	2.76583	−	1.14564i
$9$	−6.74122	+	5.96288i	−0.749024	+	0.662542i
$10$	−8.84710	−	1.75980i	−0.884710	−	0.175980i
$11$	0.768195	+	11.7204i	0.0698359	+	1.06549i	0.878663	+	0.477443i	$0.158436\pi$
$11$	0.768195	+	11.7204i	0.0698359	+	1.06549i	−0.808827	+	0.588047i	$0.799897\pi$
$12$	−30.8261	+	3.10242i	−2.56884	+	0.258535i
$13$	−15.8817	−	4.25549i	−1.22167	−	0.327345i	−0.410339	−	0.911933i	$-0.634589\pi$
$13$	−15.8817	−	4.25549i	−1.22167	−	0.327345i	−0.811330	+	0.584588i	$0.801256\pi$
$14$	−2.37722	+	36.2694i	−0.169802	+	2.59067i
$15$	6.31232	+	3.35674i	0.420821	+	0.223783i
$16$	−42.7329	−	24.6719i	−2.67081	−	1.54199i
$17$	−16.1465	−	5.31879i	−0.949796	−	0.312870i
$17$	−16.1465	−	5.31879i	−0.949796	−	0.312870i
$18$	33.4397	+	6.50361i	1.85776	+	0.361312i
$19$	−10.8319	+	26.1505i	−0.570100	+	1.37634i	0.331370	+	0.943501i	$0.392489\pi$
$19$	−10.8319	+	26.1505i	−0.570100	+	1.37634i	−0.901470	+	0.432842i	$0.857511\pi$
$20$	10.8852	+	22.0730i	0.544261	+	1.10365i
$21$	10.0901	−	26.9830i	0.480482	−	1.28490i
$22$	33.4257	−	29.3135i	1.51935	−	1.33243i
$23$	3.65244	−	7.40642i	0.158802	−	0.322018i	−0.802901	−	0.596112i	$-0.796711\pi$
$23$	3.65244	−	7.40642i	0.158802	−	0.322018i	0.961703	+	0.274094i	$0.0883780\pi$
$24$	49.2270	+	52.3353i	2.05113	+	2.18064i
$25$	−2.52187	+	19.1555i	−0.100875	+	0.766219i
$26$	23.8163	+	57.4977i	0.916012	+	2.21145i
$27$	−23.8927	−	12.5753i	−0.884915	−	0.465752i
$28$	82.4560	−	55.0953i	2.94486	−	1.96769i
$29$	6.77629	−	19.9623i	0.233665	−	0.688355i	−0.765334	−	0.643633i	$-0.777426\pi$
$29$	6.77629	−	19.9623i	0.233665	−	0.688355i	0.998999	−	0.0447223i	$-0.0142403\pi$
$30$	−4.46501	−	26.6904i	−0.148834	−	0.889679i
$31$	−0.305293	+	4.65787i	−0.00984815	+	0.150254i	0.990103	+	0.140344i	$0.0448210\pi$
$31$	−0.305293	+	4.65787i	−0.00984815	+	0.150254i	−0.999951	+	0.00990936i	$0.996846\pi$
$32$	11.8745	+	90.1959i	0.371079	+	2.81862i
$33$	−32.0647	+	14.6107i	−0.971658	+	0.442749i
$34$	21.2335	+	60.7431i	0.624516	+	1.78656i
$35$	−22.8841			−0.653832
$36$	−41.4635	−	83.1845i	−1.15176	−	2.31068i
$37$	−15.7423	+	23.5601i	−0.425468	+	0.636758i	−0.980833	−	0.194848i	$-0.937579\pi$
$37$	−15.7423	+	23.5601i	−0.425468	+	0.636758i	0.555365	+	0.831607i	$0.312579\pi$
$38$	103.488	−	27.7296i	2.72337	−	0.729726i
$39$	−4.93932	−	49.0779i	−0.126649	−	1.25841i
$40$	25.2435	−	51.1888i	0.631088	−	1.27972i
$41$	−10.7980	+	3.66544i	−0.263367	+	0.0894010i	−0.450000	−	0.893029i	$-0.648576\pi$
$41$	−10.7980	+	3.66544i	−0.263367	+	0.0894010i	0.186633	+	0.982430i	$0.440243\pi$
$42$	−104.279	+	31.8753i	−2.48283	+	0.758936i
$43$	−43.7884	−	5.76485i	−1.01833	−	0.134066i	−0.397169	−	0.917746i	$-0.630007\pi$
$43$	−43.7884	−	5.76485i	−1.01833	−	0.134066i	−0.621166	+	0.783679i	$0.713341\pi$
$44$	−118.969	−	23.6644i	−2.70384	−	0.537827i
$45$	−2.70892	+	21.2763i	−0.0601983	+	0.472806i
$46$	−30.6573	+	6.09811i	−0.666462	+	0.132568i
$47$	−7.30979	−	27.2805i	−0.155527	−	0.580436i	−0.999060	−	0.0433576i	$-0.986195\pi$
$47$	−7.30979	−	27.2805i	−0.155527	−	0.580436i	0.843532	−	0.537079i	$-0.180472\pi$
$48$	23.8025	−	146.105i	0.495885	−	3.04385i
$49$	5.64006	+	42.8405i	0.115103	+	0.874297i
$50$	63.3340	−	36.5659i	1.26668	−	0.731318i
$51$	−2.23772	−	50.9509i	−0.0438768	−	0.999037i
$52$	84.9003	−	147.052i	1.63270	−	2.82792i
$53$	−9.88153	+	23.8561i	−0.186444	+	0.450116i	−0.989270	−	0.146098i	$-0.953329\pi$
$53$	−9.88153	+	23.8561i	−0.186444	+	0.450116i	0.802826	+	0.596213i	$0.203329\pi$
$54$	17.2917	+	100.725i	0.320216	+	1.86528i
$55$	19.7926	+	19.7926i	0.359865	+	0.359865i
$56$	−217.774	−	73.9245i	−3.88883	−	1.32008i
$57$	−84.8756	−	2.59758i	−1.48905	−	0.0455717i
$58$	−75.5601	+	25.6492i	−1.30276	+	0.442228i
$59$	90.8149	+	69.6848i	1.53924	+	1.18110i	0.917411	+	0.397942i	$0.130275\pi$
$59$	90.8149	+	69.6848i	1.53924	+	1.18110i	0.621826	+	0.783156i	$0.286391\pi$
$60$	−50.3570	+	53.9956i	−0.839283	+	0.899927i
$61$	35.5239	−	40.5073i	0.582359	−	0.664054i	−0.383373	−	0.923594i	$-0.625238\pi$
$61$	35.5239	−	40.5073i	0.582359	−	0.664054i	0.965732	+	0.259540i	$0.0835709\pi$
$62$	14.6908	−	9.81610i	0.236949	−	0.158324i
$63$	86.4227	−	0.368141i	1.37179	−	0.00584351i
$64$	103.927	−	103.927i	1.62386	−	1.62386i
$65$	−35.1422	+	17.3302i	−0.540649	+	0.266619i
$66$	117.760	+	62.6221i	1.78425	+	0.948820i
$67$	41.4543	−	23.9337i	0.618721	−	0.357219i	−0.157650	−	0.987495i	$-0.550392\pi$
$67$	41.4543	−	23.9337i	0.618721	−	0.357219i	0.776371	+	0.630276i	$0.217058\pi$
$68$	96.2151	−	146.851i	1.41493	−	2.15958i
$69$	24.6600	+	2.37577i	0.357391	+	0.0344315i
$70$	52.7307	+	68.7200i	0.753295	+	0.981714i
$71$	11.7384	−	17.5678i	0.165330	−	0.247433i	−0.739549	−	0.673102i	$-0.764961\pi$
$71$	11.7384	−	17.5678i	0.165330	−	0.247433i	0.904879	+	0.425669i	$0.139961\pi$
$72$	−94.5097	+	193.723i	−1.31263	+	2.69059i
$73$	−0.366976	−	1.84491i	−0.00502707	−	0.0252728i	0.978190	−	0.207711i	$-0.0666012\pi$
$73$	−0.366976	−	1.84491i	−0.00502707	−	0.0252728i	−0.983217	+	0.182438i	$0.941601\pi$
$74$	107.024	−	7.01472i	1.44627	−	0.0947936i
$75$	−56.4200	+	13.2821i	−0.752267	+	0.177094i
$76$	−231.909	−	177.950i	−3.05144	−	2.34145i
$77$	68.6609	−	89.4807i	0.891700	−	1.16209i
$78$	−135.997	+	127.920i	−1.74355	+	1.64000i
$79$	−5.03772	−	76.8607i	−0.0637686	−	0.972921i	−0.903136	−	0.429356i	$-0.858741\pi$
$79$	−5.03772	−	76.8607i	−0.0637686	−	0.972921i	0.839367	−	0.543565i	$-0.182926\pi$
$80$	−115.332	+	22.9410i	−1.44165	+	0.286762i
$81$	9.88807	−	80.3942i	0.122075	−	0.992521i
$82$	35.8885	+	23.9799i	0.437665	+	0.292438i
$83$	37.3887	−	28.6893i	0.450466	−	0.345655i	−0.358480	−	0.933537i	$-0.616705\pi$
$83$	37.3887	−	28.6893i	0.450466	−	0.345655i	0.808946	+	0.587883i	$0.200038\pi$
$84$	242.196	+	172.776i	2.88329	+	2.05685i
$85$	−37.2875	+	15.8412i	−0.438676	+	0.186367i
$86$	83.5877	+	144.778i	0.971950	+	1.68347i
$87$	63.2048	−	2.20388i	0.726492	−	0.0253320i
$88$	124.417	+	252.292i	1.41383	+	2.86695i
$89$	−104.951	−	104.951i	−1.17922	−	1.17922i	−0.979942	−	0.199281i	$-0.936139\pi$
$89$	−104.951	−	104.951i	−1.17922	−	1.17922i	−0.199281	−	0.979942i	$-0.563861\pi$
$90$	70.1337	−	40.8910i	0.779263	−	0.454345i
$91$	87.7165	+	131.277i	0.963918	+	1.44261i
$92$	64.1193	+	56.2311i	0.696949	+	0.611208i
$93$	−13.3919	+	4.09356i	−0.143999	+	0.0440167i
$94$	−65.0785	+	84.8120i	−0.692325	+	0.902255i
$95$	21.6825	+	63.8745i	0.228237	+	0.672364i
$96$	−240.422	+	129.167i	−2.50439	+	1.34549i
$97$	−36.8553	+	108.572i	−0.379951	+	1.11930i	0.573875	+	0.818943i	$0.305439\pi$
$97$	−36.8553	+	108.572i	−0.379951	+	1.11930i	−0.953827	+	0.300358i	$0.902894\pi$
$98$	115.652	−	115.652i	1.18012	−	1.18012i
$99$	−75.0659	−	74.4291i	−0.758241	−	0.751809i
$100$	−184.343	−	76.3573i	−1.84343	−	0.763573i
$101$	20.8865	+	12.0588i	0.206797	+	0.119394i	0.599822	−	0.800133i	$-0.295238\pi$
$101$	20.8865	+	12.0588i	0.206797	+	0.119394i	−0.393025	+	0.919528i	$0.628571\pi$
$102$	−147.847	+	124.123i	−1.44948	+	1.21689i
$103$	26.0716	+	45.1574i	0.253122	+	0.438421i	0.964384	−	0.264507i	$-0.0852091\pi$
$103$	26.0716	+	45.1574i	0.253122	+	0.438421i	−0.711261	+	0.702928i	$0.751876\pi$
$104$	−390.410	+	51.3985i	−3.75394	+	0.494216i
$105$	−24.3196	−	64.2005i	−0.231615	−	0.611433i
$106$	94.4083	−	25.2966i	0.890645	−	0.238648i
$107$	−12.8285	−	64.4932i	−0.119892	−	0.602740i	−0.993282	−	0.115718i	$-0.963083\pi$
$107$	−12.8285	−	64.4932i	−0.119892	−	0.602740i	0.873390	−	0.487022i	$-0.161917\pi$
$108$	189.306	−	204.727i	1.75284	−	1.89562i
$109$	−8.95398	+	45.0147i	−0.0821466	+	0.412979i	0.917729	+	0.397207i	$0.130021\pi$
$109$	−8.95398	+	45.0147i	−0.0821466	+	0.412979i	−0.999876	+	0.0157718i	$0.994979\pi$
$110$	13.8292	−	105.043i	0.125720	−	0.954939i
$111$	−82.8266	−	19.1266i	−0.746186	−	0.172311i
$112$	152.307	+	448.683i	1.35989	+	4.00609i
$113$	−127.892	−	63.0695i	−1.13179	−	0.558137i	−0.222762	−	0.974873i	$-0.571507\pi$
$113$	−127.892	−	63.0695i	−1.13179	−	0.558137i	−0.909028	+	0.416736i	$0.863174\pi$
$114$	187.774	+	260.863i	1.64714	+	2.28827i
$115$	−5.09352	−	19.0093i	−0.0442915	−	0.165298i
$116$	181.019	+	120.953i	1.56051	+	1.04270i
$117$	132.437	−	66.0135i	1.13194	−	0.564218i
$118$		−	433.284i		−	3.67190i
$119$	82.8963	+	140.631i	0.696608	+	1.18177i
$120$	170.435	+	16.4200i	1.42029	+	0.136833i
$121$	−16.8127	+	2.21343i	−0.138948	+	0.0182928i
$122$	−203.497	−	13.3379i	−1.66801	−	0.109327i
$123$	−21.7586	−	26.3981i	−0.176899	−	0.214619i
$124$	−45.6480	−	15.4954i	−0.368129	−	0.124963i
$125$	58.6801	+	87.8210i	0.469441	+	0.702568i
$126$	−200.245	−	258.675i	−1.58925	−	2.05298i
$127$	86.5108	−	35.8340i	0.681188	−	0.282157i	−0.0151356	−	0.999885i	$-0.504818\pi$
$127$	86.5108	−	35.8340i	0.681188	−	0.282157i	0.696323	+	0.717728i	$0.254818\pi$
$128$	−190.779	−	25.1165i	−1.49046	−	0.196223i
$129$	−30.3621	−	128.973i	−0.235365	−	0.999791i
$130$	133.018	+	65.5973i	1.02322	+	0.504594i
$131$	140.098	+	159.752i	1.06945	+	1.21948i	0.974592	+	0.223987i	$0.0719074\pi$
$131$	140.098	+	159.752i	1.06945	+	1.21948i	0.0948611	+	0.995491i	$0.469759\pi$
$132$	−60.0420	−	358.911i	−0.454864	−	2.71902i
$133$	243.773	−	120.215i	1.83288	−	0.903876i
$134$	−167.393	−	69.3363i	−1.24920	−	0.517435i
$135$	−62.5686	+	15.0111i	−0.463471	+	0.111193i
$136$	−406.015	+	30.2985i	−2.98541	+	0.222783i
$137$	−17.3131	+	29.9872i	−0.126373	+	0.218885i	−0.922269	−	0.386549i	$-0.873667\pi$
$137$	−17.3131	+	29.9872i	−0.126373	+	0.218885i	0.795896	+	0.605434i	$0.207000\pi$
$138$	−49.6883	−	79.5271i	−0.360060	−	0.576283i
$139$	16.8683	+	1.10561i	0.121355	+	0.00795402i	0.125960	−	0.992035i	$-0.459799\pi$
$139$	16.8683	+	1.10561i	0.121355	+	0.00795402i	−0.00460467	+	0.999989i	$0.501466\pi$
$140$	61.1669	−	228.278i	0.436907	−	1.63056i
$141$	68.7661	−	49.4991i	0.487702	−	0.351057i
$142$	−79.8033	+	5.23059i	−0.561995	+	0.0368351i
$143$	37.6757	−	189.409i	0.263467	−	1.32454i
$144$	435.187	−	88.4929i	3.02213	−	0.614534i
$145$	−19.2255	−	46.4144i	−0.132590	−	0.320099i
$146$	−4.69459	+	5.35315i	−0.0321547	+	0.0366654i
$147$	−114.194	+	61.3508i	−0.776827	+	0.417352i
$148$	−192.943	−	220.010i	−1.30367	−	1.48655i
$149$	−156.538	−	41.9442i	−1.05059	−	0.281505i	−0.308095	−	0.951356i	$-0.599691\pi$
$149$	−156.538	−	41.9442i	−1.05059	−	0.281505i	−0.742496	+	0.669851i	$0.766358\pi$
$150$	169.891	+	138.821i	1.13261	+	0.925477i
$151$	−200.542	+	153.881i	−1.32809	+	1.01908i	−0.330940	+	0.943652i	$0.607366\pi$
$151$	−200.542	+	153.881i	−1.32809	+	1.01908i	−0.997151	+	0.0754283i	$0.975968\pi$
$152$			677.898i			4.45986i
$153$	140.563	−	60.4247i	0.918710	−	0.394933i
$154$	−426.918			−2.77220
$155$	6.77189	+	8.82530i	0.0436896	+	0.0569374i
$156$	502.774	+	81.9086i	3.22291	+	0.525055i
$157$	−57.5339	+	214.720i	−0.366458	+	1.36764i	0.498975	+	0.866616i	$0.333710\pi$
$157$	−57.5339	+	214.720i	−0.366458	+	1.36764i	−0.865433	+	0.501024i	$0.832957\pi$
$158$	−219.201	+	192.234i	−1.38735	+	1.21667i
$159$	−77.4288	−	2.36968i	−0.486974	−	0.0149036i
$160$	163.000	+	142.947i	1.01875	+	0.893421i
$161$	−73.2626	+	30.3463i	−0.455047	+	0.188487i
$162$	−264.205	+	155.555i	−1.63089	+	0.960214i
$163$	235.354	+	46.8149i	1.44389	+	0.287208i	0.853999	−	0.520274i	$-0.174170\pi$
$163$	235.354	+	46.8149i	1.44389	+	0.287208i	0.589892	+	0.807482i	$0.299170\pi$
$164$	−7.70215	−	117.512i	−0.0469643	−	0.716537i
$165$	−34.4932	+	76.5615i	−0.209050	+	0.464009i
$166$	−172.305	−	46.1691i	−1.03798	−	0.278127i
$167$	−3.93758	+	60.0759i	−0.0235783	+	0.359736i	0.969725	+	0.244200i	$0.0785252\pi$
$167$	−3.93758	+	60.0759i	−0.0235783	+	0.359736i	−0.993303	+	0.115536i	$0.963141\pi$
$168$	−24.0428	−	689.519i	−0.143112	−	4.10428i
$169$	87.7608	+	50.6687i	0.519294	+	0.299815i
$170$	133.490	+	75.4704i	0.785235	+	0.443944i
$171$	−82.9123	−	240.876i	−0.484867	−	1.40863i
$172$	174.549	−	421.397i	1.01482	−	2.44999i
$173$	68.3728	+	138.646i	0.395218	+	0.801424i	0.999987	+	0.00502271i	$0.00159879\pi$
$173$	68.3728	+	138.646i	0.395218	+	0.801424i	−0.604769	+	0.796401i	$0.706735\pi$
$174$	−152.258	−	184.723i	−0.875044	−	1.06163i
$175$	139.489	−	122.328i	0.797079	−	0.699019i
$176$	256.337	−	519.799i	1.45646	−	2.95341i
$177$	−98.9863	+	328.834i	−0.559245	+	1.85782i
$178$	−73.3298	+	556.995i	−0.411965	+	3.12919i
$179$	−30.1376	−	72.7586i	−0.168367	−	0.406473i	0.817065	−	0.576546i	$-0.195600\pi$
$179$	−30.1376	−	72.7586i	−0.168367	−	0.406473i	−0.985431	+	0.170073i	$0.945600\pi$
$180$	−204.998	−	83.8919i	−1.13888	−	0.466066i
$181$	−199.512	+	133.309i	−1.10227	+	0.736516i	−0.967123	−	0.254309i	$-0.918152\pi$
$181$	−199.512	+	133.309i	−1.10227	+	0.736516i	−0.135151	+	0.990825i	$0.543152\pi$
$182$	192.098	−	565.904i	1.05549	−	3.10936i
$183$	151.394	+	56.6128i	0.827289	+	0.309359i
$184$	12.9353	−	197.354i	0.0703004	−	1.07258i
$185$	8.81399	+	66.9489i	0.0476432	+	0.361886i
$186$	43.1510	+	30.7827i	0.231995	+	0.165498i
$187$	49.9346	−	193.330i	0.267030	−	1.03385i
$188$	291.672			1.55145
$189$	92.8767	+	242.064i	0.491411	+	1.28076i
$190$	141.850	−	212.294i	0.746581	−	1.11734i
$191$	151.302	−	40.5413i	0.792159	−	0.212258i	0.160020	−	0.987114i	$-0.448844\pi$
$191$	151.302	−	40.5413i	0.792159	−	0.212258i	0.632138	+	0.774855i	$0.282177\pi$
$192$	402.010	+	181.117i	2.09380	+	0.943319i
$193$	−130.131	+	263.880i	−0.674256	+	1.36726i	0.243418	+	0.969921i	$0.421731\pi$
$193$	−130.131	+	263.880i	−0.674256	+	1.36726i	−0.917674	+	0.397334i	$0.869935\pi$
$194$	410.961	−	139.502i	2.11835	−	0.719084i
$195$	−85.9658	−	80.1727i	−0.440850	−	0.411142i
$196$	−442.427	−	58.2466i	−2.25728	−	0.297176i
$197$	33.2719	+	6.61819i	0.168893	+	0.0335949i	0.278812	−	0.960346i	$-0.410059\pi$
$197$	33.2719	+	6.61819i	0.168893	+	0.0335949i	−0.109919	+	0.993941i	$0.535059\pi$
$198$	−50.5367	+	396.922i	−0.255236	+	2.00466i
$199$	−206.181	+	41.0119i	−1.03608	+	0.206090i	−0.683698	−	0.729765i	$-0.739630\pi$
$199$	−206.181	+	41.0119i	−1.03608	+	0.206090i	−0.352386	+	0.935855i	$0.614630\pi$
$200$	119.762	+	446.959i	0.598812	+	2.23480i
$201$	111.200	+	90.8635i	0.553232	+	0.452057i
$202$	−11.9156	−	90.5077i	−0.0589880	−	0.448058i
$203$	−175.312	+	101.217i	−0.863608	+	0.498604i
$204$	514.236	+	113.864i	2.52077	+	0.558159i
$205$	−13.5876	+	23.5344i	−0.0662808	+	0.114802i
$206$	75.5300	−	182.346i	0.366651	−	0.885173i
$207$	19.5417	+	71.7073i	0.0944043	+	0.346412i
$208$	573.680	+	573.680i	2.75808	+	2.75808i
$209$	−314.815	−	106.865i	−1.50629	−	0.511318i
$210$	−136.753	+	220.964i	−0.651204	+	1.05221i
$211$	130.860	−	44.4210i	0.620190	−	0.210526i	0.00637952	−	0.999980i	$-0.497969\pi$
$211$	130.860	−	44.4210i	0.620190	−	0.210526i	0.613810	+	0.789454i	$0.289636\pi$
$212$	−211.562	−	162.337i	−0.997934	−	0.765741i
$213$	61.7604	+	14.2619i	0.289955	+	0.0669571i
$214$	−164.110	+	187.132i	−0.766869	+	0.874447i
$215$	−87.5148	+	58.4755i	−0.407046	+	0.271979i
$216$	−643.919	−	59.2687i	−2.98111	−	0.274392i
$217$	31.6951	−	31.6951i	0.146060	−	0.146060i
$218$	155.809	−	76.8366i	0.714721	−	0.352461i
$219$	4.78584	−	2.99018i	0.0218531	−	0.0136538i
$220$	−250.343	+	144.535i	−1.13792	+	0.656979i
$221$	233.800	+	153.183i	1.05792	+	0.693135i
$222$	133.417	+	292.797i	0.600977	+	1.31890i
$223$	−93.0419	−	121.255i	−0.417228	−	0.543742i	0.536702	−	0.843772i	$-0.319670\pi$
$223$	−93.0419	−	121.255i	−0.417228	−	0.543742i	−0.953930	+	0.300030i	$0.903003\pi$
$224$	485.341	−	726.364i	2.16670	−	3.24269i
$225$	−97.2214	−	144.169i	−0.432095	−	0.640750i
$226$	105.301	+	529.382i	0.465932	+	2.34240i
$227$	−108.568	+	7.11592i	−0.478273	+	0.0313477i	−0.302634	−	0.953107i	$-0.597866\pi$
$227$	−108.568	+	7.11592i	−0.478273	+	0.0313477i	−0.175639	+	0.984455i	$0.556199\pi$
$228$	252.776	−	839.725i	1.10867	−	3.68300i
$229$	−347.860	−	266.922i	−1.51904	−	1.16560i	−0.935403	−	0.353583i	$-0.884963\pi$
$229$	−347.860	−	266.922i	−1.51904	−	1.16560i	−0.583635	−	0.812016i	$-0.698370\pi$
$230$	−45.3473	+	59.0977i	−0.197162	+	0.256947i
$231$	324.002	+	97.5320i	1.40261	+	0.422216i
$232$	−33.0210	−	503.804i	−0.142332	−	2.17157i
$233$	−317.178	+	63.0907i	−1.36128	+	0.270775i	−0.821105	−	0.570777i	$-0.806642\pi$
$233$	−317.178	+	63.0907i	−1.36128	+	0.270775i	−0.540175	+	0.841553i	$0.681642\pi$
$234$	−503.403	−	245.591i	−2.15129	−	1.04953i
$235$	−55.9628	−	37.3932i	−0.238140	−	0.159120i
$236$	−937.872	+	719.655i	−3.97403	+	3.04938i
$237$	210.276	−	95.8152i	0.887241	−	0.404283i
$238$	231.293	−	572.981i	0.971821	−	2.40748i
$239$	−124.421	−	215.504i	−0.520591	−	0.901691i	−0.999713	−	0.0239424i	$-0.992378\pi$
$239$	−124.421	−	215.504i	−0.520591	−	0.901691i	0.479122	−	0.877748i	$-0.340955\pi$
$240$	−186.927	−	299.180i	−0.778862	−	1.24658i
$241$	−1.63050	−	3.30634i	−0.00676558	−	0.0137192i	0.893464	−	0.449135i	$-0.148268\pi$
$241$	−1.63050	−	3.30634i	−0.00676558	−	0.0137192i	−0.900229	+	0.435416i	$0.856601\pi$
$242$	45.3875	+	45.3875i	0.187551	+	0.187551i
$243$	236.051	−	57.6965i	0.971404	−	0.237434i
$244$	309.124	+	462.637i	1.26690	+	1.89605i
$245$	77.4206	+	67.8960i	0.316002	+	0.277127i
$246$	−29.1350	+	126.168i	−0.118435	+	0.512878i
$247$	283.312	−	369.220i	1.14701	−	1.49482i
$248$	35.9349	+	105.861i	0.144899	+	0.426858i
$249$	120.221	+	74.4035i	0.482814	+	0.298809i
$250$	128.509	−	378.575i	0.514036	−	1.51430i
$251$	−248.209	+	248.209i	−0.988882	+	0.988882i	−0.999939	−	0.0110570i	$-0.996480\pi$
$251$	−248.209	+	248.209i	−0.988882	+	0.988882i	0.0110570	+	0.999939i	$0.496480\pi$
$252$	−227.327	+	863.085i	−0.902091	+	3.42494i
$253$	89.6119	+	37.1185i	0.354197	+	0.146713i
$254$	−306.950	−	177.218i	−1.20846	−	0.697708i
$255$	−84.0683	−	87.7736i	−0.329680	−	0.344210i
$256$	70.2275	+	121.638i	0.274326	+	0.475147i
$257$	212.312	−	27.9514i	0.826116	−	0.108760i	0.294399	−	0.955683i	$-0.404880\pi$
$257$	212.312	−	27.9514i	0.826116	−	0.108760i	0.531717	+	0.846922i	$0.321547\pi$
$258$	−317.338	+	388.362i	−1.22999	+	1.50528i
$259$	262.823	−	70.4232i	1.01476	−	0.271904i
$260$	−78.9441	−	396.879i	−0.303631	−	1.52646i
$261$	73.3524	+	174.976i	0.281044	+	0.670408i
$262$	156.905	−	788.816i	0.598875	−	3.01075i
$263$	40.8970	−	310.643i	0.155502	−	1.18115i	−0.718604	−	0.695419i	$-0.755219\pi$
$263$	40.8970	−	310.643i	0.155502	−	1.18115i	0.874106	−	0.485735i	$-0.161448\pi$
$264$	−575.574	+	617.164i	−2.18021	+	2.33774i
$265$	19.7801	+	58.2703i	0.0746419	+	0.219888i
$266$	−922.715	−	455.032i	−3.46885	−	1.71065i
$267$	182.901	−	405.970i	0.685024	−	1.52049i
$268$	127.945	+	477.495i	0.477405	+	1.78170i
$269$	−65.2192	−	43.5781i	−0.242451	−	0.162000i	0.428408	−	0.903585i	$-0.359074\pi$
$269$	−65.2192	−	43.5781i	−0.242451	−	0.162000i	−0.670859	+	0.741585i	$0.734074\pi$
$270$	189.251	+	153.301i	0.700930	+	0.567782i
$271$		−	294.599i		−	1.08708i	−0.839383	−	0.543540i	$-0.817084\pi$
$271$		−	294.599i		−	1.08708i	0.839383	−	0.543540i	$-0.182916\pi$
$272$	558.764	+	625.652i	2.05428	+	2.30019i
$273$	−275.074	+	385.597i	−1.00760	+	1.41244i
$274$	129.944	−	17.1075i	0.474248	−	0.0624360i
$275$	−226.447	−	14.8421i	−0.823444	−	0.0539714i
$276$	−89.6128	+	239.643i	−0.324684	+	0.868270i
$277$	−321.140	−	109.012i	−1.15935	−	0.393546i	−0.325502	−	0.945542i	$-0.605533\pi$
$277$	−321.140	−	109.012i	−1.15935	−	0.393546i	−0.833847	+	0.551996i	$0.813866\pi$
$278$	−35.5487	−	53.2024i	−0.127873	−	0.191376i
$279$	−25.7163	−	33.2201i	−0.0921730	−	0.119069i
$280$	−506.348	+	209.736i	−1.80839	+	0.749058i
$281$	181.374	+	23.8783i	0.645458	+	0.0849761i	0.446146	−	0.894960i	$-0.352796\pi$
$281$	181.374	+	23.8783i	0.645458	+	0.0849761i	0.199311	+	0.979936i	$0.436129\pi$
$282$	−307.097	−	92.4432i	−1.08900	−	0.327813i
$283$	371.702	+	183.303i	1.31343	+	0.647714i	0.957941	−	0.286965i	$-0.0926464\pi$
$283$	371.702	+	183.303i	1.31343	+	0.647714i	0.355493	+	0.934679i	$0.384313\pi$
$284$	143.870	+	164.052i	0.506583	+	0.577648i
$285$	−156.155	+	128.711i	−0.547912	+	0.451616i
$286$	−655.600	+	323.306i	−2.29231	+	1.13044i
$287$	101.165	+	41.9041i	0.352493	+	0.146007i
$288$	−617.876	−	537.224i	−2.14540	−	1.86536i
$289$	232.421	+	171.760i	0.804225	+	0.594325i
$290$	−95.0801	+	164.684i	−0.327862	+	0.567874i
$291$	−343.762	+	11.9866i	−1.18131	+	0.0411911i
$292$	19.3846	+	1.27054i	0.0663857	+	0.00435115i
$293$	−55.7455	+	208.045i	−0.190258	+	0.710051i	0.803186	+	0.595728i	$0.203137\pi$
$293$	−55.7455	+	208.045i	−0.190258	+	0.710051i	−0.993444	+	0.114323i	$0.963530\pi$
$294$	447.364	+	201.551i	1.52165	+	0.685546i
$295$	272.210	−	17.8416i	0.922747	−	0.0604800i
$296$	−132.393	+	665.585i	−0.447274	+	2.24860i
$297$	129.033	−	289.692i	0.434455	−	0.975395i
$298$	234.746	+	566.726i	0.787737	+	1.90177i
$299$	−89.5249	+	102.084i	−0.299414	+	0.341416i
$300$	18.3111	−	598.313i	0.0610371	−	1.99438i
$301$	279.636	+	318.864i	0.929023	+	1.05935i
$302$	924.196	+	247.637i	3.06025	+	0.819992i
$303$	−11.6339	+	71.4115i	−0.0383957	+	0.235682i
$304$	1108.06	−	850.245i	3.64494	−	2.79686i
$305$		−	128.396i		−	0.420971i
$306$	−505.344	−	282.869i	−1.65145	−	0.924410i
$307$	−299.005			−0.973958			−0.486979	−	0.873414i	$-0.661901\pi$
$307$	−299.005			−0.973958			−0.486979	+	0.873414i	$0.661901\pi$
$308$	709.081	+	924.093i	2.30221	+	3.00030i
$309$	−98.9802	+	121.133i	−0.320324	+	0.392016i
$310$	10.8978	−	40.6713i	0.0351544	−	0.131198i
$311$	−200.218	+	175.586i	−0.643787	+	0.564586i	−0.917752	−	0.397153i	$-0.869998\pi$
$311$	−200.218	+	175.586i	−0.643787	+	0.564586i	0.273965	+	0.961740i	$0.411665\pi$
$312$	−559.096	−	1040.66i	−1.79197	−	3.33544i
$313$	−95.9801	−	84.1723i	−0.306646	−	0.268921i	0.492167	−	0.870501i	$-0.336205\pi$
$313$	−95.9801	−	84.1723i	−0.306646	−	0.268921i	−0.798813	+	0.601580i	$0.794538\pi$
$314$	777.365	−	321.995i	2.47569	−	1.02546i
$315$	154.267	−	136.455i	0.489736	−	0.433192i
$316$	780.181	+	155.188i	2.46893	+	0.491100i
$317$	−8.60868	−	131.343i	−0.0271567	−	0.414332i	−0.989696	−	0.143188i	$-0.954265\pi$
$317$	−8.60868	−	131.343i	−0.0271567	−	0.414332i	0.962539	−	0.271144i	$-0.0874019\pi$
$318$	171.299	+	237.975i	0.538676	+	0.748350i
$319$	239.172	+	64.0858i	0.749754	+	0.200896i
$320$	22.9080	−	349.509i	0.0715875	−	1.09221i
$321$	167.300	−	104.529i	0.521184	−	0.325634i
$322$	259.944	+	150.079i	0.807279	+	0.466083i
$323$	313.987	−	364.628i	0.972095	−	1.12888i
$324$	775.534	+	313.523i	2.39362	+	0.967663i
$325$	121.567	−	293.490i	0.374054	−	0.903045i
$326$	−401.732	−	814.631i	−1.23231	−	2.49887i
$327$	−135.803	+	22.7183i	−0.415298	+	0.0694750i
$328$	−205.330	+	180.069i	−0.626005	+	0.548992i
$329$	−119.951	+	243.237i	−0.364593	+	0.739321i
$330$	309.392	−	72.8351i	0.937550	−	0.220713i
$331$	−41.7469	+	317.100i	−0.126124	+	0.958005i	0.804993	+	0.593284i	$0.202169\pi$
$331$	−41.7469	+	317.100i	−0.126124	+	0.958005i	−0.931117	+	0.364721i	$0.881164\pi$
$332$	186.251	+	449.650i	0.560998	+	1.35437i
$333$	−34.3634	−	252.693i	−0.103193	−	0.758838i
$334$	189.478	−	126.605i	0.567300	−	0.379058i
$335$	36.6677	−	108.019i	0.109456	−	0.322446i
$336$	−1096.90	+	904.119i	−3.26458	+	2.69083i
$337$	−28.7625	+	438.831i	−0.0853486	+	1.30217i	0.713508	+	0.700647i	$0.247105\pi$
$337$	−28.7625	+	438.831i	−0.0853486	+	1.30217i	−0.798857	+	0.601521i	$0.794562\pi$
$338$	−50.0667	−	380.295i	−0.148126	−	1.12513i
$339$	41.0243	−	425.822i	0.121016	−	1.25611i
$340$	−58.3567	−	414.299i	−0.171637	−	1.21853i
$341$	−54.8265			−0.160782
$342$	−532.288	+	804.019i	−1.55640	+	2.35093i
$343$	−30.8881	+	46.2273i	−0.0900528	+	0.134774i
$344$	−1021.72	+	273.770i	−2.97013	+	0.795843i
$345$	47.9168	−	34.4914i	0.138889	−	0.0999750i
$346$	258.801	−	524.796i	0.747979	−	1.51675i
$347$	−248.385	+	84.3153i	−0.715807	+	0.242984i	−0.655499	−	0.755196i	$-0.727542\pi$
$347$	−248.385	+	84.3153i	−0.715807	+	0.242984i	−0.0603079	+	0.998180i	$0.519208\pi$
$348$	−146.955	+	636.384i	−0.422286	+	1.82869i
$349$	59.6988	+	7.85949i	0.171057	+	0.0225200i	0.215568	−	0.976489i	$-0.430840\pi$
$349$	59.6988	+	7.85949i	0.171057	+	0.0225200i	−0.0445113	+	0.999009i	$0.514173\pi$
$350$	−688.763	−	137.003i	−1.96789	−	0.391439i
$351$	325.943	+	301.392i	0.928612	+	0.858667i
$352$	−1048.01	+	208.462i	−2.97730	+	0.592222i
$353$	−25.8783	−	96.5792i	−0.0733097	−	0.273595i	0.919535	−	0.393008i	$-0.128566\pi$
$353$	−25.8783	−	96.5792i	−0.0733097	−	0.273595i	−0.992845	+	0.119413i	$0.961899\pi$
$354$	1215.56	−	460.463i	3.43379	−	1.30074i
$355$	−6.57222	−	49.9210i	−0.0185133	−	0.140622i
$356$	1327.45	−	766.403i	3.72879	−	2.15282i
$357$	−306.437	+	382.014i	−0.858367	+	1.07007i
$358$	−149.046	+	258.156i	−0.416330	+	0.721105i
$359$	−72.2807	+	174.501i	−0.201339	+	0.486076i	−0.992009	−	0.126167i	$-0.959732\pi$
$359$	−72.2807	+	174.501i	−0.201339	+	0.486076i	0.790670	+	0.612243i	$0.209732\pi$
$360$	135.061	+	495.599i	0.375169	+	1.37666i
$361$	−311.254	−	311.254i	−0.862200	−	0.862200i
$362$	860.046	+	291.946i	2.37582	+	0.806482i
$363$	−24.0770	−	44.8151i	−0.0663279	−	0.123458i
$364$	−1544.00	+	524.117i	−4.24175	+	1.43988i
$365$	−3.55642	−	2.72894i	−0.00974363	−	0.00747655i
$366$	−178.843	−	585.078i	−0.488643	−	1.59858i
$367$	143.402	−	163.519i	0.390742	−	0.445556i	−0.522705	−	0.852514i	$-0.675077\pi$
$367$	143.402	−	163.519i	0.390742	−	0.445556i	0.913447	+	0.406958i	$0.133410\pi$
$368$	−338.809	+	226.385i	−0.920678	+	0.615177i
$369$	50.9354	−	89.0970i	0.138036	−	0.241455i
$370$	180.735	−	180.735i	0.488472	−	0.488472i
$371$	222.385	−	109.668i	0.599420	−	0.295601i
$372$	−5.03964	−	144.531i	−0.0135474	−	0.388525i
$373$	310.085	−	179.027i	0.831326	−	0.479966i	−0.0229805	−	0.999736i	$-0.507316\pi$
$373$	310.085	−	179.027i	0.831326	−	0.479966i	0.854306	+	0.519770i	$0.173982\pi$
$374$	−695.622	+	295.528i	−1.85995	+	0.790181i
$375$	−184.017	+	257.955i	−0.490713	+	0.687879i
$376$	−411.770	−	536.630i	−1.09513	−	1.42721i
$377$	−192.568	+	288.199i	−0.510791	+	0.764453i
$378$	512.897	−	836.681i	1.35687	−	2.21344i
$379$	−17.8552	−	89.7642i	−0.0471114	−	0.236845i	0.950054	−	0.312085i	$-0.101028\pi$
$379$	−17.8552	−	89.7642i	−0.0471114	−	0.236845i	−0.997165	+	0.0752405i	$0.976028\pi$
$380$	−695.129	+	45.5611i	−1.82929	+	0.119898i
$381$	192.468	+	204.621i	0.505166	+	0.537063i
$382$	−470.382	−	360.937i	−1.23137	−	0.944860i
$383$	−362.053	+	471.836i	−0.945307	+	1.23195i	0.0273315	+	0.999626i	$0.491299\pi$
$383$	−362.053	+	471.836i	−0.945307	+	1.23195i	−0.972639	+	0.232322i	$0.925368\pi$
$384$	−132.283	−	561.915i	−0.344486	−	1.46332i
$385$	−17.5795	−	268.211i	−0.0456610	−	0.696652i
$386$	1092.28	−	217.267i	2.82973	−	0.562868i
$387$	329.562	−	222.243i	0.851582	−	0.574271i
$388$	−984.539	−	657.848i	−2.53747	−	1.69548i
$389$	−23.6466	+	18.1447i	−0.0607882	+	0.0466444i	−0.638709	−	0.769449i	$-0.720531\pi$
$389$	−23.6466	+	18.1447i	−0.0607882	+	0.0466444i	0.577920	+	0.816093i	$0.303864\pi$
$390$	−42.6685	+	442.889i	−0.109406	+	1.13561i
$391$	−98.3674	+	100.161i	−0.251579	+	0.256167i
$392$	517.435	+	896.224i	1.31999	+	2.28629i
$393$	−299.290	+	562.813i	−0.761553	+	1.43209i
$394$	−56.7926	−	115.164i	−0.144144	−	0.292294i
$395$	−129.797	−	129.797i	−0.328600	−	0.328600i
$396$	943.103	−	549.871i	2.38157	−	1.38856i
$397$	−100.303	−	150.113i	−0.252651	−	0.378120i	0.683364	−	0.730077i	$-0.260516\pi$
$397$	−100.303	−	150.113i	−0.252651	−	0.378120i	−0.936016	+	0.351958i	$0.885516\pi$
$398$	598.248	+	524.650i	1.50314	+	1.31822i
$399$	596.324	+	556.139i	1.49455	+	1.39383i
$400$	580.368	−	756.350i	1.45092	−	1.89088i
$401$	16.0690	+	47.3377i	0.0400723	+	0.118049i	0.965125	−	0.261790i	$-0.0843127\pi$
$401$	16.0690	+	47.3377i	0.0400723	+	0.118049i	−0.925053	+	0.379839i	$0.875979\pi$
$402$	16.6275	−	543.299i	0.0413618	−	1.35149i
$403$	24.6701	−	72.6756i	0.0612160	−	0.180337i
$404$	−176.119	+	176.119i	−0.435938	+	0.435938i
$405$	−108.606	−	159.581i	−0.268164	−	0.394027i
$406$	707.912	+	293.227i	1.74363	+	0.722234i
$407$	−288.226	−	166.408i	−0.708173	−	0.408864i
$408$	−516.485	−	1106.86i	−1.26589	−	2.71290i
$409$	−57.0559	−	98.8238i	−0.139501	−	0.241623i	0.787807	−	0.615922i	$-0.211217\pi$
$409$	−57.0559	−	98.8238i	−0.139501	−	0.241623i	−0.927308	+	0.374300i	$0.877883\pi$
$410$	101.982	−	13.4261i	0.248736	−	0.0327467i
$411$	−102.527	−	16.7031i	−0.249458	−	0.0406401i
$412$	−520.149	+	139.374i	−1.26250	+	0.338285i
$413$	−214.445	−	1078.09i	−0.519237	−	2.61038i
$414$	170.305	−	223.914i	0.411365	−	0.540856i
$415$	21.9106	−	110.152i	0.0527966	−	0.265426i
$416$	195.240	−	1483.00i	0.469327	−	3.56489i
$417$	14.8247	+	48.4984i	0.0355508	+	0.116303i
$418$	404.501	+	1191.62i	0.967705	+	2.85077i
$419$	274.356	+	135.297i	0.654788	+	0.322906i	0.739161	−	0.673529i	$-0.235222\pi$
$419$	274.356	+	135.297i	0.654788	+	0.322906i	−0.0843734	+	0.996434i	$0.526889\pi$
$420$	705.429	−	70.9961i	1.67959	−	0.169038i
$421$	−126.659	−	472.696i	−0.300852	−	1.12279i	−0.936458	−	0.350781i	$-0.885916\pi$
$421$	−126.659	−	472.696i	−0.300852	−	1.12279i	0.635606	−	0.772014i	$-0.280750\pi$
$422$	−434.928	−	290.610i	−1.03064	−	0.688649i
$423$	211.947	+	140.316i	0.501057	+	0.331717i
$424$			618.421i			1.45854i
$425$	142.603	−	295.881i	0.335537	−	0.696191i
$426$	−99.4834	−	218.326i	−0.233529	−	0.512503i
$427$	−512.939	+	67.5297i	−1.20126	+	0.158149i
$428$	677.634	+	44.4145i	1.58326	+	0.103772i
$429$	571.418	−	95.5921i	1.33198	−	0.222826i
$430$	377.255	+	128.061i	0.877337	+	0.297816i
$431$	179.969	+	269.342i	0.417560	+	0.624923i	0.979306	−	0.202387i	$-0.0648699\pi$
$431$	179.969	+	269.342i	0.417560	+	0.624923i	−0.561745	+	0.827310i	$0.689870\pi$
$432$	710.749	+	1126.86i	1.64525	+	2.60846i
$433$	−295.899	+	122.565i	−0.683370	+	0.283061i	−0.697235	−	0.716843i	$-0.745586\pi$
$433$	−295.899	+	122.565i	−0.683370	+	0.283061i	0.0138650	+	0.999904i	$0.495586\pi$
$434$	−168.212	−	22.1456i	−0.387586	−	0.0510267i
$435$	109.782	−	103.262i	0.252373	−	0.237384i
$436$	−425.106	−	209.639i	−0.975014	−	0.480824i
$437$	154.119	+	175.739i	0.352675	+	0.402148i
$438$	−20.0071	−	7.48154i	−0.0456783	−	0.0170811i
$439$	−60.0406	+	29.6088i	−0.136767	+	0.0674459i	−0.509385	−	0.860539i	$-0.670127\pi$
$439$	−60.0406	+	29.6088i	−0.136767	+	0.0674459i	0.372618	+	0.927985i	$0.378460\pi$
$440$	619.345	+	256.541i	1.40760	+	0.583048i
$441$	−293.474	−	255.166i	−0.665474	−	0.578609i
$442$	−78.7329	−	1055.06i	−0.178129	−	2.38702i
$443$	184.336	−	319.279i	0.416108	−	0.720721i	−0.579436	−	0.815018i	$-0.696727\pi$
$443$	184.336	−	319.279i	0.416108	−	0.720721i	0.995544	+	0.0942970i	$0.0300603\pi$
$444$	412.182	−	775.105i	0.928338	−	1.74573i
$445$	−352.952	−	23.1337i	−0.793149	−	0.0519858i
$446$	−149.730	+	558.801i	−0.335718	+	1.25292i
$447$	−48.6844	−	483.737i	−0.108914	−	1.08218i
$448$	−1408.32	+	92.3065i	−3.14358	+	0.206041i
$449$	−0.944494	+	4.74829i	−0.00210355	+	0.0105753i	−0.981823	−	0.189800i	$-0.939216\pi$
$449$	−0.944494	+	4.74829i	−0.00210355	+	0.0105753i	0.979719	+	0.200375i	$0.0642161\pi$
$450$	−208.910	+	624.152i	−0.464245	+	1.38700i
$451$	−51.2554	−	123.742i	−0.113648	−	0.274371i
$452$	970.986	−	1107.20i	2.14820	−	2.44955i
$453$	−644.829	−	399.078i	−1.42346	−	0.880967i
$454$	271.536	+	309.628i	0.598097	+	0.681999i
$455$	363.439	+	97.3831i	0.798766	+	0.214029i
$456$	−1901.82	+	720.421i	−4.17065	+	1.57987i
$457$	−30.8960	+	23.7073i	−0.0676060	+	0.0518759i	−0.642012	−	0.766695i	$-0.721900\pi$
$457$	−30.8960	+	23.7073i	−0.0676060	+	0.0518759i	0.574406	+	0.818571i	$0.305233\pi$
$458$			1659.66i			3.62372i
$459$	318.899	+	330.128i	0.694769	+	0.719233i
$460$	203.240			0.441825
$461$	−32.4062	−	42.2326i	−0.0702955	−	0.0916109i	0.756882	−	0.653551i	$-0.226722\pi$
$461$	−32.4062	−	42.2326i	−0.0702955	−	0.0916109i	−0.827178	+	0.561940i	$0.810055\pi$
$462$	−453.698	−	1197.70i	−0.982030	−	2.59243i
$463$	−96.1046	+	358.667i	−0.207569	+	0.774660i	0.781082	+	0.624429i	$0.214668\pi$
$463$	−96.1046	+	358.667i	−0.207569	+	0.774660i	−0.988651	+	0.150231i	$0.951998\pi$
$464$	−782.078	+	685.864i	−1.68551	+	1.47815i
$465$	−17.5623	+	28.3771i	−0.0377685	+	0.0610261i
$466$	920.316	+	807.095i	1.97493	+	1.73196i
$467$	32.3361	−	13.3940i	0.0692422	−	0.0286810i	−0.347794	−	0.937571i	$-0.613069\pi$
$467$	32.3361	−	13.3940i	0.0692422	−	0.0286810i	0.417036	+	0.908890i	$0.363069\pi$
$468$	304.520	+	1497.56i	0.650684	+	3.19991i
$469$	−450.819	−	89.6736i	−0.961236	−	0.191202i
$470$	16.6623	+	254.217i	0.0354516	+	0.540887i
$471$	−663.530	+	66.7793i	−1.40877	+	0.141782i
$472$	2648.10	+	709.556i	5.61038	+	1.50330i
$473$	33.9283	−	517.646i	0.0717300	−	1.09439i
$474$	−772.257	−	410.667i	−1.62923	−	0.866387i
$475$	−473.609	−	273.438i	−0.997072	−	0.575660i
$476$	−1624.42	+	451.032i	−3.41264	+	0.947547i
$477$	−75.6377	−	219.742i	−0.158570	−	0.460675i
$478$	−360.451	+	870.206i	−0.754082	+	1.82052i
$479$	240.238	+	487.154i	0.501540	+	1.01702i	0.989551	+	0.144185i	$0.0460560\pi$
$479$	240.238	+	487.154i	0.501540	+	1.01702i	−0.488011	+	0.872838i	$0.662277\pi$
$480$	−227.808	+	609.205i	−0.474601	+	1.26918i
$481$	350.274	−	307.182i	0.728221	−	0.638633i
$482$	−6.17169	+	12.5149i	−0.0128043	+	0.0259646i
$483$	−162.994	−	173.285i	−0.337461	−	0.358769i
$484$	22.8588	−	173.630i	0.0472289	−	0.358739i
$485$	104.565	+	252.441i	0.215597	+	0.520498i
$486$	−717.180	−	575.903i	−1.47568	−	1.18499i
$487$	−541.852	+	362.054i	−1.11263	+	0.743437i	−0.969213	−	0.246225i	$-0.920810\pi$
$487$	−541.852	+	362.054i	−1.11263	+	0.743437i	−0.143419	+	0.989662i	$0.545810\pi$
$488$	414.769	−	1221.87i	0.849937	−	2.50383i
$489$	118.780	+	710.029i	0.242904	+	1.45200i
$490$	25.4925	−	388.940i	0.0520254	−	0.793754i
$491$	−64.1190	−	487.032i	−0.130589	−	0.991919i	−0.923774	−	0.382938i	$-0.874912\pi$
$491$	−64.1190	−	487.032i	−0.130589	−	0.991919i	0.793185	−	0.608980i	$-0.208421\pi$
$492$	321.490	−	146.491i	0.653435	−	0.297747i
$493$	−215.589	+	286.280i	−0.437300	+	0.580690i
$494$	−1761.57			−3.56593
$495$	−251.447	−	15.4053i	−0.507974	−	0.0311218i
$496$	127.964	−	191.512i	0.257992	−	0.386113i
$497$	−195.976	+	52.5116i	−0.394318	+	0.105657i
$498$	−53.5882	−	532.461i	−0.107607	−	1.06920i
$499$	374.491	−	759.392i	0.750482	−	1.52183i	−0.0995122	−	0.995036i	$-0.531728\pi$
$499$	374.491	−	759.392i	0.750482	−	1.52183i	0.849995	−	0.526791i	$-0.176605\pi$
$500$	−1032.90	+	350.621i	−2.06579	+	0.701241i
$501$	−172.725	+	52.7976i	−0.344761	+	0.105384i
$502$	1317.30	+	173.425i	2.62410	+	0.345469i
$503$	684.032	+	136.063i	1.35991	+	0.270502i	0.820549	−	0.571576i	$-0.193668\pi$
$503$	684.032	+	136.063i	1.35991	+	0.270502i	0.539356	+	0.842078i	$0.318668\pi$
$504$	1908.87	−	800.222i	3.78744	−	1.58774i
$505$	56.3708	−	11.2128i	0.111625	−	0.0222036i
$506$	−95.0230	−	354.631i	−0.187792	−	0.700851i
$507$	−48.8832	+	300.056i	−0.0964166	+	0.591827i
$508$	126.223	+	958.760i	0.248471	+	1.88732i
$509$	475.136	−	274.320i	0.933469	−	0.538938i	0.0455617	−	0.998962i	$-0.485492\pi$
$509$	475.136	−	274.320i	0.933469	−	0.538938i	0.887907	+	0.460023i	$0.152159\pi$
$510$	−69.8659	+	454.705i	−0.136992	+	0.891579i
$511$	−9.03153	+	15.6431i	−0.0176742	+	0.0306127i
$512$	−91.1009	+	219.937i	−0.177931	+	0.429565i
$513$	587.654	−	488.593i	1.14552	−	0.952422i
$514$	−573.155	−	573.155i	−1.11509	−	1.11509i
$515$	117.669	+	39.9431i	0.228483	+	0.0775594i
$516$	1367.71	+	41.8583i	2.65060	+	0.0811207i
$517$	314.123	−	106.630i	0.607588	−	0.206248i
$518$	−817.087	−	626.973i	−1.57739	−	1.21037i
$519$	−316.305	+	339.160i	−0.609451	+	0.653488i
$520$	−618.743	+	705.542i	−1.18989	+	1.35681i
$521$	288.050	−	192.469i	0.552879	−	0.369422i	−0.247527	−	0.968881i	$-0.579618\pi$
$521$	288.050	−	192.469i	0.552879	−	0.369422i	0.800405	+	0.599459i	$0.204618\pi$
$522$	356.424	−	623.463i	0.682805	−	1.19437i
$523$	188.046	−	188.046i	0.359553	−	0.359553i	−0.504095	−	0.863648i	$-0.668174\pi$
$523$	188.046	−	188.046i	0.359553	−	0.359553i	0.863648	+	0.504095i	$0.168174\pi$
$524$	−1968.05	+	970.537i	−3.75583	+	1.85217i
$525$	491.426	+	261.328i	0.936050	+	0.497769i
$526$	−1027.08	+	592.988i	−1.95263	+	1.12735i
$527$	29.7036	−	73.5846i	0.0563636	−	0.139629i
$528$	1730.69	+	166.737i	3.27783	+	0.315790i
$529$	280.520	+	365.581i	0.530284	+	0.691079i
$530$	129.405	−	193.668i	0.244160	−	0.365411i
$531$	−1027.73	+	71.7586i	−1.93545	+	0.135139i
$532$	547.616	+	2753.05i	1.02935	+	5.17491i
$533$	187.089	−	12.2625i	0.351012	−	0.0230065i
$534$	−1640.56	+	386.211i	−3.07221	+	0.723241i
$535$	−124.323	−	95.3964i	−0.232379	−	0.178311i
$536$	697.888	−	909.506i	1.30203	−	1.69684i
$537$	172.093	−	161.872i	0.320472	−	0.301438i
$538$	19.4182	+	296.265i	0.0360934	+	0.550679i
$539$	−497.775	+	99.0137i	−0.923516	+	0.183699i
$540$	17.4978	−	664.269i	0.0324033	−	1.23013i
$541$	632.053	+	422.325i	1.16831	+	0.780637i	0.979513	−	0.201380i	$-0.0645427\pi$
$541$	632.053	+	422.325i	1.16831	+	0.780637i	0.188792	+	0.982017i	$0.439543\pi$
$542$	−884.666	+	678.828i	−1.63222	+	1.25245i
$543$	−586.021	−	418.050i	−1.07923	−	0.769890i
$544$	288.001	−	1519.51i	0.529413	−	2.79321i
$545$	54.6884	+	94.7231i	0.100346	+	0.173804i
$546$	1791.77	−	62.4770i	3.28163	−	0.114427i
$547$	140.611	+	285.131i	0.257058	+	0.521263i	0.986697	−	0.162570i	$-0.0519784\pi$
$547$	140.611	+	285.131i	0.257058	+	0.521263i	−0.729639	+	0.683833i	$0.760312\pi$
$548$	−252.858	−	252.858i	−0.461420	−	0.461420i
$549$	2.06554	+	484.893i	0.00376236	+	0.883230i
$550$	477.220	+	714.210i	0.867672	+	1.29856i
$551$	448.625	+	393.433i	0.814201	+	0.714035i
$552$	567.416	−	173.444i	1.02793	−	0.314211i
$553$	−450.269	+	586.802i	−0.814230	+	1.06112i
$554$	412.626	+	1215.56i	0.744813	+	2.19415i
$555$	−178.456	+	95.8758i	−0.321542	+	0.172749i
$556$	−56.1162	+	165.313i	−0.100928	+	0.297326i
$557$	−40.1164	+	40.1164i	−0.0720223	+	0.0720223i	−0.742200	−	0.670178i	$-0.766218\pi$
$557$	−40.1164	+	40.1164i	−0.0720223	+	0.0720223i	0.670178	+	0.742200i	$0.266218\pi$
$558$	−40.5018	+	153.772i	−0.0725840	+	0.275577i
$559$	670.901	+	277.896i	1.20018	+	0.497131i
$560$	977.905	+	564.594i	1.74626	+	1.00820i
$561$	595.445	−	65.3671i	1.06140	−	0.116519i
$562$	−346.224	−	599.678i	−0.616057	−	1.06704i
$563$	−736.690	+	96.9871i	−1.30851	+	0.172268i	−0.752325	−	0.658792i	$-0.771068\pi$
$563$	−736.690	+	96.9871i	−1.30851	+	0.172268i	−0.556183	+	0.831060i	$0.687734\pi$
$564$	309.968	+	818.274i	0.549589	+	1.45084i
$565$	−328.248	+	87.9538i	−0.580970	+	0.155670i
$566$	−306.042	−	1538.58i	−0.540711	−	2.71834i
$567$	−580.399	+	517.810i	−1.02363	+	0.913246i
$568$	98.7200	−	496.299i	0.173803	−	0.873766i
$569$	10.5967	−	80.4899i	0.0186234	−	0.141459i	−0.979607	−	0.200923i	$-0.935606\pi$
$569$	10.5967	−	80.4899i	0.0186234	−	0.141459i	0.998230	+	0.0594644i	$0.0189393\pi$
$570$	746.332	+	172.345i	1.30935	+	0.302360i
$571$	−206.685	−	608.875i	−0.361971	−	1.06633i	−0.963552	−	0.267520i	$-0.913796\pi$
$571$	−206.685	−	608.875i	−0.361971	−	1.06633i	0.601581	−	0.798811i	$-0.294538\pi$
$572$	1788.72	+	882.101i	3.12714	+	1.54213i
$573$	274.530	+	381.388i	0.479110	+	0.665599i
$574$	−107.274	−	400.352i	−0.186889	−	0.697478i
$575$	132.662	+	88.6422i	0.230717	+	0.154160i
$576$	−80.8904	+	1320.30i	−0.140435	+	2.29219i
$577$			742.665i			1.28711i	0.765398	+	0.643557i	$0.222542\pi$
$577$			742.665i			1.28711i	−0.765398	+	0.643557i	$0.777458\pi$
$578$	−19.7681	−	1093.73i	−0.0342009	−	1.89226i
$579$	−878.600	−	84.6455i	−1.51744	−	0.146193i
$580$	514.390	−	67.7207i	0.886879	−	0.116760i
$581$	−451.577	−	29.5979i	−0.777241	−	0.0509431i
$582$	828.108	+	1004.68i	1.42287	+	1.72626i
$583$	−287.194	−	97.4893i	−0.492614	−	0.167220i
$584$	−25.0288	−	37.4583i	−0.0428576	−	0.0641409i
$585$	133.563	−	326.375i	0.228313	−	0.557907i
$586$	753.201	−	311.986i	1.28533	−	0.532400i
$587$	−149.223	−	19.6456i	−0.254213	−	0.0334678i	0.00234265	−	0.999997i	$-0.499254\pi$
$587$	−149.223	−	19.6456i	−0.254213	−	0.0334678i	−0.256556	+	0.966529i	$0.582588\pi$
$588$	−306.771	−	1303.11i	−0.521719	−	2.21617i
$589$	−118.499	−	58.4371i	−0.201186	−	0.0992141i
$590$	−680.817	−	776.324i	−1.15393	−	1.31580i
$591$	16.7919	+	100.376i	0.0284127	+	0.169842i
$592$	1253.99	−	618.397i	2.11822	−	1.04459i
$593$	−93.4324	−	38.7010i	−0.157559	−	0.0652630i	0.302510	−	0.953146i	$-0.402175\pi$
$593$	−93.4324	−	38.7010i	−0.157559	−	0.0652630i	−0.460069	+	0.887883i	$0.652175\pi$
$594$	−1167.26	+	280.042i	−1.96508	+	0.471451i
$595$	369.499	+	121.716i	0.621007	+	0.204564i
$596$	836.821	−	1449.42i	1.40406	−	2.43191i
$597$	−334.171	−	534.848i	−0.559751	−	0.895892i
$598$	512.840	+	33.6133i	0.857591	+	0.0562095i
$599$	175.375	−	654.509i	0.292780	−	1.09267i	−0.650184	−	0.759777i	$-0.725308\pi$
$599$	175.375	−	654.509i	0.292780	−	1.09267i	0.942964	−	0.332894i	$-0.108025\pi$
$600$	−1126.65	+	810.984i	−1.87775	+	1.35164i
$601$	−776.887	+	50.9199i	−1.29266	+	0.0847253i	−0.696158	−	0.717888i	$-0.745109\pi$
$601$	−776.887	+	50.9199i	−1.29266	+	0.0847253i	−0.596499	+	0.802613i	$0.703442\pi$
$602$	313.183	−	1574.48i	0.520237	−	2.61541i
$603$	−136.739	+	408.529i	−0.226765	+	0.677495i
$604$	−998.997	−	2411.79i	−1.65397	−	3.99303i
$605$	−26.6457	+	30.3836i	−0.0440425	+	0.0502208i
$606$	241.253	−	129.614i	0.398107	−	0.213884i
$607$	−305.711	−	348.596i	−0.503642	−	0.574294i	0.443024	−	0.896510i	$-0.353906\pi$
$607$	−305.711	−	348.596i	−0.503642	−	0.574294i	−0.946666	+	0.322216i	$0.895572\pi$
$608$	−2487.29	−	666.468i	−4.09094	−	1.09616i
$609$	−470.269	−	384.266i	−0.772199	−	0.630979i
$610$	−385.568	+	295.857i	−0.632079	+	0.485011i
$611$			464.367i			0.760012i
$612$	227.051	+	1563.68i	0.370998	+	2.55503i
$613$	−624.058			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$613$	−624.058			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$614$	688.982	+	897.898i	1.12212	+	1.46238i
$615$	−80.4646	−	13.1088i	−0.130837	−	0.0213151i
$616$	699.131	−	2609.19i	1.13495	−	4.23570i
$617$	913.137	−	800.800i	1.47996	−	1.29789i	0.623337	−	0.781953i	$-0.285776\pi$
$617$	913.137	−	800.800i	1.47996	−	1.29789i	0.856625	−	0.515939i	$-0.172557\pi$
$618$	591.831	+	18.1128i	0.957656	+	0.0293087i
$619$	796.941	+	698.899i	1.28747	+	1.12908i	0.984369	+	0.176117i	$0.0563538\pi$
$619$	796.941	+	698.899i	1.28747	+	1.12908i	0.303097	+	0.952960i	$0.401980\pi$
$620$	−106.136	+	43.9631i	−0.171188	+	0.0709083i
$621$	−180.405	+	131.029i	−0.290507	+	0.210997i
$622$	988.629	+	196.651i	1.58944	+	0.316159i
$623$	93.2157	+	1422.20i	0.149624	+	2.28282i
$624$	−999.771	+	2219.10i	−1.60220	+	3.55626i
$625$	−223.430	−	59.8678i	−0.357487	−	0.0957884i
$626$	−31.6036	+	482.177i	−0.0504849	+	0.770251i
$627$	−34.7563	−	996.771i	−0.0554328	−	1.58975i
$628$	−1988.13	−	1147.85i	−3.16581	−	1.82778i
$629$	379.495	−	296.683i	0.603331	−	0.471674i
$630$	−765.238	−	148.829i	−1.21466	−	0.236237i
$631$	−322.111	+	777.644i	−0.510476	+	1.23240i	0.433130	+	0.901331i	$0.357409\pi$
$631$	−322.111	+	777.644i	−0.510476	+	1.23240i	−0.943607	+	0.331068i	$0.892591\pi$
$632$	−815.907	−	1654.50i	−1.29099	−	2.61787i
$633$	263.690	+	319.915i	0.416572	+	0.505395i
$634$	−374.581	+	328.499i	−0.590822	+	0.518137i
$635$	98.6974	−	200.139i	0.155429	−	0.315179i
$636$	230.598	−	766.049i	0.362575	−	1.20448i
$637$	92.7336	−	704.382i	0.145579	−	1.10578i
$638$	−358.664	−	865.891i	−0.562169	−	1.35720i
$639$	25.6233	+	188.423i	0.0400991	+	0.294871i
$640$	−381.288	+	254.768i	−0.595762	+	0.398076i
$641$	239.960	−	706.899i	0.374352	−	1.10281i	−0.582649	−	0.812724i	$-0.697984\pi$
$641$	239.960	−	706.899i	0.374352	−	1.10281i	0.957002	−	0.290083i	$-0.0936828\pi$
$642$	−699.395	−	261.534i	−1.08940	−	0.407374i
$643$	−16.2926	+	248.576i	−0.0253384	+	0.386589i	0.966289	+	0.257459i	$0.0828851\pi$
$643$	−16.2926	+	248.576i	−0.0253384	+	0.386589i	−0.991628	+	0.129130i	$0.958782\pi$
$644$	−106.893	−	811.936i	−0.165983	−	1.26077i
$645$	−257.055	−	183.376i	−0.398535	−	0.284304i
$646$	−1818.46	−	102.695i	−2.81496	−	0.158971i
$647$	669.504			1.03478			0.517391	−	0.855749i	$-0.326903\pi$
$647$	669.504			1.03478			0.517391	+	0.855749i	$0.326903\pi$
$648$	−518.035	−	1869.48i	−0.799436	−	2.88499i
$649$	−746.969	+	1117.92i	−1.15095	+	1.72252i
$650$	−1161.46	+	311.212i	−1.78686	+	0.478787i
$651$	122.603	+	55.2361i	0.188330	+	0.0848481i
$652$	−1096.07	+	2222.62i	−1.68110	+	3.40893i
$653$	−364.865	+	123.855i	−0.558752	+	0.189671i	−0.586507	−	0.809944i	$-0.699497\pi$
$653$	−364.865	+	123.855i	−0.558752	+	0.189671i	0.0277553	+	0.999615i	$0.491164\pi$
$654$	381.145	+	355.460i	0.582790	+	0.543517i
$655$	502.034	+	66.0940i	0.766464	+	0.100907i
$656$	551.865	+	109.773i	0.841257	+	0.167336i
$657$	13.4749	+	10.2487i	0.0205097	+	0.0155993i
$658$	1006.82	−	200.270i	1.53013	−	0.304362i
$659$	10.7966	+	40.2934i	0.0163833	+	0.0611433i	0.973634	−	0.228118i	$-0.0732571\pi$
$659$	10.7966	+	40.2934i	0.0163833	+	0.0611433i	−0.957250	+	0.289261i	$0.906590\pi$
$660$	−671.534	−	548.725i	−1.01748	−	0.831401i
$661$	76.0875	+	577.942i	0.115110	+	0.874345i	0.947411	+	0.320021i	$0.103690\pi$
$661$	76.0875	+	577.942i	0.115110	+	0.874345i	−0.832301	+	0.554324i	$0.812977\pi$
$662$	1048.43	−	605.312i	1.58373	−	0.914368i
$663$	−181.282	+	818.709i	−0.273427	+	1.23486i
$664$	564.343	−	977.470i	0.849914	−	1.47209i
$665$	247.879	−	598.432i	0.372750	−	0.899897i
$666$	−679.644	+	685.459i	−1.02049	+	1.02922i
$667$	−123.099	−	123.099i	−0.184556	−	0.184556i
$668$	−588.756	−	199.856i	−0.881371	−	0.299185i
$669$	241.297	−	389.886i	0.360682	−	0.582789i
$670$	−408.869	+	138.792i	−0.610252	+	0.207153i
$671$	502.051	+	385.237i	0.748212	+	0.574124i
$672$	2553.57	+	589.677i	3.79995	+	0.877496i
$673$	483.139	−	550.915i	0.717889	−	0.818596i	−0.271721	−	0.962376i	$-0.587593\pi$
$673$	483.139	−	550.915i	0.717889	−	0.818596i	0.989610	+	0.143781i	$0.0459260\pi$
$674$	1384.06	−	924.802i	2.05351	−	1.37211i
$675$	301.140	−	425.963i	0.446134	−	0.631056i
$676$	−740.016	+	740.016i	−1.09470	+	1.09470i
$677$	325.237	−	160.389i	0.480409	−	0.236912i	−0.185926	−	0.982564i	$-0.559529\pi$
$677$	325.237	−	160.389i	0.480409	−	0.236912i	0.666335	+	0.745652i	$0.267862\pi$
$678$	−1373.25	+	858.006i	−2.02545	+	1.26550i
$679$	953.500	−	550.503i	1.40427	−	0.810756i
$680$	−679.858	+	692.257i	−0.999791	+	1.01802i
$681$	−135.342	−	297.021i	−0.198739	−	0.436154i
$682$	126.334	+	164.642i	0.185240	+	0.241410i
$683$	−503.591	+	753.677i	−0.737322	+	1.10348i	0.253371	+	0.967369i	$0.418461\pi$
$683$	−503.591	+	753.677i	−0.737322	+	1.10348i	−0.990694	+	0.136112i	$0.956539\pi$
$684$	2624.45	−	183.246i	3.83691	−	0.267904i
$685$	16.0985	+	80.9328i	0.0235015	+	0.118150i
$686$	209.992	−	13.7636i	0.306111	−	0.0200636i
$687$	379.159	−	1259.57i	0.551906	−	1.83344i
$688$	1728.98	+	1326.69i	2.51305	+	1.92833i
$689$	258.455	−	336.825i	0.375116	−	0.488861i
$690$	−213.988	−	64.4152i	−0.310128	−	0.0933554i
$691$	−55.0273	−	839.554i	−0.0796342	−	1.21498i	−0.831446	−	0.555606i	$-0.812486\pi$
$691$	−55.0273	−	839.554i	−0.0796342	−	1.21498i	0.751812	−	0.659378i	$-0.229180\pi$
$692$	−1565.80	+	311.458i	−2.26272	+	0.450084i
$693$	70.7043	+	1012.63i	0.102026	+	1.46122i
$694$	825.535	+	551.605i	1.18953	+	0.794820i
$695$	31.9606	−	24.5242i	0.0459864	−	0.0352866i
$696$	1378.31	−	628.045i	1.98033	−	0.902364i
$697$	193.847	−	1.75166i	0.278116	−	0.00251314i
$698$	−113.959	−	197.383i	−0.163265	−	0.282784i
$699$	−514.073	−	822.783i	−0.735440	−	1.17709i
$700$	847.434	+	1718.43i	1.21062	+	2.45490i
$701$	−336.646	−	336.646i	−0.480237	−	0.480237i	0.424970	−	0.905207i	$-0.360285\pi$
$701$	−336.646	−	336.646i	−0.480237	−	0.480237i	−0.905207	+	0.424970i	$0.860285\pi$
$702$	154.014	−	1673.27i	0.219394	−	2.38358i
$703$	−445.589	−	666.870i	−0.633839	−	0.948607i
$704$	1297.90	+	1138.23i	1.84361	+	1.61681i
$705$	45.4318	−	196.740i	0.0644423	−	0.279064i
$706$	−230.393	+	300.254i	−0.326335	+	0.425289i
$707$	−74.4430	−	219.302i	−0.105294	−	0.310187i
$708$	−3015.67	−	1866.37i	−4.25941	−	2.63611i
$709$	−137.594	+	405.338i	−0.194067	+	0.571704i	−0.999788	−	0.0205916i	$-0.993445\pi$
$709$	−137.594	+	405.338i	−0.194067	+	0.571704i	0.805721	+	0.592296i	$0.201778\pi$
$710$	−134.766	+	134.766i	−0.189812	+	0.189812i
$711$	492.272	+	488.096i	0.692366	+	0.686492i
$712$	−3284.10	−	1360.32i	−4.61250	−	1.91056i
$713$	33.3830	+	19.2737i	0.0468205	+	0.0270318i
$714$	1853.28	+	39.9610i	2.59563	+	0.0559678i
$715$	−230.113	−	398.567i	−0.321836	−	0.557437i
$716$	806.351	−	106.158i	1.12619	−	0.148265i
$717$	472.362	−	578.081i	0.658804	−	0.806250i
$718$	690.571	−	185.038i	0.961799	−	0.257713i
$719$	194.005	+	975.330i	0.269826	+	1.35651i	0.843370	+	0.537334i	$0.180568\pi$
$719$	194.005	+	975.330i	0.269826	+	1.35651i	−0.573543	+	0.819175i	$0.694432\pi$
$720$	640.685	−	842.363i	0.889840	−	1.16995i
$721$	97.6839	−	491.090i	0.135484	−	0.681124i
$722$	−217.475	+	1651.89i	−0.301212	+	2.28793i
$723$	7.54301	−	8.08805i	0.0104329	−	0.0111868i
$724$	−796.539	−	2346.53i	−1.10019	−	3.24106i
$725$	365.299	+	180.145i	0.503860	+	0.248476i
$726$	−79.0982	+	175.567i	−0.108951	+	0.241828i
$727$	95.6526	+	356.980i	0.131572	+	0.491032i	0.999988	−	0.00480285i	$-0.00152880\pi$
$727$	95.6526	+	356.980i	0.131572	+	0.491032i	−0.868417	+	0.495835i	$0.834862\pi$
$728$	3144.04	+	2100.78i	4.31874	+	2.88569i
$729$	412.723	+	600.916i	0.566150	+	0.824302i
$730$			16.9679i			0.0232437i
$731$	676.369	+	325.984i	0.925265	+	0.445942i
$732$	−969.395	+	1358.89i	−1.32431	+	1.85641i
$733$	−762.501	+	100.385i	−1.04025	+	0.136951i	−0.631246	−	0.775583i	$-0.717456\pi$
$733$	−762.501	+	100.385i	−1.04025	+	0.136951i	−0.409001	+	0.912534i	$0.634123\pi$
$734$	−821.475	−	53.8423i	−1.11918	−	0.0733546i
$735$	−108.203	+	289.355i	−0.147214	+	0.393681i
$736$	711.399	+	241.488i	0.966575	+	0.328108i
$737$	312.357	+	467.475i	0.423822	+	0.634295i
$738$	−384.922	+	52.3449i	−0.521574	+	0.0709281i
$739$	186.580	−	77.2838i	0.252476	−	0.104579i	−0.252856	−	0.967504i	$-0.581370\pi$
$739$	186.580	−	77.2838i	0.252476	−	0.104579i	0.505332	+	0.862925i	$0.331370\pi$
$740$	−691.400	−	91.0246i	−0.934325	−	0.123006i
$741$	1336.91	+	402.441i	1.80420	+	0.543106i
$742$	−841.757	−	415.109i	−1.13444	−	0.559446i
$743$	612.436	+	698.350i	0.824275	+	0.939905i	0.999000	−	0.0447120i	$-0.0142370\pi$
$743$	612.436	+	698.350i	0.824275	+	0.939905i	−0.174725	+	0.984617i	$0.555904\pi$
$744$	−258.799	+	213.315i	−0.347849	+	0.286714i
$745$	−346.379	+	170.815i	−0.464938	+	0.229282i
$746$	−1252.12	−	518.646i	−1.67845	−	0.695236i
$747$	−80.9741	+	416.345i	−0.108399	+	0.557357i
$748$	1795.07	+	1014.87i	2.39982	+	1.35678i
$749$	−315.718	+	546.840i	−0.421520	+	0.730093i
$750$	1198.65	−	41.7955i	1.59820	−	0.0557274i
$751$	1433.56	+	93.9604i	1.90887	+	0.125114i	0.973517	−	0.228614i	$-0.0734194\pi$
$751$	1433.56	+	93.9604i	1.90887	+	0.125114i	0.935348	+	0.353728i	$0.115086\pi$
$752$	−360.692	+	1346.12i	−0.479644	+	1.79005i
$753$	−960.121	−	432.563i	−1.27506	−	0.574452i
$754$	1309.17	−	85.8077i	1.73630	−	0.113803i
$755$	−117.522	+	590.822i	−0.155658	+	0.782546i
$756$	−2662.94	+	279.468i	−3.52240	+	0.369666i
$757$	−390.056	−	941.678i	−0.515265	−	1.24396i	−0.940783	−	0.339010i	$-0.889908\pi$
$757$	−390.056	−	941.678i	−0.515265	−	1.24396i	0.425518	−	0.904950i	$-0.360092\pi$
$758$	−228.415	+	260.457i	−0.301339	+	0.343611i
$759$	−8.90133	+	290.850i	−0.0117277	+	0.383201i
$760$	1065.18	+	1214.60i	1.40155	+	1.59816i
$761$	131.015	+	35.1053i	0.172161	+	0.0461305i	0.343870	−	0.939017i	$-0.388262\pi$
$761$	131.015	+	35.1053i	0.172161	+	0.0461305i	−0.171709	+	0.985148i	$0.554929\pi$
$762$	170.973	−	1049.47i	0.224374	−	1.37726i
$763$	349.652	−	268.298i	0.458260	−	0.351635i
$764$			1617.66i			2.11736i
$765$	156.904	−	329.130i	0.205103	−	0.430235i
$766$	2251.16			2.93885
$767$	−1145.75	−	1493.17i	−1.49381	−	1.94677i
$768$	−266.617	+	326.288i	−0.347157	+	0.424855i
$769$	−148.160	+	552.942i	−0.192666	+	0.719041i	0.800192	+	0.599744i	$0.204731\pi$
$769$	−148.160	+	552.942i	−0.192666	+	0.719041i	−0.992859	+	0.119297i	$0.961936\pi$
$770$	−764.918	+	670.815i	−0.993399	+	0.871188i
$771$	304.046	+	565.928i	0.394353	+	0.734018i
$772$	−2284.48	−	2003.44i	−2.95917	−	2.59513i
$773$	50.8868	−	21.0780i	0.0658303	−	0.0272678i	−0.349525	−	0.936927i	$-0.613657\pi$
$773$	50.8868	−	21.0780i	0.0658303	−	0.0272678i	0.415356	+	0.909659i	$0.363657\pi$
$774$	−1426.78	−	477.558i	−1.84338	−	0.616999i
$775$	−88.4537	−	17.5945i	−0.114134	−	0.0227026i
$776$	179.597	+	2740.12i	0.231439	+	3.53108i
$777$	476.879	+	662.499i	0.613744	+	0.852637i
$778$	108.975	+	29.1998i	0.140071	+	0.0375319i
$779$	21.1101	−	322.078i	0.0270990	−	0.413451i
$780$	1029.53	−	643.249i	1.31991	−	0.824678i
$781$	214.918	+	124.083i	0.275184	+	0.158877i
$782$	527.443	+	64.5962i	0.674479	+	0.0826038i
$783$	−412.936	+	391.740i	−0.527377	+	0.500306i
$784$	815.939	−	1969.85i	1.04074	−	2.51257i
$785$	234.303	+	475.120i	0.298476	+	0.605248i
$786$	2379.74	−	398.105i	3.02766	−	0.506495i
$787$	−698.905	+	612.923i	−0.888062	+	0.778810i	−0.976103	−	0.217307i	$-0.930273\pi$
$787$	−698.905	+	612.923i	−0.888062	+	0.778810i	0.0880410	+	0.996117i	$0.471939\pi$
$788$	−154.951	+	314.211i	−0.196639	+	0.398744i
$789$	914.960	−	215.395i	1.15965	−	0.272997i
$790$	−90.6901	+	688.860i	−0.114798	+	0.871974i
$791$	524.014	+	1265.08i	0.662470	+	1.59934i
$792$	−2343.11	−	958.874i	−2.95847	−	1.21070i
$793$	−736.558	+	492.153i	−0.928825	+	0.620621i
$794$	−219.662	+	647.103i	−0.276652	+	0.814991i
$795$	−142.454	+	117.418i	−0.179188	+	0.147695i
$796$	141.990	−	2166.36i	0.178380	−	2.72155i
$797$	−187.789	−	1426.40i	−0.235620	−	1.78971i	−0.544653	−	0.838662i	$-0.683339\pi$
$797$	−187.789	−	1426.40i	−0.235620	−	1.78971i	0.309032	−	0.951051i	$-0.399995\pi$
$798$	295.981	−	3072.21i	0.370904	−	3.84989i
$799$	−27.0715	+	479.365i	−0.0338817	+	0.599956i
$800$	−1757.69			−2.19711
$801$	1333.31	+	81.6871i	1.66455	+	0.101981i
$802$	105.126	−	157.332i	0.131080	−	0.196175i
$803$	21.3412	−	5.71836i	0.0265768	−	0.00712124i
$804$	−1203.62	+	866.391i	−1.49705	+	1.07760i
$805$	−83.5829	+	169.489i	−0.103830	+	0.210546i
$806$	−275.087	+	93.3796i	−0.341300	+	0.115856i
$807$	52.9464	−	229.282i	0.0656089	−	0.284116i
$808$	572.668	+	75.3932i	0.708748	+	0.0933084i
$809$	362.800	+	72.1654i	0.448455	+	0.0892032i	0.414151	−	0.910208i	$-0.364079\pi$
$809$	362.800	+	72.1654i	0.448455	+	0.0892032i	0.0343040	+	0.999411i	$0.489079\pi$
$810$	−228.958	+	693.854i	−0.282664	+	0.856610i
$811$	−681.113	+	135.482i	−0.839843	+	0.167055i	−0.596226	−	0.802816i	$-0.703334\pi$
$811$	−681.113	+	135.482i	−0.839843	+	0.167055i	−0.243617	+	0.969872i	$0.578334\pi$
$812$	−541.084	−	2019.35i	−0.666360	−	2.48689i
$813$	826.485	−	313.078i	1.01659	−	0.385090i
$814$	164.431	+	1248.97i	0.202003	+	1.53437i
$815$	495.249	−	285.932i	0.607667	−	0.350837i
$816$	−1161.43	+	2232.49i	−1.42332	+	2.73589i
$817$	625.065	−	1082.64i	0.765074	−	1.32515i
$818$	−165.292	+	399.051i	−0.202069	+	0.487837i
$819$	−1374.11	−	361.924i	−1.67779	−	0.441910i
$820$	−198.446	−	198.446i	−0.242008	−	0.242008i
$821$	−152.424	−	51.7411i	−0.185657	−	0.0630220i	0.227063	−	0.973880i	$-0.427088\pi$
$821$	−152.424	−	51.7411i	−0.185657	−	0.0630220i	−0.412720	+	0.910858i	$0.635421\pi$
$822$	186.089	+	346.372i	0.226386	+	0.421378i
$823$	81.5224	−	27.6731i	0.0990552	−	0.0336247i	−0.271472	−	0.962446i	$-0.587510\pi$
$823$	81.5224	−	27.6731i	0.0990552	−	0.0336247i	0.370527	+	0.928822i	$0.379177\pi$
$824$	990.750	+	760.229i	1.20237	+	0.922608i
$825$	−199.013	−	651.061i	−0.241227	−	0.789165i
$826$	−2743.31	+	3128.15i	−3.32120	+	3.78711i
$827$	−33.6452	+	22.4810i	−0.0406835	+	0.0271838i	−0.575746	−	0.817629i	$-0.695288\pi$
$827$	−33.6452	+	22.4810i	−0.0406835	+	0.0271838i	0.535062	+	0.844813i	$0.320288\pi$
$828$	−767.542	+	3.26955i	−0.926983	+	0.00394874i
$829$	563.784	−	563.784i	0.680077	−	0.680077i	−0.279940	−	0.960017i	$-0.590315\pi$
$829$	563.784	−	563.784i	0.680077	−	0.680077i	0.960017	+	0.279940i	$0.0903147\pi$
$830$	−381.269	+	188.021i	−0.459360	+	0.226531i
$831$	−35.4545	−	1016.79i	−0.0426649	−	1.22358i
$832$	−2092.80	+	1208.28i	−2.51539	+	1.45226i
$833$	136.792	−	721.724i	0.164216	−	0.866416i
$834$	111.479	−	156.270i	0.133667	−	0.187374i
$835$	87.3419	+	113.826i	0.104601	+	0.136319i
$836$	1907.49	−	2854.77i	2.28169	−	3.41479i
$837$	65.8683	−	107.450i	0.0786958	−	0.128375i
$838$	−225.892	−	1135.64i	−0.269561	−	1.35518i
$839$	104.608	−	6.85635i	0.124681	−	0.00817205i	−0.00293471	−	0.999996i	$-0.500934\pi$
$839$	104.608	−	6.85635i	0.124681	−	0.00817205i	0.127616	+	0.991824i	$0.459267\pi$
$840$	−1126.52	−	1197.65i	−1.34109	−	1.42577i
$841$	314.635	+	241.428i	0.374120	+	0.287072i
$842$	−1127.63	+	1469.56i	−1.33923	+	1.74532i
$843$	125.761	+	534.213i	0.149183	+	0.633704i
$844$	93.3413	+	1424.11i	0.110594	+	1.68734i
$845$	236.858	−	47.1140i	0.280306	−	0.0557562i
$846$	−67.0153	−	959.792i	−0.0792143	−	1.13451i
$847$	135.396	+	90.4685i	0.159853	+	0.106810i
$848$	1010.84	−	775.646i	1.19203	−	0.914677i
$849$	−119.232	+	1237.60i	−0.140438	+	1.45771i
$850$	−1217.11	+	253.552i	−1.43190	+	0.298297i
$851$	116.998	+	202.646i	0.137483	+	0.238127i
$852$	−307.347	+	577.963i	−0.360736	+	0.678361i
$853$	281.581	+	570.990i	0.330107	+	0.669390i	0.997135	−	0.0756424i	$-0.0241007\pi$
$853$	281.581	+	570.990i	0.330107	+	0.669390i	−0.667028	+	0.745032i	$0.732434\pi$
$854$	1384.73	+	1384.73i	1.62146	+	1.62146i
$855$	−527.043	−	301.302i	−0.616424	−	0.352400i
$856$	−874.940	−	1309.44i	−1.02213	−	1.52972i
$857$	−1190.16	−	1043.74i	−1.38875	−	1.21790i	−0.947189	−	0.320676i	$-0.896090\pi$
$857$	−1190.16	−	1043.74i	−1.38875	−	1.21790i	−0.441565	−	0.897229i	$-0.645577\pi$
$858$	−1603.75	−	1495.67i	−1.86917	−	1.74321i
$859$	472.415	−	615.664i	0.549960	−	0.716721i	−0.432825	−	0.901478i	$-0.642483\pi$
$859$	472.415	−	615.664i	0.549960	−	0.716721i	0.982784	+	0.184757i	$0.0591497\pi$
$860$	−349.398	−	1029.29i	−0.406277	−	1.19685i
$861$	−10.0490	+	328.348i	−0.0116713	+	0.381357i
$862$	394.129	−	1161.07i	0.457227	−	1.34695i
$863$	963.780	−	963.780i	1.11678	−	1.11678i	0.124567	−	0.992211i	$-0.460246\pi$
$863$	963.780	−	963.780i	1.11678	−	1.11678i	0.992211	−	0.124567i	$-0.0397543\pi$
$864$	850.526	−	2304.35i	0.984406	−	2.66707i
$865$	340.359	+	140.981i	0.393479	+	0.162984i
$866$	1049.88	+	606.150i	1.21234	+	0.699942i
$867$	−234.866	+	834.582i	−0.270895	+	0.962609i
$868$	231.453	+	400.889i	0.266651	+	0.461854i
$869$	896.968	−	118.088i	1.03218	−	0.135890i
$870$	−563.057	−	91.7296i	−0.647192	−	0.105436i
$871$	−760.214	+	203.699i	−0.872806	+	0.233868i
$872$	214.445	+	1078.09i	0.245923	+	1.23634i
$873$	−398.953	−	951.672i	−0.456991	−	1.09012i
$874$	172.608	−	867.757i	0.197492	−	0.992857i
$875$	132.385	−	1005.56i	0.151297	−	1.14922i
$876$	17.0361	+	55.7330i	0.0194477	+	0.0636222i
$877$	479.853	+	1413.60i	0.547153	+	1.61186i	0.770722	+	0.637172i	$0.219896\pi$
$877$	479.853	+	1413.60i	0.547153	+	1.61186i	−0.223569	+	0.974688i	$0.571771\pi$
$878$	227.262	+	112.073i	0.258841	+	0.127646i
$879$	−642.905	+	64.7035i	−0.731405	+	0.0736103i
$880$	−357.475	−	1334.12i	−0.406222	−	1.51604i
$881$	312.491	+	208.800i	0.354701	+	0.237003i	0.720135	−	0.693834i	$-0.244080\pi$
$881$	312.491	+	208.800i	0.354701	+	0.237003i	−0.365435	+	0.930837i	$0.619080\pi$
$882$	−90.0163	+	1469.26i	−0.102059	+	1.66582i
$883$			299.360i			0.339027i	0.985528	+	0.169513i	$0.0542196\pi$
$883$			299.360i			0.339027i	−0.985528	+	0.169513i	$0.945780\pi$
$884$	−2152.98	+	1922.81i	−2.43550	+	2.17512i
$885$	339.339	+	744.715i	0.383434	+	0.841485i
$886$	−1383.54	+	182.146i	−1.56155	+	0.205583i
$887$	−1519.15	−	99.5705i	−1.71269	−	0.112255i	−0.822768	−	0.568377i	$-0.807572\pi$
$887$	−1519.15	−	99.5705i	−1.71269	−	0.112255i	−0.889917	+	0.456122i	$0.849238\pi$
$888$	−2007.97	+	335.912i	−2.26123	+	0.378279i
$889$	−851.457	−	289.031i	−0.957769	−	0.325119i
$890$	743.818	+	1113.20i	0.835751	+	1.25079i
$891$	949.848	+	54.1337i	1.06605	+	0.0607561i
$892$	1458.25	−	604.028i	1.63481	−	0.677162i
$893$	792.578	+	104.345i	0.887546	+	0.116848i
$894$	−1340.46	+	1260.85i	−1.49939	+	1.41034i
$895$	−168.323	−	83.0079i	−0.188071	−	0.0927463i
$896$	1218.33	+	1389.24i	1.35974	+	1.55049i
$897$	−381.532	−	142.671i	−0.425342	−	0.159054i
$898$	16.4353	−	8.10497i	0.0183021	−	0.00902558i
$899$	90.9130	+	37.6574i	0.101127	+	0.0418881i
$900$	1698.00	−	584.473i	1.88667	−	0.649414i
$901$	286.438	−	332.636i	0.317911	−	0.369185i
$902$	−253.485	+	439.049i	−0.281025	+	0.486750i
$903$	−597.383	+	1123.37i	−0.661553	+	1.24405i
$904$	−3407.86	−	223.363i	−3.76976	−	0.247083i
$905$	−148.000	+	552.345i	−0.163536	+	0.610326i
$906$	287.431	+	2855.97i	0.317253	+	3.15228i
$907$	609.308	−	39.9362i	0.671784	−	0.0440310i	0.274305	−	0.961643i	$-0.411552\pi$
$907$	609.308	−	39.9362i	0.671784	−	0.0440310i	0.397478	+	0.917612i	$0.369885\pi$
$908$	219.207	−	1102.03i	0.241417	−	1.21369i
$909$	−212.706	+	43.2526i	−0.234000	+	0.0475826i
$910$	−545.016	−	1315.78i	−0.598918	−	1.44592i
$911$	−680.346	+	775.786i	−0.746812	+	0.851576i	−0.993057	−	0.117631i	$-0.962470\pi$
$911$	−680.346	+	775.786i	−0.746812	+	0.851576i	0.246245	+	0.969208i	$0.420803\pi$
$912$	3562.90	+	2205.04i	3.90668	+	2.41781i
$913$	364.972	+	416.171i	0.399750	+	0.455828i
$914$	142.384	+	38.1516i	0.155781	+	0.0417414i
$915$	360.211	−	136.450i	0.393673	−	0.149126i
$916$	3592.45	−	2756.58i	3.92189	−	3.00937i
$917$		−	2040.37i		−	2.22505i
$918$	256.536	−	1718.34i	0.279451	−	1.87182i
$919$	−171.601			−0.186725			−0.0933626	−	0.995632i	$-0.529762\pi$
$919$	−171.601			−0.186725			−0.0933626	+	0.995632i	$0.529762\pi$
$920$	−286.925	−	373.928i	−0.311875	−	0.406444i
$921$	−317.761	−	838.847i	−0.345017	−	0.910800i
$922$	−52.1506	+	194.629i	−0.0565625	+	0.211094i
$923$	−261.185	+	229.053i	−0.282974	+	0.248161i
$924$	−1838.95	+	2971.36i	−1.99020	+	3.21576i
$925$	−411.604	−	360.967i	−0.444977	−	0.390235i
$926$	1298.51	−	537.861i	1.40228	−	0.580843i
$927$	−445.023	−	148.954i	−0.480067	−	0.160684i
$928$	1880.98	+	374.151i	2.02692	+	0.403180i
$929$	−21.1889	−	323.279i	−0.0228082	−	0.347986i	−0.993977	−	0.109592i	$-0.965046\pi$
$929$	−21.1889	−	323.279i	−0.0228082	−	0.347986i	0.971168	−	0.238394i	$-0.0766211\pi$
$930$	125.683	−	12.6491i	0.135143	−	0.0136011i
$931$	−1181.40	−	316.554i	−1.26895	−	0.340015i
$932$	218.431	−	3332.61i	0.234368	−	3.57576i
$933$	−705.378	−	375.103i	−0.756032	−	0.402040i
$934$	−114.732	−	66.2406i	−0.122839	−	0.0709214i
$935$	−214.309	−	424.855i	−0.229208	−	0.454390i
$936$	2325.36	−	2674.46i	2.48436	−	2.85733i
$937$	204.386	−	493.432i	0.218128	−	0.526608i	−0.776500	−	0.630117i	$-0.783007\pi$
$937$	204.386	−	493.432i	0.218128	−	0.526608i	0.994629	+	0.103509i	$0.0330069\pi$
$938$	769.514	+	1560.42i	0.820377	+	1.66356i
$939$	134.141	−	358.720i	0.142855	−	0.382024i
$940$	522.595	−	458.303i	0.555952	−	0.487557i
$941$	−264.653	+	536.662i	−0.281246	+	0.570311i	−0.990957	−	0.134183i	$-0.957159\pi$
$941$	−264.653	+	536.662i	−0.281246	+	0.570311i	0.709710	+	0.704493i	$0.248826\pi$
$942$	1729.47	+	1838.67i	1.83596	+	1.95188i
$943$	−12.2914	+	93.3626i	−0.0130344	+	0.0990059i
$944$	−2161.53	−	5218.41i	−2.28976	−	5.52797i
$945$	546.764	+	287.775i	0.578586	+	0.304524i
$946$	−1632.65	+	1090.90i	−1.72584	+	1.15317i
$947$	−144.390	+	425.359i	−0.152471	+	0.449165i	−0.996148	−	0.0876858i	$-0.972053\pi$
$947$	−144.390	+	425.359i	−0.152471	+	0.449165i	0.843677	+	0.536851i	$0.180386\pi$
$948$	393.747	+	2353.69i	0.415345	+	2.48280i
$949$	−2.02280	+	30.8620i	−0.00213151	+	0.0325206i
$950$	270.190	+	2052.30i	0.284410	+	2.16031i
$951$	359.329	−	163.733i	0.377844	−	0.172170i
$952$	3123.11	+	2351.92i	3.28058	+	2.47050i
$953$	−262.054			−0.274978			−0.137489	−	0.990503i	$-0.543903\pi$
$953$	−262.054			−0.274978			−0.137489	+	0.990503i	$0.543903\pi$
$954$	−485.586	+	733.476i	−0.509000	+	0.768843i
$955$	207.389	−	310.379i	0.217161	−	0.325005i
$956$	2482.30	−	665.131i	2.59655	−	0.695744i
$957$	74.3840	+	739.092i	0.0777262	+	0.772301i
$958$	909.333	−	1843.95i	0.949200	−	1.92479i
$959$	314.857	−	106.880i	0.328318	−	0.111449i
$960$	1004.88	−	307.165i	1.04675	−	0.319964i
$961$	931.176	+	122.592i	0.968966	+	0.127567i
$962$	−1729.57	−	344.034i	−1.79789	−	0.357623i
$963$	471.045	+	358.268i	0.489143	+	0.372033i
$964$	37.3402	−	7.42742i	0.0387346	−	0.00770480i
$965$	181.475	+	677.274i	0.188057	+	0.701839i
$966$	−144.790	+	888.755i	−0.149886	+	0.920036i
$967$	118.666	+	901.356i	0.122715	+	0.932116i	0.936431	+	0.350853i	$0.114108\pi$
$967$	118.666	+	901.356i	0.122715	+	0.932116i	−0.813715	+	0.581264i	$0.802559\pi$
$968$	−351.722	+	203.067i	−0.363349	+	0.209779i
$969$	1356.63	+	493.378i	1.40003	+	0.509162i
$970$	517.127	−	895.690i	0.533121	−	0.923392i
$971$	129.172	−	311.850i	0.133030	−	0.321163i	−0.843302	−	0.537440i	$-0.819391\pi$
$971$	129.172	−	311.850i	0.133030	−	0.321163i	0.976332	+	0.216277i	$0.0693914\pi$
$972$	−55.3948	+	2508.92i	−0.0569905	+	2.58119i
$973$	−114.783	−	114.783i	−0.117968	−	0.117968i
$974$	2335.79	+	792.894i	2.39814	+	0.814060i
$975$	952.567	+	29.1529i	0.976992	+	0.0299004i
$976$	−2517.43	+	854.552i	−2.57933	+	0.875566i
$977$	−1138.00	−	873.216i	−1.16479	−	0.893772i	−0.169013	−	0.985614i	$-0.554058\pi$
$977$	−1138.00	−	873.216i	−1.16479	−	0.893772i	−0.995774	+	0.0918415i	$0.970725\pi$
$978$	1858.48	−	1992.77i	1.90029	−	2.03760i
$979$	1149.44	−	1310.69i	1.17410	−	1.33880i
$980$	−884.227	+	590.822i	−0.902272	+	0.602879i
$981$	−208.057	−	356.845i	−0.212086	−	0.363757i
$982$	−1314.79	+	1314.79i	−1.33889	+	1.33889i
$983$	−764.993	+	377.253i	−0.778223	+	0.383777i	−0.787606	−	0.616179i	$-0.788680\pi$
$983$	−764.993	+	377.253i	−0.778223	+	0.383777i	0.00938309	+	0.999956i	$0.497013\pi$
$984$	−723.387	−	384.680i	−0.735149	−	0.390935i
$985$	70.0131	−	40.4221i	0.0710792	−	0.0410376i
$986$	1356.46	−	12.2574i	1.37572	−	0.0124314i
$987$	−809.866	−	78.0235i	−0.820533	−	0.0790512i
$988$	2925.85	+	3813.04i	2.96138	+	3.85935i
$989$	−202.631	+	303.259i	−0.204885	+	0.306632i
$990$	533.135	+	790.582i	0.538520	+	0.798568i
$991$	−154.589	−	777.173i	−0.155993	−	0.784231i	−0.976988	−	0.213295i	$-0.931580\pi$
$991$	−154.589	−	777.173i	−0.155993	−	0.784231i	0.820995	−	0.570936i	$-0.193420\pi$
$992$	−423.746	+	27.7738i	−0.427163	+	0.0279977i
$993$	−933.976	+	219.871i	−0.940560	+	0.221421i
$994$	609.267	+	467.507i	0.612945	+	0.470329i
$995$	−304.976	+	397.453i	−0.306509	+	0.399450i
$996$	−1063.54	+	1000.38i	−1.06781	+	1.00439i
$997$	−7.44449	−	113.581i	−0.00746690	−	0.113923i	0.992498	−	0.122258i	$-0.0390135\pi$
$997$	−7.44449	−	113.581i	−0.00746690	−	0.113923i	−0.999965	+	0.00833508i	$0.997347\pi$
$998$	−3143.34	+	625.249i	−3.14964	+	0.626502i
$999$	672.402	−	364.949i	0.673075	−	0.365315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.t.a.7.2	✓	544
9.4	even	3	inner	153.3.t.a.58.33	yes	544
17.5	odd	16	inner	153.3.t.a.124.33	yes	544
153.22	odd	48	inner	153.3.t.a.22.2	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.2	✓	544	1.1	even	1	trivial
153.3.t.a.22.2	yes	544	153.22	odd	48	inner
153.3.t.a.58.33	yes	544	9.4	even	3	inner
153.3.t.a.124.33	yes	544	17.5	odd	16	inner

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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.t (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30425 - 3.00295i) q^{2} +(1.06273 + 2.80546i) q^{3} +(-2.67290 + 9.97539i) q^{4} +(1.79172 - 1.57130i) q^{5} +(5.97588 - 9.65580i) q^{6} +(-7.21963 - 6.33144i) q^{7} +(22.1266 - 9.16514i) q^{8} +(-6.74122 + 5.96288i) q^{9} +(-8.84710 - 1.75980i) q^{10} +(0.768195 + 11.7204i) q^{11} +(-30.8261 + 3.10242i) q^{12} +(-15.8817 - 4.25549i) q^{13} +(-2.37722 + 36.2694i) q^{14} +(6.31232 + 3.35674i) q^{15} +(-42.7329 - 24.6719i) q^{16} +(-16.1465 - 5.31879i) q^{17} +(33.4397 + 6.50361i) q^{18} +(-10.8319 + 26.1505i) q^{19} +(10.8852 + 22.0730i) q^{20} +(10.0901 - 26.9830i) q^{21} +(33.4257 - 29.3135i) q^{22} +(3.65244 - 7.40642i) q^{23} +(49.2270 + 52.3353i) q^{24} +(-2.52187 + 19.1555i) q^{25} +(23.8163 + 57.4977i) q^{26} +(-23.8927 - 12.5753i) q^{27} +(82.4560 - 55.0953i) q^{28} +(6.77629 - 19.9623i) q^{29} +(-4.46501 - 26.6904i) q^{30} +(-0.305293 + 4.65787i) q^{31} +(11.8745 + 90.1959i) q^{32} +(-32.0647 + 14.6107i) q^{33} +(21.2335 + 60.7431i) q^{34} -22.8841 q^{35} +(-41.4635 - 83.1845i) q^{36} +(-15.7423 + 23.5601i) q^{37} +(103.488 - 27.7296i) q^{38} +(-4.93932 - 49.0779i) q^{39} +(25.2435 - 51.1888i) q^{40} +(-10.7980 + 3.66544i) q^{41} +(-104.279 + 31.8753i) q^{42} +(-43.7884 - 5.76485i) q^{43} +(-118.969 - 23.6644i) q^{44} +(-2.70892 + 21.2763i) q^{45} +(-30.6573 + 6.09811i) q^{46} +(-7.30979 - 27.2805i) q^{47} +(23.8025 - 146.105i) q^{48} +(5.64006 + 42.8405i) q^{49} +(63.3340 - 36.5659i) q^{50} +(-2.23772 - 50.9509i) q^{51} +(84.9003 - 147.052i) q^{52} +(-9.88153 + 23.8561i) q^{53} +(17.2917 + 100.725i) q^{54} +(19.7926 + 19.7926i) q^{55} +(-217.774 - 73.9245i) q^{56} +(-84.8756 - 2.59758i) q^{57} +(-75.5601 + 25.6492i) q^{58} +(90.8149 + 69.6848i) q^{59} +(-50.3570 + 53.9956i) q^{60} +(35.5239 - 40.5073i) q^{61} +(14.6908 - 9.81610i) q^{62} +(86.4227 - 0.368141i) q^{63} +(103.927 - 103.927i) q^{64} +(-35.1422 + 17.3302i) q^{65} +(117.760 + 62.6221i) q^{66} +(41.4543 - 23.9337i) q^{67} +(96.2151 - 146.851i) q^{68} +(24.6600 + 2.37577i) q^{69} +(52.7307 + 68.7200i) q^{70} +(11.7384 - 17.5678i) q^{71} +(-94.5097 + 193.723i) q^{72} +(-0.366976 - 1.84491i) q^{73} +(107.024 - 7.01472i) q^{74} +(-56.4200 + 13.2821i) q^{75} +(-231.909 - 177.950i) q^{76} +(68.6609 - 89.4807i) q^{77} +(-135.997 + 127.920i) q^{78} +(-5.03772 - 76.8607i) q^{79} +(-115.332 + 22.9410i) q^{80} +(9.88807 - 80.3942i) q^{81} +(35.8885 + 23.9799i) q^{82} +(37.3887 - 28.6893i) q^{83} +(242.196 + 172.776i) q^{84} +(-37.2875 + 15.8412i) q^{85} +(83.5877 + 144.778i) q^{86} +(63.2048 - 2.20388i) q^{87} +(124.417 + 252.292i) q^{88} +(-104.951 - 104.951i) q^{89} +(70.1337 - 40.8910i) q^{90} +(87.7165 + 131.277i) q^{91} +(64.1193 + 56.2311i) q^{92} +(-13.3919 + 4.09356i) q^{93} +(-65.0785 + 84.8120i) q^{94} +(21.6825 + 63.8745i) q^{95} +(-240.422 + 129.167i) q^{96} +(-36.8553 + 108.572i) q^{97} +(115.652 - 115.652i) q^{98} +(-75.0659 - 74.4291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} + 176 q^{12} - 8 q^{13} - 8 q^{14} - 40 q^{15} - 32 q^{17} + 32 q^{18} - 32 q^{19} - 8 q^{20}+ \cdots + 448 q^{99}+O(q^{100}) \) 544 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^5 - 16 * q^6 - 8 * q^7 - 32 * q^8 - 16 * q^9 - 32 * q^10 - 8 * q^11 + 176 * q^12 - 8 * q^13 - 8 * q^14 - 40 * q^15 - 32 * q^17 + 32 * q^18 - 32 * q^19 - 8 * q^20 - 256 * q^21 - 8 * q^22 - 8 * q^23 + 176 * q^24 - 8 * q^25 - 32 * q^26 - 16 * q^27 - 32 * q^28 - 8 * q^29 - 16 * q^30 - 8 * q^31 - 72 * q^32 + 40 * q^34 - 64 * q^35 + 16 * q^36 - 32 * q^37 + 88 * q^38 - 192 * q^39 - 8 * q^40 - 440 * q^41 - 400 * q^42 - 248 * q^43 - 800 * q^44 - 176 * q^45 - 32 * q^46 + 112 * q^47 - 248 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 + 160 * q^53 - 312 * q^54 - 32 * q^55 - 488 * q^56 - 296 * q^57 - 8 * q^58 + 568 * q^59 + 2080 * q^60 - 8 * q^61 + 1120 * q^62 - 88 * q^63 - 288 * q^64 - 248 * q^65 - 24 * q^66 - 8 * q^68 - 416 * q^69 - 40 * q^70 - 32 * q^71 + 632 * q^72 - 32 * q^73 - 8 * q^74 + 752 * q^75 - 8 * q^76 - 8 * q^77 - 2304 * q^78 - 8 * q^79 - 432 * q^80 + 768 * q^81 + 352 * q^82 - 296 * q^83 - 8 * q^85 + 1184 * q^86 - 688 * q^87 - 8 * q^88 - 1184 * q^89 - 1136 * q^90 + 640 * q^91 - 2024 * q^92 - 528 * q^93 - 8 * q^94 + 472 * q^95 - 1064 * q^96 - 8 * q^97 - 848 * q^98 + 448 * q^99

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