LMFDB - Embedded newform 209.3.x.a.3.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,3,Mod(3,209)] 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("209.3"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(90)) chi = DirichletCharacter(H, H._module([72, 65])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	209.x (of order $90$, degree $24$, 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:	$5.69483752513$
Analytic rank:	$0$
Dimension:	$912$
Relative dimension:	$38$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			3.6
Character	$\chi$	$=$	209.3
Dual form			209.3.x.a.70.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.209688 + 2.99868i) q^{2} +(4.53353 - 3.54199i) q^{3} +(-4.98704 - 0.700883i) q^{4} +(1.36261 - 1.31585i) q^{5} +(9.67065 + 14.3373i) q^{6} +(5.43065 - 1.15432i) q^{7} +(0.647514 - 3.04631i) q^{8} +(5.82998 - 23.3828i) q^{9} +(3.66010 + 4.36194i) q^{10} +(-7.13597 - 8.37126i) q^{11} +(-25.0914 + 14.4865i) q^{12} +(0.0935062 + 0.326095i) q^{13} +(2.32270 + 16.5268i) q^{14} +(1.51669 - 10.7918i) q^{15} +(-10.3647 - 2.97203i) q^{16} +(0.454121 + 1.82138i) q^{17} +(68.8949 + 22.3853i) q^{18} +(13.0048 + 13.8519i) q^{19} +(-7.71764 + 5.60719i) q^{20} +(20.5315 - 24.4684i) q^{21} +(26.5990 - 19.6431i) q^{22} +(3.24484 + 18.4024i) q^{23} +(-7.85447 - 16.1040i) q^{24} +(-0.747262 + 21.3988i) q^{25} +(-0.997462 + 0.212017i) q^{26} +(-35.3309 - 79.3544i) q^{27} +(-27.8919 + 1.95039i) q^{28} +(7.82864 - 3.16297i) q^{29} +(32.0431 + 6.81098i) q^{30} +(-18.4396 + 41.4160i) q^{31} +(15.3462 - 42.1634i) q^{32} +(-62.0020 - 12.6759i) q^{33} +(-5.55696 + 0.979841i) q^{34} +(5.88093 - 8.71884i) q^{35} +(-45.4629 + 112.525i) q^{36} +(17.1833 + 5.58318i) q^{37} +(-44.2644 + 36.0927i) q^{38} +(1.57894 + 1.14716i) q^{39} +(-3.12620 - 5.00296i) q^{40} +(-26.7092 + 20.8675i) q^{41} +(69.0678 + 66.6980i) q^{42} +(-7.90444 + 44.8283i) q^{43} +(29.7201 + 46.7493i) q^{44} +(-22.8243 - 39.5329i) q^{45} +(-55.8633 + 5.87147i) q^{46} +(-13.1325 - 8.20611i) q^{47} +(-57.5157 + 23.2378i) q^{48} +(-16.6042 + 7.39266i) q^{49} +(-64.0114 - 6.72787i) q^{50} +(8.51007 + 6.64879i) q^{51} +(-0.237765 - 1.69179i) q^{52} +(26.7893 - 27.7411i) q^{53} +(245.367 - 89.3063i) q^{54} +(-20.7389 - 2.01684i) q^{55} -17.2909i q^{56} +(108.021 + 16.7352i) q^{57} +(7.84318 + 24.1388i) q^{58} +(-33.5047 - 53.6188i) q^{59} +(-15.1276 + 52.7561i) q^{60} +(25.2783 - 51.8282i) q^{61} +(-120.327 - 63.9789i) q^{62} +(4.66937 - 133.713i) q^{63} +(83.8159 + 37.3172i) q^{64} +(0.556506 + 0.321299i) q^{65} +(51.0120 - 183.266i) q^{66} +(-48.5792 - 57.8944i) q^{67} +(-0.988145 - 9.40157i) q^{68} +(79.8916 + 71.9348i) q^{69} +(24.9118 + 19.4633i) q^{70} +(-60.5893 - 62.7421i) q^{71} +(-67.4562 - 32.9006i) q^{72} +(4.54114 + 130.041i) q^{73} +(-20.3453 + 50.3564i) q^{74} +(72.4064 + 99.6589i) q^{75} +(-55.1469 - 78.1948i) q^{76} +(-48.4161 - 37.2242i) q^{77} +(-3.77106 + 4.49418i) q^{78} +(103.836 + 70.0383i) q^{79} +(-18.0338 + 9.58874i) q^{80} +(-249.746 - 132.792i) q^{81} +(-56.9744 - 84.4680i) q^{82} +(11.4100 - 108.559i) q^{83} +(-119.541 + 107.635i) q^{84} +(3.01546 + 1.88427i) q^{85} +(-132.768 - 33.1029i) q^{86} +(24.2882 - 42.0684i) q^{87} +(-30.1221 + 16.3179i) q^{88} +(-17.0068 + 46.7259i) q^{89} +(123.333 - 60.1533i) q^{90} +(0.884218 + 1.66297i) q^{91} +(-3.28422 - 94.0478i) q^{92} +(63.0984 + 253.074i) q^{93} +(27.3612 - 37.6595i) q^{94} +(35.9475 + 1.76226i) q^{95} +(-79.7696 - 245.506i) q^{96} +(5.01516 - 71.7201i) q^{97} +(-18.6865 - 51.3408i) q^{98} +(-237.346 + 118.054i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 912 q - 18 q^{2} - 30 q^{3} - 18 q^{4} - 18 q^{5} - 54 q^{6} + 18 q^{7} - 27 q^{8} + 18 q^{9} - 48 q^{10} + 3 q^{11} - 72 q^{12} - 18 q^{13} + 102 q^{14} - 90 q^{15} + 6 q^{16} + 54 q^{17} - 18 q^{19} - 30 q^{20}+ \cdots - 372 q^{99}+O(q^{100}) $ 912 * q - 18 * q^2 - 30 * q^3 - 18 * q^4 - 18 * q^5 - 54 * q^6 + 18 * q^7 - 27 * q^8 + 18 * q^9 - 48 * q^10 + 3 * q^11 - 72 * q^12 - 18 * q^13 + 102 * q^14 - 90 * q^15 + 6 * q^16 + 54 * q^17 - 18 * q^19 - 30 * q^20 - 102 * q^21 + 48 * q^22 - 48 * q^23 + 216 * q^24 - 414 * q^25 - 57 * q^26 - 207 * q^27 - 114 * q^28 + 351 * q^29 + 231 * q^30 - 135 * q^31 - 162 * q^32 - 564 * q^33 - 132 * q^34 - 48 * q^35 + 45 * q^36 + 186 * q^38 - 36 * q^39 + 72 * q^40 + 342 * q^41 + 237 * q^42 - 576 * q^43 + 1173 * q^44 + 174 * q^45 - 747 * q^46 - 174 * q^47 - 267 * q^48 + 456 * q^49 - 891 * q^50 - 186 * q^51 + 603 * q^52 - 63 * q^53 + 474 * q^54 - 72 * q^55 - 444 * q^57 + 132 * q^58 + 540 * q^59 - 591 * q^60 + 438 * q^61 - 408 * q^62 - 312 * q^63 - 585 * q^64 - 1152 * q^65 - 2268 * q^66 - 636 * q^67 + 999 * q^68 + 675 * q^69 + 1923 * q^70 - 42 * q^71 + 426 * q^72 - 396 * q^73 - 258 * q^74 + 2112 * q^76 - 396 * q^77 - 2550 * q^78 - 18 * q^79 - 978 * q^80 - 372 * q^81 - 72 * q^82 + 177 * q^83 + 1917 * q^84 - 54 * q^85 - 72 * q^86 + 216 * q^87 + 360 * q^88 + 690 * q^89 + 1152 * q^90 - 780 * q^91 - 1314 * q^92 + 876 * q^93 - 1002 * q^95 - 3396 * q^96 + 774 * q^97 - 1962 * q^98 - 372 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.209688	+	2.99868i	−0.104844	+	1.49934i	0.605703	+	0.795691i	$0.292892\pi$
$2$	−0.209688	+	2.99868i	−0.104844	+	1.49934i	−0.710547	+	0.703649i	$0.751553\pi$
$3$	4.53353	−	3.54199i	1.51118	−	1.18066i	0.580808	−	0.814041i	$-0.302737\pi$
$3$	4.53353	−	3.54199i	1.51118	−	1.18066i	0.930370	−	0.366621i	$-0.119485\pi$
$4$	−4.98704	−	0.700883i	−1.24676	−	0.175221i
$5$	1.36261	−	1.31585i	0.272521	−	0.263171i	−0.545821	−	0.837902i	$-0.683782\pi$
$5$	1.36261	−	1.31585i	0.272521	−	0.263171i	0.818342	+	0.574731i	$0.194893\pi$
$6$	9.67065	+	14.3373i	1.61178	+	2.38955i
$7$	5.43065	−	1.15432i	0.775808	−	0.164903i	0.197040	−	0.980395i	$-0.436867\pi$
$7$	5.43065	−	1.15432i	0.775808	−	0.164903i	0.578768	+	0.815492i	$0.303534\pi$
$8$	0.647514	−	3.04631i	0.0809392	−	0.380789i
$9$	5.82998	−	23.3828i	0.647775	−	2.59808i
$10$	3.66010	+	4.36194i	0.366010	+	0.436194i
$11$	−7.13597	−	8.37126i	−0.648725	−	0.761023i
$11$	−7.13597	−	8.37126i	−0.648725	−	0.761023i
$12$	−25.0914	+	14.4865i	−2.09095	+	1.20721i
$13$	0.0935062	+	0.326095i	0.00719279	+	0.0250842i	0.964776	−	0.263072i	$-0.0847356\pi$
$13$	0.0935062	+	0.326095i	0.00719279	+	0.0250842i	−0.957583	+	0.288156i	$0.906958\pi$
$14$	2.32270	+	16.5268i	0.165907	+	1.18049i
$15$	1.51669	−	10.7918i	0.101113	−	0.719454i
$16$	−10.3647	−	2.97203i	−0.647794	−	0.185752i
$17$	0.454121	+	1.82138i	0.0267130	+	0.107140i	0.982172	−	0.187983i	$-0.0601950\pi$
$17$	0.454121	+	1.82138i	0.0267130	+	0.107140i	−0.955459	+	0.295123i	$0.904639\pi$
$18$	68.8949	+	22.3853i	3.82750	+	1.24363i
$19$	13.0048	+	13.8519i	0.684464	+	0.729047i
$19$	13.0048	+	13.8519i	0.684464	+	0.729047i
$20$	−7.71764	+	5.60719i	−0.385882	+	0.280360i
$21$	20.5315	−	24.4684i	0.977689	−	1.16516i
$22$	26.5990	−	19.6431i	1.20905	−	0.892870i
$23$	3.24484	+	18.4024i	0.141080	+	0.800105i	0.970431	+	0.241377i	$0.0775991\pi$
$23$	3.24484	+	18.4024i	0.141080	+	0.800105i	−0.829351	+	0.558727i	$0.811290\pi$
$24$	−7.85447	−	16.1040i	−0.327269	−	0.671002i
$25$	−0.747262	+	21.3988i	−0.0298905	+	0.855951i
$26$	−0.997462	+	0.212017i	−0.0383639	+	0.00815450i
$27$	−35.3309	−	79.3544i	−1.30855	−	2.93905i
$28$	−27.8919	+	1.95039i	−0.996140	+	0.0696569i
$29$	7.82864	−	3.16297i	0.269953	−	0.109068i	−0.235639	−	0.971841i	$-0.575718\pi$
$29$	7.82864	−	3.16297i	0.269953	−	0.109068i	0.505592	+	0.862772i	$0.331274\pi$
$30$	32.0431	+	6.81098i	1.06810	+	0.227033i
$31$	−18.4396	+	41.4160i	−0.594826	+	1.33600i	0.325757	+	0.945454i	$0.394381\pi$
$31$	−18.4396	+	41.4160i	−0.594826	+	1.33600i	−0.920583	+	0.390548i	$0.872286\pi$
$32$	15.3462	−	42.1634i	0.479570	−	1.31761i
$33$	−62.0020	−	12.6759i	−1.87885	−	0.384117i
$34$	−5.55696	+	0.979841i	−0.163440	+	0.0288189i
$35$	5.88093	−	8.71884i	0.168027	−	0.249110i
$36$	−45.4629	+	112.525i	−1.26286	+	3.12568i
$37$	17.1833	+	5.58318i	0.464412	+	0.150897i	0.531871	−	0.846825i	$-0.321489\pi$
$37$	17.1833	+	5.58318i	0.464412	+	0.150897i	−0.0674587	+	0.997722i	$0.521489\pi$
$38$	−44.2644	+	36.0927i	−1.16485	+	0.949807i
$39$	1.57894	+	1.14716i	0.0404856	+	0.0294145i
$40$	−3.12620	−	5.00296i	−0.0781549	−	0.125074i
$41$	−26.7092	+	20.8675i	−0.651444	+	0.508964i	−0.886327	−	0.463060i	$-0.846752\pi$
$41$	−26.7092	+	20.8675i	−0.651444	+	0.508964i	0.234883	+	0.972024i	$0.424529\pi$
$42$	69.0678	+	66.6980i	1.64447	+	1.58805i
$43$	−7.90444	+	44.8283i	−0.183824	+	1.04252i	0.743632	+	0.668589i	$0.233101\pi$
$43$	−7.90444	+	44.8283i	−0.183824	+	1.04252i	−0.927457	+	0.373931i	$0.878010\pi$
$44$	29.7201	+	46.7493i	0.675457	+	1.06248i
$45$	−22.8243	−	39.5329i	−0.507208	−	0.878509i
$46$	−55.8633	+	5.87147i	−1.21442	+	0.127641i
$47$	−13.1325	−	8.20611i	−0.279415	−	0.174598i	0.382971	−	0.923760i	$-0.374901\pi$
$47$	−13.1325	−	8.20611i	−0.279415	−	0.174598i	−0.662387	+	0.749162i	$0.730456\pi$
$48$	−57.5157	+	23.2378i	−1.19824	+	0.484122i
$49$	−16.6042	+	7.39266i	−0.338861	+	0.150871i
$50$	−64.0114	−	6.72787i	−1.28023	−	0.134557i
$51$	8.51007	+	6.64879i	0.166864	+	0.130369i
$52$	−0.237765	−	1.69179i	−0.00457240	−	0.0325343i
$53$	26.7893	−	27.7411i	0.505458	−	0.523417i	−0.417315	−	0.908762i	$-0.637029\pi$
$53$	26.7893	−	27.7411i	0.505458	−	0.523417i	0.922772	+	0.385345i	$0.125918\pi$
$54$	245.367	−	89.3063i	4.54383	−	1.65382i
$55$	−20.7389	−	2.01684i	−0.377071	−	0.0366697i
$56$		−	17.2909i		−	0.308766i
$57$	108.021	+	16.7352i	1.89510	+	0.293600i
$58$	7.84318	+	24.1388i	0.135227	+	0.416186i
$59$	−33.5047	−	53.6188i	−0.567877	−	0.908792i	−0.999976	−	0.00696638i	$-0.997783\pi$
$59$	−33.5047	−	53.6188i	−0.567877	−	0.908792i	0.432099	−	0.901826i	$-0.357773\pi$
$60$	−15.1276	+	52.7561i	−0.252126	+	0.879269i
$61$	25.2783	−	51.8282i	0.414398	−	0.849642i	−0.584860	−	0.811134i	$-0.698851\pi$
$61$	25.2783	−	51.8282i	0.414398	−	0.849642i	0.999258	−	0.0385082i	$-0.0122606\pi$
$62$	−120.327	−	63.9789i	−1.94076	−	1.03192i
$63$	4.66937	−	133.713i	0.0741170	−	2.12243i
$64$	83.8159	+	37.3172i	1.30962	+	0.583082i
$65$	0.556506	+	0.321299i	0.00856163	+	0.00494306i
$66$	51.0120	−	183.266i	0.772909	−	2.77676i
$67$	−48.5792	−	57.8944i	−0.725063	−	0.864096i	0.270050	−	0.962846i	$-0.412960\pi$
$67$	−48.5792	−	57.8944i	−0.725063	−	0.864096i	−0.995112	+	0.0987505i	$0.968515\pi$
$68$	−0.988145	−	9.40157i	−0.0145315	−	0.138258i
$69$	79.8916	+	71.9348i	1.15785	+	1.04253i
$70$	24.9118	+	19.4633i	0.355883	+	0.278047i
$71$	−60.5893	−	62.7421i	−0.853371	−	0.883692i	0.140961	−	0.990015i	$-0.454981\pi$
$71$	−60.5893	−	62.7421i	−0.853371	−	0.883692i	−0.994332	+	0.106324i	$0.966092\pi$
$72$	−67.4562	−	32.9006i	−0.936891	−	0.456952i
$73$	4.54114	+	130.041i	0.0622074	+	1.78139i	0.484366	+	0.874865i	$0.339050\pi$
$73$	4.54114	+	130.041i	0.0622074	+	1.78139i	−0.422159	+	0.906522i	$0.638728\pi$
$74$	−20.3453	+	50.3564i	−0.274936	+	0.680491i
$75$	72.4064	+	99.6589i	0.965419	+	1.32879i
$76$	−55.1469	−	78.1948i	−0.725618	−	1.02888i
$77$	−48.4161	−	37.2242i	−0.628781	−	0.483431i
$78$	−3.77106	+	4.49418i	−0.0483470	+	0.0576177i
$79$	103.836	+	70.0383i	1.31438	+	0.886561i	0.998070	−	0.0620946i	$-0.0197781\pi$
$79$	103.836	+	70.0383i	1.31438	+	0.886561i	0.316311	+	0.948656i	$0.397556\pi$
$80$	−18.0338	+	9.58874i	−0.225422	+	0.119859i
$81$	−249.746	−	132.792i	−3.08328	−	1.63941i
$82$	−56.9744	−	84.4680i	−0.694810	−	1.03010i
$83$	11.4100	−	108.559i	0.137470	−	1.30794i	−0.680531	−	0.732719i	$-0.738251\pi$
$83$	11.4100	−	108.559i	0.137470	−	1.30794i	0.818001	−	0.575217i	$-0.195083\pi$
$84$	−119.541	+	107.635i	−1.42310	+	1.28137i
$85$	3.01546	+	1.88427i	0.0354760	+	0.0221678i
$86$	−132.768	−	33.1029i	−1.54382	−	0.384917i
$87$	24.2882	−	42.0684i	0.279175	−	0.483544i
$88$	−30.1221	+	16.3179i	−0.342296	+	0.185431i
$89$	−17.0068	+	46.7259i	−0.191088	+	0.525010i	−0.997826	−	0.0658989i	$-0.979009\pi$
$89$	−17.0068	+	46.7259i	−0.191088	+	0.525010i	0.806738	+	0.590909i	$0.201231\pi$
$90$	123.333	−	60.1533i	1.37036	−	0.668370i
$91$	0.884218	+	1.66297i	0.00971668	+	0.0182744i
$92$	−3.28422	−	94.0478i	−0.0356980	−	1.02226i
$93$	63.0984	+	253.074i	0.678477	+	2.72122i
$94$	27.3612	−	37.6595i	0.291077	−	0.400633i
$95$	35.9475	+	1.76226i	0.378395	+	0.0185501i
$96$	−79.7696	−	245.506i	−0.830933	−	2.55735i
$97$	5.01516	−	71.7201i	0.0517027	−	0.739382i	−0.900681	−	0.434481i	$-0.856932\pi$
$97$	5.01516	−	71.7201i	0.0517027	−	0.739382i	0.952384	−	0.304902i	$-0.0986236\pi$
$98$	−18.6865	−	51.3408i	−0.190679	−	0.523885i
$99$	−237.346	+	118.054i	−2.39743	+	1.19247i
$100$	18.7247	−	106.193i	0.187247	−	1.06193i
$101$	−89.8648	+	25.7683i	−0.889751	+	0.255132i	−0.689217	−	0.724555i	$-0.742045\pi$
$101$	−89.8648	+	25.7683i	−0.889751	+	0.255132i	−0.200534	+	0.979687i	$0.564268\pi$
$102$	−21.7221	+	24.1248i	−0.212961	+	0.236518i
$103$	150.122	−	135.171i	1.45750	−	1.31234i	0.597679	−	0.801735i	$-0.296090\pi$
$103$	150.122	−	135.171i	1.45750	−	1.31234i	0.859818	−	0.510601i	$-0.170577\pi$
$104$	1.05393	−	0.0736982i	0.0101340	−	0.000708637i
$105$	−4.22059	−	60.3573i	−0.0401961	−	0.574832i
$106$	77.5692	+	86.1494i	0.731785	+	0.812730i
$107$	99.5846	+	89.6663i	0.930697	+	0.838003i	0.987051	−	0.160408i	$-0.0512809\pi$
$107$	99.5846	+	89.6663i	0.930697	+	0.838003i	−0.0563539	+	0.998411i	$0.517948\pi$
$108$	120.578	+	420.507i	1.11647	+	3.89358i
$109$	−167.433	−	29.5229i	−1.53608	−	0.270853i	−0.659352	−	0.751835i	$-0.729169\pi$
$109$	−167.433	−	29.5229i	−1.53608	−	0.270853i	−0.876730	+	0.480982i	$0.840280\pi$
$110$	10.3965	−	61.7664i	0.0945140	−	0.561512i
$111$	97.6764	−	35.5513i	0.879968	−	0.320282i
$112$	−59.7178	−	4.17588i	−0.533195	−	0.0372846i
$113$	83.6656	−	27.1846i	0.740403	−	0.240572i	0.0855565	−	0.996333i	$-0.472733\pi$
$113$	83.6656	−	27.1846i	0.740403	−	0.240572i	0.654847	+	0.755762i	$0.272733\pi$
$114$	−72.8342	+	320.411i	−0.638897	+	2.81062i
$115$	28.6363	+	20.8055i	0.249012	+	0.180918i
$116$	−41.2586	+	10.2869i	−0.355678	+	0.0886804i
$117$	8.17014	−	0.285308i	0.0698302	−	0.00243853i
$118$	167.811	−	89.2267i	1.42213	−	0.756159i
$119$	4.56863	+	9.36708i	0.0383918	+	0.0787149i
$120$	−31.8931	−	11.6081i	−0.265776	−	0.0967346i
$121$	−19.1558	+	119.474i	−0.158313	+	0.987389i
$122$	150.116	+	86.6693i	1.23046	+	0.710404i
$123$	−47.1747	+	189.207i	−0.383534	+	1.53827i
$124$	120.987	−	193.619i	0.975700	−	1.56145i
$125$	58.8269	+	65.3339i	0.470615	+	0.522671i
$126$	399.984	+	42.0401i	3.17448	+	0.333651i
$127$	−50.5523	+	34.0980i	−0.398050	+	0.268488i	−0.741865	−	0.670549i	$-0.766058\pi$
$127$	−50.5523	+	34.0980i	−0.398050	+	0.268488i	0.343815	+	0.939037i	$0.388281\pi$
$128$	−45.2180	+	85.0427i	−0.353266	+	0.664396i
$129$	122.946	+	231.228i	0.953071	+	1.79247i
$130$	−1.08016	+	1.60141i	−0.00830896	+	0.0123185i
$131$	−98.1898	−	82.3910i	−0.749540	−	0.628939i	0.185841	−	0.982580i	$-0.440499\pi$
$131$	−98.1898	−	82.3910i	−0.749540	−	0.628939i	−0.935381	+	0.353641i	$0.884943\pi$
$132$	300.322	+	106.671i	2.27517	+	0.808115i
$133$	86.6141	+	60.2131i	0.651234	+	0.452730i
$134$	183.793	−	133.534i	1.37159	−	0.996520i
$135$	−152.561	−	61.6387i	−1.13008	−	0.456583i
$136$	5.84254	−	0.204026i	0.0429598	−	0.00150019i
$137$	−53.7427	+	110.189i	−0.392283	+	0.804299i	0.607666	+	0.794193i	$0.292106\pi$
$137$	−53.7427	+	110.189i	−0.392283	+	0.804299i	−0.999949	+	0.0101064i	$0.996783\pi$
$138$	−232.462	+	224.486i	−1.68450	+	1.62671i
$139$	10.1742	−	13.0224i	0.0731955	−	0.0936860i	−0.750019	−	0.661416i	$-0.769956\pi$
$139$	10.1742	−	13.0224i	0.0731955	−	0.0936860i	0.823215	+	0.567730i	$0.192178\pi$
$140$	−35.4393	+	39.3593i	−0.253138	+	0.281138i
$141$	−88.6026	+	9.31251i	−0.628387	+	0.0660462i
$142$	200.848	−	168.532i	1.41442	−	1.18684i
$143$	2.06257	−	3.10977i	0.0144235	−	0.0217466i
$144$	−129.920	+	225.029i	−0.902225	+	1.56270i
$145$	6.50534	−	14.6112i	0.0448644	−	0.100767i
$146$	−390.904	−	13.6507i	−2.67743	−	0.0934978i
$147$	−49.0909	+	92.3266i	−0.333952	+	0.628072i
$148$	−81.7804	−	39.8870i	−0.552570	−	0.269507i
$149$	−235.133	−	67.4234i	−1.57808	−	0.452506i	−0.631604	−	0.775292i	$-0.717603\pi$
$149$	−235.133	−	67.4234i	−1.57808	−	0.452506i	−0.946472	+	0.322786i	$0.895381\pi$
$150$	−314.028	+	196.226i	−2.09352	+	1.30818i
$151$	−38.0766	+	12.3718i	−0.252163	+	0.0819327i	−0.432371	−	0.901696i	$-0.642323\pi$
$151$	−38.0766	+	12.3718i	−0.252163	+	0.0819327i	0.180208	+	0.983629i	$0.442323\pi$
$152$	50.6180	−	30.6474i	0.333013	−	0.201628i
$153$	45.2364			0.295663
$154$	121.776	−	137.379i	0.790751	−	0.892071i
$155$	29.3715	+	80.6976i	0.189494	+	0.520630i
$156$	−7.07019	−	6.82761i	−0.0453218	−	0.0437667i
$157$	160.691	−	22.5837i	1.02351	−	0.143845i	0.392607	−	0.919706i	$-0.371573\pi$
$157$	160.691	−	22.5837i	1.02351	−	0.143845i	0.630903	+	0.775862i	$0.282685\pi$
$158$	−231.796	+	296.685i	−1.46706	+	1.87775i
$159$	23.1915	−	220.652i	0.145858	−	1.38775i
$160$	−34.5701	−	77.6456i	−0.216063	−	0.485285i
$161$	38.8639	+	96.1915i	0.241391	+	0.597463i
$162$	450.570	−	721.063i	2.78130	−	4.45101i
$163$	−9.89664	−	94.1602i	−0.0607156	−	0.577670i	−0.982013	−	0.188812i	$-0.939536\pi$
$163$	−9.89664	−	94.1602i	−0.0607156	−	0.577670i	0.921298	−	0.388858i	$-0.127130\pi$
$164$	147.826	−	85.3471i	0.901375	−	0.520409i
$165$	−101.164	+	64.3134i	−0.613115	+	0.389778i
$166$	323.140	+	56.9784i	1.94663	+	0.343243i
$167$	20.8822	−	21.6241i	0.125043	−	0.129486i	−0.653899	−	0.756582i	$-0.726868\pi$
$167$	20.8822	−	21.6241i	0.125043	−	0.129486i	0.778942	+	0.627096i	$0.215757\pi$
$168$	−61.2441	−	78.3889i	−0.364548	−	0.466601i
$169$	143.223	−	89.4954i	0.847471	−	0.529558i
$170$	−6.28262	+	8.64728i	−0.0369566	+	0.0508664i
$171$	399.713	−	223.332i	2.33750	−	1.30604i
$172$	70.8392	−	218.021i	0.411856	−	1.26756i
$173$	−104.516	−	42.2272i	−0.604139	−	0.244088i	0.0520991	−	0.998642i	$-0.483409\pi$
$173$	−104.516	−	42.2272i	−0.604139	−	0.244088i	−0.656238	+	0.754554i	$0.727853\pi$
$174$	121.057	+	81.6537i	0.695728	+	0.469274i
$175$	20.6429	+	117.072i	0.117960	+	0.668983i
$176$	49.0826	+	107.974i	0.278879	+	0.613489i
$177$	−341.812	−	124.409i	−1.93114	−	0.702877i
$178$	−136.550	−	60.7959i	−0.767134	−	0.341550i
$179$	−42.7093	+	200.932i	−0.238600	+	1.12252i	0.681798	+	0.731540i	$0.261198\pi$
$179$	−42.7093	+	200.932i	−0.238600	+	1.12252i	−0.920398	+	0.390983i	$0.872135\pi$
$180$	86.1180	+	213.149i	0.478433	+	1.18416i
$181$	5.93697	+	84.9027i	0.0328010	+	0.469075i	0.986001	+	0.166737i	$0.0533230\pi$
$181$	5.93697	+	84.9027i	0.0328010	+	0.469075i	−0.953201	+	0.302339i	$0.902233\pi$
$182$	−5.17213	+	2.30278i	−0.0284183	+	0.0126526i
$183$	−68.9746	−	324.500i	−0.376911	−	1.77323i
$184$	58.1605	+	2.03101i	0.316090	+	0.0110381i
$185$	30.7607	−	15.0030i	0.166274	−	0.0810972i
$186$	−772.118	+	136.145i	−4.15117	+	0.731964i
$187$	12.0066	−	16.7989i	0.0642066	−	0.0898335i
$188$	59.7409	+	50.1285i	0.317771	+	0.266641i
$189$	−283.470	−	390.163i	−1.49984	−	2.06436i
$190$	−12.8222	+	107.426i	−0.0674853	+	0.565398i
$191$	54.2653	−	167.012i	0.284112	−	0.874406i	−0.702552	−	0.711633i	$-0.747956\pi$
$191$	54.2653	−	167.012i	0.284112	−	0.874406i	0.986663	−	0.162773i	$-0.0520440\pi$
$192$	512.159	−	127.696i	2.66750	−	0.665081i
$193$	68.6855	−	239.535i	0.355883	−	1.24111i	−0.556179	−	0.831062i	$-0.687733\pi$
$193$	68.6855	−	239.535i	0.355883	−	1.24111i	0.912063	−	0.410051i	$-0.134489\pi$
$194$	214.014	+	30.0777i	1.10316	+	0.155040i
$195$	3.66097	−	0.514516i	0.0187742	−	0.00263855i
$196$	87.9871	−	25.2299i	0.448914	−	0.128724i
$197$	19.2182	+	33.2869i	0.0975542	+	0.168969i	0.910672	−	0.413131i	$-0.135565\pi$
$197$	19.2182	+	33.2869i	0.0975542	+	0.168969i	−0.813118	+	0.582100i	$0.802231\pi$
$198$	−304.239	−	736.478i	−1.53656	−	3.71959i
$199$	−111.072	+	93.2005i	−0.558151	+	0.468344i	−0.877690	−	0.479229i	$-0.840916\pi$
$199$	−111.072	+	93.2005i	−0.558151	+	0.468344i	0.319539	+	0.947573i	$0.396472\pi$
$200$	64.7035	+	16.1324i	0.323518	+	0.0806620i
$201$	−425.297	−	90.3996i	−2.11590	−	0.449749i
$202$	−58.4274	−	274.879i	−0.289244	−	1.36079i
$203$	38.8635	−	26.2138i	0.191446	−	0.129132i
$204$	−37.7800	−	39.1224i	−0.185196	−	0.191776i
$205$	−8.93554	+	63.5797i	−0.0435880	+	0.310145i
$206$	373.855	+	478.512i	1.81483	+	2.32287i
$207$	449.216	+	31.4123i	2.17013	+	0.151750i
$208$		−	3.65778i		−	0.0175855i
$209$	23.1558	−	207.713i	0.110793	−	0.993843i
$210$	181.877			0.866082
$211$	−6.13072	+	87.6734i	−0.0290555	+	0.415514i	0.961162	+	0.275984i	$0.0890036\pi$
$211$	−6.13072	+	87.6734i	−0.0290555	+	0.415514i	−0.990218	+	0.139530i	$0.955441\pi$
$212$	−153.042	+	119.570i	−0.721898	+	0.564008i
$213$	−496.915	−	69.8369i	−2.33294	−	0.327873i
$214$	−289.762	+	279.820i	−1.35403	+	1.30757i
$215$	48.2169	+	71.4845i	0.224265	+	0.332486i
$216$	−264.616	+	56.2458i	−1.22507	+	0.260397i
$217$	−52.3317	+	246.201i	−0.241160	+	1.13457i
$218$	123.639	−	495.887i	0.567149	−	2.27471i
$219$	481.192	+	573.462i	2.19722	+	2.61855i
$220$	102.012	+	24.5936i	0.463691	+	0.111789i
$221$	−0.551479	+	0.318397i	−0.00249538	+	0.00144071i
$222$	86.1254	+	300.355i	0.387952	+	1.35295i
$223$	−0.465748	−	3.31397i	−0.00208855	−	0.0148608i	0.989196	−	0.146600i	$-0.0468329\pi$
$223$	−0.465748	−	3.31397i	−0.00208855	−	0.0148608i	−0.991284	+	0.131739i	$0.957944\pi$
$224$	34.6700	−	246.690i	0.154777	−	1.10129i
$225$	496.006	+	142.227i	2.20447	+	0.632122i
$226$	63.9742	+	256.587i	0.283072	+	1.13534i
$227$	−122.674	−	39.8591i	−0.540413	−	0.175591i	0.0260764	−	0.999660i	$-0.491699\pi$
$227$	−122.674	−	39.8591i	−0.540413	−	0.175591i	−0.566489	+	0.824069i	$0.691699\pi$
$228$	−526.975	−	159.169i	−2.31130	−	0.698110i
$229$	276.702	−	201.036i	1.20831	−	0.877887i	0.213231	−	0.977002i	$-0.431601\pi$
$229$	276.702	−	201.036i	1.20831	−	0.877887i	0.995076	+	0.0991150i	$0.0316012\pi$
$230$	−68.3938	+	81.5085i	−0.297364	+	0.354385i
$231$	−351.344	+	2.73197i	−1.52097	+	0.0118267i
$232$	−4.56626	−	25.8965i	−0.0196821	−	0.111623i
$233$	163.700	+	335.634i	0.702573	+	1.44049i	0.888947	+	0.458010i	$0.151438\pi$
$233$	163.700	+	335.634i	0.702573	+	1.44049i	−0.186374	+	0.982479i	$0.559674\pi$
$234$	−0.857635	+	24.5595i	−0.00366511	+	0.104955i
$235$	−28.6925	+	6.09878i	−0.122096	+	0.0259523i
$236$	129.509	+	290.882i	0.548766	+	1.23255i
$237$	718.819	−	50.2647i	3.03299	−	0.212087i
$238$	−29.0469	+	11.7357i	−0.122046	+	0.0493096i
$239$	381.077	+	81.0004i	1.59446	+	0.338914i	0.917696	−	0.397283i	$-0.130047\pi$
$239$	381.077	+	81.0004i	1.59446	+	0.338914i	0.676768	+	0.736197i	$0.263380\pi$
$240$	−47.7937	+	107.346i	−0.199140	+	0.447276i
$241$	−2.57913	+	7.08611i	−0.0107018	+	0.0294029i	−0.944929	−	0.327277i	$-0.893869\pi$
$241$	−2.57913	+	7.08611i	−0.0107018	+	0.0294029i	0.934227	+	0.356680i	$0.116091\pi$
$242$	−354.248	−	82.4946i	−1.46383	−	0.340887i
$243$	−832.678	+	146.824i	−3.42666	+	0.604213i
$244$	−162.389	+	240.752i	−0.665530	+	0.986689i
$245$	−12.8973	+	31.9220i	−0.0526421	+	0.130294i
$246$	−557.480	−	181.136i	−2.26618	−	0.736326i
$247$	−3.30100	+	5.53604i	−0.0133644	+	0.0224131i
$248$	114.226	+	82.9902i	0.460590	+	0.334638i
$249$	−332.786	−	532.569i	−1.33649	−	2.13883i
$250$	−208.251	+	162.703i	−0.833003	+	0.650814i
$251$	106.796	+	103.132i	0.425483	+	0.410884i	0.876325	−	0.481720i	$-0.159988\pi$
$251$	106.796	+	103.132i	0.425483	+	0.410884i	−0.450843	+	0.892603i	$0.648876\pi$
$252$	−117.004	+	663.561i	−0.464300	+	2.63318i
$253$	130.896	−	158.482i	0.517376	−	0.626413i
$254$	−91.6487	−	158.740i	−0.360822	−	0.624961i
$255$	20.3447	−	2.13832i	0.0797832	−	0.00838556i
$256$	65.6924	+	41.0492i	0.256611	+	0.160348i
$257$	−191.096	+	77.2078i	−0.743564	+	0.300419i	−0.714954	−	0.699171i	$-0.753552\pi$
$257$	−191.096	+	77.2078i	−0.743564	+	0.300419i	−0.0286098	+	0.999591i	$0.509108\pi$
$258$	−719.160	+	320.191i	−2.78744	+	1.24105i
$259$	99.7611	+	10.4853i	0.385178	+	0.0404838i
$260$	−2.55012	−	1.99238i	−0.00980817	−	0.00766298i
$261$	−28.3183	−	201.495i	−0.108499	−	0.772012i
$262$	267.653	−	277.163i	1.02158	−	1.05788i
$263$	105.180	−	38.2823i	0.399923	−	0.145560i	−0.134225	−	0.990951i	$-0.542855\pi$
$263$	105.180	−	38.2823i	0.399923	−	0.145560i	0.534148	+	0.845391i	$0.320632\pi$
$264$	−78.7618	+	180.670i	−0.298340	+	0.684355i
$265$		−	73.0510i		−	0.275664i
$266$	−198.722	+	247.102i	−0.747075	+	0.928955i
$267$	88.4013	+	272.071i	0.331091	+	1.01899i
$268$	201.689	+	322.770i	0.752571	+	1.20437i
$269$	66.3191	−	231.282i	0.246539	−	0.859785i	−0.736507	−	0.676429i	$-0.763526\pi$
$269$	66.3191	−	231.282i	0.246539	−	0.859785i	0.983047	−	0.183355i	$-0.0586958\pi$
$270$	216.825	−	444.557i	0.803055	−	1.64651i
$271$	319.283	+	169.766i	1.17817	+	0.626442i	0.938792	−	0.344486i	$-0.111947\pi$
$271$	319.283	+	169.766i	1.17817	+	0.626442i	0.239374	+	0.970927i	$0.423058\pi$
$272$	0.706368	−	20.2277i	0.00259694	−	0.0743666i
$273$	9.89886	+	4.40726i	0.0362596	+	0.0161438i
$274$	−319.152	−	184.263i	−1.16479	−	0.672491i
$275$	184.467	−	146.446i	0.670790	−	0.532529i
$276$	−348.005	−	414.736i	−1.26089	−	1.50267i
$277$	−0.875511	−	8.32993i	−0.00316069	−	0.0300719i	0.992828	−	0.119552i	$-0.0381460\pi$
$277$	−0.875511	−	8.32993i	−0.00316069	−	0.0300719i	−0.995989	+	0.0894805i	$0.971479\pi$
$278$	36.9165	+	33.2397i	0.132793	+	0.119567i
$279$	860.919	+	672.623i	3.08573	+	2.41084i
$280$	−22.7523	−	23.5607i	−0.0812583	−	0.0841454i
$281$	−150.065	−	73.1915i	−0.534039	−	0.260468i	0.151560	−	0.988448i	$-0.451570\pi$
$281$	−150.065	−	73.1915i	−0.534039	−	0.260468i	−0.685598	+	0.727980i	$0.740459\pi$
$282$	−9.34632	−	267.644i	−0.0331430	−	0.949091i
$283$	−82.8742	+	205.121i	−0.292842	+	0.724809i	0.707003	+	0.707210i	$0.250046\pi$
$283$	−82.8742	+	205.121i	−0.292842	+	0.724809i	−0.999845	+	0.0175985i	$0.994398\pi$
$284$	258.187	+	355.363i	0.909108	+	1.25128i
$285$	169.211	−	119.336i	0.593724	−	0.418724i
$286$	8.89270	+	6.83706i	0.0310934	+	0.0239058i
$287$	−120.961	+	144.155i	−0.421466	+	0.502283i
$288$	−896.429	−	604.649i	−3.11260	−	2.09948i
$289$	252.061	−	134.023i	0.872182	−	0.463748i
$290$	42.4503	+	22.5712i	0.146380	+	0.0778319i
$291$	−231.295	−	342.909i	−0.794829	−	1.17838i
$292$	68.4968	−	651.704i	0.234578	−	2.23186i
$293$	258.702	−	232.936i	0.882941	−	0.795004i	−0.0967931	−	0.995305i	$-0.530858\pi$
$293$	258.702	−	232.936i	0.882941	−	0.795004i	0.979735	+	0.200300i	$0.0641918\pi$
$294$	−266.564	−	166.568i	−0.906681	−	0.566557i
$295$	−116.208	−	28.9740i	−0.393926	−	0.0982169i
$296$	28.1345	−	48.7304i	0.0950490	−	0.164630i
$297$	−412.176	+	862.035i	−1.38780	+	2.90247i
$298$	251.486	−	690.952i	0.843912	−	2.31863i
$299$	−5.69752	+	2.77887i	−0.0190552	+	0.00929386i
$300$	−291.245	−	547.751i	−0.970815	−	1.82584i
$301$	8.81999	+	252.571i	0.0293023	+	0.839108i
$302$	−29.1150	−	116.774i	−0.0964072	−	0.386668i
$303$	−316.134	+	435.121i	−1.04335	+	1.43604i
$304$	−93.6228	−	182.222i	−0.307970	−	0.599413i
$305$	−33.7540	−	103.884i	−0.110669	−	0.340603i
$306$	−9.48553	+	135.649i	−0.0309985	+	0.443299i
$307$	79.0180	+	217.100i	0.257388	+	0.707167i	0.999326	+	0.0366992i	$0.0116843\pi$
$307$	79.0180	+	217.100i	0.257388	+	0.707167i	−0.741939	+	0.670468i	$0.766093\pi$
$308$	215.363	+	219.573i	0.699231	+	0.712898i
$309$	201.812	−	1144.53i	0.653112	−	3.70398i
$310$	−248.145	+	71.1545i	−0.800469	+	0.229531i
$311$	285.361	−	316.925i	0.917559	−	1.01905i	−0.0821888	−	0.996617i	$-0.526191\pi$
$311$	285.361	−	316.925i	0.917559	−	1.01905i	0.999748	−	0.0224362i	$-0.00714227\pi$
$312$	4.51701	−	4.06713i	0.0144776	−	0.0130357i
$313$	−526.191	+	36.7949i	−1.68112	+	0.117555i	−0.878126	−	0.478430i	$-0.841206\pi$
$313$	−526.191	+	36.7949i	−1.68112	+	0.117555i	−0.802996	+	0.595985i	$0.796762\pi$
$314$	34.0261	+	486.596i	0.108364	+	1.54967i
$315$	−169.585	−	188.343i	−0.538364	−	0.597914i
$316$	−468.746	−	422.061i	−1.48337	−	1.33564i
$317$	−116.423	−	406.017i	−0.367267	−	1.28081i	−0.900505	−	0.434846i	$-0.856803\pi$
$317$	−116.423	−	406.017i	−0.367267	−	1.28081i	0.533238	−	0.845965i	$-0.320975\pi$
$318$	656.803	+	115.812i	2.06542	+	0.364189i
$319$	−82.3430	−	42.9646i	−0.258128	−	0.134685i
$320$	163.312	−	59.4408i	0.510351	−	0.185752i
$321$	769.067	+	53.7784i	2.39585	+	0.167534i
$322$	−296.597	+	96.3702i	−0.921108	+	0.299286i
$323$	−19.3238	+	29.9771i	−0.0598260	+	0.0928084i
$324$	1152.42	+	837.283i	3.55685	+	2.58421i
$325$	−7.04791	+	1.75724i	−0.0216859	+	0.00540690i
$326$	284.432	−	9.93257i	0.872489	−	0.0304680i
$327$	−863.633	+	459.202i	−2.64108	+	1.40429i
$328$	46.2744	+	94.8766i	0.141080	+	0.289258i
$329$	−80.7906	−	29.4054i	−0.245564	−	0.0893781i
$330$	−171.642	−	316.844i	−0.520129	−	0.960134i
$331$	29.0176	+	16.7533i	0.0876666	+	0.0506143i	0.543192	−	0.839608i	$-0.317215\pi$
$331$	29.0176	+	16.7533i	0.0876666	+	0.0506143i	−0.455526	+	0.890223i	$0.650549\pi$
$332$	−132.989	+	533.390i	−0.400569	+	1.60660i
$333$	230.728	−	369.242i	0.692877	−	1.10884i
$334$	60.4651	+	67.1533i	0.181033	+	0.201058i
$335$	−142.375	−	14.9642i	−0.425000	−	0.0446693i
$336$	−285.524	+	192.588i	−0.849773	+	0.573179i
$337$	113.117	−	212.743i	0.335660	−	0.631284i	−0.656771	−	0.754090i	$-0.728078\pi$
$337$	113.117	−	212.743i	0.335660	−	0.631284i	0.992431	+	0.122806i	$0.0391893\pi$
$338$	238.336	+	448.245i	0.705136	+	1.32617i
$339$	283.013	−	419.584i	0.834847	−	1.23771i
$340$	−13.7176	−	11.5104i	−0.0403458	−	0.0338541i
$341$	478.289	−	141.181i	1.40261	−	0.414020i
$342$	585.886	+	1245.44i	1.71312	+	3.64164i
$343$	−301.729	+	219.219i	−0.879675	+	0.639122i
$344$	131.443	+	53.1064i	0.382101	+	0.154379i
$345$	203.517	−	7.10696i	0.589903	−	0.0205999i
$346$	148.542	−	304.556i	0.429311	−	0.880218i
$347$	141.985	−	137.113i	0.409178	−	0.395138i	−0.461382	−	0.887202i	$-0.652646\pi$
$347$	141.985	−	137.113i	0.409178	−	0.395138i	0.870559	+	0.492063i	$0.163757\pi$
$348$	−150.611	+	192.773i	−0.432791	+	0.553947i
$349$	−9.88897	+	10.9828i	−0.0283351	+	0.0314694i	−0.757146	−	0.653246i	$-0.773407\pi$
$349$	−9.88897	+	10.9828i	−0.0283351	+	0.0314694i	0.728811	+	0.684715i	$0.240073\pi$
$350$	−355.390	+	37.3530i	−1.01540	+	0.106723i
$351$	22.5734	−	18.9414i	0.0643118	−	0.0539640i
$352$	−462.471	+	172.410i	−1.31384	+	0.489801i
$353$	−93.1847	+	161.401i	−0.263979	+	0.457225i	−0.967296	−	0.253651i	$-0.918368\pi$
$353$	−93.1847	+	161.401i	−0.263979	+	0.457225i	0.703316	+	0.710877i	$0.251702\pi$
$354$	444.737	−	998.896i	1.25632	−	2.82174i
$355$	−165.119	−	5.76608i	−0.465124	−	0.0162425i
$356$	117.563	−	221.104i	0.330233	−	0.621079i
$357$	53.8901	+	26.2839i	0.150953	+	0.0736245i
$358$	−593.574	−	170.205i	−1.65803	−	0.475432i
$359$	−440.736	+	275.403i	−1.22768	+	0.767138i	−0.979474	−	0.201569i	$-0.935396\pi$
$359$	−440.736	+	275.403i	−1.22768	+	0.767138i	−0.248204	+	0.968708i	$0.579840\pi$
$360$	−135.209	+	43.9320i	−0.375580	+	0.122033i
$361$	−22.7500	+	360.282i	−0.0630193	+	0.998012i
$362$	−255.841			−0.706743
$363$	336.332	+	609.490i	0.926534	+	1.67903i
$364$	−3.24408	−	8.91304i	−0.00891231	−	0.0244864i
$365$	177.303	+	171.220i	0.485762	+	0.469095i
$366$	987.535	−	138.789i	2.69818	−	0.379205i
$367$	−274.850	+	351.791i	−0.748909	+	0.958560i	−0.999956	−	0.00941519i	$-0.997003\pi$
$367$	−274.850	+	351.791i	−0.748909	+	0.958560i	0.251047	+	0.967975i	$0.419225\pi$
$368$	21.0607	−	200.379i	0.0572302	−	0.544509i
$369$	332.226	+	746.192i	0.900342	+	2.02220i
$370$	38.5390	+	95.3874i	0.104159	+	0.257804i
$371$	113.461	−	181.576i	0.305825	−	0.489422i
$372$	−137.299	−	1306.31i	−0.369084	−	3.51160i
$373$	−39.9085	+	23.0412i	−0.106993	+	0.0617726i	−0.552542	−	0.833485i	$-0.686342\pi$
$373$	−39.9085	+	23.0412i	−0.106993	+	0.0617726i	0.445549	+	0.895258i	$0.353009\pi$
$374$	47.8568	+	39.5266i	0.127959	+	0.105686i
$375$	498.106	+	87.8295i	1.32828	+	0.234212i
$376$	−33.5018	+	34.6922i	−0.0891006	+	0.0922664i
$377$	1.76346	+	2.25712i	0.00467760	+	0.00598706i
$378$	1229.42	−	768.224i	3.25242	−	2.03234i
$379$	228.534	−	314.550i	0.602991	−	0.829946i	−0.392987	−	0.919544i	$-0.628558\pi$
$379$	228.534	−	314.550i	0.602991	−	0.829946i	0.995978	+	0.0895979i	$0.0285582\pi$
$380$	−178.037	−	33.9834i	−0.468517	−	0.0894301i
$381$	−108.406	+	333.640i	−0.284531	+	0.875695i
$382$	489.435	+	197.745i	1.28124	+	0.517656i
$383$	82.7753	+	55.8327i	0.216124	+	0.145777i	0.662484	−	0.749076i	$-0.269502\pi$
$383$	82.7753	+	55.8327i	0.216124	+	0.145777i	−0.446360	+	0.894853i	$0.647280\pi$
$384$	96.2226	+	545.705i	0.250580	+	1.42111i
$385$	−114.954	+	12.9866i	−0.298581	+	0.0337314i
$386$	703.886	+	256.193i	1.82354	+	0.663714i
$387$	1002.13	+	446.176i	2.58948	+	1.15291i
$388$	−75.2782	+	354.156i	−0.194016	+	0.912773i
$389$	−111.710	−	276.492i	−0.287173	−	0.710777i	−0.999956	−	0.00939292i	$-0.997010\pi$
$389$	−111.710	−	276.492i	−0.287173	−	0.710777i	0.712783	−	0.701384i	$-0.247434\pi$
$390$	0.775207	+	11.0860i	0.00198771	+	0.0284256i
$391$	−32.0442	+	14.2670i	−0.0819545	+	0.0364885i
$392$	11.7689	+	55.3684i	0.0300227	+	0.141246i
$393$	−736.974	−	25.7357i	−1.87525	−	0.0654853i
$394$	−103.846	+	50.6493i	−0.263570	+	0.128552i
$395$	233.648	−	41.1985i	0.591514	−	0.104300i
$396$	1266.39	−	422.391i	3.19796	−	1.06664i
$397$	−530.208	−	444.897i	−1.33554	−	1.12065i	−0.982749	−	0.184943i	$-0.940790\pi$
$397$	−530.208	−	444.897i	−1.33554	−	1.12065i	−0.352786	−	0.935704i	$-0.614766\pi$
$398$	−256.188	−	352.612i	−0.643688	−	0.885961i
$399$	605.942	−	33.8078i	1.51865	−	0.0847312i
$400$	71.3430	−	219.571i	0.178358	−	0.548928i
$401$	−711.156	+	177.311i	−1.77346	+	0.442172i	−0.984948	−	0.172853i	$-0.944702\pi$
$401$	−711.156	+	177.311i	−1.77346	+	0.442172i	−0.788508	+	0.615025i	$0.789146\pi$
$402$	360.259	−	1256.37i	0.896167	−	3.12531i
$403$	−15.2298	−	2.14041i	−0.0377910	−	0.00531118i
$404$	466.220	−	65.5230i	1.15401	−	0.162186i
$405$	−515.041	+	147.686i	−1.27171	+	0.364656i
$406$	70.4575	+	122.036i	0.173541	+	0.300581i
$407$	−75.8810	−	183.687i	−0.186440	−	0.451319i
$408$	25.7647	−	21.6191i	0.0631487	−	0.0529881i
$409$	−224.472	−	55.9672i	−0.548832	−	0.136839i	−0.0423709	−	0.999102i	$-0.513491\pi$
$409$	−224.472	−	55.9672i	−0.548832	−	0.136839i	−0.506461	+	0.862263i	$0.669047\pi$
$410$	−188.781	−	40.1267i	−0.460442	−	0.0978701i
$411$	146.643	+	689.901i	0.356796	+	1.67859i
$412$	−843.404	+	568.883i	−2.04710	+	1.38078i
$413$	−243.846	−	252.510i	−0.590426	−	0.611404i
$414$	−188.391	+	1340.47i	−0.455050	+	3.23785i
$415$	−127.300	−	162.937i	−0.306747	−	0.392619i
$416$	15.1843	+	1.06179i	0.0365006	+	0.00255237i
$417$		−	95.0741i		−	0.227995i
$418$	618.010	+	112.992i	1.47849	+	0.270316i
$419$	125.926			0.300539			0.150269	−	0.988645i	$-0.451986\pi$
$419$	125.926			0.300539			0.150269	+	0.988645i	$0.451986\pi$
$420$	−21.2551	+	303.962i	−0.0506074	+	0.723720i
$421$	−413.876	+	323.355i	−0.983078	+	0.768065i	−0.972744	−	0.231882i	$-0.925512\pi$
$421$	−413.876	+	323.355i	−0.983078	+	0.768065i	−0.0103344	+	0.999947i	$0.503290\pi$
$422$	−261.619	−	36.7681i	−0.619950	−	0.0871283i
$423$	−268.444	+	259.233i	−0.634619	+	0.612844i
$424$	−67.1616	−	99.5712i	−0.158400	−	0.234838i
$425$	−39.3146	+	8.35658i	−0.0925050	+	0.0196626i
$426$	313.616	−	1475.45i	0.736187	−	3.46349i
$427$	77.4513	−	310.640i	0.181385	−	0.727495i
$428$	−433.787	−	516.967i	−1.01352	−	1.20787i
$429$	−1.66404	−	21.4038i	−0.00387887	−	0.0498924i
$430$	−224.470	+	129.598i	−0.522023	+	0.301390i
$431$	−151.902	−	529.746i	−0.352442	−	1.22911i	−0.915373	−	0.402606i	$-0.868104\pi$
$431$	−151.902	−	529.746i	−0.352442	−	1.22911i	0.562932	−	0.826504i	$-0.309673\pi$
$432$	130.350	+	927.490i	0.301737	+	2.14697i
$433$	60.6670	−	431.668i	0.140109	−	0.996924i	−0.785613	−	0.618718i	$-0.787652\pi$
$433$	60.6670	−	431.668i	0.140109	−	0.996924i	0.925721	−	0.378206i	$-0.123459\pi$
$434$	−727.306	−	208.552i	−1.67582	−	0.480534i
$435$	−22.2606	−	89.2824i	−0.0511738	−	0.205247i
$436$	814.302	+	264.583i	1.86767	+	0.606842i
$437$	−212.710	+	284.267i	−0.486750	+	0.650496i
$438$	−1820.53	+	1322.69i	−4.15646	+	3.01984i
$439$	300.942	−	358.649i	0.685517	−	0.816967i	−0.305289	−	0.952260i	$-0.598753\pi$
$439$	300.942	−	358.649i	0.685517	−	0.816967i	0.990806	+	0.135293i	$0.0431975\pi$
$440$	−19.5726	+	61.8712i	−0.0444832	+	0.140616i
$441$	76.0587	+	431.351i	0.172469	+	0.978119i
$442$	−0.839131	−	1.72047i	−0.00189849	−	0.00389247i
$443$	14.9818	−	429.022i	0.0338189	−	0.968446i	−0.857339	−	0.514752i	$-0.827884\pi$
$443$	14.9818	−	429.022i	0.0338189	−	0.968446i	0.891158	−	0.453694i	$-0.149894\pi$
$444$	−512.033	+	108.836i	−1.15323	+	0.245126i
$445$	38.3108	+	86.0476i	0.0860918	+	0.193365i
$446$	10.0352	−	0.701729i	0.0225004	−	0.00157338i
$447$	−1304.80	+	527.172i	−2.91901	+	1.17936i
$448$	498.251	+	105.907i	1.11217	+	0.236399i
$449$	−97.3687	+	218.694i	−0.216857	+	0.487068i	−0.988915	−	0.148484i	$-0.952561\pi$
$449$	−97.3687	+	218.694i	−0.216857	+	0.487068i	0.772058	+	0.635552i	$0.219227\pi$
$450$	−530.501	+	1457.54i	−1.17889	+	3.23898i
$451$	365.283	+	74.6796i	0.809941	+	0.165587i
$452$	−436.297	+	76.9309i	−0.965258	+	0.170201i
$453$	−128.801	+	190.955i	−0.284328	+	0.421534i
$454$	145.248	−	359.501i	0.319929	−	0.791853i
$455$	3.39307	+	1.10248i	0.00745730	+	0.00242302i
$456$	120.926	−	318.229i	0.265188	−	0.697871i
$457$	354.253	+	257.380i	0.775170	+	0.563194i	0.903525	−	0.428534i	$-0.140970\pi$
$457$	354.253	+	257.380i	0.775170	+	0.563194i	−0.128356	+	0.991728i	$0.540970\pi$
$458$	544.822	+	871.897i	1.18957	+	1.90370i
$459$	128.490	−	100.387i	0.279935	−	0.218709i
$460$	−128.228	−	123.829i	−0.278757	−	0.269193i
$461$	39.4495	−	223.729i	0.0855738	−	0.485313i	−0.911658	−	0.410951i	$-0.865197\pi$
$461$	39.4495	−	223.729i	0.0855738	−	0.485313i	0.997231	−	0.0743622i	$-0.0236921\pi$
$462$	65.4803	−	1054.14i	0.141732	−	2.28169i
$463$	−81.2816	−	140.784i	−0.175554	−	0.304069i	0.764799	−	0.644269i	$-0.222838\pi$
$463$	−81.2816	−	140.784i	−0.175554	−	0.304069i	−0.940353	+	0.340200i	$0.889505\pi$
$464$	−90.5420	+	9.51635i	−0.195134	+	0.0205094i
$465$	418.987	+	261.812i	0.901047	+	0.563036i
$466$	−1040.78	+	420.504i	−2.23344	+	0.902370i
$467$	359.136	−	159.898i	0.769027	−	0.342393i	0.0155605	−	0.999879i	$-0.495047\pi$
$467$	359.136	−	159.898i	0.769027	−	0.342393i	0.753467	+	0.657486i	$0.228380\pi$
$468$	−40.9448	−	4.30347i	−0.0874888	−	0.00919545i
$469$	−330.646	−	258.329i	−0.705001	−	0.550807i
$470$	−12.2718	−	87.3185i	−0.0261102	−	0.185784i
$471$	648.507	−	671.549i	1.37687	−	1.42579i
$472$	−185.034	+	67.3469i	−0.392022	+	0.142684i
$473$	431.675	−	253.724i	0.912633	−	0.536413i
$474$			2166.05i			4.56972i
$475$	−306.132	+	267.936i	−0.644488	+	0.564076i
$476$	−16.2187	−	49.9161i	−0.0340729	−	0.104866i
$477$	−492.482	−	788.137i	−1.03246	−	1.65228i
$478$	−322.802	+	1125.74i	−0.675317	+	2.35511i
$479$	−26.2813	+	53.8847i	−0.0548671	+	0.112494i	−0.924466	−	0.381265i	$-0.875489\pi$
$479$	−26.2813	+	53.8847i	−0.0548671	+	0.112494i	0.869599	+	0.493759i	$0.164378\pi$
$480$	−431.744	−	229.562i	−0.899467	−	0.478255i
$481$	−0.213905	+	6.12544i	−0.000444709	+	0.0127348i
$482$	−20.7082	−	9.21987i	−0.0429630	−	0.0191284i
$483$	516.900	+	298.432i	1.07019	+	0.617872i
$484$	179.268	−	582.396i	0.370389	−	1.20330i
$485$	−87.5395	−	104.326i	−0.180494	−	0.215104i
$486$	−265.674	−	2527.72i	−0.546655	−	5.20108i
$487$	−317.536	−	285.910i	−0.652024	−	0.587085i	0.275294	−	0.961360i	$-0.411225\pi$
$487$	−317.536	−	285.910i	−0.652024	−	0.587085i	−0.927318	+	0.374275i	$0.877891\pi$
$488$	−141.517	−	110.565i	−0.289993	−	0.226568i
$489$	−378.381	−	391.825i	−0.773785	−	0.801278i
$490$	−93.0194	−	45.3686i	−0.189835	−	0.0925889i
$491$	8.95112	+	256.327i	0.0182304	+	0.522050i	0.973816	+	0.227337i	$0.0730019\pi$
$491$	8.95112	+	256.327i	0.0182304	+	0.522050i	−0.955586	+	0.294713i	$0.904776\pi$
$492$	367.874	−	910.520i	0.747711	−	1.85065i
$493$	9.31612	+	12.8225i	0.0188968	+	0.0260092i
$494$	−15.9086	−	11.0595i	−0.0322037	−	0.0223876i
$495$	−168.066	+	473.174i	−0.339528	+	0.955907i
$496$	314.211	−	374.462i	0.633490	−	0.754964i
$497$	−401.464	−	270.791i	−0.807775	−	0.544851i
$498$	1666.78	−	886.245i	3.34696	−	1.77961i
$499$	866.224	+	460.579i	1.73592	+	0.923005i	0.954094	+	0.299508i	$0.0968227\pi$
$499$	866.224	+	460.579i	1.73592	+	0.923005i	0.781826	+	0.623496i	$0.214288\pi$
$500$	−247.581	−	367.054i	−0.495162	−	0.734107i
$501$	18.0777	−	171.998i	0.0360833	−	0.343309i
$502$	−331.653	+	298.622i	−0.660664	+	0.594864i
$503$	142.292	+	88.9141i	0.282887	+	0.176768i	0.663940	−	0.747786i	$-0.268883\pi$
$503$	142.292	+	88.9141i	0.282887	+	0.176768i	−0.381053	+	0.924553i	$0.624438\pi$
$504$	−404.309	−	100.806i	−0.802200	−	0.200011i
$505$	−88.5431	+	153.361i	−0.175333	+	0.303686i
$506$	447.791	+	425.748i	0.884962	+	0.841398i
$507$	332.313	−	913.022i	0.655450	−	1.80083i
$508$	276.005	−	134.617i	0.543317	−	0.264993i
$509$	−256.063	−	481.585i	−0.503072	−	0.946140i	−0.997057	−	0.0766697i	$-0.975571\pi$
$509$	−256.063	−	481.585i	−0.503072	−	0.946140i	0.493985	−	0.869470i	$-0.335540\pi$
$510$	2.14608	+	61.4557i	0.00420800	+	0.120501i
$511$	174.771	+	700.967i	0.342017	+	1.37176i
$512$	−363.323	+	500.071i	−0.709614	+	0.976701i
$513$	639.738	−	1521.39i	1.24705	−	2.96567i
$514$	−191.451	−	589.225i	−0.372472	−	1.14635i
$515$	26.6927	−	381.724i	0.0518305	−	0.741211i
$516$	−451.074	−	1239.31i	−0.874174	−	2.40177i
$517$	25.0178	+	168.494i	0.0483904	+	0.325908i
$518$	−52.3608	+	296.953i	−0.101083	+	0.573268i
$519$	−623.395	+	178.756i	−1.20115	+	0.344423i
$520$	1.33912	−	1.48724i	0.00257523	−	0.00286009i
$521$	−311.735	+	280.688i	−0.598340	+	0.538748i	−0.911684	−	0.410892i	$-0.865217\pi$
$521$	−311.735	+	280.688i	−0.598340	+	0.538748i	0.313344	+	0.949640i	$0.398551\pi$
$522$	610.158	−	42.6664i	1.16888	−	0.0817363i
$523$	−12.5077	−	178.869i	−0.0239154	−	0.342006i	−0.994756	−	0.102279i	$-0.967387\pi$
$523$	−12.5077	−	178.869i	−0.0239154	−	0.342006i	0.970840	−	0.239727i	$-0.0770579\pi$
$524$	431.930	+	479.707i	0.824294	+	0.915471i
$525$	508.253	+	457.633i	0.968100	+	0.871681i
$526$	92.7414	+	323.428i	0.176314	+	0.614881i
$527$	−83.8081	−	14.7776i	−0.159029	−	0.0280410i
$528$	604.960	+	315.654i	1.14576	+	0.597829i
$529$	168.978	−	61.5029i	0.319429	−	0.116263i
$530$	219.056	+	15.3179i	0.413314	+	0.0289017i
$531$	−1449.09	+	470.837i	−2.72898	+	0.886698i
$532$	−389.746	−	360.992i	−0.732605	−	0.678556i
$533$	−9.30227	−	6.75850i	−0.0174527	−	0.0126801i
$534$	−834.392	+	208.037i	−1.56253	+	0.389583i
$535$	253.683	−	8.85879i	0.474173	−	0.0165585i
$536$	−207.820	+	110.500i	−0.387724	+	0.206157i
$537$	518.073	+	1062.21i	0.964754	+	1.97804i
$538$	679.634	+	247.367i	1.26326	+	0.459789i
$539$	180.373	+	86.2441i	0.334643	+	0.160008i
$540$	717.626	+	414.322i	1.32894	+	0.767263i
$541$	52.8507	−	211.973i	0.0976908	−	0.391817i	−0.901467	−	0.432848i	$-0.857509\pi$
$541$	52.8507	−	211.973i	0.0976908	−	0.391817i	0.999158	+	0.0410312i	$0.0130643\pi$
$542$	−576.023	+	921.829i	−1.06277	+	1.70079i
$543$	327.639	+	363.880i	0.603388	+	0.670130i
$544$	83.7646	+	8.80402i	0.153979	+	0.0161839i
$545$	−266.993	+	180.089i	−0.489896	+	0.330439i
$546$	−15.2916	+	28.7594i	−0.0280066	+	0.0526728i
$547$	96.4732	+	181.440i	0.176368	+	0.331700i	0.955415	−	0.295265i	$-0.0954080\pi$
$547$	96.4732	+	181.440i	0.176368	+	0.331700i	−0.779048	+	0.626965i	$0.784297\pi$
$548$	345.247	−	511.849i	0.630012	−	0.934032i
$549$	−1064.51	−	893.233i	−1.93901	−	1.62702i
$550$	400.463	+	583.866i	0.728114	+	1.06157i
$551$	145.623	+	67.3076i	0.264289	+	0.122155i
$552$	270.867	−	196.796i	0.490700	−	0.356515i
$553$	644.745	+	260.494i	1.16590	+	0.471056i
$554$	25.1624	−	0.878690i	0.0454195	−	0.00158608i
$555$	86.3143	−	176.970i	0.155521	−	0.318866i
$556$	−59.8662	+	57.8121i	−0.107673	+	0.103979i
$557$	24.9738	−	31.9650i	0.0448362	−	0.0573877i	−0.765070	−	0.643947i	$-0.777296\pi$
$557$	24.9738	−	31.9650i	0.0448362	−	0.0573877i	0.809906	+	0.586559i	$0.199518\pi$
$558$	−2197.51	+	2440.58i	−3.93818	+	4.37380i
$559$	−15.3574	+	1.61413i	−0.0274730	+	0.00288753i
$560$	−86.8668	+	72.8899i	−0.155119	+	0.130161i
$561$	−5.06884	−	118.686i	−0.00903537	−	0.211561i
$562$	250.945	−	434.649i	0.446521	−	0.773397i
$563$	−75.1351	+	168.756i	−0.133455	+	0.299745i	−0.967895	−	0.251353i	$-0.919124\pi$
$563$	−75.1351	+	168.756i	−0.133455	+	0.299745i	0.834440	+	0.551098i	$0.185791\pi$
$564$	448.392	+	15.6582i	0.795021	+	0.0277627i
$565$	78.2324	−	147.134i	0.138464	−	0.260414i
$566$	−597.714	−	291.525i	−1.05603	−	0.515061i
$567$	−1509.57	−	432.862i	−2.66238	−	0.763425i
$568$	−230.364	+	143.948i	−0.405571	+	0.253429i
$569$	386.329	−	125.526i	0.678961	−	0.220608i	0.0508208	−	0.998708i	$-0.483816\pi$
$569$	386.329	−	125.526i	0.678961	−	0.220608i	0.628141	+	0.778100i	$0.283816\pi$
$570$	322.370	+	532.434i	0.565561	+	0.934094i
$571$	160.928			0.281835			0.140918	−	0.990021i	$-0.454995\pi$
$571$	160.928			0.281835			0.140918	+	0.990021i	$0.454995\pi$
$572$	−12.4657	+	14.0629i	−0.0217932	+	0.0245855i
$573$	−345.539	−	949.360i	−0.603034	−	1.65682i
$574$	−406.912	−	392.950i	−0.708905	−	0.684582i
$575$	−396.214	+	55.6842i	−0.689068	+	0.0968421i
$576$	1361.22	−	1742.29i	2.36324	−	3.02481i
$577$	−30.4873	+	290.068i	−0.0528377	+	0.502717i	0.935814	+	0.352493i	$0.114666\pi$
$577$	−30.4873	+	290.068i	−0.0528377	+	0.502717i	−0.988652	+	0.150224i	$0.952001\pi$
$578$	349.038	+	783.952i	0.603872	+	1.35632i
$579$	−537.041	−	1329.22i	−0.927531	−	2.29572i
$580$	−42.6832	+	68.3073i	−0.0735917	+	0.117771i
$581$	−63.3480	−	602.716i	−0.109033	−	1.03738i
$582$	1076.77	−	621.676i	1.85013	−	1.06817i
$583$	−423.395	−	26.3001i	−0.726235	−	0.0451117i
$584$	399.087	+	70.3697i	0.683367	+	0.120496i
$585$	10.7573	−	11.1395i	0.0183885	−	0.0190418i
$586$	644.254	+	824.608i	1.09941	+	1.40718i
$587$	−171.972	+	107.460i	−0.292968	+	0.183067i	−0.668438	−	0.743768i	$-0.733037\pi$
$587$	−171.972	+	107.460i	−0.292968	+	0.183067i	0.375470	+	0.926834i	$0.377481\pi$
$588$	309.529	−	426.030i	0.526409	−	0.724540i
$589$	−813.494	+	283.184i	−1.38114	+	0.480788i
$590$	111.251	−	342.396i	0.188561	−	0.580332i
$591$	205.028	+	82.8366i	0.346917	+	0.140163i
$592$	−161.506	−	108.937i	−0.272814	−	0.184016i
$593$	124.129	+	703.973i	0.209324	+	1.18714i	0.890488	+	0.455007i	$0.150363\pi$
$593$	124.129	+	703.973i	0.209324	+	1.18714i	−0.681164	+	0.732131i	$0.738526\pi$
$594$	−2498.54	−	1416.74i	−4.20629	−	2.38509i
$595$	18.5510	+	6.75200i	0.0311781	+	0.0113479i
$596$	1125.36	+	501.044i	1.88819	+	0.840678i
$597$	−173.434	+	815.943i	−0.290509	+	1.36674i
$598$	−7.13823	−	17.6677i	−0.0119368	−	0.0295447i
$599$	19.5877	+	280.117i	0.0327006	+	0.467640i	0.986125	+	0.166007i	$0.0530874\pi$
$599$	19.5877	+	280.117i	0.0327006	+	0.467640i	−0.953424	+	0.301633i	$0.902468\pi$
$600$	350.476	−	156.042i	0.584127	−	0.260070i
$601$	−176.752	−	831.555i	−0.294097	−	1.38362i	−0.838549	−	0.544826i	$-0.816596\pi$
$601$	−176.752	−	831.555i	−0.294097	−	1.38362i	0.544452	−	0.838792i	$-0.316738\pi$
$602$	−759.230	−	26.5129i	−1.26118	−	0.0440414i
$603$	−1636.95	+	798.392i	−2.71467	+	1.32403i
$604$	198.561	−	35.0116i	0.328743	−	0.0579663i
$605$	131.109	+	188.003i	0.216708	+	0.310748i
$606$	−1238.50	−	1039.23i	−2.04373	−	1.71489i
$607$	−330.660	−	455.115i	−0.544745	−	0.749777i	0.444542	−	0.895758i	$-0.353366\pi$
$607$	−330.660	−	455.115i	−0.544745	−	0.749777i	−0.989287	+	0.145980i	$0.953366\pi$
$608$	783.618	−	335.753i	1.28885	−	0.552225i
$609$	83.3403	−	256.495i	0.136848	−	0.421174i
$610$	318.593	−	79.4341i	0.522283	−	0.130220i
$611$	1.44800	−	5.04977i	0.00236988	−	0.00826476i
$612$	−225.596	−	31.7054i	−0.368620	−	0.0518062i
$613$	−1013.31	+	142.411i	−1.65303	+	0.232318i	−0.903172	−	0.429279i	$-0.858768\pi$
$613$	−1013.31	+	142.411i	−1.65303	+	0.232318i	−0.749859	+	0.661598i	$0.769879\pi$
$614$	−667.583	+	191.426i	−1.08727	+	0.311769i
$615$	184.689	+	319.890i	0.300307	+	0.520147i
$616$	−144.747	+	123.387i	−0.234978	+	0.200304i
$617$	505.960	−	424.551i	0.820032	−	0.688089i	−0.132947	−	0.991123i	$-0.542444\pi$
$617$	505.960	−	424.551i	0.820032	−	0.688089i	0.952980	+	0.303034i	$0.0979997\pi$
$618$	3389.77	+	845.163i	5.48506	+	1.36758i
$619$	472.984	+	100.536i	0.764110	+	0.162417i	0.573451	−	0.819240i	$-0.305604\pi$
$619$	472.984	+	100.536i	0.764110	+	0.162417i	0.190659	+	0.981656i	$0.438938\pi$
$620$	−89.9174	−	423.028i	−0.145028	−	0.682304i
$621$	1345.67	−	907.666i	2.16694	−	1.46162i
$622$	890.521	+	922.162i	1.43171	+	1.48258i
$623$	−38.4215	+	273.383i	−0.0616718	+	0.438818i
$624$	−12.9558	−	16.5827i	−0.0207625	−	0.0265748i
$625$	−367.864	−	25.7235i	−0.588582	−	0.0411577i
$626$		−	1585.59i		−	2.53290i
$627$	−630.740	−	1023.69i	−1.00596	−	1.63268i
$628$	−817.201			−1.30128
$629$	−2.36581	+	33.8327i	−0.00376122	+	0.0537880i
$630$	600.340	−	469.037i	0.952921	−	0.744504i
$631$	902.521	+	126.841i	1.43030	+	0.201016i	0.811418	−	0.584466i	$-0.198696\pi$
$631$	902.521	+	126.841i	1.43030	+	0.201016i	0.618884	+	0.785482i	$0.287585\pi$
$632$	280.594	−	270.966i	0.443978	−	0.428744i
$633$	282.744	+	419.185i	0.446673	+	0.662220i
$634$	1241.93	−	263.980i	1.95888	−	0.416372i
$635$	−24.0150	+	112.982i	−0.0378189	+	0.177924i
$636$	−270.308	+	1084.15i	−0.425013	+	1.70463i
$637$	−3.96330	−	4.72328i	−0.00622183	−	0.00741488i
$638$	146.104	−	237.911i	0.229002	−	0.372901i
$639$	−1820.32	+	1050.96i	−2.84870	+	1.64470i
$640$	50.2894	+	175.380i	0.0785773	+	0.274031i
$641$	−57.4146	−	408.526i	−0.0895704	−	0.637327i	−0.982380	−	0.186893i	$-0.940158\pi$
$641$	−57.4146	−	408.526i	−0.0895704	−	0.637327i	0.892810	−	0.450434i	$-0.148731\pi$
$642$	−322.528	+	2294.91i	−0.502381	+	3.57462i
$643$	−474.541	−	136.072i	−0.738010	−	0.211621i	−0.114486	−	0.993425i	$-0.536522\pi$
$643$	−474.541	−	136.072i	−0.738010	−	0.211621i	−0.623524	+	0.781804i	$0.714300\pi$
$644$	−126.397	−	506.950i	−0.196268	−	0.787189i
$645$	471.790	+	153.294i	0.731458	+	0.237665i
$646$	−85.8398	−	64.2317i	−0.132879	−	0.0994299i
$647$	713.727	−	518.553i	1.10313	−	0.801472i	0.121564	−	0.992584i	$-0.461209\pi$
$647$	713.727	−	518.553i	1.10313	−	0.801472i	0.981568	+	0.191111i	$0.0612091\pi$
$648$	−566.240	+	674.819i	−0.873828	+	1.04139i
$649$	−209.768	+	663.098i	−0.323217	+	1.02172i
$650$	−3.79154	−	21.5029i	−0.00583314	−	0.0330814i
$651$	634.794	+	1301.52i	0.975106	+	1.99926i
$652$	−16.6403	+	476.517i	−0.0255220	+	0.730854i
$653$	−524.873	+	111.565i	−0.803787	+	0.170850i	−0.591445	−	0.806345i	$-0.701442\pi$
$653$	−524.873	+	111.565i	−0.803787	+	0.170850i	−0.212342	+	0.977195i	$0.568109\pi$
$654$	−1195.91	−	2686.05i	−1.82860	−	4.10711i
$655$	−242.209	+	16.9369i	−0.369784	+	0.0258578i
$656$	338.852	−	136.905i	0.516543	−	0.208697i
$657$	3067.20	+	651.953i	4.66849	+	0.992318i
$658$	105.118	−	236.099i	0.159754	−	0.358814i
$659$	42.3379	−	116.323i	0.0642457	−	0.176514i	−0.903416	−	0.428765i	$-0.858949\pi$
$659$	42.3379	−	116.323i	0.0642457	−	0.176514i	0.967662	+	0.252251i	$0.0811710\pi$
$660$	549.585	−	249.829i	0.832705	−	0.378529i
$661$	−887.026	+	156.407i	−1.34195	+	0.236621i	−0.798080	−	0.602551i	$-0.794151\pi$
$661$	−887.026	+	156.407i	−1.34195	+	0.236621i	−0.543865	+	0.839172i	$0.683040\pi$
$662$	−56.3225	+	83.5016i	−0.0850794	+	0.126135i
$663$	−1.37239	+	3.39679i	−0.00206998	+	0.00512337i
$664$	−323.316	−	105.052i	−0.486921	−	0.158210i
$665$	197.253	−	31.9248i	0.296621	−	0.0480072i
$666$	1058.86	+	769.305i	1.58988	+	1.15511i
$667$	83.6090	+	133.802i	0.125351	+	0.200603i
$668$	−119.296	+	93.2044i	−0.178587	+	0.139528i
$669$	−13.8495	−	13.3743i	−0.0207018	−	0.0199915i
$670$	74.7272	−	423.799i	0.111533	−	0.632536i
$671$	−614.252	+	158.233i	−0.915428	+	0.235817i
$672$	−716.593	−	1241.18i	−1.06636	−	1.84699i
$673$	−1254.08	+	131.809i	−1.86342	+	0.195853i	−0.968268	−	0.249916i	$-0.919597\pi$
$673$	−1254.08	+	131.809i	−1.86342	+	0.195853i	−0.895148	+	0.445769i	$0.852930\pi$
$674$	614.228	+	383.812i	0.911317	+	0.569454i
$675$	1724.49	−	696.739i	2.55480	−	1.03221i
$676$	−776.982	+	345.935i	−1.14938	+	0.511738i
$677$	−620.529	−	65.2203i	−0.916587	−	0.0963372i	−0.365525	−	0.930802i	$-0.619111\pi$
$677$	−620.529	−	65.2203i	−0.916587	−	0.0963372i	−0.551062	+	0.834464i	$0.685777\pi$
$678$	1198.85	+	936.648i	1.76822	+	1.38149i
$679$	−55.5524	−	395.276i	−0.0818151	−	0.582145i
$680$	7.69261	−	7.96594i	0.0113127	−	0.0117146i
$681$	−697.326	+	253.806i	−1.02397	+	0.372696i
$682$	323.065	+	1463.84i	0.473702	+	2.14639i
$683$			565.365i			0.827767i	0.910330	+	0.413884i	$0.135828\pi$
$683$			565.365i			0.827767i	−0.910330	+	0.413884i	$0.864172\pi$
$684$	−2149.92	+	833.614i	−3.14315	+	1.21873i
$685$	71.7624	+	220.862i	0.104763	+	0.322426i
$686$	−594.098	−	950.755i	−0.866032	−	1.38594i
$687$	542.373	−	1891.48i	0.789480	−	2.75325i
$688$	215.159	−	441.140i	0.312730	−	0.641192i
$689$	11.5512	+	6.14188i	0.0167652	+	0.00891419i
$690$	−21.3635	+	611.771i	−0.0309616	+	0.886625i
$691$	876.163	+	390.093i	1.26796	+	0.564534i	0.926830	−	0.375481i	$-0.122522\pi$
$691$	876.163	+	390.093i	1.26796	+	0.564534i	0.341134	+	0.940015i	$0.389189\pi$
$692$	491.629	+	283.842i	0.710447	+	0.410177i
$693$	−1152.67	+	915.086i	−1.66330	+	1.32047i
$694$	381.386	+	454.518i	0.549547	+	0.654924i
$695$	−3.27211	−	31.1321i	−0.00470808	−	0.0447944i
$696$	−112.426	−	101.229i	−0.161532	−	0.145444i
$697$	−50.1369	−	39.1712i	−0.0719324	−	0.0561997i
$698$	−30.8603	−	31.9568i	−0.0442125	−	0.0457834i
$699$	1930.95	+	941.786i	2.76244	+	1.34733i
$700$	−20.8935	−	598.311i	−0.0298478	−	0.854730i
$701$	47.2652	−	116.985i	0.0674254	−	0.166884i	−0.889709	−	0.456528i	$-0.849093\pi$
$701$	47.2652	−	116.985i	0.0674254	−	0.166884i	0.957134	+	0.289645i	$0.0935371\pi$
$702$	52.0657	+	71.6623i	0.0741676	+	0.102083i
$703$	146.127	+	310.629i	0.207863	+	0.441862i
$704$	−285.716	−	967.939i	−0.405846	−	1.37491i
$705$	−108.477	+	129.277i	−0.153868	+	0.183372i
$706$	−464.449	−	313.275i	−0.657860	−	0.443732i
$707$	−458.280	+	243.672i	−0.648204	+	0.344656i
$708$	1617.43	+	860.004i	2.28451	+	1.21469i
$709$	786.806	+	1166.49i	1.10974	+	1.64526i	0.657755	+	0.753232i	$0.271506\pi$
$709$	786.806	+	1166.49i	1.10974	+	1.64526i	0.451985	+	0.892026i	$0.350716\pi$
$710$	51.9141	−	493.930i	0.0731185	−	0.695676i
$711$	2243.05	−	2019.65i	3.15478	−	2.84058i
$712$	131.329	+	82.0637i	0.184451	+	0.115258i
$713$	−821.988	−	204.945i	−1.15286	−	0.287440i
$714$	−90.1173	+	156.088i	−0.126215	+	0.218610i
$715$	−1.28153	−	6.95143i	−0.00179236	−	0.00972228i
$716$	353.823	−	972.120i	0.494166	−	1.35771i
$717$	2014.53	−	982.551i	2.80966	−	1.37036i
$718$	−733.427	−	1379.38i	−1.02149	−	1.92114i
$719$	−28.0102	−	802.108i	−0.0389572	−	1.11559i	−0.848724	−	0.528837i	$-0.822628\pi$
$719$	−28.0102	−	802.108i	−0.0389572	−	1.11559i	0.809766	−	0.586752i	$-0.199594\pi$
$720$	119.075	+	477.582i	0.165381	+	0.663308i
$721$	659.231	−	907.354i	0.914329	−	1.25847i
$722$	−1075.60	−	143.767i	−1.48975	−	0.199123i
$723$	13.4063	+	41.2604i	0.0185426	+	0.0570683i
$724$	29.8989	−	427.574i	0.0412968	−	0.590572i
$725$	61.8338	+	169.887i	0.0852880	+	0.234327i
$726$	−1898.19	+	880.748i	−2.61458	+	1.21315i
$727$	43.2821	−	245.465i	0.0595352	−	0.337641i	−0.940462	−	0.339898i	$-0.889607\pi$
$727$	43.2821	−	245.465i	0.0595352	−	0.337641i	0.999997	+	0.00225717i	$0.000718480\pi$
$728$	5.63848	−	1.61681i	0.00774516	−	0.00222089i
$729$	−1551.53	+	1723.15i	−2.12830	+	2.36371i
$730$	−550.611	+	495.773i	−0.754262	+	0.679141i
$731$	−85.2389	+	5.96049i	−0.116606	+	0.00815388i
$732$	116.543	+	1666.64i	0.159211	+	2.27683i
$733$	856.077	+	950.770i	1.16791	+	1.29709i	0.946792	+	0.321847i	$0.104304\pi$
$733$	856.077	+	950.770i	1.16791	+	1.29709i	0.221118	+	0.975247i	$0.429030\pi$
$734$	−997.277	−	897.952i	−1.35869	−	1.22337i
$735$	54.5967	+	190.401i	0.0742813	+	0.259050i
$736$	825.705	+	145.594i	1.12188	+	0.197818i
$737$	−137.989	+	819.802i	−0.187231	+	1.11235i
$738$	−2307.26	+	839.772i	−3.12636	+	1.13790i
$739$	−263.550	−	18.4292i	−0.356630	−	0.0249380i	−0.109682	−	0.993967i	$-0.534983\pi$
$739$	−263.550	−	18.4292i	−0.356630	−	0.0249380i	−0.246948	+	0.969029i	$0.579428\pi$
$740$	−163.920	+	53.2609i	−0.221514	+	0.0719741i
$741$	4.64336	+	36.7899i	0.00626635	+	0.0496490i
$742$	520.696	+	378.308i	0.701746	+	0.509849i
$743$	329.939	−	82.2631i	0.444064	−	0.110718i	−0.0134709	−	0.999909i	$-0.504288\pi$
$743$	329.939	−	82.2631i	0.444064	−	0.110718i	0.457535	+	0.889192i	$0.348733\pi$
$744$	811.799	−	28.3486i	1.09113	−	0.0381030i
$745$	−409.114	+	217.530i	−0.549146	+	0.291986i
$746$	−60.7248	−	124.504i	−0.0814005	−	0.166896i
$747$	−2471.88	−	899.692i	−3.30908	−	1.20441i
$748$	−71.6516	+	75.3614i	−0.0957909	+	0.100750i
$749$	644.313	+	371.994i	0.860231	+	0.496655i
$750$	−367.819	+	1475.24i	−0.490426	+	1.96699i
$751$	255.466	−	408.832i	0.340168	−	0.544383i	−0.633095	−	0.774074i	$-0.718216\pi$
$751$	255.466	−	408.832i	0.340168	−	0.544383i	0.973264	+	0.229691i	$0.0737715\pi$
$752$	111.726	+	124.084i	0.148572	+	0.165006i
$753$	849.456	+	89.2814i	1.12809	+	0.118568i
$754$	−7.13816	+	4.81475i	−0.00946706	+	0.00638561i
$755$	−35.6039	+	66.9613i	−0.0471575	+	0.0886904i
$756$	1140.22	+	2144.44i	1.50823	+	2.83656i
$757$	−302.909	+	449.081i	−0.400144	+	0.593238i	−0.974230	−	0.225557i	$-0.927580\pi$
$757$	−302.909	+	449.081i	−0.400144	+	0.593238i	0.574086	+	0.818795i	$0.305358\pi$
$758$	895.313	+	751.257i	1.18115	+	0.991104i
$759$	32.0799	−	1182.12i	0.0422659	−	1.55747i
$760$	28.6449	−	108.366i	0.0376907	−	0.142587i
$761$	324.307	−	235.623i	0.426159	−	0.309623i	−0.353952	−	0.935264i	$-0.615162\pi$
$761$	324.307	−	235.623i	0.426159	−	0.309623i	0.780111	+	0.625641i	$0.215162\pi$
$762$	−977.748	−	395.036i	−1.28313	−	0.518420i
$763$	−943.349	+	32.9425i	−1.23637	+	0.0431749i
$764$	−387.679	+	794.860i	−0.507433	+	1.04039i
$765$	61.6394	−	59.5245i	0.0805744	−	0.0778098i
$766$	−184.781	+	236.509i	−0.241229	+	0.308759i
$767$	14.3519	−	15.9394i	0.0187117	−	0.0207815i
$768$	443.214	−	46.5837i	0.577102	−	0.0606558i
$769$	−393.647	+	330.309i	−0.511895	+	0.429531i	−0.861795	−	0.507256i	$-0.830660\pi$
$769$	−393.647	+	330.309i	−0.511895	+	0.429531i	0.349901	+	0.936787i	$0.386215\pi$
$770$	−14.8382	−	347.433i	−0.0192704	−	0.451211i
$771$	−592.871	+	1026.88i	−0.768964	+	1.33188i
$772$	−510.423	+	1146.43i	−0.661170	+	1.48501i
$773$	46.3049	+	1.61700i	0.0599028	+	0.00209185i	0.0648352	−	0.997896i	$-0.479348\pi$
$773$	46.3049	+	1.61700i	0.0599028	+	0.00209185i	−0.00493242	+	0.999988i	$0.501570\pi$
$774$	−1548.07	+	2911.50i	−2.00009	+	3.76163i
$775$	−872.474	−	425.534i	−1.12577	−	0.549076i
$776$	−215.234	−	61.7175i	−0.277364	−	0.0795328i
$777$	489.409	−	305.817i	0.629870	−	0.393587i
$778$	852.536	−	277.006i	1.09581	−	0.356049i
$779$	−636.403	−	98.5951i	−0.816948	−	0.126566i
$780$	−18.6180			−0.0238693
$781$	−92.8664	+	954.935i	−0.118907	+	1.22271i
$782$	−36.0629	−	99.0819i	−0.0461162	−	0.126703i
$783$	−527.589	−	509.486i	−0.673804	−	0.650685i
$784$	194.069	−	27.2746i	0.247537	−	0.0347890i
$785$	189.242	−	242.219i	0.241073	−	0.308559i
$786$	231.708	−	2204.55i	0.294794	−	2.80478i
$787$	90.2877	+	202.789i	0.114724	+	0.257674i	0.961777	−	0.273834i	$-0.0882921\pi$
$787$	90.2877	+	202.789i	0.114724	+	0.257674i	−0.847053	+	0.531508i	$0.821625\pi$
$788$	−72.5116	−	179.473i	−0.0920198	−	0.227757i
$789$	341.241	−	546.099i	0.432498	−	0.692141i
$790$	74.5478	+	709.275i	0.0943643	+	0.897816i
$791$	422.979	−	244.207i	0.534740	−	0.308732i
$792$	205.946	+	799.470i	0.260033	+	1.00943i
$793$	19.2646	+	3.39687i	0.0242933	+	0.00428356i
$794$	1445.28	−	1496.63i	1.82025	−	1.88493i
$795$	−258.745	−	331.179i	−0.325466	−	0.416577i
$796$	619.243	−	386.946i	0.777944	−	0.486113i
$797$	498.194	−	685.706i	0.625087	−	0.860358i	−0.372624	−	0.927982i	$-0.621542\pi$
$797$	498.194	−	685.706i	0.625087	−	0.860358i	0.997711	+	0.0676240i	$0.0215418\pi$
$798$	−25.6802	+	1824.12i	−0.0321808	+	2.28586i
$799$	8.98268	−	27.6459i	0.0112424	−	0.0346006i
$800$	890.779	+	359.898i	1.11347	+	0.449872i
$801$	993.431	+	670.077i	1.24024	+	0.836551i
$802$	−382.578	−	2169.71i	−0.477030	−	2.70537i
$803$	1056.20	−	965.986i	1.31532	−	1.20297i
$804$	2057.61	+	748.909i	2.55922	+	0.931479i
$805$	179.530	+	79.9320i	0.223019	+	0.0992944i
$806$	9.61190	−	45.2204i	0.0119254	−	0.0561047i
$807$	−518.538	−	1283.43i	−0.642550	−	1.59037i
$808$	20.3097	+	290.442i	0.0251357	+	0.359457i
$809$	267.839	−	119.250i	0.331074	−	0.147404i	−0.234466	−	0.972124i	$-0.575334\pi$
$809$	267.839	−	119.250i	0.331074	−	0.147404i	0.565540	+	0.824721i	$0.308668\pi$
$810$	−334.864	−	1575.41i	−0.413412	−	1.94495i
$811$	61.2227	+	2.13794i	0.0754903	+	0.00263618i	0.0726198	−	0.997360i	$-0.476864\pi$
$811$	61.2227	+	2.13794i	0.0754903	+	0.00263618i	0.00287058	+	0.999996i	$0.499086\pi$
$812$	−212.187	+	103.490i	−0.261314	+	0.127451i
$813$	2048.79	−	361.257i	2.52003	−	0.444350i
$814$	566.729	−	189.026i	0.696228	−	0.232219i
$815$	−137.386	−	115.281i	−0.168572	−	0.141449i
$816$	−68.4440	−	94.2050i	−0.0838774	−	0.115447i
$817$	−723.753	+	473.492i	−0.885867	+	0.579550i
$818$	214.897	−	661.385i	0.262710	−	0.808539i
$819$	44.0399	−	10.9804i	0.0537727	−	0.0134070i
$820$	89.1238	−	310.812i	0.108688	−	0.379038i
$821$	−98.5633	−	13.8522i	−0.120053	−	0.0168723i	0.0788908	−	0.996883i	$-0.474862\pi$
$821$	−98.5633	−	13.8522i	−0.120053	−	0.0168723i	−0.198944	+	0.980011i	$0.563751\pi$
$822$	−2099.54	+	295.071i	−2.55419	+	0.358968i
$823$	−955.403	+	273.957i	−1.16088	+	0.332877i	−0.800153	−	0.599795i	$-0.795249\pi$
$823$	−955.403	+	273.957i	−1.16088	+	0.332877i	−0.360725	+	0.932672i	$0.617471\pi$
$824$	−314.566	−	544.844i	−0.381755	−	0.661218i
$825$	317.580	−	1317.30i	0.384945	−	1.59672i
$826$	808.327	−	678.267i	0.978605	−	0.821147i
$827$	733.627	+	182.914i	0.887094	+	0.221177i	0.658713	−	0.752394i	$-0.271101\pi$
$827$	733.627	+	182.914i	0.887094	+	0.221177i	0.228381	+	0.973572i	$0.426657\pi$
$828$	−2218.24	−	471.502i	−2.67904	−	0.569447i
$829$	47.4008	+	223.003i	0.0571783	+	0.269003i	0.997445	−	0.0714354i	$-0.0227580\pi$
$829$	47.4008	+	223.003i	0.0571783	+	0.269003i	−0.940267	+	0.340438i	$0.889425\pi$
$830$	515.289	−	347.567i	0.620830	−	0.418755i
$831$	−33.4736	−	34.6630i	−0.0402812	−	0.0417124i
$832$	−4.33166	+	30.8213i	−0.00520632	+	0.0370449i
$833$	−21.0051	−	26.8853i	−0.0252162	−	0.0322753i
$834$	285.097	+	19.9359i	0.341842	+	0.0239040i
$835$		−	56.9431i		−	0.0681953i
$836$	−261.062	+	1019.64i	−0.312275	+	1.21967i
$837$	3938.03			4.70494
$838$	−26.4051	+	377.611i	−0.0315097	+	0.450609i
$839$	215.417	−	168.302i	0.256754	−	0.200598i	−0.479060	−	0.877782i	$-0.659022\pi$
$839$	215.417	−	168.302i	0.256754	−	0.200598i	0.735814	+	0.677184i	$0.236800\pi$
$840$	−186.600	−	26.2249i	−0.222143	−	0.0312202i
$841$	−553.682	+	534.684i	−0.658361	+	0.635772i
$842$	−882.854	−	1308.89i	−1.04852	−	1.55450i
$843$	−939.568	+	199.711i	−1.11455	+	0.236905i
$844$	92.0229	−	432.934i	0.109032	−	0.512955i
$845$	77.3932	−	310.407i	0.0915896	−	0.367346i
$846$	−721.067	−	859.335i	−0.852326	−	1.01576i
$847$	33.8827	+	670.934i	0.0400031	+	0.792130i
$848$	−360.110	+	207.910i	−0.424658	+	0.245177i
$849$	350.822	+	1223.46i	0.413218	+	1.44106i
$850$	−16.8149	−	119.644i	−0.0197822	−	0.140758i
$851$	−46.9870	+	334.330i	−0.0552139	+	0.392867i
$852$	2429.19	+	696.559i	2.85116	+	0.817557i
$853$	−148.299	−	594.795i	−0.173856	−	0.697297i	−0.992421	−	0.122884i	$-0.960786\pi$
$853$	−148.299	−	594.795i	−0.173856	−	0.697297i	0.818565	−	0.574413i	$-0.194770\pi$
$854$	915.270	+	297.389i	1.07174	+	0.348231i
$855$	250.780	−	830.278i	0.293310	−	0.971086i
$856$	337.634	−	245.305i	0.394432	−	0.286572i
$857$	−1002.78	+	1195.06i	−1.17010	+	1.39447i	−0.267740	+	0.963491i	$0.586277\pi$
$857$	−1002.78	+	1195.06i	−1.17010	+	1.39447i	−0.902361	+	0.430981i	$0.858168\pi$
$858$	64.5321	−	0.501788i	0.0752123	−	0.000584835i
$859$	−232.534	−	1318.77i	−0.270703	−	1.53523i	−0.752288	−	0.658834i	$-0.771050\pi$
$859$	−232.534	−	1318.77i	−0.270703	−	1.53523i	0.481585	−	0.876399i	$-0.340061\pi$
$860$	−190.357	−	390.290i	−0.221346	−	0.453826i
$861$	−37.7834	+	1081.97i	−0.0438831	+	1.25665i
$862$	1620.39	−	344.425i	1.87981	−	0.399565i
$863$	506.045	+	1136.60i	0.586379	+	1.31703i	0.926375	+	0.376602i	$0.122908\pi$
$863$	506.045	+	1136.60i	0.586379	+	1.31703i	−0.339996	+	0.940427i	$0.610426\pi$
$864$	−3888.05	+	271.879i	−4.50006	+	0.314675i
$865$	−197.979	+	79.9888i	−0.228878	+	0.0924726i
$866$	1281.71	+	272.437i	1.48004	+	0.314592i
$867$	668.018	−	1500.39i	0.770494	−	1.73056i
$868$	433.539	−	1191.14i	0.499468	−	1.37228i
$869$	−154.663	−	1369.03i	−0.177978	−	1.57541i
$870$	272.397	−	48.0310i	0.313100	−	0.0552080i
$871$	14.3366	−	21.2549i	0.0164600	−	0.0244029i
$872$	−198.351	+	490.936i	−0.227467	+	0.563000i
$873$	−1647.78	−	535.395i	−1.88749	−	0.613281i
$874$	−807.823	−	697.456i	−0.924282	−	0.798004i
$875$	394.885	+	286.901i	0.451297	+	0.327887i
$876$	−1997.79	−	3197.14i	−2.28058	−	3.64970i
$877$	1083.66	−	846.645i	1.23564	−	0.965388i	0.235661	−	0.971835i	$-0.424275\pi$
$877$	1083.66	−	846.645i	1.23564	−	0.965388i	0.999979	+	0.00644765i	$0.00205237\pi$
$878$	1012.37	+	977.633i	1.15304	+	1.11348i
$879$	347.777	−	1972.34i	0.395651	−	2.24385i
$880$	208.958	+	82.5405i	0.237453	+	0.0937961i
$881$	167.923	+	290.851i	0.190605	+	0.330137i	0.945451	−	0.325765i	$-0.105622\pi$
$881$	167.923	+	290.851i	0.190605	+	0.330137i	−0.754846	+	0.655902i	$0.772288\pi$
$882$	−1309.43	+	137.627i	−1.48462	+	0.156039i
$883$	−704.698	−	440.344i	−0.798073	−	0.498691i	0.0685545	−	0.997647i	$-0.478161\pi$
$883$	−704.698	−	440.344i	−0.798073	−	0.498691i	−0.866627	+	0.498956i	$0.833717\pi$
$884$	2.97341	−	1.20133i	0.00336358	−	0.00135898i
$885$	−629.460	+	280.253i	−0.711254	+	0.316671i
$886$	1283.36	+	134.886i	1.44848	+	0.152242i
$887$	82.3316	+	64.3245i	0.0928203	+	0.0725191i	0.661003	−	0.750383i	$-0.270131\pi$
$887$	82.3316	+	64.3245i	0.0928203	+	0.0725191i	−0.568183	+	0.822902i	$0.692353\pi$
$888$	−45.0536	−	320.573i	−0.0507360	−	0.361005i
$889$	−235.172	+	243.528i	−0.264536	+	0.273935i
$890$	−266.062	+	96.8388i	−0.298947	+	0.108808i
$891$	670.541	+	3038.29i	0.752572	+	3.40998i
$892$			16.8533i			0.0188939i
$893$	−57.1157	−	288.629i	−0.0639594	−	0.323213i
$894$	−1307.22	−	4023.21i	−1.46222	−	4.50024i
$895$	206.201	+	329.990i	0.230392	+	0.368704i
$896$	−147.397	+	514.034i	−0.164505	+	0.573698i
$897$	−15.9872	+	32.7786i	−0.0178230	+	0.0365425i
$898$	−635.375	−	337.835i	−0.707545	−	0.376208i
$899$	−13.3591	+	382.555i	−0.0148600	+	0.425534i
$900$	−2373.92	−	1056.94i	−2.63769	−	1.17437i
$901$	62.6926	+	36.1956i	0.0695811	+	0.0401727i
$902$	−300.536	+	1079.71i	−0.333188	+	1.19702i
$903$	934.590	+	1113.80i	1.03498	+	1.23345i
$904$	−28.6381	−	272.474i	−0.0316794	−	0.301409i
$905$	119.809	+	107.877i	0.132386	+	0.119201i
$906$	−545.605	−	426.273i	−0.602213	−	0.470500i
$907$	460.660	+	477.027i	0.507894	+	0.525939i	0.923497	−	0.383607i	$-0.125318\pi$
$907$	460.660	+	477.027i	0.507894	+	0.525939i	−0.415603	+	0.909546i	$0.636429\pi$
$908$	583.842	+	284.759i	0.642998	+	0.313611i
$909$	78.6247	+	2251.52i	0.0864958	+	2.47692i
$910$	−4.01746	+	9.94356i	−0.00441479	+	0.0109270i
$911$	−178.076	−	245.101i	−0.195473	−	0.269046i	0.700018	−	0.714126i	$-0.253175\pi$
$911$	−178.076	−	245.101i	−0.195473	−	0.269046i	−0.895491	+	0.445079i	$0.853175\pi$
$912$	−1069.87	−	494.497i	−1.17310	−	0.542212i
$913$	−990.194	+	679.156i	−1.08455	+	0.743873i
$914$	−846.081	+	1008.32i	−0.925691	+	1.10320i
$915$	−520.980	−	351.406i	−0.569378	−	0.384050i
$916$	−1520.83	+	808.639i	−1.66029	+	0.882793i
$917$	−628.340	−	334.094i	−0.685213	−	0.364334i
$918$	274.087	+	406.350i	0.298570	+	0.442648i
$919$	−31.9908	+	304.373i	−0.0348105	+	0.331200i	0.963233	+	0.268669i	$0.0865838\pi$
$919$	−31.9908	+	304.373i	−0.0348105	+	0.331200i	−0.998043	+	0.0625307i	$0.980083\pi$
$920$	81.9225	−	73.7633i	0.0890462	−	0.0801775i
$921$	1127.20	+	704.351i	1.22388	+	0.764767i
$922$	662.620	+	165.210i	0.718677	+	0.179186i
$923$	14.7944	−	25.6247i	0.0160286	−	0.0277624i
$924$	1754.08	+	232.626i	1.89835	+	0.251760i
$925$	−132.314	+	363.529i	−0.143042	+	0.393004i
$926$	439.209	−	214.217i	0.474308	−	0.231336i
$927$	−2285.45	−	4298.31i	−2.46543	−	4.63680i
$928$	−13.2218	−	378.622i	−0.0142476	−	0.407998i
$929$	123.311	+	494.574i	0.132735	+	0.532372i	0.999437	+	0.0335459i	$0.0106800\pi$
$929$	123.311	+	494.574i	0.132735	+	0.532372i	−0.866702	+	0.498827i	$0.833764\pi$
$930$	−872.947	+	1201.51i	−0.938652	+	1.29194i
$931$	−318.337	−	133.859i	−0.341930	−	0.143780i
$932$	−581.136	−	1788.55i	−0.623537	−	1.91905i
$933$	171.148	−	2447.54i	0.183439	−	2.62330i
$934$	404.175	+	1110.46i	0.432736	+	1.18893i
$935$	−5.74454	−	38.6892i	−0.00614389	−	0.0413789i
$936$	4.42114	−	25.0735i	0.00472344	−	0.0267880i
$937$	−311.193	+	89.2331i	−0.332116	+	0.0952328i	−0.437551	−	0.899193i	$-0.644154\pi$
$937$	−311.193	+	89.2331i	−0.332116	+	0.0952328i	0.105435	+	0.994426i	$0.466376\pi$
$938$	843.977	−	937.332i	0.899762	−	0.999287i
$939$	−2255.18	+	2030.57i	−2.40168	+	2.16248i
$940$	147.365	−	10.3048i	0.156771	−	0.0109625i
$941$	73.2810	+	1047.97i	0.0778757	+	1.11367i	0.866625	+	0.498959i	$0.166284\pi$
$941$	73.2810	+	1047.97i	0.0778757	+	1.11367i	−0.788750	+	0.614715i	$0.789271\pi$
$942$	1877.78	+	2085.48i	1.99339	+	2.21389i
$943$	−470.680	−	423.802i	−0.499130	−	0.449419i
$944$	187.910	+	655.320i	0.199057	+	0.694195i
$945$	−899.657	−	158.634i	−0.952018	−	0.167866i
$946$	670.318	+	1347.66i	0.708582	+	1.42459i
$947$	−42.2249	+	15.3686i	−0.0445881	+	0.0162287i	−0.364218	−	0.931314i	$-0.618664\pi$
$947$	−42.2249	+	15.3686i	−0.0445881	+	0.0162287i	0.319630	+	0.947542i	$0.396441\pi$
$948$	−3620.01	−	253.136i	−3.81857	−	0.267021i
$949$	−41.9812	+	13.6405i	−0.0442373	+	0.0143736i
$950$	−739.262	−	974.174i	−0.778171	−	1.02545i
$951$	−1965.92	−	1428.32i	−2.06721	−	1.50192i
$952$	31.4933	−	7.85216i	0.0330812	−	0.00824806i
$953$	−806.235	+	28.1543i	−0.845997	+	0.0295429i	−0.454618	−	0.890687i	$-0.650224\pi$
$953$	−806.235	+	28.1543i	−0.845997	+	0.0295429i	−0.391379	+	0.920230i	$0.628002\pi$
$954$	2466.64	−	1311.53i	2.58557	−	1.37477i
$955$	−145.821	−	298.977i	−0.152692	−	0.313064i
$956$	−1843.67	−	671.042i	−1.92853	−	0.701927i
$957$	−525.485	+	96.8760i	−0.549096	+	0.101229i
$958$	−156.072	−	90.1083i	−0.162915	−	0.0940588i
$959$	−164.665	+	660.435i	−0.171705	+	0.688670i
$960$	529.843	−	847.926i	0.551920	−	0.883256i
$961$	−732.235	−	813.229i	−0.761951	−	0.846232i
$962$	−18.3234	−	1.92586i	−0.0190472	−	0.00200194i
$963$	2677.22	−	1805.81i	2.78009	−	1.87519i
$964$	17.8288	−	33.5310i	0.0184946	−	0.0347832i
$965$	−221.602	−	416.772i	−0.229639	−	0.431888i
$966$	−1003.29	+	1487.44i	−1.03860	+	1.53979i
$967$	−82.1099	−	68.8983i	−0.0849119	−	0.0712496i	0.599344	−	0.800492i	$-0.295428\pi$
$967$	−82.1099	−	68.8983i	−0.0849119	−	0.0712496i	−0.684256	+	0.729242i	$0.739873\pi$
$968$	351.552	+	135.716i	0.363173	+	0.140202i
$969$	18.5734	+	204.347i	0.0191676	+	0.210884i
$970$	331.195	−	240.627i	0.341438	−	0.248069i
$971$	696.962	+	281.591i	0.717778	+	0.290001i	0.704294	−	0.709908i	$-0.251264\pi$
$971$	696.962	+	281.591i	0.717778	+	0.290001i	0.0134833	+	0.999909i	$0.495708\pi$
$972$	4255.51	−	148.606i	4.37809	−	0.152886i
$973$	40.2205	−	82.4642i	0.0413365	−	0.0847525i
$974$	923.937	−	892.235i	0.948600	−	0.916053i
$975$	−25.7278	+	32.9301i	−0.0263875	+	0.0337745i
$976$	−416.037	+	462.056i	−0.426268	+	0.473418i
$977$	−326.776	+	34.3456i	−0.334469	+	0.0351541i	−0.270275	−	0.962783i	$-0.587115\pi$
$977$	−326.776	+	34.3456i	−0.334469	+	0.0351541i	−0.0641946	+	0.997937i	$0.520448\pi$
$978$	1254.30	−	1052.48i	1.28251	−	1.07616i
$979$	512.515	−	191.066i	0.523508	−	0.195164i
$980$	86.6930	−	150.157i	0.0884622	−	0.153221i
$981$	−1666.46	+	3742.93i	−1.69873	+	3.81542i
$982$	−770.519	−	26.9071i	−0.784642	−	0.0274003i
$983$	−313.024	+	588.712i	−0.318437	+	0.598893i	−0.989838	−	0.142201i	$-0.954582\pi$
$983$	−313.024	+	588.712i	−0.318437	+	0.598893i	0.671400	+	0.741095i	$0.265693\pi$
$984$	545.838	+	266.223i	0.554713	+	0.270552i
$985$	69.9875	+	20.0686i	0.0710533	+	0.0203742i
$986$	−40.4042	+	25.2473i	−0.0409779	+	0.0256058i
$987$	−470.421	+	152.849i	−0.476617	+	0.154862i
$988$	20.3423	−	25.2948i	0.0205894	−	0.0256021i
$989$	−850.598			−0.860058
$990$	−1383.66	−	603.196i	−1.39763	−	0.609289i
$991$	518.412	+	1424.33i	0.523120	+	1.43726i	0.867029	+	0.498258i	$0.166027\pi$
$991$	518.412	+	1424.33i	0.523120	+	1.43726i	−0.343909	+	0.939003i	$0.611751\pi$
$992$	1463.26	+	1413.06i	1.47506	+	1.42445i
$993$	190.892	−	26.8282i	0.192238	−	0.0270173i
$994$	896.198	−	1147.08i	0.901608	−	1.15401i
$995$	−28.7093	+	273.150i	−0.0288535	+	0.274523i
$996$	1286.35	+	2889.19i	1.29151	+	2.90079i
$997$	338.612	+	838.094i	0.339631	+	0.840616i	0.996260	+	0.0864027i	$0.0275372\pi$
$997$	338.612	+	838.094i	0.339631	+	0.840616i	−0.656629	+	0.754213i	$0.728018\pi$
$998$	−1562.77	+	2500.95i	−1.56590	+	2.50596i
$999$	−164.049	−	1560.83i	−0.164214	−	1.56239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.3.x.a.3.6	✓	912
11.4	even	5	inner	209.3.x.a.136.6	yes	912
19.13	odd	18	inner	209.3.x.a.146.6	yes	912
209.70	odd	90	inner	209.3.x.a.70.6	yes	912

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.3.x.a.3.6	✓	912	1.1	even	1	trivial
209.3.x.a.70.6	yes	912	209.70	odd	90	inner
209.3.x.a.136.6	yes	912	11.4	even	5	inner
209.3.x.a.146.6	yes	912	19.13	odd	18	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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	209.x (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.209688 + 2.99868i) q^{2} +(4.53353 - 3.54199i) q^{3} +(-4.98704 - 0.700883i) q^{4} +(1.36261 - 1.31585i) q^{5} +(9.67065 + 14.3373i) q^{6} +(5.43065 - 1.15432i) q^{7} +(0.647514 - 3.04631i) q^{8} +(5.82998 - 23.3828i) q^{9} +(3.66010 + 4.36194i) q^{10} +(-7.13597 - 8.37126i) q^{11} +(-25.0914 + 14.4865i) q^{12} +(0.0935062 + 0.326095i) q^{13} +(2.32270 + 16.5268i) q^{14} +(1.51669 - 10.7918i) q^{15} +(-10.3647 - 2.97203i) q^{16} +(0.454121 + 1.82138i) q^{17} +(68.8949 + 22.3853i) q^{18} +(13.0048 + 13.8519i) q^{19} +(-7.71764 + 5.60719i) q^{20} +(20.5315 - 24.4684i) q^{21} +(26.5990 - 19.6431i) q^{22} +(3.24484 + 18.4024i) q^{23} +(-7.85447 - 16.1040i) q^{24} +(-0.747262 + 21.3988i) q^{25} +(-0.997462 + 0.212017i) q^{26} +(-35.3309 - 79.3544i) q^{27} +(-27.8919 + 1.95039i) q^{28} +(7.82864 - 3.16297i) q^{29} +(32.0431 + 6.81098i) q^{30} +(-18.4396 + 41.4160i) q^{31} +(15.3462 - 42.1634i) q^{32} +(-62.0020 - 12.6759i) q^{33} +(-5.55696 + 0.979841i) q^{34} +(5.88093 - 8.71884i) q^{35} +(-45.4629 + 112.525i) q^{36} +(17.1833 + 5.58318i) q^{37} +(-44.2644 + 36.0927i) q^{38} +(1.57894 + 1.14716i) q^{39} +(-3.12620 - 5.00296i) q^{40} +(-26.7092 + 20.8675i) q^{41} +(69.0678 + 66.6980i) q^{42} +(-7.90444 + 44.8283i) q^{43} +(29.7201 + 46.7493i) q^{44} +(-22.8243 - 39.5329i) q^{45} +(-55.8633 + 5.87147i) q^{46} +(-13.1325 - 8.20611i) q^{47} +(-57.5157 + 23.2378i) q^{48} +(-16.6042 + 7.39266i) q^{49} +(-64.0114 - 6.72787i) q^{50} +(8.51007 + 6.64879i) q^{51} +(-0.237765 - 1.69179i) q^{52} +(26.7893 - 27.7411i) q^{53} +(245.367 - 89.3063i) q^{54} +(-20.7389 - 2.01684i) q^{55} -17.2909i q^{56} +(108.021 + 16.7352i) q^{57} +(7.84318 + 24.1388i) q^{58} +(-33.5047 - 53.6188i) q^{59} +(-15.1276 + 52.7561i) q^{60} +(25.2783 - 51.8282i) q^{61} +(-120.327 - 63.9789i) q^{62} +(4.66937 - 133.713i) q^{63} +(83.8159 + 37.3172i) q^{64} +(0.556506 + 0.321299i) q^{65} +(51.0120 - 183.266i) q^{66} +(-48.5792 - 57.8944i) q^{67} +(-0.988145 - 9.40157i) q^{68} +(79.8916 + 71.9348i) q^{69} +(24.9118 + 19.4633i) q^{70} +(-60.5893 - 62.7421i) q^{71} +(-67.4562 - 32.9006i) q^{72} +(4.54114 + 130.041i) q^{73} +(-20.3453 + 50.3564i) q^{74} +(72.4064 + 99.6589i) q^{75} +(-55.1469 - 78.1948i) q^{76} +(-48.4161 - 37.2242i) q^{77} +(-3.77106 + 4.49418i) q^{78} +(103.836 + 70.0383i) q^{79} +(-18.0338 + 9.58874i) q^{80} +(-249.746 - 132.792i) q^{81} +(-56.9744 - 84.4680i) q^{82} +(11.4100 - 108.559i) q^{83} +(-119.541 + 107.635i) q^{84} +(3.01546 + 1.88427i) q^{85} +(-132.768 - 33.1029i) q^{86} +(24.2882 - 42.0684i) q^{87} +(-30.1221 + 16.3179i) q^{88} +(-17.0068 + 46.7259i) q^{89} +(123.333 - 60.1533i) q^{90} +(0.884218 + 1.66297i) q^{91} +(-3.28422 - 94.0478i) q^{92} +(63.0984 + 253.074i) q^{93} +(27.3612 - 37.6595i) q^{94} +(35.9475 + 1.76226i) q^{95} +(-79.7696 - 245.506i) q^{96} +(5.01516 - 71.7201i) q^{97} +(-18.6865 - 51.3408i) q^{98} +(-237.346 + 118.054i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 912 q - 18 q^{2} - 30 q^{3} - 18 q^{4} - 18 q^{5} - 54 q^{6} + 18 q^{7} - 27 q^{8} + 18 q^{9} - 48 q^{10} + 3 q^{11} - 72 q^{12} - 18 q^{13} + 102 q^{14} - 90 q^{15} + 6 q^{16} + 54 q^{17} - 18 q^{19} - 30 q^{20}+ \cdots - 372 q^{99}+O(q^{100}) \) 912 * q - 18 * q^2 - 30 * q^3 - 18 * q^4 - 18 * q^5 - 54 * q^6 + 18 * q^7 - 27 * q^8 + 18 * q^9 - 48 * q^10 + 3 * q^11 - 72 * q^12 - 18 * q^13 + 102 * q^14 - 90 * q^15 + 6 * q^16 + 54 * q^17 - 18 * q^19 - 30 * q^20 - 102 * q^21 + 48 * q^22 - 48 * q^23 + 216 * q^24 - 414 * q^25 - 57 * q^26 - 207 * q^27 - 114 * q^28 + 351 * q^29 + 231 * q^30 - 135 * q^31 - 162 * q^32 - 564 * q^33 - 132 * q^34 - 48 * q^35 + 45 * q^36 + 186 * q^38 - 36 * q^39 + 72 * q^40 + 342 * q^41 + 237 * q^42 - 576 * q^43 + 1173 * q^44 + 174 * q^45 - 747 * q^46 - 174 * q^47 - 267 * q^48 + 456 * q^49 - 891 * q^50 - 186 * q^51 + 603 * q^52 - 63 * q^53 + 474 * q^54 - 72 * q^55 - 444 * q^57 + 132 * q^58 + 540 * q^59 - 591 * q^60 + 438 * q^61 - 408 * q^62 - 312 * q^63 - 585 * q^64 - 1152 * q^65 - 2268 * q^66 - 636 * q^67 + 999 * q^68 + 675 * q^69 + 1923 * q^70 - 42 * q^71 + 426 * q^72 - 396 * q^73 - 258 * q^74 + 2112 * q^76 - 396 * q^77 - 2550 * q^78 - 18 * q^79 - 978 * q^80 - 372 * q^81 - 72 * q^82 + 177 * q^83 + 1917 * q^84 - 54 * q^85 - 72 * q^86 + 216 * q^87 + 360 * q^88 + 690 * q^89 + 1152 * q^90 - 780 * q^91 - 1314 * q^92 + 876 * q^93 - 1002 * q^95 - 3396 * q^96 + 774 * q^97 - 1962 * q^98 - 372 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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