LMFDB - Embedded newform 153.3.i.a.101.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(50,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.50"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.i (of order $6$, degree $2$, 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:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.8
Character	$\chi$	$=$	153.101
Dual form			153.3.i.a.50.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.44623 - 1.41233i) q^{2} +(0.529325 + 2.95293i) q^{3} +(1.98938 + 3.44570i) q^{4} +(-1.84354 - 3.19311i) q^{5} +(2.87567 - 7.97115i) q^{6} +(-1.20670 - 0.696687i) q^{7} +0.0600221i q^{8} +(-8.43963 + 3.12612i) q^{9} +10.4148i q^{10} +(9.91827 - 17.1789i) q^{11} +(-9.12189 + 7.69839i) q^{12} +(8.79901 + 15.2403i) q^{13} +(1.96791 + 3.40852i) q^{14} +(8.45321 - 7.13406i) q^{15} +(8.04227 - 13.9296i) q^{16} +(10.4620 - 13.3995i) q^{17} +(25.0604 + 4.27234i) q^{18} +17.1257 q^{19} +(7.33500 - 12.7046i) q^{20} +(1.41854 - 3.93207i) q^{21} +(-48.5248 + 28.0158i) q^{22} +(-8.76780 - 15.1863i) q^{23} +(-0.177241 + 0.0317712i) q^{24} +(5.70269 - 9.87734i) q^{25} -49.7086i q^{26} +(-13.6985 - 23.2669i) q^{27} -5.54389i q^{28} +(6.20471 - 10.7469i) q^{29} +(-30.7542 + 5.51282i) q^{30} +(29.8091 - 17.2103i) q^{31} +(-39.1386 + 22.5967i) q^{32} +(55.9783 + 20.1947i) q^{33} +(-44.5171 + 18.0024i) q^{34} +5.13750i q^{35} +(-27.5613 - 22.8614i) q^{36} -13.0363i q^{37} +(-41.8935 - 24.1872i) q^{38} +(-40.3461 + 34.0500i) q^{39} +(0.191657 - 0.110653i) q^{40} +(15.2683 + 26.4454i) q^{41} +(-9.02347 + 7.61532i) q^{42} +(-17.3388 + 30.0317i) q^{43} +78.9246 q^{44} +(25.5409 + 21.1855i) q^{45} +49.5322i q^{46} +(74.8051 + 43.1887i) q^{47} +(45.3902 + 16.3750i) q^{48} +(-23.5293 - 40.7539i) q^{49} +(-27.9002 + 16.1082i) q^{50} +(45.1056 + 23.8010i) q^{51} +(-35.0091 + 60.6375i) q^{52} -11.8546i q^{53} +(0.649177 + 76.2633i) q^{54} -73.1391 q^{55} +(0.0418166 - 0.0724285i) q^{56} +(9.06506 + 50.5710i) q^{57} +(-30.3564 + 17.5263i) q^{58} +(-77.9699 + 45.0160i) q^{59} +(41.3984 + 14.9349i) q^{60} +(-1.04031 - 0.600624i) q^{61} -97.2267 q^{62} +(12.3620 + 2.10750i) q^{63} +63.3182 q^{64} +(32.4427 - 56.1925i) q^{65} +(-108.414 - 128.461i) q^{66} +(29.0384 + 50.2960i) q^{67} +(66.9835 + 9.39240i) q^{68} +(40.2030 - 33.9292i) q^{69} +(7.25586 - 12.5675i) q^{70} -119.490 q^{71} +(-0.187636 - 0.506564i) q^{72} -108.335i q^{73} +(-18.4117 + 31.8899i) q^{74} +(32.1857 + 11.6113i) q^{75} +(34.0694 + 59.0100i) q^{76} +(-23.9367 + 13.8199i) q^{77} +(146.786 - 26.3120i) q^{78} +(-2.99178 - 1.72730i) q^{79} -59.3052 q^{80} +(61.4547 - 52.7667i) q^{81} -86.2557i q^{82} +(-37.0145 - 21.3704i) q^{83} +(16.3707 - 2.93452i) q^{84} +(-62.0733 - 8.70389i) q^{85} +(84.8297 - 48.9765i) q^{86} +(35.0191 + 12.6335i) q^{87} +(1.03112 + 0.595315i) q^{88} -43.3483i q^{89} +(-32.5580 - 87.8971i) q^{90} -24.5206i q^{91} +(34.8849 - 60.4224i) q^{92} +(66.5996 + 78.9144i) q^{93} +(-121.994 - 211.300i) q^{94} +(-31.5720 - 54.6843i) q^{95} +(-87.4436 - 103.613i) q^{96} +(42.1943 + 24.3609i) q^{97} +132.925i q^{98} +(-30.0030 + 175.990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Character values

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

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.44623	−	1.41233i	−1.22312	−	0.706167i	−0.257536	−	0.966269i	$-0.582911\pi$
$2$	−2.44623	−	1.41233i	−1.22312	−	0.706167i	−0.965581	+	0.260102i	$0.916244\pi$
$3$	0.529325	+	2.95293i	0.176442	+	0.984311i
$3$	0.529325	+	2.95293i	0.176442	+	0.984311i
$4$	1.98938	+	3.44570i	0.497344	+	0.861425i
$5$	−1.84354	−	3.19311i	−0.368709	−	0.638623i	0.620655	−	0.784084i	$-0.286867\pi$
$5$	−1.84354	−	3.19311i	−0.368709	−	0.638623i	−0.989364	+	0.145461i	$0.953533\pi$
$6$	2.87567	−	7.97115i	0.479279	−	1.32853i
$7$	−1.20670	−	0.696687i	−0.172385	−	0.0995267i	0.411325	−	0.911489i	$-0.365066\pi$
$7$	−1.20670	−	0.696687i	−0.172385	−	0.0995267i	−0.583710	+	0.811962i	$0.698400\pi$
$8$			0.0600221i			0.00750276i
$9$	−8.43963	+	3.12612i	−0.937737	+	0.347347i
$10$			10.4148i			1.04148i
$11$	9.91827	−	17.1789i	0.901661	−	1.56172i	0.0763223	−	0.997083i	$-0.475682\pi$
$11$	9.91827	−	17.1789i	0.901661	−	1.56172i	0.825338	−	0.564639i	$-0.190984\pi$
$12$	−9.12189	+	7.69839i	−0.760158	+	0.641532i
$13$	8.79901	+	15.2403i	0.676847	+	1.17233i	0.975925	+	0.218105i	$0.0699874\pi$
$13$	8.79901	+	15.2403i	0.676847	+	1.17233i	−0.299079	+	0.954228i	$0.596679\pi$
$14$	1.96791	+	3.40852i	0.140565	+	0.243466i
$15$	8.45321	−	7.13406i	0.563548	−	0.475604i
$16$	8.04227	−	13.9296i	0.502642	−	0.870602i
$17$	10.4620	−	13.3995i	0.615413	−	0.788205i
$17$	10.4620	−	13.3995i	0.615413	−	0.788205i
$18$	25.0604	+	4.27234i	1.39225	+	0.237352i
$19$	17.1257			0.901352			0.450676	−	0.892688i	$-0.351183\pi$
$19$	17.1257			0.901352			0.450676	+	0.892688i	$0.351183\pi$
$20$	7.33500	−	12.7046i	0.366750	−	0.635230i
$21$	1.41854	−	3.93207i	0.0675493	−	0.187242i
$22$	−48.5248	+	28.0158i	−2.20567	+	1.27345i
$23$	−8.76780	−	15.1863i	−0.381209	−	0.660273i	0.610027	−	0.792381i	$-0.291159\pi$
$23$	−8.76780	−	15.1863i	−0.381209	−	0.660273i	−0.991235	+	0.132108i	$0.957825\pi$
$24$	−0.177241	+	0.0317712i	−0.00738505	+	0.00132380i
$25$	5.70269	−	9.87734i	0.228107	−	0.395094i
$26$		−	49.7086i		−	1.91187i
$27$	−13.6985	−	23.2669i	−0.507353	−	0.861738i
$28$		−	5.54389i		−	0.197996i
$29$	6.20471	−	10.7469i	0.213956	−	0.370582i	−0.738993	−	0.673713i	$-0.764699\pi$
$29$	6.20471	−	10.7469i	0.213956	−	0.370582i	0.952949	+	0.303131i	$0.0980319\pi$
$30$	−30.7542	+	5.51282i	−1.02514	+	0.183761i
$31$	29.8091	−	17.2103i	0.961584	−	0.555171i	0.0649238	−	0.997890i	$-0.479320\pi$
$31$	29.8091	−	17.2103i	0.961584	−	0.555171i	0.896660	+	0.442719i	$0.145986\pi$
$32$	−39.1386	+	22.5967i	−1.22308	+	0.706147i
$33$	55.9783	+	20.1947i	1.69631	+	0.611962i
$34$	−44.5171	+	18.0024i	−1.30933	+	0.529482i
$35$			5.13750i			0.146786i
$36$	−27.5613	−	22.8614i	−0.765591	−	0.635039i
$37$		−	13.0363i		−	0.352333i	−0.984360	−	0.176167i	$-0.943630\pi$
$37$		−	13.0363i		−	0.352333i	0.984360	−	0.176167i	$-0.0563698\pi$
$38$	−41.8935	−	24.1872i	−1.10246	−	0.636505i
$39$	−40.3461	+	34.0500i	−1.03452	+	0.873076i
$40$	0.191657	−	0.110653i	0.00479143	−	0.00276633i
$41$	15.2683	+	26.4454i	0.372397	+	0.645011i	0.989934	−	0.141531i	$-0.0452026\pi$
$41$	15.2683	+	26.4454i	0.372397	+	0.645011i	−0.617537	+	0.786542i	$0.711869\pi$
$42$	−9.02347	+	7.61532i	−0.214845	+	0.181317i
$43$	−17.3388	+	30.0317i	−0.403229	+	0.698413i	−0.994114	−	0.108343i	$-0.965445\pi$
$43$	−17.3388	+	30.0317i	−0.403229	+	0.698413i	0.590885	+	0.806756i	$0.298779\pi$
$44$	78.9246			1.79374
$45$	25.5409	+	21.1855i	0.567576	+	0.470790i
$46$			49.5322i			1.07679i
$47$	74.8051	+	43.1887i	1.59160	+	0.918909i	0.993033	+	0.117834i	$0.0375952\pi$
$47$	74.8051	+	43.1887i	1.59160	+	0.918909i	0.598564	+	0.801075i	$0.295738\pi$
$48$	45.3902	+	16.3750i	0.945630	+	0.341146i
$49$	−23.5293	−	40.7539i	−0.480189	−	0.831711i
$50$	−27.9002	+	16.1082i	−0.558004	+	0.322164i
$51$	45.1056	+	23.8010i	0.884423	+	0.466686i
$52$	−35.0091	+	60.6375i	−0.673251	+	1.16611i
$53$		−	11.8546i		−	0.223672i	−0.993727	−	0.111836i	$-0.964327\pi$
$53$		−	11.8546i		−	0.223672i	0.993727	−	0.111836i	$-0.0356731\pi$
$54$	0.649177	+	76.2633i	0.0120218	+	1.41228i
$55$	−73.1391			−1.32980
$56$	0.0418166	−	0.0724285i	0.000746725	−	0.00129337i
$57$	9.06506	+	50.5710i	0.159036	+	0.887211i
$58$	−30.3564	+	17.5263i	−0.523385	+	0.302177i
$59$	−77.9699	+	45.0160i	−1.32152	+	0.762982i	−0.983972	−	0.178324i	$-0.942932\pi$
$59$	−77.9699	+	45.0160i	−1.32152	+	0.762982i	−0.337553	+	0.941307i	$0.609599\pi$
$60$	41.3984	+	14.9349i	0.689974	+	0.248915i
$61$	−1.04031	−	0.600624i	−0.0170543	−	0.00984629i	0.491449	−	0.870907i	$-0.336468\pi$
$61$	−1.04031	−	0.600624i	−0.0170543	−	0.00984629i	−0.508503	+	0.861060i	$0.669801\pi$
$62$	−97.2267			−1.56817
$63$	12.3620	+	2.10750i	0.196222	+	0.0334523i
$64$	63.3182			0.989347
$65$	32.4427	−	56.1925i	0.499119	−	0.864499i
$66$	−108.414	−	128.461i	−1.64264	−	1.94638i
$67$	29.0384	+	50.2960i	0.433409	+	0.750687i	0.997164	−	0.0752549i	$-0.0239771\pi$
$67$	29.0384	+	50.2960i	0.433409	+	0.750687i	−0.563755	+	0.825942i	$0.690644\pi$
$68$	66.9835	+	9.39240i	0.985051	+	0.138124i
$69$	40.2030	−	33.9292i	0.582652	−	0.491727i
$70$	7.25586	−	12.5675i	0.103655	−	0.179536i
$71$	−119.490			−1.68296			−0.841481	−	0.540287i	$-0.818316\pi$
$71$	−119.490			−1.68296			−0.841481	+	0.540287i	$0.818316\pi$
$72$	−0.187636	−	0.506564i	−0.00260606	−	0.00703561i
$73$		−	108.335i		−	1.48404i	−0.670377	−	0.742021i	$-0.733867\pi$
$73$		−	108.335i		−	1.48404i	0.670377	−	0.742021i	$-0.266133\pi$
$74$	−18.4117	+	31.8899i	−0.248806	+	0.430945i
$75$	32.1857	+	11.6113i	0.429143	+	0.154818i
$76$	34.0694	+	59.0100i	0.448282	+	0.776447i
$77$	−23.9367	+	13.8199i	−0.310866	+	0.179479i
$78$	146.786	−	26.3120i	1.88187	−	0.337333i
$79$	−2.99178	−	1.72730i	−0.0378706	−	0.0218646i	0.480945	−	0.876751i	$-0.340294\pi$
$79$	−2.99178	−	1.72730i	−0.0378706	−	0.0218646i	−0.518816	+	0.854886i	$0.673627\pi$
$80$	−59.3052			−0.741314
$81$	61.4547	−	52.7667i	0.758700	−	0.651440i
$82$		−	86.2557i		−	1.05190i
$83$	−37.0145	−	21.3704i	−0.445958	−	0.257474i	0.260163	−	0.965565i	$-0.416224\pi$
$83$	−37.0145	−	21.3704i	−0.445958	−	0.257474i	−0.706122	+	0.708090i	$0.749557\pi$
$84$	16.3707	−	2.93452i	0.194890	−	0.0349348i
$85$	−62.0733	−	8.70389i	−0.730274	−	0.102399i
$86$	84.8297	−	48.9765i	0.986392	−	0.569494i
$87$	35.0191	+	12.6335i	0.402519	+	0.145213i
$88$	1.03112	+	0.595315i	0.0117172	+	0.00676494i
$89$		−	43.3483i		−	0.487060i	−0.969893	−	0.243530i	$-0.921695\pi$
$89$		−	43.3483i		−	0.487060i	0.969893	−	0.243530i	$-0.0783054\pi$
$90$	−32.5580	−	87.8971i	−0.361755	−	0.976634i
$91$		−	24.5206i		−	0.269457i
$92$	34.8849	−	60.4224i	0.379183	−	0.656765i
$93$	66.5996	+	78.9144i	0.716124	+	0.848542i
$94$	−121.994	−	211.300i	−1.29781	−	2.24787i
$95$	−31.5720	−	54.6843i	−0.332337	−	0.575624i
$96$	−87.4436	−	103.613i	−0.910871	−	1.07930i
$97$	42.1943	+	24.3609i	0.434993	+	0.251143i	0.701471	−	0.712698i	$-0.252527\pi$
$97$	42.1943	+	24.3609i	0.434993	+	0.251143i	−0.266478	+	0.963841i	$0.585860\pi$
$98$			132.925i			1.35637i
$99$	−30.0030	+	175.990i	−0.303061	+	1.77767i
$100$	45.3791			0.453791
$101$	49.3410	+	28.4870i	0.488524	+	0.282050i	0.723962	−	0.689840i	$-0.242319\pi$
$101$	49.3410	+	28.4870i	0.488524	+	0.282050i	−0.235438	+	0.971889i	$0.575652\pi$
$102$	−76.7239	−	121.927i	−0.752195	−	1.19536i
$103$	30.2358	+	52.3700i	0.293552	+	0.508446i	0.974647	−	0.223749i	$-0.0718294\pi$
$103$	30.2358	+	52.3700i	0.293552	+	0.508446i	−0.681095	+	0.732195i	$0.738496\pi$
$104$	−0.914756	+	0.528135i	−0.00879573	+	0.00507822i
$105$	−15.1707	+	2.71941i	−0.144483	+	0.0258991i
$106$	−16.7427	+	28.9991i	−0.157950	+	0.273577i
$107$	2.02648			0.0189390			0.00946952	−	0.999955i	$-0.496986\pi$
$107$	2.02648			0.0189390			0.00946952	+	0.999955i	$0.496986\pi$
$108$	52.9193	−	93.4877i	0.489993	−	0.865627i
$109$		−	57.0549i		−	0.523440i	−0.965144	−	0.261720i	$-0.915710\pi$
$109$		−	57.0549i		−	0.523440i	0.965144	−	0.261720i	$-0.0842896\pi$
$110$	178.915	+	103.297i	1.62650	+	0.939062i
$111$	38.4954	−	6.90046i	0.346806	−	0.0621663i
$112$	−19.4092	+	11.2059i	−0.173296	+	0.100053i
$113$	86.9813	+	150.656i	0.769746	+	1.33324i	0.937701	+	0.347445i	$0.112951\pi$
$113$	86.9813	+	150.656i	0.769746	+	1.33324i	−0.167954	+	0.985795i	$0.553716\pi$
$114$	49.2479	−	136.511i	0.431999	−	1.19747i
$115$	−32.3276	+	55.9931i	−0.281110	+	0.486897i
$116$	49.3740			0.425638
$117$	−121.904	−	101.116i	−1.04191	−	0.864239i
$118$	254.310			2.15517
$119$	−21.9597	+	8.88036i	−0.184536	+	0.0746249i
$120$	0.428201	+	0.507379i	0.00356834	+	0.00422816i
$121$	−136.244	−	235.982i	−1.12598	−	1.95026i
$122$	1.69656	+	2.93853i	0.0139063	+	0.0240863i
$123$	−70.0097	+	59.0845i	−0.569185	+	0.480361i
$124$	118.603	+	68.4755i	0.956476	+	0.552222i
$125$	−134.230			−1.07384
$126$	−27.2639	−	22.6147i	−0.216380	−	0.179482i
$127$	44.1786			0.347863			0.173932	−	0.984758i	$-0.444353\pi$
$127$	44.1786			0.347863			0.173932	+	0.984758i	$0.444353\pi$
$128$	1.66336	+	0.960340i	0.0129950	+	0.00750265i
$129$	−97.8596	−	35.3039i	−0.758602	−	0.273673i
$130$	−158.725	+	91.6399i	−1.22096	+	0.704923i
$131$	−10.9841	−	19.0250i	−0.0838479	−	0.145229i	0.821052	−	0.570854i	$-0.193388\pi$
$131$	−10.9841	−	19.0250i	−0.0838479	−	0.145229i	−0.904900	+	0.425625i	$0.860054\pi$
$132$	41.7768	+	233.059i	0.316491	+	1.76560i
$133$	−20.6655	−	11.9312i	−0.155380	−	0.0897086i
$134$		−	164.048i		−	1.22424i
$135$	−49.0400	+	86.6346i	−0.363260	+	0.641738i
$136$	0.804264	+	0.627952i	0.00591371	+	0.00461730i
$137$	−61.9886	−	35.7891i	−0.452471	−	0.261234i	0.256402	−	0.966570i	$-0.417463\pi$
$137$	−61.9886	−	35.7891i	−0.452471	−	0.261234i	−0.708873	+	0.705336i	$0.750796\pi$
$138$	−146.265	+	26.2187i	−1.05989	+	0.189990i
$139$	167.030	−	96.4351i	1.20166	−	0.693778i	0.240734	−	0.970591i	$-0.422612\pi$
$139$	167.030	−	96.4351i	1.20166	−	0.693778i	0.960924	+	0.276813i	$0.0892784\pi$
$140$	−17.7023	+	10.2204i	−0.126445	+	0.0730029i
$141$	−87.9372	+	243.755i	−0.623668	+	1.72876i
$142$	292.301	+	168.760i	2.05846	+	1.18845i
$143$	349.084			2.44114
$144$	−24.3281	+	142.702i	−0.168945	+	0.990986i
$145$	−45.7546			−0.315549
$146$	−153.005	+	265.013i	−1.04798	+	1.81516i
$147$	107.889	−	91.0524i	0.733937	−	0.619404i
$148$	44.9193	−	25.9342i	0.303509	−	0.175231i
$149$	107.129	−	61.8512i	0.718989	−	0.415108i	−0.0953916	−	0.995440i	$-0.530410\pi$
$149$	107.129	−	61.8512i	0.718989	−	0.415108i	0.814380	+	0.580331i	$0.197077\pi$
$150$	−62.3347	−	73.8610i	−0.415565	−	0.492407i
$151$	36.8378	−	63.8049i	0.243959	−	0.422549i	−0.717879	−	0.696167i	$-0.754887\pi$
$151$	36.8378	−	63.8049i	0.243959	−	0.422549i	0.961838	+	0.273618i	$0.0882205\pi$
$152$			1.02792i			0.00676263i
$153$	−46.4072	+	145.792i	−0.303315	+	0.952890i
$154$	78.0730			0.506968
$155$	−109.909	−	63.4559i	−0.709089	−	0.409393i
$156$	−197.590	−	71.2825i	−1.26660	−	0.456939i
$157$	3.12950	+	5.42045i	0.0199331	+	0.0345252i	0.875820	−	0.482638i	$-0.160321\pi$
$157$	3.12950	+	5.42045i	0.0199331	+	0.0345252i	−0.855887	+	0.517163i	$0.826988\pi$
$158$	4.87906	+	8.45078i	0.0308801	+	0.0534860i
$159$	35.0059	−	6.27494i	0.220163	−	0.0394650i
$160$	144.308	+	83.3161i	0.901923	+	0.520725i
$161$			24.4336i			0.151762i
$162$	−224.857	+	42.2851i	−1.38800	+	0.261019i
$163$		−	47.6644i		−	0.292420i	−0.989254	−	0.146210i	$-0.953293\pi$
$163$		−	47.6644i		−	0.292420i	0.989254	−	0.146210i	$-0.0467074\pi$
$164$	−60.7487	+	105.220i	−0.370419	+	0.641584i
$165$	−38.7144	−	215.975i	−0.234632	−	1.30894i
$166$	60.3642	+	104.554i	0.363640	+	0.629842i
$167$	61.6977	+	106.864i	0.369447	+	0.639902i	0.989479	−	0.144675i	$-0.0462137\pi$
$167$	61.6977	+	106.864i	0.369447	+	0.639902i	−0.620032	+	0.784577i	$0.712880\pi$
$168$	0.236011	+	0.0851434i	0.00140483	+	0.000506806i
$169$	−70.3451	+	121.841i	−0.416243	+	0.720954i
$170$	139.553	+	108.960i	0.820900	+	0.640941i
$171$	−144.534	+	53.5370i	−0.845231	+	0.313082i
$172$	−137.974			−0.802173
$173$	63.7569	−	110.430i	0.368537	−	0.638325i	−0.620800	−	0.783969i	$-0.713192\pi$
$173$	63.7569	−	110.430i	0.368537	−	0.638325i	0.989337	+	0.145644i	$0.0465254\pi$
$174$	−67.8222	−	80.3632i	−0.389783	−	0.461858i
$175$	−13.7628	+	7.94598i	−0.0786448	+	0.0454056i
$176$	−159.531	−	276.315i	−0.906425	−	1.56997i
$177$	−174.201	−	206.412i	−0.984184	−	1.16617i
$178$	−61.2223	+	106.040i	−0.343946	+	0.595731i
$179$		−	176.481i		−	0.985925i	−0.870050	−	0.492963i	$-0.835914\pi$
$179$		−	176.481i		−	0.985925i	0.870050	−	0.492963i	$-0.164086\pi$
$180$	−22.1886	+	130.152i	−0.123270	+	0.723068i
$181$			184.304i			1.01825i	0.860692	+	0.509126i	$0.170031\pi$
$181$			184.304i			1.01825i	−0.860692	+	0.509126i	$0.829969\pi$
$182$	−34.6313	+	59.9832i	−0.190282	+	0.329578i
$183$	1.22294	−	3.38989i	0.00668273	−	0.0185240i
$184$	0.911511	−	0.526261i	0.00495387	−	0.00286012i
$185$	−41.6265	+	24.0331i	−0.225008	+	0.129908i
$186$	−51.4646	−	287.104i	−0.276691	−	1.54357i
$187$	−126.424	−	312.626i	−0.676063	−	1.67180i
$188$			343.674i			1.82806i
$189$	0.320231	+	37.6197i	0.00169434	+	0.199046i
$190$			178.361i			0.938741i
$191$	−43.0602	−	24.8608i	−0.225446	−	0.130161i	0.383023	−	0.923739i	$-0.374883\pi$
$191$	−43.0602	−	24.8608i	−0.225446	−	0.130161i	−0.608469	+	0.793577i	$0.708216\pi$
$192$	33.5159	+	186.975i	0.174562	+	0.973826i
$193$	70.3903	−	40.6399i	0.364717	−	0.210569i	−0.306431	−	0.951893i	$-0.599135\pi$
$193$	70.3903	−	40.6399i	0.364717	−	0.210569i	0.671148	+	0.741324i	$0.265802\pi$
$194$	−68.8115	−	119.185i	−0.354698	−	0.614356i
$195$	183.105	+	66.0571i	0.939002	+	0.338755i
$196$	93.6170	−	162.149i	0.477638	−	0.827293i
$197$	−197.609			−1.00309			−0.501546	−	0.865131i	$-0.667235\pi$
$197$	−197.609			−1.00309			−0.501546	+	0.865131i	$0.667235\pi$
$198$	321.951	−	388.138i	1.62601	−	1.96029i
$199$			356.582i			1.79187i	0.444187	+	0.895934i	$0.353493\pi$
$199$			356.582i			1.79187i	−0.444187	+	0.895934i	$0.646507\pi$
$200$	0.592859	+	0.342287i	0.00296429	+	0.00171144i
$201$	−133.150	+	112.372i	−0.662438	+	0.559062i
$202$	−80.4664	−	139.372i	−0.398348	−	0.689960i
$203$	−14.9744	+	8.64549i	−0.0737656	+	0.0425886i
$204$	7.72091	+	202.769i	0.0378476	+	0.993967i
$205$	56.2955	−	97.5067i	0.274612	−	0.475642i
$206$		−	170.812i		−	0.829186i
$207$	121.471	+	100.757i	0.586817	+	0.486750i
$208$	283.056			1.36085
$209$	169.857	−	294.201i	0.812714	−	1.40766i
$210$	40.9518	+	14.7738i	0.195008	+	0.0703513i
$211$	−152.648	+	88.1313i	−0.723450	+	0.417684i	−0.816021	−	0.578022i	$-0.803825\pi$
$211$	−152.648	+	88.1313i	−0.723450	+	0.417684i	0.0925713	+	0.995706i	$0.470491\pi$
$212$	40.8474	−	23.5833i	0.192676	−	0.111242i
$213$	−63.2492	−	352.847i	−0.296945	−	1.65656i
$214$	−4.95724	−	2.86206i	−0.0231647	−	0.0133741i
$215$	127.860			0.594696
$216$	1.39653	−	0.822215i	0.00646541	−	0.00380655i
$217$	−47.9608			−0.221017
$218$	−80.5806	+	139.570i	−0.369636	+	0.640228i
$219$	319.906	−	57.3445i	1.46076	−	0.261847i
$220$	−145.501	−	252.015i	−0.661368	−	1.14552i
$221$	296.268	+	41.5426i	1.34058	+	0.187976i
$222$	−103.915	−	37.4883i	−0.468084	−	0.168866i
$223$	−124.855	+	216.256i	−0.559889	+	0.969756i	0.437616	+	0.899162i	$0.355823\pi$
$223$	−124.855	+	216.256i	−0.559889	+	0.969756i	−0.997505	+	0.0705940i	$0.977511\pi$
$224$	62.9714			0.281122
$225$	−17.2508	+	101.188i	−0.0766701	+	0.449726i
$226$		−	491.387i		−	2.17428i
$227$	−141.368	+	244.856i	−0.622766	+	1.07866i	0.366202	+	0.930535i	$0.380658\pi$
$227$	−141.368	+	244.856i	−0.622766	+	1.07866i	−0.988968	+	0.148128i	$0.952675\pi$
$228$	−156.219	+	131.840i	−0.685170	+	0.578247i
$229$	160.551	+	278.083i	0.701096	+	1.21433i	0.968082	+	0.250634i	$0.0806390\pi$
$229$	160.551	+	278.083i	0.701096	+	1.21433i	−0.266986	+	0.963700i	$0.586028\pi$
$230$	158.162	−	91.3149i	0.687661	−	0.397021i
$231$	−53.4794	−	63.3683i	−0.231513	−	0.274322i
$232$	0.645050	+	0.372420i	0.00278039	+	0.00160526i
$233$	−308.597			−1.32445			−0.662225	−	0.749305i	$-0.730388\pi$
$233$	−308.597			−1.32445			−0.662225	+	0.749305i	$0.730388\pi$
$234$	155.395	+	419.522i	0.664082	+	1.79283i
$235$		−	318.481i		−	1.35524i
$236$	−310.223	−	179.107i	−1.31450	−	0.758929i
$237$	3.51699	−	9.74883i	0.0148396	−	0.0411343i
$238$	66.2607	+	9.29106i	0.278406	+	0.0390381i
$239$	−345.060	+	199.221i	−1.44377	+	0.833559i	−0.998098	−	0.0616393i	$-0.980367\pi$
$239$	−345.060	+	199.221i	−1.44377	+	0.833559i	−0.445668	+	0.895198i	$0.647034\pi$
$240$	−31.3917	−	175.124i	−0.130799	−	0.729684i
$241$	−257.575	−	148.711i	−1.06878	−	0.617058i	−0.140929	−	0.990020i	$-0.545009\pi$
$241$	−257.575	−	148.711i	−1.06878	−	0.617058i	−0.927847	+	0.372962i	$0.878342\pi$
$242$			769.688i			3.18053i
$243$	188.346	+	153.541i	0.775086	+	0.631856i
$244$		−	4.77947i		−	0.0195880i
$245$	−86.7545	+	150.263i	−0.354100	+	0.613319i
$246$	254.707	−	45.6573i	1.03540	−	0.185599i
$247$	150.689	+	261.001i	0.610077	+	1.05668i
$248$	1.03300	+	1.78920i	0.00416531	+	0.00721453i
$249$	43.5125	−	120.613i	0.174749	−	0.484391i
$250$	328.358	+	189.577i	1.31343	+	0.758310i
$251$		−	129.889i		−	0.517488i	−0.965946	−	0.258744i	$-0.916691\pi$
$251$		−	129.889i		−	0.517488i	0.965946	−	0.258744i	$-0.0833085\pi$
$252$	17.3309	+	46.7884i	0.0687734	+	0.185668i
$253$	−347.845			−1.37488
$254$	−108.071	−	62.3950i	−0.425478	−	0.245650i
$255$	−7.15493	−	187.905i	−0.0280585	−	0.736884i
$256$	−129.349	−	224.039i	−0.505270	−	0.875153i
$257$	247.879	−	143.113i	0.964510	−	0.556860i	0.0669517	−	0.997756i	$-0.478673\pi$
$257$	247.879	−	143.113i	0.964510	−	0.556860i	0.897558	+	0.440896i	$0.145339\pi$
$258$	189.527	+	224.572i	0.734600	+	0.870434i
$259$	−9.08225	+	15.7309i	−0.0350666	+	0.0607371i
$260$	258.163			0.992935
$261$	−18.7694	+	110.096i	−0.0719134	+	0.421825i
$262$			62.0528i			0.236843i
$263$	392.362	+	226.530i	1.49187	+	0.861333i	0.999957	−	0.00931071i	$-0.00296373\pi$
$263$	392.362	+	226.530i	1.49187	+	0.861333i	0.491915	+	0.870643i	$0.336297\pi$
$264$	−1.21213	+	3.35993i	−0.00459140	+	0.0127270i
$265$	−37.8531	+	21.8545i	−0.142842	+	0.0824698i
$266$	33.7018	+	58.3733i	0.126699	+	0.219448i
$267$	128.005	−	22.9454i	0.479419	−	0.0859377i
$268$	−115.537	+	200.115i	−0.431107	+	0.746699i
$269$	492.362			1.83034			0.915171	−	0.403065i	$-0.132055\pi$
$269$	492.362			1.83034			0.915171	+	0.403065i	$0.132055\pi$
$270$	242.320	−	142.668i	0.897483	−	0.528399i
$271$	−368.404			−1.35943			−0.679713	−	0.733478i	$-0.737896\pi$
$271$	−368.404			−1.35943			−0.679713	+	0.733478i	$0.737896\pi$
$272$	−102.511	−	253.494i	−0.376880	−	0.931965i
$273$	72.4078	−	12.9794i	0.265230	−	0.0475435i
$274$	101.092	+	175.097i	0.368950	+	0.639041i
$275$	−113.122	−	195.932i	−0.411351	−	0.712481i
$276$	196.889	+	71.0296i	0.713365	+	0.257354i
$277$	64.1297	+	37.0253i	0.231515	+	0.133665i	0.611271	−	0.791421i	$-0.290659\pi$
$277$	64.1297	+	37.0253i	0.231515	+	0.133665i	−0.379756	+	0.925087i	$0.623992\pi$
$278$	−544.794			−1.95969
$279$	−197.776	+	238.435i	−0.708876	+	0.854607i
$280$	−0.308363			−0.00110130
$281$	27.0876	+	15.6390i	0.0963971	+	0.0556549i	0.547424	−	0.836856i	$-0.315609\pi$
$281$	27.0876	+	15.6390i	0.0963971	+	0.0556549i	−0.451027	+	0.892511i	$0.648942\pi$
$282$	559.379	−	472.086i	1.98361	−	1.67406i
$283$	−161.385	+	93.1759i	−0.570267	+	0.329244i	−0.757256	−	0.653118i	$-0.773460\pi$
$283$	−161.385	+	93.1759i	−0.570267	+	0.329244i	0.186989	+	0.982362i	$0.440127\pi$
$284$	−237.711	−	411.728i	−0.837011	−	1.44974i
$285$	144.767	−	122.176i	0.507955	−	0.428687i
$286$	−853.940	−	493.023i	−2.98581	−	1.72386i
$287$		−	42.5489i		−	0.148254i
$288$	259.676	−	313.060i	0.901651	−	1.08701i
$289$	−70.0920	−	280.371i	−0.242533	−	0.970143i
$290$	111.927	+	64.6208i	0.385954	+	0.222831i
$291$	−49.6016	+	137.492i	−0.170452	+	0.472481i
$292$	373.290	−	215.519i	1.27839	−	0.738079i
$293$	226.180	−	130.585i	0.771945	−	0.445683i	−0.0616231	−	0.998099i	$-0.519628\pi$
$293$	226.180	−	130.585i	0.771945	−	0.445683i	0.833568	+	0.552417i	$0.186294\pi$
$294$	−392.518	+	70.3604i	−1.33509	+	0.239321i
$295$	287.482	+	165.978i	0.974516	+	0.562637i
$296$	0.782468			0.00264347
$297$	−535.567	+	4.55891i	−1.80326	+	0.0153499i
$298$	−349.418			−1.17254
$299$	154.296	−	267.248i	0.516040	−	0.893807i
$300$	24.0203	+	134.002i	0.0800677	+	0.446672i
$301$	41.8455	−	24.1595i	0.139022	−	0.0802641i
$302$	−180.228	+	104.055i	−0.596781	+	0.344551i
$303$	−58.0028	+	160.779i	−0.191429	+	0.530625i
$304$	137.729	−	238.554i	0.453057	−	0.784719i
$305$			4.42911i			0.0145217i
$306$	319.430	−	291.100i	1.04389	−	0.951306i
$307$	443.373			1.44421			0.722106	−	0.691783i	$-0.243174\pi$
$307$	443.373			1.44421			0.722106	+	0.691783i	$0.243174\pi$
$308$	−95.2382	−	54.9858i	−0.309215	−	0.178525i
$309$	−138.640	+	117.005i	−0.448675	+	0.378657i
$310$	179.242	+	310.456i	0.578199	+	1.00147i
$311$	148.284	+	256.836i	0.476799	+	0.825840i	0.999647	−	0.0265862i	$-0.00846365\pi$
$311$	148.284	+	256.836i	0.476799	+	0.825840i	−0.522848	+	0.852426i	$0.675130\pi$
$312$	−2.04375	−	2.42166i	−0.00655048	−	0.00776173i
$313$	−433.167	−	250.089i	−1.38392	−	0.799006i	−0.391298	−	0.920264i	$-0.627974\pi$
$313$	−433.167	−	250.089i	−1.38392	−	0.799006i	−0.992621	+	0.121258i	$0.961307\pi$
$314$		−	17.6796i		−	0.0563044i
$315$	−16.0605	−	43.3586i	−0.0509856	−	0.137646i
$316$		−	13.7450i		−	0.0434969i
$317$	−189.329	+	327.928i	−0.597254	+	1.03447i	0.395971	+	0.918263i	$0.370408\pi$
$317$	−189.329	+	327.928i	−0.597254	+	1.03447i	−0.993225	+	0.116211i	$0.962925\pi$
$318$	−94.4949	−	34.0900i	−0.297154	−	0.107201i
$319$	−123.080	−	213.181i	−0.385831	−	0.668278i
$320$	−116.730	−	202.182i	−0.364781	−	0.631820i
$321$	1.07267	+	5.98405i	0.00334164	+	0.0186419i
$322$	34.5085	−	59.7704i	0.107169	−	0.185622i
$323$	179.169	−	229.475i	0.554704	−	0.710450i
$324$	304.074	+	106.782i	0.938502	+	0.329573i
$325$	200.712			0.617575
$326$	−67.3180	+	116.598i	−0.206497	+	0.357663i
$327$	168.479	−	30.2006i	0.515227	−	0.0923566i
$328$	−1.58731	+	0.916434i	−0.00483936	+	0.00279401i
$329$	−60.1781	−	104.231i	−0.182912	−	0.316813i
$330$	−210.324	+	583.003i	−0.637346	+	1.76667i
$331$	−82.0944	+	142.192i	−0.248019	+	0.429582i	−0.962976	−	0.269587i	$-0.913113\pi$
$331$	−82.0944	+	142.192i	−0.248019	+	0.429582i	0.714957	+	0.699169i	$0.246446\pi$
$332$		−	170.055i		−	0.512213i
$333$	40.7532	+	110.022i	0.122382	+	0.330396i
$334$		−	348.551i		−	1.04357i
$335$	107.067	−	185.446i	0.319604	−	0.553570i
$336$	−43.3640	−	51.3825i	−0.129060	−	0.152924i
$337$	46.6553	−	26.9365i	0.138443	−	0.0799301i	−0.429179	−	0.903220i	$-0.641197\pi$
$337$	46.6553	−	26.9365i	0.138443	−	0.0799301i	0.567622	+	0.823289i	$0.307864\pi$
$338$	344.161	−	198.702i	1.01823	−	0.587875i
$339$	−398.836	+	336.596i	−1.17651	+	0.992909i
$340$	−93.4960	−	231.201i	−0.274988	−	0.680003i
$341$		−	682.785i		−	2.00230i
$342$	429.177	+	73.1668i	1.25490	+	0.213938i
$343$			133.845i			0.390220i
$344$	−1.80257	−	1.04071i	−0.00524002	−	0.00302533i
$345$	−182.456	−	65.8228i	−0.528857	−	0.190791i
$346$	−311.929	+	180.092i	−0.901528	+	0.520497i
$347$	−66.4656	−	115.122i	−0.191543	−	0.331763i	0.754218	−	0.656624i	$-0.228016\pi$
$347$	−66.4656	−	115.122i	−0.191543	−	0.331763i	−0.945762	+	0.324861i	$0.894683\pi$
$348$	26.1349	+	145.798i	0.0751003	+	0.418960i
$349$	100.388	−	173.877i	0.287644	−	0.498214i	−0.685603	−	0.727976i	$-0.740461\pi$
$349$	100.388	−	173.877i	0.287644	−	0.498214i	0.973247	+	0.229762i	$0.0737947\pi$
$350$	44.8895			0.128256
$351$	234.062	−	413.496i	0.666843	−	1.17805i
$352$			896.481i			2.54682i
$353$	−351.282	−	202.813i	−0.995133	−	0.574540i	−0.0883284	−	0.996091i	$-0.528152\pi$
$353$	−351.282	−	202.813i	−0.995133	−	0.574540i	−0.906805	+	0.421551i	$0.861486\pi$
$354$	134.613	+	750.961i	0.380262	+	2.12136i
$355$	220.286	+	381.546i	0.620523	+	1.07478i
$356$	149.365	−	86.2361i	0.419566	−	0.242236i
$357$	−37.8470	−	60.1451i	−0.106014	−	0.168474i
$358$	−249.250	+	431.713i	−0.696228	+	1.20590i
$359$			485.639i			1.35276i	0.736555	+	0.676378i	$0.236451\pi$
$359$			485.639i			1.35276i	−0.736555	+	0.676378i	$0.763549\pi$
$360$	−1.27160	+	1.53302i	−0.00353222	+	0.00425838i
$361$	−67.7107			−0.187564
$362$	260.298	−	450.850i	0.719056	−	1.24544i
$363$	624.720	−	527.230i	1.72099	−	1.45243i
$364$	84.4907	−	48.7807i	0.232117	−	0.134013i
$365$	−345.926	+	199.721i	−0.947743	+	0.547180i
$366$	−7.77926	+	6.56528i	−0.0212548	+	0.0179379i
$367$	−160.726	−	92.7954i	−0.437946	−	0.252848i	0.264780	−	0.964309i	$-0.414701\pi$
$367$	−160.726	−	92.7954i	−0.437946	−	0.252848i	−0.702726	+	0.711460i	$0.748034\pi$
$368$	−282.052			−0.766446
$369$	−211.530	−	175.459i	−0.573253	−	0.475499i
$370$	135.771			0.366948
$371$	−8.25895	+	14.3049i	−0.0222613	+	0.0385578i
$372$	−139.424	+	386.473i	−0.374796	+	1.03890i
$373$	115.761	+	200.505i	0.310352	+	0.537546i	0.978439	−	0.206538i	$-0.0662197\pi$
$373$	115.761	+	200.505i	0.310352	+	0.537546i	−0.668086	+	0.744084i	$0.732886\pi$
$374$	−132.271	+	943.309i	−0.353665	+	2.52222i
$375$	−71.0512	−	396.372i	−0.189470	−	1.05699i
$376$	−2.59228	+	4.48996i	−0.00689435	+	0.0119414i
$377$	218.381			0.579261
$378$	52.3483	−	92.4790i	0.138488	−	0.244653i
$379$			384.647i			1.01490i	0.861681	+	0.507450i	$0.169412\pi$
$379$			384.647i			1.01490i	−0.861681	+	0.507450i	$0.830588\pi$
$380$	125.617	−	217.575i	0.330571	−	0.572566i
$381$	23.3849	+	130.457i	0.0613776	+	0.342406i
$382$	70.2235	+	121.631i	0.183831	+	0.318405i
$383$	−550.654	+	317.920i	−1.43774	+	0.830079i	−0.997692	−	0.0678966i	$-0.978371\pi$
$383$	−550.654	+	317.920i	−1.43774	+	0.830079i	−0.440046	+	0.897975i	$0.645038\pi$
$384$	−1.95536	+	5.42011i	−0.00509209	+	0.0141149i
$385$	88.2567	+	50.9551i	0.229238	+	0.132351i
$386$	−229.588			−0.594788
$387$	52.4504	−	307.660i	0.135531	−	0.794988i
$388$			193.852i			0.499618i
$389$	98.7344	+	57.0043i	0.253816	+	0.146541i	0.621510	−	0.783406i	$-0.286519\pi$
$389$	98.7344	+	57.0043i	0.253816	+	0.146541i	−0.367694	+	0.929947i	$0.619853\pi$
$390$	−354.624	−	420.197i	−0.909292	−	1.07743i
$391$	−295.217	−	41.3952i	−0.755031	−	0.105870i
$392$	2.44613	−	1.41227i	0.00624013	−	0.00360274i
$393$	50.3654	−	42.5057i	0.128156	−	0.108157i
$394$	483.398	+	279.090i	1.22690	+	0.708350i
$395$			12.7375i			0.0322467i
$396$	−666.095	+	246.728i	−1.68206	+	0.623051i
$397$			319.137i			0.803871i	0.915668	+	0.401936i	$0.131662\pi$
$397$			319.137i			0.803871i	−0.915668	+	0.401936i	$0.868338\pi$
$398$	503.613	−	872.283i	1.26536	−	2.19167i
$399$	24.2934	−	67.3394i	0.0608857	−	0.168771i
$400$	−91.7251	−	158.873i	−0.229313	−	0.397181i
$401$	387.164	+	670.588i	0.965496	+	1.67229i	0.708276	+	0.705936i	$0.249473\pi$
$401$	387.164	+	670.588i	0.965496	+	1.67229i	0.257221	+	0.966353i	$0.417193\pi$
$402$	484.422	−	86.8347i	1.20503	−	0.216007i
$403$	524.581	+	302.867i	1.30169	+	0.751531i
$404$			226.685i			0.561103i
$405$	−281.784	−	98.9541i	−0.695764	−	0.244331i
$406$	48.8413			0.120299
$407$	−223.950	−	129.298i	−0.550247	−	0.317685i
$408$	−1.42858	+	2.70733i	−0.00350143	+	0.00663561i
$409$	9.35760	+	16.2078i	0.0228792	+	0.0396280i	0.877238	−	0.480055i	$-0.159383\pi$
$409$	9.35760	+	16.2078i	0.0228792	+	0.0396280i	−0.854359	+	0.519683i	$0.826050\pi$
$410$	−275.424	+	159.016i	−0.671766	+	0.387844i
$411$	72.8707	−	201.992i	0.177301	−	0.491465i
$412$	−120.301	+	208.367i	−0.291992	+	0.505745i
$413$	125.448			0.303749
$414$	−154.844	−	418.034i	−0.374019	−	1.00974i
$415$			157.589i			0.379732i
$416$	−688.763	−	397.657i	−1.65568	−	0.955907i
$417$	373.180	+	442.184i	0.894916	+	1.06039i
$418$	−831.021	+	479.790i	−1.98809	+	1.14782i
$419$	−289.963	−	502.231i	−0.692036	−	1.19864i	−0.971170	−	0.238390i	$-0.923380\pi$
$419$	−289.963	−	502.231i	−0.692036	−	1.19864i	0.279133	−	0.960252i	$-0.409953\pi$
$420$	−39.5504	−	46.8637i	−0.0941677	−	0.111580i
$421$	149.481	−	258.909i	0.355062	−	0.614985i	−0.632067	−	0.774914i	$-0.717793\pi$
$421$	149.481	−	258.909i	0.355062	−	0.614985i	0.987128	+	0.159929i	$0.0511266\pi$
$422$	497.883			1.17982
$423$	−766.340	−	130.647i	−1.81168	−	0.308858i
$424$	0.711538			0.00167816
$425$	−72.6896	−	179.750i	−0.171034	−	0.422941i
$426$	−343.615	+	952.475i	−0.806608	+	2.23586i
$427$	0.836894	+	1.44954i	0.00195994	+	0.00339471i
$428$	4.03142	+	6.98263i	0.00941921	+	0.0163146i
$429$	184.779	+	1030.82i	0.430720	+	2.40285i
$430$	−312.775	−	180.581i	−0.727383	−	0.419955i
$431$	−210.336			−0.488018			−0.244009	−	0.969773i	$-0.578463\pi$
$431$	−210.336			−0.488018			−0.244009	+	0.969773i	$0.578463\pi$
$432$	−434.267	+	3.69662i	−1.00525	+	0.00855698i
$433$	−530.660			−1.22554			−0.612771	−	0.790260i	$-0.709945\pi$
$433$	−530.660			−1.22554			−0.612771	+	0.790260i	$0.709945\pi$
$434$	117.323	+	67.7366i	0.270330	+	0.156075i
$435$	−24.2191	−	135.110i	−0.0556761	−	0.310599i
$436$	196.594	−	113.504i	0.450904	−	0.260329i
$437$	−150.155	−	260.075i	−0.343603	−	0.595138i
$438$	−863.555	−	311.536i	−1.97159	−	0.711270i
$439$	−231.727	−	133.788i	−0.527853	−	0.304756i	0.212289	−	0.977207i	$-0.431908\pi$
$439$	−231.727	−	133.788i	−0.527853	−	0.304756i	−0.740142	+	0.672451i	$0.765242\pi$
$440$		−	4.38996i		−	0.00997718i
$441$	325.980	+	270.392i	0.739183	+	0.613134i
$442$	−666.069	−	520.052i	−1.50694	−	1.17659i
$443$	674.555	+	389.455i	1.52270	+	0.879130i	0.999640	+	0.0268335i	$0.00854238\pi$
$443$	674.555	+	389.455i	1.52270	+	0.879130i	0.523058	+	0.852297i	$0.324791\pi$
$444$	100.359	+	118.916i	0.226033	+	0.267829i
$445$	−138.416	+	79.9146i	−0.311048	+	0.179583i
$446$	610.850	−	352.674i	1.36962	−	0.790750i
$447$	239.349	+	283.606i	0.535455	+	0.634466i
$448$	−76.4060	−	44.1130i	−0.170549	−	0.0984665i
$449$	80.4398			0.179153			0.0895766	−	0.995980i	$-0.471449\pi$
$449$	80.4398			0.179153			0.0895766	+	0.995980i	$0.471449\pi$
$450$	185.111	−	223.167i	0.411358	−	0.495926i
$451$	605.739			1.34310
$452$	−346.077	+	599.423i	−0.765657	+	1.32616i
$453$	207.911	+	75.0060i	0.458964	+	0.165576i
$454$	691.638	−	399.318i	1.52343	−	0.879554i
$455$	−78.2971	+	45.2049i	−0.172082	+	0.0993514i
$456$	−3.03538	+	0.544104i	−0.00665653	+	0.00119321i
$457$	218.961	−	379.252i	0.479127	−	0.829872i	−0.520587	−	0.853809i	$-0.674287\pi$
$457$	218.961	−	379.252i	0.479127	−	0.829872i	0.999713	+	0.0239367i	$0.00762001\pi$
$458$		−	907.007i		−	1.98036i
$459$	−455.079	−	59.8658i	−0.991458	−	0.130427i
$460$	−257.247			−0.559233
$461$	657.551	+	379.637i	1.42636	+	0.823509i	0.996831	−	0.0795452i	$-0.0253468\pi$
$461$	657.551	+	379.637i	1.42636	+	0.823509i	0.429527	+	0.903054i	$0.358680\pi$
$462$	41.3260	+	230.544i	0.0894503	+	0.499014i
$463$	248.865	+	431.047i	0.537506	+	0.930987i	0.999038	+	0.0438634i	$0.0139666\pi$
$463$	248.865	+	431.047i	0.537506	+	0.930987i	−0.461532	+	0.887124i	$0.652700\pi$
$464$	−99.8000	−	172.859i	−0.215086	−	0.372540i
$465$	129.203	−	358.142i	0.277857	−	0.770198i
$466$	754.900	+	435.842i	1.61996	+	0.935283i
$467$			56.4240i			0.120822i	0.998174	+	0.0604112i	$0.0192412\pi$
$467$			56.4240i			0.120822i	−0.998174	+	0.0604112i	$0.980759\pi$
$468$	105.903	−	621.200i	0.226289	−	1.32735i
$469$		−	80.9228i		−	0.172543i
$470$	−449.802	+	779.080i	−0.957026	+	1.65762i
$471$	−14.3497	+	12.1104i	−0.0304665	+	0.0257121i
$472$	−2.70195	−	4.67992i	−0.00572447	−	0.00991508i
$473$	343.942	+	595.726i	0.727151	+	1.25946i
$474$	−22.3720	+	18.8808i	−0.0471983	+	0.0398328i
$475$	97.6624	−	169.156i	0.205605	−	0.356119i
$476$	−74.2852	−	58.0003i	−0.156061	−	0.121849i
$477$	37.0590	+	100.048i	0.0776918	+	0.209745i
$478$	1125.46			2.35453
$479$	149.317	−	258.625i	0.311727	−	0.539927i	−0.667009	−	0.745049i	$-0.732426\pi$
$479$	149.317	−	258.625i	0.311727	−	0.539927i	0.978736	+	0.205122i	$0.0657593\pi$
$480$	−169.641	+	470.232i	−0.353419	+	0.979651i
$481$	198.678	−	114.707i	0.413052	−	0.238476i
$482$	420.059	+	727.563i	0.871492	+	1.50947i
$483$	−72.1509	+	12.9333i	−0.149381	+	0.0267771i
$484$	542.081	−	938.912i	1.12000	−	1.93990i
$485$		−	179.642i		−	0.370395i
$486$	−243.887	−	641.604i	−0.501826	−	1.32017i
$487$			768.554i			1.57814i	0.614303	+	0.789070i	$0.289437\pi$
$487$			768.554i			1.57814i	−0.614303	+	0.789070i	$0.710563\pi$
$488$	0.0360507	−	0.0624416i	7.38744e−5	−	0.000127954i
$489$	140.750	−	25.2300i	0.287832	−	0.0515950i
$490$	424.443	−	245.053i	0.866211	−	0.500107i
$491$	−49.6394	+	28.6593i	−0.101099	+	0.0583693i	−0.549697	−	0.835364i	$-0.685257\pi$
$491$	−49.6394	+	28.6593i	−0.101099	+	0.0583693i	0.448598	+	0.893734i	$0.351923\pi$
$492$	−342.863	−	123.691i	−0.696876	−	0.251405i
$493$	−79.0887	−	195.574i	−0.160423	−	0.396702i
$494$		−	851.293i		−	1.72327i
$495$	617.267	−	228.642i	1.24700	−	0.461903i
$496$		−	553.639i		−	1.11621i
$497$	144.189	+	83.2474i	0.290118	+	0.167500i
$498$	−276.788	+	233.594i	−0.555800	+	0.469065i
$499$	−187.998	+	108.541i	−0.376750	+	0.217517i	−0.676404	−	0.736531i	$-0.736462\pi$
$499$	−187.998	+	108.541i	−0.376750	+	0.217517i	0.299653	+	0.954048i	$0.403129\pi$
$500$	−267.034	−	462.516i	−0.534067	−	0.925031i
$501$	−282.903	+	238.755i	−0.564676	+	0.476557i
$502$	−183.447	+	317.740i	−0.365433	+	0.632948i
$503$	−449.219			−0.893080			−0.446540	−	0.894764i	$-0.647344\pi$
$503$	−449.219			−0.893080			−0.446540	+	0.894764i	$0.647344\pi$
$504$	−0.126496	+	0.741994i	−0.000250985	+	0.00147221i
$505$		−	210.068i		−	0.415977i
$506$	850.911	+	491.274i	1.68164	+	0.970897i
$507$	−397.025	−	143.231i	−0.783086	−	0.282506i
$508$	87.8879	+	152.226i	0.173008	+	0.299658i
$509$	−114.228	+	65.9498i	−0.224417	+	0.129567i	−0.607994	−	0.793942i	$-0.708026\pi$
$509$	−114.228	+	65.9498i	−0.224417	+	0.129567i	0.383577	+	0.923509i	$0.374692\pi$
$510$	−247.883	+	469.766i	−0.486044	+	0.921109i
$511$	−75.4757	+	130.728i	−0.147702	+	0.255827i
$512$			723.054i			1.41221i
$513$	−234.597	−	398.462i	−0.457304	−	0.776729i
$514$	−808.494			−1.57294
$515$	111.482	−	193.093i	0.216470	−	0.374937i
$516$	−73.0330	−	407.428i	−0.141537	−	0.789588i
$517$	1483.87	−	856.715i	2.87016	−	1.65709i
$518$	44.4346	−	25.6543i	0.0857811	−	0.0495258i
$519$	359.841	+	129.816i	0.693336	+	0.250128i
$520$	3.37279	+	1.94728i	0.00648613	+	0.00374477i
$521$	−736.381			−1.41340			−0.706700	−	0.707514i	$-0.749817\pi$
$521$	−736.381			−1.41340			−0.706700	+	0.707514i	$0.749817\pi$
$522$	201.407	−	242.813i	0.385837	−	0.465159i
$523$	92.6839			0.177216			0.0886079	−	0.996067i	$-0.471758\pi$
$523$	92.6839			0.177216			0.0886079	+	0.996067i	$0.471758\pi$
$524$	43.7029	−	75.6957i	0.0834025	−	0.144457i
$525$	−30.7490	−	36.4347i	−0.0585694	−	0.0693995i
$526$	−639.873	−	1108.29i	−1.21649	−	2.10702i
$527$	81.2546	−	579.481i	0.154183	−	1.09958i
$528$	731.497	−	617.345i	1.38541	−	1.16921i
$529$	110.752	−	191.827i	0.209360	−	0.362622i
$530$	123.463			0.232950
$531$	517.312	−	623.662i	0.974222	−	1.17450i
$532$		−	94.9429i		−	0.178464i
$533$	−268.691	+	465.387i	−0.504112	+	0.873147i
$534$	−345.536	−	124.656i	−0.647071	−	0.233438i
$535$	−3.73590	−	6.47077i	−0.00698299	−	0.0120949i
$536$	−3.01887	+	1.74295i	−0.00563222	+	0.00325177i
$537$	521.136	−	93.4157i	0.970457	−	0.173958i
$538$	−1204.43	−	695.380i	−2.23872	−	1.29253i
$539$	−933.478			−1.73187
$540$	−396.076	+	3.37152i	−0.733474	+	0.00624356i
$541$		−	875.030i		−	1.61743i	−0.588200	−	0.808716i	$-0.700163\pi$
$541$		−	875.030i		−	1.61743i	0.588200	−	0.808716i	$-0.299837\pi$
$542$	901.203	+	520.310i	1.66274	+	0.959982i
$543$	−544.237	+	97.5566i	−1.00228	+	0.179662i
$544$	−106.685	+	760.845i	−0.196113	+	1.39861i
$545$	−182.183	+	105.183i	−0.334280	+	0.192997i
$546$	−195.458	−	70.5134i	−0.357981	−	0.129145i
$547$	−435.805	−	251.612i	−0.796718	−	0.459985i	0.0456041	−	0.998960i	$-0.485479\pi$
$547$	−435.805	−	251.612i	−0.796718	−	0.459985i	−0.842322	+	0.538974i	$0.818812\pi$
$548$		−	284.792i		−	0.519693i
$549$	10.6575	+	1.81690i	0.0194125	+	0.00330947i
$550$			639.062i			1.16193i
$551$	106.260	−	184.048i	0.192849	−	0.334025i
$552$	2.03650	+	2.41307i	0.00368931	+	0.00437150i
$553$	2.40678	+	4.16867i	0.00435223	+	0.00753828i
$554$	−104.584	−	181.145i	−0.188780	−	0.326977i
$555$	−93.0020	−	110.199i	−0.167571	−	0.198557i
$556$	664.573	+	383.691i	1.19527	+	0.690092i
$557$		−	228.618i		−	0.410446i	−0.978715	−	0.205223i	$-0.934208\pi$
$557$		−	228.618i		−	0.410446i	0.978715	−	0.205223i	$-0.0657919\pi$
$558$	820.558	−	303.943i	1.47053	−	0.544700i
$559$	−610.258			−1.09170
$560$	71.5634	+	41.3171i	0.127792	+	0.0737806i
$561$	856.245	−	538.802i	1.52628	−	0.960431i
$562$	−44.1750	−	76.5134i	−0.0786033	−	0.136145i
$563$	507.200	−	292.832i	0.900888	−	0.520128i	0.0233997	−	0.999726i	$-0.492551\pi$
$563$	507.200	−	292.832i	0.900888	−	0.520128i	0.877488	+	0.479598i	$0.159218\pi$
$564$	−1014.85	+	181.916i	−1.79938	+	0.322545i
$565$	320.708	−	555.482i	0.567624	−	0.983154i
$566$	526.382			0.930004
$567$	−110.919	+	20.8587i	−0.195625	+	0.0367878i
$568$		−	7.17205i		−	0.0126269i
$569$	205.791	+	118.814i	0.361672	+	0.208811i	0.669814	−	0.742529i	$-0.266374\pi$
$569$	205.791	+	118.814i	0.361672	+	0.208811i	−0.308142	+	0.951340i	$0.599707\pi$
$570$	−526.687	+	94.4108i	−0.924013	+	0.165633i
$571$	802.747	−	463.466i	1.40586	−	0.811675i	0.410876	−	0.911691i	$-0.365223\pi$
$571$	802.747	−	463.466i	1.40586	−	0.811675i	0.994986	+	0.100016i	$0.0318896\pi$
$572$	694.458	+	1202.84i	1.21409	+	2.10286i
$573$	50.6194	−	140.313i	0.0883411	−	0.244875i
$574$	−60.0932	+	104.085i	−0.104692	+	0.181332i
$575$	−200.000			−0.347826
$576$	−534.382	+	197.941i	−0.927747	+	0.343647i
$577$	−114.402			−0.198270			−0.0991352	−	0.995074i	$-0.531608\pi$
$577$	−114.402			−0.198270			−0.0991352	+	0.995074i	$0.531608\pi$
$578$	−224.516	+	784.847i	−0.388437	+	1.35787i
$579$	157.266	+	186.346i	0.271617	+	0.321841i
$580$	−91.0232	−	157.657i	−0.156936	−	0.271822i
$581$	29.7769	+	51.5751i	0.0512511	+	0.0887696i
$582$	315.522	−	266.283i	0.542133	−	0.457531i
$583$	−203.650	−	117.577i	−0.349313	−	0.201676i
$584$	6.50249			0.0111344
$585$	−98.1400	+	575.664i	−0.167761	+	0.984040i
$586$	−737.719			−1.25891
$587$	−18.0108	−	10.3985i	−0.0306828	−	0.0177147i	0.484580	−	0.874747i	$-0.338972\pi$
$587$	−18.0108	−	10.3985i	−0.0306828	−	0.0177147i	−0.515263	+	0.857032i	$0.672306\pi$
$588$	528.370	+	190.615i	0.898589	+	0.324175i
$589$	510.501	−	294.738i	0.866726	−	0.500404i
$590$	−468.832	−	812.042i	−0.794631	−	1.37634i
$591$	−104.599	−	583.526i	−0.176987	−	0.987354i
$592$	−181.591	−	104.842i	−0.306742	−	0.177098i
$593$			995.431i			1.67864i	0.543640	+	0.839318i	$0.317046\pi$
$593$			995.431i			1.67864i	−0.543640	+	0.839318i	$0.682954\pi$
$594$	1316.56	+	745.247i	2.21643	+	1.25463i
$595$	68.8398	+	53.7486i	0.115697	+	0.0903338i
$596$	426.241	+	246.090i	0.715169	+	0.412903i
$597$	−1052.96	+	188.748i	−1.76376	+	0.316160i
$598$	−754.888	+	435.835i	−1.26235	+	0.728820i
$599$	−508.130	+	293.369i	−0.848297	+	0.489765i	−0.860076	−	0.510166i	$-0.829584\pi$
$599$	−508.130	+	293.369i	−0.848297	+	0.489765i	0.0117787	+	0.999931i	$0.496251\pi$
$600$	−0.696936	+	1.93185i	−0.00116156	+	0.00321975i
$601$	325.334	+	187.832i	0.541321	+	0.312532i	0.745614	−	0.666378i	$-0.232156\pi$
$601$	325.334	+	187.832i	0.541321	+	0.312532i	−0.204293	+	0.978910i	$0.565489\pi$
$602$	−136.485			−0.226719
$603$	−402.305	−	333.702i	−0.667173	−	0.553403i
$604$	293.137			0.485326
$605$	−502.344	+	870.085i	−0.830320	+	1.43816i
$606$	368.963	−	311.385i	0.608850	−	0.513836i
$607$	−123.401	+	71.2454i	−0.203296	+	0.117373i	−0.598192	−	0.801353i	$-0.704114\pi$
$607$	−123.401	+	71.2454i	−0.203296	+	0.117373i	0.394896	+	0.918726i	$0.370781\pi$
$608$	−670.276	+	386.984i	−1.10243	+	0.636487i
$609$	−33.4559	−	39.6422i	−0.0549358	−	0.0650939i
$610$	6.25538	−	10.8346i	0.0102547	−	0.0177617i
$611$			1520.07i			2.48784i
$612$	−594.677	+	130.130i	−0.971695	+	0.212631i
$613$	−785.715			−1.28175			−0.640877	−	0.767644i	$-0.721429\pi$
$613$	−785.715			−1.28175			−0.640877	+	0.767644i	$0.721429\pi$
$614$	−1084.59	−	626.191i	−1.76644	−	1.01985i
$615$	317.729	+	114.624i	0.516633	+	0.186381i
$616$	−0.829497	−	1.43673i	−0.00134659	−	0.00233235i
$617$	−329.263	−	570.301i	−0.533652	−	0.924313i	−0.999227	−	0.0393043i	$-0.987486\pi$
$617$	−329.263	−	570.301i	−0.533652	−	0.924313i	0.465575	−	0.885008i	$-0.345848\pi$
$618$	504.397	−	90.4152i	0.816177	−	0.146303i
$619$	953.354	+	550.419i	1.54015	+	0.889207i	0.998828	+	0.0483917i	$0.0154096\pi$
$619$	953.354	+	550.419i	1.54015	+	0.889207i	0.541323	+	0.840815i	$0.317924\pi$
$620$		−	504.950i		−	0.814436i
$621$	−233.232	+	412.029i	−0.375574	+	0.663493i
$622$		−	837.709i		−	1.34680i
$623$	−30.2002	+	52.3083i	−0.0484755	+	0.0839620i
$624$	149.829	+	835.846i	0.240110	+	1.33950i
$625$	104.892	+	181.678i	0.167827	+	0.290684i
$626$	706.418	+	1223.55i	1.12846	+	1.95456i
$627$	958.666	+	345.849i	1.52897	+	0.551593i
$628$	−12.4515	+	21.5666i	−0.0198272	+	0.0343418i
$629$	−174.680	−	136.387i	−0.277711	−	0.216831i
$630$	−21.9492	+	128.748i	−0.0348399	+	0.204362i
$631$	479.339			0.759650			0.379825	−	0.925058i	$-0.375984\pi$
$631$	479.339			0.759650			0.379825	+	0.925058i	$0.375984\pi$
$632$	0.103676	−	0.179573i	0.000164045	−	0.000284134i
$633$	−341.046	−	404.109i	−0.538778	−	0.638403i
$634$	926.288	−	534.793i	1.46102	−	0.843522i
$635$	−81.4453	−	141.067i	−0.128260	−	0.222153i
$636$	91.2614	+	108.136i	0.143493	+	0.170026i
$637$	414.068	−	717.187i	0.650029	−	1.12588i
$638$			695.320i			1.08984i
$639$	1008.45	−	373.541i	1.57817	−	0.584572i
$640$		−	7.08172i		−	0.0110652i
$641$	129.365	−	224.067i	0.201818	−	0.349558i	−0.747297	−	0.664491i	$-0.768649\pi$
$641$	129.365	−	224.067i	0.201818	−	0.349558i	0.949114	+	0.314932i	$0.101982\pi$
$642$	5.82749	−	16.1534i	0.00907708	−	0.0251610i
$643$	−794.502	+	458.706i	−1.23562	+	0.713384i	−0.968195	−	0.250195i	$-0.919505\pi$
$643$	−794.502	+	458.706i	−1.23562	+	0.713384i	−0.267422	+	0.963579i	$0.586172\pi$
$644$	−84.1910	+	48.6077i	−0.130731	+	0.0754778i
$645$	67.6794	+	377.561i	0.104929	+	0.585366i
$646$	−762.386	+	308.303i	−1.18016	+	0.477250i
$647$		−	194.253i		−	0.300236i	−0.988668	−	0.150118i	$-0.952035\pi$
$647$		−	194.253i		−	0.300236i	0.988668	−	0.150118i	$-0.0479653\pi$
$648$	3.16716	+	3.68864i	0.00488760	+	0.00569234i
$649$			1785.92i			2.75180i
$650$	−490.988	−	283.472i	−0.755367	−	0.436111i
$651$	−25.3868	−	141.625i	−0.0389967	−	0.217550i
$652$	164.237	−	94.8223i	0.251897	−	0.145433i
$653$	−34.9563	−	60.5460i	−0.0535318	−	0.0927198i	0.838018	−	0.545643i	$-0.183715\pi$
$653$	−34.9563	−	60.5460i	−0.0535318	−	0.0927198i	−0.891550	+	0.452923i	$0.850381\pi$
$654$	−454.793	−	164.071i	−0.695403	−	0.250874i
$655$	−40.4993	+	70.1468i	−0.0618310	+	0.107094i
$656$	491.167			0.748730
$657$	338.669	+	914.308i	0.515478	+	1.39164i
$658$			339.966i			0.516666i
$659$	−207.820	−	119.985i	−0.315356	−	0.182071i	0.333965	−	0.942586i	$-0.391613\pi$
$659$	−207.820	−	119.985i	−0.315356	−	0.182071i	−0.649321	+	0.760515i	$0.724947\pi$
$660$	667.167	−	563.053i	1.01086	−	0.853110i
$661$	88.4982	+	153.283i	0.133885	+	0.231896i	0.925171	−	0.379550i	$-0.123921\pi$
$661$	88.4982	+	153.283i	0.133885	+	0.231896i	−0.791286	+	0.611446i	$0.790588\pi$
$662$	401.644	−	231.889i	0.606713	−	0.350286i
$663$	34.1496	+	896.849i	0.0515076	+	1.35271i
$664$	1.28269	−	2.22169i	0.00193177	−	0.00334592i
$665$			87.9832i			0.132306i
$666$	55.6957	−	326.696i	0.0836272	−	0.490535i
$667$	−217.607			−0.326247
$668$	−245.480	+	425.184i	−0.367485	+	0.636502i
$669$	−704.677	−	254.220i	−1.05333	−	0.379999i
$670$	−523.823	+	302.430i	−0.781826	+	0.451387i
$671$	−20.6362	+	11.9143i	−0.0307543	+	0.0177560i
$672$	33.3323	+	185.950i	0.0496017	+	0.276712i
$673$	−192.239	−	110.989i	−0.285645	−	0.164917i	0.350331	−	0.936626i	$-0.386069\pi$
$673$	−192.239	−	110.989i	−0.285645	−	0.164917i	−0.635976	+	0.771709i	$0.719402\pi$
$674$	−152.173			−0.225776
$675$	−307.934	+	2.62123i	−0.456198	+	0.00388330i
$676$	−559.771			−0.828064
$677$	188.617	−	326.694i	0.278607	−	0.482561i	−0.692432	−	0.721483i	$-0.743461\pi$
$677$	188.617	−	326.694i	0.278607	−	0.482561i	0.971039	+	0.238922i	$0.0767940\pi$
$678$	1451.03	−	260.103i	2.14017	−	0.383633i
$679$	−33.9439	−	58.7925i	−0.0499910	−	0.0865869i
$680$	0.522426	−	3.72577i	0.000768273	−	0.00547907i
$681$	−797.874	−	287.841i	−1.17162	−	0.422675i
$682$	−964.321	+	1670.25i	−1.41396	+	2.44905i
$683$	−539.646			−0.790111			−0.395055	−	0.918657i	$-0.629275\pi$
$683$	−539.646			−0.790111			−0.395055	+	0.918657i	$0.629275\pi$
$684$	−472.006	−	391.517i	−0.690067	−	0.572393i
$685$			263.915i			0.385278i
$686$	189.035	−	327.417i	0.275561	−	0.477285i
$687$	−736.175	+	621.292i	−1.07158	+	0.904356i
$688$	278.887	+	483.047i	0.405359	+	0.702103i
$689$	180.668	−	104.309i	0.262218	−	0.151392i
$690$	353.366	+	418.707i	0.512124	+	0.606821i
$691$	−451.625	−	260.746i	−0.653582	−	0.377346i	0.136245	−	0.990675i	$-0.456497\pi$
$691$	−451.625	−	260.746i	−0.653582	−	0.377346i	−0.789827	+	0.613329i	$0.789830\pi$
$692$	507.346			0.733159
$693$	158.814	−	191.464i	0.229169	−	0.276282i
$694$			375.486i			0.541047i
$695$	−615.856	−	355.565i	−0.886124	−	0.511604i
$696$	−0.758289	+	2.10192i	−0.00108950	+	0.00302000i
$697$	514.092	+	72.0859i	0.737578	+	0.103423i
$698$	−491.144	+	283.562i	−0.703645	+	0.406250i
$699$	−163.348	−	911.266i	−0.233688	−	1.30367i
$700$	−54.7589	−	31.6151i	−0.0782270	−	0.0451644i
$701$			795.541i			1.13487i	0.823420	+	0.567433i	$0.192063\pi$
$701$			795.541i			1.13487i	−0.823420	+	0.567433i	$0.807937\pi$
$702$	−1156.57	+	680.935i	−1.64753	+	0.969993i
$703$		−	223.256i		−	0.317577i
$704$	628.007	−	1087.74i	0.892055	−	1.54509i
$705$	940.454	−	168.580i	1.33398	−	0.239121i
$706$	572.879	+	992.255i	0.811443	+	1.40546i
$707$	−39.6931	−	68.7504i	−0.0561430	−	0.0972425i
$708$	364.683	−	1010.87i	0.515089	−	1.42779i
$709$	524.674	+	302.920i	0.740019	+	0.427250i	0.822076	−	0.569377i	$-0.192816\pi$
$709$	524.674	+	302.920i	0.740019	+	0.427250i	−0.0820571	+	0.996628i	$0.526149\pi$
$710$		−	1244.47i		−	1.75277i
$711$	30.6493	+	5.22514i	0.0431073	+	0.00734900i
$712$	2.60186			0.00365429
$713$	−522.720	−	301.793i	−0.733128	−	0.423272i
$714$	7.63760	+	200.581i	0.0106969	+	0.280926i
$715$	−643.551	−	1114.66i	−0.900072	−	1.55897i
$716$	608.099	−	351.086i	0.849301	−	0.490344i
$717$	−770.934	−	913.487i	−1.07522	−	1.27404i
$718$	685.885	−	1187.99i	0.955272	−	1.65458i
$719$	−85.3362			−0.118687			−0.0593437	−	0.998238i	$-0.518901\pi$
$719$	−85.3362			−0.118687			−0.0593437	+	0.998238i	$0.518901\pi$
$720$	500.514	−	185.395i	0.695158	−	0.257493i
$721$		−	84.2596i		−	0.116865i
$722$	165.636	+	95.6302i	0.229413	+	0.132452i
$723$	302.793	−	839.318i	0.418800	−	1.16088i
$724$	−635.055	+	366.649i	−0.877148	+	0.506422i
$725$	−70.7670	−	122.572i	−0.0976097	−	0.169065i
$726$	−2272.84	+	407.415i	−3.13063	+	0.561178i
$727$	227.901	−	394.736i	0.313482	−	0.542966i	−0.665632	−	0.746280i	$-0.731838\pi$
$727$	227.901	−	394.736i	0.313482	−	0.542966i	0.979114	+	0.203314i	$0.0651712\pi$
$728$	1.47178			0.00202167
$729$	−353.700	+	637.446i	−0.485185	+	0.874412i
$730$	1128.29			1.54560
$731$	221.010	+	546.524i	0.302340	+	0.747639i
$732$	14.1134	−	2.52989i	0.0192807	−	0.00345614i
$733$	−391.901	−	678.792i	−0.534653	−	0.926046i	−0.999180	−	0.0404872i	$-0.987109\pi$
$733$	−391.901	−	678.792i	−0.534653	−	0.926046i	0.464527	−	0.885559i	$-0.346224\pi$
$734$	262.116	+	453.999i	0.357107	+	0.618527i
$735$	−489.638	−	176.642i	−0.666175	−	0.240329i
$736$	686.319	+	396.247i	0.932499	+	0.538379i
$737$	1152.04			1.56315
$738$	269.646	+	727.966i	0.365374	+	0.986403i
$739$	153.070			0.207131			0.103565	−	0.994623i	$-0.466975\pi$
$739$	153.070			0.207131			0.103565	+	0.994623i	$0.466975\pi$
$740$	−165.621	−	95.6216i	−0.223813	−	0.129218i
$741$	−690.955	+	583.129i	−0.932464	+	0.786949i
$742$	40.4067	−	23.3288i	0.0544564	−	0.0314404i
$743$	−208.917	−	361.854i	−0.281180	−	0.487018i	0.690496	−	0.723337i	$-0.257392\pi$
$743$	−208.917	−	361.854i	−0.281180	−	0.487018i	−0.971676	+	0.236318i	$0.924059\pi$
$744$	−4.73661	+	3.99744i	−0.00636641	+	0.00537291i
$745$	−394.995	−	228.051i	−0.530195	−	0.306108i
$746$		−	653.975i		−	0.876642i
$747$	379.195	+	64.6458i	0.507624	+	0.0865406i
$748$	825.711	−	1057.55i	1.10389	−	1.41384i
$749$	−2.44534	−	1.41182i	−0.00326481	−	0.00188494i
$750$	−386.001	+	1069.97i	−0.514669	+	1.42662i
$751$	−298.480	+	172.328i	−0.397444	+	0.229464i	−0.685380	−	0.728185i	$-0.740364\pi$
$751$	−298.480	+	172.328i	−0.397444	+	0.229464i	0.287937	+	0.957649i	$0.407031\pi$
$752$	1203.21	−	694.671i	1.60001	−	0.923765i
$753$	383.555	−	68.7537i	0.509369	−	0.0913064i
$754$	−534.212	−	308.427i	−0.708504	−	0.409055i
$755$	−271.648			−0.359799
$756$	−128.989	+	75.9432i	−0.170621	+	0.100454i
$757$	−612.380			−0.808956			−0.404478	−	0.914548i	$-0.632547\pi$
$757$	−612.380			−0.808956			−0.404478	+	0.914548i	$0.632547\pi$
$758$	543.250	−	940.936i	0.716688	−	1.24134i
$759$	−184.123	−	1027.16i	−0.242587	−	1.35331i
$760$	3.28226	−	1.89502i	0.00431877	−	0.00249344i
$761$	689.897	−	398.312i	0.906567	−	0.523407i	0.0272418	−	0.999629i	$-0.491328\pi$
$761$	689.897	−	398.312i	0.906567	−	0.523407i	0.879325	+	0.476222i	$0.157994\pi$
$762$	127.043	−	352.155i	0.166724	−	0.462145i
$763$	−39.7494	+	68.8480i	−0.0520962	+	0.0902333i
$764$		−	197.830i		−	0.258940i
$765$	551.085	−	120.591i	0.720372	−	0.157635i
$766$	1796.04			2.34470
$767$	−1372.12	−	792.192i	−1.78894	−	1.03284i
$768$	593.105	−	500.549i	0.772272	−	0.651756i
$769$	−133.749	−	231.661i	−0.173926	−	0.301249i	0.765863	−	0.643004i	$-0.222312\pi$
$769$	−133.749	−	231.661i	−0.173926	−	0.301249i	−0.939789	+	0.341755i	$0.888979\pi$
$770$	−143.931	−	249.296i	−0.186924	−	0.323761i
$771$	553.812	+	656.217i	0.718303	+	0.851124i
$772$	280.066	+	161.696i	0.362779	+	0.209451i
$773$		−	218.543i		−	0.282721i	−0.989958	−	0.141361i	$-0.954852\pi$
$773$		−	218.543i		−	0.282721i	0.989958	−	0.141361i	$-0.0451477\pi$
$774$	−562.825	+	678.531i	−0.727164	+	0.876656i
$775$		−	392.580i		−	0.506554i
$776$	−1.46219	+	2.53259i	−0.00188427	+	0.00326365i
$777$	−51.2598	−	18.4925i	−0.0659715	−	0.0237999i
$778$	−161.018	−	278.892i	−0.206964	−	0.358473i
$779$	261.480	+	452.896i	0.335661	+	0.581382i
$780$	136.652	+	762.338i	0.175195	+	0.977357i
$781$	−1185.14	+	2052.72i	−1.51746	+	2.62832i
$782$	663.706	+	518.207i	0.848729	+	0.662669i
$783$	−335.042	+	2.85198i	−0.427896	+	0.00364238i
$784$	−756.915			−0.965452
$785$	11.5387	−	19.9857i	0.0146990	−	0.0254595i
$786$	−183.238	+	32.8461i	−0.233127	+	0.0417889i
$787$	−1306.69	+	754.419i	−1.66034	+	0.958601i	−0.687795	+	0.725905i	$0.741421\pi$
$787$	−1306.69	+	754.419i	−1.66034	+	0.958601i	−0.972549	+	0.232696i	$0.925245\pi$
$788$	−393.119	−	680.901i	−0.498881	−	0.864088i
$789$	−461.242	+	1278.53i	−0.584591	+	1.62044i
$790$	17.9895	−	31.1588i	0.0227716	−	0.0394415i
$791$		−	242.395i		−	0.306441i
$792$	−10.5633	−	1.80084i	−0.0133375	−	0.00227379i
$793$		−	21.1396i		−	0.0266577i
$794$	450.728	−	780.684i	0.567668	−	0.983229i
$795$	−84.5715	−	100.210i	−0.106379	−	0.126050i
$796$	−1228.67	+	709.375i	−1.54356	+	0.891175i
$797$	593.926	−	342.903i	0.745202	−	0.430243i	−0.0787556	−	0.996894i	$-0.525095\pi$
$797$	593.926	−	342.903i	0.745202	−	0.430243i	0.823958	+	0.566651i	$0.191761\pi$
$798$	−154.533	+	130.418i	−0.193651	+	0.163431i
$799$	1361.32	−	550.507i	1.70378	−	0.688996i
$800$			515.448i			0.644310i
$801$	135.512	+	365.844i	0.169179	+	0.456734i
$802$		−	2187.22i		−	2.72721i
$803$	−1861.08	−	1074.50i	−2.31766	−	1.33810i
$804$	−652.084	−	235.246i	−0.811050	−	0.292595i
$805$	78.0194	−	45.0445i	0.0969185	−	0.0559559i
$806$	−855.499	−	1481.77i	−1.06141	−	1.83842i
$807$	260.620	+	1453.91i	0.322949	+	1.80163i
$808$	−1.70985	+	2.96155i	−0.00211615	+	0.00366528i
$809$	228.169			0.282039			0.141019	−	0.990007i	$-0.454962\pi$
$809$	228.169			0.282039			0.141019	+	0.990007i	$0.454962\pi$
$810$	549.554	+	640.039i	0.678462	+	0.790171i
$811$		−	63.4735i		−	0.0782657i	−0.999234	−	0.0391328i	$-0.987540\pi$
$811$		−	63.4735i		−	0.0782657i	0.999234	−	0.0391328i	$-0.0124595\pi$
$812$	−59.5795	−	34.3982i	−0.0733738	−	0.0423624i
$813$	−195.006	−	1087.87i	−0.239859	−	1.33810i
$814$	365.224	+	632.586i	0.448678	+	0.777132i
$815$	−152.198	+	87.8714i	−0.186746	+	0.107818i
$816$	694.290	−	436.890i	0.850846	−	0.535404i
$817$	−296.940	+	514.314i	−0.363451	+	0.629516i
$818$		−	52.8643i		−	0.0646262i
$819$	76.6545	+	206.945i	0.0935953	+	0.252680i
$820$	447.972			0.546307
$821$	−339.051	+	587.254i	−0.412973	+	0.715291i	−0.995213	−	0.0977260i	$-0.968843\pi$
$821$	−339.051	+	587.254i	−0.412973	+	0.715291i	0.582240	+	0.813017i	$0.302176\pi$
$822$	−463.539	+	391.202i	−0.563916	+	0.475915i
$823$	389.065	−	224.627i	0.472740	−	0.272936i	−0.244646	−	0.969612i	$-0.578672\pi$
$823$	389.065	−	224.627i	0.472740	−	0.272936i	0.717386	+	0.696676i	$0.245338\pi$
$824$	−3.14335	+	1.81482i	−0.00381475	+	0.00220245i
$825$	518.697	−	437.752i	0.628723	−	0.530609i
$826$	−306.876	−	177.175i	−0.371520	−	0.214497i
$827$	1047.69			1.26686			0.633430	−	0.773800i	$-0.281647\pi$
$827$	1047.69			1.26686			0.633430	+	0.773800i	$0.281647\pi$
$828$	−105.528	+	618.997i	−0.127449	+	0.747581i
$829$	838.983			1.01204			0.506021	−	0.862521i	$-0.331116\pi$
$829$	838.983			1.01204			0.506021	+	0.862521i	$0.331116\pi$
$830$	222.568	−	385.499i	0.268154	−	0.464457i
$831$	−75.3878	+	208.969i	−0.0907194	+	0.251467i
$832$	557.138	+	964.991i	0.669637	+	1.15984i
$833$	−792.244	−	111.088i	−0.951073	−	0.133359i
$834$	−288.373	−	1608.74i	−0.345771	−	1.92895i
$835$	227.485	−	394.016i	0.272437	−	0.471875i
$836$	1351.64			1.61679
$837$	−808.772	−	457.810i	−0.966275	−	0.546966i
$838$			1638.10i			1.95477i
$839$	−21.6089	+	37.4278i	−0.0257556	+	0.0446100i	−0.878616	−	0.477529i	$-0.841532\pi$
$839$	−21.6089	+	37.4278i	−0.0257556	+	0.0446100i	0.852860	+	0.522139i	$0.174866\pi$
$840$	−0.163224	−	0.910576i	−0.000194315	−	0.00108402i
$841$	343.503	+	594.965i	0.408446	+	0.707449i
$842$	−731.331	+	422.234i	−0.868564	+	0.501465i
$843$	−31.8428	+	88.2659i	−0.0377732	+	0.104705i
$844$	−607.348	−	350.652i	−0.719607	−	0.415465i
$845$	518.737			0.613890
$846$	1690.13	+	1401.92i	1.99779	+	1.65712i
$847$			379.678i			0.448262i
$848$	−165.130	−	95.3380i	−0.194729	−	0.112427i
$849$	−360.568	−	427.240i	−0.424697	−	0.503227i
$850$	−76.0513	+	542.373i	−0.0894722	+	0.638086i
$851$	−197.973	+	114.300i	−0.232636	+	0.134313i
$852$	1089.98	−	919.883i	1.27932	−	1.07967i
$853$	1071.00	+	618.341i	1.25557	+	0.724902i	0.972209	−	0.234113i	$-0.0752185\pi$
$853$	1071.00	+	618.341i	1.25557	+	0.724902i	0.283357	+	0.959014i	$0.408552\pi$
$854$		−	4.72790i		−	0.00553618i
$855$	437.406	+	362.817i	0.511585	+	0.424347i
$856$			0.121633i			0.000142095i
$857$	−153.442	+	265.770i	−0.179046	+	0.310117i	−0.941554	−	0.336862i	$-0.890634\pi$
$857$	−153.442	+	265.770i	−0.179046	+	0.310117i	0.762508	+	0.646979i	$0.223968\pi$
$858$	1003.85	−	2782.60i	1.16999	−	3.24312i
$859$	−37.9520	−	65.7347i	−0.0441815	−	0.0765247i	0.843089	−	0.537774i	$-0.180735\pi$
$859$	−37.9520	−	65.7347i	−0.0441815	−	0.0765247i	−0.887271	+	0.461249i	$0.847401\pi$
$860$	254.361	+	440.566i	0.295769	+	0.512286i
$861$	125.644	−	22.5222i	0.145928	−	0.0261582i
$862$	514.531	+	297.065i	0.596904	+	0.344622i
$863$		−	264.341i		−	0.306305i	−0.988203	−	0.153152i	$-0.951057\pi$
$863$		−	264.341i		−	0.306305i	0.988203	−	0.153152i	$-0.0489425\pi$
$864$	1061.90	+	601.094i	1.22905	+	0.695711i
$865$	−470.155			−0.543532
$866$	1298.12	+	749.469i	1.49898	+	0.865438i
$867$	790.816	−	355.385i	0.912130	−	0.409902i
$868$	−95.4120	−	165.258i	−0.109922	−	0.190390i
$869$	−59.3465	+	34.2637i	−0.0682929	+	0.0394289i
$870$	−131.575	+	364.717i	−0.151236	+	0.419215i
$871$	−511.019	+	885.111i	−0.586704	+	1.01620i
$872$	3.42455			0.00392724
$873$	−432.260	−	73.6923i	−0.495143	−	0.0844127i
$874$			848.274i			0.970565i
$875$	161.975	+	93.5162i	0.185114	+	0.106876i
$876$	834.005	+	988.221i	0.952061	+	1.12811i
$877$	−483.379	+	279.079i	−0.551173	+	0.318220i	−0.749595	−	0.661897i	$-0.769752\pi$
$877$	−483.379	+	279.079i	−0.551173	+	0.318220i	0.198422	+	0.980117i	$0.436418\pi$
$878$	377.906	+	654.553i	0.430417	+	0.745504i
$879$	505.331	+	598.772i	0.574894	+	0.681197i
$880$	−588.204	+	1018.80i	−0.668414	+	1.15773i
$881$	615.701			0.698866			0.349433	−	0.936961i	$-0.386374\pi$
$881$	615.701			0.698866			0.349433	+	0.936961i	$0.386374\pi$
$882$	−415.539	−	1121.84i	−0.471133	−	1.27192i
$883$	1536.97			1.74062			0.870311	−	0.492502i	$-0.163918\pi$
$883$	1536.97			1.74062			0.870311	+	0.492502i	$0.163918\pi$
$884$	446.245	+	1103.49i	0.504802	+	1.24830i
$885$	−337.950	+	936.772i	−0.381864	+	1.05850i
$886$	−1100.08	−	1905.40i	−1.24163	−	2.15056i
$887$	−320.893	−	555.804i	−0.361774	−	0.626611i	0.626479	−	0.779438i	$-0.284495\pi$
$887$	−320.893	−	555.804i	−0.361774	−	0.626611i	−0.988253	+	0.152828i	$0.951162\pi$
$888$	0.414180	+	2.31058i	0.000466419	+	0.00260200i
$889$	−53.3103	−	30.7787i	−0.0599666	−	0.0346217i
$890$	451.464			0.507263
$891$	−296.951	−	1579.08i	−0.333279	−	1.77226i
$892$	−993.535			−1.11383
$893$	1281.09	+	739.637i	1.43459	+	0.828261i
$894$	−184.956	−	1031.81i	−0.206886	−	1.15415i
$895$	−563.523	+	325.350i	−0.629634	+	0.363520i
$896$	−1.33811	−	2.31768i	−0.00149343	−	0.00258670i
$897$	870.839	+	314.164i	0.970835	+	0.350239i
$898$	−196.775	−	113.608i	−0.219125	−	0.126512i
$899$		−	427.140i		−	0.475127i
$900$	−382.983	+	141.861i	−0.425537	+	0.157623i
$901$	−158.846	−	124.023i	−0.176299	−	0.137651i
$902$	−1481.78	−	855.507i	−1.64277	−	0.948455i
$903$	93.4912	+	110.779i	0.103534	+	0.122678i
$904$	−9.04269	+	5.22080i	−0.0100030	+	0.00577522i
$905$	588.503	−	339.772i	0.650279	−	0.375439i
$906$	−402.665	−	477.122i	−0.444443	−	0.526625i
$907$	−1383.50	−	798.765i	−1.52536	−	0.880667i	−0.999548	−	0.0300668i	$-0.990428\pi$
$907$	−1383.50	−	798.765i	−1.52536	−	0.880667i	−0.525813	−	0.850600i	$-0.676239\pi$
$908$	−1124.94			−1.23892
$909$	−505.473	−	86.1739i	−0.556076	−	0.0948008i
$910$	255.378			0.280635
$911$	−544.648	+	943.358i	−0.597858	+	1.03552i	0.395279	+	0.918561i	$0.370648\pi$
$911$	−544.648	+	943.358i	−0.597858	+	1.03552i	−0.993137	+	0.116959i	$0.962686\pi$
$912$	777.339	+	280.433i	0.852345	+	0.307492i
$913$	−734.240	+	423.914i	−0.804206	+	0.464309i
$914$	−1071.26	+	618.492i	−1.17206	+	0.676687i
$915$	−13.0789	+	2.34444i	−0.0142938	+	0.00256223i
$916$	−638.792	+	1106.42i	−0.697372	+	1.20788i
$917$			30.6099i			0.0333805i
$918$	1028.68	+	789.170i	1.12057	+	0.859662i
$919$	1463.53			1.59253			0.796264	−	0.604949i	$-0.206807\pi$
$919$	1463.53			1.59253			0.796264	+	0.604949i	$0.206807\pi$
$920$	−3.36082	−	1.94037i	−0.00365307	−	0.00210910i
$921$	234.689	+	1309.25i	0.254819	+	1.42155i
$922$	−1072.35	−	1857.36i	−1.16307	−	2.01450i
$923$	−1051.40	−	1821.07i	−1.13911	−	1.97299i
$924$	111.957	−	310.337i	0.121166	−	0.335863i
$925$	−128.764	−	74.3422i	−0.139205	−	0.0803699i
$926$		−	1405.92i		−	1.51827i
$927$	−418.894	−	347.462i	−0.451881	−	0.374824i
$928$			560.824i			0.604336i
$929$	199.305	−	345.206i	0.214537	−	0.371589i	−0.738592	−	0.674152i	$-0.764509\pi$
$929$	199.305	−	345.206i	0.214537	−	0.371589i	0.953129	+	0.302564i	$0.0978425\pi$
$930$	−821.878	+	693.621i	−0.883740	+	0.745829i
$931$	−402.955	−	697.938i	−0.432819	−	0.749665i
$932$	−613.915	−	1063.33i	−0.658707	−	1.14091i
$933$	−679.930	+	573.824i	−0.728756	+	0.615031i
$934$	79.6896	−	138.026i	0.0853207	−	0.147780i
$935$	−765.183	+	980.025i	−0.818377	+	1.04816i
$936$	6.06919	−	7.31690i	0.00648418	−	0.00781720i
$937$	−125.284			−0.133707			−0.0668536	−	0.997763i	$-0.521296\pi$
$937$	−125.284			−0.133707			−0.0668536	+	0.997763i	$0.521296\pi$
$938$	−114.290	+	197.956i	−0.121844	+	0.211041i
$939$	509.210	−	1411.49i	0.542289	−	1.50318i
$940$	1097.39	−	633.579i	1.16744	−	0.674020i
$941$	232.137	+	402.073i	0.246692	+	0.427282i	0.962606	−	0.270906i	$-0.0873232\pi$
$941$	232.137	+	402.073i	0.246692	+	0.427282i	−0.715914	+	0.698188i	$0.753990\pi$
$942$	52.2066	−	9.35825i	0.0554211	−	0.00993445i
$943$	267.738	−	463.736i	0.283922	−	0.491767i
$944$			1448.12i			1.53403i
$945$	119.534	−	70.3762i	0.126491	−	0.0744722i
$946$		−	1943.05i		−	2.05396i
$947$	411.814	−	713.284i	0.434862	−	0.753203i	−0.562422	−	0.826850i	$-0.690130\pi$
$947$	411.814	−	713.284i	0.434862	−	0.753203i	0.997284	+	0.0736468i	$0.0234638\pi$
$948$	40.5881	−	7.27559i	0.0428145	−	0.00767467i
$949$	1651.06	−	953.241i	1.73979	−	1.00447i
$950$	−477.810	+	275.864i	−0.502958	+	0.290383i
$951$	−1068.57	−	385.497i	−1.12362	−	0.405359i
$952$	−0.533018	−	1.31807i	−0.000559892	−	0.00138453i
$953$			926.275i			0.971957i	0.873971	+	0.485978i	$0.161537\pi$
$953$			926.275i			0.971957i	−0.873971	+	0.485978i	$0.838463\pi$
$954$	50.6470	−	297.082i	0.0530891	−	0.311406i
$955$			183.328i			0.191966i
$956$	−1372.91	−	792.649i	−1.43610	−	0.829131i
$957$	564.359	−	476.289i	0.589717	−	0.497689i
$958$	−730.530	+	421.772i	−0.762557	+	0.440263i
$959$	49.8676	+	86.3733i	0.0519996	+	0.0900660i
$960$	535.243	−	451.716i	0.557544	−	0.470537i
$961$	111.888	−	193.796i	0.116429	−	0.201661i
$962$	−648.018			−0.673615
$963$	−17.1027	+	6.33502i	−0.0177598	+	0.00657842i
$964$		−	1183.37i		−	1.22756i
$965$	−259.535	−	149.843i	−0.268949	−	0.155278i
$966$	194.764	+	70.2632i	0.201619	+	0.0727363i
$967$	685.245	+	1186.88i	0.708630	+	1.22738i	0.965366	+	0.260901i	$0.0840196\pi$
$967$	685.245	+	1186.88i	0.708630	+	1.22738i	−0.256736	+	0.966482i	$0.582647\pi$
$968$	14.1641	−	8.17765i	0.0146323	−	0.00844798i
$969$	772.464	+	407.608i	0.797177	+	0.420648i
$970$	−253.714	+	439.446i	−0.261561	+	0.453037i
$971$			182.369i			0.187815i	0.995581	+	0.0939076i	$0.0299358\pi$
$971$			182.369i			0.187815i	−0.995581	+	0.0939076i	$0.970064\pi$
$972$	−154.365	+	954.434i	−0.158812	+	0.981928i
$973$	−268.740			−0.276198
$974$	1085.46	−	1880.06i	1.11443	−	1.93025i
$975$	106.242	+	592.689i	0.108966	+	0.607886i
$976$	−16.7329	+	9.66076i	−0.0171444	+	0.00989832i
$977$	366.032	−	211.328i	0.374649	−	0.216303i	−0.300839	−	0.953675i	$-0.597267\pi$
$977$	366.032	−	211.328i	0.374649	−	0.216303i	0.675487	+	0.737372i	$0.263933\pi$
$978$	−379.940	−	137.067i	−0.388487	−	0.140151i
$979$	−744.679	−	429.940i	−0.760652	−	0.439163i
$980$	−690.349			−0.704437
$981$	178.361	+	481.522i	0.181815	+	0.490849i
$982$	161.906			0.164874
$983$	−807.232	+	1398.17i	−0.821192	+	1.42235i	0.0836025	+	0.996499i	$0.473357\pi$
$983$	−807.232	+	1398.17i	−0.821192	+	1.42235i	−0.904795	+	0.425848i	$0.859976\pi$
$984$	−3.54637	−	4.20213i	−0.00360404	−	0.00427046i
$985$	364.301	+	630.988i	0.369849	+	0.640597i
$986$	−82.7464	+	590.119i	−0.0839213	+	0.598498i
$987$	275.935	−	232.874i	0.279569	−	0.235941i
$988$	−599.554	+	1038.46i	−0.606836	+	1.05107i
$989$	608.094			0.614857
$990$	−1832.90	−	312.475i	−1.85141	−	0.315632i
$991$		−	651.023i		−	0.656936i	−0.944515	−	0.328468i	$-0.893468\pi$
$991$		−	651.023i		−	0.656936i	0.944515	−	0.328468i	$-0.106532\pi$
$992$	−777.792	+	1347.18i	−0.784064	+	1.35804i
$993$	−463.337	−	167.154i	−0.466603	−	0.168332i
$994$	−235.146	−	407.285i	−0.236566	−	0.409744i
$995$	1138.61	−	657.375i	1.14433	−	0.660678i
$996$	502.160	−	90.0142i	0.504177	−	0.0903757i
$997$	−1123.30	−	648.540i	−1.12668	−	0.650491i	−0.183585	−	0.983004i	$-0.558770\pi$
$997$	−1123.30	−	648.540i	−1.12668	−	0.650491i	−0.943099	+	0.332513i	$0.892104\pi$
$998$	613.185			0.614413
$999$	−303.316	+	178.579i	−0.303619	+	0.178758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.101.8	yes	68
3.2	odd	2		459.3.i.a.305.27		68
9.4	even	3		459.3.i.a.152.28		68
9.5	odd	6	inner	153.3.i.a.50.7	✓	68
17.16	even	2	inner	153.3.i.a.101.7	yes	68
51.50	odd	2		459.3.i.a.305.28		68
153.50	odd	6	inner	153.3.i.a.50.8	yes	68
153.67	even	6		459.3.i.a.152.27		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.7	✓	68	9.5	odd	6	inner
153.3.i.a.50.8	yes	68	153.50	odd	6	inner
153.3.i.a.101.7	yes	68	17.16	even	2	inner
153.3.i.a.101.8	yes	68	1.1	even	1	trivial
459.3.i.a.152.27		68	153.67	even	6
459.3.i.a.152.28		68	9.4	even	3
459.3.i.a.305.27		68	3.2	odd	2
459.3.i.a.305.28		68	51.50	odd	2

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.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44623 - 1.41233i) q^{2} +(0.529325 + 2.95293i) q^{3} +(1.98938 + 3.44570i) q^{4} +(-1.84354 - 3.19311i) q^{5} +(2.87567 - 7.97115i) q^{6} +(-1.20670 - 0.696687i) q^{7} +0.0600221i q^{8} +(-8.43963 + 3.12612i) q^{9} +10.4148i q^{10} +(9.91827 - 17.1789i) q^{11} +(-9.12189 + 7.69839i) q^{12} +(8.79901 + 15.2403i) q^{13} +(1.96791 + 3.40852i) q^{14} +(8.45321 - 7.13406i) q^{15} +(8.04227 - 13.9296i) q^{16} +(10.4620 - 13.3995i) q^{17} +(25.0604 + 4.27234i) q^{18} +17.1257 q^{19} +(7.33500 - 12.7046i) q^{20} +(1.41854 - 3.93207i) q^{21} +(-48.5248 + 28.0158i) q^{22} +(-8.76780 - 15.1863i) q^{23} +(-0.177241 + 0.0317712i) q^{24} +(5.70269 - 9.87734i) q^{25} -49.7086i q^{26} +(-13.6985 - 23.2669i) q^{27} -5.54389i q^{28} +(6.20471 - 10.7469i) q^{29} +(-30.7542 + 5.51282i) q^{30} +(29.8091 - 17.2103i) q^{31} +(-39.1386 + 22.5967i) q^{32} +(55.9783 + 20.1947i) q^{33} +(-44.5171 + 18.0024i) q^{34} +5.13750i q^{35} +(-27.5613 - 22.8614i) q^{36} -13.0363i q^{37} +(-41.8935 - 24.1872i) q^{38} +(-40.3461 + 34.0500i) q^{39} +(0.191657 - 0.110653i) q^{40} +(15.2683 + 26.4454i) q^{41} +(-9.02347 + 7.61532i) q^{42} +(-17.3388 + 30.0317i) q^{43} +78.9246 q^{44} +(25.5409 + 21.1855i) q^{45} +49.5322i q^{46} +(74.8051 + 43.1887i) q^{47} +(45.3902 + 16.3750i) q^{48} +(-23.5293 - 40.7539i) q^{49} +(-27.9002 + 16.1082i) q^{50} +(45.1056 + 23.8010i) q^{51} +(-35.0091 + 60.6375i) q^{52} -11.8546i q^{53} +(0.649177 + 76.2633i) q^{54} -73.1391 q^{55} +(0.0418166 - 0.0724285i) q^{56} +(9.06506 + 50.5710i) q^{57} +(-30.3564 + 17.5263i) q^{58} +(-77.9699 + 45.0160i) q^{59} +(41.3984 + 14.9349i) q^{60} +(-1.04031 - 0.600624i) q^{61} -97.2267 q^{62} +(12.3620 + 2.10750i) q^{63} +63.3182 q^{64} +(32.4427 - 56.1925i) q^{65} +(-108.414 - 128.461i) q^{66} +(29.0384 + 50.2960i) q^{67} +(66.9835 + 9.39240i) q^{68} +(40.2030 - 33.9292i) q^{69} +(7.25586 - 12.5675i) q^{70} -119.490 q^{71} +(-0.187636 - 0.506564i) q^{72} -108.335i q^{73} +(-18.4117 + 31.8899i) q^{74} +(32.1857 + 11.6113i) q^{75} +(34.0694 + 59.0100i) q^{76} +(-23.9367 + 13.8199i) q^{77} +(146.786 - 26.3120i) q^{78} +(-2.99178 - 1.72730i) q^{79} -59.3052 q^{80} +(61.4547 - 52.7667i) q^{81} -86.2557i q^{82} +(-37.0145 - 21.3704i) q^{83} +(16.3707 - 2.93452i) q^{84} +(-62.0733 - 8.70389i) q^{85} +(84.8297 - 48.9765i) q^{86} +(35.0191 + 12.6335i) q^{87} +(1.03112 + 0.595315i) q^{88} -43.3483i q^{89} +(-32.5580 - 87.8971i) q^{90} -24.5206i q^{91} +(34.8849 - 60.4224i) q^{92} +(66.5996 + 78.9144i) q^{93} +(-121.994 - 211.300i) q^{94} +(-31.5720 - 54.6843i) q^{95} +(-87.4436 - 103.613i) q^{96} +(42.1943 + 24.3609i) q^{97} +132.925i q^{98} +(-30.0030 + 175.990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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