LMFDB - Embedded newform 231.2.l.b.32.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(32,231)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.10
Character	$\chi$	$=$	231.32
Dual form			231.2.l.b.65.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468581 - 0.811606i) q^{2} +(-0.688798 + 1.58920i) q^{3} +(0.560864 - 0.971445i) q^{4} +(-2.73832 + 1.58097i) q^{5} +(1.61256 - 0.185636i) q^{6} +(0.0402023 - 2.64545i) q^{7} -2.92556 q^{8} +(-2.05112 - 2.18928i) q^{9} +O(q^{10})$	\(q+(-0.468581 - 0.811606i) q^{2} +(-0.688798 + 1.58920i) q^{3} +(0.560864 - 0.971445i) q^{4} +(-2.73832 + 1.58097i) q^{5} +(1.61256 - 0.185636i) q^{6} +(0.0402023 - 2.64545i) q^{7} -2.92556 q^{8} +(-2.05112 - 2.18928i) q^{9} +(2.56625 + 1.48162i) q^{10} +(-0.269754 - 3.30564i) q^{11} +(1.15750 + 1.56045i) q^{12} -1.78405i q^{13} +(-2.16590 + 1.20698i) q^{14} +(-0.626328 - 5.44070i) q^{15} +(0.249134 + 0.431513i) q^{16} +(2.35195 - 4.07369i) q^{17} +(-0.815715 + 2.69055i) q^{18} +(-6.24385 + 3.60489i) q^{19} +3.54683i q^{20} +(4.17645 + 1.88607i) q^{21} +(-2.55647 + 1.76789i) q^{22} +(0.462754 - 0.267171i) q^{23} +(2.01512 - 4.64931i) q^{24} +(2.49892 - 4.32826i) q^{25} +(-1.44795 + 0.835972i) q^{26} +(4.89200 - 1.75166i) q^{27} +(-2.54736 - 1.52279i) q^{28} -6.46212 q^{29} +(-4.12222 + 3.05774i) q^{30} +(-1.71277 + 2.96661i) q^{31} +(-2.69208 + 4.66283i) q^{32} +(5.43912 + 1.84822i) q^{33} -4.40831 q^{34} +(4.07228 + 7.30763i) q^{35} +(-3.27716 + 0.764660i) q^{36} +(2.08135 + 3.60500i) q^{37} +(5.85150 + 3.37836i) q^{38} +(2.83521 + 1.22885i) q^{39} +(8.01112 - 4.62522i) q^{40} -0.272850 q^{41} +(-0.426263 - 4.27341i) q^{42} -5.32723i q^{43} +(-3.36254 - 1.59196i) q^{44} +(9.07778 + 2.75218i) q^{45} +(-0.433675 - 0.250382i) q^{46} +(7.52310 - 4.34347i) q^{47} +(-0.857364 + 0.0986989i) q^{48} +(-6.99677 - 0.212706i) q^{49} -4.68379 q^{50} +(4.85390 + 6.54366i) q^{51} +(-1.73311 - 1.00061i) q^{52} +(9.61932 + 5.55372i) q^{53} +(-3.71396 - 3.14958i) q^{54} +(5.96478 + 8.62541i) q^{55} +(-0.117614 + 7.73942i) q^{56} +(-1.42814 - 12.4058i) q^{57} +(3.02802 + 5.24469i) q^{58} +(-3.88158 - 2.24103i) q^{59} +(-5.63663 - 2.44305i) q^{60} +(-1.14182 + 0.659230i) q^{61} +3.21029 q^{62} +(-5.87407 + 5.33810i) q^{63} +6.04237 q^{64} +(2.82053 + 4.88530i) q^{65} +(-1.04864 - 5.28047i) q^{66} +(0.766303 - 1.32728i) q^{67} +(-2.63825 - 4.56958i) q^{68} +(0.105844 + 0.919435i) q^{69} +(4.02272 - 6.72930i) q^{70} -15.2685i q^{71} +(6.00067 + 6.40486i) q^{72} +(0.516234 + 0.298048i) q^{73} +(1.95056 - 3.37847i) q^{74} +(5.15722 + 6.95258i) q^{75} +8.08741i q^{76} +(-8.75573 + 0.580726i) q^{77} +(-0.331185 - 2.87689i) q^{78} +(10.5470 - 6.08934i) q^{79} +(-1.36442 - 0.787747i) q^{80} +(-0.585853 + 8.98091i) q^{81} +(0.127852 + 0.221447i) q^{82} +3.20502 q^{83} +(4.17463 - 2.99937i) q^{84} +14.8734i q^{85} +(-4.32361 + 2.49624i) q^{86} +(4.45109 - 10.2696i) q^{87} +(0.789183 + 9.67085i) q^{88} +(-7.21745 + 4.16700i) q^{89} +(-2.01999 - 8.65720i) q^{90} +(-4.71961 - 0.0717229i) q^{91} -0.599386i q^{92} +(-3.53478 - 4.76533i) q^{93} +(-7.05036 - 4.07053i) q^{94} +(11.3984 - 19.7427i) q^{95} +(-5.55586 - 7.49001i) q^{96} -6.02514 q^{97} +(3.10592 + 5.77829i) q^{98} +(-6.68365 + 7.37081i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9}+O(q^{10}) $ 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9	$ 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9} + 14 q^{12} + 4 q^{15} - 28 q^{16} - 24 q^{22} - 36 q^{27} - 4 q^{31} - 26 q^{33} + 56 q^{34} + 12 q^{36} - 28 q^{37} + 96 q^{42} + 30 q^{45} - 72 q^{48} + 24 q^{49} - 80 q^{55} + 16 q^{58} - 32 q^{60} + 256 q^{64} - 42 q^{66} + 16 q^{67} + 36 q^{69} - 76 q^{70} + 34 q^{75} + 104 q^{78} - 26 q^{81} - 4 q^{82} - 16 q^{88} - 36 q^{91} + 52 q^{93} - 144 q^{97} - 36 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9 + 14 * q^12 + 4 * q^15 - 28 * q^16 - 24 * q^22 - 36 * q^27 - 4 * q^31 - 26 * q^33 + 56 * q^34 + 12 * q^36 - 28 * q^37 + 96 * q^42 + 30 * q^45 - 72 * q^48 + 24 * q^49 - 80 * q^55 + 16 * q^58 - 32 * q^60 + 256 * q^64 - 42 * q^66 + 16 * q^67 + 36 * q^69 - 76 * q^70 + 34 * q^75 + 104 * q^78 - 26 * q^81 - 4 * q^82 - 16 * q^88 - 36 * q^91 + 52 * q^93 - 144 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.468581	−	0.811606i	−0.331337	−	0.573892i	0.651438	−	0.758702i	$-0.274166\pi$
$2$	−0.468581	−	0.811606i	−0.331337	−	0.573892i	−0.982774	+	0.184810i	$0.940833\pi$
$3$	−0.688798	+	1.58920i	−0.397678	+	0.917525i
$3$	−0.688798	+	1.58920i	−0.397678	+	0.917525i
$4$	0.560864	−	0.971445i	0.280432	−	0.485723i
$5$	−2.73832	+	1.58097i	−1.22461	+	0.707031i	−0.965898	−	0.258923i	$-0.916632\pi$
$5$	−2.73832	+	1.58097i	−1.22461	+	0.707031i	−0.258715	+	0.965954i	$0.583299\pi$
$6$	1.61256	−	0.185636i	0.658325	−	0.0757858i
$7$	0.0402023	−	2.64545i	0.0151950	−	0.999885i
$7$	0.0402023	−	2.64545i	0.0151950	−	0.999885i
$8$	−2.92556			−1.03434
$9$	−2.05112	−	2.18928i	−0.683705	−	0.729758i
$10$	2.56625	+	1.48162i	0.811518	+	0.468530i
$11$	−0.269754	−	3.30564i	−0.0813339	−	0.996687i
$11$	−0.269754	−	3.30564i	−0.0813339	−	0.996687i
$12$	1.15750	+	1.56045i	0.334141	+	0.450465i
$13$		−	1.78405i		−	0.494807i	−0.968913	−	0.247403i	$-0.920423\pi$
$13$		−	1.78405i		−	0.494807i	0.968913	−	0.247403i	$-0.0795773\pi$
$14$	−2.16590	+	1.20698i	−0.578860	+	0.322578i
$15$	−0.626328	−	5.44070i	−0.161717	−	1.40478i
$16$	0.249134	+	0.431513i	0.0622836	+	0.107878i
$17$	2.35195	−	4.07369i	0.570431	−	0.988015i	−0.426091	−	0.904680i	$-0.640110\pi$
$17$	2.35195	−	4.07369i	0.570431	−	0.988015i	0.996522	−	0.0833349i	$-0.0265571\pi$
$18$	−0.815715	+	2.69055i	−0.192266	+	0.634168i
$19$	−6.24385	+	3.60489i	−1.43244	+	0.827018i	−0.997306	−	0.0733490i	$-0.976631\pi$
$19$	−6.24385	+	3.60489i	−1.43244	+	0.827018i	−0.435131	+	0.900367i	$0.643298\pi$
$20$			3.54683i			0.793096i
$21$	4.17645	+	1.88607i	0.911377	+	0.411574i
$22$	−2.55647	+	1.76789i	−0.545042	+	0.376916i
$23$	0.462754	−	0.267171i	0.0964908	−	0.0557090i	−0.450978	−	0.892535i	$-0.648925\pi$
$23$	0.462754	−	0.267171i	0.0964908	−	0.0557090i	0.547469	+	0.836826i	$0.315591\pi$
$24$	2.01512	−	4.64931i	0.411335	−	0.949036i
$25$	2.49892	−	4.32826i	0.499785	−	0.865652i
$26$	−1.44795	+	0.835972i	−0.283965	+	0.163948i
$27$	4.89200	−	1.75166i	0.941466	−	0.337108i
$28$	−2.54736	−	1.52279i	−0.481405	−	0.287780i
$29$	−6.46212			−1.19999			−0.599993	−	0.800006i	$-0.704830\pi$
$29$	−6.46212			−1.19999			−0.599993	+	0.800006i	$0.704830\pi$
$30$	−4.12222	+	3.05774i	−0.752611	+	0.558264i
$31$	−1.71277	+	2.96661i	−0.307623	+	0.532818i	−0.977842	−	0.209345i	$-0.932867\pi$
$31$	−1.71277	+	2.96661i	−0.307623	+	0.532818i	0.670219	+	0.742163i	$0.266200\pi$
$32$	−2.69208	+	4.66283i	−0.475898	+	0.824279i
$33$	5.43912	+	1.84822i	0.946830	+	0.321734i
$34$	−4.40831			−0.756019
$35$	4.07228	+	7.30763i	0.688341	+	1.23521i
$36$	−3.27716	+	0.764660i	−0.546193	+	0.127443i
$37$	2.08135	+	3.60500i	0.342172	+	0.592658i	0.984836	−	0.173490i	$-0.0555043\pi$
$37$	2.08135	+	3.60500i	0.342172	+	0.592658i	−0.642664	+	0.766148i	$0.722171\pi$
$38$	5.85150	+	3.37836i	0.949238	+	0.548043i
$39$	2.83521	+	1.22885i	0.453998	+	0.196773i
$40$	8.01112	−	4.62522i	1.26667	−	0.731312i
$41$	−0.272850			−0.0426121			−0.0213060	−	0.999773i	$-0.506782\pi$
$41$	−0.272850			−0.0426121			−0.0213060	+	0.999773i	$0.506782\pi$
$42$	−0.426263	−	4.27341i	−0.0657737	−	0.659401i
$43$		−	5.32723i		−	0.812395i	−0.913785	−	0.406198i	$-0.866854\pi$
$43$		−	5.32723i		−	0.812395i	0.913785	−	0.406198i	$-0.133146\pi$
$44$	−3.36254	−	1.59196i	−0.506922	−	0.239997i
$45$	9.07778	+	2.75218i	1.35324	+	0.410271i
$46$	−0.433675	−	0.250382i	−0.0639419	−	0.0369168i
$47$	7.52310	−	4.34347i	1.09736	−	0.633560i	0.161832	−	0.986818i	$-0.448260\pi$
$47$	7.52310	−	4.34347i	1.09736	−	0.633560i	0.935526	+	0.353259i	$0.114926\pi$
$48$	−0.857364	+	0.0986989i	−0.123750	+	0.0142460i
$49$	−6.99677	−	0.212706i	−0.999538	−	0.0303866i
$50$	−4.68379			−0.662388
$51$	4.85390	+	6.54366i	0.679681	+	0.916296i
$52$	−1.73311	−	1.00061i	−0.240339	−	0.138760i
$53$	9.61932	+	5.55372i	1.32132	+	0.762862i	0.983938	−	0.178508i	$-0.0571270\pi$
$53$	9.61932	+	5.55372i	1.32132	+	0.762862i	0.337377	+	0.941370i	$0.390460\pi$
$54$	−3.71396	−	3.14958i	−0.505406	−	0.428603i
$55$	5.96478	+	8.62541i	0.804291	+	1.16305i
$56$	−0.117614	+	7.73942i	−0.0157169	+	1.03422i
$57$	−1.42814	−	12.4058i	−0.189162	−	1.64318i
$58$	3.02802	+	5.24469i	0.397599	+	0.688662i
$59$	−3.88158	−	2.24103i	−0.505339	−	0.291758i	0.225577	−	0.974225i	$-0.427573\pi$
$59$	−3.88158	−	2.24103i	−0.505339	−	0.291758i	−0.730916	+	0.682468i	$0.760907\pi$
$60$	−5.63663	−	2.44305i	−0.727686	−	0.315397i
$61$	−1.14182	+	0.659230i	−0.146195	+	0.0844057i	−0.571313	−	0.820732i	$-0.693566\pi$
$61$	−1.14182	+	0.659230i	−0.146195	+	0.0844057i	0.425118	+	0.905138i	$0.360233\pi$
$62$	3.21029			0.407707
$63$	−5.87407	+	5.33810i	−0.740063	+	0.672537i
$64$	6.04237			0.755297
$65$	2.82053	+	4.88530i	0.349843	+	0.605947i
$66$	−1.04864	−	5.28047i	−0.129079	−	0.649980i
$67$	0.766303	−	1.32728i	0.0936188	−	0.162153i	−0.815413	−	0.578880i	$-0.803490\pi$
$67$	0.766303	−	1.32728i	0.0936188	−	0.162153i	0.909031	+	0.416728i	$0.136823\pi$
$68$	−2.63825	−	4.56958i	−0.319934	−	0.554142i
$69$	0.105844	+	0.919435i	0.0127422	+	0.110687i
$70$	4.02272	−	6.72930i	0.480807	−	0.804305i
$71$		−	15.2685i		−	1.81204i	−0.423234	−	0.906021i	$-0.639105\pi$
$71$		−	15.2685i		−	1.81204i	0.423234	−	0.906021i	$-0.360895\pi$
$72$	6.00067	+	6.40486i	0.707185	+	0.754820i
$73$	0.516234	+	0.298048i	0.0604206	+	0.0348838i	0.529906	−	0.848056i	$-0.322227\pi$
$73$	0.516234	+	0.298048i	0.0604206	+	0.0348838i	−0.469485	+	0.882940i	$0.655561\pi$
$74$	1.95056	−	3.37847i	0.226748	−	0.392739i
$75$	5.15722	+	6.95258i	0.595505	+	0.802815i
$76$			8.08741i			0.927690i
$77$	−8.75573	+	0.580726i	−0.997808	+	0.0661799i
$78$	−0.331185	−	2.87689i	−0.0374993	−	0.325744i
$79$	10.5470	−	6.08934i	1.18663	−	0.685104i	0.229095	−	0.973404i	$-0.426423\pi$
$79$	10.5470	−	6.08934i	1.18663	−	0.685104i	0.957540	+	0.288300i	$0.0930901\pi$
$80$	−1.36442	−	0.787747i	−0.152547	−	0.0880728i
$81$	−0.585853	+	8.98091i	−0.0650947	+	0.997879i
$82$	0.127852	+	0.221447i	0.0141189	+	0.0244547i
$83$	3.20502			0.351796			0.175898	−	0.984408i	$-0.443717\pi$
$83$	3.20502			0.351796			0.175898	+	0.984408i	$0.443717\pi$
$84$	4.17463	−	2.99937i	0.455490	−	0.327258i
$85$			14.8734i			1.61325i
$86$	−4.32361	+	2.49624i	−0.466227	+	0.269176i
$87$	4.45109	−	10.2696i	0.477207	−	1.10102i
$88$	0.789183	+	9.67085i	0.0841272	+	1.03092i
$89$	−7.21745	+	4.16700i	−0.765049	+	0.441701i	−0.831105	−	0.556115i	$-0.812291\pi$
$89$	−7.21745	+	4.16700i	−0.765049	+	0.441701i	0.0660568	+	0.997816i	$0.478958\pi$
$90$	−2.01999	−	8.65720i	−0.212925	−	0.912549i
$91$	−4.71961	−	0.0717229i	−0.494749	−	0.00751861i
$92$		−	0.599386i		−	0.0624903i
$93$	−3.53478	−	4.76533i	−0.366540	−	0.494142i
$94$	−7.05036	−	4.07053i	−0.727189	−	0.419843i
$95$	11.3984	−	19.7427i	1.16945	−	2.02555i
$96$	−5.55586	−	7.49001i	−0.567043	−	0.764446i
$97$	−6.02514			−0.611760			−0.305880	−	0.952070i	$-0.598951\pi$
$97$	−6.02514			−0.611760			−0.305880	+	0.952070i	$0.598951\pi$
$98$	3.10592	+	5.77829i	0.313745	+	0.583695i
$99$	−6.68365	+	7.37081i	−0.671732	+	0.740794i
$100$	−2.80311	−	4.85513i	−0.280311	−	0.485513i
$101$	−3.92046	+	6.79044i	−0.390100	+	0.675674i	−0.992462	−	0.122549i	$-0.960893\pi$
$101$	−3.92046	+	6.79044i	−0.390100	+	0.675674i	0.602362	+	0.798223i	$0.294226\pi$
$102$	3.03643	−	7.00568i	0.300652	−	0.693666i
$103$	−5.51941	−	9.55989i	−0.543843	−	0.941964i	−0.998679	−	0.0513887i	$-0.983635\pi$
$103$	−5.51941	−	9.55989i	−0.543843	−	0.941964i	0.454835	−	0.890575i	$-0.349698\pi$
$104$			5.21935i			0.511800i
$105$	−14.4183	+	1.43819i	−1.40708	+	0.140353i
$106$		−	10.4095i		−	1.01106i
$107$	0.783533	+	1.35712i	0.0757470	+	0.131198i	0.901411	−	0.432965i	$-0.142533\pi$
$107$	0.783533	+	1.35712i	0.0757470	+	0.131198i	−0.825664	+	0.564162i	$0.809199\pi$
$108$	1.04210	−	5.73476i	0.100276	−	0.551827i
$109$	−7.03267	−	4.06031i	−0.673607	−	0.388907i	0.123835	−	0.992303i	$-0.460481\pi$
$109$	−7.03267	−	4.06031i	−0.673607	−	0.388907i	−0.797442	+	0.603396i	$0.793814\pi$
$110$	4.20545	−	8.88275i	0.400974	−	0.846937i
$111$	−7.16270	+	0.824563i	−0.679853	+	0.0782640i
$112$	1.15156	−	0.641723i	0.108812	−	0.0606372i
$113$			4.59925i			0.432661i	0.976320	+	0.216330i	$0.0694089\pi$
$113$			4.59925i			0.432661i	−0.976320	+	0.216330i	$0.930591\pi$
$114$	−9.39939	+	6.97219i	−0.880334	+	0.653005i
$115$	−0.844777	+	1.46320i	−0.0787759	+	0.136444i
$116$	−3.62437	+	6.27759i	−0.336514	+	0.582860i
$117$	−3.90578	+	3.65929i	−0.361089	+	0.338302i
$118$			4.20042i			0.386680i
$119$	−10.6822	−	6.38572i	−0.979234	−	0.585378i
$120$	1.83236	+	15.9171i	0.167271	+	1.45303i
$121$	−10.8545	+	1.78342i	−0.986770	+	0.162129i
$122$	1.07007	+	0.617805i	0.0968795	+	0.0559334i
$123$	0.187939	−	0.433614i	0.0169459	−	0.0390977i
$124$	1.92126	+	3.32773i	0.172535	+	0.298839i
$125$		−	0.00681387i		−	0.000609451i
$126$	7.08491	+	2.26610i	0.631174	+	0.201880i
$127$		−	0.203320i		−	0.0180418i	−0.999959	−	0.00902088i	$-0.997129\pi$
$127$		−	0.203320i		−	0.0180418i	0.999959	−	0.00902088i	$-0.00287147\pi$
$128$	2.55283	+	4.42163i	0.225640	+	0.390821i
$129$	8.46604	+	3.66939i	0.745393	+	0.323071i
$130$	2.64329	−	4.57831i	0.231832	−	0.401545i
$131$	−5.19706	−	9.00158i	−0.454070	−	0.786472i	0.544565	−	0.838719i	$-0.316695\pi$
$131$	−5.19706	−	9.00158i	−0.454070	−	0.786472i	−0.998634	+	0.0522474i	$0.983362\pi$
$132$	4.84606	−	4.24721i	0.421795	−	0.369672i
$133$	9.28552	+	16.6627i	0.805157	+	1.44484i
$134$	−1.43630			−0.124077
$135$	−10.6265	+	12.5307i	−0.914586	+	1.07847i
$136$	−6.88077	+	11.9178i	−0.590021	+	1.02195i
$137$	−1.70496	−	0.984357i	−0.145664	−	0.0840993i	0.425397	−	0.905007i	$-0.360135\pi$
$137$	−1.70496	−	0.984357i	−0.145664	−	0.0840993i	−0.571061	+	0.820908i	$0.693468\pi$
$138$	0.696622	−	0.516733i	0.0593004	−	0.0439873i
$139$		−	14.7039i		−	1.24717i	−0.781754	−	0.623586i	$-0.785675\pi$
$139$		−	14.7039i		−	1.24717i	0.781754	−	0.623586i	$-0.214325\pi$
$140$	9.38296	+	0.142591i	0.793005	+	0.0120511i
$141$	1.72074	+	14.9475i	0.144912	+	1.25881i
$142$	−12.3920	+	7.15454i	−1.03992	+	0.600396i
$143$	−5.89742	+	0.481255i	−0.493167	+	0.0402446i
$144$	0.433698	−	1.43051i	0.0361415	−	0.119209i
$145$	17.6953	−	10.2164i	1.46952	−	0.848426i
$146$		−	0.558637i		−	0.0462332i
$147$	5.15739	−	10.9728i	0.425374	−	0.905017i
$148$	4.66941			0.383824
$149$	−5.29621	−	9.17331i	−0.433883	−	0.751507i	0.563321	−	0.826238i	$-0.309523\pi$
$149$	−5.29621	−	9.17331i	−0.433883	−	0.751507i	−0.997204	+	0.0747314i	$0.976190\pi$
$150$	3.22618	−	7.44348i	0.263417	−	0.607757i
$151$	14.5883	+	8.42258i	1.18718	+	0.685420i	0.957665	−	0.287884i	$-0.0929519\pi$
$151$	14.5883	+	8.42258i	1.18718	+	0.685420i	0.229517	+	0.973305i	$0.426285\pi$
$152$	18.2668	−	10.5463i	1.48163	−	0.855420i
$153$	−13.7425	+	3.20655i	−1.11102	+	0.259234i
$154$	4.57409	+	6.83408i	0.368590	+	0.550706i
$155$		−	10.8314i		−	0.869995i
$156$	2.78393	−	2.06504i	0.222893	−	0.165335i
$157$	1.61510	−	2.79743i	0.128899	−	0.223259i	−0.794351	−	0.607459i	$-0.792189\pi$
$157$	1.61510	−	2.79743i	0.128899	−	0.223259i	0.923250	+	0.384199i	$0.125522\pi$
$158$	−9.88428	−	5.70669i	−0.786351	−	0.454000i
$159$	−15.4517	+	11.4616i	−1.22540	+	0.908967i
$160$		−	17.0244i		−	1.34590i
$161$	−0.688182	−	1.23493i	−0.0542364	−	0.0973261i
$162$	7.56348	−	3.73280i	0.594243	−	0.293277i
$163$	−6.56336	−	11.3681i	−0.514082	−	0.890417i	−0.999867	−	0.0163379i	$-0.994799\pi$
$163$	−6.56336	−	11.3681i	−0.514082	−	0.890417i	0.485784	−	0.874079i	$-0.338534\pi$
$164$	−0.153032	+	0.265059i	−0.0119498	+	0.0206977i
$165$	−17.8160	+	3.53807i	−1.38698	+	0.275438i
$166$	−1.50181	−	2.60121i	−0.116563	−	0.201893i
$167$	20.1667			1.56054			0.780272	−	0.625440i	$-0.215081\pi$
$167$	20.1667			1.56054			0.780272	+	0.625440i	$0.215081\pi$
$168$	−12.2185	−	5.51781i	−0.942676	−	0.425708i
$169$	9.81716			0.755166
$170$	12.0713	−	6.96940i	0.925830	−	0.534528i
$171$	20.6989	+	6.27546i	1.58289	+	0.479897i
$172$	−5.17511	−	2.98785i	−0.394599	−	0.227822i
$173$	1.80703	+	3.12987i	0.137386	+	0.237959i	0.926506	−	0.376279i	$-0.122797\pi$
$173$	1.80703	+	3.12987i	0.137386	+	0.237959i	−0.789120	+	0.614238i	$0.789463\pi$
$174$	−10.4206	+	1.19960i	−0.789981	+	0.0909418i
$175$	−11.3497	−	6.78477i	−0.857958	−	0.512880i
$176$	1.35922	−	0.939950i	0.102455	−	0.0708514i
$177$	6.23507	−	4.62499i	0.468657	−	0.347636i
$178$	6.76392	+	3.90515i	0.506977	+	0.292703i
$179$	13.0707	+	7.54635i	0.976947	+	0.564041i	0.901347	−	0.433098i	$-0.142580\pi$
$179$	13.0707	+	7.54635i	0.976947	+	0.564041i	0.0755999	+	0.997138i	$0.475913\pi$
$180$	7.76500	−	7.27497i	0.578769	−	0.542244i
$181$	17.0763			1.26927			0.634636	−	0.772811i	$-0.281150\pi$
$181$	17.0763			1.26927			0.634636	+	0.772811i	$0.281150\pi$
$182$	2.15331	+	3.86407i	0.159614	+	0.286424i
$183$	−0.261165	−	2.26866i	−0.0193059	−	0.167704i
$184$	−1.35381	+	0.781625i	−0.0998046	+	0.0576222i
$185$	−11.3988	−	6.58109i	−0.838055	−	0.483851i
$186$	−2.21124	+	5.10179i	−0.162136	+	0.374081i
$187$	−14.1006	−	6.67579i	−1.03114	−	0.488182i
$188$		−	9.74438i		−	0.710682i
$189$	−4.43727	−	13.0119i	−0.322764	−	0.946480i
$190$	−21.3643			−1.54993
$191$	11.2551	−	6.49812i	0.814388	−	0.470187i	−0.0340893	−	0.999419i	$-0.510853\pi$
$191$	11.2551	−	6.49812i	0.814388	−	0.470187i	0.848477	+	0.529232i	$0.177520\pi$
$192$	−4.16197	+	9.60254i	−0.300365	+	0.693004i
$193$	−9.40394	−	5.42937i	−0.676911	−	0.390815i	0.121779	−	0.992557i	$-0.461140\pi$
$193$	−9.40394	−	5.42937i	−0.676911	−	0.390815i	−0.798690	+	0.601743i	$0.794473\pi$
$194$	2.82326	+	4.89004i	0.202698	+	0.351084i
$195$	−9.70649	+	1.11740i	−0.695096	+	0.0800188i
$196$	−4.13087	+	6.67768i	−0.295062	+	0.476977i
$197$	4.91397			0.350106			0.175053	−	0.984559i	$-0.443990\pi$
$197$	4.91397			0.350106			0.175053	+	0.984559i	$0.443990\pi$
$198$	9.11402	+	1.97067i	0.647705	+	0.140049i
$199$	7.91125	−	13.7027i	0.560814	−	0.971358i	−0.436612	−	0.899650i	$-0.643822\pi$
$199$	7.91125	−	13.7027i	0.560814	−	0.971358i	0.997426	−	0.0717077i	$-0.0228449\pi$
$200$	−7.31076	+	12.6626i	−0.516949	+	0.895381i
$201$	1.58148	+	2.13203i	0.111549	+	0.150382i
$202$	7.34821			0.517018
$203$	−0.259792	+	17.0952i	−0.0182338	+	1.19985i
$204$	9.07919	−	1.04519i	0.635670	−	0.0731778i
$205$	0.747151	−	0.431368i	0.0521833	−	0.0301280i
$206$	−5.17258	+	8.95916i	−0.360390	+	0.624214i
$207$	−1.53407	−	0.465097i	−0.106625	−	0.0323265i
$208$	0.769841	−	0.444468i	0.0533789	−	0.0308183i
$209$	13.6008	+	19.6675i	0.940784	+	1.36043i
$210$	7.92336	+	11.0280i	0.546764	+	0.761007i
$211$			11.6217i			0.800072i	0.916499	+	0.400036i	$0.131002\pi$
$211$			11.6217i			0.800072i	−0.916499	+	0.400036i	$0.868998\pi$
$212$	10.7903	−	6.22976i	0.741079	−	0.427862i
$213$	24.2648	+	10.5169i	1.66259	+	0.720608i
$214$	0.734297	−	1.27184i	0.0501955	−	0.0869412i
$215$	8.42219	+	14.5877i	0.574388	+	0.994870i
$216$	−14.3119	+	5.12461i	−0.973799	+	0.348685i
$217$	7.77914	+	4.65031i	0.528083	+	0.315684i
$218$			7.61033i			0.515437i
$219$	−0.829238	+	0.615104i	−0.0560347	+	0.0415649i
$220$	11.7245	−	0.956773i	0.790469	−	0.0645057i
$221$	−7.26767	−	4.19599i	−0.488877	−	0.282253i
$222$	4.02552	+	5.42691i	0.270175	+	0.364230i
$223$	4.27079			0.285993			0.142996	−	0.989723i	$-0.454326\pi$
$223$	4.27079			0.285993			0.142996	+	0.989723i	$0.454326\pi$
$224$	12.2270	+	7.30922i	0.816953	+	0.488368i
$225$	−14.6013	+	3.40693i	−0.973422	+	0.227129i
$226$	3.73278	−	2.15512i	0.248301	−	0.143356i
$227$	−13.9676	+	24.1925i	−0.927059	+	1.60571i	−0.138843	+	0.990314i	$0.544338\pi$
$227$	−13.9676	+	24.1925i	−0.927059	+	1.60571i	−0.788216	+	0.615399i	$0.788995\pi$
$228$	−12.8525	−	5.57059i	−0.851179	−	0.368921i
$229$	4.87568	+	8.44492i	0.322194	+	0.558056i	0.980940	−	0.194309i	$-0.0622464\pi$
$229$	4.87568	+	8.44492i	0.322194	+	0.558056i	−0.658747	+	0.752365i	$0.728913\pi$
$230$	1.58339			0.104405
$231$	5.10804	−	14.3146i	0.336084	−	0.941832i
$232$	18.9053			1.24120
$233$	−9.45487	−	16.3763i	−0.619409	−	1.07285i	−0.989594	−	0.143890i	$-0.954039\pi$
$233$	−9.45487	−	16.3763i	−0.619409	−	1.07285i	0.370184	−	0.928958i	$-0.379295\pi$
$234$	4.80008	+	1.45528i	0.313791	+	0.0951344i
$235$	−13.7338	+	23.7876i	−0.895892	+	1.55173i
$236$	−4.35408	+	2.51383i	−0.283426	+	0.163636i
$237$	2.41240	+	20.9557i	0.156702	+	1.36122i
$238$	−0.177224	+	11.6619i	−0.0114877	+	0.755931i
$239$	−24.0475			−1.55550			−0.777751	−	0.628572i	$-0.783640\pi$
$239$	−24.0475			−1.55550			−0.777751	+	0.628572i	$0.783640\pi$
$240$	2.19170	−	1.62573i	0.141473	−	0.104941i
$241$	−16.0852	−	9.28678i	−1.03614	−	0.598214i	−0.117400	−	0.993085i	$-0.537456\pi$
$241$	−16.0852	−	9.28678i	−1.03614	−	0.598214i	−0.918737	+	0.394871i	$0.870789\pi$
$242$	6.53363	+	7.97387i	0.419997	+	0.512580i
$243$	−13.8689	−	7.11707i	−0.889693	−	0.456560i
$244$			1.47895i			0.0946803i
$245$	19.4957	−	10.4792i	1.24553	−	0.669492i
$246$	−0.439988	+	0.0506510i	−0.0280526	+	0.00322939i
$247$	6.43130	+	11.1393i	0.409214	+	0.708779i
$248$	5.01082	−	8.67900i	0.318188	−	0.551117i
$249$	−2.20761	+	5.09341i	−0.139901	+	0.322782i
$250$	−0.00553018	+	0.00319285i	−0.000349759	+	0.000201933i
$251$		−	9.20292i		−	0.580883i	−0.956893	−	0.290442i	$-0.906198\pi$
$251$		−	9.20292i		−	0.580883i	0.956893	−	0.290442i	$-0.0938022\pi$
$252$	1.89112	+	8.70029i	0.119129	+	0.548066i
$253$	−1.00800	−	1.45762i	−0.0633724	−	0.0916401i
$254$	−0.165016	+	0.0952719i	−0.0103540	+	0.00597789i
$255$	−23.6368	−	10.2448i	−1.48020	−	0.641553i
$256$	8.43479	−	14.6095i	0.527174	−	0.913092i
$257$	−7.73965	+	4.46849i	−0.482786	+	0.278737i	−0.721577	−	0.692334i	$-0.756582\pi$
$257$	−7.73965	+	4.46849i	−0.482786	+	0.278737i	0.238791	+	0.971071i	$0.423249\pi$
$258$	−0.988929	−	8.59049i	−0.0615680	−	0.534820i
$259$	9.62051	−	5.36116i	0.597789	−	0.333127i
$260$	6.32773			0.392429
$261$	13.2545	+	14.1474i	0.820436	+	0.875699i
$262$	−4.87049	+	8.43593i	−0.300900	+	0.521174i
$263$	6.09106	−	10.5500i	0.375591	−	0.650543i	−0.614824	−	0.788664i	$-0.710773\pi$
$263$	6.09106	−	10.5500i	0.375591	−	0.650543i	0.990415	+	0.138121i	$0.0441064\pi$
$264$	−15.9125	−	5.40709i	−0.979347	−	0.332783i
$265$	−35.1210			−2.15747
$266$	9.17252	−	15.3440i	0.562403	−	0.940801i
$267$	−1.65083	−	14.3402i	−0.101029	−	0.877606i
$268$	−0.859584	−	1.48884i	−0.0525074	−	0.0909456i
$269$	12.6920	+	7.32776i	0.773848	+	0.446781i	0.834245	−	0.551393i	$-0.185904\pi$
$269$	12.6920	+	7.32776i	0.773848	+	0.446781i	−0.0603979	+	0.998174i	$0.519237\pi$
$270$	15.1494	+	2.75290i	0.921962	+	0.167536i
$271$	−3.17148	+	1.83106i	−0.192654	+	0.111229i	−0.593224	−	0.805037i	$-0.702145\pi$
$271$	−3.17148	+	1.83106i	−0.192654	+	0.111229i	0.400571	+	0.916266i	$0.368812\pi$
$272$	2.34380			0.142114
$273$	3.36484	−	7.45100i	0.203649	−	0.450955i
$274$			1.84500i			0.111461i
$275$	−14.9818	−	7.09296i	−0.903434	−	0.427722i
$276$	0.952545	+	0.412856i	0.0573365	+	0.0248510i
$277$	3.17609	+	1.83372i	0.190833	+	0.110177i	0.592372	−	0.805664i	$-0.298191\pi$
$277$	3.17609	+	1.83372i	0.190833	+	0.110177i	−0.401540	+	0.915842i	$0.631525\pi$
$278$	−11.9338	+	6.88999i	−0.715742	+	0.413234i
$279$	10.0078	−	2.33513i	0.599152	−	0.139800i
$280$	−11.9137	−	21.3789i	−0.711981	−	1.27764i
$281$	12.7023			0.757755			0.378878	−	0.925447i	$-0.376310\pi$
$281$	12.7023			0.757755			0.378878	+	0.925447i	$0.376310\pi$
$282$	11.3252	−	8.40067i	0.674404	−	0.500253i
$283$	−0.676315	−	0.390471i	−0.0402028	−	0.0232111i	0.479764	−	0.877398i	$-0.340722\pi$
$283$	−0.676315	−	0.390471i	−0.0402028	−	0.0232111i	−0.519967	+	0.854187i	$0.674056\pi$
$284$	−14.8325	−	8.56357i	−0.880149	−	0.508154i
$285$	23.5238	+	31.7131i	1.39343	+	1.87852i
$286$	3.15401	+	4.56087i	0.186500	+	0.269690i
$287$	−0.0109692	+	0.721811i	−0.000647492	+	0.0426072i
$288$	15.7300	−	3.67028i	0.926898	−	0.216273i
$289$	−2.56331	−	4.43978i	−0.150783	−	0.261164i
$290$	−16.5834	−	9.57442i	−0.973810	−	0.562229i
$291$	4.15010	−	9.57515i	0.243283	−	0.561305i
$292$	0.579074	−	0.334328i	0.0338877	−	0.0195651i
$293$	−23.7016			−1.38466			−0.692332	−	0.721579i	$-0.743417\pi$
$293$	−23.7016			−1.38466			−0.692332	+	0.721579i	$0.743417\pi$
$294$	−11.3222	+	0.955854i	−0.660324	+	0.0557465i
$295$	14.1720			0.825126
$296$	−6.08912	−	10.5467i	−0.353923	−	0.613012i
$297$	−7.11001	−	15.6987i	−0.412564	−	0.910928i
$298$	−4.96341	+	8.59687i	−0.287522	+	0.498003i
$299$	−0.476646	−	0.825576i	−0.0275652	−	0.0477443i
$300$	9.64656	−	1.11050i	0.556944	−	0.0641149i
$301$	−14.0929	−	0.214167i	−0.812302	−	0.0123444i
$302$		−	15.7866i		−	0.908419i
$303$	−8.09096	−	10.9076i	−0.464814	−	0.626627i
$304$	−3.11111	−	1.79620i	−0.178435	−	0.103019i
$305$	2.08444	−	3.61036i	0.119355	−	0.206729i
$306$	9.04195	+	9.65100i	0.516894	+	0.551711i
$307$		−	22.2786i		−	1.27150i	−0.771893	−	0.635752i	$-0.780690\pi$
$307$		−	22.2786i		−	1.27150i	0.771893	−	0.635752i	$-0.219310\pi$
$308$	−4.34663	+	8.83142i	−0.247672	+	0.503217i
$309$	18.9943	−	2.18661i	1.08055	−	0.124392i
$310$	−8.79079	+	5.07536i	−0.499283	+	0.288261i
$311$	−24.2108	−	13.9781i	−1.37287	−	0.792625i	−0.381578	−	0.924337i	$-0.624619\pi$
$311$	−24.2108	−	13.9781i	−1.37287	−	0.792625i	−0.991288	+	0.131712i	$0.957953\pi$
$312$	−8.29460	−	3.59508i	−0.469589	−	0.203531i
$313$	2.43634	+	4.21987i	0.137710	+	0.238521i	0.926630	−	0.375976i	$-0.122692\pi$
$313$	2.43634	+	4.21987i	0.137710	+	0.238521i	−0.788919	+	0.614497i	$0.789359\pi$
$314$	−3.02722			−0.170836
$315$	7.64570	−	23.9041i	0.430786	−	1.34685i
$316$		−	13.6612i		−	0.768500i
$317$	5.27726	−	3.04683i	0.296401	−	0.171127i	−0.344424	−	0.938814i	$-0.611926\pi$
$317$	5.27726	−	3.04683i	0.296401	−	0.171127i	0.640825	+	0.767687i	$0.278593\pi$
$318$	16.5427	+	7.17001i	0.927670	+	0.402074i
$319$	1.74318	+	21.3614i	0.0975995	+	1.19601i
$320$	−16.5459	+	9.55280i	−0.924946	+	0.534018i
$321$	−2.69643	+	0.310410i	−0.150500	+	0.0173254i
$322$	−0.679807	+	1.13720i	−0.0378842	+	0.0633735i
$323$			33.9140i			1.88703i
$324$	8.39588	+	5.60620i	0.466438	+	0.311455i
$325$	−7.72184	−	4.45820i	−0.428330	−	0.247297i
$326$	−6.15093	+	10.6537i	−0.340669	+	0.590055i
$327$	11.2967	−	8.37958i	0.624711	−	0.463392i
$328$	0.798241			0.0440755
$329$	−11.1880	−	20.0766i	−0.616812	−	1.10686i
$330$	11.2198	+	12.8017i	0.617628	+	0.704712i
$331$	0.936773	+	1.62254i	0.0514897	+	0.0891828i	0.890622	−	0.454745i	$-0.150270\pi$
$331$	0.936773	+	1.62254i	0.0514897	+	0.0891828i	−0.839132	+	0.543928i	$0.816936\pi$
$332$	1.79758	−	3.11350i	0.0986550	−	0.170875i
$333$	3.62325	−	11.9509i	0.198553	−	0.654906i
$334$	−9.44972	−	16.3674i	−0.517066	−	0.895584i
$335$			4.84600i			0.264765i
$336$	0.226635	+	2.27208i	0.0123639	+	0.123952i
$337$			9.37434i			0.510653i	0.966855	+	0.255326i	$0.0821829\pi$
$337$			9.37434i			0.510653i	−0.966855	+	0.255326i	$0.917817\pi$
$338$	−4.60013	−	7.96767i	−0.250214	−	0.433384i
$339$	−7.30913	−	3.16795i	−0.396977	−	0.172060i
$340$	14.4487	+	8.34197i	0.783591	+	0.452407i
$341$	10.2686	+	4.86155i	0.556073	+	0.263267i
$342$	−4.60593	−	19.7399i	−0.249060	−	1.06741i
$343$	−0.843989	+	18.5010i	−0.0455711	+	0.998961i
$344$			15.5852i			0.840295i
$345$	−1.74343	−	2.35037i	−0.0938633	−	0.126540i
$346$	1.69348	−	2.93319i	0.0910420	−	0.157689i
$347$	−3.89515	+	6.74660i	−0.209103	+	0.362176i	−0.951432	−	0.307859i	$-0.900388\pi$
$347$	−3.89515	+	6.74660i	−0.209103	+	0.362176i	0.742329	+	0.670035i	$0.233721\pi$
$348$	−7.47990	−	10.0838i	−0.400965	−	0.540551i
$349$			22.5765i			1.20849i	0.796798	+	0.604245i	$0.206525\pi$
$349$			22.5765i			1.20849i	−0.796798	+	0.604245i	$0.793475\pi$
$350$	−0.188299	+	12.3907i	−0.0100650	+	0.662311i
$351$	−3.12506	−	8.72758i	−0.166803	−	0.465844i
$352$	16.1398	+	7.64124i	0.860255	+	0.407279i
$353$	−12.2759	−	7.08749i	−0.653380	−	0.377229i	0.136370	−	0.990658i	$-0.456456\pi$
$353$	−12.2759	−	7.08749i	−0.653380	−	0.377229i	−0.789750	+	0.613429i	$0.789790\pi$
$354$	−6.67531	−	2.89324i	−0.354788	−	0.153774i
$355$	24.1391	+	41.8101i	1.28117	+	2.21905i
$356$			9.34848i			0.495469i
$357$	17.5060	−	12.5776i	0.926518	−	0.665680i
$358$		−	14.1443i		−	0.747549i
$359$	8.70834	+	15.0833i	0.459609	+	0.796065i	0.998940	−	0.0460281i	$-0.0146564\pi$
$359$	8.70834	+	15.0833i	0.459609	+	0.796065i	−0.539332	+	0.842093i	$0.681323\pi$
$360$	−26.5576	−	8.05169i	−1.39971	−	0.424361i
$361$	16.4904	−	28.5623i	0.867918	−	1.50328i
$362$	−8.00163	−	13.8592i	−0.420557	−	0.728425i
$363$	4.64232	−	18.4783i	0.243659	−	0.969861i
$364$	−2.71673	+	4.54462i	−0.142396	+	0.238203i
$365$	−1.88482			−0.0986558
$366$	−1.71888	+	1.27501i	−0.0898471	+	0.0666459i
$367$	8.84702	−	15.3235i	0.461811	−	0.799880i	−0.537241	−	0.843429i	$-0.680533\pi$
$367$	8.84702	−	15.3235i	0.461811	−	0.799880i	0.999051	+	0.0435495i	$0.0138666\pi$
$368$	0.230576	+	0.133123i	0.0120196	+	0.00693951i
$369$	0.559648	+	0.597345i	0.0291341	+	0.0310965i
$370$			12.3351i			0.641271i
$371$	15.0788	−	25.2241i	0.782851	−	1.30957i
$372$	−6.61179	+	0.761143i	−0.342805	+	0.0394634i
$373$	25.6488	−	14.8083i	1.32804	−	0.766747i	0.343047	−	0.939318i	$-0.388541\pi$
$373$	25.6488	−	14.8083i	1.32804	−	0.766747i	0.984997	+	0.172572i	$0.0552076\pi$
$374$	1.18916	+	14.5723i	0.0614900	+	0.753514i
$375$	0.0108286	+	0.00469338i	0.000559187	+	0.000242365i
$376$	−22.0093	+	12.7071i	−1.13504	+	0.655318i
$377$			11.5287i			0.593761i
$378$	−8.48135	+	9.69846i	−0.436234	+	0.498835i
$379$	−31.4441			−1.61518			−0.807588	−	0.589747i	$-0.799227\pi$
$379$	−31.4441			−1.61518			−0.807588	+	0.589747i	$0.799227\pi$
$380$	−12.7859	−	22.1459i	−0.655905	−	1.13606i
$381$	0.323117	+	0.140047i	0.0165538	+	0.00717480i
$382$	−10.5478	−	6.08978i	−0.539673	−	0.311580i
$383$	−10.1885	+	5.88231i	−0.520606	+	0.300572i	−0.737183	−	0.675694i	$-0.763844\pi$
$383$	−10.1885	+	5.88231i	−0.520606	+	0.300572i	0.216576	+	0.976266i	$0.430511\pi$
$384$	−8.78524	+	1.01135i	−0.448320	+	0.0516101i
$385$	23.0579	−	15.4327i	1.17514	−	0.786525i
$386$			10.1764i			0.517965i
$387$	−11.6628	+	10.9268i	−0.592852	+	0.555439i
$388$	−3.37928	+	5.85309i	−0.171557	+	0.297146i
$389$	7.04576	+	4.06787i	0.357234	+	0.206249i	0.667867	−	0.744281i	$-0.267208\pi$
$389$	7.04576	+	4.06787i	0.357234	+	0.206249i	−0.310633	+	0.950530i	$0.600541\pi$
$390$	5.45516	+	7.35425i	0.276233	+	0.372397i
$391$		−	2.51349i		−	0.127112i
$392$	20.4695	+	0.622285i	1.03387	+	0.0314301i
$393$	17.8850	−	2.05891i	0.902181	−	0.103858i
$394$	−2.30259	−	3.98820i	−0.116003	−	0.200923i
$395$	−19.2541	+	33.3491i	−0.968779	+	1.67797i
$396$	3.41172	+	10.6268i	0.171445	+	0.534018i
$397$	−1.71821	−	2.97603i	−0.0862345	−	0.149363i	0.819682	−	0.572819i	$-0.194150\pi$
$397$	−1.71821	−	2.97603i	−0.0862345	−	0.149363i	−0.905917	+	0.423456i	$0.860817\pi$
$398$	−14.8282			−0.743272
$399$	−32.8762	+	3.27933i	−1.64587	+	0.164172i
$400$	2.49027			0.124513
$401$	−22.9134	+	13.2291i	−1.14424	+	0.660628i	−0.947477	−	0.319823i	$-0.896376\pi$
$401$	−22.9134	+	13.2291i	−1.14424	+	0.660628i	−0.196764	+	0.980451i	$0.563043\pi$
$402$	0.989320	−	2.28257i	0.0493428	−	0.113844i
$403$	5.29258	+	3.05567i	0.263642	+	0.152214i
$404$	4.39769	+	7.61703i	0.218793	+	0.378961i
$405$	−12.5943	−	25.5188i	−0.625815	−	1.26804i
$406$	13.9963	−	7.79962i	0.694624	−	0.387089i
$407$	11.3554	−	7.85264i	0.562865	−	0.389241i
$408$	−14.2004	−	19.1439i	−0.703024	−	0.947765i
$409$	25.8646	+	14.9329i	1.27892	+	0.738386i	0.976650	−	0.214835i	$-0.0689215\pi$
$409$	25.8646	+	14.9329i	1.27892	+	0.738386i	0.302272	+	0.953222i	$0.402255\pi$
$410$	−0.700201	−	0.404261i	−0.0345805	−	0.0199651i
$411$	2.73871	−	2.03149i	0.135091	−	0.100206i
$412$	−12.3826			−0.610044
$413$	−6.08458	+	10.1784i	−0.299402	+	0.500847i
$414$	0.341361	+	1.46300i	0.0167770	+	0.0719023i
$415$	−8.77635	+	5.06703i	−0.430814	+	0.248731i
$416$	8.31872	+	4.80281i	0.407859	+	0.235477i
$417$	23.3675	+	10.1280i	1.14431	+	0.495973i
$418$	9.58917	−	20.2542i	0.469022	−	0.990667i
$419$			5.99538i			0.292893i	0.989219	+	0.146447i	$0.0467837\pi$
$419$			5.99538i			0.292893i	−0.989219	+	0.146447i	$0.953216\pi$
$420$	−6.68957	+	14.8132i	−0.326417	+	0.722809i
$421$	−36.0696			−1.75792			−0.878962	−	0.476892i	$-0.841763\pi$
$421$	−36.0696			−1.75792			−0.878962	+	0.476892i	$0.841763\pi$
$422$	9.43225	−	5.44571i	0.459155	−	0.265093i
$423$	−24.9398	−	7.56120i	−1.21261	−	0.367638i
$424$	−28.1419	−	16.2478i	−1.36669	−	0.789061i
$425$	−11.7547	−	20.3597i	−0.570185	−	0.987590i
$426$	−2.83440	−	24.6214i	−0.137327	−	1.19291i
$427$	1.69805	+	3.04712i	0.0821745	+	0.147461i
$428$	1.75782			0.0849676
$429$	3.29732	−	9.70367i	0.159196	−	0.468498i
$430$	7.89295	−	13.6710i	0.380632	−	0.659274i
$431$	7.00987	−	12.1415i	0.337654	−	0.584833i	−0.646337	−	0.763052i	$-0.723700\pi$
$431$	7.00987	−	12.1415i	0.337654	−	0.584833i	0.983991	+	0.178218i	$0.0570334\pi$
$432$	1.97463	+	1.67456i	0.0950045	+	0.0805675i
$433$	17.0980			0.821679			0.410839	−	0.911708i	$-0.365236\pi$
$433$	17.0980			0.821679			0.410839	+	0.911708i	$0.365236\pi$
$434$	0.129061	−	8.49264i	0.00619512	−	0.407660i
$435$	4.04741	+	35.1585i	0.194058	+	1.68572i
$436$	−7.88874	+	4.55457i	−0.377802	+	0.218124i
$437$	−1.92624	+	3.33635i	−0.0921447	+	0.159599i
$438$	0.887787	+	0.384788i	0.0424201	+	0.0183859i
$439$	−18.4983	+	10.6800i	−0.882877	+	0.509729i	−0.871606	−	0.490207i	$-0.836921\pi$
$439$	−18.4983	+	10.6800i	−0.882877	+	0.509729i	−0.0112711	+	0.999936i	$0.503588\pi$
$440$	−17.4503	−	25.2342i	−0.831912	−	1.20299i
$441$	13.8855	+	15.7541i	0.661214	+	0.750197i
$442$			7.86464i			0.374083i
$443$	9.98238	−	5.76333i	0.474277	−	0.273824i	−0.243751	−	0.969838i	$-0.578378\pi$
$443$	9.98238	−	5.76333i	0.474277	−	0.273824i	0.718028	+	0.696014i	$0.245045\pi$
$444$	−3.21628	+	7.42064i	−0.152638	+	0.352168i
$445$	13.1758	−	22.8211i	0.624592	−	1.08183i
$446$	−2.00121	−	3.46619i	−0.0947599	−	0.164129i
$447$	18.2262	−	2.09819i	0.862072	−	0.0992408i
$448$	0.242917	−	15.9848i	0.0114768	−	0.755209i
$449$		−	7.13108i		−	0.336537i	−0.985741	−	0.168268i	$-0.946183\pi$
$449$		−	7.13108i		−	0.336537i	0.985741	−	0.168268i	$-0.0538175\pi$
$450$	9.60699	+	10.2541i	0.452878	+	0.483383i
$451$	0.0736026	+	0.901944i	0.00346581	+	0.0424709i
$452$	4.46792	+	2.57955i	0.210153	+	0.121332i
$453$	−23.4336	+	17.3823i	−1.10101	+	0.816694i
$454$	26.1797			1.22867
$455$	13.0372	−	7.26515i	0.611192	−	0.340596i
$456$	4.17811	+	36.2939i	0.195658	+	1.69962i
$457$	−9.99558	+	5.77095i	−0.467574	+	0.269954i	−0.715223	−	0.698896i	$-0.753675\pi$
$457$	−9.99558	+	5.77095i	−0.467574	+	0.269954i	0.247650	+	0.968850i	$0.420342\pi$
$458$	4.56929	−	7.91425i	0.213509	−	0.369809i
$459$	4.36998	−	24.0483i	0.203973	−	1.12248i
$460$	0.947611	+	1.64131i	0.0441826	+	0.0765265i
$461$	36.2405			1.68789			0.843945	−	0.536429i	$-0.180227\pi$
$461$	36.2405			1.68789			0.843945	+	0.536429i	$0.180227\pi$
$462$	−14.0113	+	2.56184i	−0.651867	+	0.119188i
$463$	8.34136			0.387656			0.193828	−	0.981036i	$-0.437910\pi$
$463$	8.34136			0.387656			0.193828	+	0.981036i	$0.437910\pi$
$464$	−1.60994	−	2.78849i	−0.0747394	−	0.129452i
$465$	17.2132	+	7.46061i	0.798242	+	0.345978i
$466$	−8.86074	+	15.3473i	−0.410466	+	0.710948i
$467$	17.7748	−	10.2623i	0.822520	−	0.474882i	−0.0287650	−	0.999586i	$-0.509157\pi$
$467$	17.7748	−	10.2623i	0.822520	−	0.474882i	0.851285	+	0.524704i	$0.175824\pi$
$468$	1.36419	+	5.84662i	0.0630598	+	0.270260i
$469$	−3.48043	−	2.08057i	−0.160711	−	0.0960719i
$470$	25.7415			1.18737
$471$	3.33320	+	4.49358i	0.153586	+	0.207053i
$472$	11.3558	+	6.55628i	0.522694	+	0.301777i
$473$	−17.6099	+	1.43704i	−0.809704	+	0.0660753i
$474$	15.8773	−	11.7773i	0.729271	−	0.540951i
$475$			36.0333i			1.65332i
$476$	−12.1946	+	6.79563i	−0.558940	+	0.311477i
$477$	−7.57172	−	32.4507i	−0.346685	−	1.48581i
$478$	11.2682	+	19.5171i	0.515395	+	0.892690i
$479$	−17.4458	+	30.2170i	−0.797118	+	1.38065i	0.124367	+	0.992236i	$0.460310\pi$
$479$	−17.4458	+	30.2170i	−0.797118	+	1.38065i	−0.921485	+	0.388413i	$0.873023\pi$
$480$	27.0552	+	11.7264i	1.23489	+	0.535233i
$481$	6.43150	−	3.71323i	0.293251	−	0.169309i
$482$			17.4064i			0.792841i
$483$	2.43657	−	0.243042i	0.110868	−	0.0110588i
$484$	−4.35539	+	11.5448i	−0.197972	+	0.524762i
$485$	16.4987	−	9.52555i	0.749169	−	0.432533i
$486$	0.722461	+	14.5910i	0.0327715	+	0.661862i
$487$	16.8939	−	29.2611i	0.765535	−	1.32595i	−0.174428	−	0.984670i	$-0.555808\pi$
$487$	16.8939	−	29.2611i	0.765535	−	1.32595i	0.939963	−	0.341276i	$-0.110859\pi$
$488$	3.34047	−	1.92862i	0.151216	−	0.0873045i
$489$	22.5870	−	2.60019i	1.02142	−	0.117585i
$490$	−17.6403	−	10.9124i	−0.796906	−	0.492973i
$491$	25.5711			1.15401			0.577005	−	0.816741i	$-0.304221\pi$
$491$	25.5711			1.15401			0.577005	+	0.816741i	$0.304221\pi$
$492$	−0.315824	−	0.425771i	−0.0142385	−	0.0191952i
$493$	−15.1986	+	26.3247i	−0.684509	+	1.18560i
$494$	6.02717	−	10.4394i	0.271175	−	0.469689i
$495$	6.64895	−	30.7503i	0.298848	−	1.38212i
$496$	−1.70684			−0.0766394
$497$	−40.3921	−	0.613830i	−1.81183	−	0.0275340i
$498$	5.16829	−	0.594968i	0.231596	−	0.0266612i
$499$	−0.602291	−	1.04320i	−0.0269623	−	0.0467000i	0.852229	−	0.523168i	$-0.175250\pi$
$499$	−0.602291	−	1.04320i	−0.0269623	−	0.0467000i	−0.879192	+	0.476468i	$0.841917\pi$
$500$	−0.00661930	−	0.00382166i	−0.000296024	−	0.000170910i
$501$	−13.8908	+	32.0489i	−0.620594	+	1.43184i
$502$	−7.46914	+	4.31231i	−0.333364	+	0.192468i
$503$	−21.3345			−0.951259			−0.475630	−	0.879646i	$-0.657780\pi$
$503$	−21.3345			−0.951259			−0.475630	+	0.879646i	$0.657780\pi$
$504$	17.1850	−	15.6170i	0.765479	−	0.695634i
$505$		−	24.7925i		−	1.10325i
$506$	−0.710687	+	1.50111i	−0.0315939	+	0.0667326i
$507$	−6.76204	+	15.6014i	−0.300313	+	0.692884i
$508$	−0.197514	−	0.114035i	−0.00876329	−	0.00505949i
$509$	−6.21542	+	3.58847i	−0.275494	+	0.159056i	−0.631382	−	0.775472i	$-0.717512\pi$
$509$	−6.21542	+	3.58847i	−0.275494	+	0.159056i	0.355888	+	0.934529i	$0.384178\pi$
$510$	2.76105	+	23.9843i	0.122261	+	1.06204i
$511$	0.809223	−	1.35369i	0.0357979	−	0.0598835i
$512$	−5.59819			−0.247408
$513$	−24.2304	+	28.5722i	−1.06980	+	1.26150i
$514$	7.25330	+	4.18770i	0.319930	+	0.184711i
$515$	30.2278	+	17.4520i	1.33199	+	0.769028i
$516$	8.31291	−	6.16627i	0.365955	−	0.271455i
$517$	−16.3873	−	23.6970i	−0.720713	−	1.04219i
$518$	−8.85914	−	5.29592i	−0.389248	−	0.232689i
$519$	−6.21866	+	0.715886i	−0.272969	+	0.0314239i
$520$	−8.25163	−	14.2922i	−0.361858	−	0.626757i
$521$	−14.3980	−	8.31267i	−0.630786	−	0.364185i	0.150270	−	0.988645i	$-0.451986\pi$
$521$	−14.3980	−	8.31267i	−0.630786	−	0.364185i	−0.781057	+	0.624460i	$0.785319\pi$
$522$	5.27125	−	17.3866i	0.230716	−	0.760993i
$523$	0.418988	−	0.241903i	0.0183211	−	0.0105777i	−0.490811	−	0.871266i	$-0.663300\pi$
$523$	0.418988	−	0.241903i	0.0183211	−	0.0105777i	0.509133	+	0.860688i	$0.329966\pi$
$524$	−11.6594			−0.509343
$525$	18.6000	−	13.3636i	0.811771	−	0.583237i
$526$	−11.4166			−0.497788
$527$	8.05670	+	13.9546i	0.350955	+	0.607872i
$528$	0.557540	+	2.80751i	0.0242638	+	0.122181i
$529$	−11.3572	+	19.6713i	−0.493793	+	0.855275i
$530$	16.4570	+	28.5044i	0.714848	+	1.23815i
$531$	3.05533	+	13.0945i	0.132590	+	0.568251i
$532$	21.3948	+	0.325133i	0.927583	+	0.0140963i
$533$			0.486779i			0.0210847i
$534$	−10.8650	+	8.05936i	−0.470176	+	0.348763i
$535$	−4.29113	−	2.47748i	−0.185522	−	0.107111i
$536$	−2.24187	+	3.88303i	−0.0968340	+	0.167721i
$537$	−20.9957	+	15.5740i	−0.906031	+	0.672067i
$538$		−	13.7346i		−	0.592140i
$539$	1.18428	+	23.1861i	0.0510105	+	0.998698i
$540$	6.21287	+	17.3511i	0.267359	+	0.746673i
$541$	−3.82589	+	2.20888i	−0.164488	+	0.0949672i	−0.579984	−	0.814628i	$-0.696941\pi$
$541$	−3.82589	+	2.20888i	−0.164488	+	0.0949672i	0.415496	+	0.909595i	$0.363608\pi$
$542$	2.97219	+	1.71599i	0.127667	+	0.0737083i
$543$	−11.7621	+	27.1377i	−0.504761	+	1.16459i
$544$	12.6633	+	21.9334i	0.542934	+	0.940389i
$545$	25.6769			1.09988
$546$	−7.62397	+	0.760474i	−0.326276	+	0.0325453i
$547$		−	25.9908i		−	1.11129i	−0.831421	−	0.555643i	$-0.812472\pi$
$547$		−	25.9908i		−	1.11129i	0.831421	−	0.555643i	$-0.187528\pi$
$548$	−1.91250	+	1.10418i	−0.0816979	+	0.0471683i
$549$	3.78524	+	1.14760i	0.161550	+	0.0489784i
$550$	1.26347	+	15.4829i	0.0538746	+	0.660193i
$551$	40.3485	−	23.2952i	1.71890	−	0.992410i
$552$	−0.309655	−	2.68986i	−0.0131798	−	0.114488i
$553$	−15.6850	−	28.1464i	−0.666994	−	1.19691i
$554$		−	3.43698i		−	0.146023i
$555$	18.3101	−	13.5819i	0.777222	−	0.576520i
$556$	−14.2841	−	8.24692i	−0.605780	−	0.349747i
$557$	7.54225	−	13.0636i	0.319575	−	0.553521i	−0.660824	−	0.750541i	$-0.729793\pi$
$557$	7.54225	−	13.0636i	0.319575	−	0.553521i	0.980399	+	0.197020i	$0.0631264\pi$
$558$	−6.58467	−	7.02820i	−0.278751	−	0.297528i
$559$	−9.50405			−0.401979
$560$	−2.13879	+	3.57782i	−0.0903806	+	0.151191i
$561$	20.3216	−	17.8104i	0.857979	−	0.751956i
$562$	−5.95205	−	10.3093i	−0.251072	−	0.434870i
$563$	8.33116	−	14.4300i	0.351116	−	0.608152i	−0.635329	−	0.772242i	$-0.719135\pi$
$563$	8.33116	−	14.4300i	0.351116	−	0.608152i	0.986445	+	0.164090i	$0.0524688\pi$
$564$	15.4858	+	6.71191i	0.652069	+	0.282622i
$565$	−7.27127	−	12.5942i	−0.305905	−	0.529842i
$566$			0.731869i			0.0307627i
$567$	23.7350	+	1.91089i	0.996775	+	0.0802500i
$568$			44.6691i			1.87427i
$569$	8.58116	+	14.8630i	0.359741	+	0.623090i	0.987917	−	0.154981i	$-0.0495317\pi$
$569$	8.58116	+	14.8630i	0.359741	+	0.623090i	−0.628176	+	0.778071i	$0.716198\pi$
$570$	14.7157	−	33.9522i	0.616373	−	1.42210i
$571$	−37.5397	−	21.6736i	−1.57099	−	0.907010i	−0.996048	−	0.0888142i	$-0.971692\pi$
$571$	−37.5397	−	21.6736i	−1.57099	−	0.907010i	−0.574939	−	0.818196i	$-0.694974\pi$
$572$	−2.84014	+	5.99894i	−0.118752	+	0.250828i
$573$	2.57434	+	22.3624i	0.107545	+	0.934205i
$574$	0.590966	−	0.329324i	0.0246664	−	0.0137457i
$575$		−	2.67056i		−	0.111370i
$576$	−12.3936	−	13.2284i	−0.516400	−	0.551184i
$577$	−13.1127	+	22.7118i	−0.545888	+	0.945505i	0.452663	+	0.891682i	$0.350474\pi$
$577$	−13.1127	+	22.7118i	−0.545888	+	0.945505i	−0.998550	+	0.0538233i	$0.982859\pi$
$578$	−2.40223	+	4.16079i	−0.0999198	+	0.173066i
$579$	15.1058	−	11.2050i	0.627774	−	0.465664i
$580$		−	22.9201i		−	0.951704i
$581$	0.128849	−	8.47870i	0.00534556	−	0.351756i
$582$	−9.71590	+	1.11849i	−0.402737	+	0.0463627i
$583$	15.7637	−	33.2961i	0.652867	−	1.37898i
$584$	−1.51027	−	0.871957i	−0.0624956	−	0.0360818i
$585$	4.91003	−	16.1952i	0.203005	−	0.669590i
$586$	11.1061	+	19.2364i	0.458790	+	0.794648i
$587$		−	23.1144i		−	0.954032i	−0.878895	−	0.477016i	$-0.841718\pi$
$587$		−	23.1144i		−	0.954032i	0.878895	−	0.477016i	$-0.158282\pi$
$588$	−7.76683	−	11.1643i	−0.320299	−	0.460410i
$589$		−	24.6974i		−	1.01764i
$590$	−6.64073	−	11.5021i	−0.273394	−	0.473533i
$591$	−3.38473	+	7.80928i	−0.139229	+	0.321231i
$592$	−1.03707	+	1.79626i	−0.0426233	+	0.0738258i
$593$	−2.15569	−	3.73376i	−0.0885235	−	0.153327i	0.818364	−	0.574701i	$-0.194882\pi$
$593$	−2.15569	−	3.73376i	−0.0885235	−	0.153327i	−0.906887	+	0.421373i	$0.861548\pi$
$594$	−9.40951	+	13.1266i	−0.386077	+	0.538591i
$595$	39.3468	+	0.597946i	1.61306	+	0.0245134i
$596$	−11.8818			−0.486698
$597$	16.3271	+	22.0109i	0.668222	+	0.900848i
$598$	−0.446695	+	0.773698i	−0.0182667	+	0.0316389i
$599$	26.3280	+	15.2005i	1.07573	+	0.621074i	0.929742	−	0.368212i	$-0.120030\pi$
$599$	26.3280	+	15.2005i	1.07573	+	0.621074i	0.145990	+	0.989286i	$0.453363\pi$
$600$	−15.0878	−	20.3402i	−0.615956	−	0.830386i
$601$			8.53320i			0.348077i	0.984739	+	0.174038i	$0.0556816\pi$
$601$			8.53320i			0.348077i	−0.984739	+	0.174038i	$0.944318\pi$
$602$	6.42984	+	11.5382i	0.262061	+	0.470263i
$603$	−4.47755	+	1.04475i	−0.182340	+	0.0425454i
$604$	16.3642	−	9.44785i	0.665848	−	0.384428i
$605$	26.9034	−	22.0441i	1.09378	−	0.896221i
$606$	−5.06143	+	11.6778i	−0.205607	+	0.474377i
$607$	−9.14667	+	5.28083i	−0.371252	+	0.214342i	−0.674005	−	0.738727i	$-0.735427\pi$
$607$	−9.14667	+	5.28083i	−0.371252	+	0.214342i	0.302753	+	0.953069i	$0.402094\pi$
$608$		−	38.8187i		−	1.57430i
$609$	−26.9887	−	12.1880i	−1.09364	−	0.493882i
$610$	−3.90692			−0.158187
$611$	−7.74896	−	13.4216i	−0.313490	−	0.542980i
$612$	−4.59271	+	15.1486i	−0.185649	+	0.612345i
$613$	7.43694	+	4.29372i	0.300375	+	0.173422i	0.642611	−	0.766192i	$-0.277851\pi$
$613$	7.43694	+	4.29372i	0.300375	+	0.173422i	−0.342236	+	0.939614i	$0.611184\pi$
$614$	−18.0814	+	10.4393i	−0.729706	+	0.421296i
$615$	0.170894	+	1.48450i	0.00689111	+	0.0598608i
$616$	25.6154	−	1.69895i	1.03208	−	0.0684527i
$617$			33.7157i			1.35734i	0.734442	+	0.678672i	$0.237444\pi$
$617$			33.7157i			1.35734i	−0.734442	+	0.678672i	$0.762556\pi$
$618$	−10.6750	−	14.3913i	−0.429413	−	0.578903i
$619$	−4.38303	+	7.59162i	−0.176169	+	0.305133i	−0.940565	−	0.339613i	$-0.889704\pi$
$619$	−4.38303	+	7.59162i	−0.176169	+	0.305133i	0.764396	+	0.644747i	$0.223037\pi$
$620$	−10.5221	−	6.07492i	−0.422576	−	0.243975i
$621$	1.79580	−	2.11759i	0.0720628	−	0.0849759i
$622$			26.1995i			1.05050i
$623$	10.7334	+	19.2609i	0.430025	+	0.771672i
$624$	0.176084	+	1.52958i	0.00704900	+	0.0612322i
$625$	12.5054	+	21.6600i	0.500215	+	0.866398i
$626$	2.28325	−	3.95470i	0.0912570	−	0.158062i
$627$	−40.6237	+	8.06742i	−1.62235	+	0.322182i
$628$	−1.81170	−	3.13796i	−0.0722948	−	0.125218i
$629$	19.5809			0.780741
$630$	−22.9834	+	4.99572i	−0.915679	+	0.199034i
$631$	36.6240			1.45798			0.728989	−	0.684526i	$-0.239991\pi$
$631$	36.6240			1.45798			0.728989	+	0.684526i	$0.239991\pi$
$632$	−30.8560	+	17.8147i	−1.22739	+	0.708632i
$633$	−18.4692	−	8.00501i	−0.734086	−	0.318171i
$634$	−4.94565	−	2.85537i	−0.196417	−	0.113401i
$635$	0.321443	+	0.556755i	0.0127561	+	0.0220942i
$636$	2.46803	+	21.4389i	0.0978638	+	0.850109i
$637$	−0.379478	+	12.4826i	−0.0150355	+	0.494578i
$638$	16.5202	−	11.4243i	0.654042	−	0.452293i
$639$	−33.4270	+	31.3175i	−1.32235	+	1.23890i
$640$	−13.9809	−	8.07189i	−0.552644	−	0.319069i
$641$	−39.8662	−	23.0168i	−1.57462	−	0.909107i	−0.995591	−	0.0938000i	$-0.970099\pi$
$641$	−39.8662	−	23.0168i	−1.57462	−	0.909107i	−0.579029	−	0.815307i	$-0.696568\pi$
$642$	1.51543	+	2.04299i	0.0598091	+	0.0806302i
$643$	8.47291			0.334139			0.167070	−	0.985945i	$-0.446570\pi$
$643$	8.47291			0.334139			0.167070	+	0.985945i	$0.446570\pi$
$644$	−1.58564	−	0.0240967i	−0.0624831	−	0.000949543i
$645$	−28.9839	+	3.33660i	−1.14124	+	0.131378i
$646$	27.5248	−	15.8915i	1.08295	−	0.625241i
$647$	27.6552	+	15.9667i	1.08724	+	0.627717i	0.932840	−	0.360292i	$-0.117323\pi$
$647$	27.6552	+	15.9667i	1.08724	+	0.627717i	0.154398	+	0.988009i	$0.450656\pi$
$648$	1.71395	−	26.2742i	0.0673303	−	1.03215i
$649$	−6.36096	+	13.4356i	−0.249690	+	0.527394i
$650$			8.35611i			0.327754i
$651$	−12.7485	+	9.15949i	−0.499654	+	0.358989i
$652$	−14.7246			−0.576661
$653$	1.24667	−	0.719766i	0.0487860	−	0.0281666i	−0.475409	−	0.879765i	$-0.657700\pi$
$653$	1.24667	−	0.719766i	0.0487860	−	0.0281666i	0.524195	+	0.851598i	$0.324366\pi$
$654$	−12.0943	−	5.24198i	−0.472926	−	0.204978i
$655$	28.4624	+	16.4328i	1.11212	+	0.642082i
$656$	−0.0679764	−	0.117739i	−0.00265403	−	0.00459692i
$657$	−0.406346	−	1.74151i	−0.0158531	−	0.0679427i
$658$	−11.0518	+	18.4877i	−0.430844	+	0.720726i
$659$	−16.5339			−0.644069			−0.322035	−	0.946728i	$-0.604367\pi$
$659$	−16.5339			−0.644069			−0.322035	+	0.946728i	$0.604367\pi$
$660$	−6.55534	+	19.2917i	−0.255166	+	0.750927i
$661$	18.0751	−	31.3070i	0.703040	−	1.21770i	−0.264355	−	0.964425i	$-0.585159\pi$
$661$	18.0751	−	31.3070i	0.703040	−	1.21770i	0.967394	−	0.253275i	$-0.0815077\pi$
$662$	0.877908	−	1.52058i	0.0341209	−	0.0590991i
$663$	11.6742	−	8.65960i	0.453389	−	0.336311i
$664$	−9.37648			−0.363878
$665$	−51.7699	−	30.9476i	−2.00755	−	1.20010i
$666$	−11.3972	+	2.65932i	−0.441633	+	0.103046i
$667$	−2.99037	+	1.72649i	−0.115788	+	0.0668500i
$668$	11.3108	−	19.5908i	0.437627	−	0.757992i
$669$	−2.94171	+	6.78713i	−0.113733	+	0.262406i
$670$	3.93304	−	2.27074i	0.151947	−	0.0877265i
$671$	2.48718	+	3.59661i	0.0960167	+	0.138846i
$672$	−20.0378	+	14.3966i	−0.772974	+	0.555362i
$673$			36.5302i			1.40814i	0.710133	+	0.704068i	$0.248635\pi$
$673$			36.5302i			1.40814i	−0.710133	+	0.704068i	$0.751365\pi$
$674$	7.60827	−	4.39264i	0.293060	−	0.169198i
$675$	4.64307	−	25.5511i	0.178712	−	0.983463i
$676$	5.50610	−	9.53684i	0.211773	−	0.366801i
$677$	0.0438436	+	0.0759394i	0.00168505	+	0.00291859i	0.866867	−	0.498540i	$-0.166130\pi$
$677$	0.0438436	+	0.0759394i	0.00168505	+	0.00291859i	−0.865182	+	0.501459i	$0.832797\pi$
$678$	0.853788	+	7.41657i	0.0327895	+	0.284832i
$679$	−0.242224	+	15.9392i	−0.00929572	+	0.611689i
$680$		−	43.5131i		−	1.66865i
$681$	−28.8259	−	38.8610i	−1.10461	−	1.48916i
$682$	−0.865988	−	10.6120i	−0.0331604	−	0.406356i
$683$	5.15185	+	2.97442i	0.197130	+	0.113813i	0.595316	−	0.803492i	$-0.297027\pi$
$683$	5.15185	+	2.97442i	0.197130	+	0.113813i	−0.398186	+	0.917305i	$0.630360\pi$
$684$	17.7056	−	16.5882i	0.676989	−	0.634266i
$685$	6.22495			0.237843
$686$	15.4110	−	7.98423i	0.588395	−	0.304840i
$687$	−16.7790	+	1.93158i	−0.640160	+	0.0736945i
$688$	2.29877	−	1.32720i	0.0876398	−	0.0505989i
$689$	9.90811	−	17.1614i	0.377469	−	0.653796i
$690$	−1.09063	+	2.51632i	−0.0415197	+	0.0957946i
$691$	−24.3780	−	42.2239i	−0.927382	−	1.60627i	−0.787685	−	0.616078i	$-0.788720\pi$
$691$	−24.3780	−	42.2239i	−0.927382	−	1.60627i	−0.139697	−	0.990194i	$-0.544613\pi$
$692$	4.05399			0.154110
$693$	19.2304	+	17.9776i	0.730502	+	0.682911i
$694$	7.30077			0.277133
$695$	23.2465	+	40.2641i	0.881789	+	1.52730i
$696$	−13.0220	+	30.0444i	−0.493596	+	1.13883i
$697$	−0.641730	+	1.11151i	−0.0243073	+	0.0421014i
$698$	18.3232	−	10.5789i	0.693543	−	0.400417i
$699$	32.5378	−	3.74571i	1.23069	−	0.141676i
$700$	−12.9567	+	7.22029i	−0.489717	+	0.272901i
$701$	−9.08783			−0.343243			−0.171621	−	0.985163i	$-0.554901\pi$
$701$	−9.08783			−0.343243			−0.171621	+	0.985163i	$0.554901\pi$
$702$	−5.61901	+	6.62589i	−0.212076	+	0.250078i
$703$	−25.9913	−	15.0061i	−0.980279	−	0.565964i
$704$	−1.62996	−	19.9739i	−0.0614313	−	0.752794i
$705$	−28.3434	−	38.2105i	−1.06748	−	1.43909i
$706$			13.2842i			0.499959i
$707$	17.8061	+	10.6444i	0.669668	+	0.400322i
$708$	−0.995898	−	8.65103i	−0.0374281	−	0.325125i
$709$	−10.5093	−	18.2026i	−0.394684	−	0.683612i	0.598377	−	0.801215i	$-0.295813\pi$
$709$	−10.5093	−	18.2026i	−0.394684	−	0.683612i	−0.993061	+	0.117602i	$0.962479\pi$
$710$	22.6222	−	39.1828i	0.848996	−	1.47050i
$711$	−34.9644	−	10.6004i	−1.31127	−	0.397548i
$712$	21.1151	−	12.1908i	0.791323	−	0.456870i
$713$			1.83041i			0.0685494i
$714$	−18.4111	−	8.31436i	−0.689018	−	0.311157i
$715$	15.3882	−	10.6415i	0.575485	−	0.397968i
$716$	14.6617	−	8.46495i	0.547935	−	0.316350i
$717$	16.5639	−	38.2163i	0.618589	−	1.42721i
$718$	8.16112	−	14.1355i	0.304570	−	0.527531i
$719$	−12.7609	+	7.36753i	−0.475903	+	0.274763i	−0.718707	−	0.695313i	$-0.755266\pi$
$719$	−12.7609	+	7.36753i	−0.475903	+	0.274763i	0.242805	+	0.970075i	$0.421933\pi$
$720$	1.07398	+	4.60285i	0.0400250	+	0.171538i
$721$	−25.5121	+	14.2170i	−0.950119	+	0.529467i
$722$	−30.9084			−1.15029
$723$	25.8380	−	19.1658i	0.960925	−	0.712786i
$724$	9.57750	−	16.5887i	0.355945	−	0.616515i
$725$	−16.1483	+	27.9697i	−0.599734	+	1.03877i
$726$	−17.1724	+	4.89086i	−0.637328	+	0.181517i
$727$	−39.8933			−1.47956			−0.739780	−	0.672849i	$-0.765070\pi$
$727$	−39.8933			−1.47956			−0.739780	+	0.672849i	$0.765070\pi$
$728$	13.8075	+	0.209830i	0.511741	+	0.00777682i
$729$	20.8633	−	17.1383i	0.772716	−	0.634752i
$730$	0.883188	+	1.52973i	0.0326883	+	0.0566177i
$731$	−21.7015	−	12.5294i	−0.802659	−	0.463415i
$732$	−2.35035	−	1.01870i	−0.0868716	−	0.0376522i
$733$	−12.3955	+	7.15654i	−0.457838	+	0.264333i	−0.711135	−	0.703056i	$-0.751818\pi$
$733$	−12.3955	+	7.15654i	−0.457838	+	0.264333i	0.253297	+	0.967389i	$0.418485\pi$
$734$	−16.5822			−0.612059
$735$	3.22500	+	38.2006i	0.118956	+	1.40905i
$736$			2.87699i			0.106047i
$737$	−4.59421	−	2.17508i	−0.169230	−	0.0801201i
$738$	0.222568	−	0.734118i	0.00819285	−	0.0270232i
$739$	23.6055	+	13.6287i	0.868344	+	0.501338i	0.866797	−	0.498660i	$-0.166174\pi$
$739$	23.6055	+	13.6287i	0.868344	+	0.501338i	0.00154620	+	0.999999i	$0.499508\pi$
$740$	−12.7863	+	7.38220i	−0.470035	+	0.271375i
$741$	−22.1325	+	2.54787i	−0.813058	+	0.0935985i
$742$	−27.5377	−	0.418484i	−1.01094	−	0.0153630i
$743$	−10.4272			−0.382537			−0.191268	−	0.981538i	$-0.561260\pi$
$743$	−10.4272			−0.382537			−0.191268	+	0.981538i	$0.561260\pi$
$744$	10.3412	+	13.9413i	0.379128	+	0.511112i
$745$	29.0054	+	16.7463i	1.06268	+	0.613536i
$746$	−24.0371	−	13.8778i	−0.880059	−	0.508102i
$747$	−6.57386	−	7.01666i	−0.240525	−	0.256726i
$748$	−14.3937	+	9.95374i	−0.526285	+	0.363945i
$749$	3.62169	−	2.01824i	0.132334	−	0.0737447i
$750$	−0.00126490	−	0.0109878i	−4.61877e−5	−	0.000401217i
$751$	6.22156	+	10.7761i	0.227028	+	0.393224i	0.956926	−	0.290332i	$-0.0937658\pi$
$751$	6.22156	+	10.7761i	0.227028	+	0.393224i	−0.729898	+	0.683556i	$0.760432\pi$
$752$	3.74853	+	2.16421i	0.136695	+	0.0789207i
$753$	14.6253	+	6.33895i	0.532975	+	0.231004i
$754$	9.35679	−	5.40215i	0.340754	−	0.196735i
$755$	−53.2634			−1.93845
$756$	−15.1291	−	2.98737i	−0.550240	−	0.108650i
$757$	−1.95153			−0.0709296			−0.0354648	−	0.999371i	$-0.511291\pi$
$757$	−1.95153			−0.0709296			−0.0354648	+	0.999371i	$0.511291\pi$
$758$	14.7341	+	25.5202i	0.535167	+	0.926936i
$759$	3.01077	−	0.597905i	0.109284	−	0.0217026i
$760$	−33.3468	+	57.7584i	−1.20962	+	2.09512i
$761$	−13.6061	−	23.5665i	−0.493222	−	0.854285i	0.506748	−	0.862094i	$-0.330847\pi$
$761$	−13.6061	−	23.5665i	−0.493222	−	0.854285i	−0.999970	+	0.00780951i	$0.997514\pi$
$762$	−0.0377437	−	0.327866i	−0.00136731	−	0.0118773i
$763$	−11.0241	+	18.4413i	−0.399098	+	0.667620i
$764$		−	14.5782i		−	0.527422i
$765$	32.5620	−	30.5071i	1.17728	−	1.10299i
$766$	9.54823	+	5.51268i	0.344992	+	0.199181i
$767$	−3.99811	+	6.92494i	−0.144364	+	0.250045i
$768$	17.4075	+	23.4675i	0.628140	+	0.846812i
$769$			6.79843i			0.245158i	0.992459	+	0.122579i	$0.0391164\pi$
$769$			6.79843i			0.245158i	−0.992459	+	0.122579i	$0.960884\pi$
$770$	−23.3298	−	11.4824i	−0.840746	−	0.413797i
$771$	−1.77027	−	15.3777i	−0.0637547	−	0.553816i
$772$	−10.5487	+	6.09028i	−0.379655	+	0.219194i
$773$	22.6281	+	13.0643i	0.813877	+	0.469892i	0.848300	−	0.529515i	$-0.177626\pi$
$773$	22.6281	+	13.0643i	0.813877	+	0.469892i	−0.0344236	+	0.999407i	$0.510960\pi$
$774$	14.3332	+	4.34550i	0.515195	+	0.156196i
$775$	8.56017	+	14.8266i	0.307490	+	0.532589i
$776$	17.6269			0.632770
$777$	1.89338	+	18.9817i	0.0679246	+	0.680964i
$778$		−	7.62451i		−	0.273352i
$779$	1.70364	−	0.983596i	0.0610391	−	0.0352410i
$780$	−4.35853	+	10.0560i	−0.156060	+	0.360064i
$781$	−50.4722	+	4.11875i	−1.80604	+	0.147380i
$782$	−2.03996	+	1.17777i	−0.0729488	+	0.0421170i
$783$	−31.6127	+	11.3195i	−1.12975	+	0.404525i
$784$	−1.65135	−	3.07219i	−0.0589768	−	0.109721i
$785$			10.2137i			0.364542i
$786$	−10.0516	−	13.5508i	−0.358529	−	0.483342i
$787$	37.8237	+	21.8375i	1.34827	+	0.778423i	0.988004	−	0.154427i	$-0.0493532\pi$
$787$	37.8237	+	21.8375i	1.34827	+	0.778423i	0.360264	+	0.932850i	$0.382687\pi$
$788$	2.75607	−	4.77365i	0.0981808	−	0.170054i
$789$	12.5706	+	16.9468i	0.447525	+	0.603320i
$790$	36.0884			1.28397
$791$	12.1671	+	0.184900i	0.432611	+	0.00657430i
$792$	19.5534	−	21.5638i	0.694801	−	0.766235i
$793$	1.17610	+	2.03706i	0.0417645	+	0.0723383i
$794$	−1.61024	+	2.78902i	−0.0571453	+	0.0989786i
$795$	24.1913	−	55.8143i	0.857976	−	1.97953i
$796$	−8.87427	−	15.3707i	−0.314540	−	0.544800i
$797$			14.3281i			0.507529i	0.967266	+	0.253764i	$0.0816688\pi$
$797$			14.3281i			0.507529i	−0.967266	+	0.253764i	$0.918331\pi$
$798$	18.0667	+	25.1459i	0.639553	+	0.890155i
$799$		−	40.8624i		−	1.44561i
$800$	13.4546	+	23.3041i	0.475693	+	0.823924i
$801$	23.9265	+	7.25400i	0.845403	+	0.256307i
$802$	21.4736	+	12.3978i	0.758258	+	0.437780i
$803$	0.845981	−	1.78688i	0.0298540	−	0.0630576i
$804$	2.95815	−	0.340539i	0.104326	−	0.0120099i
$805$	3.83685	+	2.29364i	0.135231	+	0.0808401i
$806$		−	5.72731i		−	0.201736i
$807$	−20.3875	+	15.1229i	−0.717675	+	0.532350i
$808$	11.4696	−	19.8659i	0.403498	−	0.698878i
$809$	20.3250	−	35.2040i	0.714590	−	1.23771i	−0.248527	−	0.968625i	$-0.579947\pi$
$809$	20.3250	−	35.2040i	0.714590	−	1.23771i	0.963117	−	0.269081i	$-0.0867201\pi$
$810$	−14.8098	+	22.1792i	−0.520362	+	0.779298i
$811$		−	36.6474i		−	1.28686i	−0.765503	−	0.643432i	$-0.777510\pi$
$811$		−	36.6474i		−	1.28686i	0.765503	−	0.643432i	$-0.222490\pi$
$812$	16.4613	+	9.84045i	0.577679	+	0.345332i
$813$	−0.725405	−	6.30135i	−0.0254411	−	0.220998i
$814$	−11.6942	−	5.53648i	−0.409880	−	0.194054i
$815$	35.9451	+	20.7529i	1.25910	+	0.726944i
$816$	−1.61441	+	3.72477i	−0.0565155	+	0.130393i
$817$	19.2041	+	33.2624i	0.671866	+	1.16371i
$818$		−	27.9891i		−	0.978618i
$819$	9.52344	+	10.4796i	0.332776	+	0.366188i
$820$		−	0.967755i		−	0.0337955i
$821$	2.04040	+	3.53407i	0.0712103	+	0.123340i	0.899432	−	0.437061i	$-0.143981\pi$
$821$	2.04040	+	3.53407i	0.0712103	+	0.123340i	−0.828222	+	0.560401i	$0.810647\pi$
$822$	−2.93208	−	1.27083i	−0.102268	−	0.0443254i
$823$	−1.31021	+	2.26935i	−0.0456711	+	0.0791046i	−0.887957	−	0.459926i	$-0.847876\pi$
$823$	−1.31021	+	2.26935i	−0.0456711	+	0.0791046i	0.842286	+	0.539031i	$0.181209\pi$
$824$	16.1474	+	27.9681i	0.562520	+	0.974314i
$825$	21.5915	−	18.9234i	0.751721	−	0.658828i
$826$	11.1120	+	0.168866i	0.386635	+	0.00587562i
$827$	−4.57929			−0.159238			−0.0796188	−	0.996825i	$-0.525370\pi$
$827$	−4.57929			−0.159238			−0.0796188	+	0.996825i	$0.525370\pi$
$828$	−1.31222	+	1.22941i	−0.0456029	+	0.0427250i
$829$	5.86512	−	10.1587i	0.203704	−	0.352826i	−0.746015	−	0.665929i	$-0.768035\pi$
$829$	5.86512	−	10.1587i	0.203704	−	0.352826i	0.949719	+	0.313103i	$0.101369\pi$
$830$	8.22486	+	4.74862i	0.285489	+	0.164827i
$831$	−5.10183	+	3.78439i	−0.176981	+	0.131279i
$832$		−	10.7799i		−	0.373726i
$833$	−17.3225	+	28.0024i	−0.600190	+	0.970226i
$834$	−2.72959	−	23.7110i	−0.0945179	−	0.821045i
$835$	−55.2228	+	31.8829i	−1.91106	+	1.10335i
$836$	26.7340	−	2.18161i	0.924616	−	0.0754527i
$837$	−3.18238	+	17.5128i	−0.109999	+	0.605333i
$838$	4.86588	−	2.80932i	0.168089	−	0.0970463i
$839$			25.0233i			0.863900i	0.901897	+	0.431950i	$0.142174\pi$
$839$			25.0233i			0.863900i	−0.901897	+	0.431950i	$0.857826\pi$
$840$	42.1815	−	4.20751i	1.45540	−	0.145173i
$841$	12.7590			0.439965
$842$	16.9015	+	29.2743i	0.582464	+	1.00886i
$843$	−8.74931	+	20.1865i	−0.301342	+	0.695259i
$844$	11.2899	+	6.51820i	0.388613	+	0.224366i
$845$	−26.8825	+	15.5206i	−0.924787	+	0.533926i
$846$	5.54960	+	23.7843i	0.190799	+	0.817721i
$847$	4.28156	+	28.7866i	0.147116	+	0.989119i
$848$			5.53449i			0.190055i
$849$	1.08638	−	0.805845i	0.0372845	−	0.0276565i
$850$	−11.0160	+	19.0803i	−0.377846	+	0.654449i
$851$	1.92630	+	1.11215i	0.0660328	+	0.0381241i
$852$	23.8259	−	17.6733i	0.816260	−	0.605478i
$853$		−	24.9854i		−	0.855482i	−0.903901	−	0.427741i	$-0.859310\pi$
$853$		−	24.9854i		−	0.855482i	0.903901	−	0.427741i	$-0.140690\pi$
$854$	1.67739	−	2.80597i	0.0573990	−	0.0960184i
$855$	−66.6016	+	15.5402i	−2.27773	+	0.531463i
$856$	−2.29228	−	3.97034i	−0.0783484	−	0.135703i
$857$	14.7911	−	25.6189i	0.505254	−	0.875126i	−0.494728	−	0.869048i	$-0.664732\pi$
$857$	14.7911	−	25.6189i	0.505254	−	0.875126i	0.999982	−	0.00607746i	$-0.00193453\pi$
$858$	−9.42062	+	1.87083i	−0.321615	+	0.0638691i
$859$	−8.06405	−	13.9674i	−0.275142	−	0.476560i	0.695029	−	0.718982i	$-0.255392\pi$
$859$	−8.06405	−	13.9674i	−0.275142	−	0.476560i	−0.970171	+	0.242422i	$0.922058\pi$
$860$	18.8948			0.644308
$861$	−1.13955	−	0.514614i	−0.0388357	−	0.0175380i
$862$	−13.1388			−0.447508
$863$	2.21121	−	1.27664i	0.0752705	−	0.0434575i	−0.461892	−	0.886936i	$-0.652829\pi$
$863$	2.21121	−	1.27664i	0.0752705	−	0.0434575i	0.537163	+	0.843479i	$0.319496\pi$
$864$	−5.00197	+	27.5262i	−0.170170	+	0.936460i
$865$	−9.89644	−	5.71371i	−0.336489	−	0.194272i
$866$	−8.01181	−	13.8769i	−0.272252	−	0.471555i
$867$	8.82130	−	1.01550i	0.299587	−	0.0344882i
$868$	8.88056	−	4.94882i	0.301426	−	0.167974i
$869$	−22.9742	−	33.2221i	−0.779348	−	1.12698i
$870$	26.6383	−	19.7595i	0.903122	−	0.669909i
$871$	−2.36793	−	1.36712i	−0.0802342	−	0.0463232i
$872$	20.5745	+	11.8787i	0.696741	+	0.402264i
$873$	12.3583	+	13.1907i	0.418263	+	0.446437i
$874$	3.61040			0.122124
$875$	−0.0180257		0.000273933i	−0.000609381		9.26064e-6i
$876$	0.132450	+	1.15055i	0.00447507	+	0.0388735i
$877$	−21.3586	+	12.3314i	−0.721228	+	0.416401i	−0.815204	−	0.579173i	$-0.803375\pi$
$877$	−21.3586	+	12.3314i	−0.721228	+	0.416401i	0.0939766	+	0.995574i	$0.470042\pi$
$878$	17.3359	+	10.0089i	0.585059	+	0.337784i
$879$	16.3256	−	37.6666i	0.550650	−	1.27046i
$880$	−2.23595	+	4.72277i	−0.0753738	+	0.159204i
$881$		−	19.4665i		−	0.655843i	−0.944705	−	0.327921i	$-0.893652\pi$
$881$		−	19.4665i		−	0.655843i	0.944705	−	0.327921i	$-0.106348\pi$
$882$	6.27966	−	18.6516i	0.211447	−	0.628033i
$883$	−16.9017			−0.568786			−0.284393	−	0.958708i	$-0.591792\pi$
$883$	−16.9017			−0.568786			−0.284393	+	0.958708i	$0.591792\pi$
$884$	−8.15235	+	4.70676i	−0.274193	+	0.158306i
$885$	−9.76164	+	22.5222i	−0.328134	+	0.757074i
$886$	−9.35510	−	5.40117i	−0.314291	−	0.181456i
$887$	−0.0833345	−	0.144340i	−0.00279810	−	0.00484645i	0.864623	−	0.502421i	$-0.167557\pi$
$887$	−0.0833345	−	0.144340i	−0.00279810	−	0.00484645i	−0.867421	+	0.497575i	$0.834224\pi$
$888$	20.9549	−	2.41231i	0.703201	−	0.0809518i
$889$	−0.537873	−	0.00817394i	−0.0180397	−	0.000274145i
$890$	−24.6957			−0.827801
$891$	29.8457	−	0.486022i	0.999867	−	0.0162824i
$892$	2.39533	−	4.14883i	0.0802016	−	0.138913i
$893$	−31.3154	+	54.2399i	−1.04793	+	1.81507i
$894$	−10.2434	−	13.8094i	−0.342589	−	0.461854i
$895$	−47.7222			−1.59518
$896$	11.7998	−	6.57561i	0.394204	−	0.219676i
$897$	1.64032	−	0.188832i	0.0547686	−	0.00630491i
$898$	−5.78763	+	3.34149i	−0.193136	+	0.111507i
$899$	11.0681	−	19.1706i	0.369143	−	0.639374i
$900$	−4.87972	+	16.0952i	−0.162657	+	0.536507i
$901$	45.2483	−	26.1241i	1.50744	−	0.870320i
$902$	0.697534	−	0.482370i	0.0232254	−	0.0160612i
$903$	10.0475	−	22.2489i	0.334360	−	0.740398i
$904$		−	13.4554i		−	0.447520i
$905$	−46.7604	+	26.9971i	−1.55437	+	0.897415i
$906$	25.0881	+	10.8738i	0.833498	+	0.361258i
$907$	14.1529	−	24.5135i	0.469939	−	0.813959i	−0.529470	−	0.848329i	$-0.677609\pi$
$907$	14.1529	−	24.5135i	0.469939	−	0.813959i	0.999409	+	0.0343700i	$0.0109425\pi$
$908$	15.6678	+	27.1374i	0.519954	+	0.900587i
$909$	22.9075	−	5.34500i	0.759792	−	0.177283i
$910$	−12.0054	−	7.17674i	−0.397975	−	0.237907i
$911$		−	29.4492i		−	0.975694i	−0.872929	−	0.487847i	$-0.837782\pi$
$911$		−	29.4492i		−	0.975694i	0.872929	−	0.487847i	$-0.162218\pi$
$912$	4.99745	−	3.70696i	0.165482	−	0.122750i
$913$	−0.864567	−	10.5946i	−0.0286130	−	0.350631i
$914$	9.36748	+	5.40831i	0.309849	+	0.178891i
$915$	4.30183	+	5.79941i	0.142214	+	0.191722i
$916$	10.9384			0.361414
$917$	−24.0221	+	13.3867i	−0.793280	+	0.442067i
$918$	−21.5654	+	7.72188i	−0.711766	+	0.254860i
$919$	11.7748	−	6.79816i	0.388413	−	0.224250i	−0.293059	−	0.956094i	$-0.594673\pi$
$919$	11.7748	−	6.79816i	0.388413	−	0.224250i	0.681472	+	0.731844i	$0.261340\pi$
$920$	2.47145	−	4.28068i	0.0814813	−	0.141130i
$921$	35.4051	+	15.3454i	1.16664	+	0.505649i
$922$	−16.9816	−	29.4130i	−0.559260	−	0.968667i
$923$	−27.2398			−0.896610
$924$	−11.0409	−	12.9907i	−0.363220	−	0.427364i
$925$	20.8045			0.684048
$926$	−3.90860	−	6.76989i	−0.128445	−	0.222472i
$927$	−9.60830	+	31.6919i	−0.315578	+	1.04090i
$928$	17.3966	−	30.1317i	0.571070	−	0.989123i
$929$	26.1617	−	15.1045i	0.858337	−	0.495561i	−0.00511820	−	0.999987i	$-0.501629\pi$
$929$	26.1617	−	15.1045i	0.858337	−	0.495561i	0.863455	+	0.504426i	$0.168296\pi$
$930$	−2.01069	−	17.4662i	−0.0659333	−	0.572740i
$931$	44.4535	−	23.8945i	1.45691	−	0.783109i
$932$	−21.2116			−0.694809
$933$	38.8903	−	28.8477i	1.27321	−	0.944430i
$934$	−16.6579	−	9.61742i	−0.545062	−	0.314692i
$935$	49.1661	−	4.01217i	1.60790	−	0.131212i
$936$	11.4266	−	10.7055i	0.373490	−	0.349920i
$937$		−	52.6530i		−	1.72010i	−0.510210	−	0.860050i	$-0.670432\pi$
$937$		−	52.6530i		−	1.72010i	0.510210	−	0.860050i	$-0.329568\pi$
$938$	−0.0577425	+	3.79965i	−0.00188536	+	0.124063i
$939$	−8.38437	+	0.965201i	−0.273614	+	0.0314981i
$940$	15.4056	+	26.6832i	0.502474	+	0.870310i
$941$	5.96169	−	10.3259i	0.194345	−	0.336616i	−0.752340	−	0.658775i	$-0.771075\pi$
$941$	5.96169	−	10.3259i	0.194345	−	0.336616i	0.946686	+	0.322159i	$0.104408\pi$
$942$	2.08514	−	4.81085i	0.0679375	−	0.156746i
$943$	−0.126263	+	0.0728977i	−0.00411167	+	0.00237388i
$944$		−	2.23327i		−	0.0726868i
$945$	32.7221	+	28.6157i	1.06445	+	0.930867i
$946$	9.41797	+	13.6189i	0.306205	+	0.442789i
$947$	−50.3045	+	29.0433i	−1.63468	+	0.943782i	−0.652055	+	0.758172i	$0.726093\pi$
$947$	−50.3045	+	29.0433i	−1.63468	+	0.943782i	−0.982624	+	0.185610i	$0.940574\pi$
$948$	21.7103	+	9.40978i	0.705119	+	0.305615i
$949$	0.531732	−	0.920987i	0.0172608	−	0.0298965i
$950$	29.2449	−	16.8845i	0.948829	−	0.547807i
$951$	1.20705	+	10.4853i	0.0391414	+	0.340008i
$952$	31.2514	+	18.6818i	1.01286	+	0.605482i
$953$	29.0612			0.941383			0.470692	−	0.882298i	$-0.344004\pi$
$953$	29.0612			0.941383			0.470692	+	0.882298i	$0.344004\pi$
$954$	−22.7892	+	21.3510i	−0.737827	+	0.691264i
$955$	−20.5466	+	35.5878i	−0.664873	+	1.15159i
$956$	−13.4874	+	23.3608i	−0.436213	+	0.755543i
$957$	−35.1483	−	11.9434i	−1.13618	−	0.386076i
$958$	32.6990			1.05646
$959$	−2.67261	+	4.47080i	−0.0863030	+	0.144370i
$960$	−3.78451	−	32.8748i	−0.122145	−	1.06103i
$961$	9.63283	+	16.6845i	0.310736	+	0.538211i
$962$	−6.02736	−	3.47990i	−0.194330	−	0.112196i
$963$	1.36399	−	4.49898i	0.0439540	−	0.144978i
$964$	−18.0432	+	10.4172i	−0.581132	+	0.335517i
$965$	34.3346			1.10527
$966$	−1.33898	−	1.86365i	−0.0430811	−	0.0599619i
$967$			48.4487i			1.55801i	0.627020	+	0.779003i	$0.284274\pi$
$967$			48.4487i			1.55801i	−0.627020	+	0.779003i	$0.715726\pi$
$968$	31.7554	−	5.21750i	1.02066	−	0.167697i
$969$	−53.8962	−	23.3599i	−1.73139	−	0.750428i
$970$	−15.4620	−	8.92698i	−0.496454	−	0.286628i
$971$	−33.6506	+	19.4282i	−1.07990	+	0.623480i	−0.930869	−	0.365353i	$-0.880948\pi$
$971$	−33.6506	+	19.4282i	−1.07990	+	0.623480i	−0.149030	+	0.988833i	$0.547615\pi$
$972$	−14.6924	+	9.48120i	−0.471260	+	0.304110i
$973$	−38.8985	−	0.591133i	−1.24703	−	0.0189508i
$974$	−31.6646			−1.01460
$975$	12.4038	−	9.20074i	0.397238	−	0.294660i
$976$	−0.568933	−	0.328474i	−0.0182111	−	0.0105142i
$977$	−14.5635	−	8.40822i	−0.465926	−	0.269003i	0.248607	−	0.968605i	$-0.420027\pi$
$977$	−14.5635	−	8.40822i	−0.465926	−	0.269003i	−0.714533	+	0.699602i	$0.753361\pi$
$978$	−12.6942	−	17.1133i	−0.405914	−	0.547224i
$979$	15.7215	+	22.7342i	0.502462	+	0.726589i
$980$	0.754433	−	24.8164i	0.0240995	−	0.792730i
$981$	5.53567	+	23.7246i	0.176740	+	0.757468i
$982$	−11.9821	−	20.7537i	−0.382366	−	0.662277i
$983$	17.8258	+	10.2918i	0.568556	+	0.328256i	0.756573	−	0.653910i	$-0.226872\pi$
$983$	17.8258	+	10.2918i	0.568556	+	0.328256i	−0.188016	+	0.982166i	$0.560206\pi$
$984$	−0.549827	+	1.26857i	−0.0175278	+	0.0404404i
$985$	−13.4560	+	7.76882i	−0.428744	+	0.247535i
$986$	28.4870			0.907211
$987$	39.6120	−	3.95120i	1.26086	−	0.125768i
$988$	14.4284			0.459027
$989$	−1.42328	−	2.46520i	−0.0452577	−	0.0783887i
$990$	−28.0726	+	9.01265i	−0.892207	+	0.286441i
$991$	−21.9377	+	37.9973i	−0.696875	+	1.20702i	0.272669	+	0.962108i	$0.412094\pi$
$991$	−21.9377	+	37.9973i	−0.696875	+	1.20702i	−0.969544	+	0.244915i	$0.921240\pi$
$992$	−9.22185	−	15.9727i	−0.292794	−	0.507134i
$993$	−3.22379	+	0.371119i	−0.102304	+	0.0117771i
$994$	18.4288	+	33.0701i	0.584525	+	1.04892i
$995$			50.0297i			1.58605i
$996$	3.70980	+	5.00128i	0.117550	+	0.158472i
$997$	1.04216	+	0.601694i	0.0330057	+	0.0190558i	0.516412	−	0.856340i	$-0.327267\pi$
$997$	1.04216	+	0.601694i	0.0330057	+	0.0190558i	−0.483406	+	0.875396i	$0.660601\pi$
$998$	−0.564444	+	0.977646i	−0.0178672	+	0.0309468i
$999$	16.4967	+	13.9898i	0.521933	+	0.442619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.l.b.32.10	yes	48
3.2	odd	2	inner	231.2.l.b.32.15	yes	48
7.2	even	3	inner	231.2.l.b.65.9	yes	48
11.10	odd	2	inner	231.2.l.b.32.16	yes	48
21.2	odd	6	inner	231.2.l.b.65.16	yes	48
33.32	even	2	inner	231.2.l.b.32.9	✓	48
77.65	odd	6	inner	231.2.l.b.65.15	yes	48
231.65	even	6	inner	231.2.l.b.65.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.l.b.32.9	✓	48	33.32	even	2	inner
231.2.l.b.32.10	yes	48	1.1	even	1	trivial
231.2.l.b.32.15	yes	48	3.2	odd	2	inner
231.2.l.b.32.16	yes	48	11.10	odd	2	inner
231.2.l.b.65.9	yes	48	7.2	even	3	inner
231.2.l.b.65.10	yes	48	231.65	even	6	inner
231.2.l.b.65.15	yes	48	77.65	odd	6	inner
231.2.l.b.65.16	yes	48	21.2	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.468581 - 0.811606i) q^{2} +(-0.688798 + 1.58920i) q^{3} +(0.560864 - 0.971445i) q^{4} +(-2.73832 + 1.58097i) q^{5} +(1.61256 - 0.185636i) q^{6} +(0.0402023 - 2.64545i) q^{7} -2.92556 q^{8} +(-2.05112 - 2.18928i) q^{9} +O(q^{10})\)	\(q+(-0.468581 - 0.811606i) q^{2} +(-0.688798 + 1.58920i) q^{3} +(0.560864 - 0.971445i) q^{4} +(-2.73832 + 1.58097i) q^{5} +(1.61256 - 0.185636i) q^{6} +(0.0402023 - 2.64545i) q^{7} -2.92556 q^{8} +(-2.05112 - 2.18928i) q^{9} +(2.56625 + 1.48162i) q^{10} +(-0.269754 - 3.30564i) q^{11} +(1.15750 + 1.56045i) q^{12} -1.78405i q^{13} +(-2.16590 + 1.20698i) q^{14} +(-0.626328 - 5.44070i) q^{15} +(0.249134 + 0.431513i) q^{16} +(2.35195 - 4.07369i) q^{17} +(-0.815715 + 2.69055i) q^{18} +(-6.24385 + 3.60489i) q^{19} +3.54683i q^{20} +(4.17645 + 1.88607i) q^{21} +(-2.55647 + 1.76789i) q^{22} +(0.462754 - 0.267171i) q^{23} +(2.01512 - 4.64931i) q^{24} +(2.49892 - 4.32826i) q^{25} +(-1.44795 + 0.835972i) q^{26} +(4.89200 - 1.75166i) q^{27} +(-2.54736 - 1.52279i) q^{28} -6.46212 q^{29} +(-4.12222 + 3.05774i) q^{30} +(-1.71277 + 2.96661i) q^{31} +(-2.69208 + 4.66283i) q^{32} +(5.43912 + 1.84822i) q^{33} -4.40831 q^{34} +(4.07228 + 7.30763i) q^{35} +(-3.27716 + 0.764660i) q^{36} +(2.08135 + 3.60500i) q^{37} +(5.85150 + 3.37836i) q^{38} +(2.83521 + 1.22885i) q^{39} +(8.01112 - 4.62522i) q^{40} -0.272850 q^{41} +(-0.426263 - 4.27341i) q^{42} -5.32723i q^{43} +(-3.36254 - 1.59196i) q^{44} +(9.07778 + 2.75218i) q^{45} +(-0.433675 - 0.250382i) q^{46} +(7.52310 - 4.34347i) q^{47} +(-0.857364 + 0.0986989i) q^{48} +(-6.99677 - 0.212706i) q^{49} -4.68379 q^{50} +(4.85390 + 6.54366i) q^{51} +(-1.73311 - 1.00061i) q^{52} +(9.61932 + 5.55372i) q^{53} +(-3.71396 - 3.14958i) q^{54} +(5.96478 + 8.62541i) q^{55} +(-0.117614 + 7.73942i) q^{56} +(-1.42814 - 12.4058i) q^{57} +(3.02802 + 5.24469i) q^{58} +(-3.88158 - 2.24103i) q^{59} +(-5.63663 - 2.44305i) q^{60} +(-1.14182 + 0.659230i) q^{61} +3.21029 q^{62} +(-5.87407 + 5.33810i) q^{63} +6.04237 q^{64} +(2.82053 + 4.88530i) q^{65} +(-1.04864 - 5.28047i) q^{66} +(0.766303 - 1.32728i) q^{67} +(-2.63825 - 4.56958i) q^{68} +(0.105844 + 0.919435i) q^{69} +(4.02272 - 6.72930i) q^{70} -15.2685i q^{71} +(6.00067 + 6.40486i) q^{72} +(0.516234 + 0.298048i) q^{73} +(1.95056 - 3.37847i) q^{74} +(5.15722 + 6.95258i) q^{75} +8.08741i q^{76} +(-8.75573 + 0.580726i) q^{77} +(-0.331185 - 2.87689i) q^{78} +(10.5470 - 6.08934i) q^{79} +(-1.36442 - 0.787747i) q^{80} +(-0.585853 + 8.98091i) q^{81} +(0.127852 + 0.221447i) q^{82} +3.20502 q^{83} +(4.17463 - 2.99937i) q^{84} +14.8734i q^{85} +(-4.32361 + 2.49624i) q^{86} +(4.45109 - 10.2696i) q^{87} +(0.789183 + 9.67085i) q^{88} +(-7.21745 + 4.16700i) q^{89} +(-2.01999 - 8.65720i) q^{90} +(-4.71961 - 0.0717229i) q^{91} -0.599386i q^{92} +(-3.53478 - 4.76533i) q^{93} +(-7.05036 - 4.07053i) q^{94} +(11.3984 - 19.7427i) q^{95} +(-5.55586 - 7.49001i) q^{96} -6.02514 q^{97} +(3.10592 + 5.77829i) q^{98} +(-6.68365 + 7.37081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9}+O(q^{10}) \) 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9	\( 48 q - 6 q^{3} - 36 q^{4} - 10 q^{9} + 14 q^{12} + 4 q^{15} - 28 q^{16} - 24 q^{22} - 36 q^{27} - 4 q^{31} - 26 q^{33} + 56 q^{34} + 12 q^{36} - 28 q^{37} + 96 q^{42} + 30 q^{45} - 72 q^{48} + 24 q^{49} - 80 q^{55} + 16 q^{58} - 32 q^{60} + 256 q^{64} - 42 q^{66} + 16 q^{67} + 36 q^{69} - 76 q^{70} + 34 q^{75} + 104 q^{78} - 26 q^{81} - 4 q^{82} - 16 q^{88} - 36 q^{91} + 52 q^{93} - 144 q^{97} - 36 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 36 * q^4 - 10 * q^9 + 14 * q^12 + 4 * q^15 - 28 * q^16 - 24 * q^22 - 36 * q^27 - 4 * q^31 - 26 * q^33 + 56 * q^34 + 12 * q^36 - 28 * q^37 + 96 * q^42 + 30 * q^45 - 72 * q^48 + 24 * q^49 - 80 * q^55 + 16 * q^58 - 32 * q^60 + 256 * q^64 - 42 * q^66 + 16 * q^67 + 36 * q^69 - 76 * q^70 + 34 * q^75 + 104 * q^78 - 26 * q^81 - 4 * q^82 - 16 * q^88 - 36 * q^91 + 52 * q^93 - 144 * q^97 - 36 * q^99

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