LMFDB - Embedded newform 640.2.bm.a.221.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			221.15
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12323 - 0.859269i) q^{2} +(0.972809 + 0.0958133i) q^{3} +(0.523313 + 1.93032i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01036 - 0.943525i) q^{6} +(0.372040 + 1.87037i) q^{7} +(1.07086 - 2.61787i) q^{8} +(-2.00518 - 0.398855i) q^{9} +O(q^{10})$	\(q+(-1.12323 - 0.859269i) q^{2} +(0.972809 + 0.0958133i) q^{3} +(0.523313 + 1.93032i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01036 - 0.943525i) q^{6} +(0.372040 + 1.87037i) q^{7} +(1.07086 - 2.61787i) q^{8} +(-2.00518 - 0.398855i) q^{9} +(0.228318 - 1.39566i) q^{10} +(2.30643 + 1.89284i) q^{11} +(0.324133 + 1.92797i) q^{12} +(-0.360242 - 0.192554i) q^{13} +(1.18926 - 2.42055i) q^{14} +(0.374079 + 0.903107i) q^{15} +(-3.45229 + 2.02033i) q^{16} +(-1.23653 + 2.98524i) q^{17} +(1.90956 + 2.17100i) q^{18} +(4.79678 - 1.45509i) q^{19} +(-1.45570 + 1.37147i) q^{20} +(0.182717 + 1.85516i) q^{21} +(-0.964205 - 4.10794i) q^{22} +(1.24239 - 0.830138i) q^{23} +(1.29257 - 2.44409i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(0.239181 + 0.525828i) q^{26} +(-4.71871 - 1.43141i) q^{27} +(-3.41572 + 1.69695i) q^{28} +(4.42313 + 5.38960i) q^{29} +(0.355833 - 1.33584i) q^{30} +(-6.83331 + 6.83331i) q^{31} +(5.61373 + 0.697140i) q^{32} +(2.06236 + 2.06236i) q^{33} +(3.95404 - 2.29062i) q^{34} +(-1.47414 + 1.20980i) q^{35} +(-0.279419 - 4.07937i) q^{36} +(-1.98665 + 6.54910i) q^{37} +(-6.63822 - 2.48732i) q^{38} +(-0.331998 - 0.221834i) q^{39} +(2.81356 - 0.289641i) q^{40} +(2.34091 + 3.50342i) q^{41} +(1.38885 - 2.24078i) q^{42} +(-7.42248 + 0.731050i) q^{43} +(-2.44680 + 5.44270i) q^{44} +(-0.593476 - 1.95643i) q^{45} +(-2.10881 - 0.135107i) q^{46} +(2.41607 + 1.00077i) q^{47} +(-3.55199 + 1.63462i) q^{48} +(3.10729 - 1.28708i) q^{49} +(1.33849 - 0.456551i) q^{50} +(-1.48893 + 2.78559i) q^{51} +(0.183171 - 0.796149i) q^{52} +(8.24541 - 10.0471i) q^{53} +(4.07026 + 5.66245i) q^{54} +(-0.582090 + 2.92637i) q^{55} +(5.29479 + 1.02896i) q^{56} +(4.80576 - 0.955926i) q^{57} +(-0.337099 - 9.85445i) q^{58} +(2.43757 - 1.30291i) q^{59} +(-1.54753 + 1.19470i) q^{60} +(-0.913943 + 9.27942i) q^{61} +(13.5471 - 1.80376i) q^{62} -3.89882i q^{63} +(-5.70651 - 5.60676i) q^{64} -0.408474i q^{65} +(-0.544391 - 4.08863i) q^{66} +(0.224645 - 2.28086i) q^{67} +(-6.40957 - 0.824679i) q^{68} +(1.28815 - 0.688528i) q^{69} +(2.69535 - 0.0922017i) q^{70} +(6.83247 - 1.35906i) q^{71} +(-3.19142 + 4.82218i) q^{72} +(2.17243 - 10.9215i) q^{73} +(7.85891 - 5.64911i) q^{74} +(-0.620129 + 0.755630i) q^{75} +(5.31900 + 8.49786i) q^{76} +(-2.68222 + 5.01808i) q^{77} +(0.182297 + 0.534447i) q^{78} +(-7.90819 + 3.27568i) q^{79} +(-3.40917 - 2.09227i) q^{80} +(1.21325 + 0.502546i) q^{81} +(0.380988 - 5.94664i) q^{82} +(-0.306088 - 1.00904i) q^{83} +(-3.48543 + 1.32353i) q^{84} +(-3.21564 + 0.316713i) q^{85} +(8.96535 + 5.55676i) q^{86} +(3.78647 + 5.66685i) q^{87} +(7.42507 - 4.01097i) q^{88} +(7.16260 + 4.78589i) q^{89} +(-1.01449 + 2.70749i) q^{90} +(0.226122 - 0.745424i) q^{91} +(2.25259 + 1.96379i) q^{92} +(-7.30223 + 5.99278i) q^{93} +(-1.85388 - 3.20015i) q^{94} +(3.54446 + 3.54446i) q^{95} +(5.39429 + 1.21605i) q^{96} +(5.48386 - 5.48386i) q^{97} +(-4.59616 - 1.22430i) q^{98} +(-3.86984 - 4.71541i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	−1.12323	−	0.859269i	−0.794247	−	0.607595i
$2$	−1.12323	−	0.859269i	−0.794247	−	0.607595i
$3$	0.972809	+	0.0958133i	0.561651	+	0.0553178i	0.374859	−	0.927082i	$-0.377691\pi$
$3$	0.972809	+	0.0958133i	0.561651	+	0.0553178i	0.186792	+	0.982399i	$0.440191\pi$
$4$	0.523313	+	1.93032i	0.261657	+	0.965161i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$6$	−1.01036	−	0.943525i	−0.412479	−	0.385193i
$7$	0.372040	+	1.87037i	0.140618	+	0.706933i	0.985187	+	0.171486i	$0.0548569\pi$
$7$	0.372040	+	1.87037i	0.140618	+	0.706933i	−0.844569	+	0.535447i	$0.820143\pi$
$8$	1.07086	−	2.61787i	0.378607	−	0.925558i
$9$	−2.00518	−	0.398855i	−0.668393	−	0.132952i
$10$	0.228318	−	1.39566i	0.0722006	−	0.441347i
$11$	2.30643	+	1.89284i	0.695414	+	0.570712i	0.914300	−	0.405039i	$-0.132742\pi$
$11$	2.30643	+	1.89284i	0.695414	+	0.570712i	−0.218885	+	0.975751i	$0.570242\pi$
$12$	0.324133	+	1.92797i	0.0935693	+	0.556558i
$13$	−0.360242	−	0.192554i	−0.0999132	−	0.0534047i	0.420683	−	0.907208i	$-0.361790\pi$
$13$	−0.360242	−	0.192554i	−0.0999132	−	0.0534047i	−0.520596	+	0.853803i	$0.674290\pi$
$14$	1.18926	−	2.42055i	0.317844	−	0.646918i
$15$	0.374079	+	0.903107i	0.0965868	+	0.233181i
$16$	−3.45229	+	2.02033i	−0.863071	+	0.505082i
$17$	−1.23653	+	2.98524i	−0.299902	+	0.724028i	0.700049	+	0.714095i	$0.253162\pi$
$17$	−1.23653	+	2.98524i	−0.299902	+	0.724028i	−0.999951	+	0.00993241i	$0.996838\pi$
$18$	1.90956	+	2.17100i	0.450088	+	0.511709i
$19$	4.79678	−	1.45509i	1.10046	−	0.333820i	0.312728	−	0.949843i	$-0.398757\pi$
$19$	4.79678	−	1.45509i	1.10046	−	0.333820i	0.787728	+	0.616023i	$0.211257\pi$
$20$	−1.45570	+	1.37147i	−0.325505	+	0.306670i
$21$	0.182717	+	1.85516i	0.0398721	+	0.404829i
$22$	−0.964205	−	4.10794i	−0.205569	−	0.875817i
$23$	1.24239	−	0.830138i	0.259056	−	0.173096i	−0.419260	−	0.907866i	$-0.637710\pi$
$23$	1.24239	−	0.830138i	0.259056	−	0.173096i	0.678316	+	0.734771i	$0.262710\pi$
$24$	1.29257	−	2.44409i	0.263845	−	0.498897i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	0.239181	+	0.525828i	0.0469073	+	0.103123i
$27$	−4.71871	−	1.43141i	−0.908117	−	0.275474i
$28$	−3.41572	+	1.69695i	−0.645511	+	0.320693i
$29$	4.42313	+	5.38960i	0.821355	+	1.00082i	0.999857	+	0.0168848i	$0.00537484\pi$
$29$	4.42313	+	5.38960i	0.821355	+	1.00082i	−0.178502	+	0.983940i	$0.557125\pi$
$30$	0.355833	−	1.33584i	0.0649659	−	0.243889i
$31$	−6.83331	+	6.83331i	−1.22730	+	1.22730i	−0.262318	+	0.964982i	$0.584487\pi$
$31$	−6.83331	+	6.83331i	−1.22730	+	1.22730i	−0.964982	+	0.262318i	$0.915513\pi$
$32$	5.61373	+	0.697140i	0.992377	+	0.123238i
$33$	2.06236	+	2.06236i	0.359010	+	0.359010i
$34$	3.95404	−	2.29062i	0.678112	−	0.392838i
$35$	−1.47414	+	1.20980i	−0.249175	+	0.204493i
$36$	−0.279419	−	4.07937i	−0.0465698	−	0.679895i
$37$	−1.98665	+	6.54910i	−0.326603	+	1.07666i	0.627858	+	0.778328i	$0.283932\pi$
$37$	−1.98665	+	6.54910i	−0.326603	+	1.07666i	−0.954461	+	0.298337i	$0.903568\pi$
$38$	−6.63822	−	2.48732i	−1.07686	−	0.403496i
$39$	−0.331998	−	0.221834i	−0.0531622	−	0.0355218i
$40$	2.81356	−	0.289641i	0.444863	−	0.0457962i
$41$	2.34091	+	3.50342i	0.365589	+	0.547143i	0.967970	−	0.251066i	$-0.0807811\pi$
$41$	2.34091	+	3.50342i	0.365589	+	0.547143i	−0.602381	+	0.798209i	$0.705781\pi$
$42$	1.38885	−	2.24078i	0.214304	−	0.345760i
$43$	−7.42248	+	0.731050i	−1.13192	+	0.111484i	−0.646582	−	0.762844i	$-0.723802\pi$
$43$	−7.42248	+	0.731050i	−1.13192	+	0.111484i	−0.485335	+	0.874328i	$0.661302\pi$
$44$	−2.44680	+	5.44270i	−0.368869	+	0.820517i
$45$	−0.593476	−	1.95643i	−0.0884702	−	0.291647i
$46$	−2.10881	−	0.135107i	−0.310927	−	0.0199204i
$47$	2.41607	+	1.00077i	0.352419	+	0.145977i	0.551868	−	0.833931i	$-0.313915\pi$
$47$	2.41607	+	1.00077i	0.352419	+	0.145977i	−0.199449	+	0.979908i	$0.563915\pi$
$48$	−3.55199	+	1.63462i	−0.512685	+	0.235937i
$49$	3.10729	−	1.28708i	0.443898	−	0.183869i
$50$	1.33849	−	0.456551i	0.189291	−	0.0645661i
$51$	−1.48893	+	2.78559i	−0.208492	+	0.390061i
$52$	0.183171	−	0.796149i	0.0254012	−	0.110406i
$53$	8.24541	−	10.0471i	1.13259	−	1.38007i	0.217876	−	0.975976i	$-0.430087\pi$
$53$	8.24541	−	10.0471i	1.13259	−	1.38007i	0.914718	−	0.404094i	$-0.132413\pi$
$54$	4.07026	+	5.66245i	0.553892	+	0.770562i
$55$	−0.582090	+	2.92637i	−0.0784890	+	0.394591i
$56$	5.29479	+	1.02896i	0.707546	+	0.137500i
$57$	4.80576	−	0.955926i	0.636539	−	0.126615i
$58$	−0.337099	−	9.85445i	−0.0442632	−	1.29395i
$59$	2.43757	−	1.30291i	0.317345	−	0.169624i	−0.305032	−	0.952342i	$-0.598667\pi$
$59$	2.43757	−	1.30291i	0.317345	−	0.169624i	0.622377	+	0.782718i	$0.286167\pi$
$60$	−1.54753	+	1.19470i	−0.199785	+	0.154235i
$61$	−0.913943	+	9.27942i	−0.117018	+	1.18811i	0.739922	+	0.672693i	$0.234862\pi$
$61$	−0.913943	+	9.27942i	−0.117018	+	1.18811i	−0.856940	+	0.515416i	$0.827638\pi$
$62$	13.5471	−	1.80376i	1.72048	−	0.229078i
$63$		−	3.89882i		−	0.491205i
$64$	−5.70651	−	5.60676i	−0.713314	−	0.700845i
$65$		−	0.408474i		−	0.0506650i
$66$	−0.544391	−	4.08863i	−0.0670100	−	0.503275i
$67$	0.224645	−	2.28086i	0.0274448	−	0.278652i	−0.971661	−	0.236378i	$-0.924040\pi$
$67$	0.224645	−	2.28086i	0.0274448	−	0.278652i	0.999106	−	0.0422740i	$-0.0134602\pi$
$68$	−6.40957	−	0.824679i	−0.777275	−	0.100007i
$69$	1.28815	−	0.688528i	0.155074	−	0.0828890i
$70$	2.69535	−	0.0922017i	0.322155	−	0.0110202i
$71$	6.83247	−	1.35906i	0.810865	−	0.161291i	0.227791	−	0.973710i	$-0.426850\pi$
$71$	6.83247	−	1.35906i	0.810865	−	0.161291i	0.583074	+	0.812419i	$0.301850\pi$
$72$	−3.19142	+	4.82218i	−0.376113	+	0.568300i
$73$	2.17243	−	10.9215i	0.254263	−	1.27827i	−0.616809	−	0.787113i	$-0.711575\pi$
$73$	2.17243	−	10.9215i	0.254263	−	1.27827i	0.871072	−	0.491155i	$-0.163425\pi$
$74$	7.85891	−	5.64911i	0.913579	−	0.656696i
$75$	−0.620129	+	0.755630i	−0.0716064	+	0.0872526i
$76$	5.31900	+	8.49786i	0.610132	+	0.974771i
$77$	−2.68222	+	5.01808i	−0.305668	+	0.571864i
$78$	0.182297	+	0.534447i	0.0206410	+	0.0605142i
$79$	−7.90819	+	3.27568i	−0.889741	+	0.368543i	−0.780267	−	0.625447i	$-0.784917\pi$
$79$	−7.90819	+	3.27568i	−0.889741	+	0.368543i	−0.109474	+	0.993990i	$0.534917\pi$
$80$	−3.40917	−	2.09227i	−0.381156	−	0.233923i
$81$	1.21325	+	0.502546i	0.134806	+	0.0558385i
$82$	0.380988	−	5.94664i	0.0420731	−	0.656697i
$83$	−0.306088	−	1.00904i	−0.0335975	−	0.110756i	0.938538	−	0.345176i	$-0.112181\pi$
$83$	−0.306088	−	1.00904i	−0.0335975	−	0.110756i	−0.972135	+	0.234420i	$0.924681\pi$
$84$	−3.48543	+	1.32353i	−0.380292	+	0.144409i
$85$	−3.21564	+	0.316713i	−0.348786	+	0.0343524i
$86$	8.96535	+	5.55676i	0.966759	+	0.599201i
$87$	3.78647	+	5.66685i	0.405952	+	0.607550i
$88$	7.42507	−	4.01097i	0.791515	−	0.427571i
$89$	7.16260	+	4.78589i	0.759234	+	0.507304i	0.873903	−	0.486100i	$-0.161581\pi$
$89$	7.16260	+	4.78589i	0.759234	+	0.507304i	−0.114670	+	0.993404i	$0.536581\pi$
$90$	−1.01449	+	2.70749i	−0.106936	+	0.285394i
$91$	0.226122	−	0.745424i	0.0237040	−	0.0781416i
$92$	2.25259	+	1.96379i	0.234849	+	0.204739i
$93$	−7.30223	+	5.99278i	−0.757206	+	0.621423i
$94$	−1.85388	−	3.20015i	−0.191213	−	0.330070i
$95$	3.54446	+	3.54446i	0.363654	+	0.363654i
$96$	5.39429	+	1.21605i	0.550553	+	0.124113i
$97$	5.48386	−	5.48386i	0.556801	−	0.556801i	−0.371594	−	0.928395i	$-0.621189\pi$
$97$	5.48386	−	5.48386i	0.556801	−	0.556801i	0.928395	+	0.371594i	$0.121189\pi$
$98$	−4.59616	−	1.22430i	−0.464283	−	0.123673i
$99$	−3.86984	−	4.71541i	−0.388933	−	0.473916i
$100$	−1.89574	−	0.637310i	−0.189574	−	0.0637310i
$101$	5.05116	+	1.53225i	0.502609	+	0.152465i	0.531400	−	0.847121i	$-0.321666\pi$
$101$	5.05116	+	1.53225i	0.502609	+	0.152465i	−0.0287917	+	0.999585i	$0.509166\pi$
$102$	4.06599	−	1.84948i	0.402593	−	0.183126i
$103$	5.96014	−	8.91998i	0.587270	−	0.878912i	−0.412212	−	0.911088i	$-0.635244\pi$
$103$	5.96014	−	8.91998i	0.587270	−	0.878912i	0.999482	+	0.0321760i	$0.0102437\pi$
$104$	−0.889850	+	0.736870i	−0.0872570	+	0.0722560i
$105$	−1.54997	+	1.03566i	−0.151262	+	0.101070i
$106$	−17.8947	+	4.20018i	−1.73808	+	0.407958i
$107$	−1.20820	−	12.2670i	−0.116801	−	1.18590i	−0.857653	−	0.514229i	$-0.828078\pi$
$107$	−1.20820	−	12.2670i	−0.116801	−	1.18590i	0.740852	−	0.671668i	$-0.234422\pi$
$108$	0.293708	−	9.85771i	0.0282621	−	0.948559i
$109$	5.18967	−	1.57427i	0.497080	−	0.150788i	−0.0317830	−	0.999495i	$-0.510119\pi$
$109$	5.18967	−	1.57427i	0.497080	−	0.150788i	0.528863	+	0.848707i	$0.322619\pi$
$110$	3.16836	−	2.78682i	0.302091	−	0.265713i
$111$	−2.56012	+	6.18067i	−0.242996	+	0.586643i
$112$	−5.06315	−	5.70541i	−0.478422	−	0.539110i
$113$	1.15127	+	2.77940i	0.108302	+	0.261464i	0.968734	−	0.248101i	$-0.0798064\pi$
$113$	1.15127	+	2.77940i	0.108302	+	0.261464i	−0.860432	+	0.509565i	$0.829806\pi$
$114$	−6.21940	−	3.05571i	−0.582500	−	0.286194i
$115$	1.31777	+	0.704365i	0.122883	+	0.0656824i
$116$	−8.08899	+	11.3585i	−0.751043	+	1.05461i
$117$	0.645549	+	0.529789i	0.0596811	+	0.0489790i
$118$	−3.85752	−	0.631057i	−0.355113	−	0.0580935i
$119$	−6.04354	−	1.20214i	−0.554011	−	0.110200i
$120$	2.76481	−	0.0121886i	0.252391	−	0.00111266i
$121$	−0.409213	−	2.05725i	−0.0372011	−	0.187023i
$122$	9.00009	−	9.63765i	0.814830	−	0.872552i
$123$	1.94159	+	3.63245i	0.175067	+	0.327527i
$124$	−16.7665	−	9.61453i	−1.50567	−	0.863410i
$125$	−0.995185	−	0.0980171i	−0.0890120	−	0.00876692i
$126$	−3.35013	+	4.37929i	−0.298453	+	0.390138i
$127$	−10.8367			−0.961599			−0.480799	−	0.876831i	$-0.659653\pi$
$127$	−10.8367			−0.961599			−0.480799	+	0.876831i	$0.659653\pi$
$128$	1.59204	+	11.2011i	0.140717	+	0.990050i
$129$	−7.29069			−0.641910
$130$	−0.350989	+	0.458813i	−0.0307838	+	0.0402405i
$131$	−12.1073	−	1.19246i	−1.05782	−	0.104186i	−0.445881	−	0.895092i	$-0.647110\pi$
$131$	−12.1073	−	1.19246i	−1.05782	−	0.104186i	−0.611938	+	0.790906i	$0.709610\pi$
$132$	−2.90175	+	5.06027i	−0.252565	+	0.440440i
$133$	4.50614	+	8.43040i	0.390732	+	0.731008i
$134$	−2.21220	+	2.36891i	−0.191105	+	0.204643i
$135$	−0.961999	−	4.83629i	−0.0827957	−	0.416242i
$136$	6.49083	+	6.43385i	0.556584	+	0.551698i
$137$	−8.27259	−	1.64552i	−0.706775	−	0.140586i	−0.171401	−	0.985201i	$-0.554829\pi$
$137$	−8.27259	−	1.64552i	−0.706775	−	0.140586i	−0.535374	+	0.844615i	$0.679829\pi$
$138$	−2.03852	−	0.333485i	−0.173530	−	0.0283881i
$139$	−15.0272	−	12.3325i	−1.27459	−	1.04603i	−0.996336	−	0.0855197i	$-0.972745\pi$
$139$	−15.0272	−	12.3325i	−1.27459	−	1.04603i	−0.278252	−	0.960508i	$-0.589755\pi$
$140$	−3.10673	−	2.21246i	−0.262567	−	0.186987i
$141$	2.25448	+	1.20505i	0.189862	+	0.101483i
$142$	−8.84227	−	4.34439i	−0.742027	−	0.364573i
$143$	−0.466401	−	1.12599i	−0.0390024	−	0.0941601i
$144$	7.72827	−	2.67416i	0.644022	−	0.222846i
$145$	−2.66816	+	6.44150i	−0.221578	+	0.534937i
$146$	−11.8247	+	10.4007i	−0.978617	+	0.860772i
$147$	3.14612	−	0.954364i	0.259487	−	0.0787146i
$148$	−13.6815	−	0.407637i	−1.12461	−	0.0335076i
$149$	1.93269	+	19.6230i	0.158333	+	1.60758i	0.665951	+	0.745995i	$0.268026\pi$
$149$	1.93269	+	19.6230i	0.158333	+	1.60758i	−0.507619	+	0.861582i	$0.669474\pi$
$150$	1.34584	−	0.315892i	0.109887	−	0.0257925i
$151$	18.2462	−	12.1917i	1.48485	−	0.992146i	0.492287	−	0.870433i	$-0.336161\pi$
$151$	18.2462	−	12.1917i	1.48485	−	0.992146i	0.992565	−	0.121713i	$-0.0388389\pi$
$152$	1.32746	−	14.1155i	0.107671	−	1.14492i
$153$	3.67014	−	5.49275i	0.296713	−	0.444063i
$154$	7.32465	−	3.33174i	0.590237	−	0.268479i
$155$	−9.24764	−	2.80524i	−0.742789	−	0.225322i
$156$	0.254472	−	0.756951i	0.0203740	−	0.0606046i
$157$	−4.67077	−	5.69135i	−0.372768	−	0.454219i	0.552511	−	0.833505i	$-0.313670\pi$
$157$	−4.67077	−	5.69135i	−0.372768	−	0.454219i	−0.925279	+	0.379286i	$0.876170\pi$
$158$	11.6974	+	3.11590i	0.930599	+	0.247888i
$159$	8.98385	−	8.98385i	0.712466	−	0.712466i
$160$	2.03147	+	5.27950i	0.160602	+	0.417381i
$161$	2.01488	+	2.01488i	0.158795	+	0.158795i
$162$	−0.930947	−	1.60699i	−0.0731421	−	0.126257i
$163$	−12.9658	+	10.6408i	−1.01556	+	0.833449i	−0.986106	−	0.166117i	$-0.946877\pi$
$163$	−12.9658	+	10.6408i	−1.01556	+	0.833449i	−0.0294550	+	0.999566i	$0.509377\pi$
$164$	−5.53771	+	6.35211i	−0.432422	+	0.496016i
$165$	−0.846647	+	2.79102i	−0.0659114	+	0.217281i
$166$	−0.523225	+	1.39640i	−0.0406102	+	0.108381i
$167$	−1.15300	−	0.770413i	−0.0892222	−	0.0596163i	0.510159	−	0.860080i	$-0.329587\pi$
$167$	−1.15300	−	0.770413i	−0.0892222	−	0.0596163i	−0.599381	+	0.800464i	$0.704587\pi$
$168$	5.05223	+	1.50829i	0.389788	+	0.116367i
$169$	−7.12972	−	10.6704i	−0.548440	−	0.820798i
$170$	3.88407	+	2.40736i	0.297894	+	0.184636i
$171$	−10.1988	+	1.00449i	−0.779919	+	0.0768153i
$172$	−5.29544	−	13.9452i	−0.403774	−	1.06331i
$173$	−1.81750	−	5.99150i	−0.138182	−	0.455525i	0.860349	−	0.509705i	$-0.170246\pi$
$173$	−1.81750	−	5.99150i	−0.138182	−	0.455525i	−0.998531	+	0.0541800i	$0.982746\pi$
$174$	0.616255	−	9.61880i	0.0467182	−	0.729199i
$175$	−1.76185	−	0.729782i	−0.133183	−	0.0551663i
$176$	−11.7866	−	1.87487i	−0.888449	−	0.141324i
$177$	2.49613	−	1.03393i	0.187621	−	0.0777150i
$178$	−3.93291	−	11.5303i	−0.294784	−	0.864231i
$179$	5.79689	−	10.8452i	0.433280	−	0.810609i	−0.566631	−	0.823972i	$-0.691753\pi$
$179$	5.79689	−	10.8452i	0.433280	−	0.810609i	0.999911	+	0.0133624i	$0.00425350\pi$
$180$	3.46596	−	2.16943i	0.258338	−	0.161699i
$181$	−5.45729	+	6.64973i	−0.405637	+	0.494271i	−0.935259	−	0.353963i	$-0.884834\pi$
$181$	−5.45729	+	6.64973i	−0.405637	+	0.494271i	0.529622	+	0.848234i	$0.322334\pi$
$182$	−0.894507	+	0.642986i	−0.0663053	+	0.0476613i
$183$	−1.77818	+	8.93954i	−0.131447	+	0.660830i
$184$	−0.842768	−	4.14138i	−0.0621297	−	0.305306i
$185$	−6.71229	+	1.33516i	−0.493497	+	0.0981627i
$186$	13.3515	−	0.456726i	0.978982	−	0.0334888i
$187$	−8.50254	+	4.54470i	−0.621767	+	0.332342i
$188$	−0.667443	+	5.18750i	−0.0486783	+	0.378337i
$189$	0.921710	−	9.35828i	0.0670445	−	0.680715i
$190$	−0.935616	−	7.02690i	−0.0678767	−	0.509785i
$191$			18.3142i			1.32517i	0.748986	+	0.662585i	$0.230541\pi$
$191$			18.3142i			1.32517i	−0.748986	+	0.662585i	$0.769459\pi$
$192$	−5.01414	−	6.00106i	−0.361864	−	0.433089i
$193$		−	22.0214i		−	1.58513i	−0.609786	−	0.792566i	$-0.708745\pi$
$193$		−	22.0214i		−	1.58513i	0.609786	−	0.792566i	$-0.291255\pi$
$194$	−10.8718	+	1.44755i	−0.780547	+	0.103928i
$195$	0.0391373	−	0.397367i	0.00280268	−	0.0284561i
$196$	4.11057	+	5.32452i	0.293612	+	0.380323i
$197$	3.25750	−	1.74117i	0.232087	−	0.124053i	−0.351255	−	0.936280i	$-0.614245\pi$
$197$	3.25750	−	1.74117i	0.232087	−	0.124053i	0.583342	+	0.812227i	$0.301745\pi$
$198$	0.294930	+	8.62174i	0.0209598	+	0.612720i
$199$	8.35323	−	1.66156i	0.592145	−	0.117785i	0.110083	−	0.993922i	$-0.464888\pi$
$199$	8.35323	−	1.66156i	0.592145	−	0.117785i	0.482061	+	0.876137i	$0.339888\pi$
$200$	1.58174	+	2.34480i	0.111846	+	0.165802i
$201$	0.437074	−	2.19732i	0.0308288	−	0.154987i
$202$	−4.35702	−	6.06138i	−0.306559	−	0.426477i
$203$	−8.43497	+	10.2780i	−0.592019	+	0.721377i
$204$	−6.15627	−	1.41638i	−0.431025	−	0.0991663i
$205$	−1.98625	+	3.71600i	−0.138725	+	0.259537i
$206$	−14.3593	+	4.89787i	−1.00046	+	0.341251i
$207$	−2.82232	+	1.16904i	−0.196165	+	0.0812540i
$208$	1.63268	−	0.0630574i	0.113206	−	0.00437225i
$209$	13.8177	+	5.72347i	0.955788	+	0.395900i
$210$	2.63089	+	0.168555i	0.181549	+	0.0116314i
$211$	−5.09613	−	16.7997i	−0.350832	−	1.15654i	−0.937872	−	0.346981i	$-0.887207\pi$
$211$	−5.09613	−	16.7997i	−0.350832	−	1.15654i	0.587040	−	0.809558i	$-0.300293\pi$
$212$	23.7090	+	10.6585i	1.62834	+	0.732031i
$213$	6.77691	−	0.667467i	0.464346	−	0.0457341i
$214$	−9.18358	+	14.8169i	−0.627777	+	1.01286i
$215$	−4.14366	−	6.20143i	−0.282595	−	0.422934i
$216$	−8.80033	+	10.8201i	−0.598786	+	0.736218i
$217$	−15.3231	−	10.2386i	−1.04020	−	0.695039i
$218$	−7.18194	−	2.69105i	−0.486422	−	0.182261i
$219$	3.15978	−	10.4164i	0.213518	−	0.703876i
$220$	−5.95344	+	0.407785i	−0.401381	+	0.0274929i
$221$	1.02027	−	0.837313i	0.0686307	−	0.0563237i
$222$	8.18647	−	4.74252i	0.549440	−	0.318297i
$223$	0.372262	+	0.372262i	0.0249285	+	0.0249285i	0.719461	−	0.694533i	$-0.244389\pi$
$223$	0.372262	+	0.372262i	0.0249285	+	0.0249285i	−0.694533	+	0.719461i	$0.744389\pi$
$224$	0.784621	+	10.7591i	0.0524247	+	0.718874i
$225$	1.44565	−	1.44565i	0.0963769	−	0.0963769i
$226$	1.09511	−	4.11117i	0.0728458	−	0.273471i
$227$	−9.80095	−	11.9425i	−0.650512	−	0.792651i	0.338424	−	0.940994i	$-0.390106\pi$
$227$	−9.80095	−	11.9425i	−0.650512	−	0.792651i	−0.988936	+	0.148342i	$0.952606\pi$
$228$	4.36017	+	8.77642i	0.288759	+	0.581233i
$229$	5.31874	+	1.61342i	0.351472	+	0.106618i	0.461084	−	0.887356i	$-0.347461\pi$
$229$	5.31874	+	1.61342i	0.351472	+	0.106618i	−0.109612	+	0.993975i	$0.534961\pi$
$230$	−0.874931	−	1.92349i	−0.0576913	−	0.126831i
$231$	−3.09009	+	4.62464i	−0.203313	+	0.304279i
$232$	18.8459	−	5.80768i	1.23729	−	0.381293i
$233$	9.20684	−	6.15181i	0.603160	−	0.403019i	−0.216158	−	0.976358i	$-0.569353\pi$
$233$	9.20684	−	6.15181i	0.603160	−	0.403019i	0.819318	+	0.573340i	$0.194353\pi$
$234$	−0.269873	−	1.14978i	−0.0176421	−	0.0751633i
$235$	0.256328	+	2.60254i	0.0167210	+	0.169771i
$236$	3.79065	+	4.02347i	0.246750	+	0.261906i
$237$	−8.00701	+	2.42890i	−0.520111	+	0.157774i
$238$	5.75536	+	6.54331i	0.373065	+	0.424140i
$239$	5.36741	−	12.9581i	0.347189	−	0.838188i	−0.649761	−	0.760139i	$-0.725131\pi$
$239$	5.36741	−	12.9581i	0.347189	−	0.838188i	0.996950	−	0.0780491i	$-0.0248691\pi$
$240$	−3.11600	−	2.36202i	−0.201137	−	0.152468i
$241$	9.41867	+	22.7387i	0.606710	+	1.46473i	0.866558	+	0.499077i	$0.166328\pi$
$241$	9.41867	+	22.7387i	0.606710	+	1.46473i	−0.259848	+	0.965650i	$0.583672\pi$
$242$	−1.30809	+	2.66240i	−0.0840872	+	0.171145i
$243$	14.1785	+	7.57856i	0.909550	+	0.486165i
$244$	−18.3906	+	3.09184i	−1.17733	+	0.197935i
$245$	2.59987	+	2.13366i	0.166100	+	0.136314i
$246$	0.940396	−	5.74844i	0.0599575	−	0.366507i
$247$	−2.00818	−	0.399453i	−0.127778	−	0.0254166i
$248$	10.5712	+	25.2063i	0.671272	+	1.60060i
$249$	−0.201086	−	1.01093i	−0.0127433	−	0.0640649i
$250$	1.03360	+	0.965228i	0.0653708	+	0.0610464i
$251$	−9.08531	−	16.9974i	−0.573459	−	1.07287i	−0.986747	−	0.162266i	$-0.948120\pi$
$251$	−9.08531	−	16.9974i	−0.573459	−	1.07287i	0.413288	−	0.910601i	$-0.364380\pi$
$252$	7.52597	−	2.04030i	0.474092	−	0.128527i
$253$	4.43680	+	0.436986i	0.278939	+	0.0274731i
$254$	12.1721	+	9.31161i	0.763747	+	0.584263i
$255$	−3.15855			−0.197796
$256$	7.83656	−	13.9495i	0.489785	−	0.871843i
$257$	14.1982			0.885657			0.442828	−	0.896606i	$-0.353975\pi$
$257$	14.1982			0.885657			0.442828	+	0.896606i	$0.353975\pi$
$258$	8.18916	+	6.26467i	0.509835	+	0.390021i
$259$	−12.9883	−	1.27924i	−0.807056	−	0.0794881i
$260$	0.788487	−	0.213760i	0.0488999	−	0.0132568i
$261$	−6.71950	−	12.5713i	−0.415927	−	0.778145i
$262$	12.5747	+	11.7428i	0.776867	+	0.725475i
$263$	−0.537759	−	2.70350i	−0.0331596	−	0.166705i	0.960657	−	0.277737i	$-0.0895843\pi$
$263$	−0.537759	−	2.70350i	−0.0331596	−	0.166705i	−0.993817	+	0.111032i	$0.964584\pi$
$264$	7.60748	−	3.19048i	0.468208	−	0.196361i
$265$	12.7476	+	2.53565i	0.783077	+	0.155764i
$266$	2.18252	−	13.3413i	0.133819	−	0.818008i
$267$	6.50928	+	5.34203i	0.398362	+	0.326927i
$268$	4.52036	−	0.759968i	0.276125	−	0.0464224i
$269$	10.0567	+	5.37543i	0.613169	+	0.327745i	0.748580	−	0.663044i	$-0.230736\pi$
$269$	10.0567	+	5.37543i	0.613169	+	0.327745i	−0.135412	+	0.990789i	$0.543236\pi$
$270$	−3.07513	+	6.25891i	−0.187146	+	0.380905i
$271$	−1.55599	−	3.75650i	−0.0945198	−	0.228191i	0.869547	−	0.493850i	$-0.164411\pi$
$271$	−1.55599	−	3.75650i	−0.0945198	−	0.228191i	−0.964067	+	0.265659i	$0.914411\pi$
$272$	−1.76232	−	12.8041i	−0.106856	−	0.776363i
$273$	0.291395	−	0.703489i	0.0176360	−	0.0425771i
$274$	7.87812	+	8.95669i	0.475935	+	0.541094i
$275$	−2.85522	+	0.866121i	−0.172176	+	0.0522291i
$276$	2.00318	+	2.12622i	0.120578	+	0.127983i
$277$	2.59338	+	26.3310i	0.155821	+	1.58208i	0.681773	+	0.731564i	$0.261209\pi$
$277$	2.59338	+	26.3310i	0.155821	+	1.58208i	−0.525952	+	0.850514i	$0.676291\pi$
$278$	6.28213	+	26.7647i	0.376777	+	1.60524i
$279$	16.4275	−	10.9765i	0.983490	−	0.657147i
$280$	1.58849	+	5.15464i	0.0949304	+	0.308048i
$281$	11.7635	−	17.6054i	0.701753	−	1.05025i	−0.293783	−	0.955872i	$-0.594914\pi$
$281$	11.7635	−	17.6054i	0.701753	−	1.05025i	0.995537	−	0.0943761i	$-0.0300856\pi$
$282$	−1.49686	−	3.29076i	−0.0891365	−	0.195962i
$283$	20.5670	+	6.23892i	1.22258	+	0.370865i	0.834628	−	0.550814i	$-0.185683\pi$
$283$	20.5670	+	6.23892i	1.22258	+	0.370865i	0.387952	+	0.921680i	$0.373183\pi$
$284$	6.19896	+	12.4777i	0.367840	+	0.740413i
$285$	3.10847	+	3.78769i	0.184130	+	0.224363i
$286$	−0.443652	+	1.66552i	−0.0262337	+	0.0984840i
$287$	−5.68179	+	5.68179i	−0.335385	+	0.335385i
$288$	−10.9785	−	3.63696i	−0.646913	−	0.214310i
$289$	4.63815	+	4.63815i	0.272832	+	0.272832i
$290$	8.53194	−	4.94265i	0.501013	−	0.290242i
$291$	5.86017	−	4.80932i	0.343529	−	0.281927i
$292$	22.2189	−	1.52190i	1.30026	−	0.0890624i
$293$	5.28557	−	17.4242i	0.308786	−	1.01793i	−0.655970	−	0.754787i	$-0.727740\pi$
$293$	5.28557	−	17.4242i	0.308786	−	1.01793i	0.964756	−	0.263145i	$-0.0847596\pi$
$294$	−4.35388	−	1.63139i	−0.253924	−	0.0951443i
$295$	2.29813	+	1.53556i	0.133802	+	0.0894038i
$296$	15.0173	+	12.2140i	0.872861	+	0.709922i
$297$	−8.17396	−	12.2332i	−0.474301	−	0.709842i
$298$	14.6905	−	23.7019i	0.851001	−	1.37302i
$299$	−0.607407	+	0.0598244i	−0.0351273	+	0.00345973i
$300$	−1.78313	−	0.801618i	−0.102949	−	0.0462814i
$301$	−4.12879	−	13.6108i	−0.237979	−	0.784513i
$302$	−30.9707	−	1.98422i	−1.78216	−	0.114179i
$303$	4.76700	+	1.97456i	0.273857	+	0.113435i
$304$	−13.6201	+	14.7144i	−0.781166	+	0.843931i
$305$	−8.61455	+	3.56826i	−0.493268	+	0.204318i
$306$	−8.84218	+	3.01601i	−0.505474	+	0.172414i
$307$	−8.17842	+	15.3007i	−0.466767	+	0.873259i	0.532867	+	0.846199i	$0.321115\pi$
$307$	−8.17842	+	15.3007i	−0.466767	+	0.873259i	−0.999634	+	0.0270603i	$0.991385\pi$
$308$	−11.0902	−	2.55152i	−0.631921	−	0.145386i
$309$	6.65273	−	8.10638i	0.378461	−	0.461156i
$310$	7.97682	+	11.0972i	0.453053	+	0.630276i
$311$	1.75579	−	8.82697i	0.0995619	−	0.500532i	−0.898537	−	0.438898i	$-0.855369\pi$
$311$	1.75579	−	8.82697i	0.0995619	−	0.500532i	0.998099	−	0.0616336i	$-0.0196310\pi$
$312$	−0.936256	+	0.631574i	−0.0530051	+	0.0357558i
$313$	−1.14837	+	0.228425i	−0.0649097	+	0.0129113i	−0.227438	−	0.973792i	$-0.573035\pi$
$313$	−1.14837	+	0.228425i	−0.0649097	+	0.0129113i	0.162529	+	0.986704i	$0.448035\pi$
$314$	0.355972	+	10.4062i	0.0200886	+	0.587254i
$315$	3.43845	−	1.83789i	0.193735	−	0.103553i
$316$	−10.4616	−	13.5511i	−0.588510	−	0.762311i
$317$	−1.55403	+	15.7783i	−0.0872830	+	0.886199i	0.847456	+	0.530865i	$0.178133\pi$
$317$	−1.55403	+	15.7783i	−0.0872830	+	0.886199i	−0.934739	+	0.355334i	$0.884367\pi$
$318$	−17.8105	+	2.37143i	−0.998764	+	0.132983i
$319$			20.8030i			1.16474i
$320$	2.25469	−	7.67570i	0.126041	−	0.429085i
$321$		−	12.0492i		−	0.672522i
$322$	−0.531860	−	3.99451i	−0.0296394	−	0.222605i
$323$	−1.58756	+	16.1188i	−0.0883344	+	0.896874i
$324$	−0.335164	+	2.60496i	−0.0186202	+	0.144720i
$325$	0.360242	−	0.192554i	0.0199826	−	0.0106809i
$326$	23.7069	−	0.810961i	1.31301	−	0.0449150i
$327$	5.19939	−	1.03422i	0.287527	−	0.0571927i
$328$	11.6783	−	2.37653i	0.644827	−	0.131222i
$329$	−0.972933	+	4.89126i	−0.0536395	+	0.269664i
$330$	3.34922	−	2.40748i	0.184369	−	0.132527i
$331$	−11.4269	+	13.9237i	−0.628080	+	0.765318i	−0.985693	−	0.168552i	$-0.946091\pi$
$331$	−11.4269	+	13.9237i	−0.628080	+	0.765318i	0.357612	+	0.933870i	$0.383591\pi$
$332$	1.78759	−	1.11889i	0.0981065	−	0.0614071i
$333$	6.59572	−	12.3397i	0.361443	−	0.676213i
$334$	0.633103	+	1.85610i	0.0346419	+	0.101561i
$335$	2.11744	−	0.877071i	0.115688	−	0.0479195i
$336$	−4.37882	−	6.03539i	−0.238884	−	0.329257i
$337$	24.5642	+	10.1748i	1.33810	+	0.554258i	0.932954	−	0.359995i	$-0.117222\pi$
$337$	24.5642	+	10.1748i	1.33810	+	0.554258i	0.405143	+	0.914253i	$0.367222\pi$
$338$	−1.16038	+	18.1117i	−0.0631161	+	0.985145i
$339$	0.853658	+	2.81413i	0.0463644	+	0.152843i
$340$	−2.29415	−	6.04149i	−0.124418	−	0.327646i
$341$	−28.6949	+	2.82620i	−1.55392	+	0.153047i
$342$	12.3187	+	7.63521i	0.666121	+	0.412865i
$343$	10.9797	+	16.4323i	0.592848	+	0.887260i
$344$	−6.03465	+	20.2139i	−0.325367	+	1.08986i
$345$	1.21445	+	0.811473i	0.0653841	+	0.0436882i
$346$	−3.10683	+	8.29158i	−0.167024	+	0.445758i
$347$	2.20944	−	7.28356i	0.118609	−	0.391002i	−0.877453	−	0.479663i	$-0.840759\pi$
$347$	2.20944	−	7.28356i	0.118609	−	0.391002i	0.996062	+	0.0886613i	$0.0282589\pi$
$348$	−8.95733	+	10.2746i	−0.480163	+	0.550778i
$349$	−21.4826	+	17.6303i	−1.14994	+	0.943727i	−0.998995	−	0.0448157i	$-0.985730\pi$
$349$	−21.4826	+	17.6303i	−1.14994	+	0.943727i	−0.150940	+	0.988543i	$0.548230\pi$
$350$	1.35189	+	2.33362i	0.0722617	+	0.124737i
$351$	1.42426	+	1.42426i	0.0760212	+	0.0760212i
$352$	11.6281	+	12.2338i	0.619780	+	0.652063i
$353$	−14.0667	+	14.0667i	−0.748696	+	0.748696i	−0.974234	−	0.225538i	$-0.927586\pi$
$353$	−14.0667	+	14.0667i	−0.748696	+	0.748696i	0.225538	+	0.974234i	$0.427586\pi$
$354$	−3.69216	−	0.983499i	−0.196236	−	0.0522724i
$355$	4.41939	+	5.38505i	0.234557	+	0.285809i
$356$	−5.49003	+	16.3306i	−0.290971	+	0.865522i
$357$	−5.76403	−	1.74850i	−0.305065	−	0.0925404i
$358$	−15.8302	+	7.20064i	−0.836653	+	0.380565i
$359$	15.0989	−	22.5970i	0.796887	−	1.19263i	−0.180998	−	0.983483i	$-0.557933\pi$
$359$	15.0989	−	22.5970i	0.796887	−	1.19263i	0.977885	−	0.209142i	$-0.0670671\pi$
$360$	−5.75721	−	0.541420i	−0.303432	−	0.0285354i
$361$	5.09388	−	3.40362i	0.268099	−	0.179138i
$362$	11.8437	−	2.77993i	0.622493	−	0.146110i
$363$	−0.200974	−	2.04052i	−0.0105484	−	0.107099i
$364$	1.55724	+	0.0463976i	0.0816216	+	0.00243190i
$365$	10.6560	−	3.23246i	0.557761	−	0.169195i
$366$	9.67879	−	8.51326i	0.505918	−	0.444995i
$367$	5.06193	−	12.2206i	0.264231	−	0.637909i	−0.734961	−	0.678109i	$-0.762800\pi$
$367$	5.06193	−	12.2206i	0.264231	−	0.637909i	0.999192	+	0.0402002i	$0.0127996\pi$
$368$	−2.61193	+	5.37591i	−0.136156	+	0.280238i
$369$	−3.29659	−	7.95868i	−0.171614	−	0.414312i
$370$	8.68673	+	4.26797i	0.451602	+	0.221881i
$371$	21.8593	+	11.6841i	1.13488	+	0.606606i
$372$	−15.3894	−	10.9595i	−0.797901	−	0.568226i
$373$	−19.1389	−	15.7069i	−0.990977	−	0.813274i	−0.00855816	−	0.999963i	$-0.502724\pi$
$373$	−19.1389	−	15.7069i	−0.990977	−	0.813274i	−0.982419	+	0.186689i	$0.940224\pi$
$374$	13.4555	+	2.20120i	0.695766	+	0.113821i
$375$	−0.958733	−	0.190704i	−0.0495088	−	0.00984791i
$376$	5.20715	−	5.25327i	0.268538	−	0.270917i
$377$	−0.555613	−	2.79325i	−0.0286155	−	0.143860i
$378$	−9.07657	+	9.71955i	−0.466849	+	0.499920i
$379$	−3.34699	−	6.26177i	−0.171923	−	0.321645i	0.781172	−	0.624315i	$-0.214622\pi$
$379$	−3.34699	−	6.26177i	−0.171923	−	0.321645i	−0.953095	+	0.302670i	$0.902122\pi$
$380$	−4.98708	+	8.69681i	−0.255832	+	0.446137i
$381$	−10.5420	−	1.03830i	−0.540083	−	0.0531936i
$382$	15.7368	−	20.5712i	0.805167	−	1.05251i
$383$	12.8377			0.655978			0.327989	−	0.944682i	$-0.393629\pi$
$383$	12.8377			0.655978			0.327989	+	0.944682i	$0.393629\pi$
$384$	0.475529	+	11.0491i	0.0242668	+	0.563847i
$385$	−5.68995			−0.289987
$386$	−18.9223	+	24.7352i	−0.963118	+	1.25899i
$387$	15.1750	+	1.49460i	0.771387	+	0.0759750i
$388$	13.4554	+	7.71583i	0.683094	+	0.391712i
$389$	8.82156	+	16.5040i	0.447271	+	0.836785i	0.999994	+	0.00342024i	$0.00108870\pi$
$389$	8.82156	+	16.5040i	0.447271	+	0.836785i	−0.552723	+	0.833365i	$0.686411\pi$
$390$	−0.385406	+	0.412708i	−0.0195158	+	0.0208983i
$391$	0.941914	+	4.73532i	0.0476346	+	0.239475i
$392$	−0.0419368	−	9.51277i	−0.00211813	−	0.480467i
$393$	−11.6638	−	2.32008i	−0.588362	−	0.117033i
$394$	−5.15507	−	0.843326i	−0.259709	−	0.0424862i
$395$	−6.61678	−	5.43025i	−0.332927	−	0.273226i
$396$	7.07712	−	9.93766i	0.355639	−	0.499386i
$397$	−27.8177	−	14.8689i	−1.39613	−	0.746247i	−0.409978	−	0.912095i	$-0.634464\pi$
$397$	−27.8177	−	14.8689i	−1.39613	−	0.746247i	−0.986151	+	0.165849i	$0.946964\pi$
$398$	−10.8104	−	5.31135i	−0.541875	−	0.266234i
$399$	3.57587	+	8.63291i	0.179017	+	0.432186i
$400$	0.238147	−	3.99290i	0.0119073	−	0.199645i
$401$	4.99221	−	12.0523i	0.249299	−	0.601861i	−0.748846	−	0.662744i	$-0.769392\pi$
$401$	4.99221	−	12.0523i	0.249299	−	0.601861i	0.998145	+	0.0608829i	$0.0193916\pi$
$402$	−2.37902	+	2.09254i	−0.118655	+	0.104366i
$403$	3.77743	−	1.14587i	0.188167	−	0.0570798i
$404$	−0.314401	+	10.5522i	−0.0156420	+	0.524992i
$405$	0.128718	+	1.30689i	0.00639604	+	0.0649401i
$406$	18.3061	−	4.29675i	0.908514	−	0.213244i
$407$	−16.9784	+	11.3446i	−0.841590	+	0.562332i
$408$	5.69789	+	6.88082i	0.282088	+	0.340651i
$409$	18.3013	−	27.3899i	0.904942	−	1.35434i	−0.0300028	−	0.999550i	$-0.509552\pi$
$409$	18.3013	−	27.3899i	0.904942	−	1.35434i	0.934945	−	0.354792i	$-0.115448\pi$
$410$	5.42407	−	2.46723i	0.267876	−	0.121848i
$411$	−7.88999	−	2.39340i	−0.389184	−	0.118058i
$412$	20.3375	+	6.83705i	1.00195	+	0.336837i
$413$	3.34380	+	4.07443i	0.164538	+	0.200490i
$414$	4.17465	+	1.11202i	0.205173	+	0.0546528i
$415$	0.745602	−	0.745602i	0.0366002	−	0.0366002i
$416$	−1.88807	−	1.33208i	−0.0925701	−	0.0653108i
$417$	−13.4370	−	13.4370i	−0.658010	−	0.658010i
$418$	−10.6025	−	18.3019i	−0.518585	−	0.895175i
$419$	21.7470	−	17.8473i	1.06241	−	0.871899i	0.0703340	−	0.997523i	$-0.477593\pi$
$419$	21.7470	−	17.8473i	1.06241	−	0.871899i	0.992078	+	0.125625i	$0.0400935\pi$
$420$	−2.81027	−	2.44997i	−0.137127	−	0.119546i
$421$	−0.302778	+	0.998126i	−0.0147565	+	0.0486457i	−0.964009	−	0.265868i	$-0.914341\pi$
$421$	−0.302778	+	0.998126i	−0.0147565	+	0.0486457i	0.949253	+	0.314514i	$0.101841\pi$
$422$	−8.71131	+	23.2490i	−0.424060	+	1.13174i
$423$	−4.44548	−	2.97038i	−0.216147	−	0.144425i
$424$	−17.4722	−	32.3444i	−0.848526	−	1.57078i
$425$	−1.79516	−	2.68665i	−0.0870781	−	0.130322i
$426$	−8.18559	−	5.07346i	−0.396593	−	0.245810i
$427$	−17.6960	+	1.74290i	−0.856368	+	0.0843449i
$428$	23.0470	−	8.75171i	1.11402	−	0.423030i
$429$	−0.345834	−	1.14006i	−0.0166970	−	0.0550427i
$430$	−0.674389	+	10.5262i	−0.0325219	+	0.507617i
$431$	14.0420	+	5.81638i	0.676378	+	0.280165i	0.694312	−	0.719674i	$-0.255709\pi$
$431$	14.0420	+	5.81638i	0.676378	+	0.280165i	−0.0179338	+	0.999839i	$0.505709\pi$
$432$	19.1823	−	4.59172i	0.922907	−	0.220919i
$433$	−4.67235	+	1.93535i	−0.224539	+	0.0930070i	−0.492117	−	0.870529i	$-0.663777\pi$
$433$	−4.67235	+	1.93535i	−0.224539	+	0.0930070i	0.267578	+	0.963536i	$0.413777\pi$
$434$	8.41375	+	24.6670i	0.403873	+	1.18405i
$435$	−3.21279	+	6.01070i	−0.154041	+	0.288191i
$436$	5.75467	+	9.19389i	0.275599	+	0.440308i
$437$	4.75154	−	5.78977i	0.227297	−	0.276962i
$438$	−12.4997	+	8.98497i	−0.597258	+	0.429319i
$439$	4.15946	−	20.9110i	0.198520	−	0.998029i	−0.745088	−	0.666966i	$-0.767593\pi$
$439$	4.15946	−	20.9110i	0.198520	−	0.998029i	0.943609	−	0.331063i	$-0.107407\pi$
$440$	7.03751	+	4.65757i	0.335500	+	0.222041i
$441$	−6.74403	+	1.34147i	−0.321144	+	0.0638795i
$442$	−1.86548	+	0.0638138i	−0.0887317	+	0.00303531i
$443$	5.53389	−	2.95793i	0.262923	−	0.140535i	−0.334669	−	0.942336i	$-0.608624\pi$
$443$	5.53389	−	2.95793i	0.262923	−	0.140535i	0.597592	+	0.801801i	$0.296124\pi$
$444$	−13.2704	−	1.70742i	−0.629787	−	0.0810307i
$445$	−0.844357	+	8.57290i	−0.0400264	+	0.406394i
$446$	−0.0982645	−	0.738011i	−0.00465296	−	0.0349458i
$447$			19.2746i			0.911657i
$448$	8.36366	−	12.7592i	0.395146	−	0.602816i
$449$			2.94347i			0.138911i	0.997585	+	0.0694554i	$0.0221262\pi$
$449$			2.94347i			0.138911i	−0.997585	+	0.0694554i	$0.977874\pi$
$450$	−2.86601	+	0.381603i	−0.135105	+	0.0179890i
$451$	−1.23226	+	12.5114i	−0.0580250	+	0.589137i
$452$	−4.76267	+	3.67681i	−0.224017	+	0.172943i
$453$	18.9182	−	10.1120i	0.888853	−	0.475102i
$454$	0.746956	+	21.8359i	0.0350564	+	1.02481i
$455$	0.763998	−	0.151969i	0.0358168	−	0.00712440i
$456$	2.64382	−	13.6045i	0.123808	−	0.637091i
$457$	4.64646	−	23.3594i	0.217352	−	1.09270i	−0.705841	−	0.708370i	$-0.749431\pi$
$457$	4.64646	−	23.3594i	0.217352	−	1.09270i	0.923194	−	0.384335i	$-0.125569\pi$
$458$	−4.58783	−	6.38249i	−0.214375	−	0.298234i
$459$	10.1079	−	12.3165i	0.471797	−	0.574886i
$460$	−0.670042	+	2.91233i	−0.0312409	+	0.135788i
$461$	−2.35754	+	4.41064i	−0.109801	+	0.205424i	−0.930820	−	0.365477i	$-0.880906\pi$
$461$	−2.35754	+	4.41064i	−0.109801	+	0.205424i	0.821019	+	0.570901i	$0.193406\pi$
$462$	7.44471	−	2.53934i	0.346359	−	0.118141i
$463$	0.968401	−	0.401125i	0.0450054	−	0.0186418i	−0.360067	−	0.932926i	$-0.617246\pi$
$463$	0.968401	−	0.401125i	0.0450054	−	0.0186418i	0.405073	+	0.914285i	$0.367246\pi$
$464$	−26.1587	−	9.67028i	−1.21439	−	0.448931i
$465$	−8.72741	−	3.61501i	−0.404724	−	0.167642i
$466$	−15.6275	−	1.00122i	−0.723930	−	0.0463806i
$467$	3.76037	+	12.3963i	0.174009	+	0.573631i	0.999951	+	0.00987597i	$0.00314367\pi$
$467$	3.76037	+	12.3963i	0.174009	+	0.573631i	−0.825942	+	0.563755i	$0.809356\pi$
$468$	−0.684838	+	1.52336i	−0.0316566	+	0.0704175i
$469$	4.34963	−	0.428401i	0.200847	−	0.0197817i
$470$	1.94836	−	3.14352i	0.0898714	−	0.145000i
$471$	−3.99846	−	5.98412i	−0.184239	−	0.275734i
$472$	−0.800548	−	7.77649i	−0.0368482	−	0.357942i
$473$	−18.5032	−	12.3634i	−0.850777	−	0.568471i
$474$	11.0808	+	4.15195i	0.508959	+	0.190705i
$475$	−1.45509	+	4.79678i	−0.0667640	+	0.220091i
$476$	−0.842159	−	12.2951i	−0.0386003	−	0.563544i
$477$	−20.5408	+	16.8574i	−0.940501	+	0.771849i
$478$	−17.1633	+	9.94291i	−0.785033	+	0.454778i
$479$	−5.60453	−	5.60453i	−0.256077	−	0.256077i	0.567379	−	0.823457i	$-0.307957\pi$
$479$	−5.60453	−	5.60453i	−0.256077	−	0.256077i	−0.823457	+	0.567379i	$0.807957\pi$
$480$	1.47039	+	5.33059i	0.0671137	+	0.243307i
$481$	1.97673	−	1.97673i	0.0901309	−	0.0901309i
$482$	8.95926	−	33.6340i	0.408083	−	1.53199i
$483$	1.76704	+	2.15315i	0.0804032	+	0.0979716i
$484$	3.75701	−	1.86650i	0.170773	−	0.0848409i
$485$	7.42140	+	2.25126i	0.336988	+	0.102224i
$486$	−9.41375	−	20.6956i	−0.427016	−	0.938773i
$487$	−13.1453	+	19.6733i	−0.595669	+	0.891482i	−0.999730	−	0.0232504i	$-0.992598\pi$
$487$	−13.1453	+	19.6733i	−0.595669	+	0.891482i	0.404061	+	0.914732i	$0.367598\pi$
$488$	23.3136	+	12.3296i	1.05536	+	0.558133i
$489$	−13.6328	+	9.10914i	−0.616496	+	0.411929i
$490$	−1.08688	−	4.63059i	−0.0491001	−	0.209189i
$491$	−0.241797	−	2.45500i	−0.0109121	−	0.110793i	0.988186	−	0.153262i	$-0.0489777\pi$
$491$	−0.241797	−	2.45500i	−0.0109121	−	0.110793i	−0.999098	+	0.0424688i	$0.986478\pi$
$492$	−5.99575	+	5.64880i	−0.270309	+	0.254668i
$493$	−21.5586	+	6.53973i	−0.970950	+	0.294535i
$494$	1.91243	+	2.17425i	0.0860441	+	0.0978241i
$495$	2.33439	−	5.63572i	0.104923	−	0.253307i
$496$	9.78502	−	37.3961i	0.439360	−	1.67913i
$497$	5.08390	+	12.2736i	0.228044	+	0.550547i
$498$	−0.642792	+	1.30830i	−0.0288042	+	0.0586261i
$499$	26.1641	+	13.9850i	1.17127	+	0.626054i	0.938094	−	0.346381i	$-0.112590\pi$
$499$	26.1641	+	13.9850i	1.17127	+	0.626054i	0.233172	+	0.972436i	$0.425090\pi$
$500$	−0.331589	−	1.97232i	−0.0148291	−	0.0882049i
$501$	−1.04784	−	0.859938i	−0.0468139	−	0.0384192i
$502$	−4.40042	+	26.8988i	−0.196400	+	1.20055i
$503$	−35.8464	−	7.13029i	−1.59831	−	0.317924i	−0.686057	−	0.727548i	$-0.740660\pi$
$503$	−35.8464	−	7.13029i	−1.59831	−	0.317924i	−0.912255	+	0.409624i	$0.865660\pi$
$504$	−10.2066	−	4.17509i	−0.454638	−	0.185973i
$505$	1.02977	+	5.17702i	0.0458243	+	0.230374i
$506$	−4.60808	−	4.30324i	−0.204854	−	0.191302i
$507$	−5.91349	−	11.0634i	−0.262627	−	0.491341i
$508$	−5.67098	−	20.9183i	−0.251609	−	0.928098i
$509$	−38.5612	−	3.79795i	−1.70920	−	0.168341i	−0.804371	−	0.594127i	$-0.797498\pi$
$509$	−38.5612	−	3.79795i	−1.70920	−	0.168341i	−0.904824	+	0.425786i	$0.859998\pi$
$510$	3.54780	+	2.71405i	0.157099	+	0.120180i
$511$	21.2355			0.939404
$512$	−20.7887	+	8.93485i	−0.918738	+	0.394868i
$513$	−24.7174			−1.09130
$514$	−15.9479	−	12.2000i	−0.703430	−	0.538121i
$515$	10.6763	+	1.05153i	0.470455	+	0.0463357i
$516$	−3.81532	−	14.0734i	−0.167960	−	0.619546i
$517$	3.67819	+	6.88142i	0.161767	+	0.302644i
$518$	13.4897	+	12.5974i	0.592706	+	0.553497i
$519$	−1.19402	−	6.00272i	−0.0524115	−	0.263490i
$520$	−1.06933	−	0.437420i	−0.0468934	−	0.0191821i
$521$	10.1653	+	2.02201i	0.445352	+	0.0885860i	0.412672	−	0.910880i	$-0.364596\pi$
$521$	10.1653	+	2.02201i	0.445352	+	0.0885860i	0.0326803	+	0.999466i	$0.489596\pi$
$522$	−3.25455	+	19.8944i	−0.142448	+	0.870754i
$523$	3.50591	+	2.87722i	0.153303	+	0.125812i	0.707918	−	0.706295i	$-0.249635\pi$
$523$	3.50591	+	2.87722i	0.153303	+	0.125812i	−0.554615	+	0.832107i	$0.687135\pi$
$524$	−4.03407	−	23.9950i	−0.176229	−	1.04823i
$525$	−1.64402	−	0.878747i	−0.0717509	−	0.0383517i
$526$	−1.71900	+	3.49874i	−0.0749520	+	0.152552i
$527$	−11.9495	−	28.8487i	−0.520529	−	1.25667i
$528$	−11.2865	−	2.95321i	−0.491181	−	0.128522i
$529$	−7.94732	+	19.1865i	−0.345536	+	0.834197i
$530$	−12.1397	−	13.8017i	−0.527316	−	0.599509i
$531$	−5.40744	+	1.64033i	−0.234663	+	0.0711843i
$532$	−13.9153	+	13.1100i	−0.603303	+	0.568393i
$533$	−0.168699	−	1.71283i	−0.00730718	−	0.0741910i
$534$	−2.72121	−	11.5936i	−0.117758	−	0.501703i
$535$	10.2490	−	6.84817i	0.443103	−	0.296072i
$536$	−5.73044	−	3.03058i	−0.247517	−	0.130901i
$537$	6.67838	−	9.99490i	0.288193	−	0.431312i
$538$	−6.67712	−	14.6793i	−0.287871	−	0.632869i
$539$	9.60297	+	2.91303i	0.413629	+	0.125473i
$540$	8.83218	−	4.38786i	0.380076	−	0.188824i
$541$	−22.4020	−	27.2969i	−0.963137	−	1.17359i	−0.984777	−	0.173820i	$-0.944389\pi$
$541$	−22.4020	−	27.2969i	−0.963137	−	1.17359i	0.0216404	−	0.999766i	$-0.493111\pi$
$542$	−1.48010	+	5.55645i	−0.0635756	+	0.238670i
$543$	−5.94604	+	5.94604i	−0.255169	+	0.255169i
$544$	−9.02267	+	15.8963i	−0.386844	+	0.681549i
$545$	3.83477	+	3.83477i	0.164264	+	0.164264i
$546$	−0.931791	+	0.539797i	−0.0398770	+	0.0231012i
$547$	−14.7023	+	12.0659i	−0.628627	+	0.515900i	−0.893896	−	0.448274i	$-0.852039\pi$
$547$	−14.7023	+	12.0659i	−0.628627	+	0.515900i	0.265270	+	0.964174i	$0.414539\pi$
$548$	−1.15277	−	16.8299i	−0.0492441	−	0.718937i
$549$	5.53376	−	18.2424i	0.236175	−	0.778566i
$550$	3.95131	+	1.48054i	0.168485	+	0.0631306i
$551$	29.0591	+	19.4167i	1.23796	+	0.827179i
$552$	−0.423053	−	4.10952i	−0.0180063	−	0.174913i
$553$	−9.06889	−	13.5726i	−0.385648	−	0.577164i
$554$	19.7125	−	31.8043i	0.837502	−	1.35124i
$555$	−6.65770	+	0.655726i	−0.282603	+	0.0278340i
$556$	15.9417	−	35.4610i	0.676081	−	1.50388i
$557$	−6.59597	−	21.7440i	−0.279480	−	0.921323i	−0.978505	−	0.206225i	$-0.933882\pi$
$557$	−6.59597	−	21.7440i	−0.279480	−	0.921323i	0.699024	−	0.715098i	$-0.253618\pi$
$558$	−27.8837	−	1.78645i	−1.18041	−	0.0756265i
$559$	2.81466	+	1.16587i	0.119047	+	0.0493110i
$560$	2.64497	−	7.15481i	0.111770	−	0.302346i
$561$	−8.70679	+	3.60647i	−0.367601	+	0.152265i
$562$	−28.3410	+	9.66693i	−1.19549	+	0.407775i
$563$	−16.3907	+	30.6648i	−0.690784	+	1.29237i	0.254802	+	0.966993i	$0.417990\pi$
$563$	−16.3907	+	30.6648i	−0.690784	+	1.29237i	−0.945586	+	0.325373i	$0.894510\pi$
$564$	−1.14633	+	4.98250i	−0.0482690	+	0.209801i
$565$	−1.90851	+	2.32553i	−0.0802917	+	0.0978357i
$566$	−17.7406	−	24.6803i	−0.745694	−	1.03739i
$567$	−0.488569	+	2.45620i	−0.0205180	+	0.103151i
$568$	3.75878	−	19.3419i	0.157715	−	0.811569i
$569$	17.4560	−	3.47221i	0.731793	−	0.145563i	0.184891	−	0.982759i	$-0.440807\pi$
$569$	17.4560	−	3.47221i	0.731793	−	0.145563i	0.546902	+	0.837196i	$0.315807\pi$
$570$	−0.236905	−	6.92548i	−0.00992285	−	0.290076i
$571$	2.67201	−	1.42822i	0.111820	−	0.0597690i	−0.414539	−	0.910032i	$-0.636057\pi$
$571$	2.67201	−	1.42822i	0.111820	−	0.0597690i	0.526358	+	0.850263i	$0.323557\pi$
$572$	1.92945	−	1.48955i	0.0806744	−	0.0622812i
$573$	−1.75475	+	17.8162i	−0.0733056	+	0.744284i
$574$	11.2642	−	1.49980i	0.470157	−	0.0626004i
$575$			1.49421i			0.0623128i
$576$	9.20629	+	13.5186i	0.383595	+	0.563276i
$577$			28.7871i			1.19842i	0.800591	+	0.599211i	$0.204519\pi$
$577$			28.7871i			1.19842i	−0.800591	+	0.599211i	$0.795481\pi$
$578$	−1.22431	−	9.19514i	−0.0509247	−	0.382467i
$579$	2.10994	−	21.4226i	0.0876861	−	0.890292i
$580$	−13.8304	−	1.77948i	−0.574278	−	0.0738888i
$581$	1.77339	−	0.947899i	0.0735728	−	0.0393255i
$582$	−10.7148	+	0.366531i	−0.444145	+	0.0151932i
$583$	38.0349	−	7.56561i	1.57524	−	0.313336i
$584$	−26.2648	−	17.3826i	−1.08685	−	0.719297i
$585$	−0.162922	+	0.819064i	−0.00673600	+	0.0338641i
$586$	−20.9090	+	15.0297i	−0.863742	+	0.620872i
$587$	4.09717	−	4.99241i	0.169108	−	0.206059i	−0.681560	−	0.731763i	$-0.738698\pi$
$587$	4.09717	−	4.99241i	0.169108	−	0.206059i	0.850668	+	0.525704i	$0.176198\pi$
$588$	3.48863	+	5.57359i	0.143869	+	0.229851i
$589$	−22.8348	+	42.7209i	−0.940892	+	1.76029i
$590$	−1.26188	−	3.69951i	−0.0519507	−	0.152306i
$591$	3.33575	−	1.38171i	0.137215	−	0.0568361i
$592$	−6.37284	−	26.6230i	−0.261922	−	1.09420i
$593$	17.0496	+	7.06219i	0.700144	+	0.290009i	0.704219	−	0.709982i	$-0.251297\pi$
$593$	17.0496	+	7.06219i	0.700144	+	0.290009i	−0.00407515	+	0.999992i	$0.501297\pi$
$594$	−1.33033	+	20.7644i	−0.0545840	+	0.851973i
$595$	−1.78872	−	5.89661i	−0.0733303	−	0.241738i
$596$	−36.8673	+	13.9997i	−1.51014	+	0.573450i
$597$	8.28529	−	0.816030i	0.339094	−	0.0333979i
$598$	0.733666	+	0.454729i	0.0300018	+	0.0185953i
$599$	7.31946	+	10.9543i	0.299065	+	0.447582i	0.950319	−	0.311277i	$-0.100757\pi$
$599$	7.31946	+	10.9543i	0.299065	+	0.447582i	−0.651254	+	0.758860i	$0.725757\pi$
$600$	1.31407	+	2.43259i	0.0536467	+	0.0993103i
$601$	37.9929	+	25.3860i	1.54976	+	1.03552i	0.976335	+	0.216262i	$0.0693865\pi$
$601$	37.9929	+	25.3860i	1.54976	+	1.03552i	0.573427	+	0.819256i	$0.305614\pi$
$602$	−7.05773	+	18.8359i	−0.287652	+	0.767692i
$603$	−1.36019	+	4.48394i	−0.0553911	+	0.182600i
$604$	33.0824	+	28.8409i	1.34610	+	1.17352i
$605$	1.62143	−	1.33067i	0.0659206	−	0.0540996i
$606$	−3.65779	−	6.31402i	−0.148587	−	0.256490i
$607$	26.4470	+	26.4470i	1.07345	+	1.07345i	0.997080	+	0.0763697i	$0.0243329\pi$
$607$	26.4470	+	26.4470i	1.07345	+	1.07345i	0.0763697	+	0.997080i	$0.475667\pi$
$608$	27.9422	−	4.82444i	1.13321	−	0.195657i
$609$	−9.19039	+	9.19039i	−0.372413	+	0.372413i
$610$	12.7423	+	3.39422i	0.515919	+	0.137428i
$611$	−0.677668	−	0.825741i	−0.0274155	−	0.0334059i
$612$	12.5234	+	4.21012i	0.506229	+	0.170184i
$613$	43.5745	+	13.2182i	1.75996	+	0.533878i	0.994036	−	0.109054i	$-0.0347822\pi$
$613$	43.5745	+	13.2182i	1.75996	+	0.533878i	0.765923	+	0.642932i	$0.222282\pi$
$614$	22.3337	−	10.1589i	0.901316	−	0.409978i
$615$	−2.28828	+	3.42465i	−0.0922724	+	0.138095i
$616$	10.2644	+	12.3954i	0.413565	+	0.499425i
$617$	−30.8190	+	20.5926i	−1.24072	+	0.829025i	−0.990278	−	0.139105i	$-0.955577\pi$
$617$	−30.8190	+	20.5926i	−1.24072	+	0.829025i	−0.250447	+	0.968130i	$0.580577\pi$
$618$	−14.4381	+	3.38888i	−0.580787	+	0.136321i
$619$	2.13796	+	21.7070i	0.0859317	+	0.872479i	0.937442	+	0.348141i	$0.113187\pi$
$619$	2.13796	+	21.7070i	0.0859317	+	0.872479i	−0.851510	+	0.524338i	$0.824313\pi$
$620$	0.575604	−	19.3190i	0.0231168	−	0.775868i
$621$	−7.05074	+	2.13882i	−0.282937	+	0.0858279i
$622$	−9.55691	+	8.40606i	−0.383197	+	0.337052i
$623$	−6.28662	+	15.1772i	−0.251868	+	0.608063i
$624$	1.59433	+	0.0950897i	0.0638242	+	0.00380663i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	1.48617	+	0.730183i	0.0593992	+	0.0291840i
$627$	12.8936	+	6.89175i	0.514919	+	0.275230i
$628$	8.54186	−	11.9945i	0.340857	−	0.478631i
$629$	−17.0941	−	14.0288i	−0.681586	−	0.559363i
$630$	−5.44143	−	0.890171i	−0.216792	−	0.0354653i
$631$	−13.2139	−	2.62840i	−0.526036	−	0.104635i	−0.0750733	−	0.997178i	$-0.523919\pi$
$631$	−13.2139	−	2.62840i	−0.526036	−	0.104635i	−0.450962	+	0.892543i	$0.648919\pi$
$632$	0.106731	+	24.2104i	0.00424553	+	0.963039i
$633$	−3.34793	−	16.8312i	−0.133068	−	0.668979i
$634$	15.3034	−	16.3874i	0.607774	−	0.650828i
$635$	−5.10837	−	9.55709i	−0.202720	−	0.379262i
$636$	22.0431	+	12.6404i	0.874065	+	0.501223i
$637$	−1.36721	−	0.134658i	−0.0541708	−	0.00533535i
$638$	17.8754	−	23.3667i	0.707693	−	0.925095i
$639$	−14.2424			−0.563421
$640$	−9.12804	+	6.68423i	−0.360817	+	0.264217i
$641$	2.65839			0.105000			0.0525000	−	0.998621i	$-0.483281\pi$
$641$	2.65839			0.105000			0.0525000	+	0.998621i	$0.483281\pi$
$642$	−10.3535	+	13.5341i	−0.408621	+	0.534149i
$643$	16.7779	+	1.65248i	0.661655	+	0.0651673i	0.423270	−	0.906004i	$-0.360882\pi$
$643$	16.7779	+	1.65248i	0.661655	+	0.0651673i	0.238385	+	0.971171i	$0.423382\pi$
$644$	−2.83496	+	4.94379i	−0.111713	+	0.194813i
$645$	−3.43681	−	6.42982i	−0.135324	−	0.253174i
$646$	15.6336	−	16.7411i	0.615095	−	0.658668i
$647$	0.287969	+	1.44772i	0.0113212	+	0.0569158i	0.986033	−	0.166550i	$-0.0532628\pi$
$647$	0.287969	+	1.44772i	0.0113212	+	0.0569158i	−0.974712	+	0.223466i	$0.928263\pi$
$648$	2.61483	−	2.63799i	0.102720	−	0.103630i
$649$	8.08829	+	1.60886i	0.317493	+	0.0631533i
$650$	−0.570092	−	0.0932622i	−0.0223608	−	0.00365804i
$651$	−13.9254	−	11.4283i	−0.545781	−	0.447911i
$652$	−27.3253	−	19.4597i	−1.07014	−	0.762102i
$653$	24.0450	+	12.8523i	0.940954	+	0.502950i	0.869194	−	0.494472i	$-0.164638\pi$
$653$	24.0450	+	12.8523i	0.940954	+	0.502950i	0.0717600	+	0.997422i	$0.477138\pi$
$654$	−6.72881	−	3.30600i	−0.263117	−	0.129275i
$655$	−4.65568	−	11.2398i	−0.181912	−	0.439176i
$656$	−15.1596	−	7.36541i	−0.591882	−	0.287571i
$657$	−8.71221	+	21.0331i	−0.339896	+	0.820581i
$658$	5.29574	−	4.65803i	0.206450	−	0.181589i
$659$	−6.19306	+	1.87864i	−0.241247	+	0.0731816i	−0.408593	−	0.912717i	$-0.633980\pi$
$659$	−6.19306	+	1.87864i	−0.241247	+	0.0731816i	0.167346	+	0.985898i	$0.446480\pi$
$660$	−5.83063	−	0.173722i	−0.226957	−	0.00676213i
$661$	−1.31399	−	13.3411i	−0.0511082	−	0.518910i	−0.986322	−	0.164828i	$-0.947293\pi$
$661$	−1.31399	−	13.3411i	−0.0511082	−	0.518910i	0.935214	−	0.354082i	$-0.115207\pi$
$662$	24.7994	−	5.82084i	0.963855	−	0.226233i
$663$	1.07275	−	0.716790i	0.0416622	−	0.0278378i
$664$	−2.96931	−	0.279240i	−0.115231	−	0.0108366i
$665$	−5.31077	+	7.94812i	−0.205943	+	0.308215i
$666$	−18.0117	+	8.19291i	−0.697939	+	0.317469i
$667$	9.96937	+	3.02417i	0.386015	+	0.117096i
$668$	0.883762	−	2.62884i	0.0341938	−	0.101713i
$669$	0.326472	+	0.397808i	0.0126221	+	0.0153801i
$670$	−3.13202	−	0.834291i	−0.121000	−	0.0322315i
$671$	−19.6724	+	19.6724i	−0.759444	+	0.759444i
$672$	−0.267581	+	10.5417i	−0.0103221	+	0.406657i
$673$	−16.7104	−	16.7104i	−0.644140	−	0.644140i	0.307430	−	0.951571i	$-0.400531\pi$
$673$	−16.7104	−	16.7104i	−0.644140	−	0.644140i	−0.951571	+	0.307430i	$0.900531\pi$
$674$	−18.8485	−	32.5360i	−0.726016	−	1.25324i
$675$	3.81175	−	3.12822i	0.146714	−	0.120405i
$676$	16.8662	−	19.3466i	0.648699	−	0.744100i
$677$	−2.83569	+	9.34802i	−0.108985	+	0.359274i	−0.994421	−	0.105487i	$-0.966360\pi$
$677$	−2.83569	+	9.34802i	−0.108985	+	0.359274i	0.885436	+	0.464761i	$0.153860\pi$
$678$	1.45924	−	3.89446i	0.0560418	−	0.149566i
$679$	12.2970	+	8.21663i	0.471917	+	0.315325i
$680$	−2.61440	+	8.75730i	−0.100257	+	0.335827i
$681$	−8.39020	−	12.5568i	−0.321513	−	0.481179i
$682$	34.6596	+	21.4821i	1.32718	+	0.822594i
$683$	−44.2920	+	4.36238i	−1.69478	+	0.166922i	−0.898789	−	0.438381i	$-0.855552\pi$
$683$	−44.2920	+	4.36238i	−1.69478	+	0.166922i	−0.795995	+	0.605303i	$0.793052\pi$
$684$	−7.27614	−	19.1612i	−0.278210	−	0.732648i
$685$	−2.44845	−	8.07147i	−0.0935506	−	0.308395i
$686$	1.78697	−	27.8918i	0.0682268	−	1.06492i
$687$	5.01953	+	2.07916i	0.191507	+	0.0793249i
$688$	24.1476	−	17.5196i	0.920617	−	0.667929i
$689$	−4.90494	+	2.03169i	−0.186863	+	0.0774014i
$690$	−0.666845	−	1.95502i	−0.0253863	−	0.0744263i
$691$	13.7332	−	25.6930i	0.522435	−	0.977407i	−0.472918	−	0.881107i	$-0.656799\pi$
$691$	13.7332	−	25.6930i	0.522435	−	0.977407i	0.995352	−	0.0963000i	$-0.0307008\pi$
$692$	10.6144	−	6.64379i	0.403499	−	0.252559i
$693$	7.37982	−	8.99234i	0.280336	−	0.341591i
$694$	−8.74026	+	6.28264i	−0.331776	+	0.238486i
$695$	3.79252	−	19.0663i	0.143858	−	0.723225i
$696$	18.8899	−	3.84408i	0.716019	−	0.145709i
$697$	−13.3532	+	2.65611i	−0.505788	+	0.100607i
$698$	39.2791	−	1.34365i	1.48674	−	0.0508579i
$699$	9.54592	−	5.10240i	0.361060	−	0.192990i
$700$	0.486715	−	3.78284i	0.0183961	−	0.142978i
$701$	4.70467	−	47.7673i	0.177693	−	1.80415i	−0.331458	−	0.943470i	$-0.607541\pi$
$701$	4.70467	−	47.7673i	0.177693	−	1.80415i	0.509151	−	0.860677i	$-0.329959\pi$
$702$	−0.375955	−	2.82360i	−0.0141895	−	0.106570i
$703$			34.3053i			1.29385i
$704$	−2.54898	−	23.7331i	−0.0960681	−	0.894474i
$705$			2.55633i			0.0962770i
$706$	27.8873	−	3.71314i	1.04955	−	0.139746i
$707$	−0.986646	+	10.0176i	−0.0371066	+	0.376750i
$708$	3.30208	+	4.27726i	0.124100	+	0.160749i
$709$	18.4260	−	9.84891i	0.692004	−	0.369884i	−0.0876011	−	0.996156i	$-0.527920\pi$
$709$	18.4260	−	9.84891i	0.692004	−	0.369884i	0.779605	+	0.626272i	$0.215420\pi$
$710$	−0.336813	−	9.84612i	−0.0126404	−	0.369518i
$711$	17.1639	−	3.41410i	0.643695	−	0.128039i
$712$	20.1990	−	13.6257i	0.756990	−	0.510646i
$713$	−2.81704	+	14.1622i	−0.105499	+	0.530379i
$714$	4.97193	+	6.91683i	0.186070	+	0.258856i
$715$	0.773176	−	0.942117i	0.0289151	−	0.0352332i
$716$	23.9683	+	5.51441i	0.895739	+	0.206083i
$717$	6.46302	−	12.0915i	0.241366	−	0.451564i
$718$	−36.3765	+	12.4078i	−1.35756	+	0.463055i
$719$	−23.4191	+	9.70051i	−0.873385	+	0.361768i	−0.773928	−	0.633274i	$-0.781711\pi$
$719$	−23.4191	+	9.70051i	−0.873385	+	0.361768i	−0.0994574	+	0.995042i	$0.531711\pi$
$720$	6.00148	+	5.55514i	0.223662	+	0.207028i
$721$	18.9011	+	7.82908i	0.703913	+	0.291570i
$722$	−8.64625	−	0.553946i	−0.321780	−	0.0206157i
$723$	6.98389	+	23.0228i	0.259734	+	0.856228i
$724$	−15.6920	−	7.05444i	−0.583188	−	0.262176i
$725$	−6.93865	+	0.683398i	−0.257695	+	0.0253808i
$726$	−1.52761	+	2.46467i	−0.0566951	+	0.0914726i
$727$	16.1516	+	24.1726i	0.599031	+	0.896513i	0.999807	−	0.0196631i	$-0.00625936\pi$
$727$	16.1516	+	24.1726i	0.599031	+	0.896513i	−0.400776	+	0.916176i	$0.631259\pi$
$728$	−1.70928	−	1.39020i	−0.0633501	−	0.0515244i
$729$	9.79113	+	6.54222i	0.362634	+	0.242305i
$730$	−14.7468	−	5.52556i	−0.545802	−	0.204510i
$731$	6.99574	−	23.0619i	0.258747	−	0.852973i
$732$	−18.1867	+	1.24571i	−0.672201	+	0.0460428i
$733$	3.43334	−	2.81767i	0.126813	−	0.104073i	−0.568849	−	0.822442i	$-0.692611\pi$
$733$	3.43334	−	2.81767i	0.126813	−	0.104073i	0.695662	+	0.718369i	$0.255111\pi$
$734$	−16.1865	+	9.37702i	−0.597455	+	0.346112i
$735$	2.32474	+	2.32474i	0.0857494	+	0.0857494i
$736$	7.55316	−	3.79405i	0.278413	−	0.139851i
$737$	4.83543	−	4.83543i	0.178115	−	0.178115i
$738$	−3.13580	+	11.7721i	−0.115430	+	0.433338i
$739$	−16.6844	−	20.3299i	−0.613744	−	0.747849i	0.369682	−	0.929158i	$-0.379467\pi$
$739$	−16.6844	−	20.3299i	−0.613744	−	0.747849i	−0.983426	+	0.181309i	$0.941967\pi$
$740$	−6.08991	−	12.2582i	−0.223870	−	0.450619i
$741$	−1.91531	−	0.581002i	−0.0703605	−	0.0213436i
$742$	−14.5134	−	31.9070i	−0.532804	−	1.17134i
$743$	−3.49719	+	5.23392i	−0.128300	+	0.192014i	−0.890058	−	0.455847i	$-0.849336\pi$
$743$	−3.49719	+	5.23392i	−0.128300	+	0.192014i	0.761758	+	0.647861i	$0.224336\pi$
$744$	7.86866	+	25.5337i	0.288479	+	0.936113i
$745$	−16.3949	+	10.9547i	−0.600661	+	0.401349i
$746$	8.00106	+	34.0881i	0.292940	+	1.24805i
$747$	0.211302	+	2.14538i	0.00773113	+	0.0784955i
$748$	−13.2222	−	14.0343i	−0.483453	−	0.513146i
$749$	22.4944	−	6.82359i	0.821926	−	0.249329i
$750$	0.913017	+	1.03801i	0.0333387	+	0.0379029i
$751$	−17.7232	+	42.7877i	−0.646731	+	1.56135i	0.170703	+	0.985323i	$0.445396\pi$
$751$	−17.7232	+	42.7877i	−0.646731	+	1.56135i	−0.817433	+	0.576023i	$0.804604\pi$
$752$	−10.3628	+	1.42631i	−0.377893	+	0.0520121i
$753$	−7.20969	−	17.4057i	−0.262736	−	0.634300i
$754$	−1.77607	+	3.61490i	−0.0646807	+	0.131647i
$755$	19.3533	+	10.3446i	0.704339	+	0.376477i
$756$	18.5468	−	3.11812i	0.674542	−	0.113405i
$757$	−3.01599	−	2.47516i	−0.109618	−	0.0899612i	0.577988	−	0.816046i	$-0.303838\pi$
$757$	−3.01599	−	2.47516i	−0.109618	−	0.0899612i	−0.687606	+	0.726084i	$0.741338\pi$
$758$	−1.62109	+	9.90940i	−0.0588808	+	0.359926i
$759$	4.27429	+	0.850208i	0.155147	+	0.0308606i
$760$	13.0746	−	5.48331i	0.474264	−	0.198901i
$761$	−5.21737	−	26.2295i	−0.189130	−	0.950818i	−0.952426	−	0.304770i	$-0.901420\pi$
$761$	−5.21737	−	26.2295i	−0.189130	−	0.950818i	0.763296	−	0.646048i	$-0.223580\pi$
$762$	10.9490	+	10.2247i	0.396639	+	0.370401i
$763$	4.87523	+	9.12090i	0.176495	+	0.330199i
$764$	−35.3524	+	9.58408i	−1.27900	+	0.346740i
$765$	6.57426	+	0.647509i	0.237693	+	0.0234107i
$766$	−14.4198	−	11.0311i	−0.521009	−	0.398569i
$767$	−1.12900			−0.0407657
$768$	8.96002	−	12.8193i	0.323317	−	0.462578i
$769$	−26.9203			−0.970770			−0.485385	−	0.874301i	$-0.661320\pi$
$769$	−26.9203			−0.970770			−0.485385	+	0.874301i	$0.661320\pi$
$770$	6.39115	+	4.88919i	0.230321	+	0.176194i
$771$	13.8121	+	1.36037i	0.497430	+	0.0489926i
$772$	42.5083	−	11.5241i	1.52991	−	0.414760i
$773$	0.230719	+	0.431645i	0.00829838	+	0.0155252i	0.886036	−	0.463616i	$-0.153448\pi$
$773$	0.230719	+	0.431645i	0.00829838	+	0.0155252i	−0.877738	+	0.479141i	$0.840948\pi$
$774$	−15.7608	−	14.7182i	−0.566510	−	0.529034i
$775$	−1.88531	−	9.47808i	−0.0677222	−	0.340463i
$776$	−8.48358	−	20.2285i	−0.304543	−	0.726160i
$777$	−12.5126	−	2.48891i	−0.448887	−	0.0892892i
$778$	4.27267	−	26.1179i	0.153183	−	0.936374i
$779$	16.3266	+	13.3989i	0.584962	+	0.480066i
$780$	0.787528	−	0.132400i	0.0281980	−	0.00474069i
$781$	18.3311	+	9.79818i	0.655938	+	0.350606i
$782$	3.01092	−	6.12824i	0.107670	−	0.219145i
$783$	−13.1568	−	31.7633i	−0.470185	−	1.13513i
$784$	−8.12692	+	10.7211i	−0.290247	+	0.382897i
$785$	2.81754	−	6.80214i	0.100562	−	0.242779i
$786$	11.1076	+	12.6284i	0.396197	+	0.450439i
$787$	−5.35634	+	1.62483i	−0.190933	+	0.0579189i	−0.384303	−	0.923207i	$-0.625558\pi$
$787$	−5.35634	+	1.62483i	−0.190933	+	0.0579189i	0.193370	+	0.981126i	$0.438058\pi$
$788$	5.06571	+	5.37685i	0.180459	+	0.191542i
$789$	−0.264106	−	2.68151i	−0.00940241	−	0.0954642i
$790$	2.76615	+	11.7851i	0.0984153	+	0.419293i
$791$	−4.77019	+	3.18734i	−0.169609	+	0.113329i
$792$	−16.4884	+	5.08118i	−0.585890	+	0.180552i
$793$	2.11603	−	3.16686i	0.0751423	−	0.112458i
$794$	18.4694	+	40.6041i	0.655456	+	1.44099i
$795$	12.1580	+	3.68809i	0.431200	+	0.130803i
$796$	7.57870	+	15.2549i	0.268620	+	0.540696i
$797$	22.9153	+	27.9223i	0.811701	+	0.989060i	0.999976	+	0.00694367i	$0.00221026\pi$
$797$	22.9153	+	27.9223i	0.811701	+	0.989060i	−0.188275	+	0.982116i	$0.560290\pi$
$798$	3.40145	−	12.7694i	0.120410	−	0.452033i
$799$	−5.97507	+	5.97507i	−0.211383	+	0.211383i
$800$	−3.69847	+	4.28034i	−0.130761	+	0.151333i
$801$	−12.4534	−	12.4534i	−0.440020	−	0.440020i
$802$	−15.9636	+	9.24787i	−0.563693	+	0.326554i
$803$	25.6832	−	21.0777i	0.906341	−	0.743815i
$804$	4.47026	−	0.306193i	0.157654	−	0.0107986i
$805$	−0.827159	+	2.72678i	−0.0291535	+	0.0961063i
$806$	−5.22755	−	1.95874i	−0.184133	−	0.0689938i
$807$	9.26822	+	6.19283i	0.326257	+	0.217998i
$808$	9.42033	−	11.5825i	0.331406	−	0.407469i
$809$	21.8937	+	32.7663i	0.769743	+	1.15200i	0.984509	+	0.175336i	$0.0561012\pi$
$809$	21.8937	+	32.7663i	0.769743	+	1.15200i	−0.214766	+	0.976666i	$0.568899\pi$
$810$	0.978393	−	1.57855i	0.0343772	−	0.0554647i
$811$	−15.1866	+	1.49575i	−0.533274	+	0.0525229i	−0.361070	−	0.932539i	$-0.617589\pi$
$811$	−15.1866	+	1.49575i	−0.533274	+	0.0525229i	−0.172203	+	0.985061i	$0.555089\pi$
$812$	−24.2541	−	10.9036i	−0.851151	−	0.382640i
$813$	−1.15376	−	3.80344i	−0.0404641	−	0.133392i
$814$	28.8189	+	1.84636i	1.01010	+	0.0647149i
$815$	−15.4964	−	6.41880i	−0.542814	−	0.224841i
$816$	−0.487595	−	12.6248i	−0.0170693	−	0.441956i
$817$	−34.5402	+	14.3070i	−1.20841	+	0.500540i
$818$	−44.0920	+	15.0395i	−1.54164	+	0.525844i
$819$	−0.750731	+	1.40452i	−0.0262327	+	0.0490778i
$820$	−8.21251	−	1.88946i	−0.286793	−	0.0659828i
$821$	6.17561	−	7.52500i	0.215530	−	0.262624i	−0.654011	−	0.756485i	$-0.726915\pi$
$821$	6.17561	−	7.52500i	0.215530	−	0.262624i	0.869541	+	0.493861i	$0.164415\pi$
$822$	6.80574	+	9.46798i	0.237377	+	0.330234i
$823$	4.02104	−	20.2151i	0.140165	−	0.704655i	−0.845235	−	0.534395i	$-0.820539\pi$
$823$	4.02104	−	20.2151i	0.140165	−	0.704655i	0.985399	−	0.170260i	$-0.0544607\pi$
$824$	−16.9689	−	25.1550i	−0.591139	−	0.876314i
$825$	−2.86057	+	0.569002i	−0.0995922	+	0.0198101i
$826$	−0.254840	−	7.44976i	−0.00886700	−	0.259210i
$827$	−2.77059	+	1.48091i	−0.0963430	+	0.0514964i	−0.518864	−	0.854856i	$-0.673645\pi$
$827$	−2.77059	+	1.48091i	−0.0963430	+	0.0514964i	0.422522	+	0.906353i	$0.361145\pi$
$828$	−3.73358	−	4.83621i	−0.129751	−	0.168070i
$829$	−4.53693	+	46.0642i	−0.157574	+	1.59988i	0.513236	+	0.858248i	$0.328447\pi$
$829$	−4.53693	+	46.0642i	−0.157574	+	1.59988i	−0.670810	+	0.741629i	$0.734053\pi$
$830$	−1.47816	+	0.196814i	−0.0513076	+	0.00683150i
$831$			25.8635i			0.897196i
$832$	0.976125	+	3.11860i	0.0338410	+	0.108118i
$833$			10.8675i			0.376537i
$834$	3.54690	+	26.6388i	0.122819	+	0.922427i
$835$	0.135921	−	1.38003i	0.00470374	−	0.0477579i
$836$	−3.81716	+	29.6677i	−0.132019	+	1.02608i
$837$	42.0257	−	22.4632i	1.45262	−	0.776442i
$838$	−39.7627	+	1.36019i	−1.37358	+	0.0469870i
$839$	−38.0162	+	7.56190i	−1.31247	+	0.261066i	−0.801221	−	0.598369i	$-0.795816\pi$
$839$	−38.0162	+	7.56190i	−1.31247	+	0.261066i	−0.511246	+	0.859435i	$0.670816\pi$
$840$	1.05141	+	5.16667i	0.0362772	+	0.178267i
$841$	−3.82610	+	19.2351i	−0.131934	+	0.663279i
$842$	1.19775	−	0.860962i	0.0412772	−	0.0296707i
$843$	13.1305	−	15.9996i	0.452238	−	0.551054i
$844$	29.7620	−	18.6287i	1.02445	−	0.641226i
$845$	6.04950	−	11.3178i	0.208109	−	0.389345i
$846$	2.44097	+	7.15630i	0.0839223	+	0.246039i
$847$	3.69558	−	1.53076i	0.126981	−	0.0525974i
$848$	−8.16716	+	51.3438i	−0.280462	+	1.76315i
$849$	19.4100	+	8.03987i	0.666148	+	0.275928i
$850$	−0.292166	+	4.56026i	−0.0100212	+	0.156416i
$851$	2.96846	+	9.78572i	0.101758	+	0.335450i
$852$	4.83487	+	12.7323i	0.165640	+	0.436202i
$853$	20.1284	−	1.98247i	0.689183	−	0.0678786i	0.252638	−	0.967561i	$-0.418702\pi$
$853$	20.1284	−	1.98247i	0.689183	−	0.0678786i	0.436545	+	0.899682i	$0.356202\pi$
$854$	21.3744	+	13.2479i	0.731415	+	0.453334i
$855$	−5.69355	−	8.52100i	−0.194715	−	0.291412i
$856$	−33.4073	−	9.97338i	−1.14184	−	0.340883i
$857$	41.7674	+	27.9081i	1.42675	+	0.953323i	0.998772	+	0.0495328i	$0.0157732\pi$
$857$	41.7674	+	27.9081i	1.42675	+	0.953323i	0.427976	+	0.903790i	$0.359227\pi$
$858$	−0.591167	+	1.57772i	−0.0201821	+	0.0538625i
$859$	1.17401	−	3.87021i	0.0400569	−	0.132050i	−0.934631	−	0.355618i	$-0.884270\pi$
$859$	1.17401	−	3.87021i	0.0400569	−	0.132050i	0.974688	+	0.223568i	$0.0717705\pi$
$860$	9.80231	−	11.2439i	0.334256	−	0.383413i
$861$	−6.07168	+	4.98290i	−0.206922	+	0.169817i
$862$	−10.7746	−	18.5990i	−0.366985	−	0.633484i
$863$	−31.1306	−	31.1306i	−1.05970	−	1.05970i	−0.998101	−	0.0615977i	$-0.980380\pi$
$863$	−31.1306	−	31.1306i	−1.05970	−	1.05970i	−0.0615977	−	0.998101i	$-0.519620\pi$
$864$	−25.4917	−	11.3251i	−0.867245	−	0.385289i
$865$	4.42727	−	4.42727i	0.150532	−	0.150532i
$866$	6.91113	+	1.84095i	0.234850	+	0.0625581i
$867$	4.06763	+	4.95642i	0.138144	+	0.168329i
$868$	11.7449	−	34.9365i	0.398649	−	1.18582i
$869$	−24.4400	−	7.41379i	−0.829070	−	0.251496i
$870$	8.77352	−	3.99078i	0.297450	−	0.135300i
$871$	−0.520115	+	0.778407i	−0.0176234	+	0.0263753i
$872$	1.43618	−	15.2717i	0.0486353	−	0.517165i
$873$	−13.1834	+	8.80885i	−0.446190	+	0.298134i
$874$	−10.3121	+	2.42042i	−0.348811	+	0.0818719i
$875$	−0.186920	−	1.89783i	−0.00631905	−	0.0641583i
$876$	21.7606	+	0.648352i	0.735222	+	0.0219058i
$877$	8.30200	−	2.51838i	0.280339	−	0.0850398i	−0.146984	−	0.989139i	$-0.546957\pi$
$877$	8.30200	−	2.51838i	0.280339	−	0.0850398i	0.427323	+	0.904099i	$0.359457\pi$
$878$	−22.6403	+	19.9139i	−0.764072	+	0.672062i
$879$	6.81131	−	16.4440i	0.229740	−	0.554641i
$880$	−3.90267	−	11.2787i	−0.131559	−	0.380204i
$881$	−3.15318	−	7.61244i	−0.106233	−	0.256470i	0.861820	−	0.507214i	$-0.169325\pi$
$881$	−3.15318	−	7.61244i	−0.106233	−	0.256470i	−0.968053	+	0.250744i	$0.919325\pi$
$882$	8.72781	+	4.28815i	0.293881	+	0.144389i
$883$	37.5500	+	20.0709i	1.26366	+	0.675440i	0.960707	−	0.277565i	$-0.0895275\pi$
$883$	37.5500	+	20.0709i	1.26366	+	0.675440i	0.302953	+	0.953006i	$0.402028\pi$
$884$	2.15020	+	1.53127i	0.0723192	+	0.0515022i
$885$	2.08851	+	1.71400i	0.0702046	+	0.0576154i
$886$	−8.75751	−	1.43265i	−0.294214	−	0.0481310i
$887$	−29.5936	−	5.88654i	−0.993656	−	0.197651i	−0.328621	−	0.944462i	$-0.606584\pi$
$887$	−29.5936	−	5.88654i	−0.993656	−	0.197651i	−0.665036	+	0.746811i	$0.731584\pi$
$888$	13.4387	+	13.3207i	0.450972	+	0.447014i
$889$	−4.03167	−	20.2686i	−0.135218	−	0.679786i
$890$	8.31484	−	8.90385i	0.278714	−	0.298458i
$891$	1.84705	+	3.45558i	0.0618784	+	0.115766i
$892$	−0.523776	+	0.913396i	−0.0175373	+	0.0305827i
$893$	13.0455	+	1.28487i	0.436552	+	0.0429966i
$894$	16.5621	−	21.6499i	0.553918	−	0.724081i
$895$	12.2973			0.411052
$896$	−20.3580	+	7.14496i	−0.680112	+	0.238696i
$897$	−0.596623			−0.0199207
$898$	2.52923	−	3.30621i	0.0844015	−	0.110330i
$899$	−67.0535	−	6.60419i	−2.23636	−	0.220262i
$900$	3.54711	+	2.03405i	0.118237	+	0.0678016i
$901$	19.7972	+	37.0380i	0.659541	+	1.23392i
$902$	12.1348	−	12.9944i	0.404043	−	0.432665i
$903$	−2.71243	−	13.6363i	−0.0902639	−	0.453787i
$904$	8.50897	−	0.0375116i	0.283004	−	0.00124762i
$905$	−8.43709	−	1.67824i	−0.280458	−	0.0557866i
$906$	−29.9384	−	4.89767i	−0.994638	−	0.162714i
$907$	43.0129	+	35.2998i	1.42822	+	1.17211i	0.956997	+	0.290097i	$0.0936875\pi$
$907$	43.0129	+	35.2998i	1.42822	+	1.17211i	0.471224	+	0.882014i	$0.343812\pi$
$908$	17.9239	−	25.1687i	0.594825	−	0.835252i
$909$	−9.51733	−	5.08712i	−0.315670	−	0.168729i
$910$	−0.988731	−	0.485783i	−0.0327761	−	0.0161036i
$911$	−0.0696306	−	0.168103i	−0.00230696	−	0.00556950i	0.922722	−	0.385466i	$-0.125959\pi$
$911$	−0.0696306	−	0.168103i	−0.00230696	−	0.00556950i	−0.925029	+	0.379897i	$0.875959\pi$
$912$	−14.6596	+	13.0093i	−0.485428	+	0.430782i
$913$	1.20397	−	2.90665i	0.0398457	−	0.0961959i
$914$	−25.2910	+	22.2455i	−0.836553	+	0.735815i
$915$	−8.72220	+	2.64585i	−0.288347	+	0.0874691i
$916$	−0.331056	+	11.1112i	−0.0109384	+	0.367125i
$917$	−2.27404	−	23.0888i	−0.0750956	−	0.762458i
$918$	−21.9368	+	5.14894i	−0.724021	+	0.169940i
$919$	−28.9159	+	19.3210i	−0.953849	+	0.637341i	−0.932015	−	0.362420i	$-0.881951\pi$
$919$	−28.9159	+	19.3210i	−0.953849	+	0.637341i	−0.0218339	+	0.999762i	$0.506951\pi$
$920$	3.25509	−	2.69549i	0.107317	−	0.0888676i
$921$	−9.42205	+	14.1011i	−0.310467	+	0.464647i
$922$	6.43799	−	2.92843i	0.212024	−	0.0964426i
$923$	−2.72304	−	0.826025i	−0.0896299	−	0.0271889i
$924$	−10.5441	−	3.54473i	−0.346877	−	0.116613i
$925$	−4.34165	−	5.29032i	−0.142753	−	0.173945i
$926$	−1.43242	−	0.381559i	−0.0470721	−	0.0125388i
$927$	−15.5089	+	15.5089i	−0.509380	+	0.509380i
$928$	21.0730	+	33.3393i	0.691754	+	1.09442i
$929$	30.8694	+	30.8694i	1.01279	+	1.01279i	0.999917	+	0.0128766i	$0.00409885\pi$
$929$	30.8694	+	30.8694i	1.01279	+	1.01279i	0.0128766	+	0.999917i	$0.495901\pi$
$930$	6.69666	+	11.5597i	0.219592	+	0.379058i
$931$	13.0322	−	10.6952i	0.427112	−	0.350521i
$932$	16.6930	+	14.5528i	0.546799	+	0.476694i
$933$	2.55379	−	8.41873i	0.0836074	−	0.275617i
$934$	6.42795	−	17.1551i	0.210329	−	0.561331i
$935$	−8.01614	−	5.35621i	−0.262156	−	0.175167i
$936$	2.07821	−	1.12264i	0.0679285	−	0.0366945i
$937$	−8.75239	−	13.0989i	−0.285928	−	0.427922i	0.660505	−	0.750822i	$-0.270342\pi$
$937$	−8.75239	−	13.0989i	−0.285928	−	0.427922i	−0.946433	+	0.322900i	$0.895342\pi$
$938$	−5.25377	−	3.25631i	−0.171542	−	0.106322i
$939$	−1.13903	+	0.112185i	−0.0371708	+	0.00366101i
$940$	−4.88960	+	1.85674i	−0.159481	+	0.0605601i
$941$	−10.8649	−	35.8168i	−0.354186	−	1.16760i	−0.935325	−	0.353791i	$-0.884893\pi$
$941$	−10.8649	−	35.8168i	−0.354186	−	1.16760i	0.581138	−	0.813805i	$-0.302607\pi$
$942$	−0.650757	+	10.1573i	−0.0212028	+	0.330943i
$943$	5.81665	+	2.40934i	0.189416	+	0.0784588i
$944$	−5.78290	+	9.42271i	−0.188217	+	0.306683i
$945$	8.68775	−	3.59859i	0.282613	−	0.117062i
$946$	10.1599	+	29.7862i	0.330327	+	0.968434i
$947$	22.7232	−	42.5121i	0.738405	−	1.38146i	−0.179139	−	0.983824i	$-0.557331\pi$
$947$	22.7232	−	42.5121i	0.738405	−	1.38146i	0.917544	−	0.397634i	$-0.130169\pi$
$948$	−8.87873	−	14.1850i	−0.288368	−	0.460708i
$949$	−2.88558	+	3.51609i	−0.0936699	+	0.114137i
$950$	5.75613	−	4.13760i	0.186753	−	0.134241i
$951$	−3.02355	+	15.2004i	−0.0980453	+	0.492907i
$952$	−9.61884	+	14.5339i	−0.311748	+	0.471047i
$953$	−20.1721	+	4.01248i	−0.653439	+	0.129977i	−0.510667	−	0.859778i	$-0.670602\pi$
$953$	−20.1721	+	4.01248i	−0.653439	+	0.129977i	−0.142772	+	0.989756i	$0.545602\pi$
$954$	37.5573	−	1.28475i	1.21596	−	0.0415953i
$955$	−16.1517	+	8.63327i	−0.522657	+	0.279366i
$956$	27.8221	+	3.57969i	0.899831	+	0.115776i
$957$	−1.99320	+	20.2373i	−0.0644312	+	0.654181i
$958$	1.47940	+	11.1110i	0.0477974	+	0.358980i
$959$		−	16.0850i		−	0.519412i
$960$	2.92882	−	7.25096i	0.0945271	−	0.234024i
$961$		−	62.3883i		−	2.01253i
$962$	−3.91887	+	0.521788i	−0.126349	+	0.0168231i
$963$	−2.47011	+	25.0795i	−0.0795983	+	0.808175i
$964$	−38.9640	+	30.0805i	−1.25495	+	0.968828i
$965$	19.4211	−	10.3808i	0.625187	−	0.334170i
$966$	−0.134671	−	3.93686i	−0.00433297	−	0.126666i
$967$	16.1851	−	3.21941i	0.520477	−	0.103529i	0.0721408	−	0.997394i	$-0.477017\pi$
$967$	16.1851	−	3.21941i	0.520477	−	0.103529i	0.448336	+	0.893865i	$0.352017\pi$
$968$	−5.82383	−	1.13176i	−0.187185	−	0.0363763i
$969$	−3.08879	+	15.5284i	−0.0992263	+	0.498844i
$970$	−6.40154	−	8.90567i	−0.205541	−	0.285944i
$971$	−5.75765	+	7.01572i	−0.184772	+	0.225145i	−0.857156	−	0.515058i	$-0.827771\pi$
$971$	−5.75765	+	7.01572i	−0.184772	+	0.225145i	0.672384	+	0.740203i	$0.265271\pi$
$972$	−7.20927	+	31.3350i	−0.231237	+	1.00507i
$973$	17.4756	−	32.6945i	0.560242	−	1.04814i
$974$	31.6699	−	10.8024i	1.01477	−	0.346131i
$975$	0.368896	−	0.152802i	0.0118141	−	0.00489357i
$976$	−15.5923	−	33.8817i	−0.499097	−	1.08453i
$977$	37.5241	+	15.5430i	1.20050	+	0.497264i	0.891161	−	0.453687i	$-0.149892\pi$
$977$	37.5241	+	15.5430i	1.20050	+	0.497264i	0.309341	+	0.950951i	$0.399892\pi$
$978$	23.1400	+	1.48253i	0.739936	+	0.0474061i
$979$	7.46110	+	24.5960i	0.238458	+	0.786090i
$980$	−2.75810	+	6.13516i	−0.0881043	+	0.195980i
$981$	−11.0341	+	1.08677i	−0.352292	+	0.0346978i
$982$	−1.83791	+	2.96531i	−0.0586502	+	0.0946270i
$983$	−10.2830	−	15.3896i	−0.327978	−	0.490853i	0.630434	−	0.776243i	$-0.282877\pi$
$983$	−10.2830	−	15.3896i	−0.327978	−	0.490853i	−0.958412	+	0.285390i	$0.907877\pi$
$984$	11.5885	−	1.19297i	0.369427	−	0.0380305i
$985$	3.07115	+	2.05208i	0.0978550	+	0.0653846i
$986$	29.8348	+	11.1790i	0.950132	+	0.356011i
$987$	−1.41513	+	4.66504i	−0.0450439	+	0.148490i
$988$	−0.279838	−	4.08548i	−0.00890282	−	0.129976i
$989$	−8.61473	+	7.06993i	−0.273933	+	0.224811i
$990$	−7.46467	+	4.32437i	−0.237243	+	0.137437i
$991$	25.8320	+	25.8320i	0.820580	+	0.820580i	0.986191	−	0.165611i	$-0.0529597\pi$
$991$	25.8320	+	25.8320i	0.820580	+	0.820580i	−0.165611	+	0.986191i	$0.552960\pi$
$992$	−43.1242	+	33.5966i	−1.36919	+	1.06669i
$993$	−12.4503	+	12.4503i	−0.395098	+	0.395098i
$994$	4.83593	−	18.1546i	0.153386	−	0.575829i
$995$	5.40305	+	6.58364i	0.171288	+	0.208715i
$996$	1.84618	−	0.917192i	0.0584986	−	0.0290623i
$997$	−21.6860	−	6.57838i	−0.686803	−	0.208339i	−0.0724517	−	0.997372i	$-0.523082\pi$
$997$	−21.6860	−	6.57838i	−0.686803	−	0.208339i	−0.614352	+	0.789032i	$0.710582\pi$
$998$	−17.3715	−	38.1904i	−0.549887	−	1.20890i
$999$	18.7488	−	28.0596i	0.593187	−	0.887767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.15	✓	1024
128.117	even	32	inner	640.2.bm.a.501.15	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.15	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.15	yes	1024	128.117	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12323 - 0.859269i) q^{2} +(0.972809 + 0.0958133i) q^{3} +(0.523313 + 1.93032i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01036 - 0.943525i) q^{6} +(0.372040 + 1.87037i) q^{7} +(1.07086 - 2.61787i) q^{8} +(-2.00518 - 0.398855i) q^{9} +O(q^{10})\)	\(q+(-1.12323 - 0.859269i) q^{2} +(0.972809 + 0.0958133i) q^{3} +(0.523313 + 1.93032i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01036 - 0.943525i) q^{6} +(0.372040 + 1.87037i) q^{7} +(1.07086 - 2.61787i) q^{8} +(-2.00518 - 0.398855i) q^{9} +(0.228318 - 1.39566i) q^{10} +(2.30643 + 1.89284i) q^{11} +(0.324133 + 1.92797i) q^{12} +(-0.360242 - 0.192554i) q^{13} +(1.18926 - 2.42055i) q^{14} +(0.374079 + 0.903107i) q^{15} +(-3.45229 + 2.02033i) q^{16} +(-1.23653 + 2.98524i) q^{17} +(1.90956 + 2.17100i) q^{18} +(4.79678 - 1.45509i) q^{19} +(-1.45570 + 1.37147i) q^{20} +(0.182717 + 1.85516i) q^{21} +(-0.964205 - 4.10794i) q^{22} +(1.24239 - 0.830138i) q^{23} +(1.29257 - 2.44409i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(0.239181 + 0.525828i) q^{26} +(-4.71871 - 1.43141i) q^{27} +(-3.41572 + 1.69695i) q^{28} +(4.42313 + 5.38960i) q^{29} +(0.355833 - 1.33584i) q^{30} +(-6.83331 + 6.83331i) q^{31} +(5.61373 + 0.697140i) q^{32} +(2.06236 + 2.06236i) q^{33} +(3.95404 - 2.29062i) q^{34} +(-1.47414 + 1.20980i) q^{35} +(-0.279419 - 4.07937i) q^{36} +(-1.98665 + 6.54910i) q^{37} +(-6.63822 - 2.48732i) q^{38} +(-0.331998 - 0.221834i) q^{39} +(2.81356 - 0.289641i) q^{40} +(2.34091 + 3.50342i) q^{41} +(1.38885 - 2.24078i) q^{42} +(-7.42248 + 0.731050i) q^{43} +(-2.44680 + 5.44270i) q^{44} +(-0.593476 - 1.95643i) q^{45} +(-2.10881 - 0.135107i) q^{46} +(2.41607 + 1.00077i) q^{47} +(-3.55199 + 1.63462i) q^{48} +(3.10729 - 1.28708i) q^{49} +(1.33849 - 0.456551i) q^{50} +(-1.48893 + 2.78559i) q^{51} +(0.183171 - 0.796149i) q^{52} +(8.24541 - 10.0471i) q^{53} +(4.07026 + 5.66245i) q^{54} +(-0.582090 + 2.92637i) q^{55} +(5.29479 + 1.02896i) q^{56} +(4.80576 - 0.955926i) q^{57} +(-0.337099 - 9.85445i) q^{58} +(2.43757 - 1.30291i) q^{59} +(-1.54753 + 1.19470i) q^{60} +(-0.913943 + 9.27942i) q^{61} +(13.5471 - 1.80376i) q^{62} -3.89882i q^{63} +(-5.70651 - 5.60676i) q^{64} -0.408474i q^{65} +(-0.544391 - 4.08863i) q^{66} +(0.224645 - 2.28086i) q^{67} +(-6.40957 - 0.824679i) q^{68} +(1.28815 - 0.688528i) q^{69} +(2.69535 - 0.0922017i) q^{70} +(6.83247 - 1.35906i) q^{71} +(-3.19142 + 4.82218i) q^{72} +(2.17243 - 10.9215i) q^{73} +(7.85891 - 5.64911i) q^{74} +(-0.620129 + 0.755630i) q^{75} +(5.31900 + 8.49786i) q^{76} +(-2.68222 + 5.01808i) q^{77} +(0.182297 + 0.534447i) q^{78} +(-7.90819 + 3.27568i) q^{79} +(-3.40917 - 2.09227i) q^{80} +(1.21325 + 0.502546i) q^{81} +(0.380988 - 5.94664i) q^{82} +(-0.306088 - 1.00904i) q^{83} +(-3.48543 + 1.32353i) q^{84} +(-3.21564 + 0.316713i) q^{85} +(8.96535 + 5.55676i) q^{86} +(3.78647 + 5.66685i) q^{87} +(7.42507 - 4.01097i) q^{88} +(7.16260 + 4.78589i) q^{89} +(-1.01449 + 2.70749i) q^{90} +(0.226122 - 0.745424i) q^{91} +(2.25259 + 1.96379i) q^{92} +(-7.30223 + 5.99278i) q^{93} +(-1.85388 - 3.20015i) q^{94} +(3.54446 + 3.54446i) q^{95} +(5.39429 + 1.21605i) q^{96} +(5.48386 - 5.48386i) q^{97} +(-4.59616 - 1.22430i) q^{98} +(-3.86984 - 4.71541i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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