LMFDB - Embedded newform 153.3.t.a.58.33

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			58.33
Character	$\chi$	$=$	153.58
Dual form			153.3.t.a.124.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.75276 - 0.494060i) q^{2} +(-2.99860 + 0.0917708i) q^{3} +(9.97539 - 2.67290i) q^{4} +(-2.25664 - 0.766027i) q^{5} +(-11.2077 + 1.82588i) q^{6} +(9.09301 - 3.08666i) q^{7} +(22.1266 - 9.16514i) q^{8} +(8.98316 - 0.550367i) q^{9} +(-8.84710 - 1.75980i) q^{10} +(-10.5343 - 5.19492i) q^{11} +(-29.6669 + 8.93039i) q^{12} +(4.25549 + 15.8817i) q^{13} +(32.5989 - 16.0760i) q^{14} +(6.83706 + 2.08991i) 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} +(-24.5584 - 1.60964i) q^{20} +(-26.9830 + 10.0901i) q^{21} +(-42.0991 - 14.2907i) q^{22} +(-8.24036 + 0.540102i) q^{23} +(-65.5077 + 29.5131i) q^{24} +(-15.3282 - 11.7617i) q^{25} +(23.8163 + 57.4977i) q^{26} +(-26.8863 + 2.47472i) q^{27} +(82.4560 - 55.0953i) q^{28} +(13.8997 + 15.8496i) q^{29} +(26.6904 + 4.46501i) q^{30} +(4.18648 - 2.06454i) q^{31} +(72.1747 - 55.3816i) q^{32} +(32.0647 + 14.6107i) q^{33} +(-63.2218 - 11.9828i) q^{34} -22.8841 q^{35} +(88.1394 - 29.5012i) q^{36} +(-15.7423 + 23.5601i) q^{37} +(-27.7296 + 103.488i) q^{38} +(-14.2180 - 47.2323i) q^{39} +(-56.9526 + 3.73287i) q^{40} +(8.57338 + 7.51866i) q^{41} +(-96.2755 + 51.1970i) q^{42} +(26.8867 - 35.0394i) q^{43} +(-118.969 - 23.6644i) q^{44} +(-20.6934 - 5.63936i) q^{45} +(-30.6573 + 6.09811i) q^{46} +(27.2805 + 7.30979i) q^{47} +(-125.875 + 77.9026i) q^{48} +(34.2810 - 26.3047i) q^{49} +(-63.3340 - 36.5659i) q^{50} +(48.9050 + 14.4671i) q^{51} +(84.9003 + 147.052i) q^{52} +(-9.88153 + 23.8561i) q^{53} +(-99.6753 + 22.5705i) q^{54} +(19.7926 + 19.7926i) q^{55} +(172.908 - 151.636i) q^{56} +(30.0806 - 79.4089i) q^{57} +(59.9929 + 52.6124i) q^{58} +(14.9413 - 113.490i) q^{59} +(73.7885 + 2.57292i) q^{60} +(17.3184 + 51.0183i) q^{61} +(14.6908 - 9.81610i) q^{62} +(79.9851 - 32.7324i) q^{63} +(103.927 - 103.927i) q^{64} +(2.56269 - 39.0991i) q^{65} +(127.550 + 38.9886i) q^{66} +(-41.4543 - 23.9337i) q^{67} +(-175.285 - 9.89897i) q^{68} +(24.6600 - 2.37577i) q^{69} +(-85.8786 + 11.3061i) q^{70} +(11.7384 - 17.5678i) q^{71} +(193.723 - 94.5097i) q^{72} +(-0.366976 - 1.84491i) q^{73} +(-47.4371 + 96.1929i) q^{74} +(47.0425 + 33.8620i) q^{75} +(-38.1548 + 289.814i) q^{76} +(-111.823 - 14.7218i) q^{77} +(-76.6921 - 170.227i) q^{78} +(69.0822 + 34.0676i) q^{79} +(-115.332 + 22.9410i) q^{80} +(80.3942 - 9.88807i) q^{81} +(35.8885 + 23.9799i) q^{82} +(6.15136 + 46.7242i) q^{83} +(-242.196 + 172.776i) q^{84} +(32.3626 + 24.3713i) q^{85} +(83.5877 - 144.778i) q^{86} +(-43.1342 - 46.2509i) q^{87} +(-280.700 - 18.3980i) q^{88} +(-104.951 - 104.951i) q^{89} +(-80.4434 - 10.9394i) q^{90} +(87.7165 + 131.277i) q^{91} +(-80.7572 + 27.4134i) q^{92} +(-12.3641 + 6.57492i) q^{93} +(105.989 + 13.9537i) q^{94} +(44.4757 - 50.7148i) q^{95} +(-211.340 + 172.691i) q^{96} +(-75.5986 - 86.2037i) q^{97} +(115.652 - 115.652i) q^{98} +(-97.4900 - 40.8691i) 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 $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.75276	−	0.494060i	1.87638	−	0.247030i	0.895986	−	0.444082i	$-0.146470\pi$
$2$	3.75276	−	0.494060i	1.87638	−	0.247030i	0.980393	+	0.197052i	$0.0631369\pi$
$3$	−2.99860	+	0.0917708i	−0.999532	+	0.0305903i
$3$	−2.99860	+	0.0917708i	−0.999532	+	0.0305903i
$4$	9.97539	−	2.67290i	2.49385	−	0.668225i
$5$	−2.25664	−	0.766027i	−0.451328	−	0.153205i	0.0865142	−	0.996251i	$-0.472427\pi$
$5$	−2.25664	−	0.766027i	−0.451328	−	0.153205i	−0.537843	+	0.843045i	$0.680761\pi$
$6$	−11.2077	+	1.82588i	−1.86794	+	0.304313i
$7$	9.09301	−	3.08666i	1.29900	−	0.440951i	0.415591	−	0.909552i	$-0.363575\pi$
$7$	9.09301	−	3.08666i	1.29900	−	0.440951i	0.883410	+	0.468600i	$0.155242\pi$
$8$	22.1266	−	9.16514i	2.76583	−	1.14564i
$9$	8.98316	−	0.550367i	0.998128	−	0.0611519i
$10$	−8.84710	−	1.75980i	−0.884710	−	0.175980i
$11$	−10.5343	−	5.19492i	−0.957660	−	0.472266i	−0.104850	−	0.994488i	$-0.533436\pi$
$11$	−10.5343	−	5.19492i	−0.957660	−	0.472266i	−0.852809	+	0.522222i	$0.825103\pi$
$12$	−29.6669	+	8.93039i	−2.47224	+	0.744199i
$13$	4.25549	+	15.8817i	0.327345	+	1.22167i	0.911933	+	0.410339i	$0.134589\pi$
$13$	4.25549	+	15.8817i	0.327345	+	1.22167i	−0.584588	+	0.811330i	$0.698744\pi$
$14$	32.5989	−	16.0760i	2.32849	−	1.14828i
$15$	6.83706	+	2.08991i	0.455804	+	0.139327i
$16$	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	$0.857511\pi$
$20$	−24.5584	−	1.60964i	−1.22792	−	0.0804821i
$21$	−26.9830	+	10.0901i	−1.28490	+	0.480482i
$22$	−42.0991	−	14.2907i	−1.91360	−	0.649578i
$23$	−8.24036	+	0.540102i	−0.358277	+	0.0234827i	−0.243479	−	0.969906i	$-0.578289\pi$
$23$	−8.24036	+	0.540102i	−0.358277	+	0.0234827i	−0.114798	+	0.993389i	$0.536622\pi$
$24$	−65.5077	+	29.5131i	−2.72949	+	1.22971i
$25$	−15.3282	−	11.7617i	−0.613128	−	0.470470i
$26$	23.8163	+	57.4977i	0.916012	+	2.21145i
$27$	−26.8863	+	2.47472i	−0.995791	+	0.0916563i
$28$	82.4560	−	55.0953i	2.94486	−	1.96769i
$29$	13.8997	+	15.8496i	0.479301	+	0.546538i	0.940070	−	0.340982i	$-0.110760\pi$
$29$	13.8997	+	15.8496i	0.479301	+	0.546538i	−0.460769	+	0.887520i	$0.652426\pi$
$30$	26.6904	+	4.46501i	0.889679	+	0.148834i
$31$	4.18648	−	2.06454i	0.135048	−	0.0665981i	−0.373510	−	0.927626i	$-0.621846\pi$
$31$	4.18648	−	2.06454i	0.135048	−	0.0665981i	0.508557	+	0.861028i	$0.330179\pi$
$32$	72.1747	−	55.3816i	2.25546	−	1.73067i
$33$	32.0647	+	14.6107i	0.971658	+	0.442749i
$34$	−63.2218	−	11.9828i	−1.85947	−	0.352434i
$35$	−22.8841			−0.653832
$36$	88.1394	−	29.5012i	2.44832	−	0.819478i
$37$	−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	$0.312579\pi$
$38$	−27.7296	+	103.488i	−0.729726	+	2.72337i
$39$	−14.2180	−	47.2323i	−0.364563	−	1.21108i
$40$	−56.9526	+	3.73287i	−1.42381	+	0.0933217i
$41$	8.57338	+	7.51866i	0.209107	+	0.183382i	0.757493	−	0.652844i	$-0.226424\pi$
$41$	8.57338	+	7.51866i	0.209107	+	0.183382i	−0.548386	+	0.836225i	$0.684757\pi$
$42$	−96.2755	+	51.1970i	−2.29227	+	1.21898i
$43$	26.8867	−	35.0394i	0.625272	−	0.814870i	−0.368103	−	0.929785i	$-0.619993\pi$
$43$	26.8867	−	35.0394i	0.625272	−	0.814870i	0.993375	+	0.114914i	$0.0366594\pi$
$44$	−118.969	−	23.6644i	−2.70384	−	0.537827i
$45$	−20.6934	−	5.63936i	−0.459853	−	0.125319i
$46$	−30.6573	+	6.09811i	−0.666462	+	0.132568i
$47$	27.2805	+	7.30979i	0.580436	+	0.155527i	0.537079	−	0.843532i	$-0.319528\pi$
$47$	27.2805	+	7.30979i	0.580436	+	0.155527i	0.0433576	+	0.999060i	$0.486195\pi$
$48$	−125.875	+	77.9026i	−2.62239	+	1.62297i
$49$	34.2810	−	26.3047i	0.699611	−	0.536831i
$50$	−63.3340	−	36.5659i	−1.26668	−	0.731318i
$51$	48.9050	+	14.4671i	0.958922	+	0.283669i
$52$	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	$0.203329\pi$
$54$	−99.6753	+	22.5705i	−1.84584	+	0.417972i
$55$	19.7926	+	19.7926i	0.359865	+	0.359865i
$56$	172.908	−	151.636i	3.08764	−	2.70779i
$57$	30.0806	−	79.4089i	0.527731	−	1.39314i
$58$	59.9929	+	52.6124i	1.03436	+	0.907110i
$59$	14.9413	−	113.490i	0.253242	−	1.92357i	−0.114077	−	0.993472i	$-0.536391\pi$
$59$	14.9413	−	113.490i	0.253242	−	1.92357i	0.367320	−	0.930095i	$-0.380275\pi$
$60$	73.7885	+	2.57292i	1.22981	+	0.0428821i
$61$	17.3184	+	51.0183i	0.283908	+	0.836365i	0.991542	+	0.129786i	$0.0414291\pi$
$61$	17.3184	+	51.0183i	0.283908	+	0.836365i	−0.707634	+	0.706579i	$0.750238\pi$
$62$	14.6908	−	9.81610i	0.236949	−	0.158324i
$63$	79.9851	−	32.7324i	1.26960	−	0.519562i
$64$	103.927	−	103.927i	1.62386	−	1.62386i
$65$	2.56269	−	39.0991i	0.0394260	−	0.601525i
$66$	127.550	+	38.9886i	1.93257	+	0.590737i
$67$	−41.4543	−	23.9337i	−0.618721	−	0.357219i	0.157650	−	0.987495i	$-0.449608\pi$
$67$	−41.4543	−	23.9337i	−0.618721	−	0.357219i	−0.776371	+	0.630276i	$0.782942\pi$
$68$	−175.285	−	9.89897i	−2.57771	−	0.145573i
$69$	24.6600	−	2.37577i	0.357391	−	0.0344315i
$70$	−85.8786	+	11.3061i	−1.22684	+	0.161516i
$71$	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	$0.139961\pi$
$72$	193.723	−	94.5097i	2.69059	−	1.31263i
$73$	−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	$0.941601\pi$
$74$	−47.4371	+	96.1929i	−0.641042	+	1.29990i
$75$	47.0425	+	33.8620i	0.627233	+	0.451494i
$76$	−38.1548	+	289.814i	−0.502037	+	3.81335i
$77$	−111.823	−	14.7218i	−1.45225	−	0.191192i
$78$	−76.6921	−	170.227i	−0.983233	−	2.18239i
$79$	69.0822	+	34.0676i	0.874458	+	0.431235i	0.823401	−	0.567461i	$-0.192074\pi$
$79$	69.0822	+	34.0676i	0.874458	+	0.431235i	0.0510578	+	0.998696i	$0.483741\pi$
$80$	−115.332	+	22.9410i	−1.44165	+	0.286762i
$81$	80.3942	−	9.88807i	0.992521	−	0.122075i
$82$	35.8885	+	23.9799i	0.437665	+	0.292438i
$83$	6.15136	+	46.7242i	0.0741128	+	0.562942i	0.987707	+	0.156316i	$0.0499617\pi$
$83$	6.15136	+	46.7242i	0.0741128	+	0.562942i	−0.913594	+	0.406627i	$0.866705\pi$
$84$	−242.196	+	172.776i	−2.88329	+	2.05685i
$85$	32.3626	+	24.3713i	0.380737	+	0.286721i
$86$	83.5877	−	144.778i	0.971950	−	1.68347i
$87$	−43.1342	−	46.2509i	−0.495795	−	0.531620i
$88$	−280.700	−	18.3980i	−3.18977	−	0.209068i
$89$	−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	$-0.563861\pi$
$90$	−80.4434	−	10.9394i	−0.893815	−	0.121549i
$91$	87.7165	+	131.277i	0.963918	+	1.44261i
$92$	−80.7572	+	27.4134i	−0.877796	+	0.297972i
$93$	−12.3641	+	6.57492i	−0.132947	+	0.0706981i
$94$	105.989	+	13.9537i	1.12754	+	0.148443i
$95$	44.4757	−	50.7148i	0.468166	−	0.533841i
$96$	−211.340	+	172.691i	−2.20146	+	1.79886i
$97$	−75.5986	−	86.2037i	−0.779367	−	0.888698i	0.216796	−	0.976217i	$-0.430439\pi$
$97$	−75.5986	−	86.2037i	−0.779367	−	0.888698i	−0.996163	+	0.0875194i	$0.972106\pi$
$98$	115.652	−	115.652i	1.18012	−	1.18012i
$99$	−97.4900	−	40.8691i	−0.984747	−	0.412819i
$100$	−184.343	−	76.3573i	−1.84343	−	0.763573i
$101$	−20.8865	+	12.0588i	−0.206797	+	0.119394i	−0.599822	−	0.800133i	$-0.704762\pi$
$101$	−20.8865	+	12.0588i	−0.206797	+	0.119394i	0.393025	+	0.919528i	$0.371429\pi$
$102$	190.676	+	30.1296i	1.86938	+	0.295388i
$103$	26.0716	−	45.1574i	0.253122	−	0.438421i	−0.711261	−	0.702928i	$-0.751876\pi$
$103$	26.0716	−	45.1574i	0.253122	−	0.438421i	0.964384	+	0.264507i	$0.0852091\pi$
$104$	239.717	+	312.406i	2.30498	+	3.00390i
$105$	68.6202	−	2.10010i	0.653526	−	0.0200009i
$106$	−25.2966	+	94.4083i	−0.238648	+	0.890645i
$107$	−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	$-0.161917\pi$
$108$	−261.587	+	96.5508i	−2.42210	+	0.893989i
$109$	−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	$0.994979\pi$
$110$	84.0556	+	64.4981i	0.764142	+	0.586346i
$111$	45.0428	−	72.0918i	0.405791	−	0.649476i
$112$	312.417	−	356.243i	2.78944	−	3.18074i
$113$	9.32635	+	142.293i	0.0825341	+	1.25923i	0.815418	+	0.578873i	$0.196507\pi$
$113$	9.32635	+	142.293i	0.0825341	+	1.25923i	−0.732884	+	0.680354i	$0.761826\pi$
$114$	73.6526	−	312.864i	0.646075	−	2.74442i
$115$	19.0093	+	5.09352i	0.165298	+	0.0442915i
$116$	181.019	+	120.953i	1.56051	+	1.04270i
$117$	46.9685	+	140.326i	0.401440	+	1.19936i
$118$		−	433.284i		−	3.67190i
$119$	−163.238	+	1.47507i	−1.37175	+	0.0123955i
$120$	170.435	−	16.4200i	1.42029	−	0.136833i
$121$	10.3232	+	13.4535i	0.0853160	+	0.111186i
$122$	90.1977	+	182.903i	0.739325	+	1.49920i
$123$	−26.3981	−	21.7586i	−0.214619	−	0.176899i
$124$	36.2434	−	31.7846i	0.292286	−	0.256328i
$125$	58.6801	+	87.8210i	0.469441	+	0.702568i
$126$	283.993	−	162.354i	2.25391	−	1.28853i
$127$	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	$0.254818\pi$
$128$	117.141	−	152.661i	0.915164	−	1.19266i
$129$	−77.4068	+	107.537i	−0.600052	+	0.833616i
$130$	−9.70015	−	147.996i	−0.0746165	−	1.13843i
$131$	68.2997	−	201.205i	0.521372	−	1.53591i	−0.293318	−	0.956015i	$-0.594759\pi$
$131$	68.2997	−	201.205i	0.521372	−	1.53591i	0.814690	−	0.579897i	$-0.196907\pi$
$132$	358.911	+	60.0420i	2.71902	+	0.454864i
$133$	−17.7768	+	271.221i	−0.133660	+	2.03926i
$134$	−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	0.795896	−	0.605434i	$-0.207000\pi$
$137$	−17.3131	−	29.9872i	−0.126373	−	0.218885i	−0.922269	+	0.386549i	$0.873667\pi$
$138$	91.3691	−	21.0992i	0.662095	−	0.152893i
$139$	−7.47668	−	15.1612i	−0.0537890	−	0.109073i	0.868319	−	0.496007i	$-0.165201\pi$
$139$	−7.47668	−	15.1612i	−0.0537890	−	0.109073i	−0.922108	+	0.386934i	$0.873534\pi$
$140$	−228.278	+	61.1669i	−1.63056	+	0.436907i
$141$	−82.4740	−	19.4155i	−0.584922	−	0.137699i
$142$	35.3718	−	71.7270i	0.249097	−	0.505120i
$143$	37.6757	−	189.409i	0.263467	−	1.32454i
$144$	370.298	−	245.150i	2.57151	−	1.70243i
$145$	−19.2255	−	46.4144i	−0.132590	−	0.320099i
$146$	−2.28867	−	6.74221i	−0.0156758	−	0.0461795i
$147$	−100.381	+	82.0232i	−0.682862	+	0.557981i
$148$	−94.0623	+	277.099i	−0.635556	+	1.87229i
$149$	41.9442	+	156.538i	0.281505	+	1.05059i	0.951356	+	0.308095i	$0.0996915\pi$
$149$	41.9442	+	156.538i	0.281505	+	1.05059i	−0.669851	+	0.742496i	$0.733642\pi$
$150$	193.269	+	103.834i	1.28846	+	0.692228i
$151$	−32.9941	−	250.615i	−0.218504	−	1.65970i	−0.651757	−	0.758428i	$-0.725968\pi$
$151$	−32.9941	−	250.615i	−0.218504	−	1.65970i	0.433253	−	0.901272i	$-0.357366\pi$
$152$			677.898i			4.45986i
$153$	−147.974	−	38.8930i	−0.967151	−	0.254203i
$154$	−426.918			−2.77220
$155$	−11.0289	+	1.45198i	−0.0711540	+	0.00936760i
$156$	−268.077	−	433.157i	−1.71844	−	2.77665i
$157$	214.720	−	57.5339i	1.36764	−	0.366458i	0.501024	−	0.865433i	$-0.332957\pi$
$157$	214.720	−	57.5339i	1.36764	−	0.366458i	0.866616	+	0.498975i	$0.166290\pi$
$158$	276.080	+	93.7166i	1.74734	+	0.593143i
$159$	27.4414	−	72.4417i	0.172588	−	0.455608i
$160$	−205.296	+	69.6887i	−1.28310	+	0.435554i
$161$	−73.2626	+	30.3463i	−0.455047	+	0.188487i
$162$	296.815	−	76.8271i	1.83219	−	0.474241i
$163$	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	$0.299170\pi$
$164$	105.619	+	52.0858i	0.644021	+	0.317596i
$165$	−61.1664	−	57.5336i	−0.370705	−	0.348689i
$166$	46.1691	+	172.305i	0.278127	+	1.03798i
$167$	53.9960	−	26.6279i	0.323329	−	0.159448i	−0.273379	−	0.961906i	$-0.588141\pi$
$167$	53.9960	−	26.6279i	0.323329	−	0.159448i	0.596709	+	0.802458i	$0.296475\pi$
$168$	−504.565	+	470.563i	−3.00336	+	2.80097i
$169$	−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
$173$	−154.258	−	10.1106i	−0.891662	−	0.0584426i	−0.387319	−	0.921946i	$-0.626599\pi$
$173$	−154.258	−	10.1106i	−0.891662	−	0.0584426i	−0.504343	+	0.863503i	$0.668265\pi$
$174$	−184.723	−	152.258i	−1.06163	−	0.875044i
$175$	−175.684	−	59.6366i	−1.00391	−	0.340781i
$176$	−578.328	+	37.9056i	−3.28595	+	0.215373i
$177$	−34.3878	+	341.683i	−0.194281	+	1.93041i
$178$	−445.707	−	342.003i	−2.50397	−	1.92137i
$179$	−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	$0.945600\pi$
$180$	−221.498	−	0.943530i	−1.23054	−	0.00524184i
$181$	−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	$0.543152\pi$
$182$	394.038	+	449.314i	2.16504	+	2.46876i
$183$	−56.6128	−	151.394i	−0.309359	−	0.827289i
$184$	−177.381	+	87.4747i	−0.964028	+	0.475406i
$185$	53.5724	−	41.1076i	0.289581	−	0.222203i
$186$	−43.1510	+	30.7827i	−0.231995	+	0.165498i
$187$	142.461	+	139.909i	0.761824	+	0.748179i
$188$	291.672			1.55145
$189$	−236.839	+	105.492i	−1.25312	+	0.558157i
$190$	141.850	−	212.294i	0.746581	−	1.11734i
$191$	−40.5413	+	151.302i	−0.212258	+	0.792159i	0.774855	+	0.632138i	$0.217823\pi$
$191$	−40.5413	+	151.302i	−0.212258	+	0.792159i	−0.987114	+	0.160020i	$0.948844\pi$
$192$	−302.098	+	321.173i	−1.57343	+	1.67278i
$193$	293.593	−	19.2431i	1.52121	−	0.0997051i	0.718267	−	0.695767i	$-0.244935\pi$
$193$	293.593	−	19.2431i	1.52121	−	0.0997051i	0.802938	+	0.596062i	$0.203269\pi$
$194$	−326.293	−	286.151i	−1.68192	−	1.47501i
$195$	−4.09632	+	117.478i	−0.0210068	+	0.602449i
$196$	271.656	−	354.029i	1.38600	−	1.80627i
$197$	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	$0.535059\pi$
$198$	−386.048	−	105.206i	−1.94974	−	0.531343i
$199$	−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	$0.614630\pi$
$200$	−446.959	−	119.762i	−2.23480	−	0.598812i
$201$	126.501	+	67.9631i	0.629359	+	0.338125i
$202$	−72.4242	+	55.5731i	−0.358536	+	0.275114i
$203$	175.312	+	101.217i	0.863608	+	0.498604i
$204$	526.516	+	13.5970i	2.58096	+	0.0666519i
$205$	−13.5876	−	23.5344i	−0.0662808	−	0.114802i
$206$	75.5300	−	182.346i	0.366651	−	0.885173i
$207$	−73.7272	+	9.38705i	−0.356170	+	0.0453481i
$208$	573.680	+	573.680i	2.75808	+	2.75808i
$209$	249.956	−	219.205i	1.19596	−	1.04883i
$210$	256.478	−	41.7837i	1.22132	−	0.198970i
$211$	−103.900	−	91.1176i	−0.492416	−	0.431837i	0.376782	−	0.926302i	$-0.377031\pi$
$211$	−103.900	−	91.1176i	−0.492416	−	0.431837i	−0.869198	+	0.494465i	$0.835364\pi$
$212$	−34.8072	+	264.387i	−0.164185	+	1.24711i
$213$	−33.5865	+	53.7558i	−0.157683	+	0.252375i
$214$	−80.0057	−	235.689i	−0.373859	−	1.10135i
$215$	−87.5148	+	58.4755i	−0.407046	+	0.271979i
$216$	−572.223	+	301.174i	−2.64918	+	1.39433i
$217$	31.6951	−	31.6951i	0.146060	−	0.146060i
$218$	−11.3622	+	173.353i	−0.0521200	+	0.795197i
$219$	1.26972	+	5.49847i	0.00579782	+	0.0251072i
$220$	250.343	+	144.535i	1.13792	+	0.656979i
$221$	15.7600	−	279.068i	0.0713123	−	1.26275i
$222$	133.417	−	292.797i	0.600977	−	1.31890i
$223$	151.530	−	19.9494i	0.679509	−	0.0894590i	0.217131	−	0.976142i	$-0.430330\pi$
$223$	151.530	−	19.9494i	0.679509	−	0.0894590i	0.462377	+	0.886683i	$0.346997\pi$
$224$	485.341	−	726.364i	2.16670	−	3.24269i
$225$	−144.169	−	97.2214i	−0.640750	−	0.432095i
$226$	105.301	+	529.382i	0.465932	+	2.34240i
$227$	48.1214	−	97.5805i	0.211989	−	0.429870i	−0.764743	−	0.644335i	$-0.777134\pi$
$227$	48.1214	−	97.5805i	0.211989	−	0.429870i	0.976732	+	0.214465i	$0.0688008\pi$
$228$	87.8143	−	872.538i	0.385150	−	3.82692i
$229$	−57.2315	+	434.717i	−0.249919	+	1.89833i	0.161490	+	0.986874i	$0.448370\pi$
$229$	−57.2315	+	434.717i	−0.249919	+	1.89833i	−0.411409	+	0.911451i	$0.634963\pi$
$230$	73.8538	+	9.72303i	0.321103	+	0.0422741i
$231$	336.663	+	33.8826i	1.45742	+	0.146678i
$232$	452.817	+	223.305i	1.95180	+	0.962521i
$233$	−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	$0.681642\pi$
$234$	245.591	+	503.403i	1.04953	+	2.15129i
$235$	−55.9628	−	37.3932i	−0.238140	−	0.159120i
$236$	−154.303	−	1172.05i	−0.653827	−	4.96631i
$237$	−210.276	−	95.8152i	−0.887241	−	0.404283i
$238$	−611.863	+	86.1848i	−2.57085	+	0.362121i
$239$	−124.421	+	215.504i	−0.520591	+	0.901691i	0.479122	+	0.877748i	$0.340955\pi$
$239$	−124.421	+	215.504i	−0.520591	+	0.901691i	−0.999713	+	0.0239424i	$0.992378\pi$
$240$	343.729	−	79.3749i	1.43221	−	0.330729i
$241$	3.67862	+	0.241110i	0.0152640	+	0.00100046i	0.0730332	−	0.997330i	$-0.476732\pi$
$241$	3.67862	+	0.241110i	0.0152640	+	0.00100046i	−0.0577692	+	0.998330i	$0.518399\pi$
$242$	45.3875	+	45.3875i	0.187551	+	0.187551i
$243$	−240.162	+	37.0282i	−0.988322	+	0.152379i
$244$	309.124	+	462.637i	1.26690	+	1.89605i
$245$	−97.5100	+	33.1002i	−0.398000	+	0.135103i
$246$	−109.816	−	68.6126i	−0.446406	−	0.278913i
$247$	−461.410	−	60.7457i	−1.86806	−	0.245934i
$248$	73.7107	−	84.0510i	0.297221	−	0.338915i
$249$	−22.7334	−	139.543i	−0.0912986	−	0.560412i
$250$	263.601	+	300.580i	1.05440	+	1.20232i
$251$	−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	$0.496480\pi$
$252$	710.392	−	540.311i	2.81902	−	2.14409i
$253$	89.6119	+	37.1185i	0.354197	+	0.146713i
$254$	306.950	−	177.218i	1.20846	−	0.697708i
$255$	−99.2790	−	70.1097i	−0.389329	−	0.274940i
$256$	70.2275	−	121.638i	0.274326	−	0.475147i
$257$	−130.362	−	169.892i	−0.507247	−	0.661057i	0.467598	−	0.883941i	$-0.345120\pi$
$257$	−130.362	−	169.892i	−0.507247	−	0.661057i	−0.974845	+	0.222884i	$0.928453\pi$
$258$	−237.359	+	441.802i	−0.919997	+	1.71241i
$259$	−70.4232	+	262.823i	−0.271904	+	1.01476i
$260$	−78.9441	−	396.879i	−0.303631	−	1.52646i
$261$	133.586	+	134.729i	0.511825	+	0.516205i
$262$	156.905	−	788.816i	0.598875	−	3.01075i
$263$	248.577	+	190.740i	0.945158	+	0.725245i	0.961553	−	0.274620i	$-0.0885521\pi$
$263$	248.577	+	190.740i	0.945158	+	0.725245i	−0.0163946	+	0.999866i	$0.505219\pi$
$264$	843.393	+	29.4082i	3.19467	+	0.111395i
$265$	40.5735	−	46.2652i	0.153108	−	0.174586i
$266$	67.2876	+	1026.61i	0.252961	+	3.85944i
$267$	324.337	+	305.074i	1.21474	+	1.14260i
$268$	−477.495	−	127.945i	−1.78170	−	0.477405i
$269$	−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	$0.734074\pi$
$270$	242.221	+	25.4204i	0.897115	+	0.0941497i
$271$		−	294.599i		−	1.08708i	−0.839383	−	0.543540i	$-0.817084\pi$
$271$		−	294.599i		−	1.08708i	0.839383	−	0.543540i	$-0.182916\pi$
$272$	−821.213	+	171.078i	−3.01916	+	0.628962i
$273$	−275.074	−	385.597i	−1.00760	−	1.41244i
$274$	−79.7875	−	103.981i	−0.291195	−	0.379493i
$275$	100.370	+	203.530i	0.364981	+	0.740109i
$276$	239.643	−	89.6128i	0.868270	−	0.324684i
$277$	254.977	−	223.609i	0.920495	−	0.807252i	−0.0611189	−	0.998130i	$-0.519467\pi$
$277$	254.977	−	223.609i	0.920495	−	0.807252i	0.981614	+	0.190878i	$0.0611335\pi$
$278$	−35.5487	−	53.2024i	−0.127873	−	0.191376i
$279$	36.4715	−	20.8502i	0.130722	−	0.0747319i
$280$	−506.348	+	209.736i	−1.80839	+	0.749058i
$281$	−111.366	+	145.135i	−0.396320	+	0.516495i	−0.948305	−	0.317359i	$-0.897204\pi$
$281$	−111.366	+	145.135i	−0.396320	+	0.516495i	0.551985	+	0.833854i	$0.313871\pi$
$282$	−319.097	−	32.1147i	−1.13155	−	0.113882i
$283$	−27.1058	−	413.555i	−0.0957802	−	1.46132i	−0.727490	−	0.686119i	$-0.759313\pi$
$283$	−27.1058	−	413.555i	−0.0957802	−	1.46132i	0.631709	−	0.775205i	$-0.282354\pi$
$284$	70.1383	−	206.621i	0.246966	−	0.727538i
$285$	−128.711	+	156.155i	−0.451616	+	0.547912i
$286$	47.8087	−	729.419i	0.167163	−	2.55042i
$287$	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
$291$	234.601	+	251.552i	0.806188	+	0.864441i
$292$	−8.59200	−	17.4228i	−0.0294246	−	0.0596673i
$293$	208.045	−	55.7455i	0.710051	−	0.190258i	0.114323	−	0.993444i	$-0.463530\pi$
$293$	208.045	−	55.7455i	0.710051	−	0.190258i	0.595728	+	0.803186i	$0.296863\pi$
$294$	−336.180	+	357.407i	−1.14347	+	1.21567i
$295$	−120.654	+	244.662i	−0.408996	+	0.829362i
$296$	−132.393	+	665.585i	−0.447274	+	2.24860i
$297$	296.084	+	113.603i	0.996915	+	0.382502i
$298$	234.746	+	566.726i	0.787737	+	1.90177i
$299$	−43.6445	−	128.573i	−0.145968	−	0.430009i
$300$	559.777	+	212.047i	1.86592	+	0.706824i
$301$	136.326	−	401.604i	0.452911	−	1.33423i
$302$	−247.637	−	924.196i	−0.819992	−	3.06025i
$303$	61.5235	−	38.0763i	0.203048	−	0.125664i
$304$	182.303	+	1384.73i	0.599682	+	4.55504i
$305$		−	128.396i		−	0.420971i
$306$	−574.526	−	72.8479i	−1.87754	−	0.238065i
$307$	−299.005			−0.973958			−0.486979	−	0.873414i	$-0.661901\pi$
$307$	−299.005			−0.973958			−0.486979	+	0.873414i	$0.661901\pi$
$308$	−1154.83	+	152.036i	−3.74944	+	0.493623i
$309$	−74.0341	+	137.801i	−0.239593	+	0.445959i
$310$	−40.6713	+	10.8978i	−0.131198	+	0.0351544i
$311$	252.171	+	85.6006i	0.810840	+	0.275243i	0.695909	−	0.718130i	$-0.255002\pi$
$311$	252.171	+	85.6006i	0.810840	+	0.275243i	0.114931	+	0.993373i	$0.463335\pi$
$312$	−747.486	−	914.780i	−2.39579	−	2.93199i
$313$	120.885	−	41.0350i	0.386215	−	0.131102i	−0.121577	−	0.992582i	$-0.538795\pi$
$313$	120.885	−	41.0350i	0.386215	−	0.131102i	0.507792	+	0.861480i	$0.330462\pi$
$314$	777.365	−	321.995i	2.47569	−	1.02546i
$315$	−205.572	+	12.5947i	−0.652608	+	0.0399831i
$316$	780.181	+	155.188i	2.46893	+	0.491100i
$317$	118.051	+	58.2162i	0.372400	+	0.183647i	0.618852	−	0.785508i	$-0.287598\pi$
$317$	118.051	+	58.2162i	0.372400	+	0.183647i	−0.246452	+	0.969155i	$0.579265\pi$
$318$	67.1905	−	285.414i	0.211291	−	0.897528i
$319$	−64.0858	−	239.172i	−0.200896	−	0.749754i
$320$	−314.137	+	154.915i	−0.981680	+	0.484111i
$321$	44.3861	+	192.212i	0.138274	+	0.598791i
$322$	−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
$326$	906.357	+	59.4058i	2.78024	+	0.182226i
$327$	22.7183	−	135.803i	0.0694750	−	0.415298i
$328$	258.609	+	87.7861i	0.788444	+	0.267641i
$329$	270.625	−	17.7377i	0.822567	−	0.0539139i
$330$	−257.968	−	185.690i	−0.781720	−	0.562697i
$331$	−253.743	−	194.704i	−0.766595	−	0.588229i	0.149701	−	0.988731i	$-0.452169\pi$
$331$	−253.743	−	194.704i	−0.766595	−	0.588229i	−0.916296	+	0.400503i	$0.868836\pi$
$332$	186.251	+	449.650i	0.560998	+	1.35437i
$333$	−128.449	+	220.308i	−0.385733	+	0.661585i
$334$	189.478	−	126.605i	0.567300	−	0.379058i
$335$	75.2138	+	85.7648i	0.224519	+	0.256014i
$336$	−904.119	+	1096.90i	−2.69083	+	3.26458i
$337$	394.420	−	194.506i	1.17038	−	0.577170i	0.250024	−	0.968240i	$-0.419562\pi$
$337$	394.420	−	194.506i	1.17038	−	0.577170i	0.920361	+	0.391070i	$0.127895\pi$
$338$	−304.312	+	233.506i	−0.900330	+	0.690847i
$339$	−41.0243	−	425.822i	−0.121016	−	1.25611i
$340$	387.972	+	156.611i	1.14109	+	0.460621i
$341$	−54.8265			−0.160782
$342$	−192.143	+	944.912i	−0.561821	+	2.76290i
$343$	−30.8881	+	46.2273i	−0.0900528	+	0.134774i
$344$	273.770	−	1021.72i	0.795843	−	2.97013i
$345$	−57.4686	−	13.5289i	−0.166576	−	0.0392143i
$346$	−583.887	+	38.2700i	−1.68753	+	0.110607i
$347$	197.212	+	172.950i	0.568333	+	0.498415i	0.894603	−	0.446862i	$-0.147458\pi$
$347$	197.212	+	172.950i	0.568333	+	0.498415i	−0.326270	+	0.945277i	$0.605792\pi$
$348$	−553.904	−	346.078i	−1.59168	−	0.994477i
$349$	−36.6559	+	47.7709i	−0.105031	+	0.136879i	−0.842911	−	0.538052i	$-0.819160\pi$
$349$	−36.6559	+	47.7709i	−0.105031	+	0.136879i	0.737880	+	0.674932i	$0.235827\pi$
$350$	−688.763	−	137.003i	−1.96789	−	0.391439i
$351$	−153.717	−	416.470i	−0.437941	−	1.18652i
$352$	−1048.01	+	208.462i	−2.97730	+	0.592222i
$353$	96.5792	+	25.8783i	0.273595	+	0.0733097i	0.393008	−	0.919535i	$-0.371434\pi$
$353$	96.5792	+	25.8783i	0.273595	+	0.0733097i	−0.119413	+	0.992845i	$0.538101\pi$
$354$	39.7628	+	1299.24i	0.112324	+	3.67018i
$355$	−39.9467	+	30.6522i	−0.112526	+	0.0863442i
$356$	−1327.45	−	766.403i	−3.72879	−	2.15282i
$357$	489.349	−	19.4036i	1.37072	−	0.0543518i
$358$	−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	$0.209732\pi$
$360$	−509.560	+	64.8778i	−1.41544	+	0.180216i
$361$	−311.254	−	311.254i	−0.862200	−	0.862200i
$362$	−682.856	+	598.849i	−1.88634	+	1.65428i
$363$	−32.1899	−	39.3943i	−0.0886773	−	0.108524i
$364$	1225.90	+	1075.08i	3.36785	+	2.95353i
$365$	−0.585119	+	4.44442i	−0.00160307	+	0.0121765i
$366$	−287.252	−	540.174i	−0.784841	−	1.47589i
$367$	69.9105	+	205.950i	0.190492	+	0.561171i	0.999651	−	0.0264188i	$-0.00841034\pi$
$367$	69.9105	+	205.950i	0.190492	+	0.561171i	−0.809159	+	0.587590i	$0.800077\pi$
$368$	−338.809	+	226.385i	−0.920678	+	0.615177i
$369$	81.1541	+	62.8228i	0.219930	+	0.170251i
$370$	180.735	−	180.735i	0.488472	−	0.488472i
$371$	−16.2171	+	247.425i	−0.0437118	+	0.666913i
$372$	−105.763	+	98.6354i	−0.284308	+	0.265149i
$373$	−310.085	−	179.027i	−0.831326	−	0.479966i	0.0229805	−	0.999736i	$-0.492684\pi$
$373$	−310.085	−	179.027i	−0.831326	−	0.479966i	−0.854306	+	0.519770i	$0.826018\pi$
$374$	603.745	+	454.662i	1.61429	+	1.21567i
$375$	−184.017	−	257.955i	−0.490713	−	0.687879i
$376$	670.620	−	88.2888i	1.78356	−	0.234811i
$377$	−192.568	+	288.199i	−0.510791	+	0.764453i
$378$	−836.681	+	512.897i	−2.21344	+	1.35687i
$379$	−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	$0.976028\pi$
$380$	308.107	−	624.780i	0.810809	−	1.64416i
$381$	−256.123	+	115.391i	−0.672238	+	0.302863i
$382$	−77.3894	+	587.831i	−0.202590	+	1.53882i
$383$	589.649	+	77.6287i	1.53955	+	0.202686i	0.852036	−	0.523483i	$-0.175368\pi$
$383$	589.649	+	77.6287i	1.53955	+	0.202686i	0.687516	+	0.726169i	$0.258701\pi$
$384$	−337.249	+	468.519i	−0.878252	+	1.22010i
$385$	241.067	+	118.881i	0.626149	+	0.308782i
$386$	1092.28	−	217.267i	2.82973	−	0.562868i
$387$	222.243	−	329.562i	0.574271	−	0.851582i
$388$	−984.539	−	657.848i	−2.53747	−	1.69548i
$389$	−3.89045	−	29.5509i	−0.0100012	−	0.0759664i	0.985716	−	0.168414i	$-0.0538644\pi$
$389$	−3.89045	−	29.5509i	−0.0100012	−	0.0759664i	−0.995718	+	0.0924472i	$0.970531\pi$
$390$	42.6685	+	442.889i	0.109406	+	1.13561i
$391$	135.926	+	35.1080i	0.347637	+	0.0897902i
$392$	517.435	−	896.224i	1.31999	−	2.28629i
$393$	−186.339	+	609.599i	−0.474144	+	1.55114i
$394$	128.131	+	8.39816i	0.325206	+	0.0213151i
$395$	−129.797	−	129.797i	−0.328600	−	0.328600i
$396$	−1081.74	−	147.104i	−2.73167	−	0.371475i
$397$	−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	$0.885516\pi$
$398$	−753.484	+	255.773i	−1.89318	+	0.642647i
$399$	28.4152	−	814.914i	0.0712160	−	2.04239i
$400$	−945.202	−	124.438i	−2.36301	−	0.311096i
$401$	32.9612	−	37.5850i	0.0821974	−	0.0937282i	−0.709279	−	0.704928i	$-0.750979\pi$
$401$	32.9612	−	37.5850i	0.0821974	−	0.0937282i	0.791477	+	0.611200i	$0.209313\pi$
$402$	508.306	+	192.550i	1.26444	+	0.478980i
$403$	50.6039	+	57.7027i	0.125568	+	0.143183i
$404$	−176.119	+	176.119i	−0.435938	+	0.435938i
$405$	−188.995	−	39.2703i	−0.466655	−	0.0969636i
$406$	707.912	+	293.227i	1.74363	+	0.722234i
$407$	288.226	−	166.408i	0.708173	−	0.408864i
$408$	1214.70	−	128.113i	2.97720	−	0.314003i
$409$	−57.0559	+	98.8238i	−0.139501	+	0.241623i	−0.927308	−	0.374300i	$-0.877883\pi$
$409$	−57.0559	+	98.8238i	−0.139501	+	0.241623i	0.787807	+	0.615922i	$0.211217\pi$
$410$	−62.6182	−	81.6057i	−0.152727	−	0.199038i
$411$	54.6671	+	88.3308i	0.133010	+	0.214917i
$412$	139.374	−	520.149i	0.338285	−	1.26250i
$413$	−214.445	−	1078.09i	−0.519237	−	2.61038i
$414$	−272.043	+	71.6530i	−0.657108	+	0.173075i
$415$	21.9106	−	110.152i	0.0527966	−	0.265426i
$416$	1186.69	+	910.581i	2.85262	+	2.18890i
$417$	23.8109	+	44.7762i	0.0571005	+	0.107377i
$418$	829.723	−	946.118i	1.98498	−	2.26344i
$419$	−20.0070	−	305.248i	−0.0477494	−	0.728516i	−0.952873	−	0.303368i	$-0.901889\pi$
$419$	−20.0070	−	305.248i	−0.0477494	−	0.728516i	0.905124	−	0.425148i	$-0.139778\pi$
$420$	678.901	−	204.364i	1.61643	−	0.486581i
$421$	472.696	+	126.659i	1.12279	+	0.300852i	0.772014	−	0.635606i	$-0.219250\pi$
$421$	472.696	+	126.659i	1.12279	+	0.300852i	0.350781	+	0.936458i	$0.385916\pi$
$422$	−434.928	−	290.610i	−1.03064	−	0.688649i
$423$	249.088	+	50.6507i	0.588861	+	0.119742i
$424$			618.421i			1.45854i
$425$	184.939	+	271.439i	0.435151	+	0.638679i
$426$	−99.4834	+	218.326i	−0.233529	+	0.512503i
$427$	314.952	+	410.453i	0.737592	+	0.961249i
$428$	−300.353	−	609.056i	−0.701760	−	1.42303i
$429$	−95.5921	+	571.418i	−0.222826	+	1.33198i
$430$	−299.531	+	262.682i	−0.696585	+	0.610888i
$431$	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	$0.689870\pi$
$432$	−1087.88	+	769.088i	−2.51823	+	1.78030i
$433$	−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	$0.495586\pi$
$434$	103.285	−	134.603i	0.237983	−	0.310146i
$435$	61.9089	+	137.414i	0.142319	+	0.315894i
$436$	31.0002	+	472.972i	0.0711015	+	1.08480i
$437$	75.1349	−	221.340i	0.171933	−	0.506499i
$438$	7.48154	+	20.0071i	0.0170811	+	0.0456783i
$439$	4.37838	−	66.8011i	0.00997352	−	0.152167i	−0.989967	−	0.141296i	$-0.954873\pi$
$439$	4.37838	−	66.8011i	0.00997352	−	0.152167i	0.999941	−	0.0108705i	$-0.00346026\pi$
$440$	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	0.995544	−	0.0942970i	$-0.0300603\pi$
$443$	184.336	+	319.279i	0.416108	+	0.720721i	−0.579436	+	0.815018i	$0.696727\pi$
$444$	256.625	−	839.539i	0.577985	−	1.89085i
$445$	156.441	+	317.232i	0.351554	+	0.712880i
$446$	558.801	−	149.730i	1.25292	−	0.335718i
$447$	−140.139	−	465.545i	−0.313511	−	1.04149i
$448$	624.223	−	1265.80i	1.39335	−	2.82544i
$449$	−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	$0.0642161\pi$
$450$	−589.064	−	293.620i	−1.30903	−	0.652490i
$451$	−51.2554	−	123.742i	−0.113648	−	0.274371i
$452$	473.368	+	1394.50i	1.04727	+	3.08517i
$453$	121.935	+	748.465i	0.269172	+	1.65224i
$454$	132.377	−	389.971i	0.291580	−	0.858967i
$455$	−97.3831	−	363.439i	−0.214029	−	0.798766i
$456$	−62.2113	−	2032.74i	−0.136428	−	4.45777i
$457$	−5.08315	−	38.6103i	−0.0111229	−	0.0844865i	0.984983	−	0.172651i	$-0.0552332\pi$
$457$	−5.08315	−	38.6103i	−0.0111229	−	0.0844865i	−0.996106	+	0.0881644i	$0.971900\pi$
$458$			1659.66i			3.62372i
$459$	447.284	+	103.045i	0.974475	+	0.224498i
$460$	203.240			0.441825
$461$	52.7777	−	6.94831i	0.114485	−	0.0150723i	−0.0730659	−	0.997327i	$-0.523278\pi$
$461$	52.7777	−	6.94831i	0.114485	−	0.0150723i	0.187551	+	0.982255i	$0.439945\pi$
$462$	1280.15	−	39.1786i	2.77090	−	0.0848022i
$463$	358.667	−	96.1046i	0.774660	−	0.207569i	0.150231	−	0.988651i	$-0.451998\pi$
$463$	358.667	−	96.1046i	0.774660	−	0.207569i	0.624429	+	0.781082i	$0.285332\pi$
$464$	985.014	+	334.367i	2.12288	+	0.720619i
$465$	32.9379	−	5.36603i	0.0708342	−	0.0115398i
$466$	−1159.12	+	393.469i	−2.48739	+	0.844354i
$467$	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	$0.363069\pi$
$468$	843.605	+	1274.26i	1.80258	+	2.72278i
$469$	−450.819	−	89.6736i	−0.961236	−	0.191202i
$470$	−228.489	−	112.679i	−0.486148	−	0.239742i
$471$	−638.577	+	192.226i	−1.35579	+	0.408123i
$472$	−709.556	−	2648.10i	−1.50330	−	5.61038i
$473$	−465.258	+	229.440i	−0.983633	+	0.485074i
$474$	−836.454	−	255.682i	−1.76467	−	0.539414i
$475$	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
$479$	−542.006	−	35.5250i	−1.13154	−	0.0741649i	−0.511894	−	0.859049i	$-0.671056\pi$
$479$	−542.006	−	35.5250i	−1.13154	−	0.0741649i	−0.619643	+	0.784884i	$0.712723\pi$
$480$	609.205	−	227.808i	1.26918	−	0.474601i
$481$	−441.165	−	149.755i	−0.917183	−	0.311342i
$482$	13.9241	−	0.912634i	0.0288882	−	0.00189343i
$483$	216.900	−	97.7198i	0.449068	−	0.202318i
$484$	138.938	+	106.611i	0.287062	+	0.220271i
$485$	104.565	+	252.441i	0.215597	+	0.520498i
$486$	−882.977	+	257.612i	−1.81682	+	0.530067i
$487$	−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	$0.545810\pi$
$488$	850.786	+	970.136i	1.74341	+	1.98798i
$489$	−710.029	−	118.780i	−1.45200	−	0.242904i
$490$	−349.578	+	172.393i	−0.713424	+	0.351822i
$491$	−389.723	+	299.045i	−0.793733	+	0.609052i	−0.923985	−	0.382428i	$-0.875088\pi$
$491$	−389.723	+	299.045i	−0.793733	+	0.609052i	0.130253	+	0.991481i	$0.458421\pi$
$492$	−321.490	−	146.491i	−0.653435	−	0.297747i
$493$	−140.132	−	329.846i	−0.284243	−	0.669058i
$494$	−1761.57			−3.56593
$495$	188.693	+	166.907i	0.381198	+	0.337186i
$496$	127.964	−	191.512i	0.257992	−	0.386113i
$497$	52.5116	−	195.976i	0.105657	−	0.394318i
$498$	−154.255	−	512.438i	−0.309749	−	1.02899i
$499$	−844.898	+	55.3776i	−1.69318	+	0.110977i	−0.881212	−	0.472721i	$-0.843272\pi$
$499$	−844.898	+	55.3776i	−1.69318	+	0.110977i	−0.811971	+	0.583698i	$0.801605\pi$
$500$	820.094	+	719.203i	1.64019	+	1.43841i
$501$	−159.469	+	84.8016i	−0.318301	+	0.169265i
$502$	−808.839	+	1054.10i	−1.61123	+	2.09980i
$503$	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	$0.318668\pi$
$504$	1469.80	−	1457.33i	2.91627	−	2.89153i
$505$	56.3708	−	11.2128i	0.111625	−	0.0222036i
$506$	354.631	+	95.0230i	0.700851	+	0.187792i
$507$	258.509	−	159.989i	0.509880	−	0.315560i
$508$	767.199	−	588.692i	1.51023	−	1.15884i
$509$	−475.136	−	274.320i	−0.933469	−	0.538938i	−0.0455617	−	0.998962i	$-0.514508\pi$
$509$	−475.136	−	274.320i	−0.933469	−	0.538938i	−0.887907	+	0.460023i	$0.847841\pi$
$510$	−407.208	−	214.055i	−0.798448	−	0.419715i
$511$	−9.03153	−	15.6431i	−0.0176742	−	0.0306127i
$512$	−91.1009	+	219.937i	−0.177931	+	0.429565i
$513$	226.515	−	729.898i	0.441550	−	1.42280i
$514$	−573.155	−	573.155i	−1.11509	−	1.11509i
$515$	−93.4261	+	81.9325i	−0.181410	+	0.159092i
$516$	−484.729	+	1279.62i	−0.939397	+	2.47988i
$517$	−249.406	−	218.723i	−0.482410	−	0.423062i
$518$	−134.431	+	1021.10i	−0.259519	+	1.97124i
$519$	463.484	+	16.1612i	0.893033	+	0.0311391i
$520$	−301.645	−	888.618i	−0.580087	−	1.70888i
$521$	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	$0.204618\pi$
$522$	567.882	+	439.607i	1.08790	+	0.842159i
$523$	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	$0.168174\pi$
$524$	143.517	−	2189.65i	0.273888	−	4.17873i
$525$	532.278	+	162.704i	1.01386	+	0.309911i
$526$	1027.08	+	592.988i	1.95263	+	1.12735i
$527$	−78.5779	+	11.0682i	−0.149104	+	0.0210023i
$528$	1730.69	−	166.737i	3.27783	−	0.315790i
$529$	−456.862	+	60.1471i	−0.863634	+	0.113700i
$530$	129.405	−	193.668i	0.244160	−	0.365411i
$531$	71.7586	−	1027.73i	0.135139	−	1.93545i
$532$	547.616	+	2753.05i	1.02935	+	5.17491i
$533$	−82.9251	+	168.155i	−0.155582	+	0.315489i
$534$	1367.88	+	984.627i	2.56158	+	1.84387i
$535$	−20.4542	+	155.365i	−0.0382321	+	0.290402i
$536$	−1136.60	−	149.636i	−2.12052	−	0.279172i
$537$	97.0476	+	215.408i	0.180722	+	0.401132i
$538$	−266.282	−	131.316i	−0.494948	−	0.244082i
$539$	−497.775	+	99.0137i	−0.923516	+	0.183699i
$540$	664.269	−	17.4978i	1.23013	−	0.0324033i
$541$	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	$0.439543\pi$
$542$	−145.549	−	1105.56i	−0.268541	−	2.03977i
$543$	586.021	−	418.050i	1.07923	−	0.769890i
$544$	−1459.93	+	510.339i	−2.68370	+	0.938122i
$545$	54.6884	−	94.7231i	0.100346	−	0.173804i
$546$	−1222.79	−	1311.15i	−2.23955	−	2.40137i
$547$	−317.236	−	20.7927i	−0.579956	−	0.0380123i	−0.227397	−	0.973802i	$-0.573022\pi$
$547$	−317.236	−	20.7927i	−0.579956	−	0.0380123i	−0.352559	+	0.935790i	$0.614688\pi$
$548$	−252.858	−	252.858i	−0.461420	−	0.461420i
$549$	183.652	+	448.774i	0.334522	+	0.817438i
$550$	477.220	+	714.210i	0.867672	+	1.29856i
$551$	−565.035	+	191.804i	−1.02547	+	0.348101i
$552$	523.867	−	278.580i	0.949034	−	0.504674i
$553$	733.320	+	96.5434i	1.32608	+	0.174581i
$554$	846.391	−	965.124i	1.52778	−	1.74210i
$555$	−156.870	+	128.181i	−0.282648	+	0.230958i
$556$	−115.107	−	131.255i	−0.207027	−	0.236069i
$557$	−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	$0.266218\pi$
$558$	126.568	−	96.2649i	0.226824	−	0.172518i
$559$	670.901	+	277.896i	1.20018	+	0.497131i
$560$	−977.905	+	564.594i	−1.74626	+	1.00820i
$561$	−440.023	−	406.458i	−0.784354	−	0.724524i
$562$	−346.224	+	599.678i	−0.616057	+	1.06704i
$563$	452.338	+	589.499i	0.803443	+	1.04707i	0.997810	+	0.0661381i	$0.0210678\pi$
$563$	452.338	+	589.499i	0.803443	+	1.04707i	−0.194368	+	0.980929i	$0.562266\pi$
$564$	−874.607	+	26.7670i	−1.55072	+	0.0474592i
$565$	87.9538	−	328.248i	0.155670	−	0.580970i
$566$	−306.042	−	1538.58i	−0.540711	−	2.71834i
$567$	700.504	−	338.062i	1.23546	−	0.596229i
$568$	98.7200	−	496.299i	0.173803	−	0.873766i
$569$	64.4080	+	49.4220i	0.113195	+	0.0868576i	0.663808	−	0.747903i	$-0.268939\pi$
$569$	64.4080	+	49.4220i	0.113195	+	0.0868576i	−0.550613	+	0.834761i	$0.685606\pi$
$570$	−405.870	+	649.602i	−0.712052	+	1.13965i
$571$	−423.959	+	483.432i	−0.742485	+	0.846642i	−0.992582	−	0.121579i	$-0.961204\pi$
$571$	−423.959	+	483.432i	−0.742485	+	0.846642i	0.250097	+	0.968221i	$0.419538\pi$
$572$	−130.440	−	1990.13i	−0.228042	−	3.47925i
$573$	107.682	−	457.415i	0.187927	−	0.798281i
$574$	400.352	+	107.274i	0.697478	+	0.186889i
$575$	132.662	+	88.6422i	0.230717	+	0.154160i
$576$	876.396	−	990.792i	1.52152	−	1.72013i
$577$			742.665i			1.28711i	0.765398	+	0.643557i	$0.222542\pi$
$577$			742.665i			1.28711i	−0.765398	+	0.643557i	$0.777458\pi$
$578$	957.079	+	529.744i	1.65585	+	0.916512i
$579$	−878.600	+	84.6455i	−1.51744	+	0.146193i
$580$	−315.843	−	411.614i	−0.544556	−	0.709680i
$581$	200.156	+	405.876i	0.344503	+	0.698582i
$582$	1004.68	+	828.108i	1.72626	+	1.42287i
$583$	228.025	−	199.973i	0.391124	−	0.343007i
$584$	−25.0288	−	37.4583i	−0.0428576	−	0.0641409i
$585$	1.50218	−	352.644i	0.00256783	−	0.602810i
$586$	753.201	−	311.986i	1.28533	−	0.532400i
$587$	91.6250	−	119.408i	0.156090	−	0.203421i	−0.708761	−	0.705448i	$-0.750746\pi$
$587$	91.6250	−	119.408i	0.156090	−	0.203421i	0.864852	+	0.502027i	$0.167412\pi$
$588$	−782.098	+	1086.52i	−1.33010	+	1.84782i
$589$	8.64135	+	131.841i	0.0146712	+	0.223839i
$590$	−331.907	+	977.767i	−0.562555	+	1.65723i
$591$	−100.376	−	16.7919i	−0.169842	−	0.0284127i
$592$	−91.4451	+	1395.18i	−0.154468	+	2.35673i
$593$	−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
$597$	614.489	−	141.900i	1.02930	−	0.237688i
$598$	−227.310	−	460.939i	−0.380117	−	0.770800i
$599$	−654.509	+	175.375i	−1.09267	+	0.292780i	−0.759777	−	0.650184i	$-0.774692\pi$
$599$	−654.509	+	175.375i	−1.09267	+	0.292780i	−0.332894	+	0.942964i	$0.608025\pi$
$600$	1351.24	+	318.101i	2.25207	+	0.530168i
$601$	344.346	−	698.264i	0.572955	−	1.16184i	−0.396834	−	0.917890i	$-0.629891\pi$
$601$	344.346	−	698.264i	0.572955	−	1.16184i	0.969789	−	0.243947i	$-0.0784422\pi$
$602$	313.183	−	1574.48i	0.520237	−	2.61541i
$603$	−385.563	−	192.185i	−0.639408	−	0.318714i
$604$	−998.997	−	2411.79i	−1.65397	−	3.99303i
$605$	−12.9901	−	38.2676i	−0.0214713	−	0.0632523i
$606$	212.071	−	173.288i	0.349952	−	0.285953i
$607$	−149.038	+	439.051i	−0.245532	+	0.723314i	0.752380	+	0.658729i	$0.228906\pi$
$607$	−149.038	+	439.051i	−0.245532	+	0.723314i	−0.997912	+	0.0645848i	$0.979428\pi$
$608$	666.468	+	2487.29i	1.09616	+	4.09094i
$609$	−534.980	−	287.419i	−0.878457	−	0.471953i
$610$	−63.4355	−	481.840i	−0.103993	−	0.789902i
$611$			464.367i			0.760012i
$612$	−1580.06	+	7.54693i	−2.58179	+	0.0123316i
$613$	−624.058			−1.01804			−0.509019	−	0.860755i	$-0.669992\pi$
$613$	−624.058			−1.01804			−0.509019	+	0.860755i	$0.669992\pi$
$614$	−1122.09	+	147.726i	−1.82751	+	0.240597i
$615$	42.9034	+	69.3231i	0.0697616	+	0.112720i
$616$	−2609.19	+	699.131i	−4.23570	+	1.13495i
$617$	−1150.08	−	390.400i	−1.86399	−	0.632739i	−0.988860	−	0.148849i	$-0.952443\pi$
$617$	−1150.08	−	390.400i	−1.86399	−	0.632739i	−0.875129	−	0.483890i	$-0.839224\pi$
$618$	−209.750	+	553.712i	−0.339401	+	0.895975i
$619$	−1003.73	+	340.722i	−1.62154	+	0.550439i	−0.976836	−	0.213991i	$-0.931354\pi$
$619$	−1003.73	+	340.722i	−1.62154	+	0.550439i	−0.644707	+	0.764430i	$0.723020\pi$
$620$	−106.136	+	43.9631i	−0.171188	+	0.0709083i
$621$	220.217	−	34.9140i	0.354616	−	0.0562222i
$622$	988.629	+	196.651i	1.58944	+	0.316159i
$623$	−1278.27	−	630.371i	−2.05179	−	1.01183i
$624$	−1772.88	−	1667.59i	−2.84116	−	2.67242i
$625$	59.8678	+	223.430i	0.0957884	+	0.357487i
$626$	433.380	−	213.719i	0.692300	−	0.341404i
$627$	−729.400	+	680.247i	−1.16332	+	1.08492i
$628$	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	$0.892591\pi$
$632$	1840.79	+	120.652i	2.91264	+	0.190905i
$633$	319.915	+	263.690i	0.505395	+	0.416572i
$634$	471.779	+	160.147i	0.744130	+	0.252598i
$635$	−222.674	+	14.5948i	−0.350667	+	0.0229840i
$636$	80.1096	−	795.983i	0.125959	−	1.25155i
$637$	563.646	+	432.500i	0.884844	+	0.678965i
$638$	−358.664	−	865.891i	−0.562169	−	1.35720i
$639$	95.7791	−	164.274i	0.149889	−	0.257080i
$640$	−381.288	+	254.768i	−0.595762	+	0.398076i
$641$	492.213	+	561.261i	0.767882	+	0.875602i	0.995164	−	0.0982271i	$-0.0313172\pi$
$641$	492.213	+	561.261i	0.767882	+	0.875602i	−0.227282	+	0.973829i	$0.572984\pi$
$642$	261.534	+	699.395i	0.407374	+	1.08940i
$643$	223.420	−	110.178i	0.347465	−	0.171351i	−0.260179	−	0.965560i	$-0.583782\pi$
$643$	223.420	−	110.178i	0.347465	−	0.171351i	0.607644	+	0.794210i	$0.292115\pi$
$644$	−649.710	+	498.540i	−1.00887	+	0.774131i
$645$	257.055	−	183.376i	0.398535	−	0.284304i
$646$	998.168	−	1523.49i	1.54515	−	2.35834i
$647$	669.504			1.03478			0.517391	−	0.855749i	$-0.326903\pi$
$647$	669.504			1.03478			0.517391	+	0.855749i	$0.326903\pi$
$648$	1688.23	−	955.614i	2.60529	−	1.47471i
$649$	−746.969	+	1117.92i	−1.15095	+	1.72252i
$650$	311.212	−	1161.46i	0.478787	−	1.78686i
$651$	−92.1322	+	97.9495i	−0.141524	+	0.150460i
$652$	2472.88	−	162.081i	3.79276	−	0.248591i
$653$	289.694	+	254.055i	0.443636	+	0.389058i	0.851814	−	0.523844i	$-0.175503\pi$
$653$	289.694	+	254.055i	0.443636	+	0.389058i	−0.408179	+	0.912902i	$0.633836\pi$
$654$	18.1618	−	520.858i	0.0277703	−	0.796420i
$655$	−308.256	+	401.727i	−0.470620	+	0.613324i
$656$	551.865	+	109.773i	0.841257	+	0.167336i
$657$	−4.31198	−	16.3712i	−0.00656314	−	0.0249181i
$658$	1006.82	−	200.270i	1.53013	−	0.304362i
$659$	−40.2934	−	10.7966i	−0.0611433	−	0.0163833i	0.228118	−	0.973634i	$-0.426743\pi$
$659$	−40.2934	−	10.7966i	−0.0611433	−	0.0163833i	−0.289261	+	0.957250i	$0.593410\pi$
$660$	−763.940	−	410.429i	−1.15749	−	0.621862i
$661$	462.469	−	354.865i	0.699650	−	0.536860i	−0.196559	−	0.980492i	$-0.562977\pi$
$661$	462.469	−	354.865i	0.699650	−	0.536860i	0.896209	+	0.443632i	$0.146310\pi$
$662$	−1048.43	−	605.312i	−1.58373	−	0.914368i
$663$	−21.6476	+	838.259i	−0.0326510	+	1.26434i
$664$	564.343	+	977.470i	0.849914	+	1.47209i
$665$	247.879	−	598.432i	0.372750	−	0.899897i
$666$	−373.193	+	890.223i	−0.560350	+	1.33667i
$667$	−123.099	−	123.099i	−0.184556	−	0.184556i
$668$	467.458	−	409.950i	0.699787	−	0.613697i
$669$	−452.548	+	73.7261i	−0.676454	+	0.110203i
$670$	324.632	+	284.695i	0.484525	+	0.424917i
$671$	82.5997	−	627.407i	0.123099	−	0.935033i
$672$	−1388.68	+	2222.61i	−2.06649	+	3.30746i
$673$	235.537	+	693.868i	0.349980	+	1.03101i	0.969303	+	0.245871i	$0.0790740\pi$
$673$	235.537	+	693.868i	0.349980	+	1.03101i	−0.619322	+	0.785137i	$0.712593\pi$
$674$	1384.06	−	924.802i	2.05351	−	1.37211i
$675$	441.226	+	278.297i	0.653669	+	0.412292i
$676$	−740.016	+	740.016i	−1.09470	+	1.09470i
$677$	−23.7174	+	361.858i	−0.0350331	+	0.534502i	0.943888	+	0.330265i	$0.107138\pi$
$677$	−23.7174	+	361.858i	−0.0350331	+	0.534502i	−0.978921	+	0.204237i	$0.934529\pi$
$678$	−364.336	−	1577.74i	−0.537369	−	2.32705i
$679$	−953.500	−	550.503i	−1.40427	−	0.810756i
$680$	939.441	+	242.646i	1.38153	+	0.356832i
$681$	−135.342	+	297.021i	−0.198739	+	0.436154i
$682$	−205.751	+	27.0876i	−0.301687	+	0.0397179i
$683$	−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	$0.956539\pi$
$684$	−183.246	+	2624.45i	−0.267904	+	3.83691i
$685$	16.0985	+	80.9328i	0.0235015	+	0.118150i
$686$	−93.0766	+	188.741i	−0.135680	+	0.275132i
$687$	131.720	−	1308.79i	0.191732	−	1.90508i
$688$	284.459	−	2160.68i	0.413458	−	3.14053i
$689$	−420.926	−	55.4160i	−0.610924	−	0.0804296i
$690$	−222.350	−	22.3778i	−0.322246	−	0.0324316i
$691$	754.588	+	372.122i	1.09202	+	0.538527i	0.896892	−	0.442250i	$-0.145820\pi$
$691$	754.588	+	372.122i	1.09202	+	0.538527i	0.195132	+	0.980777i	$0.437486\pi$
$692$	−1565.80	+	311.458i	−2.26272	+	0.450084i
$693$	−1012.63	−	70.7043i	−1.46122	−	0.102026i
$694$	825.535	+	551.605i	1.18953	+	0.794820i
$695$	5.25830	+	39.9407i	0.00756590	+	0.0574687i
$696$	−1378.31	−	628.045i	−1.98033	−	0.902364i
$697$	−98.4403	−	167.000i	−0.141234	−	0.239599i
$698$	−113.959	+	197.383i	−0.163265	+	0.282784i
$699$	945.300	−	218.291i	1.35236	−	0.312291i
$700$	−1911.92	−	125.314i	−2.73131	−	0.179020i
$701$	−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	$0.860285\pi$
$702$	−782.625	−	1486.96i	−1.11485	−	2.11818i
$703$	−445.589	−	666.870i	−0.633839	−	0.948607i
$704$	−1634.69	+	554.902i	−2.32200	+	0.788213i
$705$	171.242	+	106.991i	0.242896	+	0.151761i
$706$	375.224	+	49.3991i	0.531478	+	0.0699705i
$707$	−152.700	+	174.121i	−0.215982	+	0.246281i
$708$	570.252	+	3500.34i	0.805441	+	4.94398i
$709$	−282.236	−	321.829i	−0.398077	−	0.453920i	0.517727	−	0.855546i	$-0.326778\pi$
$709$	−282.236	−	321.829i	−0.398077	−	0.453920i	−0.915804	+	0.401626i	$0.868445\pi$
$710$	−134.766	+	134.766i	−0.189812	+	0.189812i
$711$	639.326	+	268.014i	0.899193	+	0.376953i
$712$	−3284.10	−	1360.32i	−4.61250	−	1.91056i
$713$	−33.3830	+	19.2737i	−0.0468205	+	0.0270318i
$714$	1826.82	−	314.585i	2.55857	−	0.440595i
$715$	−230.113	+	398.567i	−0.321836	+	0.557437i
$716$	−495.111	−	645.241i	−0.691496	−	0.901175i
$717$	353.312	−	657.628i	0.492765	−	0.917194i
$718$	−185.038	+	690.571i	−0.257713	+	0.961799i
$719$	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	$0.694432\pi$
$720$	−1023.42	+	269.558i	−1.42142	+	0.374386i
$721$	97.6839	−	491.090i	0.135484	−	0.681124i
$722$	−1321.84	−	1014.28i	−1.83080	−	1.40483i
$723$	−11.0528	−	0.385400i	−0.0152875	−	0.000533057i
$724$	−1633.88	+	1863.09i	−2.25675	+	2.57333i
$725$	−26.6389	−	406.430i	−0.0367433	−	0.560594i
$726$	−140.264	−	131.933i	−0.193201	−	0.181726i
$727$	−356.980	−	95.6526i	−0.491032	−	0.131572i	0.00480285	−	0.999988i	$-0.498471\pi$
$727$	−356.980	−	95.6526i	−0.491032	−	0.131572i	−0.495835	+	0.868417i	$0.665138\pi$
$728$	3144.04	+	2100.78i	4.31874	+	2.88569i
$729$	716.752	−	133.072i	0.983198	−	0.182541i
$730$			16.9679i			0.0232437i
$731$	−620.494	+	422.761i	−0.848829	+	0.578332i
$732$	−969.395	−	1358.89i	−1.32431	−	1.85641i
$733$	468.187	+	610.153i	0.638727	+	0.832405i	0.994778	−	0.102062i	$-0.0325439\pi$
$733$	468.187	+	610.153i	0.638727	+	0.832405i	−0.356051	+	0.934466i	$0.615877\pi$
$734$	364.109	+	738.339i	0.496061	+	1.00591i
$735$	289.355	−	108.203i	0.393681	−	0.147214i
$736$	−564.834	+	495.346i	−0.767437	+	0.673025i
$737$	312.357	+	467.475i	0.423822	+	0.634295i
$738$	335.590	+	195.664i	0.454729	+	0.265127i
$739$	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	$0.331370\pi$
$740$	424.530	−	553.258i	0.573689	−	0.747646i
$741$	1389.16	+	139.808i	1.87470	+	0.188675i
$742$	61.3839	+	936.538i	0.0827277	+	1.26218i
$743$	298.570	−	879.560i	0.401844	−	1.18380i	−0.538222	−	0.842803i	$-0.680904\pi$
$743$	298.570	−	879.560i	0.401844	−	1.18380i	0.940066	−	0.340992i	$-0.110763\pi$
$744$	−213.315	+	258.799i	−0.286714	+	0.347849i
$745$	25.2592	−	385.381i	0.0339050	−	0.517290i
$746$	−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
$750$	−818.018	−	877.126i	−1.09069	−	1.16950i
$751$	−635.407	−	1288.48i	−0.846081	−	1.71568i	−0.684744	−	0.728783i	$-0.740086\pi$
$751$	−635.407	−	1288.48i	−0.846081	−	1.71568i	−0.161337	−	0.986899i	$-0.551581\pi$
$752$	1346.12	−	360.692i	1.79005	−	0.479644i
$753$	721.501	−	767.058i	0.958169	−	1.01867i
$754$	−580.275	+	1176.68i	−0.769595	+	1.56058i
$755$	−117.522	+	590.822i	−0.155658	+	0.782546i
$756$	−2080.59	+	1685.37i	−2.75211	+	2.22932i
$757$	−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	$-0.360092\pi$
$758$	−111.355	−	328.042i	−0.146907	−	0.432773i
$759$	−272.116	−	103.080i	−0.358520	−	0.135810i
$760$	519.288	−	1529.77i	0.683274	−	2.01286i
$761$	−35.1053	−	131.015i	−0.0461305	−	0.172161i	0.939017	−	0.343870i	$-0.111738\pi$
$761$	−35.1053	−	131.015i	−0.0461305	−	0.172161i	−0.985148	+	0.171709i	$0.945071\pi$
$762$	−904.156	+	559.573i	−1.18656	+	0.734348i
$763$	57.5264	+	436.957i	0.0753951	+	0.572682i
$764$			1617.66i			2.11736i
$765$	304.132	+	201.120i	0.397558	+	0.262902i
$766$	2251.16			2.93885
$767$	1866.00	−	245.664i	2.43286	−	0.320292i
$768$	−199.421	+	371.187i	−0.259663	+	0.483317i
$769$	552.942	−	148.160i	0.719041	−	0.192666i	0.119297	−	0.992859i	$-0.461936\pi$
$769$	552.942	−	148.160i	0.719041	−	0.192666i	0.599744	+	0.800192i	$0.295269\pi$
$770$	963.401	+	327.031i	1.25117	+	0.424715i
$771$	406.496	+	497.473i	0.527232	+	0.645231i
$772$	2877.27	−	976.701i	3.72703	−	1.26516i
$773$	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	$0.363657\pi$
$774$	671.200	−	1346.57i	0.867184	−	1.73975i
$775$	−88.4537	−	17.5945i	−0.114134	−	0.0227026i
$776$	−2462.81	−	1214.52i	−3.17372	−	1.56511i
$777$	187.051	−	794.563i	0.240735	−	1.02260i
$778$	−29.1998	−	108.975i	−0.0375319	−	0.140071i
$779$	−289.483	+	142.757i	−0.371608	+	0.183257i
$780$	273.143	+	1182.83i	0.350184	+	1.51645i
$781$	−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
$785$	−528.618	−	34.6474i	−0.673398	−	0.0441369i
$786$	−398.105	+	2379.74i	−0.506495	+	3.02766i
$787$	880.260	+	298.808i	1.11850	+	0.379680i	0.818642	−	0.574304i	$-0.194727\pi$
$787$	880.260	+	298.808i	1.11850	+	0.379680i	0.299858	+	0.953984i	$0.403061\pi$
$788$	349.590	−	22.9133i	0.443642	−	0.0290778i
$789$	−762.885	−	549.139i	−0.966901	−	0.695993i
$790$	−551.225	−	422.970i	−0.697753	−	0.535405i
$791$	524.014	+	1265.08i	0.662470	+	1.59934i
$792$	−2531.69	−	10.7844i	−3.19658	−	0.0136167i
$793$	−736.558	+	492.153i	−0.928825	+	0.620621i
$794$	−450.577	−	513.784i	−0.567477	−	0.647083i
$795$	−117.418	+	142.454i	−0.147695	+	0.179188i
$796$	−1947.11	+	960.210i	−2.44612	+	1.20629i
$797$	−1141.41	+	875.831i	−1.43213	+	1.09891i	−0.453976	+	0.891014i	$0.649995\pi$
$797$	−1141.41	+	875.831i	−1.43213	+	1.09891i	−0.978151	+	0.207896i	$0.933339\pi$
$798$	−295.981	−	3072.21i	−0.370904	−	3.84989i
$799$	−401.606	−	263.127i	−0.502636	−	0.329320i
$800$	−1757.69			−2.19711
$801$	−1000.55	−	885.029i	−1.24913	−	1.10490i
$802$	105.126	−	157.332i	0.131080	−	0.196175i
$803$	−5.71836	+	21.3412i	−0.00712124	+	0.0265768i
$804$	1443.56	+	339.834i	1.79547	+	0.422679i
$805$	188.574	−	12.3598i	0.234253	−	0.0153537i
$806$	218.413	+	191.543i	0.270984	+	0.237646i
$807$	199.565	+	124.688i	0.247293	+	0.154508i
$808$	−351.627	+	458.249i	−0.435181	+	0.567140i
$809$	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	$0.489079\pi$
$810$	−728.656	−	53.9967i	−0.899575	−	0.0666626i
$811$	−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	$0.578334\pi$
$812$	2019.35	+	541.084i	2.48689	+	0.666360i
$813$	27.0356	+	883.382i	0.0332541	+	1.08657i
$814$	999.429	−	766.889i	1.22780	−	0.942124i
$815$	−495.249	−	285.932i	−0.607667	−	0.350837i
$816$	2446.78	−	588.356i	2.99851	−	0.721024i
$817$	625.065	+	1082.64i	0.765074	+	1.32515i
$818$	−165.292	+	399.051i	−0.202069	+	0.487837i
$819$	860.222	+	1131.01i	1.05033	+	1.38096i
$820$	−198.446	−	198.446i	−0.242008	−	0.242008i
$821$	121.021	−	106.133i	0.147407	−	0.129273i	−0.582466	−	0.812855i	$-0.697912\pi$
$821$	121.021	−	106.133i	0.147407	−	0.129273i	0.729874	+	0.683582i	$0.239579\pi$
$822$	248.793	+	304.475i	0.302668	+	0.370408i
$823$	−64.7269	−	56.7639i	−0.0786475	−	0.0689720i	0.619120	−	0.785297i	$-0.287490\pi$
$823$	−64.7269	−	56.7639i	−0.0786475	−	0.0689720i	−0.697767	+	0.716325i	$0.745823\pi$
$824$	163.003	−	1238.13i	0.197819	−	1.50258i
$825$	−319.647	−	601.093i	−0.387451	−	0.728598i
$826$	−1337.40	−	3939.85i	−1.61913	−	4.76980i
$827$	−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	$0.320288\pi$
$828$	−710.368	+	290.705i	−0.857932	+	0.351093i
$829$	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	$0.0903147\pi$
$830$	27.8034	−	424.199i	0.0334981	−	0.511083i
$831$	−744.052	+	693.912i	−0.895370	+	0.835033i
$832$	2092.80	+	1208.28i	2.51539	+	1.45226i
$833$	−693.428	+	242.397i	−0.832446	+	0.290992i
$834$	111.479	+	156.270i	0.133667	+	0.187374i
$835$	−142.247	+	18.7272i	−0.170356	+	0.0224278i
$836$	1907.49	−	2854.77i	2.28169	−	3.41479i
$837$	−107.450	+	65.8683i	−0.128375	+	0.0786958i
$838$	−225.892	−	1135.64i	−0.269561	−	1.35518i
$839$	−46.3660	+	94.0210i	−0.0552635	+	0.112063i	−0.922752	−	0.385393i	$-0.874066\pi$
$839$	−46.3660	+	94.0210i	−0.0552635	+	0.112063i	0.867489	+	0.497456i	$0.165733\pi$
$840$	1499.09	−	675.382i	1.78463	−	0.804026i
$841$	51.7652	−	393.195i	0.0615519	−	0.467533i
$842$	1836.49	+	241.779i	2.18111	+	0.287148i
$843$	320.622	−	445.421i	0.380335	−	0.528376i
$844$	−1279.99	−	631.221i	−1.51657	−	0.747892i
$845$	236.858	−	47.1140i	0.280306	−	0.0557562i
$846$	959.792	+	67.0153i	1.13451	+	0.0792143i
$847$	135.396	+	90.4685i	0.159853	+	0.106810i
$848$	166.308	+	1263.24i	0.196118	+	1.48967i
$849$	119.232	+	1237.60i	0.140438	+	1.45771i
$850$	828.138	+	927.273i	0.974280	+	1.09091i
$851$	116.998	−	202.646i	0.137483	−	0.238127i
$852$	−191.355	+	626.009i	−0.224595	+	0.734752i
$853$	−635.282	−	41.6386i	−0.744762	−	0.0488143i	−0.311703	−	0.950180i	$-0.600899\pi$
$853$	−635.282	−	41.6386i	−0.744762	−	0.0488143i	−0.433059	+	0.901365i	$0.642566\pi$
$854$	1384.73	+	1384.73i	1.62146	+	1.62146i
$855$	371.621	−	480.057i	0.434644	−	0.561471i
$856$	−874.940	−	1309.44i	−1.02213	−	1.52972i
$857$	1498.99	−	508.839i	1.74911	−	0.593744i	0.751308	−	0.659952i	$-0.229423\pi$
$857$	1498.99	−	508.839i	1.74911	−	0.593744i	0.997806	+	0.0662077i	$0.0210900\pi$
$858$	−76.4195	+	2191.62i	−0.0890670	+	2.55434i
$859$	−769.388	−	101.292i	−0.895679	−	0.117918i	−0.331388	−	0.943495i	$-0.607517\pi$
$859$	−769.388	−	101.292i	−0.895679	−	0.117918i	−0.564291	+	0.825576i	$0.690850\pi$
$860$	−716.695	+	817.235i	−0.833367	+	0.950273i
$861$	−307.200	−	116.369i	−0.356794	−	0.135156i
$862$	808.449	+	921.860i	0.937876	+	1.06944i
$863$	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	$-0.0397543\pi$
$864$	−1803.46	+	1667.62i	−2.08734	+	1.93012i
$865$	340.359	+	140.981i	0.393479	+	0.162984i
$866$	−1049.88	+	606.150i	−1.21234	+	0.699942i
$867$	−712.699	−	493.709i	−0.822029	−	0.569446i
$868$	231.453	−	400.889i	0.266651	−	0.461854i
$869$	−550.751	−	717.753i	−0.633776	−	0.825953i
$870$	300.220	+	485.094i	0.345080	+	0.557579i
$871$	203.699	−	760.214i	0.233868	−	0.872806i
$872$	214.445	+	1078.09i	0.245923	+	1.23634i
$873$	−726.558	−	732.774i	−0.832254	−	0.839375i
$874$	172.608	−	867.757i	0.197492	−	0.992857i
$875$	804.652	+	617.431i	0.919603	+	0.705636i
$876$	27.3628	+	51.4556i	0.0312361	+	0.0587393i
$877$	984.288	−	1122.37i	1.12234	−	1.27978i	0.166446	−	0.986051i	$-0.446771\pi$
$877$	984.288	−	1122.37i	1.12234	−	1.27978i	0.955889	−	0.293727i	$-0.0948958\pi$
$878$	−16.5728	−	252.852i	−0.0188756	−	0.287986i
$879$	−618.727	+	186.251i	−0.703899	+	0.211889i
$880$	1334.12	+	357.475i	1.51604	+	0.406222i
$881$	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	$0.619080\pi$
$882$	975.269	−	1102.57i	1.10575	−	1.25008i
$883$			299.360i			0.339027i	0.985528	+	0.169513i	$0.0542196\pi$
$883$			299.360i			0.339027i	−0.985528	+	0.169513i	$0.945780\pi$
$884$	−588.709	−	2825.94i	−0.665960	−	3.19677i
$885$	339.339	−	744.715i	0.383434	−	0.841485i
$886$	849.512	+	1107.11i	0.958817	+	1.24955i
$887$	673.346	+	1365.41i	0.759127	+	1.53936i	0.839972	+	0.542630i	$0.182572\pi$
$887$	673.346	+	1365.41i	0.759127	+	1.53936i	−0.0808448	+	0.996727i	$0.525762\pi$
$888$	335.912	−	2007.97i	0.378279	−	2.26123i
$889$	676.036	−	592.868i	0.760446	−	0.666893i
$890$	743.818	+	1113.20i	0.835751	+	1.25079i
$891$	−898.261	−	313.478i	−1.00815	−	0.351827i
$892$	1458.25	−	604.028i	1.63481	−	0.677162i
$893$	−486.654	+	634.220i	−0.544966	+	0.710213i
$894$	−755.917	−	1677.84i	−0.845544	−	1.87678i
$895$	12.2747	+	187.276i	0.0137148	+	0.209247i
$896$	593.951	−	1749.72i	0.662891	−	1.95282i
$897$	142.671	+	381.532i	0.159054	+	0.425342i
$898$	−1.19852	+	18.2858i	−0.00133465	+	0.0203628i
$899$	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
$903$	−371.931	+	1216.76i	−0.411884	+	1.34746i
$904$	1510.49	+	3062.98i	1.67090	+	3.38825i
$905$	552.345	−	148.000i	0.610326	−	0.163536i
$906$	827.379	+	2748.56i	0.913222	+	3.03373i
$907$	−270.068	+	547.644i	−0.297760	+	0.603797i	−0.993414	−	0.114579i	$-0.963448\pi$
$907$	−270.068	+	547.644i	−0.297760	+	0.603797i	0.695654	+	0.718377i	$0.255115\pi$
$908$	219.207	−	1102.03i	0.241417	−	1.21369i
$909$	−180.990	+	119.822i	−0.199109	+	0.131817i
$910$	−545.016	−	1315.78i	−0.598918	−	1.44592i
$911$	−331.677	−	977.090i	−0.364080	−	1.07255i	−0.962481	−	0.271349i	$-0.912530\pi$
$911$	−331.677	−	977.090i	−0.364080	−	1.07255i	0.598400	−	0.801197i	$-0.295803\pi$
$912$	−673.732	−	4135.52i	−0.738741	−	4.53456i
$913$	177.929	−	524.161i	0.194883	−	0.574108i
$914$	−38.1516	−	142.384i	−0.0417414	−	0.155781i
$915$	11.7830	+	385.009i	0.0128776	+	0.420774i
$916$	591.046	+	4489.44i	0.645247	+	4.90114i
$917$		−	2040.37i		−	2.22505i
$918$	1729.46	+	165.717i	1.88394	+	0.180519i
$919$	−171.601			−0.186725			−0.0933626	−	0.995632i	$-0.529762\pi$
$919$	−171.601			−0.186725			−0.0933626	+	0.995632i	$0.529762\pi$
$920$	467.294	−	61.5204i	0.507928	−	0.0668700i
$921$	896.595	−	27.4399i	0.973502	−	0.0297936i
$922$	194.629	−	52.1506i	0.211094	−	0.0565625i
$923$	328.958	+	111.666i	0.356401	+	0.120982i
$924$	3448.91	−	561.874i	3.73259	−	0.608089i
$925$	518.409	−	175.976i	0.560442	−	0.190244i
$926$	1298.51	−	537.861i	1.40228	−	0.580843i
$927$	209.352	−	420.005i	0.225838	−	0.453079i
$928$	1880.98	+	374.151i	2.02692	+	0.403180i
$929$	290.563	+	143.290i	0.312769	+	0.154241i	0.591898	−	0.806013i	$-0.298379\pi$
$929$	290.563	+	143.290i	0.312769	+	0.154241i	−0.279129	+	0.960254i	$0.590046\pi$
$930$	120.957	−	36.4107i	0.130061	−	0.0391513i
$931$	316.554	+	1181.40i	0.340015	+	1.26895i
$932$	−2995.34	+	1477.14i	−3.21389	+	1.58491i
$933$	−764.015	−	233.540i	−0.818880	−	0.250310i
$934$	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	$0.0330069\pi$
$938$	−1736.12	−	113.791i	−1.85087	−	0.121313i
$939$	−358.720	+	134.141i	−0.382024	+	0.142855i
$940$	−658.199	−	223.429i	−0.700212	−	0.237690i
$941$	597.090	−	39.1353i	0.634527	−	0.0415891i	0.255254	−	0.966874i	$-0.417841\pi$
$941$	597.090	−	39.1353i	0.634527	−	0.0415891i	0.379273	+	0.925285i	$0.376174\pi$
$942$	−2301.45	+	1036.87i	−2.44316	+	1.10071i
$943$	−74.7087	−	57.3260i	−0.0792245	−	0.0607911i
$944$	−2161.53	−	5218.41i	−2.28976	−	5.52797i
$945$	615.271	−	56.6318i	0.651080	−	0.0599279i
$946$	−1632.65	+	1090.90i	−1.72584	+	1.15317i
$947$	−296.177	−	337.725i	−0.312753	−	0.356626i	0.574012	−	0.818847i	$-0.305386\pi$
$947$	−296.177	−	337.725i	−0.312753	−	0.356626i	−0.886765	+	0.462221i	$0.847053\pi$
$948$	−2353.69	−	393.747i	−2.48280	−	0.415345i
$949$	27.7387	−	13.6792i	0.0292294	−	0.0144143i
$950$	1642.25	−	1260.14i	1.72868	−	1.32646i
$951$	−359.329	−	163.733i	−0.377844	−	0.172170i
$952$	−3598.38	+	1528.74i	−3.77981	+	1.60581i
$953$	−262.054			−0.274978			−0.137489	−	0.990503i	$-0.543903\pi$
$953$	−262.054			−0.274978			−0.137489	+	0.990503i	$0.543903\pi$
$954$	−175.284	+	862.007i	−0.183736	+	0.903572i
$955$	207.389	−	310.379i	0.217161	−	0.325005i
$956$	−665.131	+	2482.30i	−0.695744	+	2.59655i
$957$	214.117	+	711.298i	0.223737	+	0.743258i
$958$	−2051.57	+	134.467i	−2.14151	+	0.140362i
$959$	−249.989	−	219.234i	−0.260677	−	0.228607i
$960$	927.755	−	493.358i	0.966411	−	0.513914i
$961$	−571.755	+	745.126i	−0.594959	+	0.775366i
$962$	−1729.57	−	344.034i	−1.79789	−	0.357623i
$963$	−150.735	−	572.292i	−0.156527	−	0.594281i
$964$	37.3402	−	7.42742i	0.0387346	−	0.00770480i
$965$	−677.274	−	181.475i	−0.701839	−	0.188057i
$966$	765.694	−	473.880i	0.792643	−	0.490559i
$967$	721.265	−	553.446i	0.745879	−	0.572333i	−0.164368	−	0.986399i	$-0.552559\pi$
$967$	721.265	−	553.446i	0.745879	−	0.572333i	0.910247	+	0.414066i	$0.135892\pi$
$968$	351.722	+	203.067i	0.363349	+	0.209779i
$969$	−908.057	+	1122.19i	−0.937108	+	1.15809i
$970$	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	$0.0693914\pi$
$972$	−2296.74	+	1011.30i	−2.36290	+	1.04043i
$973$	−114.783	−	114.783i	−0.117968	−	0.117968i
$974$	−1854.56	+	1626.41i	−1.90407	+	1.66982i
$975$	−337.598	+	891.213i	−0.346254	+	0.914065i
$976$	1998.78	+	1752.88i	2.04793	+	1.79599i
$977$	−187.229	+	1422.14i	−0.191636	+	1.45562i	0.577424	+	0.816445i	$0.304058\pi$
$977$	−187.229	+	1422.14i	−0.191636	+	1.45562i	−0.769060	+	0.639177i	$0.779275\pi$
$978$	−2723.25	−	94.9568i	−2.78451	−	0.0970928i
$979$	560.368	+	1650.79i	0.572388	+	1.68620i
$980$	−884.227	+	590.822i	−0.902272	+	0.602879i
$981$	−55.6604	+	409.302i	−0.0567384	+	0.417229i
$982$	−1314.79	+	1314.79i	−1.33889	+	1.33889i
$983$	55.7860	−	851.130i	0.0567508	−	0.865850i	−0.870679	−	0.491852i	$-0.836320\pi$
$983$	55.7860	−	851.130i	0.0567508	−	0.865850i	0.927430	−	0.373998i	$-0.122013\pi$
$984$	−783.522	−	239.502i	−0.796262	−	0.243397i
$985$	−70.0131	−	40.4221i	−0.0710792	−	0.0410376i
$986$	−688.843	−	1168.60i	−0.698624	−	1.18519i
$987$	−809.866	+	78.0235i	−0.820533	+	0.0790512i
$988$	−4765.11	+	627.339i	−4.82299	+	0.634958i
$989$	−202.631	+	303.259i	−0.204885	+	0.306632i
$990$	790.582	+	533.135i	0.798568	+	0.538520i
$991$	−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	$-0.193420\pi$
$992$	187.820	−	380.861i	0.189335	−	0.383933i
$993$	778.740	+	560.552i	0.784230	+	0.564503i
$994$	100.240	−	761.395i	0.100845	−	0.765991i
$995$	496.693	+	65.3908i	0.499188	+	0.0657194i
$996$	−599.757	−	1331.23i	−0.602166	−	1.33657i
$997$	102.086	+	50.3434i	0.102393	+	0.0504949i	0.492764	−	0.870163i	$-0.335987\pi$
$997$	102.086	+	50.3434i	0.102393	+	0.0504949i	−0.390371	+	0.920658i	$0.627653\pi$
$998$	−3143.34	+	625.249i	−3.14964	+	0.626502i
$999$	364.949	−	672.402i	0.365315	−	0.673075i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.t.a.7.2	✓	544	9.7	even	3	inner
153.3.t.a.22.2	yes	544	17.5	odd	16	inner
153.3.t.a.58.33	yes	544	1.1	even	1	trivial
153.3.t.a.124.33	yes	544	153.124	odd	48	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(3.75276 - 0.494060i) q^{2} +(-2.99860 + 0.0917708i) q^{3} +(9.97539 - 2.67290i) q^{4} +(-2.25664 - 0.766027i) q^{5} +(-11.2077 + 1.82588i) q^{6} +(9.09301 - 3.08666i) q^{7} +(22.1266 - 9.16514i) q^{8} +(8.98316 - 0.550367i) q^{9} +(-8.84710 - 1.75980i) q^{10} +(-10.5343 - 5.19492i) q^{11} +(-29.6669 + 8.93039i) q^{12} +(4.25549 + 15.8817i) q^{13} +(32.5989 - 16.0760i) q^{14} +(6.83706 + 2.08991i) 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} +(-24.5584 - 1.60964i) q^{20} +(-26.9830 + 10.0901i) q^{21} +(-42.0991 - 14.2907i) q^{22} +(-8.24036 + 0.540102i) q^{23} +(-65.5077 + 29.5131i) q^{24} +(-15.3282 - 11.7617i) q^{25} +(23.8163 + 57.4977i) q^{26} +(-26.8863 + 2.47472i) q^{27} +(82.4560 - 55.0953i) q^{28} +(13.8997 + 15.8496i) q^{29} +(26.6904 + 4.46501i) q^{30} +(4.18648 - 2.06454i) q^{31} +(72.1747 - 55.3816i) q^{32} +(32.0647 + 14.6107i) q^{33} +(-63.2218 - 11.9828i) q^{34} -22.8841 q^{35} +(88.1394 - 29.5012i) q^{36} +(-15.7423 + 23.5601i) q^{37} +(-27.7296 + 103.488i) q^{38} +(-14.2180 - 47.2323i) q^{39} +(-56.9526 + 3.73287i) q^{40} +(8.57338 + 7.51866i) q^{41} +(-96.2755 + 51.1970i) q^{42} +(26.8867 - 35.0394i) q^{43} +(-118.969 - 23.6644i) q^{44} +(-20.6934 - 5.63936i) q^{45} +(-30.6573 + 6.09811i) q^{46} +(27.2805 + 7.30979i) q^{47} +(-125.875 + 77.9026i) q^{48} +(34.2810 - 26.3047i) q^{49} +(-63.3340 - 36.5659i) q^{50} +(48.9050 + 14.4671i) q^{51} +(84.9003 + 147.052i) q^{52} +(-9.88153 + 23.8561i) q^{53} +(-99.6753 + 22.5705i) q^{54} +(19.7926 + 19.7926i) q^{55} +(172.908 - 151.636i) q^{56} +(30.0806 - 79.4089i) q^{57} +(59.9929 + 52.6124i) q^{58} +(14.9413 - 113.490i) q^{59} +(73.7885 + 2.57292i) q^{60} +(17.3184 + 51.0183i) q^{61} +(14.6908 - 9.81610i) q^{62} +(79.9851 - 32.7324i) q^{63} +(103.927 - 103.927i) q^{64} +(2.56269 - 39.0991i) q^{65} +(127.550 + 38.9886i) q^{66} +(-41.4543 - 23.9337i) q^{67} +(-175.285 - 9.89897i) q^{68} +(24.6600 - 2.37577i) q^{69} +(-85.8786 + 11.3061i) q^{70} +(11.7384 - 17.5678i) q^{71} +(193.723 - 94.5097i) q^{72} +(-0.366976 - 1.84491i) q^{73} +(-47.4371 + 96.1929i) q^{74} +(47.0425 + 33.8620i) q^{75} +(-38.1548 + 289.814i) q^{76} +(-111.823 - 14.7218i) q^{77} +(-76.6921 - 170.227i) q^{78} +(69.0822 + 34.0676i) q^{79} +(-115.332 + 22.9410i) q^{80} +(80.3942 - 9.88807i) q^{81} +(35.8885 + 23.9799i) q^{82} +(6.15136 + 46.7242i) q^{83} +(-242.196 + 172.776i) q^{84} +(32.3626 + 24.3713i) q^{85} +(83.5877 - 144.778i) q^{86} +(-43.1342 - 46.2509i) q^{87} +(-280.700 - 18.3980i) q^{88} +(-104.951 - 104.951i) q^{89} +(-80.4434 - 10.9394i) q^{90} +(87.7165 + 131.277i) q^{91} +(-80.7572 + 27.4134i) q^{92} +(-12.3641 + 6.57492i) q^{93} +(105.989 + 13.9537i) q^{94} +(44.4757 - 50.7148i) q^{95} +(-211.340 + 172.691i) q^{96} +(-75.5986 - 86.2037i) q^{97} +(115.652 - 115.652i) q^{98} +(-97.4900 - 40.8691i) 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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