LMFDB - Embedded newform 500.2.l.d.243.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [500,2,Mod(7,500)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(500, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("500.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	500.l (of order $20$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,10,0,-6,0,-30,20,0,0,0,0,10,0,-14,0,-20,0,0,-12,50,0, 0,0,-12,0,40,20,0,0,50,0,60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(34)] == traces)

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

Self dual:	no
Analytic conductor:	$3.99252010106$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			243.3
Character	$\chi$	$=$	500.243
Dual form			500.2.l.d.107.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26778 - 0.626683i) q^{2} +(0.745599 - 0.118091i) q^{3} +(1.21454 + 1.58899i) q^{4} +(-1.01926 - 0.317541i) q^{6} +(-2.75590 - 2.75590i) q^{7} +(-0.543971 - 2.77563i) q^{8} +(-2.31120 + 0.750953i) q^{9} +(-0.712633 - 0.231549i) q^{11} +(1.09320 + 1.04133i) q^{12} +(-0.753078 + 1.47800i) q^{13} +(1.76680 + 5.22095i) q^{14} +(-1.04980 + 3.85978i) q^{16} +(-0.715035 + 4.51455i) q^{17} +(3.40070 + 0.496343i) q^{18} +(-2.96269 + 2.15252i) q^{19} +(-2.38025 - 1.72935i) q^{21} +(0.758355 + 0.740148i) q^{22} +(-4.00635 - 7.86291i) q^{23} +(-0.733362 - 2.00527i) q^{24} +(1.88097 - 1.40184i) q^{26} +(-3.65239 + 1.86099i) q^{27} +(1.03197 - 7.72625i) q^{28} +(-0.00370724 + 0.00510258i) q^{29} +(1.08939 + 1.49941i) q^{31} +(3.74978 - 4.23547i) q^{32} +(-0.558683 - 0.0884866i) q^{33} +(3.73570 - 5.27537i) q^{34} +(-4.00029 - 2.76042i) q^{36} +(-3.22426 - 1.64284i) q^{37} +(5.10500 - 0.872258i) q^{38} +(-0.386956 + 1.19093i) q^{39} +(-1.93115 - 5.94348i) q^{41} +(1.93388 + 3.68410i) q^{42} +(-6.10648 + 6.10648i) q^{43} +(-0.497590 - 1.41359i) q^{44} +(0.151625 + 12.4792i) q^{46} +(-0.184694 - 1.16611i) q^{47} +(-0.326924 + 3.00182i) q^{48} +8.18997i q^{49} +3.45049i q^{51} +(-3.26317 + 0.598448i) q^{52} +(1.44300 + 9.11077i) q^{53} +(5.79668 - 0.0704313i) q^{54} +(-6.15022 + 9.14848i) q^{56} +(-1.95479 + 1.95479i) q^{57} +(0.00789767 - 0.00414569i) q^{58} +(-4.58114 - 14.0993i) q^{59} +(-0.569042 + 1.75133i) q^{61} +(-0.441448 - 2.58363i) q^{62} +(8.43898 + 4.29987i) q^{63} +(-7.40819 + 3.01972i) q^{64} +(0.652834 + 0.462299i) q^{66} +(5.08652 + 0.805626i) q^{67} +(-8.04203 + 4.34691i) q^{68} +(-3.91567 - 5.38946i) q^{69} +(6.26883 - 8.62831i) q^{71} +(3.34159 + 6.00652i) q^{72} +(-6.26568 + 3.19252i) q^{73} +(3.05811 + 4.10335i) q^{74} +(-7.01865 - 2.09338i) q^{76} +(1.32582 + 2.60207i) q^{77} +(1.23691 - 1.26734i) q^{78} +(2.90976 + 2.11406i) q^{79} +(3.39461 - 2.46633i) q^{81} +(-1.27640 + 8.74525i) q^{82} +(-0.308214 + 1.94599i) q^{83} +(-0.142970 - 5.88255i) q^{84} +(11.5685 - 3.91485i) q^{86} +(-0.00216155 + 0.00424227i) q^{87} +(-0.255040 + 2.10396i) q^{88} +(-3.79225 - 1.23218i) q^{89} +(6.14862 - 1.99781i) q^{91} +(7.62825 - 15.9159i) q^{92} +(0.989314 + 0.989314i) q^{93} +(-0.496631 + 1.59412i) q^{94} +(2.29566 - 3.60078i) q^{96} +(-6.43432 + 1.01910i) q^{97} +(5.13252 - 10.3831i) q^{98} +1.82092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 10 q^{4} - 6 q^{6} - 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} - 20 q^{18} - 12 q^{21} + 50 q^{22} - 12 q^{26} + 40 q^{28} + 20 q^{29} + 50 q^{32} + 60 q^{34} - 10 q^{36} + 40 q^{37} - 70 q^{38}+ \cdots + 70 q^{98}+O(q^{100}) $ 96 * q + 10 * q^4 - 6 * q^6 - 30 * q^8 + 20 * q^9 + 10 * q^14 - 14 * q^16 - 20 * q^18 - 12 * q^21 + 50 * q^22 - 12 * q^26 + 40 * q^28 + 20 * q^29 + 50 * q^32 + 60 * q^34 - 10 * q^36 + 40 * q^37 - 70 * q^38 - 28 * q^41 - 60 * q^42 - 60 * q^44 - 6 * q^46 + 100 * q^52 + 80 * q^53 - 120 * q^54 - 6 * q^56 + 20 * q^57 + 120 * q^58 + 12 * q^61 - 20 * q^64 - 30 * q^66 + 10 * q^68 + 20 * q^69 - 150 * q^72 - 140 * q^77 - 130 * q^78 - 36 * q^81 + 50 * q^82 + 90 * q^84 - 6 * q^86 + 110 * q^88 - 160 * q^89 + 90 * q^92 - 60 * q^93 + 170 * q^94 + 14 * q^96 + 70 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.26778	−	0.626683i	−0.896456	−	0.443132i
$2$	−1.26778	−	0.626683i	−0.896456	−	0.443132i
$3$	0.745599	−	0.118091i	0.430472	−	0.0681801i	0.0625612	−	0.998041i	$-0.480073\pi$
$3$	0.745599	−	0.118091i	0.430472	−	0.0681801i	0.367911	+	0.929861i	$0.380073\pi$
$4$	1.21454	+	1.58899i	0.607268	+	0.794497i
$5$		0			0
$5$		0			0
$6$	−1.01926	−	0.317541i	−0.416112	−	0.129635i
$7$	−2.75590	−	2.75590i	−1.04163	−	1.04163i	−0.999095	−	0.0425375i	$-0.986456\pi$
$7$	−2.75590	−	2.75590i	−1.04163	−	1.04163i	−0.0425375	−	0.999095i	$-0.513544\pi$
$8$	−0.543971	−	2.77563i	−0.192323	−	0.981332i
$9$	−2.31120	+	0.750953i	−0.770399	+	0.250318i
$10$		0			0
$11$	−0.712633	−	0.231549i	−0.214867	−	0.0698145i	0.199606	−	0.979876i	$-0.436034\pi$
$11$	−0.712633	−	0.231549i	−0.214867	−	0.0698145i	−0.414473	+	0.910062i	$0.636034\pi$
$12$	1.09320	+	1.04133i	0.315581	+	0.300605i
$13$	−0.753078	+	1.47800i	−0.208866	+	0.409923i	−0.971545	−	0.236854i	$-0.923884\pi$
$13$	−0.753078	+	1.47800i	−0.208866	+	0.409923i	0.762679	+	0.646777i	$0.223884\pi$
$14$	1.76680	+	5.22095i	0.472198	+	1.39536i
$15$		0			0
$16$	−1.04980	+	3.85978i	−0.262450	+	0.964946i
$17$	−0.715035	+	4.51455i	−0.173421	+	1.09494i	0.735363	+	0.677674i	$0.237012\pi$
$17$	−0.715035	+	4.51455i	−0.173421	+	1.09494i	−0.908784	+	0.417266i	$0.862988\pi$
$18$	3.40070	+	0.496343i	0.801553	+	0.116989i
$19$	−2.96269	+	2.15252i	−0.679689	+	0.493823i	−0.873254	−	0.487265i	$-0.837995\pi$
$19$	−2.96269	+	2.15252i	−0.679689	+	0.493823i	0.193566	+	0.981087i	$0.437995\pi$
$20$		0			0
$21$	−2.38025	−	1.72935i	−0.519412	−	0.377375i
$22$	0.758355	+	0.740148i	0.161682	+	0.157800i
$23$	−4.00635	−	7.86291i	−0.835382	−	1.63953i	−0.766802	−	0.641884i	$-0.778153\pi$
$23$	−4.00635	−	7.86291i	−0.835382	−	1.63953i	−0.0685797	−	0.997646i	$-0.521847\pi$
$24$	−0.733362	−	2.00527i	−0.149697	−	0.409323i
$25$		0			0
$26$	1.88097	−	1.40184i	0.368889	−	0.274923i
$27$	−3.65239	+	1.86099i	−0.702903	+	0.358147i
$28$	1.03197	−	7.72625i	0.195023	−	1.46012i
$29$	−0.00370724	+	0.00510258i	−0.000688418	+	0.000947526i	−0.809361	−	0.587311i	$-0.800186\pi$
$29$	−0.00370724	+	0.00510258i	−0.000688418	+	0.000947526i	0.808673	+	0.588259i	$0.200186\pi$
$30$		0			0
$31$	1.08939	+	1.49941i	0.195660	+	0.269302i	0.895563	−	0.444936i	$-0.146773\pi$
$31$	1.08939	+	1.49941i	0.195660	+	0.269302i	−0.699903	+	0.714238i	$0.746773\pi$
$32$	3.74978	−	4.23547i	0.662873	−	0.748732i
$33$	−0.558683	−	0.0884866i	−0.0972542	−	0.0154035i
$34$	3.73570	−	5.27537i	0.640668	−	0.904718i
$35$		0			0
$36$	−4.00029	−	2.76042i	−0.666716	−	0.460069i
$37$	−3.22426	−	1.64284i	−0.530065	−	0.270082i	0.168409	−	0.985717i	$-0.446137\pi$
$37$	−3.22426	−	1.64284i	−0.530065	−	0.270082i	−0.698474	+	0.715636i	$0.746137\pi$
$38$	5.10500	−	0.872258i	0.828140	−	0.141499i
$39$	−0.386956	+	1.19093i	−0.0619625	+	0.190701i
$40$		0			0
$41$	−1.93115	−	5.94348i	−0.301595	−	0.928215i	−0.980926	−	0.194383i	$-0.937730\pi$
$41$	−1.93115	−	5.94348i	−0.301595	−	0.928215i	0.679330	−	0.733832i	$-0.262270\pi$
$42$	1.93388	+	3.68410i	0.298404	+	0.568468i
$43$	−6.10648	+	6.10648i	−0.931230	+	0.931230i	−0.997783	−	0.0665532i	$-0.978800\pi$
$43$	−6.10648	+	6.10648i	−0.931230	+	0.931230i	0.0665532	+	0.997783i	$0.478800\pi$
$44$	−0.497590	−	1.41359i	−0.0750145	−	0.213107i
$45$		0			0
$46$	0.151625	+	12.4792i	0.0223559	+	1.83995i
$47$	−0.184694	−	1.16611i	−0.0269404	−	0.170095i	0.970550	−	0.240901i	$-0.0774429\pi$
$47$	−0.184694	−	1.16611i	−0.0269404	−	0.170095i	−0.997490	+	0.0708061i	$0.977443\pi$
$48$	−0.326924	+	3.00182i	−0.0471874	+	0.433276i
$49$			8.18997i			1.17000i
$50$		0			0
$51$			3.45049i			0.483165i
$52$	−3.26317	+	0.598448i	−0.452520	+	0.0829898i
$53$	1.44300	+	9.11077i	0.198212	+	1.25146i	0.863298	+	0.504694i	$0.168395\pi$
$53$	1.44300	+	9.11077i	0.198212	+	1.25146i	−0.665086	+	0.746767i	$0.731605\pi$
$54$	5.79668	−	0.0704313i	0.788828	−	0.00958448i
$55$		0			0
$56$	−6.15022	+	9.14848i	−0.821857	+	1.22252i
$57$	−1.95479	+	1.95479i	−0.258918	+	0.258918i
$58$	0.00789767	−	0.00414569i	0.00103702	−	0.000544356i
$59$	−4.58114	−	14.0993i	−0.596413	−	1.83557i	−0.547563	−	0.836764i	$-0.684444\pi$
$59$	−4.58114	−	14.0993i	−0.596413	−	1.83557i	−0.0488499	−	0.998806i	$-0.515556\pi$
$60$		0			0
$61$	−0.569042	+	1.75133i	−0.0728583	+	0.224235i	−0.980854	−	0.194745i	$-0.937612\pi$
$61$	−0.569042	+	1.75133i	−0.0728583	+	0.224235i	0.907996	+	0.418980i	$0.137612\pi$
$62$	−0.441448	−	2.58363i	−0.0560639	−	0.328121i
$63$	8.43898	+	4.29987i	1.06321	+	0.541733i
$64$	−7.40819	+	3.01972i	−0.926024	+	0.377465i
$65$		0			0
$66$	0.652834	+	0.462299i	0.0803583	+	0.0569050i
$67$	5.08652	+	0.805626i	0.621417	+	0.0984228i	0.459201	−	0.888332i	$-0.348136\pi$
$67$	5.08652	+	0.805626i	0.621417	+	0.0984228i	0.162216	+	0.986755i	$0.448136\pi$
$68$	−8.04203	+	4.34691i	−0.975240	+	0.527140i
$69$	−3.91567	−	5.38946i	−0.471392	−	0.648815i
$70$		0			0
$71$	6.26883	−	8.62831i	0.743973	−	1.02399i	−0.254407	−	0.967097i	$-0.581880\pi$
$71$	6.26883	−	8.62831i	0.743973	−	1.02399i	0.998380	−	0.0568943i	$-0.0181198\pi$
$72$	3.34159	+	6.00652i	0.393810	+	0.707875i
$73$	−6.26568	+	3.19252i	−0.733342	+	0.373656i	−0.780437	−	0.625234i	$-0.785004\pi$
$73$	−6.26568	+	3.19252i	−0.733342	+	0.373656i	0.0470953	+	0.998890i	$0.485004\pi$
$74$	3.05811	+	4.10335i	0.355498	+	0.477005i
$75$		0			0
$76$	−7.01865	−	2.09338i	−0.805094	−	0.240127i
$77$	1.32582	+	2.60207i	0.151091	+	0.296533i
$78$	1.23691	−	1.26734i	0.140052	−	0.143497i
$79$	2.90976	+	2.11406i	0.327373	+	0.237851i	0.739315	−	0.673359i	$-0.235149\pi$
$79$	2.90976	+	2.11406i	0.327373	+	0.237851i	−0.411942	+	0.911210i	$0.635149\pi$
$80$		0			0
$81$	3.39461	−	2.46633i	0.377179	−	0.274036i
$82$	−1.27640	+	8.74525i	−0.140955	+	0.965751i
$83$	−0.308214	+	1.94599i	−0.0338309	+	0.213600i	−0.998813	−	0.0487173i	$-0.984487\pi$
$83$	−0.308214	+	1.94599i	−0.0338309	+	0.213600i	0.964982	+	0.262317i	$0.0844867\pi$
$84$	−0.142970	−	5.88255i	−0.0155994	−	0.641839i
$85$		0			0
$86$	11.5685	−	3.91485i	1.24746	−	0.422149i
$87$	−0.00216155	+	0.00424227i	−0.000231742	+	0.000454820i
$88$	−0.255040	+	2.10396i	−0.0271874	+	0.224283i
$89$	−3.79225	−	1.23218i	−0.401978	−	0.130611i	0.101049	−	0.994881i	$-0.467780\pi$
$89$	−3.79225	−	1.23218i	−0.401978	−	0.130611i	−0.503027	+	0.864271i	$0.667780\pi$
$90$		0			0
$91$	6.14862	−	1.99781i	0.644551	−	0.209427i
$92$	7.62825	−	15.9159i	0.795300	−	1.65934i
$93$	0.989314	+	0.989314i	0.102587	+	0.102587i
$94$	−0.496631	+	1.59412i	−0.0512235	+	0.164421i
$95$		0			0
$96$	2.29566	−	3.60078i	0.234300	−	0.367503i
$97$	−6.43432	+	1.01910i	−0.653306	+	0.103474i	−0.474285	−	0.880372i	$-0.657293\pi$
$97$	−6.43432	+	1.01910i	−0.653306	+	0.103474i	−0.179022	+	0.983845i	$0.557293\pi$
$98$	5.13252	−	10.3831i	0.518462	−	1.04885i
$99$	1.82092			0.183009
$100$		0			0
$101$	8.26277			0.822176			0.411088	−	0.911596i	$-0.365149\pi$
$101$	8.26277			0.822176			0.411088	+	0.911596i	$0.365149\pi$
$102$	2.16236	−	4.37446i	0.214106	−	0.433136i
$103$	−5.57914	+	0.883649i	−0.549729	+	0.0870685i	−0.425119	−	0.905137i	$-0.639768\pi$
$103$	−5.57914	+	0.883649i	−0.549729	+	0.0870685i	−0.124610	+	0.992206i	$0.539768\pi$
$104$	4.51202	+	1.28627i	0.442440	+	0.126129i
$105$		0			0
$106$	3.88015	−	12.4548i	0.376874	−	1.20971i
$107$	−2.63780	−	2.63780i	−0.255005	−	0.255005i	0.568014	−	0.823019i	$-0.307712\pi$
$107$	−2.63780	−	2.63780i	−0.255005	−	0.255005i	−0.823019	+	0.568014i	$0.807712\pi$
$108$	−7.39306	−	3.54339i	−0.711397	−	0.340963i
$109$	2.78468	−	0.904799i	0.266724	−	0.0866640i	−0.172602	−	0.984992i	$-0.555217\pi$
$109$	2.78468	−	0.904799i	0.266724	−	0.0866640i	0.439326	+	0.898328i	$0.355217\pi$
$110$		0			0
$111$	−2.59801	−	0.844145i	−0.246592	−	0.0801227i
$112$	13.5303	−	7.74403i	1.27850	−	0.731742i
$113$	6.81465	−	13.3745i	0.641068	−	1.25817i	−0.310455	−	0.950588i	$-0.600481\pi$
$113$	6.81465	−	13.3745i	0.641068	−	1.25817i	0.951523	−	0.307579i	$-0.0995187\pi$
$114$	3.70328	−	1.25321i	0.346844	−	0.117374i
$115$		0			0
$116$	−0.0126106		0.000306489i	−0.00117086		2.84568e-5i
$117$	0.630603	−	3.98147i	0.0582993	−	0.368087i
$118$	−3.02791	+	20.7457i	−0.278741	+	1.90980i
$119$	14.4122	−	10.4711i	1.32117	−	0.959884i
$120$		0			0
$121$	−8.44496	−	6.13562i	−0.767723	−	0.557784i
$122$	1.81895	−	1.86369i	0.164680	−	0.168731i
$123$	−2.14174	−	4.20340i	−0.193114	−	0.379008i
$124$	−1.05946	+	3.55212i	−0.0951420	+	0.318990i
$125$		0			0
$126$	−8.00412	−	10.7399i	−0.713064	−	0.956783i
$127$	10.0005	−	5.09550i	0.887400	−	0.452153i	0.0500037	−	0.998749i	$-0.484077\pi$
$127$	10.0005	−	5.09550i	0.887400	−	0.452153i	0.837396	+	0.546596i	$0.184077\pi$
$128$	11.2844	+	0.814243i	0.997407	+	0.0719696i
$129$	−3.83187	+	5.27411i	−0.337377	+	0.464360i
$130$		0			0
$131$	−0.647820	−	0.891647i	−0.0566003	−	0.0779036i	0.779779	−	0.626055i	$-0.215332\pi$
$131$	−0.647820	−	0.891647i	−0.0566003	−	0.0779036i	−0.836379	+	0.548152i	$0.815332\pi$
$132$	−0.537936	−	0.995213i	−0.0468213	−	0.0866222i
$133$	14.0970	+	2.23275i	1.22237	+	0.193604i
$134$	−5.94372	−	4.20899i	−0.513459	−	0.363602i
$135$		0			0
$136$	12.9197	−	0.471118i	1.10785	−	0.0403980i
$137$	6.71304	+	3.42046i	0.573534	+	0.292230i	0.716601	−	0.697483i	$-0.245697\pi$
$137$	6.71304	+	3.42046i	0.573534	+	0.292230i	−0.143068	+	0.989713i	$0.545697\pi$
$138$	1.58673	+	9.28654i	0.135072	+	0.790523i
$139$	−3.91451	+	12.0476i	−0.332024	+	1.02187i	0.636145	+	0.771570i	$0.280528\pi$
$139$	−3.91451	+	12.0476i	−0.332024	+	1.02187i	−0.968169	+	0.250296i	$0.919472\pi$
$140$		0			0
$141$	−0.275415	−	0.847641i	−0.0231941	−	0.0713842i
$142$	−13.3547	+	7.01023i	−1.12070	+	0.588286i
$143$	0.878896	−	0.878896i	0.0734970	−	0.0734970i
$144$	−0.472220	−	9.70907i	−0.0393517	−	0.809089i
$145$		0			0
$146$	9.94421	−	0.120825i	0.822988	−	0.00999954i
$147$	0.967165	+	6.10644i	0.0797704	+	0.503651i
$148$	−1.30552	−	7.11862i	−0.107313	−	0.585147i
$149$		−	15.6649i		−	1.28332i	−0.766990	−	0.641659i	$-0.778247\pi$
$149$		−	15.6649i		−	1.28332i	0.766990	−	0.641659i	$-0.221753\pi$
$150$		0			0
$151$			13.1571i			1.07071i	0.844628	+	0.535353i	$0.179821\pi$
$151$			13.1571i			1.07071i	−0.844628	+	0.535353i	$0.820179\pi$
$152$	7.58622	+	7.05242i	0.615323	+	0.572027i
$153$	−1.73763	−	10.9710i	−0.140479	−	0.886951i
$154$	−0.0501773	−	4.12972i	−0.00404340	−	0.332783i
$155$		0			0
$156$	−2.36235	+	0.831554i	−0.189139	+	0.0665776i
$157$	10.7749	−	10.7749i	0.859930	−	0.859930i	−0.131400	−	0.991329i	$-0.541947\pi$
$157$	10.7749	−	10.7749i	0.859930	−	0.859930i	0.991329	+	0.131400i	$0.0419471\pi$
$158$	−2.36409	−	4.50366i	−0.188077	−	0.358292i
$159$	2.15181	+	6.62258i	0.170649	+	0.525205i
$160$		0			0
$161$	−10.6283	+	32.7105i	−0.837626	+	2.57795i
$162$	−5.84923	+	0.999420i	−0.459559	+	0.0785218i
$163$	10.0328	+	5.11197i	0.785830	+	0.400401i	0.800380	−	0.599494i	$-0.204631\pi$
$163$	10.0328	+	5.11197i	0.785830	+	0.400401i	−0.0145493	+	0.999894i	$0.504631\pi$
$164$	7.09869	−	10.2872i	0.554314	−	0.803292i
$165$		0			0
$166$	1.61027	−	2.27393i	0.124981	−	0.176491i
$167$	−4.33254	−	0.686207i	−0.335262	−	0.0531003i	−0.0134660	−	0.999909i	$-0.504286\pi$
$167$	−4.33254	−	0.686207i	−0.335262	−	0.0531003i	−0.321796	+	0.946809i	$0.604286\pi$
$168$	−3.50524	+	7.54739i	−0.270435	+	0.582293i
$169$	6.02386	+	8.29113i	0.463374	+	0.637779i
$170$		0			0
$171$	5.23092	−	7.19975i	0.400019	−	0.550579i
$172$	−17.1197	−	2.28661i	−1.30537	−	0.174353i
$173$	−14.5877	+	7.43280i	−1.10908	+	0.565105i	−0.909888	−	0.414855i	$-0.863832\pi$
$173$	−14.5877	+	7.43280i	−1.10908	+	0.565105i	−0.199194	+	0.979960i	$0.563832\pi$
$174$	0.00539893	−	0.00402367i	0.000409292	−	0.000305034i
$175$		0			0
$176$	1.64185	−	2.50753i	0.123759	−	0.189012i
$177$	−5.08070	−	9.97143i	−0.381888	−	0.749498i
$178$	4.03556	+	3.93867i	0.302478	+	0.295216i
$179$	10.7676	+	7.82314i	0.804811	+	0.584729i	0.912321	−	0.409475i	$-0.134288\pi$
$179$	10.7676	+	7.82314i	0.804811	+	0.584729i	−0.107511	+	0.994204i	$0.534288\pi$
$180$		0			0
$181$	12.3668	−	8.98499i	0.919215	−	0.667849i	−0.0241132	−	0.999709i	$-0.507676\pi$
$181$	12.3668	−	8.98499i	0.919215	−	0.667849i	0.943329	+	0.331860i	$0.107676\pi$
$182$	−9.04710	−	1.32045i	−0.670616	−	0.0978786i
$183$	−0.217460	+	1.37299i	−0.0160751	+	0.101494i
$184$	−19.6451	+	15.3973i	−1.44826	+	1.13511i
$185$		0			0
$186$	−0.634247	−	1.87422i	−0.0465052	−	0.137424i
$187$	1.55490	−	3.05166i	0.113705	−	0.223159i
$188$	1.62863	−	1.70976i	0.118780	−	0.124697i
$189$	15.1943	+	4.93693i	1.10522	+	0.359109i
$190$		0			0
$191$	−9.06811	+	2.94641i	−0.656145	+	0.213194i	−0.618122	−	0.786082i	$-0.712106\pi$
$191$	−9.06811	+	2.94641i	−0.656145	+	0.213194i	−0.0380234	+	0.999277i	$0.512106\pi$
$192$	−5.16694	+	3.12635i	−0.372892	+	0.225625i
$193$	−6.86588	−	6.86588i	−0.494217	−	0.494217i	0.415415	−	0.909632i	$-0.363636\pi$
$193$	−6.86588	−	6.86588i	−0.494217	−	0.494217i	−0.909632	+	0.415415i	$0.863636\pi$
$194$	8.79596	+	2.74029i	0.631513	+	0.196741i
$195$		0			0
$196$	−13.0138	+	9.94702i	−0.929558	+	0.710502i
$197$	13.0003	−	2.05905i	0.926237	−	0.146701i	0.324947	−	0.945732i	$-0.394654\pi$
$197$	13.0003	−	2.05905i	0.926237	−	0.146701i	0.601290	+	0.799031i	$0.294654\pi$
$198$	−2.30852	−	1.14114i	−0.164060	−	0.0810971i
$199$	−25.8172			−1.83013			−0.915067	−	0.403302i	$-0.867863\pi$
$199$	−25.8172			−1.83013			−0.915067	+	0.403302i	$0.867863\pi$
$200$		0			0
$201$	3.88764			0.274213
$202$	−10.4754	−	5.17814i	−0.737045	−	0.364332i
$203$	0.0242790	−	0.00384542i	0.00170405	−	0.000269895i
$204$	−5.48280	+	4.19075i	−0.383873	+	0.293411i
$205$		0			0
$206$	7.62690	+	2.37608i	0.531391	+	0.165549i
$207$	15.1641	+	15.1641i	1.05398	+	1.05398i
$208$	−4.91417	−	4.45832i	−0.340736	−	0.309129i
$209$	2.60973	−	0.847952i	0.180519	−	0.0586540i
$210$		0			0
$211$	−23.5520	−	7.65252i	−1.62139	−	0.526821i	−0.649120	−	0.760686i	$-0.724863\pi$
$211$	−23.5520	−	7.65252i	−1.62139	−	0.526821i	−0.972269	+	0.233865i	$0.924863\pi$
$212$	−12.7244	+	13.3583i	−0.873914	+	0.917451i
$213$	3.65511	−	7.17356i	0.250444	−	0.491524i
$214$	1.69108	+	4.99721i	0.115600	+	0.341602i
$215$		0			0
$216$	7.15220	+	9.12534i	0.486645	+	0.620901i
$217$	1.12999	−	7.13447i	0.0767087	−	0.484320i
$218$	−4.09739	−	0.598028i	−0.277510	−	0.0405036i
$219$	−4.29468	+	3.12027i	−0.290207	+	0.210848i
$220$		0			0
$221$	−6.13403	−	4.45663i	−0.412619	−	0.299785i
$222$	2.76470	+	2.69832i	0.185554	+	0.181099i
$223$	−0.350575	−	0.688042i	−0.0234762	−	0.0460747i	0.878971	−	0.476876i	$-0.158231\pi$
$223$	−0.350575	−	0.688042i	−0.0234762	−	0.0460747i	−0.902447	+	0.430801i	$0.858231\pi$
$224$	−22.0065	+	1.33851i	−1.47037	+	0.0894329i
$225$		0			0
$226$	−17.0210	+	12.6853i	−1.13222	+	0.843814i
$227$	−7.51174	+	3.82742i	−0.498572	+	0.254035i	−0.685146	−	0.728406i	$-0.740262\pi$
$227$	−7.51174	+	3.82742i	−0.498572	+	0.254035i	0.186574	+	0.982441i	$0.440262\pi$
$228$	−5.48031	−	0.731984i	−0.362942	−	0.0484768i
$229$	13.8017	−	18.9964i	0.912042	−	1.25532i	−0.0544226	−	0.998518i	$-0.517332\pi$
$229$	13.8017	−	18.9964i	0.912042	−	1.25532i	0.966465	−	0.256800i	$-0.0826682\pi$
$230$		0			0
$231$	1.29581	+	1.78353i	0.0852583	+	0.117348i
$232$	0.0161795	+	0.00751426i	0.00106224	+	0.000493335i
$233$	−2.19561	−	0.347751i	−0.143839	−	0.0227819i	0.0840996	−	0.996457i	$-0.473199\pi$
$233$	−2.19561	−	0.347751i	−0.143839	−	0.0227819i	−0.227939	+	0.973675i	$0.573199\pi$
$234$	−3.29459	+	4.65244i	−0.215374	+	0.304140i
$235$		0			0
$236$	16.8397	−	24.4035i	1.09617	−	1.58853i
$237$	2.41917	+	1.23263i	0.157142	+	0.0800677i
$238$	−24.8336	+	4.24316i	−1.60972	+	0.275043i
$239$	0.258139	−	0.794470i	0.0166976	−	0.0513900i	−0.942361	−	0.334599i	$-0.891399\pi$
$239$	0.258139	−	0.794470i	0.0166976	−	0.0513900i	0.959058	+	0.283209i	$0.0913991\pi$
$240$		0			0
$241$	3.75910	+	11.5693i	0.242145	+	0.745245i	0.996093	+	0.0883110i	$0.0281469\pi$
$241$	3.75910	+	11.5693i	0.242145	+	0.745245i	−0.753948	+	0.656934i	$0.771853\pi$
$242$	6.86127	+	13.0709i	0.441059	+	0.840231i
$243$	10.9354	−	10.9354i	0.701508	−	0.701508i
$244$	−3.47397	+	1.22285i	−0.222398	+	0.0782850i
$245$		0			0
$246$	0.0810567	+	6.67118i	0.00516799	+	0.425339i
$247$	−0.950287	−	5.99987i	−0.0604653	−	0.381763i
$248$	3.56921	−	3.83937i	0.226645	−	0.243800i
$249$			1.48732i			0.0942554i
$250$		0			0
$251$			5.53474i			0.349350i	0.984626	+	0.174675i	$0.0558875\pi$
$251$			5.53474i			0.349350i	−0.984626	+	0.174675i	$0.944113\pi$
$252$	3.41698	+	18.6318i	0.215249	+	1.17370i
$253$	1.03441	+	6.53103i	0.0650330	+	0.410602i
$254$	−15.8717	+	0.192846i	−0.995879	+	0.0121002i
$255$		0			0
$256$	−13.7958	−	8.10401i	−0.862240	−	0.506500i
$257$	−13.0870	+	13.0870i	−0.816347	+	0.816347i	−0.985577	−	0.169230i	$-0.945872\pi$
$257$	−13.0870	+	13.0870i	−0.816347	+	0.816347i	0.169230	+	0.985577i	$0.445872\pi$
$258$	8.16316	−	4.28505i	0.508216	−	0.266776i
$259$	4.35823	+	13.4132i	0.270807	+	0.833459i
$260$		0			0
$261$	0.00473637	−	0.0145770i	0.000293174	−	0.000902296i
$262$	0.262513	+	1.53639i	0.0162181	+	0.0949185i
$263$	10.4335	+	5.31614i	0.643358	+	0.327807i	0.745050	−	0.667009i	$-0.232426\pi$
$263$	10.4335	+	5.31614i	0.643358	+	0.327807i	−0.101692	+	0.994816i	$0.532426\pi$
$264$	0.0583016	+	1.59883i	0.00358821	+	0.0984010i
$265$		0			0
$266$	−16.4727	−	11.6650i	−1.01001	−	0.715227i
$267$	−2.97301	−	0.470879i	−0.181945	−	0.0288173i
$268$	4.89763	+	9.06091i	0.299171	+	0.553483i
$269$	−2.93900	−	4.04519i	−0.179194	−	0.246640i	0.709966	−	0.704236i	$-0.248710\pi$
$269$	−2.93900	−	4.04519i	−0.179194	−	0.246640i	−0.889160	+	0.457597i	$0.848710\pi$
$270$		0			0
$271$	−14.8746	+	20.4731i	−0.903565	+	1.24365i	0.0657513	+	0.997836i	$0.479056\pi$
$271$	−14.8746	+	20.4731i	−0.903565	+	1.24365i	−0.969317	+	0.245815i	$0.920944\pi$
$272$	−16.6746	−	7.49926i	−1.01104	−	0.454710i
$273$	4.34849	−	2.21566i	0.263182	−	0.134098i
$274$	−6.36712	−	8.54335i	−0.384652	−	0.516122i
$275$		0			0
$276$	3.80809	−	12.7677i	0.229220	−	0.768524i
$277$	6.96028	+	13.6603i	0.418203	+	0.820769i	0.999973	+	0.00741564i	$0.00236049\pi$
$277$	6.96028	+	13.6603i	0.418203	+	0.820769i	−0.581770	+	0.813354i	$0.697640\pi$
$278$	12.5128	−	12.8206i	0.750467	−	0.768928i
$279$	−3.64378	−	2.64736i	−0.218147	−	0.158493i
$280$		0			0
$281$	−17.8125	+	12.9415i	−1.06260	+	0.772026i	−0.974568	−	0.224091i	$-0.928059\pi$
$281$	−17.8125	+	12.9415i	−1.06260	+	0.772026i	−0.0880347	+	0.996117i	$0.528059\pi$
$282$	−0.182036	+	1.24722i	−0.0108401	+	0.0742709i
$283$	0.402261	−	2.53977i	0.0239119	−	0.150974i	−0.972844	−	0.231464i	$-0.925649\pi$
$283$	0.402261	−	2.53977i	0.0239119	−	0.150974i	0.996755	+	0.0804900i	$0.0256485\pi$
$284$	21.3241	−	0.518263i	1.26535	−	0.0307532i
$285$		0			0
$286$	−1.66504	+	0.563459i	−0.0984557	+	0.0333180i
$287$	−11.0576	+	21.7017i	−0.652707	+	1.28101i
$288$	−5.48584	+	12.6049i	−0.323256	+	0.742751i
$289$	−3.70196	−	1.20284i	−0.217763	−	0.0707554i
$290$		0			0
$291$	−4.67708	+	1.51967i	−0.274175	+	0.0890849i
$292$	−12.6828	−	6.07869i	−0.742204	−	0.355728i
$293$	−12.9784	−	12.9784i	−0.758205	−	0.758205i	0.217790	−	0.975996i	$-0.430115\pi$
$293$	−12.9784	−	12.9784i	−0.758205	−	0.758205i	−0.975996	+	0.217790i	$0.930115\pi$
$294$	2.60065	−	8.34773i	0.151673	−	0.486850i
$295$		0			0
$296$	−2.80601	+	9.84300i	−0.163096	+	0.572113i
$297$	3.03372	−	0.480494i	0.176034	−	0.0278811i
$298$	−9.81692	+	19.8596i	−0.568679	+	1.15044i
$299$	14.6385			0.846564
$300$		0			0
$301$	33.6577			1.94000
$302$	8.24530	−	16.6803i	0.474464	−	0.959841i
$303$	6.16071	−	0.975761i	0.353924	−	0.0560560i
$304$	−5.19803	−	13.6951i	−0.298128	−	0.785466i
$305$		0			0
$306$	−4.67239	+	14.9977i	−0.267103	+	0.857364i
$307$	−5.84355	−	5.84355i	−0.333509	−	0.333509i	0.520409	−	0.853917i	$-0.325780\pi$
$307$	−5.84355	−	5.84355i	−0.333509	−	0.333509i	−0.853917	+	0.520409i	$0.825780\pi$
$308$	−2.52441	+	5.26703i	−0.143842	+	0.300117i
$309$	−4.05545	+	1.31770i	−0.230707	+	0.0749611i
$310$		0			0
$311$	−14.5346	−	4.72259i	−0.824184	−	0.267794i	−0.133590	−	0.991037i	$-0.542651\pi$
$311$	−14.5346	−	4.72259i	−0.824184	−	0.267794i	−0.690594	+	0.723243i	$0.742651\pi$
$312$	3.51606	+	0.426214i	0.199058	+	0.0241296i
$313$	12.1792	−	23.9030i	0.688408	−	1.35108i	−0.236778	−	0.971564i	$-0.576092\pi$
$313$	12.1792	−	23.9030i	0.688408	−	1.35108i	0.925186	−	0.379513i	$-0.123908\pi$
$314$	−20.4126	+	6.90776i	−1.15195	+	0.389827i
$315$		0			0
$316$	0.174776	+	7.19119i	0.00983190	+	0.404536i
$317$	0.573817	−	3.62294i	0.0322288	−	0.203484i	−0.966320	−	0.257345i	$-0.917152\pi$
$317$	0.573817	−	3.62294i	0.0322288	−	0.203484i	0.998548	+	0.0538600i	$0.0171525\pi$
$318$	1.42224	−	9.74448i	0.0797552	−	0.546443i
$319$	0.00382340	−	0.00277786i	0.000214069	−	0.000155530i
$320$		0			0
$321$	−2.27824	−	1.65524i	−0.127159	−	0.0923864i
$322$	33.9734	−	34.8092i	1.89327	−	1.93984i
$323$	−7.59925	−	14.9144i	−0.422834	−	0.829858i
$324$	8.04186	+	2.39857i	0.446770	+	0.133254i
$325$		0			0
$326$	−9.51582	−	12.7683i	−0.527032	−	0.707168i
$327$	1.96941	−	1.00346i	0.108909	−	0.0554917i
$328$	−15.4464	+	8.59324i	−0.852883	+	0.474482i
$329$	−2.70469	+	3.72268i	−0.149114	+	0.205238i
$330$		0			0
$331$	8.96644	+	12.3412i	0.492840	+	0.678336i	0.980909	−	0.194469i	$-0.0622984\pi$
$331$	8.96644	+	12.3412i	0.492840	+	0.678336i	−0.488069	+	0.872805i	$0.662298\pi$
$332$	−3.46650	+	1.87372i	−0.190249	+	0.102834i
$333$	8.68560	+	1.37566i	0.475968	+	0.0753859i
$334$	5.06268	+	3.58509i	0.277017	+	0.196167i
$335$		0			0
$336$	9.17370	−	7.37176i	0.500466	−	0.402162i
$337$	−26.0429	−	13.2695i	−1.41865	−	0.722838i	−0.434581	−	0.900633i	$-0.643104\pi$
$337$	−26.0429	−	13.2695i	−1.41865	−	0.722838i	−0.984068	+	0.177795i	$0.943104\pi$
$338$	−2.44102	−	14.2864i	−0.132774	−	0.777077i
$339$	3.50158	−	10.7768i	0.190180	−	0.585314i
$340$		0			0
$341$	−0.429146	−	1.32078i	−0.0232396	−	0.0715241i
$342$	−11.1436	+	5.84957i	−0.602578	+	0.316309i
$343$	3.27944	−	3.27944i	0.177073	−	0.177073i
$344$	20.2711	+	13.6276i	1.09294	+	0.734748i
$345$		0			0
$346$	23.1520	−	0.281303i	1.24466	−	0.0151230i
$347$	−0.393873	−	2.48682i	−0.0211442	−	0.133499i	0.974858	−	0.222827i	$-0.0715284\pi$
$347$	−0.393873	−	2.48682i	−0.0211442	−	0.133499i	−0.996002	+	0.0893271i	$0.971528\pi$
$348$	−0.00936623	+	0.00171771i	−0.000502082	+	9.20792e-5i
$349$			18.8483i			1.00893i	0.863434	+	0.504463i	$0.168309\pi$
$349$			18.8483i			1.00893i	−0.863434	+	0.504463i	$0.831691\pi$
$350$		0			0
$351$		−	6.79969i		−	0.362941i
$352$	−3.65293	+	2.15008i	−0.194702	+	0.114600i
$353$	3.50250	+	22.1139i	0.186419	+	1.17700i	0.886427	+	0.462869i	$0.153180\pi$
$353$	3.50250	+	22.1139i	0.186419	+	1.17700i	−0.700008	+	0.714135i	$0.746820\pi$
$354$	0.192285	+	15.8256i	0.0102198	+	0.841119i
$355$		0			0
$356$	−2.64791	−	7.52239i	−0.140339	−	0.398686i
$357$	9.50920	−	9.50920i	0.503280	−	0.503280i
$358$	−8.74837	−	16.6659i	−0.462366	−	0.880821i
$359$	7.71491	+	23.7440i	0.407177	+	1.25316i	0.919063	+	0.394110i	$0.128947\pi$
$359$	7.71491	+	23.7440i	0.407177	+	1.25316i	−0.511886	+	0.859053i	$0.671053\pi$
$360$		0			0
$361$	−1.72712	+	5.31554i	−0.0909013	+	0.279765i
$362$	−21.3091	+	3.64095i	−1.11998	+	0.191364i
$363$	−7.02112	−	3.57744i	−0.368513	−	0.187767i
$364$	10.6422	+	7.34371i	0.557805	+	0.384915i
$365$		0			0
$366$	1.13612	−	1.60437i	0.0593860	−	0.0838618i
$367$	−7.60906	−	1.20516i	−0.397190	−	0.0629087i	−0.0453553	−	0.998971i	$-0.514442\pi$
$367$	−7.60906	−	1.20516i	−0.397190	−	0.0629087i	−0.351834	+	0.936062i	$0.614442\pi$
$368$	34.5550	−	7.20916i	1.80130	−	0.375803i
$369$	8.92655	+	12.2863i	0.464697	+	0.639601i
$370$		0			0
$371$	21.1316	−	29.0852i	1.09710	−	1.51003i
$372$	−0.370455	+	2.77357i	−0.0192072	+	0.143803i
$373$	8.54114	−	4.35193i	0.442243	−	0.225334i	−0.218666	−	0.975800i	$-0.570171\pi$
$373$	8.54114	−	4.35193i	0.442243	−	0.225334i	0.660910	+	0.750465i	$0.270171\pi$
$374$	−3.88369	+	2.89440i	−0.200821	+	0.149666i
$375$		0			0
$376$	−3.13622	+	1.14697i	−0.161738	+	0.0591505i
$377$	−0.00474976	−	0.00932194i	−0.000244625	−	0.000480104i
$378$	−16.1692	−	15.7810i	−0.831652	−	0.811685i
$379$	−14.7902	−	10.7457i	−0.759723	−	0.551971i	0.139102	−	0.990278i	$-0.455578\pi$
$379$	−14.7902	−	10.7457i	−0.759723	−	0.551971i	−0.898825	+	0.438307i	$0.855578\pi$
$380$		0			0
$381$	6.85463	−	4.98018i	0.351173	−	0.255142i
$382$	13.3428	+	1.94743i	0.682679	+	0.0996392i
$383$	−2.50325	+	15.8049i	−0.127910	+	0.807591i	0.837420	+	0.546559i	$0.184063\pi$
$383$	−2.50325	+	15.8049i	−0.127910	+	0.807591i	−0.965330	+	0.261032i	$0.915937\pi$
$384$	8.50977	−	0.725487i	0.434263	−	0.0370224i
$385$		0			0
$386$	4.40170	+	13.0072i	0.224041	+	0.662047i
$387$	9.52760	−	18.6990i	0.484315	−	0.950522i
$388$	−9.43405	−	8.98636i	−0.478942	−	0.456213i
$389$	−14.5768	−	4.73629i	−0.739073	−	0.240139i	−0.0848002	−	0.996398i	$-0.527025\pi$
$389$	−14.5768	−	4.73629i	−0.739073	−	0.240139i	−0.654273	+	0.756259i	$0.727025\pi$
$390$		0			0
$391$	38.3622	−	12.4646i	1.94006	−	0.630364i
$392$	22.7323	−	4.45511i	1.14815	−	0.225017i
$393$	−0.588310	−	0.588310i	−0.0296763	−	0.0296763i
$394$	−17.7720	−	5.53667i	−0.895339	−	0.278933i
$395$		0			0
$396$	2.21157	+	2.89343i	0.111136	+	0.145400i
$397$	11.0132	−	1.74431i	0.552734	−	0.0875445i	0.126182	−	0.992007i	$-0.459728\pi$
$397$	11.0132	−	1.74431i	0.552734	−	0.0875445i	0.426553	+	0.904463i	$0.359728\pi$
$398$	32.7306	+	16.1792i	1.64064	+	0.810991i
$399$	10.7744			0.539395
$400$		0			0
$401$	−10.1423			−0.506483			−0.253242	−	0.967403i	$-0.581497\pi$
$401$	−10.1423			−0.506483			−0.253242	+	0.967403i	$0.581497\pi$
$402$	−4.92868	−	2.43632i	−0.245820	−	0.121513i
$403$	−3.03652	+	0.480938i	−0.151260	+	0.0239572i
$404$	10.0354	+	13.1295i	0.499281	+	0.653216i
$405$		0			0
$406$	−0.0331903	−	0.0103401i	−0.00164721	−	0.000513170i
$407$	1.91732	+	1.91732i	0.0950378	+	0.0950378i
$408$	9.57726	−	1.87697i	0.474145	−	0.0929237i
$409$	1.08325	−	0.351968i	0.0535630	−	0.0174037i	−0.282113	−	0.959381i	$-0.591035\pi$
$409$	1.08325	−	0.351968i	0.0535630	−	0.0174037i	0.335676	+	0.941978i	$0.391035\pi$
$410$		0			0
$411$	5.40917	+	1.75754i	0.266814	+	0.0866933i
$412$	−8.18019	−	7.79200i	−0.403009	−	0.383884i
$413$	−26.2311	+	51.4814i	−1.29075	+	2.53323i
$414$	−9.72170	−	28.7279i	−0.477795	−	1.41190i
$415$		0			0
$416$	3.43614	+	8.73180i	0.168470	+	0.428112i
$417$	−1.49594	+	9.44497i	−0.0732563	+	0.462522i
$418$	−3.83996	−	0.560455i	−0.187819	−	0.0274127i
$419$	−6.31833	+	4.59053i	−0.308670	+	0.224262i	−0.731326	−	0.682028i	$-0.761098\pi$
$419$	−6.31833	+	4.59053i	−0.308670	+	0.224262i	0.422655	+	0.906291i	$0.361098\pi$
$420$		0			0
$421$	−15.8211	−	11.4947i	−0.771074	−	0.560218i	0.131213	−	0.991354i	$-0.458113\pi$
$421$	−15.8211	−	11.4947i	−0.771074	−	0.560218i	−0.902287	+	0.431136i	$0.858113\pi$
$422$	25.0631	+	24.4614i	1.22005	+	1.19076i
$423$	1.30256	+	2.55642i	0.0633326	+	0.124297i
$424$	24.5031	−	8.96124i	1.18998	−	0.435196i
$425$		0			0
$426$	−9.12942	+	6.80390i	−0.442322	+	0.329650i
$427$	6.39471	−	3.25827i	0.309462	−	0.157679i
$428$	0.987740	−	7.39514i	0.0477442	−	0.357458i
$429$	0.551515	−	0.759095i	0.0266274	−	0.0366494i
$430$		0			0
$431$	−9.49241	−	13.0652i	−0.457233	−	0.629328i	0.516699	−	0.856167i	$-0.327161\pi$
$431$	−9.49241	−	13.0652i	−0.457233	−	0.629328i	−0.973932	+	0.226840i	$0.927161\pi$
$432$	−3.34872	−	16.0511i	−0.161115	−	0.772259i
$433$	−6.22123	−	0.985346i	−0.298973	−	0.0473527i	0.00514584	−	0.999987i	$-0.498362\pi$
$433$	−6.22123	−	0.985346i	−0.298973	−	0.0473527i	−0.304119	+	0.952634i	$0.598362\pi$
$434$	−5.90363	+	8.33680i	−0.283383	+	0.400179i
$435$		0			0
$436$	4.81982	+	3.32593i	0.230828	+	0.159283i
$437$	28.7947	+	14.6716i	1.37744	+	0.701839i
$438$	7.40013	−	1.26441i	0.353592	−	0.0604159i
$439$	9.07012	−	27.9149i	0.432893	−	1.33231i	−0.462337	−	0.886704i	$-0.652989\pi$
$439$	9.07012	−	27.9149i	0.432893	−	1.33231i	0.895230	−	0.445604i	$-0.147011\pi$
$440$		0			0
$441$	−6.15029	−	18.9286i	−0.292871	−	0.901364i
$442$	4.98371	+	9.49412i	0.237051	+	0.451589i
$443$	−1.81845	+	1.81845i	−0.0863972	+	0.0863972i	−0.748985	−	0.662587i	$-0.769458\pi$
$443$	−1.81845	+	1.81845i	−0.0863972	+	0.0863972i	0.662587	+	0.748985i	$0.269458\pi$
$444$	−1.81404	−	5.15347i	−0.0860905	−	0.244573i
$445$		0			0
$446$	0.0132679	+	1.09199i	0.000628255	+	0.0517070i
$447$	−1.84989	−	11.6797i	−0.0874967	−	0.552432i
$448$	28.7383	+	12.0942i	1.35776	+	0.571397i
$449$		−	19.3249i		−	0.911999i	−0.889980	−	0.455999i	$-0.849282\pi$
$449$		−	19.3249i		−	0.911999i	0.889980	−	0.455999i	$-0.150718\pi$
$450$		0			0
$451$			4.68267i			0.220498i
$452$	29.5286	−	5.41539i	1.38891	−	0.254718i
$453$	1.55373	+	9.80989i	0.0730008	+	0.460909i
$454$	11.9218	−	0.144853i	0.559519	−	0.00679831i
$455$		0			0
$456$	6.48911	+	4.36241i	0.303880	+	0.204289i
$457$	−15.9424	+	15.9424i	−0.745755	+	0.745755i	−0.973679	−	0.227924i	$-0.926806\pi$
$457$	−15.9424	+	15.9424i	−0.745755	+	0.745755i	0.227924	+	0.973679i	$0.426806\pi$
$458$	−29.4023	+	15.4340i	−1.37388	+	0.721183i
$459$	−5.78993	−	17.8196i	−0.270251	−	0.831747i
$460$		0			0
$461$	5.16980	−	15.9110i	0.240782	−	0.741049i	−0.755520	−	0.655125i	$-0.772616\pi$
$461$	5.16980	−	15.9110i	0.240782	−	0.741049i	0.996302	−	0.0859240i	$-0.0273842\pi$
$462$	−0.525097	−	3.07319i	−0.0244297	−	0.142978i
$463$	−24.6825	−	12.5764i	−1.14710	−	0.584474i	−0.226122	−	0.974099i	$-0.572605\pi$
$463$	−24.6825	−	12.5764i	−1.14710	−	0.584474i	−0.920974	+	0.389625i	$0.872605\pi$
$464$	−0.0158030	−	0.0196658i	−0.000733635	−	0.000912964i
$465$		0			0
$466$	2.56562	+	1.81682i	0.118850	+	0.0841627i
$467$	10.2246	+	1.61942i	0.473139	+	0.0749378i	0.388450	−	0.921470i	$-0.373010\pi$
$467$	10.2246	+	1.61942i	0.473139	+	0.0749378i	0.0846885	+	0.996407i	$0.473010\pi$
$468$	7.09242	−	3.83362i	0.327847	−	0.177209i
$469$	−11.7977	−	16.2382i	−0.544768	−	0.749809i
$470$		0			0
$471$	6.76133	−	9.30617i	0.311546	−	0.428806i
$472$	−36.6423	+	20.3851i	−1.68660	+	0.938301i
$473$	5.76563	−	2.93773i	0.265104	−	0.135077i
$474$	−2.29451	−	3.07875i	−0.105390	−	0.141412i
$475$		0			0
$476$	34.1427	+	10.1834i	1.56493	+	0.466756i
$477$	−10.1768	−	19.9732i	−0.465965	−	0.914508i
$478$	−0.825144	+	0.845442i	−0.0377412	+	0.0386696i
$479$	−19.2530	−	13.9881i	−0.879693	−	0.639134i	0.0534775	−	0.998569i	$-0.482969\pi$
$479$	−19.2530	−	13.9881i	−0.879693	−	0.639134i	−0.933170	+	0.359435i	$0.882969\pi$
$480$		0			0
$481$	4.85624	−	3.52826i	0.221425	−	0.160875i
$482$	2.48458	−	17.0231i	0.113169	−	0.775382i
$483$	−4.06161	+	25.6440i	−0.184810	+	1.16684i
$484$	−0.507250	−	20.8709i	−0.0230568	−	0.948678i
$485$		0			0
$486$	−20.7168	+	7.01068i	−0.939732	+	0.318011i
$487$	11.0199	−	21.6278i	0.499360	−	0.980049i	−0.494477	−	0.869191i	$-0.664640\pi$
$487$	11.0199	−	21.6278i	0.499360	−	0.980049i	0.993836	−	0.110858i	$-0.0353598\pi$
$488$	5.17058	+	0.626773i	0.234061	+	0.0283727i
$489$	8.08414	+	2.62670i	0.365577	+	0.118783i
$490$		0			0
$491$	−20.7954	+	6.75684i	−0.938484	+	0.304932i	−0.738028	−	0.674771i	$-0.764243\pi$
$491$	−20.7954	+	6.75684i	−0.938484	+	0.304932i	−0.200457	+	0.979703i	$0.564243\pi$
$492$	4.07795	−	8.50839i	0.183848	−	0.383588i
$493$	−0.0203851	−	0.0203851i	−0.000918097	−	0.000918097i
$494$	−2.55526	+	8.20205i	−0.114967	+	0.369028i
$495$		0			0
$496$	−6.93104	+	2.63071i	−0.311213	+	0.118122i
$497$	−41.0550	+	6.50248i	−1.84157	+	0.291676i
$498$	0.932081	−	1.88560i	0.0417675	−	0.0844958i
$499$	9.81690			0.439465			0.219732	−	0.975560i	$-0.429482\pi$
$499$	9.81690			0.439465			0.219732	+	0.975560i	$0.429482\pi$
$500$		0			0
$501$	−3.31137			−0.147941
$502$	3.46853	−	7.01684i	0.154808	−	0.313177i
$503$	−32.8952	+	5.21009i	−1.46673	+	0.232306i	−0.838149	−	0.545442i	$-0.816362\pi$
$503$	−32.8952	+	5.21009i	−1.46673	+	0.232306i	−0.628576	+	0.777748i	$0.716362\pi$
$504$	7.34428	−	25.7625i	0.327140	−	1.14755i
$505$		0			0
$506$	2.78148	−	8.92817i	0.123652	−	0.396905i
$507$	5.47049	+	5.47049i	0.242953	+	0.242953i
$508$	20.2427	+	9.70204i	0.898124	+	0.430458i
$509$	−17.4707	+	5.67657i	−0.774375	+	0.251610i	−0.669437	−	0.742869i	$-0.733464\pi$
$509$	−17.4707	+	5.67657i	−0.774375	+	0.251610i	−0.104938	+	0.994479i	$0.533464\pi$
$510$		0			0
$511$	26.0659	+	8.46931i	1.15309	+	0.374660i
$512$	12.4115	+	18.9197i	0.548514	+	0.836141i
$513$	6.81510	−	13.3754i	0.300894	−	0.590538i
$514$	24.7929	−	8.39007i	1.09357	−	0.370070i
$515$		0			0
$516$	−13.0345	+	0.316792i	−0.573811	+	0.0139460i
$517$	−0.138392	+	0.873775i	−0.00608649	+	0.0384286i
$518$	2.88058	−	19.7363i	0.126565	−	0.867163i
$519$	−9.99883	+	7.26457i	−0.438900	+	0.318879i
$520$		0			0
$521$	−10.3305	−	7.50555i	−0.452587	−	0.328824i	0.338029	−	0.941136i	$-0.390240\pi$
$521$	−10.3305	−	7.50555i	−0.452587	−	0.328824i	−0.790617	+	0.612312i	$0.790240\pi$
$522$	−0.0151399	+	0.0155123i	−0.000662653	+	0.000678954i
$523$	19.1488	+	37.5817i	0.837321	+	1.64333i	0.763270	+	0.646080i	$0.223593\pi$
$523$	19.1488	+	37.5817i	0.837321	+	1.64333i	0.0740511	+	0.997254i	$0.476407\pi$
$524$	0.630021	−	2.11232i	0.0275226	−	0.0922771i
$525$		0			0
$526$	−9.89587	−	13.2782i	−0.431480	−	0.578957i
$527$	−7.54813	+	3.84596i	−0.328802	+	0.167533i
$528$	0.928045	−	2.06350i	0.0403880	−	0.0898023i
$529$	−32.2554	+	44.3957i	−1.40241	+	1.93025i
$530$		0			0
$531$	21.1758	+	29.1460i	0.918952	+	1.26483i
$532$	13.5735	+	25.1118i	0.588487	+	1.08874i
$533$	10.2388	+	1.62166i	0.443490	+	0.0702419i
$534$	3.47404	+	2.46011i	0.150336	+	0.106459i
$535$		0			0
$536$	−0.530806	−	14.5565i	−0.0229273	−	0.628746i
$537$	8.95219	+	4.56137i	0.386315	+	0.196837i
$538$	1.19096	+	6.97024i	0.0513459	+	0.300508i
$539$	1.89638	−	5.83644i	0.0816827	−	0.251393i
$540$		0			0
$541$	−7.07714	−	21.7812i	−0.304270	−	0.936447i	−0.979949	−	0.199251i	$-0.936149\pi$
$541$	−7.07714	−	21.7812i	−0.304270	−	0.936447i	0.675678	−	0.737197i	$-0.263851\pi$
$542$	31.6878	−	16.6337i	1.36111	−	0.714481i
$543$	8.15961	−	8.15961i	0.350163	−	0.350163i
$544$	16.4400	+	19.9571i	0.704860	+	0.855653i
$545$		0			0
$546$	−6.90145	+	0.0838545i	−0.295355	+	0.00358864i
$547$	3.85178	+	24.3192i	0.164690	+	1.03981i	0.922122	+	0.386899i	$0.126454\pi$
$547$	3.85178	+	24.3192i	0.164690	+	1.03981i	−0.757432	+	0.652914i	$0.773546\pi$
$548$	2.71814	+	14.8213i	0.116113	+	0.633133i
$549$		−	4.47499i		−	0.190988i
$550$		0			0
$551$		−	0.0230973i		−	0.000983978i
$552$	−12.8291	+	13.8002i	−0.546043	+	0.587374i
$553$	−2.19286	−	13.8451i	−0.0932497	−	0.588756i
$554$	−0.263420	−	21.6802i	−0.0111917	−	0.921103i
$555$		0			0
$556$	−23.8979	+	8.41215i	−1.01350	+	0.356755i
$557$	−2.83685	+	2.83685i	−0.120201	+	0.120201i	−0.764649	−	0.644447i	$-0.777087\pi$
$557$	−2.83685	+	2.83685i	−0.120201	+	0.120201i	0.644447	+	0.764649i	$0.277087\pi$
$558$	2.96045	+	5.63976i	0.125326	+	0.238750i
$559$	−4.42671	−	13.6240i	−0.187230	−	0.576235i
$560$		0			0
$561$	0.798955	−	2.45893i	0.0337319	−	0.103816i
$562$	30.6925	−	5.24424i	1.29469	−	0.221215i
$563$	−19.6112	−	9.99243i	−0.826515	−	0.421131i	−0.0110516	−	0.999939i	$-0.503518\pi$
$563$	−19.6112	−	9.99243i	−0.826515	−	0.421131i	−0.815464	+	0.578808i	$0.803518\pi$
$564$	1.01239	−	1.46712i	0.0426295	−	0.0617771i
$565$		0			0
$566$	−2.10161	+	2.96779i	−0.0883373	+	0.124745i
$567$	−16.1522	−	2.55825i	−0.678327	−	0.107436i
$568$	−27.3590	−	12.7064i	−1.14796	−	0.533148i
$569$	−2.34646	−	3.22963i	−0.0983688	−	0.135393i	0.756995	−	0.653420i	$-0.226667\pi$
$569$	−2.34646	−	3.22963i	−0.0983688	−	0.135393i	−0.855364	+	0.518027i	$0.826667\pi$
$570$		0			0
$571$	−13.9597	+	19.2139i	−0.584197	+	0.804078i	−0.994148	−	0.108029i	$-0.965546\pi$
$571$	−13.9597	+	19.2139i	−0.584197	+	0.804078i	0.409951	+	0.912108i	$0.365546\pi$
$572$	2.46401	+	0.329109i	0.103026	+	0.0137607i
$573$	−6.41323	+	3.26770i	−0.267917	+	0.136510i
$574$	27.6186	−	20.5834i	1.15278	−	0.859135i
$575$		0			0
$576$	14.8541	−	12.5424i	0.618921	−	0.522599i
$577$	5.57748	+	10.9464i	0.232194	+	0.455706i	0.977477	−	0.211042i	$-0.0676858\pi$
$577$	5.57748	+	10.9464i	0.232194	+	0.455706i	−0.745283	+	0.666748i	$0.767686\pi$
$578$	3.93948	+	3.84490i	0.163861	+	0.159927i
$579$	−5.93000	−	4.30839i	−0.246442	−	0.179051i
$580$		0			0
$581$	6.21235	−	4.51354i	0.257732	−	0.187253i
$582$	6.88187	+	1.00443i	0.285262	+	0.0416350i
$583$	1.08125	−	6.82676i	0.0447809	−	0.282736i
$584$	12.2696	+	15.6545i	0.507719	+	0.647789i
$585$		0			0
$586$	8.32041	+	24.5871i	0.343713	+	1.01568i
$587$	−8.67508	+	17.0258i	−0.358059	+	0.702730i	−0.997831	−	0.0658352i	$-0.979029\pi$
$587$	−8.67508	+	17.0258i	−0.358059	+	0.702730i	0.639772	+	0.768565i	$0.279029\pi$
$588$	−8.52843	+	8.95331i	−0.351707	+	0.369228i
$589$	−6.45504	−	2.09737i	−0.265975	−	0.0864206i
$590$		0			0
$591$	9.44990	−	3.07046i	0.388717	−	0.126302i
$592$	9.72584	−	10.7203i	0.399730	−	0.440601i
$593$	19.5284	+	19.5284i	0.801936	+	0.801936i	0.983398	−	0.181462i	$-0.0580829\pi$
$593$	19.5284	+	19.5284i	0.801936	+	0.801936i	−0.181462	+	0.983398i	$0.558083\pi$
$594$	−4.14721	−	1.29202i	−0.170162	−	0.0530123i
$595$		0			0
$596$	24.8914	−	19.0256i	1.01959	−	0.779318i
$597$	−19.2493	+	3.04879i	−0.787822	+	0.124779i
$598$	−18.5584	−	9.17367i	−0.758907	−	0.375139i
$599$	13.5371			0.553109			0.276555	−	0.960998i	$-0.410807\pi$
$599$	13.5371			0.553109			0.276555	+	0.960998i	$0.410807\pi$
$600$		0			0
$601$	−20.0981			−0.819819			−0.409910	−	0.912126i	$-0.634440\pi$
$601$	−20.0981			−0.819819			−0.409910	+	0.912126i	$0.634440\pi$
$602$	−42.6706	−	21.0927i	−1.73912	−	0.859675i
$603$	−12.3609	+	1.95778i	−0.503376	+	0.0797270i
$604$	−20.9065	+	15.9797i	−0.850672	+	0.650206i
$605$		0			0
$606$	−8.42193	−	2.62376i	−0.342117	−	0.106583i
$607$	−13.9387	−	13.9387i	−0.565753	−	0.565753i	0.365182	−	0.930936i	$-0.381007\pi$
$607$	−13.9387	−	13.9387i	−0.565753	−	0.565753i	−0.930936	+	0.365182i	$0.881007\pi$
$608$	−1.99250	+	20.6199i	−0.0808067	+	0.836246i
$609$	0.0176483	−	0.00573428i	0.000715145	−	0.000232365i
$610$		0			0
$611$	1.86260	+	0.605195i	0.0753527	+	0.0244836i
$612$	15.3224	−	16.0857i	0.619371	−	0.650228i
$613$	−7.55485	+	14.8272i	−0.305137	+	0.598866i	−0.991754	−	0.128153i	$-0.959095\pi$
$613$	−7.55485	+	14.8272i	−0.305137	+	0.598866i	0.686617	+	0.727019i	$0.259095\pi$
$614$	3.74628	+	11.0704i	0.151188	+	0.446764i
$615$		0			0
$616$	6.50116	−	5.09543i	0.261939	−	0.205301i
$617$	−2.57536	+	16.2602i	−0.103680	+	0.654610i	0.880040	+	0.474900i	$0.157516\pi$
$617$	−2.57536	+	16.2602i	−0.103680	+	0.654610i	−0.983720	+	0.179710i	$0.942484\pi$
$618$	5.96720	+	0.870933i	0.240036	+	0.0350341i
$619$	−2.41281	+	1.75301i	−0.0969790	+	0.0704593i	−0.635218	−	0.772333i	$-0.719090\pi$
$619$	−2.41281	+	1.75301i	−0.0969790	+	0.0704593i	0.538239	+	0.842792i	$0.319090\pi$
$620$		0			0
$621$	29.2655	+	21.2626i	1.17438	+	0.853240i
$622$	15.4672	+	15.0958i	0.620177	+	0.605287i
$623$	7.05531	+	13.8468i	0.282665	+	0.554762i
$624$	−4.19049	−	2.74380i	−0.167754	−	0.109840i
$625$		0			0
$626$	−30.4201	+	22.6713i	−1.21583	+	0.906126i
$627$	1.84568	−	0.940418i	0.0737092	−	0.0375567i
$628$	30.2077	+	4.03473i	1.20542	+	0.161003i
$629$	9.72216	−	13.3814i	0.387648	−	0.533552i
$630$		0			0
$631$	−10.9928	−	15.1303i	−0.437618	−	0.602329i	0.532063	−	0.846705i	$-0.321417\pi$
$631$	−10.9928	−	15.1303i	−0.437618	−	0.602329i	−0.969681	+	0.244376i	$0.921417\pi$
$632$	4.28502	−	9.22639i	0.170449	−	0.367006i
$633$	−18.4641	−	2.92442i	−0.733881	−	0.116235i
$634$	−2.99791	+	4.23349i	−0.119062	+	0.168133i
$635$		0			0
$636$	−7.90979	+	11.4626i	−0.313644	+	0.454521i
$637$	−12.1048	−	6.16769i	−0.479608	−	0.244373i
$638$	−0.00658807	+	0.00112566i	−0.000260824	+	4.45653e-5i
$639$	−8.00905	+	24.6493i	−0.316833	+	0.975112i
$640$		0			0
$641$	6.50379	+	20.0166i	0.256884	+	0.790608i	0.993453	+	0.114245i	$0.0364449\pi$
$641$	6.50379	+	20.0166i	0.256884	+	0.790608i	−0.736568	+	0.676363i	$0.763555\pi$
$642$	1.85100	+	3.52621i	0.0730531	+	0.139169i
$643$	16.6982	−	16.6982i	0.658511	−	0.658511i	−0.296516	−	0.955028i	$-0.595825\pi$
$643$	16.6982	−	16.6982i	0.658511	−	0.658511i	0.955028	+	0.296516i	$0.0958250\pi$
$644$	−64.8852	+	22.8398i	−2.55683	+	0.900015i
$645$		0			0
$646$	0.287603	+	23.6705i	0.0113156	+	0.931302i
$647$	−0.900819	−	5.68755i	−0.0354149	−	0.223601i	0.963633	−	0.267229i	$-0.0861081\pi$
$647$	−0.900819	−	5.68755i	−0.0354149	−	0.223601i	−0.999048	+	0.0436287i	$0.986108\pi$
$648$	−8.69217	−	8.08055i	−0.341461	−	0.317434i
$649$			11.1084i			0.436042i
$650$		0			0
$651$		−	5.45290i		−	0.213716i
$652$	4.06233	+	22.1507i	0.159093	+	0.867490i
$653$	−0.646208	−	4.08000i	−0.0252881	−	0.159663i	0.971813	−	0.235754i	$-0.0757560\pi$
$653$	−0.646208	−	4.08000i	−0.0252881	−	0.159663i	−0.997101	+	0.0760913i	$0.975756\pi$
$654$	−3.12563	+	0.0379773i	−0.122222	+	0.00148503i
$655$		0			0
$656$	24.9678	−	1.21436i	0.974831	−	0.0474129i
$657$	12.0838	−	12.0838i	0.471433	−	0.471433i
$658$	5.76189	−	3.02456i	0.224622	−	0.117910i
$659$	−8.02901	−	24.7107i	−0.312766	−	0.962594i	−0.976664	−	0.214771i	$-0.931099\pi$
$659$	−8.02901	−	24.7107i	−0.312766	−	0.962594i	0.663899	−	0.747823i	$-0.268901\pi$
$660$		0			0
$661$	0.665910	−	2.04946i	0.0259009	−	0.0797148i	−0.937271	−	0.348603i	$-0.886656\pi$
$661$	0.665910	−	2.04946i	0.0259009	−	0.0797148i	0.963171	+	0.268888i	$0.0866562\pi$
$662$	−3.63343	−	21.2651i	−0.141217	−	0.826492i
$663$	−5.09982	−	2.59849i	−0.198060	−	0.100917i
$664$	5.56899	−	0.203074i	0.216119	−	0.00788081i
$665$		0			0
$666$	−10.1493	−	7.18716i	−0.393278	−	0.278497i
$667$	0.0549736	+	0.00870697i	0.00212859	+	0.000337135i
$668$	−4.17165	−	7.71780i	−0.161406	−	0.298611i
$669$	−0.342640	−	0.471604i	−0.0132472	−	0.0182333i
$670$		0			0
$671$	0.811036	−	1.11629i	0.0313097	−	0.0430941i
$672$	−16.2500	+	3.59677i	−0.626857	+	0.138749i
$673$	−23.7755	+	12.1142i	−0.916479	+	0.466969i	−0.847588	−	0.530655i	$-0.821946\pi$
$673$	−23.7755	+	12.1142i	−0.916479	+	0.466969i	−0.0688909	+	0.997624i	$0.521946\pi$
$674$	24.7009	+	33.1435i	0.951444	+	1.27664i
$675$		0			0
$676$	−5.85835	+	19.6417i	−0.225321	+	0.755452i
$677$	4.53364	+	8.89777i	0.174242	+	0.341969i	0.961568	−	0.274568i	$-0.0885349\pi$
$677$	4.53364	+	8.89777i	0.174242	+	0.341969i	−0.787326	+	0.616537i	$0.788535\pi$
$678$	−11.1929	+	11.4682i	−0.429859	+	0.440433i
$679$	20.5409	+	14.9238i	0.788286	+	0.572723i
$680$		0			0
$681$	−5.14876	+	3.74080i	−0.197301	+	0.143348i
$682$	−0.283645	+	1.94339i	−0.0108613	+	0.0744164i
$683$	6.26839	−	39.5771i	0.239853	−	1.51437i	−0.514263	−	0.857633i	$-0.671934\pi$
$683$	6.26839	−	39.5771i	0.239853	−	1.51437i	0.754116	−	0.656741i	$-0.228066\pi$
$684$	17.7935	−	0.432456i	0.680352	−	0.0165354i
$685$		0			0
$686$	−6.21279	+	2.10244i	−0.237205	+	0.0802717i
$687$	8.04723	−	15.7936i	0.307021	−	0.602562i
$688$	−17.1591	−	29.9803i	−0.654184	−	1.14299i
$689$	−14.5524	−	4.72836i	−0.554402	−	0.180136i
$690$		0			0
$691$	10.3709	−	3.36971i	0.394528	−	0.128190i	−0.105033	−	0.994469i	$-0.533495\pi$
$691$	10.3709	−	3.36971i	0.394528	−	0.128190i	0.499561	+	0.866279i	$0.333495\pi$
$692$	−29.5280	−	14.1523i	−1.12248	−	0.537991i
$693$	−5.01827	−	5.01827i	−0.190628	−	0.190628i
$694$	−1.05910	+	3.39958i	−0.0402030	+	0.129046i
$695$		0			0
$696$	0.0129508	+	0.00369197i	0.000490898	+	0.000139944i
$697$	28.2130	−	4.46850i	1.06864	−	0.169256i
$698$	11.8119	−	23.8955i	0.447087	−	0.904458i
$699$	−1.67811			−0.0634720
$700$		0			0
$701$	−11.2244			−0.423940			−0.211970	−	0.977276i	$-0.567988\pi$
$701$	−11.2244			−0.423940			−0.211970	+	0.977276i	$0.567988\pi$
$702$	−4.26125	+	8.62052i	−0.160831	+	0.325361i
$703$	13.0888	−	2.07305i	0.493652	−	0.0781867i
$704$	5.97853	−	0.436597i	0.225324	−	0.0164549i
$705$		0			0
$706$	9.41800	−	30.2305i	0.354451	−	1.13774i
$707$	−22.7714	−	22.7714i	−0.856405	−	0.856405i
$708$	9.67384	−	20.1839i	0.363565	−	0.758556i
$709$	40.0107	−	13.0003i	1.50263	−	0.488235i	0.561848	−	0.827240i	$-0.310091\pi$
$709$	40.0107	−	13.0003i	1.50263	−	0.488235i	0.940784	+	0.339006i	$0.110091\pi$
$710$		0			0
$711$	−8.31258	−	2.70092i	−0.311746	−	0.101293i
$712$	−1.35719	+	11.1961i	−0.0508627	+	0.419593i
$713$	7.42527	−	14.5729i	0.278079	−	0.545760i
$714$	−18.0148	+	6.09633i	−0.674188	+	0.228149i
$715$		0			0
$716$	0.646762	+	26.6112i	0.0241706	+	0.994507i
$717$	0.0986482	−	0.622840i	0.00368408	−	0.0232604i
$718$	5.09918	−	34.9371i	0.190300	−	1.30384i
$719$	−15.1605	+	11.0147i	−0.565391	+	0.410781i	−0.833428	−	0.552628i	$-0.813625\pi$
$719$	−15.1605	+	11.0147i	−0.565391	+	0.410781i	0.268037	+	0.963409i	$0.413625\pi$
$720$		0			0
$721$	17.8108	+	12.9403i	0.663309	+	0.481922i
$722$	5.52077	−	5.65658i	0.205462	−	0.210516i
$723$	4.16902	+	8.18215i	0.155047	+	0.304298i
$724$	29.2970	+	8.73813i	1.08881	+	0.324750i
$725$		0			0
$726$	6.65932	+	8.93542i	0.247151	+	0.331625i
$727$	−30.9449	+	15.7672i	−1.14768	+	0.584773i	−0.921141	−	0.389229i	$-0.872742\pi$
$727$	−30.9449	+	15.7672i	−1.14768	+	0.584773i	−0.226540	+	0.974002i	$0.572742\pi$
$728$	−8.88984	−	15.9795i	−0.329479	−	0.592240i
$729$	−0.536916	+	0.739001i	−0.0198858	+	0.0273704i
$730$		0			0
$731$	−23.2017	−	31.9344i	−0.858146	−	1.18114i
$732$	−2.44578	+	1.32200i	−0.0903988	+	0.0488627i
$733$	30.1255	+	4.77141i	1.11271	+	0.176236i	0.685611	−	0.727968i	$-0.259535\pi$
$733$	30.1255	+	4.77141i	1.11271	+	0.176236i	0.427100	+	0.904204i	$0.359535\pi$
$734$	8.89137	+	6.29634i	0.328186	+	0.232402i
$735$		0			0
$736$	−48.3260	−	12.5154i	−1.78132	−	0.461323i
$737$	−3.43828	−	1.75189i	−0.126651	−	0.0645318i
$738$	−3.61727	−	21.1705i	−0.133153	−	0.779297i
$739$	−2.21800	+	6.82631i	−0.0815905	+	0.251110i	−0.983528	−	0.180757i	$-0.942145\pi$
$739$	−2.21800	+	6.82631i	−0.0815905	+	0.251110i	0.901937	+	0.431867i	$0.142145\pi$
$740$		0			0
$741$	−1.41707	−	4.36128i	−0.0520572	−	0.160216i
$742$	−45.0174	+	23.6308i	−1.65264	+	0.867514i
$743$	29.7687	−	29.7687i	1.09211	−	1.09211i	0.0968046	−	0.995303i	$-0.469138\pi$
$743$	29.7687	−	29.7687i	1.09211	−	1.09211i	0.995303	−	0.0968046i	$-0.0308622\pi$
$744$	2.20781	−	3.28412i	0.0809421	−	0.120402i
$745$		0			0
$746$	−13.5556	+	0.164704i	−0.496305	+	0.00603024i
$747$	−0.749002	−	4.72901i	−0.0274046	−	0.173026i
$748$	6.73754	−	1.23563i	0.246349	−	0.0451790i
$749$			14.5390i			0.531244i
$750$		0			0
$751$		−	31.2660i		−	1.14091i	−0.821327	−	0.570457i	$-0.806766\pi$
$751$		−	31.2660i		−	1.14091i	0.821327	−	0.570457i	$-0.193234\pi$
$752$	4.69483	+	0.511306i	0.171203	+	0.0186454i
$753$	0.653605	+	4.12670i	0.0238187	+	0.150385i
$754$	0.000179761		0.0147948i	6.54649e−6		0.000538794i
$755$		0			0
$756$	10.6093	+	30.1398i	0.385857	+	1.09617i
$757$	−4.53335	+	4.53335i	−0.164767	+	0.164767i	−0.784675	−	0.619908i	$-0.787170\pi$
$757$	−4.53335	+	4.53335i	−0.164767	+	0.164767i	0.619908	+	0.784675i	$0.287170\pi$
$758$	12.0166	+	22.8920i	0.436463	+	0.831475i
$759$	1.54252	+	4.74738i	0.0559898	+	0.172319i
$760$		0			0
$761$	8.99353	−	27.6792i	0.326015	−	1.00337i	−0.644965	−	0.764212i	$-0.723128\pi$
$761$	8.99353	−	27.6792i	0.326015	−	1.00337i	0.970980	−	0.239159i	$-0.0768718\pi$
$762$	−11.8112	+	2.01810i	−0.427873	+	0.0731079i
$763$	−10.1678	−	5.18078i	−0.368101	−	0.187557i
$764$	−15.6954	−	10.8306i	−0.567839	−	0.391839i
$765$		0			0
$766$	13.0782	−	18.4684i	0.472535	−	0.667289i
$767$	24.2887	+	3.84695i	0.877013	+	0.138905i
$768$	−11.2432	−	4.41317i	−0.405703	−	0.159247i
$769$	21.5371	+	29.6433i	0.776649	+	1.06897i	0.995644	+	0.0932401i	$0.0297224\pi$
$769$	21.5371	+	29.6433i	0.776649	+	1.06897i	−0.218994	+	0.975726i	$0.570278\pi$
$770$		0			0
$771$	−8.21222	+	11.3031i	−0.295756	+	0.407073i
$772$	2.57097	−	19.2487i	0.0925314	−	0.692776i
$773$	21.7496	−	11.0820i	0.782279	−	0.398591i	−0.0167684	−	0.999859i	$-0.505338\pi$
$773$	21.7496	−	11.0820i	0.782279	−	0.398591i	0.799047	+	0.601268i	$0.205338\pi$
$774$	−23.7972	+	17.7354i	−0.855374	+	0.637486i
$775$		0			0
$776$	6.32871	+	17.3049i	0.227188	+	0.621210i
$777$	4.83348	+	9.48624i	0.173400	+	0.340317i
$778$	15.5120	+	15.1396i	0.556133	+	0.542781i
$779$	18.5149	+	13.4518i	0.663364	+	0.481962i
$780$		0			0
$781$	−6.46525	+	4.69728i	−0.231345	+	0.168082i
$782$	−56.4462	−	8.23851i	−2.01851	−	0.294609i
$783$	0.00404446	−	0.0255357i	0.000144537	−	0.000912573i
$784$	−31.6115	−	8.59784i	−1.12898	−	0.307066i
$785$		0			0
$786$	0.377164	+	1.11453i	0.0134530	+	0.0397540i
$787$	−1.57397	+	3.08909i	−0.0561060	+	0.110114i	−0.917357	−	0.398066i	$-0.869682\pi$
$787$	−1.57397	+	3.08909i	−0.0561060	+	0.110114i	0.861251	+	0.508180i	$0.169682\pi$
$788$	19.0612	+	18.1567i	0.679028	+	0.646805i
$789$	8.40701	+	2.73160i	0.299297	+	0.0972476i
$790$		0			0
$791$	−55.6393	+	18.0783i	−1.97830	+	0.642790i
$792$	−0.990527	−	5.05418i	−0.0351968	−	0.179593i
$793$	−2.15993	−	2.15993i	−0.0767014	−	0.0767014i
$794$	−15.0554	−	4.69035i	−0.534296	−	0.166454i
$795$		0			0
$796$	−31.3560	−	41.0234i	−1.11138	−	1.45404i
$797$	12.2116	−	1.93413i	0.432557	−	0.0685103i	0.0636405	−	0.997973i	$-0.479729\pi$
$797$	12.2116	−	1.93413i	0.432557	−	0.0685103i	0.368916	+	0.929463i	$0.379729\pi$
$798$	−13.6596	−	6.75214i	−0.483544	−	0.239023i
$799$	5.39653			0.190916
$800$		0			0
$801$	9.68995			0.342378
$802$	12.8582	+	6.35602i	0.454040	+	0.224439i
$803$	5.20435	−	0.824288i	0.183658	−	0.0290885i
$804$	4.72169	+	6.17744i	0.166521	+	0.217862i
$805$		0			0
$806$	4.15104	+	1.29321i	0.146214	+	0.0455515i
$807$	−2.66902	−	2.66902i	−0.0939540	−	0.0939540i
$808$	−4.49471	−	22.9343i	−0.158123	−	0.806827i
$809$	13.3278	−	4.33048i	0.468582	−	0.152251i	−0.0652027	−	0.997872i	$-0.520769\pi$
$809$	13.3278	−	4.33048i	0.468582	−	0.152251i	0.533784	+	0.845621i	$0.320769\pi$
$810$		0			0
$811$	15.0031	+	4.87481i	0.526831	+	0.171178i	0.560343	−	0.828261i	$-0.310669\pi$
$811$	15.0031	+	4.87481i	0.526831	+	0.171178i	−0.0335122	+	0.999438i	$0.510669\pi$
$812$	0.0355981	+	0.0339088i	0.00124925	+	0.00118996i
$813$	−8.67277	+	17.0213i	−0.304167	+	0.596962i
$814$	−1.22919	−	3.63229i	−0.0430830	−	0.127312i
$815$		0			0
$816$	−13.3181	−	3.62233i	−0.466228	−	0.126807i
$817$	4.94729	−	31.2360i	0.173084	−	1.09281i
$818$	−1.59389	−	0.232634i	−0.0557291	−	0.00813384i
$819$	−12.7104	+	9.23466i	−0.444138	+	0.322685i
$820$		0			0
$821$	6.24060	+	4.53406i	0.217798	+	0.158240i	0.691335	−	0.722534i	$-0.257023\pi$
$821$	6.24060	+	4.53406i	0.217798	+	0.158240i	−0.473537	+	0.880774i	$0.657023\pi$
$822$	−5.75621	−	5.61801i	−0.200771	−	0.195951i
$823$	−3.19071	−	6.26212i	−0.111221	−	0.218284i	0.828686	−	0.559714i	$-0.189089\pi$
$823$	−3.19071	−	6.26212i	−0.111221	−	0.218284i	−0.939907	+	0.341430i	$0.889089\pi$
$824$	5.48757	+	15.0049i	0.191169	+	0.522721i
$825$		0			0
$826$	65.5178	−	48.8285i	2.27965	−	1.69896i
$827$	12.1390	−	6.18514i	0.422115	−	0.215078i	−0.230012	−	0.973188i	$-0.573877\pi$
$827$	12.1390	−	6.18514i	0.422115	−	0.215078i	0.652128	+	0.758109i	$0.273877\pi$
$828$	−5.67831	+	42.5131i	−0.197335	+	1.47743i
$829$	21.4059	−	29.4626i	0.743456	−	1.02328i	−0.254956	−	0.966953i	$-0.582061\pi$
$829$	21.4059	−	29.4626i	0.743456	−	1.02328i	0.998412	−	0.0563271i	$-0.0179390\pi$
$830$		0			0
$831$	6.80275	+	9.36318i	0.235985	+	0.324805i
$832$	1.11580	−	13.2234i	0.0386835	−	0.458438i
$833$	−36.9741	−	5.85612i	−1.28108	−	0.202902i
$834$	7.81552	−	11.0367i	0.270629	−	0.382169i
$835$		0			0
$836$	4.51700	+	3.11697i	0.156224	+	0.107803i
$837$	−6.76925	−	3.44911i	−0.233980	−	0.119219i
$838$	10.8871	−	1.86020i	0.376087	−	0.0642596i
$839$	−6.64845	+	20.4618i	−0.229530	+	0.706420i	0.768270	+	0.640126i	$0.221118\pi$
$839$	−6.64845	+	20.4618i	−0.229530	+	0.706420i	−0.997800	+	0.0662946i	$0.978882\pi$
$840$		0			0
$841$	8.96148	+	27.5806i	0.309017	+	0.951055i
$842$	12.8542	+	24.4876i	0.442984	+	0.843898i
$843$	−11.7527	+	11.7527i	−0.404784	+	0.404784i
$844$	−16.4450	−	46.7183i	−0.566061	−	1.60811i
$845$		0			0
$846$	−0.0492969	−	4.05727i	−0.00169486	−	0.139492i
$847$	6.36430	+	40.1826i	0.218680	+	1.38069i
$848$	−36.6805	−	3.99481i	−1.25961	−	0.137182i
$849$		−	1.94116i		−	0.0666203i
$850$		0			0
$851$			31.9339i			1.09468i
$852$	15.8380	−	2.90460i	0.542601	−	0.0995100i
$853$	−5.12879	−	32.3819i	−0.175606	−	1.10873i	−0.905241	−	0.424898i	$-0.860310\pi$
$853$	−5.12879	−	32.3819i	−0.175606	−	1.10873i	0.729635	−	0.683837i	$-0.239690\pi$
$854$	−10.1490	+	0.123313i	−0.347292	+	0.00421969i
$855$		0			0
$856$	−5.88665	+	8.75642i	−0.201201	+	0.299288i
$857$	9.60872	−	9.60872i	0.328228	−	0.328228i	−0.523685	−	0.851912i	$-0.675443\pi$
$857$	9.60872	−	9.60872i	0.328228	−	0.328228i	0.851912	+	0.523685i	$0.175443\pi$
$858$	−1.17491	+	0.616741i	−0.0401108	+	0.0210552i
$859$	17.0359	+	52.4310i	0.581256	+	1.78892i	0.613813	+	0.789452i	$0.289635\pi$
$859$	17.0359	+	52.4310i	0.581256	+	1.78892i	−0.0325570	+	0.999470i	$0.510365\pi$
$860$		0			0
$861$	−5.68173	+	17.4866i	−0.193633	+	0.595941i
$862$	3.84657	+	22.5125i	0.131015	+	0.766779i
$863$	−2.70712	−	1.37935i	−0.0921515	−	0.0469535i	0.407307	−	0.913291i	$-0.366468\pi$
$863$	−2.70712	−	1.37935i	−0.0921515	−	0.0469535i	−0.499459	+	0.866338i	$0.666468\pi$
$864$	−5.81351	+	22.4479i	−0.197780	+	0.763692i
$865$		0			0
$866$	7.26965	+	5.14794i	0.247033	+	0.174934i
$867$	−2.90223	−	0.459668i	−0.0985648	−	0.0156111i
$868$	12.7090	−	6.86953i	0.431373	−	0.233167i
$869$	−1.58408	−	2.18030i	−0.0537363	−	0.0739616i
$870$		0			0
$871$	−5.02126	+	6.91117i	−0.170139	+	0.234176i
$872$	−4.02617	−	7.23706i	−0.136343	−	0.245078i
$873$	14.1057	−	7.18720i	0.477405	−	0.243250i
$874$	−27.3109	−	36.6455i	−0.923804	−	1.23955i
$875$		0			0
$876$	−10.1741	−	3.03454i	−0.343752	−	0.102527i
$877$	−12.3371	−	24.2129i	−0.416595	−	0.817613i	−0.999985	−	0.00542141i	$-0.998274\pi$
$877$	−12.3371	−	24.2129i	−0.416595	−	0.817613i	0.583391	−	0.812192i	$-0.301726\pi$
$878$	−28.9927	+	29.7059i	−0.978458	+	1.00253i
$879$	−11.2093	−	8.14404i	−0.378081	−	0.274692i
$880$		0			0
$881$	−4.42541	+	3.21525i	−0.149096	+	0.108325i	−0.659832	−	0.751413i	$-0.729373\pi$
$881$	−4.42541	+	3.21525i	−0.149096	+	0.108325i	0.510737	+	0.859737i	$0.329373\pi$
$882$	−4.06504	+	27.8516i	−0.136877	+	0.937814i
$883$	3.58180	−	22.6146i	0.120537	−	0.761041i	−0.851177	−	0.524879i	$-0.824110\pi$
$883$	3.58180	−	22.6146i	0.120537	−	0.761041i	0.971714	−	0.236162i	$-0.0758895\pi$
$884$	−0.368443	−	15.1597i	−0.0123921	−	0.509875i
$885$		0			0
$886$	3.44499	−	1.16581i	0.115737	−	0.0391660i
$887$	−21.2791	+	41.7627i	−0.714484	+	1.40225i	0.192589	+	0.981279i	$0.438312\pi$
$887$	−21.2791	+	41.7627i	−0.714484	+	1.40225i	−0.907073	+	0.420974i	$0.861688\pi$
$888$	−0.929787	+	7.67030i	−0.0312016	+	0.257398i
$889$	−41.6031	−	13.5177i	−1.39532	−	0.453368i
$890$		0			0
$891$	−2.99019	+	0.971570i	−0.100175	+	0.0325488i
$892$	0.667508	−	1.39271i	0.0223498	−	0.0466315i
$893$	3.05727	+	3.05727i	0.102308	+	0.102308i
$894$	−4.97424	+	15.9666i	−0.166363	+	0.534004i
$895$		0			0
$896$	−28.8546	−	33.3426i	−0.963965	−	1.11390i
$897$	10.9144	−	1.72867i	0.364422	−	0.0577188i
$898$	−12.1106	+	24.4997i	−0.404136	+	0.817567i
$899$	−0.0116895			−0.000389866
$900$		0			0
$901$	−42.1629			−1.40465
$902$	2.93455	−	5.93660i	0.0977099	−	0.197667i
$903$	25.0952	−	3.97468i	0.835115	−	0.132269i
$904$	−40.8296	−	11.6396i	−1.35797	−	0.387126i
$905$		0			0
$906$	4.17790	−	13.4105i	0.138801	−	0.445534i
$907$	37.7459	+	37.7459i	1.25333	+	1.25333i	0.954217	+	0.299114i	$0.0966911\pi$
$907$	37.7459	+	37.7459i	1.25333	+	1.25333i	0.299114	+	0.954217i	$0.403309\pi$
$908$	−15.2050	−	7.28756i	−0.504597	−	0.241846i
$909$	−19.0969	+	6.20495i	−0.633403	+	0.205805i
$910$		0			0
$911$	38.7405	+	12.5875i	1.28353	+	0.417044i	0.869822	−	0.493366i	$-0.164234\pi$
$911$	38.7405	+	12.5875i	1.28353	+	0.417044i	0.413707	+	0.910410i	$0.364234\pi$
$912$	−5.49292	−	9.59720i	−0.181889	−	0.317795i
$913$	0.670234	−	1.31541i	0.0221815	−	0.0435337i
$914$	30.2024	−	10.2207i	0.999005	−	0.338069i
$915$		0			0
$916$	46.9478	−	1.14103i	1.55120	−	0.0377006i
$917$	−0.671964	+	4.24262i	−0.0221902	+	0.140104i
$918$	−3.82686	+	26.2198i	−0.126305	+	0.865382i
$919$	−0.445380	+	0.323588i	−0.0146917	+	0.0106742i	−0.595107	−	0.803647i	$-0.702890\pi$
$919$	−0.445380	+	0.323588i	−0.0146917	+	0.0106742i	0.580415	+	0.814321i	$0.302890\pi$
$920$		0			0
$921$	−5.04702	−	3.66687i	−0.166305	−	0.120828i
$922$	−16.5253	+	16.9318i	−0.544233	+	0.557621i
$923$	8.03170	+	15.7631i	0.264367	+	0.518849i
$924$	−1.26021	+	4.22521i	−0.0414579	+	0.138999i
$925$		0			0
$926$	23.4107	+	31.4122i	0.769322	+	1.03227i
$927$	12.2309	−	6.23196i	0.401716	−	0.204684i
$928$	0.00771047	+	0.0348354i	0.000253109	+	0.00114353i
$929$	−0.175529	+	0.241595i	−0.00575892	+	0.00792648i	−0.811887	−	0.583815i	$-0.801559\pi$
$929$	−0.175529	+	0.241595i	−0.00575892	+	0.00792648i	0.806128	+	0.591741i	$0.201559\pi$
$930$		0			0
$931$	−17.6291	−	24.2644i	−0.577771	−	0.795233i
$932$	−2.11408	−	3.91117i	−0.0692489	−	0.128115i
$933$	−11.3947	−	1.80475i	−0.373046	−	0.0590847i
$934$	−11.9477	−	8.46066i	−0.390941	−	0.276841i
$935$		0			0
$936$	−11.3941	+	0.415488i	−0.372428	+	0.0135806i
$937$	−4.66050	−	2.37464i	−0.152252	−	0.0775762i	0.376205	−	0.926537i	$-0.377229\pi$
$937$	−4.66050	−	2.37464i	−0.152252	−	0.0775762i	−0.528456	+	0.848960i	$0.677229\pi$
$938$	4.78074	+	27.9799i	0.156097	+	0.913575i
$939$	6.25805	−	19.2603i	0.204224	−	0.628536i
$940$		0			0
$941$	17.5386	+	53.9783i	0.571743	+	1.75964i	0.647012	+	0.762480i	$0.276018\pi$
$941$	17.5386	+	53.9783i	0.571743	+	1.75964i	−0.0752692	+	0.997163i	$0.523982\pi$
$942$	−14.4039	+	7.56098i	−0.469305	+	0.246350i
$943$	−38.9961	+	38.9961i	−1.26989	+	1.26989i
$944$	59.2294	−	2.88074i	1.92775	−	0.0937602i
$945$		0			0
$946$	−9.15058	+	0.111182i	−0.297511	+	0.00361484i
$947$	−8.15849	−	51.5107i	−0.265115	−	1.67387i	−0.657026	−	0.753868i	$-0.728186\pi$
$947$	−8.15849	−	51.5107i	−0.265115	−	1.67387i	0.391911	−	0.920003i	$-0.371814\pi$
$948$	0.979530	+	5.34111i	0.0318137	+	0.173471i
$949$		−	11.6649i		−	0.378658i
$950$		0			0
$951$		−	2.76902i		−	0.0897917i
$952$	−36.9037	−	34.3070i	−1.19605	−	1.11190i
$953$	−7.71129	−	48.6871i	−0.249793	−	1.57713i	−0.719617	−	0.694371i	$-0.755683\pi$
$953$	−7.71129	−	48.6871i	−0.249793	−	1.57713i	0.469824	−	0.882760i	$-0.344317\pi$
$954$	0.385155	+	31.6992i	0.0124698	+	1.02630i
$955$		0			0
$956$	1.57593	−	0.554732i	0.0509691	−	0.0179413i
$957$	0.00252268	−	0.00252268i	8.15467e−5	−	8.15467e-5i
$958$	15.6425	+	29.7994i	0.505386	+	0.962776i
$959$	−9.07401	−	27.9269i	−0.293015	−	0.901807i
$960$		0			0
$961$	8.51805	−	26.2159i	0.274776	−	0.845673i
$962$	−8.36775	+	1.42974i	−0.269787	+	0.0460968i
$963$	8.07732	+	4.11560i	0.260288	+	0.132623i
$964$	−13.8180	+	20.0245i	−0.445048	+	0.644947i
$965$		0			0
$966$	21.2199	−	29.9657i	0.682740	−	0.964129i
$967$	42.4644	+	6.72570i	1.36556	+	0.216284i	0.795817	−	0.605537i	$-0.207041\pi$
$967$	42.4644	+	6.72570i	1.36556	+	0.216284i	0.569746	+	0.821821i	$0.307041\pi$
$968$	−12.4364	+	26.7776i	−0.399720	+	0.860666i
$969$	−7.42726	−	10.2227i	−0.238598	−	0.328402i
$970$		0			0
$971$	−21.5829	+	29.7063i	−0.692627	+	0.953319i	0.307372	+	0.951590i	$0.400551\pi$
$971$	−21.5829	+	29.7063i	−0.692627	+	0.953319i	−0.999999	+	0.00172953i	$0.999449\pi$
$972$	30.6578	+	4.09484i	0.983350	+	0.131342i
$973$	43.9900	−	22.4140i	1.41026	−	0.718561i
$974$	−27.5246	+	20.5133i	−0.881945	+	0.657289i
$975$		0			0
$976$	−6.16237	−	4.03492i	−0.197253	−	0.129155i
$977$	−1.15632	−	2.26941i	−0.0369940	−	0.0726048i	0.871770	−	0.489916i	$-0.162973\pi$
$977$	−1.15632	−	2.26941i	−0.0369940	−	0.0726048i	−0.908764	+	0.417311i	$0.862973\pi$
$978$	−8.60281	−	8.39626i	−0.275087	−	0.268483i
$979$	2.41718	+	1.75618i	0.0772533	+	0.0561278i
$980$		0			0
$981$	−5.75649	+	4.18234i	−0.183791	+	0.133532i
$982$	30.5984	+	4.46594i	0.976435	+	0.142514i
$983$	−5.62969	+	35.5444i	−0.179559	+	1.13369i	0.719055	+	0.694953i	$0.244575\pi$
$983$	−5.62969	+	35.5444i	−0.179559	+	1.13369i	−0.898615	+	0.438739i	$0.855425\pi$
$984$	−10.5020	+	8.23119i	−0.334792	+	0.262401i
$985$		0			0
$986$	0.0130688	+	0.0386188i	0.000416196	+	0.00122987i
$987$	−1.57700	+	3.09503i	−0.0501964	+	0.0985159i
$988$	8.37960	−	8.79707i	0.266591	−	0.279872i
$989$	72.4794	+	23.5500i	2.30471	+	0.748846i
$990$		0			0
$991$	−14.2120	+	4.61776i	−0.451459	+	0.146688i	−0.525916	−	0.850536i	$-0.676278\pi$
$991$	−14.2120	+	4.61776i	−0.451459	+	0.146688i	0.0744574	+	0.997224i	$0.476278\pi$
$992$	10.4357	+	1.00840i	0.331333	+	0.0320168i
$993$	8.14277	+	8.14277i	0.258403	+	0.258403i
$994$	56.1238	+	17.4848i	1.78014	+	0.554583i
$995$		0			0
$996$	−2.36335	+	1.80641i	−0.0748856	+	0.0572383i
$997$	25.8603	−	4.09586i	0.819003	−	0.129717i	0.267146	−	0.963656i	$-0.413919\pi$
$997$	25.8603	−	4.09586i	0.819003	−	0.129717i	0.551857	+	0.833939i	$0.313919\pi$
$998$	−12.4457	−	6.15209i	−0.393961	−	0.194741i
$999$	14.8336			0.469313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.2.l.d.243.3		96
4.3	odd	2	inner	500.2.l.d.243.6		96
5.2	odd	4		500.2.l.f.7.9		96
5.3	odd	4		100.2.l.b.47.4	yes	96
5.4	even	2		500.2.l.e.243.10		96
15.8	even	4		900.2.bj.d.847.9		96
20.3	even	4		100.2.l.b.47.1	✓	96
20.7	even	4		500.2.l.f.7.12		96
20.19	odd	2		500.2.l.e.243.7		96
25.6	even	5		500.2.l.f.143.12		96
25.8	odd	20		500.2.l.e.107.7		96
25.17	odd	20	inner	500.2.l.d.107.6		96
25.19	even	10		100.2.l.b.83.1	yes	96
60.23	odd	4		900.2.bj.d.847.12		96
75.44	odd	10		900.2.bj.d.883.12		96
100.19	odd	10		100.2.l.b.83.4	yes	96
100.31	odd	10		500.2.l.f.143.9		96
100.67	even	20	inner	500.2.l.d.107.3		96
100.83	even	20		500.2.l.e.107.10		96
300.119	even	10		900.2.bj.d.883.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.47.1	✓	96	20.3	even	4
100.2.l.b.47.4	yes	96	5.3	odd	4
100.2.l.b.83.1	yes	96	25.19	even	10
100.2.l.b.83.4	yes	96	100.19	odd	10
500.2.l.d.107.3		96	100.67	even	20	inner
500.2.l.d.107.6		96	25.17	odd	20	inner
500.2.l.d.243.3		96	1.1	even	1	trivial
500.2.l.d.243.6		96	4.3	odd	2	inner
500.2.l.e.107.7		96	25.8	odd	20
500.2.l.e.107.10		96	100.83	even	20
500.2.l.e.243.7		96	20.19	odd	2
500.2.l.e.243.10		96	5.4	even	2
500.2.l.f.7.9		96	5.2	odd	4
500.2.l.f.7.12		96	20.7	even	4
500.2.l.f.143.9		96	100.31	odd	10
500.2.l.f.143.12		96	25.6	even	5
900.2.bj.d.847.9		96	15.8	even	4
900.2.bj.d.847.12		96	60.23	odd	4
900.2.bj.d.883.9		96	300.119	even	10
900.2.bj.d.883.12		96	75.44	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	500.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26778 - 0.626683i) q^{2} +(0.745599 - 0.118091i) q^{3} +(1.21454 + 1.58899i) q^{4} +(-1.01926 - 0.317541i) q^{6} +(-2.75590 - 2.75590i) q^{7} +(-0.543971 - 2.77563i) q^{8} +(-2.31120 + 0.750953i) q^{9} +(-0.712633 - 0.231549i) q^{11} +(1.09320 + 1.04133i) q^{12} +(-0.753078 + 1.47800i) q^{13} +(1.76680 + 5.22095i) q^{14} +(-1.04980 + 3.85978i) q^{16} +(-0.715035 + 4.51455i) q^{17} +(3.40070 + 0.496343i) q^{18} +(-2.96269 + 2.15252i) q^{19} +(-2.38025 - 1.72935i) q^{21} +(0.758355 + 0.740148i) q^{22} +(-4.00635 - 7.86291i) q^{23} +(-0.733362 - 2.00527i) q^{24} +(1.88097 - 1.40184i) q^{26} +(-3.65239 + 1.86099i) q^{27} +(1.03197 - 7.72625i) q^{28} +(-0.00370724 + 0.00510258i) q^{29} +(1.08939 + 1.49941i) q^{31} +(3.74978 - 4.23547i) q^{32} +(-0.558683 - 0.0884866i) q^{33} +(3.73570 - 5.27537i) q^{34} +(-4.00029 - 2.76042i) q^{36} +(-3.22426 - 1.64284i) q^{37} +(5.10500 - 0.872258i) q^{38} +(-0.386956 + 1.19093i) q^{39} +(-1.93115 - 5.94348i) q^{41} +(1.93388 + 3.68410i) q^{42} +(-6.10648 + 6.10648i) q^{43} +(-0.497590 - 1.41359i) q^{44} +(0.151625 + 12.4792i) q^{46} +(-0.184694 - 1.16611i) q^{47} +(-0.326924 + 3.00182i) q^{48} +8.18997i q^{49} +3.45049i q^{51} +(-3.26317 + 0.598448i) q^{52} +(1.44300 + 9.11077i) q^{53} +(5.79668 - 0.0704313i) q^{54} +(-6.15022 + 9.14848i) q^{56} +(-1.95479 + 1.95479i) q^{57} +(0.00789767 - 0.00414569i) q^{58} +(-4.58114 - 14.0993i) q^{59} +(-0.569042 + 1.75133i) q^{61} +(-0.441448 - 2.58363i) q^{62} +(8.43898 + 4.29987i) q^{63} +(-7.40819 + 3.01972i) q^{64} +(0.652834 + 0.462299i) q^{66} +(5.08652 + 0.805626i) q^{67} +(-8.04203 + 4.34691i) q^{68} +(-3.91567 - 5.38946i) q^{69} +(6.26883 - 8.62831i) q^{71} +(3.34159 + 6.00652i) q^{72} +(-6.26568 + 3.19252i) q^{73} +(3.05811 + 4.10335i) q^{74} +(-7.01865 - 2.09338i) q^{76} +(1.32582 + 2.60207i) q^{77} +(1.23691 - 1.26734i) q^{78} +(2.90976 + 2.11406i) q^{79} +(3.39461 - 2.46633i) q^{81} +(-1.27640 + 8.74525i) q^{82} +(-0.308214 + 1.94599i) q^{83} +(-0.142970 - 5.88255i) q^{84} +(11.5685 - 3.91485i) q^{86} +(-0.00216155 + 0.00424227i) q^{87} +(-0.255040 + 2.10396i) q^{88} +(-3.79225 - 1.23218i) q^{89} +(6.14862 - 1.99781i) q^{91} +(7.62825 - 15.9159i) q^{92} +(0.989314 + 0.989314i) q^{93} +(-0.496631 + 1.59412i) q^{94} +(2.29566 - 3.60078i) q^{96} +(-6.43432 + 1.01910i) q^{97} +(5.13252 - 10.3831i) q^{98} +1.82092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 10 q^{4} - 6 q^{6} - 30 q^{8} + 20 q^{9} + 10 q^{14} - 14 q^{16} - 20 q^{18} - 12 q^{21} + 50 q^{22} - 12 q^{26} + 40 q^{28} + 20 q^{29} + 50 q^{32} + 60 q^{34} - 10 q^{36} + 40 q^{37} - 70 q^{38}+ \cdots + 70 q^{98}+O(q^{100}) \) 96 * q + 10 * q^4 - 6 * q^6 - 30 * q^8 + 20 * q^9 + 10 * q^14 - 14 * q^16 - 20 * q^18 - 12 * q^21 + 50 * q^22 - 12 * q^26 + 40 * q^28 + 20 * q^29 + 50 * q^32 + 60 * q^34 - 10 * q^36 + 40 * q^37 - 70 * q^38 - 28 * q^41 - 60 * q^42 - 60 * q^44 - 6 * q^46 + 100 * q^52 + 80 * q^53 - 120 * q^54 - 6 * q^56 + 20 * q^57 + 120 * q^58 + 12 * q^61 - 20 * q^64 - 30 * q^66 + 10 * q^68 + 20 * q^69 - 150 * q^72 - 140 * q^77 - 130 * q^78 - 36 * q^81 + 50 * q^82 + 90 * q^84 - 6 * q^86 + 110 * q^88 - 160 * q^89 + 90 * q^92 - 60 * q^93 + 170 * q^94 + 14 * q^96 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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