LMFDB - Embedded newform 100.2.l.b.47.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,2,Mod(3,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	100.l (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.798504020213$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	100.47
Dual form			100.2.l.b.83.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39401 - 0.238186i) q^{2} +(-0.118091 - 0.745599i) q^{3} +(1.88654 + 0.664067i) q^{4} +(0.0239387 + 2.23594i) q^{5} +(-0.0129704 + 1.06750i) q^{6} +(2.75590 - 2.75590i) q^{7} +(-2.47168 - 1.37506i) q^{8} +(2.31120 - 0.750953i) q^{9} +(0.499198 - 3.12263i) q^{10} +(0.712633 + 0.231549i) q^{11} +(0.272345 - 1.48502i) q^{12} +(-1.47800 - 0.753078i) q^{13} +(-4.49817 + 3.18534i) q^{14} +(1.66429 - 0.281894i) q^{15} +(3.11803 + 2.50557i) q^{16} +(4.51455 + 0.715035i) q^{17} +(-3.40070 + 0.496343i) q^{18} +(-2.96269 + 2.15252i) q^{19} +(-1.43965 + 4.23408i) q^{20} +(-2.38025 - 1.72935i) q^{21} +(-0.938267 - 0.492520i) q^{22} +(-7.86291 + 4.00635i) q^{23} +(-0.733362 + 2.00527i) q^{24} +(-4.99885 + 0.107051i) q^{25} +(1.88097 + 1.40184i) q^{26} +(-1.86099 - 3.65239i) q^{27} +(7.02921 - 3.36900i) q^{28} +(0.00370724 - 0.00510258i) q^{29} +(-2.38718 - 0.00344650i) q^{30} +(-1.08939 - 1.49941i) q^{31} +(-3.74978 - 4.23547i) q^{32} +(0.0884866 - 0.558683i) q^{33} +(-6.12303 - 2.07207i) q^{34} +(6.22800 + 6.09605i) q^{35} +(4.85884 + 0.118090i) q^{36} +(-1.64284 + 3.22426i) q^{37} +(4.64273 - 2.29497i) q^{38} +(-0.386956 + 1.19093i) q^{39} +(3.01539 - 5.55945i) q^{40} +(-1.93115 - 5.94348i) q^{41} +(2.90618 + 2.97767i) q^{42} +(6.10648 + 6.10648i) q^{43} +(1.19064 + 0.910061i) q^{44} +(1.73441 + 5.14972i) q^{45} +(11.9152 - 3.71207i) q^{46} +(1.16611 - 0.184694i) q^{47} +(1.49994 - 2.62069i) q^{48} -8.18997i q^{49} +(6.99396 + 1.04143i) q^{50} -3.45049i q^{51} +(-2.28820 - 2.40220i) q^{52} +(-9.11077 + 1.44300i) q^{53} +(1.72429 + 5.53473i) q^{54} +(-0.500669 + 1.59895i) q^{55} +(-10.6012 + 3.02217i) q^{56} +(1.95479 + 1.95479i) q^{57} +(-0.00638330 + 0.00623004i) q^{58} +(-4.58114 - 14.0993i) q^{59} +(3.32694 + 0.573397i) q^{60} +(-0.569042 + 1.75133i) q^{61} +(1.16148 + 2.34967i) q^{62} +(4.29987 - 8.43898i) q^{63} +(4.21840 + 6.79743i) q^{64} +(1.64846 - 3.32274i) q^{65} +(-0.256422 + 0.757734i) q^{66} +(-0.805626 + 5.08652i) q^{67} +(8.04203 + 4.34691i) q^{68} +(3.91567 + 5.38946i) q^{69} +(-7.22991 - 9.98139i) q^{70} +(-6.26883 + 8.62831i) q^{71} +(-6.74515 - 1.32192i) q^{72} +(-3.19252 - 6.26568i) q^{73} +(3.05811 - 4.10335i) q^{74} +(0.670139 + 3.71450i) q^{75} +(-7.01865 + 2.09338i) q^{76} +(2.60207 - 1.32582i) q^{77} +(0.823082 - 1.56800i) q^{78} +(2.90976 + 2.11406i) q^{79} +(-5.52767 + 7.03171i) q^{80} +(3.39461 - 2.46633i) q^{81} +(1.27640 + 8.74525i) q^{82} +(1.94599 + 0.308214i) q^{83} +(-3.34201 - 4.84312i) q^{84} +(-1.49070 + 10.1114i) q^{85} +(-7.05803 - 9.96698i) q^{86} +(-0.00424227 - 0.00216155i) q^{87} +(-1.44301 - 1.55223i) q^{88} +(3.79225 + 1.23218i) q^{89} +(-1.19120 - 7.59188i) q^{90} +(-6.14862 + 1.99781i) q^{91} +(-17.4941 + 2.33662i) q^{92} +(-0.989314 + 0.989314i) q^{93} +(-1.66956 - 0.0202857i) q^{94} +(-4.88383 - 6.57288i) q^{95} +(-2.71514 + 3.29600i) q^{96} +(1.01910 + 6.43432i) q^{97} +(-1.95073 + 11.4169i) q^{98} +1.82092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 10 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} - 10 q^{8} - 20 q^{9} - 10 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{14} - 14 q^{16} - 20 q^{17} + 20 q^{18} + 10 q^{20} - 12 q^{21} - 10 q^{22} - 20 q^{25}+ \cdots - 130 q^{98}+O(q^{100}) $ 96 * q - 10 * q^2 - 10 * q^4 - 20 * q^5 - 6 * q^6 - 10 * q^8 - 20 * q^9 - 10 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^14 - 14 * q^16 - 20 * q^17 + 20 * q^18 + 10 * q^20 - 12 * q^21 - 10 * q^22 - 20 * q^25 - 12 * q^26 - 10 * q^28 - 20 * q^29 - 10 * q^30 - 50 * q^32 - 20 * q^33 - 60 * q^34 - 10 * q^36 + 40 * q^37 + 20 * q^38 + 40 * q^40 - 28 * q^41 + 90 * q^42 + 60 * q^44 - 20 * q^45 - 6 * q^46 + 120 * q^48 + 80 * q^50 + 80 * q^52 - 40 * q^53 + 120 * q^54 - 6 * q^56 - 20 * q^57 + 60 * q^58 + 90 * q^60 + 12 * q^61 + 40 * q^62 + 20 * q^64 - 100 * q^65 - 30 * q^66 - 10 * q^68 - 20 * q^69 - 10 * q^70 - 40 * q^72 - 20 * q^73 - 20 * q^77 + 20 * q^78 - 10 * q^80 - 36 * q^81 - 50 * q^82 - 90 * q^84 + 100 * q^85 - 6 * q^86 - 130 * q^88 + 160 * q^89 - 160 * q^90 - 110 * q^92 + 60 * q^93 - 170 * q^94 + 14 * q^96 + 180 * q^97 - 130 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−1.39401	−	0.238186i	−0.985715	−	0.168423i
$2$	−1.39401	−	0.238186i	−0.985715	−	0.168423i
$3$	−0.118091	−	0.745599i	−0.0681801	−	0.430472i	−0.998041	−	0.0625612i	$-0.980073\pi$
$3$	−0.118091	−	0.745599i	−0.0681801	−	0.430472i	0.929861	−	0.367911i	$-0.119927\pi$
$4$	1.88654	+	0.664067i	0.943268	+	0.332034i
$5$	0.0239387	+	2.23594i	0.0107057	+	0.999943i
$5$	0.0239387	+	2.23594i	0.0107057	+	0.999943i
$6$	−0.0129704	+	1.06750i	−0.00529516	+	0.435806i
$7$	2.75590	−	2.75590i	1.04163	−	1.04163i	0.0425375	−	0.999095i	$-0.486456\pi$
$7$	2.75590	−	2.75590i	1.04163	−	1.04163i	0.999095	−	0.0425375i	$-0.0135442\pi$
$8$	−2.47168	−	1.37506i	−0.873871	−	0.486158i
$9$	2.31120	−	0.750953i	0.770399	−	0.250318i
$10$	0.499198	−	3.12263i	0.157860	−	0.987461i
$11$	0.712633	+	0.231549i	0.214867	+	0.0698145i	0.414473	−	0.910062i	$-0.363966\pi$
$11$	0.712633	+	0.231549i	0.214867	+	0.0698145i	−0.199606	+	0.979876i	$0.563966\pi$
$12$	0.272345	−	1.48502i	0.0786191	−	0.428688i
$13$	−1.47800	−	0.753078i	−0.409923	−	0.208866i	0.236854	−	0.971545i	$-0.423884\pi$
$13$	−1.47800	−	0.753078i	−0.409923	−	0.208866i	−0.646777	+	0.762679i	$0.723884\pi$
$14$	−4.49817	+	3.18534i	−1.20219	+	0.851318i
$15$	1.66429	−	0.281894i	0.429717	−	0.0727847i
$16$	3.11803	+	2.50557i	0.779507	+	0.626393i
$17$	4.51455	+	0.715035i	1.09494	+	0.173421i	0.677674	−	0.735363i	$-0.262988\pi$
$17$	4.51455	+	0.715035i	1.09494	+	0.173421i	0.417266	+	0.908784i	$0.362988\pi$
$18$	−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	$0.437995\pi$
$20$	−1.43965	+	4.23408i	−0.321916	+	0.946768i
$21$	−2.38025	−	1.72935i	−0.519412	−	0.377375i
$22$	−0.938267	−	0.492520i	−0.200039	−	0.105006i
$23$	−7.86291	+	4.00635i	−1.63953	+	0.835382i	−0.641884	+	0.766802i	$0.721847\pi$
$23$	−7.86291	+	4.00635i	−1.63953	+	0.835382i	−0.997646	+	0.0685797i	$0.978153\pi$
$24$	−0.733362	+	2.00527i	−0.149697	+	0.409323i
$25$	−4.99885	+	0.107051i	−0.999771	+	0.0214102i
$26$	1.88097	+	1.40184i	0.368889	+	0.274923i
$27$	−1.86099	−	3.65239i	−0.358147	−	0.702903i
$28$	7.02921	−	3.36900i	1.32839	−	0.636681i
$29$	0.00370724	−	0.00510258i	0.000688418	−	0.000947526i	−0.808673	−	0.588259i	$-0.799814\pi$
$29$	0.00370724	−	0.00510258i	0.000688418	−	0.000947526i	0.809361	+	0.587311i	$0.199814\pi$
$30$	−2.38718	−	0.00344650i	−0.435837	−	0.000629241i
$31$	−1.08939	−	1.49941i	−0.195660	−	0.269302i	0.699903	−	0.714238i	$-0.253227\pi$
$31$	−1.08939	−	1.49941i	−0.195660	−	0.269302i	−0.895563	+	0.444936i	$0.853227\pi$
$32$	−3.74978	−	4.23547i	−0.662873	−	0.748732i
$33$	0.0884866	−	0.558683i	0.0154035	−	0.0972542i
$34$	−6.12303	−	2.07207i	−1.05009	−	0.355357i
$35$	6.22800	+	6.09605i	1.05272	+	1.03042i
$36$	4.85884	+	0.118090i	0.809806	+	0.0196816i
$37$	−1.64284	+	3.22426i	−0.270082	+	0.530065i	−0.985717	−	0.168409i	$-0.946137\pi$
$37$	−1.64284	+	3.22426i	−0.270082	+	0.530065i	0.715636	+	0.698474i	$0.246137\pi$
$38$	4.64273	−	2.29497i	0.753150	−	0.372293i
$39$	−0.386956	+	1.19093i	−0.0619625	+	0.190701i
$40$	3.01539	−	5.55945i	0.476775	−	0.879025i
$41$	−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	$-0.262270\pi$
$42$	2.90618	+	2.97767i	0.448434	+	0.459465i
$43$	6.10648	+	6.10648i	0.931230	+	0.931230i	0.997783	−	0.0665532i	$-0.0212002\pi$
$43$	6.10648	+	6.10648i	0.931230	+	0.931230i	−0.0665532	+	0.997783i	$0.521200\pi$
$44$	1.19064	+	0.910061i	0.179496	+	0.137197i
$45$	1.73441	+	5.14972i	0.258551	+	0.767675i
$46$	11.9152	−	3.71207i	1.75681	−	0.547314i
$47$	1.16611	−	0.184694i	0.170095	−	0.0269404i	−0.0708061	−	0.997490i	$-0.522557\pi$
$47$	1.16611	−	0.184694i	0.170095	−	0.0269404i	0.240901	+	0.970550i	$0.422557\pi$
$48$	1.49994	−	2.62069i	0.216498	−	0.378264i
$49$		−	8.18997i		−	1.17000i
$50$	6.99396	+	1.04143i	0.989095	+	0.147280i
$51$		−	3.45049i		−	0.483165i
$52$	−2.28820	−	2.40220i	−0.317316	−	0.333125i
$53$	−9.11077	+	1.44300i	−1.25146	+	0.198212i	−0.746767	−	0.665086i	$-0.768395\pi$
$53$	−9.11077	+	1.44300i	−1.25146	+	0.198212i	−0.504694	+	0.863298i	$0.668395\pi$
$54$	1.72429	+	5.53473i	0.234646	+	0.753182i
$55$	−0.500669	+	1.59895i	−0.0675102	+	0.215602i
$56$	−10.6012	+	3.02217i	−1.41665	+	0.403854i
$57$	1.95479	+	1.95479i	0.258918	+	0.258918i
$58$	−0.00638330	+	0.00623004i	−0.000838168	+	0.000818045i
$59$	−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	$-0.515556\pi$
$60$	3.32694	+	0.573397i	0.429505	+	0.0740252i
$61$	−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	$0.137612\pi$
$62$	1.16148	+	2.34967i	0.147508	+	0.298409i
$63$	4.29987	−	8.43898i	0.541733	−	1.06321i
$64$	4.21840	+	6.79743i	0.527301	+	0.849679i
$65$	1.64846	−	3.32274i	0.204466	−	0.412136i
$66$	−0.256422	+	0.757734i	−0.0315633	+	0.0932706i
$67$	−0.805626	+	5.08652i	−0.0984228	+	0.621417i	0.888332	+	0.459201i	$0.151864\pi$
$67$	−0.805626	+	5.08652i	−0.0984228	+	0.621417i	−0.986755	+	0.162216i	$0.948136\pi$
$68$	8.04203	+	4.34691i	0.975240	+	0.527140i
$69$	3.91567	+	5.38946i	0.471392	+	0.648815i
$70$	−7.22991	−	9.98139i	−0.864139	−	1.19300i
$71$	−6.26883	+	8.62831i	−0.743973	+	1.02399i	0.254407	+	0.967097i	$0.418120\pi$
$71$	−6.26883	+	8.62831i	−0.743973	+	1.02399i	−0.998380	+	0.0568943i	$0.981880\pi$
$72$	−6.74515	−	1.32192i	−0.794923	−	0.155790i
$73$	−3.19252	−	6.26568i	−0.373656	−	0.733342i	0.625234	−	0.780437i	$-0.285004\pi$
$73$	−3.19252	−	6.26568i	−0.373656	−	0.733342i	−0.998890	+	0.0470953i	$0.985004\pi$
$74$	3.05811	−	4.10335i	0.355498	−	0.477005i
$75$	0.670139	+	3.71450i	0.0773809	+	0.428914i
$76$	−7.01865	+	2.09338i	−0.805094	+	0.240127i
$77$	2.60207	−	1.32582i	0.296533	−	0.151091i
$78$	0.823082	−	1.56800i	0.0931957	−	0.177541i
$79$	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	$0.635149\pi$
$80$	−5.52767	+	7.03171i	−0.618012	+	0.786169i
$81$	3.39461	−	2.46633i	0.377179	−	0.274036i
$82$	1.27640	+	8.74525i	0.140955	+	0.965751i
$83$	1.94599	+	0.308214i	0.213600	+	0.0338309i	0.262317	−	0.964982i	$-0.415513\pi$
$83$	1.94599	+	0.308214i	0.213600	+	0.0338309i	−0.0487173	+	0.998813i	$0.515513\pi$
$84$	−3.34201	−	4.84312i	−0.364643	−	0.528428i
$85$	−1.49070	+	10.1114i	−0.161689	+	1.09673i
$86$	−7.05803	−	9.96698i	−0.761087	−	1.07477i
$87$	−0.00424227	−	0.00216155i	−0.000454820	−	0.000231742i
$88$	−1.44301	−	1.55223i	−0.153825	−	0.165468i
$89$	3.79225	+	1.23218i	0.401978	+	0.130611i	0.503027	−	0.864271i	$-0.332220\pi$
$89$	3.79225	+	1.23218i	0.401978	+	0.130611i	−0.101049	+	0.994881i	$0.532220\pi$
$90$	−1.19120	−	7.59188i	−0.125564	−	0.800254i
$91$	−6.14862	+	1.99781i	−0.644551	+	0.209427i
$92$	−17.4941	+	2.33662i	−1.82389	+	0.243610i
$93$	−0.989314	+	0.989314i	−0.102587	+	0.102587i
$94$	−1.66956	−	0.0202857i	−0.172202	−	0.00209231i
$95$	−4.88383	−	6.57288i	−0.501071	−	0.674363i
$96$	−2.71514	+	3.29600i	−0.277113	+	0.336397i
$97$	1.01910	+	6.43432i	0.103474	+	0.653306i	0.983845	+	0.179022i	$0.0572932\pi$
$97$	1.01910	+	6.43432i	0.103474	+	0.653306i	−0.880372	+	0.474285i	$0.842707\pi$
$98$	−1.95073	+	11.4169i	−0.197054	+	1.15328i
$99$	1.82092			0.183009
$100$	−9.50160	−	3.11762i	−0.950160	−	0.311762i
$101$	8.26277			0.822176			0.411088	−	0.911596i	$-0.365149\pi$
$101$	8.26277			0.822176			0.411088	+	0.911596i	$0.365149\pi$
$102$	−0.821857	+	4.81002i	−0.0813760	+	0.476263i
$103$	0.883649	+	5.57914i	0.0870685	+	0.549729i	0.992206	+	0.124610i	$0.0397679\pi$
$103$	0.883649	+	5.57914i	0.0870685	+	0.549729i	−0.905137	+	0.425119i	$0.860232\pi$
$104$	2.61761	+	3.89371i	0.256678	+	0.381809i
$105$	3.80974	−	5.36348i	0.371793	−	0.523422i
$106$	13.0442	+	0.158491i	1.26697	+	0.0153940i
$107$	2.63780	−	2.63780i	0.255005	−	0.255005i	−0.568014	−	0.823019i	$-0.692288\pi$
$107$	2.63780	−	2.63780i	0.255005	−	0.255005i	0.823019	+	0.568014i	$0.192288\pi$
$108$	−1.08538	−	8.12618i	−0.104441	−	0.781942i
$109$	−2.78468	+	0.904799i	−0.266724	+	0.0866640i	−0.439326	−	0.898328i	$-0.644783\pi$
$109$	−2.78468	+	0.904799i	−0.266724	+	0.0866640i	0.172602	+	0.984992i	$0.444783\pi$
$110$	1.07878	−	2.10970i	0.102858	−	0.201152i
$111$	2.59801	+	0.844145i	0.246592	+	0.0801227i
$112$	15.4981	−	1.68787i	1.46443	−	0.159489i
$113$	13.3745	+	6.81465i	1.25817	+	0.641068i	0.950588	−	0.310455i	$-0.100481\pi$
$113$	13.3745	+	6.81465i	1.25817	+	0.641068i	0.307579	+	0.951523i	$0.400481\pi$
$114$	−2.25939	−	3.19060i	−0.211612	−	0.298827i
$115$	−9.14619	−	17.4851i	−0.852886	−	1.63049i
$116$	0.0103823	−	0.00716434i	0.000963972	−	0.000665192i
$117$	−3.98147	−	0.630603i	−0.368087	−	0.0582993i
$118$	3.02791	+	20.7457i	0.278741	+	1.90980i
$119$	14.4122	−	10.4711i	1.32117	−	0.959884i
$120$	−4.50121	−	1.59175i	−0.410902	−	0.145306i
$121$	−8.44496	−	6.13562i	−0.767723	−	0.557784i
$122$	1.21039	−	2.30584i	0.109584	−	0.208761i
$123$	−4.20340	+	2.14174i	−0.379008	+	0.193114i
$124$	−1.05946	−	3.55212i	−0.0951420	−	0.318990i
$125$	−0.359026	−	11.1746i	−0.0321123	−	0.999484i
$126$	−8.00412	+	10.7399i	−0.713064	+	0.956783i
$127$	5.09550	+	10.0005i	0.452153	+	0.887400i	0.998749	+	0.0500037i	$0.0159233\pi$
$127$	5.09550	+	10.0005i	0.452153	+	0.887400i	−0.546596	+	0.837396i	$0.684077\pi$
$128$	−4.26145	−	10.4805i	−0.376663	−	0.926350i
$129$	3.83187	−	5.27411i	0.337377	−	0.464360i
$130$	−3.08939	+	4.23930i	−0.270958	+	0.371811i
$131$	0.647820	+	0.891647i	0.0566003	+	0.0779036i	0.836379	−	0.548152i	$-0.184668\pi$
$131$	0.647820	+	0.891647i	0.0566003	+	0.0779036i	−0.779779	+	0.626055i	$0.784668\pi$
$132$	0.537936	−	0.995213i	0.0468213	−	0.0866222i
$133$	−2.23275	+	14.0970i	−0.193604	+	1.22237i
$134$	2.33459	−	6.89878i	0.201678	−	0.595964i
$135$	8.12198	−	4.24849i	0.699028	−	0.365651i
$136$	−10.1753	−	7.97513i	−0.872526	−	0.683862i
$137$	3.42046	−	6.71304i	0.292230	−	0.573534i	−0.697483	−	0.716601i	$-0.745697\pi$
$137$	3.42046	−	6.71304i	0.292230	−	0.573534i	0.989713	+	0.143068i	$0.0456967\pi$
$138$	−4.17480	−	8.44563i	−0.355383	−	0.718940i
$139$	−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	$0.919472\pi$
$140$	7.70115	+	15.6362i	0.650866	+	1.32150i
$141$	−0.275415	−	0.847641i	−0.0231941	−	0.0713842i
$142$	10.7940	−	10.5348i	0.905809	−	0.884062i
$143$	−0.878896	−	0.878896i	−0.0734970	−	0.0734970i
$144$	9.08795	+	3.44937i	0.757329	+	0.287448i
$145$	0.0114978	+	0.00816702i	0.000954841	+	0.000678234i
$146$	2.95802	+	9.49484i	0.244807	+	0.785798i
$147$	−6.10644	+	0.967165i	−0.503651	+	0.0797704i
$148$	−5.24040	+	4.99172i	−0.430759	+	0.410317i
$149$			15.6649i			1.28332i	0.766990	+	0.641659i	$0.221753\pi$
$149$			15.6649i			1.28332i	−0.766990	+	0.641659i	$0.778247\pi$
$150$	−0.0494399	−	5.33767i	−0.00403675	−	0.435819i
$151$		−	13.1571i		−	1.07071i	−0.844628	−	0.535353i	$-0.820179\pi$
$151$		−	13.1571i		−	1.07071i	0.844628	−	0.535353i	$-0.179821\pi$
$152$	10.2827	−	1.24646i	0.834036	−	0.101101i
$153$	10.9710	−	1.73763i	0.886951	−	0.140479i
$154$	−3.94311	+	1.22843i	−0.317745	+	0.0989900i
$155$	3.32652	−	2.47170i	0.267192	−	0.198532i
$156$	−1.52086	+	1.98976i	−0.121766	+	0.159308i
$157$	−10.7749	−	10.7749i	−0.859930	−	0.859930i	0.131400	−	0.991329i	$-0.458053\pi$
$157$	−10.7749	−	10.7749i	−0.859930	−	0.859930i	−0.991329	+	0.131400i	$0.958053\pi$
$158$	−3.55270	−	3.64009i	−0.282637	−	0.289590i
$159$	2.15181	+	6.62258i	0.170649	+	0.525205i
$160$	9.38048	−	8.48567i	0.741592	−	0.670851i
$161$	−10.6283	+	32.7105i	−0.837626	+	2.57795i
$162$	−5.31957	+	2.62954i	−0.417945	+	0.206596i
$163$	5.11197	−	10.0328i	0.400401	−	0.785830i	−0.599494	−	0.800380i	$-0.704631\pi$
$163$	5.11197	−	10.0328i	0.400401	−	0.785830i	0.999894	+	0.0145493i	$0.00463134\pi$
$164$	0.303680	−	12.4950i	0.0237134	−	0.975695i
$165$	1.25130	+	0.184477i	0.0974135	+	0.0143615i
$166$	−2.63932	−	0.893160i	−0.204851	−	0.0693227i
$167$	0.686207	−	4.33254i	0.0531003	−	0.335262i	−0.946809	−	0.321796i	$-0.895714\pi$
$167$	0.686207	−	4.33254i	0.0531003	−	0.335262i	0.999909	−	0.0134660i	$-0.00428650\pi$
$168$	3.50524	+	7.54739i	0.270435	+	0.582293i
$169$	−6.02386	−	8.29113i	−0.463374	−	0.637779i
$170$	4.48644	−	13.7403i	0.344095	−	1.05383i
$171$	−5.23092	+	7.19975i	−0.400019	+	0.550579i
$172$	7.46498	+	15.5752i	0.569199	+	1.18760i
$173$	−7.43280	−	14.5877i	−0.565105	−	1.10908i	−0.979960	−	0.199194i	$-0.936168\pi$
$173$	−7.43280	−	14.5877i	−0.565105	−	1.10908i	0.414855	−	0.909888i	$-0.363832\pi$
$174$	0.00539893	+	0.00402367i	0.000409292	+	0.000305034i
$175$	−13.4813	+	14.0714i	−1.01909	+	1.06370i
$176$	1.64185	+	2.50753i	0.123759	+	0.189012i
$177$	−9.97143	+	5.08070i	−0.749498	+	0.381888i
$178$	−4.99296	−	2.62093i	−0.374238	−	0.196447i
$179$	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	$0.534288\pi$
$180$	−0.147727	+	10.8669i	−0.0110110	+	0.809970i
$181$	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
$183$	1.37299	+	0.217460i	0.101494	+	0.0160751i
$184$	24.9436	+	0.909572i	1.83886	+	0.0670545i
$185$	−7.24858	−	3.59611i	−0.532926	−	0.264391i
$186$	1.61476	−	1.14347i	0.118400	−	0.0838436i
$187$	3.05166	+	1.55490i	0.223159	+	0.113705i
$188$	2.32256	+	0.425945i	0.169390	+	0.0310652i
$189$	−15.1943	−	4.93693i	−1.10522	−	0.359109i
$190$	5.24256	+	10.3259i	0.380335	+	0.749121i
$191$	9.06811	−	2.94641i	0.656145	−	0.213194i	0.0380234	−	0.999277i	$-0.487894\pi$
$191$	9.06811	−	2.94641i	0.656145	−	0.213194i	0.618122	+	0.786082i	$0.287894\pi$
$192$	4.57000	−	3.94796i	0.329812	−	0.284919i
$193$	6.86588	−	6.86588i	0.494217	−	0.494217i	−0.415415	−	0.909632i	$-0.636364\pi$
$193$	6.86588	−	6.86588i	0.494217	−	0.494217i	0.909632	+	0.415415i	$0.136364\pi$
$194$	0.111931	−	9.21225i	0.00803620	−	0.661401i
$195$	−2.67210	−	0.836700i	−0.191353	−	0.0599173i
$196$	5.43869	−	15.4507i	0.388478	−	1.10362i
$197$	−2.05905	−	13.0003i	−0.146701	−	0.926237i	−0.945732	−	0.324947i	$-0.894654\pi$
$197$	−2.05905	−	13.0003i	−0.146701	−	0.926237i	0.799031	−	0.601290i	$-0.205346\pi$
$198$	−2.53838	−	0.433716i	−0.180395	−	0.0308229i
$199$	−25.8172			−1.83013			−0.915067	−	0.403302i	$-0.867863\pi$
$199$	−25.8172			−1.83013			−0.915067	+	0.403302i	$0.867863\pi$
$200$	12.5028	+	6.60914i	0.884079	+	0.467337i
$201$	3.88764			0.274213
$202$	−11.5184	−	1.96807i	−0.810431	−	0.138473i
$203$	−0.00384542	−	0.0242790i	−0.000269895	−	0.00170405i
$204$	2.29136	−	6.50947i	0.160427	−	0.455754i
$205$	13.2430	−	4.46022i	0.924933	−	0.311515i
$206$	0.0970547	−	7.98786i	0.00676212	−	0.556541i
$207$	−15.1641	+	15.1641i	−1.05398	+	1.05398i
$208$	−2.72155	−	6.05135i	−0.188706	−	0.419586i
$209$	−2.60973	+	0.847952i	−0.180519	+	0.0586540i
$210$	−6.58833	+	6.56933i	−0.454638	+	0.453327i
$211$	23.5520	+	7.65252i	1.62139	+	0.526821i	0.972269	−	0.233865i	$-0.0751373\pi$
$211$	23.5520	+	7.65252i	1.62139	+	0.526821i	0.649120	+	0.760686i	$0.275137\pi$
$212$	−18.1460	−	3.32789i	−1.24628	−	0.228560i
$213$	7.17356	+	3.65511i	0.491524	+	0.250444i
$214$	−4.30540	+	3.04883i	−0.294311	+	0.208414i
$215$	−13.5075	+	13.7999i	−0.921207	+	0.941146i
$216$	−0.422504	+	11.5865i	−0.0287478	+	0.788362i
$217$	−7.13447	−	1.12999i	−0.484320	−	0.0767087i
$218$	4.09739	−	0.598028i	0.277510	−	0.0405036i
$219$	−4.29468	+	3.12027i	−0.290207	+	0.210848i
$220$	−2.00634	+	2.68399i	−0.135267	+	0.180955i
$221$	−6.13403	−	4.45663i	−0.412619	−	0.299785i
$222$	−3.42059	−	1.79556i	−0.229575	−	0.120510i
$223$	−0.688042	+	0.350575i	−0.0460747	+	0.0234762i	−0.476876	−	0.878971i	$-0.658231\pi$
$223$	−0.688042	+	0.350575i	−0.0460747	+	0.0234762i	0.430801	+	0.902447i	$0.358231\pi$
$224$	−22.0065	−	1.33851i	−1.47037	−	0.0894329i
$225$	−11.4729	+	4.00132i	−0.764863	+	0.266755i
$226$	−17.0210	−	12.6853i	−1.13222	−	0.843814i
$227$	−3.82742	−	7.51174i	−0.254035	−	0.498572i	0.728406	−	0.685146i	$-0.240262\pi$
$227$	−3.82742	−	7.51174i	−0.254035	−	0.498572i	−0.982441	+	0.186574i	$0.940262\pi$
$228$	2.38967	+	4.98589i	0.158260	+	0.330198i
$229$	−13.8017	+	18.9964i	−0.912042	+	1.25532i	0.0544226	+	0.998518i	$0.482668\pi$
$229$	−13.8017	+	18.9964i	−0.912042	+	1.25532i	−0.966465	+	0.256800i	$0.917332\pi$
$230$	8.58519	+	26.5529i	0.566091	+	1.75085i
$231$	−1.29581	−	1.78353i	−0.0852583	−	0.117348i
$232$	−0.0161795	+	0.00751426i	−0.00106224	+	0.000493335i
$233$	0.347751	−	2.19561i	0.0227819	−	0.143839i	−0.973675	−	0.227939i	$-0.926801\pi$
$233$	0.347751	−	2.19561i	0.0227819	−	0.143839i	0.996457	+	0.0840996i	$0.0268014\pi$
$234$	5.40001	+	1.82740i	0.353010	+	0.119461i
$235$	0.440880	+	2.60293i	0.0287598	+	0.169797i
$236$	0.720398	−	29.6410i	0.0468939	−	1.92946i
$237$	1.23263	−	2.41917i	0.0800677	−	0.157142i
$238$	−22.5849	+	11.1640i	−1.46396	+	0.723657i
$239$	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	$0.0913991\pi$
$240$	5.89561	+	3.29104i	0.380560	+	0.212436i
$241$	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	$0.771853\pi$
$242$	10.3109	+	10.5646i	0.662813	+	0.679118i
$243$	−10.9354	−	10.9354i	−0.701508	−	0.701508i
$244$	−2.23652	+	2.92606i	−0.143178	+	0.187322i
$245$	18.3123	−	0.196057i	1.16993	−	0.0125257i
$246$	6.36972	−	1.98442i	0.406118	−	0.126522i
$247$	5.99987	−	0.950287i	0.381763	−	0.0604653i
$248$	0.630830	+	5.20404i	0.0400577	+	0.330457i
$249$		−	1.48732i		−	0.0942554i
$250$	−2.16114	+	15.6630i	−0.136682	+	0.990615i
$251$		−	5.53474i		−	0.349350i	−0.984626	−	0.174675i	$-0.944113\pi$
$251$		−	5.53474i		−	0.349350i	0.984626	−	0.174675i	$-0.0558875\pi$
$252$	13.7159	−	13.0650i	0.864021	−	0.823019i
$253$	−6.53103	+	1.03441i	−0.410602	+	0.0650330i
$254$	−4.72122	−	15.1545i	−0.296236	−	0.950876i
$255$	7.71508	−	0.0826003i	0.483137	−	0.00517263i
$256$	3.44422	+	15.6249i	0.215264	+	0.976556i
$257$	13.0870	+	13.0870i	0.816347	+	0.816347i	0.985577	−	0.169230i	$-0.0541280\pi$
$257$	13.0870	+	13.0870i	0.816347	+	0.816347i	−0.169230	+	0.985577i	$0.554128\pi$
$258$	−6.59788	+	6.43948i	−0.410766	+	0.400904i
$259$	4.35823	+	13.4132i	0.270807	+	0.833459i
$260$	5.31639	−	5.17379i	0.329709	−	0.320865i
$261$	0.00473637	−	0.0145770i	0.000293174	−	0.000902296i
$262$	−0.690690	−	1.39727i	−0.0426710	−	0.0863235i
$263$	5.31614	−	10.4335i	0.327807	−	0.643358i	−0.667009	−	0.745050i	$-0.732426\pi$
$263$	5.31614	−	10.4335i	0.327807	−	0.643358i	0.994816	+	0.101692i	$0.0324257\pi$
$264$	−0.986934	+	1.25921i	−0.0607416	+	0.0774990i
$265$	−3.44457	−	20.3366i	−0.211598	−	1.24927i
$266$	6.47019	−	19.1196i	0.396713	−	1.17230i
$267$	0.470879	−	2.97301i	0.0288173	−	0.181945i
$268$	−4.89763	+	9.06091i	−0.299171	+	0.553483i
$269$	2.93900	+	4.04519i	0.179194	+	0.246640i	0.889160	−	0.457597i	$-0.151290\pi$
$269$	2.93900	+	4.04519i	0.179194	+	0.246640i	−0.709966	+	0.704236i	$0.751290\pi$
$270$	−12.3341	+	3.98790i	−0.750627	+	0.242696i
$271$	14.8746	−	20.4731i	0.903565	−	1.24365i	−0.0657513	−	0.997836i	$-0.520944\pi$
$271$	14.8746	−	20.4731i	0.903565	−	1.24365i	0.969317	−	0.245815i	$-0.0790556\pi$
$272$	12.2849	+	13.5410i	0.744884	+	0.821046i
$273$	2.21566	+	4.34849i	0.134098	+	0.263182i
$274$	−6.36712	+	8.54335i	−0.384652	+	0.516122i
$275$	−3.58714	−	1.08119i	−0.216312	−	0.0651981i
$276$	3.80809	+	12.7677i	0.229220	+	0.768524i
$277$	13.6603	−	6.96028i	0.820769	−	0.418203i	0.00741564	−	0.999973i	$-0.497640\pi$
$277$	13.6603	−	6.96028i	0.820769	−	0.418203i	0.813354	+	0.581770i	$0.197640\pi$
$278$	8.32644	−	15.8621i	0.499387	−	0.951348i
$279$	−3.64378	−	2.64736i	−0.218147	−	0.158493i
$280$	−7.01117	−	23.6314i	−0.418997	−	1.41225i
$281$	−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
$283$	−2.53977	−	0.402261i	−0.150974	−	0.0239119i	0.0804900	−	0.996755i	$-0.474351\pi$
$283$	−2.53977	−	0.402261i	−0.150974	−	0.0239119i	−0.231464	+	0.972844i	$0.574351\pi$
$284$	−17.5561	+	12.1147i	−1.04177	+	0.718874i
$285$	−4.32399	+	4.41758i	−0.256131	+	0.261675i
$286$	1.01585	+	1.43453i	0.0600685	+	0.0848257i
$287$	−21.7017	−	11.0576i	−1.28101	−	0.652707i
$288$	−11.8471	−	6.97309i	−0.698098	−	0.410893i
$289$	3.70196	+	1.20284i	0.217763	+	0.0707554i
$290$	−0.0140828	−	0.0141235i	−0.000826971	−	0.000829363i
$291$	4.67708	−	1.51967i	0.274175	−	0.0890849i
$292$	−1.86198	−	13.9405i	−0.108964	−	0.815804i
$293$	12.9784	−	12.9784i	0.758205	−	0.758205i	−0.217790	−	0.975996i	$-0.569885\pi$
$293$	12.9784	−	12.9784i	0.758205	−	0.758205i	0.975996	+	0.217790i	$0.0698849\pi$
$294$	8.74281	+	0.106228i	0.509891	+	0.00619532i
$295$	31.4155	−	10.5807i	1.82908	−	0.616030i
$296$	8.49414	−	5.71033i	0.493712	−	0.331906i
$297$	−0.480494	−	3.03372i	−0.0278811	−	0.176034i
$298$	3.73115	−	21.8370i	0.216140	−	1.26498i
$299$	14.6385			0.846564
$300$	−1.20244	+	7.45255i	−0.0694228	+	0.430273i
$301$	33.6577			1.94000
$302$	−3.13382	+	18.3411i	−0.180331	+	1.05541i
$303$	−0.975761	−	6.16071i	−0.0560560	−	0.353924i
$304$	−14.6311	−	0.711611i	−0.839149	−	0.0408137i
$305$	−3.92949	−	1.23042i	−0.225002	−	0.0704535i
$306$	−15.7076	−	0.190851i	−0.897941	−	0.0109102i
$307$	5.84355	−	5.84355i	0.333509	−	0.333509i	−0.520409	−	0.853917i	$-0.674220\pi$
$307$	5.84355	−	5.84355i	0.333509	−	0.333509i	0.853917	+	0.520409i	$0.174220\pi$
$308$	5.78933	−	0.773259i	0.329878	−	0.0440605i
$309$	4.05545	−	1.31770i	0.230707	−	0.0749611i
$310$	−5.22593	+	2.65325i	−0.296813	+	0.150694i
$311$	14.5346	+	4.72259i	0.824184	+	0.267794i	0.690594	−	0.723243i	$-0.257349\pi$
$311$	14.5346	+	4.72259i	0.824184	+	0.267794i	0.133590	+	0.991037i	$0.457349\pi$
$312$	2.59403	−	2.41150i	0.146858	−	0.136524i
$313$	23.9030	+	12.1792i	1.35108	+	0.688408i	0.971564	−	0.236778i	$-0.0760915\pi$
$313$	23.9030	+	12.1792i	1.35108	+	0.688408i	0.379513	+	0.925186i	$0.376092\pi$
$314$	12.4539	+	17.5867i	0.702814	+	0.992477i
$315$	18.9720	+	9.41224i	1.06895	+	0.530320i
$316$	4.08548	+	5.92053i	0.229826	+	0.333056i
$317$	−3.62294	−	0.573817i	−0.203484	−	0.0322288i	0.0538600	−	0.998548i	$-0.482848\pi$
$317$	−3.62294	−	0.573817i	−0.203484	−	0.0322288i	−0.257345	+	0.966320i	$0.582848\pi$
$318$	−1.42224	−	9.74448i	−0.0797552	−	0.546443i
$319$	0.00382340	−	0.00277786i	0.000214069	−	0.000155530i
$320$	−15.0977	+	9.59482i	−0.843985	+	0.536367i
$321$	−2.27824	−	1.65524i	−0.127159	−	0.0923864i
$322$	22.6071	−	43.0673i	1.25985	−	2.40005i
$323$	−14.9144	+	7.59925i	−0.829858	+	0.422834i
$324$	8.04186	−	2.39857i	0.446770	−	0.133254i
$325$	7.46892	+	3.60630i	0.414301	+	0.200042i
$326$	−9.51582	+	12.7683i	−0.527032	+	0.707168i
$327$	1.00346	+	1.96941i	0.0554917	+	0.108909i
$328$	−3.39946	+	17.3458i	−0.187704	+	0.957763i
$329$	2.70469	−	3.72268i	0.149114	−	0.205238i
$330$	−1.70039	−	0.555204i	−0.0936031	−	0.0305630i
$331$	−8.96644	−	12.3412i	−0.492840	−	0.678336i	0.488069	−	0.872805i	$-0.337702\pi$
$331$	−8.96644	−	12.3412i	−0.492840	−	0.678336i	−0.980909	+	0.194469i	$0.937702\pi$
$332$	3.46650	+	1.87372i	0.190249	+	0.102834i
$333$	−1.37566	+	8.68560i	−0.0753859	+	0.475968i
$334$	−1.98853	+	5.87616i	−0.108807	+	0.321529i
$335$	−11.3924	−	1.67957i	−0.622435	−	0.0917645i
$336$	−3.08867	−	11.3560i	−0.168501	−	0.619523i
$337$	−13.2695	+	26.0429i	−0.722838	+	1.41865i	0.177795	+	0.984068i	$0.443104\pi$
$337$	−13.2695	+	26.0429i	−0.722838	+	1.41865i	−0.900633	+	0.434581i	$0.856896\pi$
$338$	6.42250	+	12.9927i	0.349338	+	0.706711i
$339$	3.50158	−	10.7768i	0.190180	−	0.585314i
$340$	−9.52690	+	18.0856i	−0.516669	+	0.980827i
$341$	−0.429146	−	1.32078i	−0.0232396	−	0.0715241i
$342$	9.00684	−	8.79060i	0.487034	−	0.475341i
$343$	−3.27944	−	3.27944i	−0.177073	−	0.177073i
$344$	−6.69647	−	23.4901i	−0.361050	−	1.26650i
$345$	−11.9568	+	8.88423i	−0.643731	+	0.478311i
$346$	6.88683	+	22.1058i	0.370238	+	1.18842i
$347$	2.48682	−	0.393873i	0.133499	−	0.0211442i	−0.0893271	−	0.996002i	$-0.528472\pi$
$347$	2.48682	−	0.393873i	0.133499	−	0.0211442i	0.222827	+	0.974858i	$0.428472\pi$
$348$	−0.00656779	−	0.00689499i	−0.000352070	−	0.000369610i
$349$		−	18.8483i		−	1.00893i	−0.863434	−	0.504463i	$-0.831691\pi$
$349$		−	18.8483i		−	1.00893i	0.863434	−	0.504463i	$-0.168309\pi$
$350$	22.1447	−	16.4046i	1.18368	−	0.876862i
$351$			6.79969i			0.362941i
$352$	−1.69150	−	3.88659i	−0.0901572	−	0.207156i
$353$	−22.1139	+	3.50250i	−1.17700	+	0.186419i	−0.714135	−	0.700008i	$-0.753180\pi$
$353$	−22.1139	+	3.50250i	−1.17700	+	0.186419i	−0.462869	+	0.886427i	$0.653180\pi$
$354$	15.1104	−	4.70750i	0.803110	−	0.250201i
$355$	−19.4424	−	13.8102i	−1.03190	−	0.732968i
$356$	6.33597	+	4.84286i	0.335806	+	0.256671i
$357$	−9.50920	−	9.50920i	−0.503280	−	0.503280i
$358$	−13.1468	−	13.4702i	−0.694832	−	0.711925i
$359$	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	$0.671053\pi$
$360$	2.79427	−	15.1134i	0.147271	−	0.796545i
$361$	−1.72712	+	5.31554i	−0.0909013	+	0.279765i
$362$	−19.3795	+	9.57959i	−1.01857	+	0.503492i
$363$	−3.57744	+	7.02112i	−0.187767	+	0.368513i
$364$	−12.9263	−	0.314162i	−0.677521	−	0.0164666i
$365$	13.9333	−	7.28828i	0.729300	−	0.381486i
$366$	−1.86217	−	0.630168i	−0.0973370	−	0.0329394i
$367$	1.20516	−	7.60906i	0.0629087	−	0.397190i	−0.936062	−	0.351834i	$-0.885558\pi$
$367$	1.20516	−	7.60906i	0.0629087	−	0.397190i	0.998971	−	0.0453553i	$-0.0144420\pi$
$368$	−34.5550	−	7.20916i	−1.80130	−	0.375803i
$369$	−8.92655	−	12.2863i	−0.464697	−	0.639601i
$370$	9.24806	+	6.73953i	0.480784	+	0.350371i
$371$	−21.1316	+	29.0852i	−1.09710	+	1.51003i
$372$	−2.52335	+	1.20940i	−0.130829	+	0.0627047i
$373$	4.35193	+	8.54114i	0.225334	+	0.442243i	0.975800	−	0.218666i	$-0.0701706\pi$
$373$	4.35193	+	8.54114i	0.225334	+	0.442243i	−0.750465	+	0.660910i	$0.770171\pi$
$374$	−3.88369	−	2.89440i	−0.200821	−	0.149666i
$375$	−8.28936	+	1.58731i	−0.428061	+	0.0819683i
$376$	−3.13622	−	1.14697i	−0.161738	−	0.0591505i
$377$	−0.00932194	+	0.00474976i	−0.000480104	+	0.000244625i
$378$	20.0051	+	10.5012i	1.02895	+	0.540124i
$379$	−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	$0.855578\pi$
$380$	−4.84870	−	15.6432i	−0.248733	−	0.802477i
$381$	6.85463	−	4.98018i	0.351173	−	0.255142i
$382$	−13.3428	+	1.94743i	−0.682679	+	0.0996392i
$383$	15.8049	+	2.50325i	0.807591	+	0.127910i	0.546559	−	0.837420i	$-0.315937\pi$
$383$	15.8049	+	2.50325i	0.807591	+	0.127910i	0.261032	+	0.965330i	$0.415937\pi$
$384$	−7.31098	+	4.41499i	−0.373087	+	0.225301i
$385$	3.02675	+	5.78633i	0.154257	+	0.294899i
$386$	−11.2065	+	7.93576i	−0.570394	+	0.403919i
$387$	18.6990	+	9.52760i	0.950522	+	0.484315i
$388$	−2.35026	+	12.8153i	−0.119316	+	0.650599i
$389$	14.5768	+	4.73629i	0.739073	+	0.240139i	0.654273	−	0.756259i	$-0.272975\pi$
$389$	14.5768	+	4.73629i	0.739073	+	0.240139i	0.0848002	+	0.996398i	$0.472975\pi$
$390$	3.52565	+	1.80283i	0.178528	+	0.0912896i
$391$	−38.3622	+	12.4646i	−1.94006	+	0.630364i
$392$	−11.2617	+	20.2430i	−0.568803	+	1.02243i
$393$	0.588310	−	0.588310i	0.0296763	−	0.0296763i
$394$	−0.226154	+	18.6131i	−0.0113935	+	0.937713i
$395$	−4.65726	+	6.55665i	−0.234332	+	0.329901i
$396$	3.43522	+	1.20921i	0.172627	+	0.0607651i
$397$	−1.74431	−	11.0132i	−0.0875445	−	0.552734i	−0.992007	−	0.126182i	$-0.959728\pi$
$397$	−1.74431	−	11.0132i	−0.0875445	−	0.552734i	0.904463	−	0.426553i	$-0.140272\pi$
$398$	35.9895	+	6.14929i	1.80399	+	0.308236i
$399$	10.7744			0.539395
$400$	−15.8548	−	12.1912i	−0.792740	−	0.609560i
$401$	−10.1423			−0.506483			−0.253242	−	0.967403i	$-0.581497\pi$
$401$	−10.1423			−0.506483			−0.253242	+	0.967403i	$0.581497\pi$
$402$	−5.41942	−	0.925981i	−0.270296	−	0.0461837i
$403$	0.480938	+	3.03652i	0.0239572	+	0.151260i
$404$	15.5880	+	5.48703i	0.775532	+	0.272990i
$405$	5.59582	+	7.53110i	0.278059	+	0.374223i
$406$	−0.000422357		0.0347611i	−2.09612e−5		0.00172517i
$407$	−1.91732	+	1.91732i	−0.0950378	+	0.0950378i
$408$	−4.74464	+	8.52850i	−0.234895	+	0.422224i
$409$	−1.08325	+	0.351968i	−0.0535630	+	0.0174037i	−0.335676	−	0.941978i	$-0.608965\pi$
$409$	−1.08325	+	0.351968i	−0.0535630	+	0.0174037i	0.282113	+	0.959381i	$0.408965\pi$
$410$	−19.5233	+	3.06330i	−0.964186	+	0.151285i
$411$	−5.40917	−	1.75754i	−0.266814	−	0.0866933i
$412$	−2.03789	+	11.1120i	−0.100400	+	0.547451i
$413$	−51.4814	−	26.2311i	−2.53323	−	1.29075i
$414$	24.7509	−	17.5271i	1.21644	−	0.861410i
$415$	−0.642564	+	4.35849i	−0.0315422	+	0.213950i
$416$	2.35253	+	9.08388i	0.115342	+	0.445374i
$417$	9.44497	+	1.49594i	0.462522	+	0.0732563i
$418$	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	$0.361098\pi$
$420$	10.7489	−	7.58848i	0.524494	−	0.370280i
$421$	−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	$0.858113\pi$
$422$	−31.0091	−	16.2775i	−1.50950	−	0.792374i
$423$	2.55642	−	1.30256i	0.124297	−	0.0633326i
$424$	24.5031	+	8.96124i	1.18998	+	0.435196i
$425$	−22.6441	−	3.09107i	−1.09840	−	0.149939i
$426$	−9.12942	−	6.80390i	−0.442322	−	0.329650i
$427$	3.25827	+	6.39471i	0.157679	+	0.309462i
$428$	6.72797	−	3.22462i	0.325209	−	0.155868i
$429$	−0.551515	+	0.759095i	−0.0266274	+	0.0366494i
$430$	22.1166	−	16.0199i	1.06656	−	0.772549i
$431$	9.49241	+	13.0652i	0.457233	+	0.629328i	0.973932	−	0.226840i	$-0.0728393\pi$
$431$	9.49241	+	13.0652i	0.457233	+	0.629328i	−0.516699	+	0.856167i	$0.672839\pi$
$432$	3.34872	−	16.0511i	0.161115	−	0.772259i
$433$	0.985346	−	6.22123i	0.0473527	−	0.298973i	−0.952634	−	0.304119i	$-0.901638\pi$
$433$	0.985346	−	6.22123i	0.0473527	−	0.298973i	0.999987	+	0.00514584i	$0.00163798\pi$
$434$	9.67639	+	3.27455i	0.464481	+	0.157183i
$435$	0.00473153	−	0.00953722i	0.000226860	−	0.000457275i
$436$	−5.85425	−	0.142283i	−0.280368	−	0.00681410i
$437$	14.6716	−	28.7947i	0.701839	−	1.37744i
$438$	6.73003	−	3.32675i	0.321573	−	0.158958i
$439$	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	$-0.147011\pi$
$440$	3.43615	−	3.26364i	0.163812	−	0.155588i
$441$	−6.15029	−	18.9286i	−0.292871	−	0.901364i
$442$	7.48940	+	7.67363i	0.356234	+	0.364997i
$443$	1.81845	+	1.81845i	0.0863972	+	0.0863972i	0.748985	−	0.662587i	$-0.230542\pi$
$443$	1.81845	+	1.81845i	0.0863972	+	0.0863972i	−0.662587	+	0.748985i	$0.730542\pi$
$444$	4.34067	+	3.31776i	0.205999	+	0.157454i
$445$	−2.66429	+	8.50875i	−0.126300	+	0.403353i
$446$	1.04264	−	0.324824i	0.0493705	−	0.0153808i
$447$	11.6797	−	1.84989i	0.552432	−	0.0874967i
$448$	30.3585	+	7.10754i	1.43431	+	0.335800i
$449$			19.3249i			0.911999i	0.889980	+	0.455999i	$0.150718\pi$
$449$			19.3249i			0.911999i	−0.889980	+	0.455999i	$0.849282\pi$
$450$	16.9465	−	2.84520i	0.798864	−	0.134124i
$451$		−	4.68267i		−	0.220498i
$452$	20.7061	+	21.7376i	0.973932	+	1.02245i
$453$	−9.80989	+	1.55373i	−0.460909	+	0.0730008i
$454$	3.54628	+	11.3831i	0.166435	+	0.534235i
$455$	−4.61417	−	13.7001i	−0.216316	−	0.642272i
$456$	−2.14365	−	7.51957i	−0.100386	−	0.352136i
$457$	15.9424	+	15.9424i	0.745755	+	0.745755i	0.973679	−	0.227924i	$-0.0731937\pi$
$457$	15.9424	+	15.9424i	0.745755	+	0.745755i	−0.227924	+	0.973679i	$0.573194\pi$
$458$	23.7644	−	23.1938i	1.11044	−	1.08378i
$459$	−5.78993	−	17.8196i	−0.270251	−	0.831747i
$460$	−5.64334	−	39.0599i	−0.263122	−	1.82118i
$461$	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	$-0.0273842\pi$
$462$	1.38157	+	2.79491i	0.0642763	+	0.130031i
$463$	−12.5764	+	24.6825i	−0.584474	+	1.14710i	0.389625	+	0.920974i	$0.372605\pi$
$463$	−12.5764	+	24.6825i	−0.584474	+	1.14710i	−0.974099	+	0.226122i	$0.927395\pi$
$464$	0.0243442	−	0.00662124i	0.00113015	−	0.000307383i
$465$	−2.23573	−	2.18836i	−0.103679	−	0.101483i
$466$	−1.00773	+	2.97788i	−0.0466823	+	0.137947i
$467$	−1.61942	+	10.2246i	−0.0749378	+	0.473139i	0.921470	+	0.388450i	$0.126990\pi$
$467$	−1.61942	+	10.2246i	−0.0749378	+	0.473139i	−0.996407	+	0.0846885i	$0.973010\pi$
$468$	−7.09242	−	3.83362i	−0.327847	−	0.177209i
$469$	11.7977	+	16.2382i	0.544768	+	0.749809i
$470$	0.00539029	−	3.73353i	0.000248636	−	0.172215i
$471$	−6.76133	+	9.30617i	−0.311546	+	0.428806i
$472$	−8.06430	+	41.1483i	−0.371190	+	1.89400i
$473$	2.93773	+	5.76563i	0.135077	+	0.265104i
$474$	−2.29451	+	3.07875i	−0.105390	+	0.141412i
$475$	14.5796	−	11.0773i	0.668960	−	0.508262i
$476$	34.1427	−	10.1834i	1.56493	−	0.466756i
$477$	−19.9732	+	10.1768i	−0.914508	+	0.465965i
$478$	−0.549080	+	1.04601i	−0.0251143	+	0.0478436i
$479$	−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	$0.882969\pi$
$480$	−7.43466	−	5.99200i	−0.339344	−	0.273496i
$481$	4.85624	−	3.52826i	0.221425	−	0.160875i
$482$	−2.48458	−	17.0231i	−0.113169	−	0.775382i
$483$	25.6440	+	4.06161i	1.16684	+	0.184810i
$484$	−11.8572	−	17.1831i	−0.538966	−	0.781049i
$485$	−14.3624	+	2.43267i	−0.652161	+	0.110462i
$486$	12.6394	+	17.8488i	0.573337	+	0.809637i
$487$	21.6278	+	11.0199i	0.980049	+	0.499360i	0.869191	−	0.494477i	$-0.164640\pi$
$487$	21.6278	+	11.0199i	0.980049	+	0.499360i	0.110858	+	0.993836i	$0.464640\pi$
$488$	3.81468	−	3.54626i	0.172682	−	0.160532i
$489$	−8.08414	−	2.62670i	−0.365577	−	0.118783i
$490$	−25.5742	−	4.08842i	−1.15533	−	0.184696i
$491$	20.7954	−	6.75684i	0.938484	−	0.304932i	0.200457	−	0.979703i	$-0.435757\pi$
$491$	20.7954	−	6.75684i	0.938484	−	0.304932i	0.738028	+	0.674771i	$0.235757\pi$
$492$	−9.35212	+	1.24913i	−0.421626	+	0.0563150i
$493$	0.0203851	−	0.0203851i	0.000918097	−	0.000918097i
$494$	−8.59024	−	0.104374i	−0.386493	−	0.00469600i
$495$	0.0435904	+	4.07146i	0.00195924	+	0.182999i
$496$	0.360145	−	7.40475i	0.0161710	−	0.332483i
$497$	6.50248	+	41.0550i	0.291676	+	1.84157i
$498$	−0.354259	+	2.07335i	−0.0158747	+	0.0929089i
$499$	9.81690			0.439465			0.219732	−	0.975560i	$-0.429482\pi$
$499$	9.81690			0.439465			0.219732	+	0.975560i	$0.429482\pi$
$500$	6.74335	−	21.3196i	0.301572	−	0.953443i
$501$	−3.31137			−0.147941
$502$	−1.31830	+	7.71549i	−0.0588385	+	0.344359i
$503$	5.21009	+	32.8952i	0.232306	+	1.46673i	0.777748	+	0.628576i	$0.216362\pi$
$503$	5.21009	+	32.8952i	0.232306	+	1.46673i	−0.545442	+	0.838149i	$0.683638\pi$
$504$	−22.2320	+	14.9459i	−0.990294	+	0.665742i
$505$	0.197800	+	18.4750i	0.00880199	+	0.822129i
$506$	9.35071	+	0.113614i	0.415690	+	0.00505075i
$507$	−5.47049	+	5.47049i	−0.242953	+	0.242953i
$508$	2.97185	+	22.2500i	0.131855	+	0.987186i
$509$	17.4707	−	5.67657i	0.774375	−	0.251610i	0.104938	−	0.994479i	$-0.466536\pi$
$509$	17.4707	−	5.67657i	0.774375	−	0.251610i	0.669437	+	0.742869i	$0.266536\pi$
$510$	−10.7746	−	1.72248i	−0.477107	−	0.0762726i
$511$	−26.0659	−	8.46931i	−1.15309	−	0.374660i
$512$	−1.07965	−	22.6016i	−0.0477144	−	0.998861i
$513$	13.3754	+	6.81510i	0.590538	+	0.300894i
$514$	−15.1263	−	21.3606i	−0.667194	−	0.942176i
$515$	−12.4535	+	2.10934i	−0.548766	+	0.0929488i
$516$	10.7313	−	7.40518i	0.472420	−	0.325995i
$517$	0.873775	+	0.138392i	0.0384286	+	0.00608649i
$518$	−2.88058	−	19.7363i	−0.126565	−	0.867163i
$519$	−9.99883	+	7.26457i	−0.438900	+	0.318879i
$520$	−8.64343	+	5.94603i	−0.379040	+	0.260751i
$521$	−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	$0.790240\pi$
$522$	−0.0100746	+	0.0191924i	−0.000440953	+	0.000840029i
$523$	37.5817	−	19.1488i	1.64333	−	0.837321i	0.646080	−	0.763270i	$-0.276407\pi$
$523$	37.5817	−	19.1488i	1.64333	−	0.837321i	0.997254	−	0.0740511i	$-0.0235928\pi$
$524$	0.630021	+	2.11232i	0.0275226	+	0.0922771i
$525$	12.0836	+	8.38996i	0.527373	+	0.366168i
$526$	−9.89587	+	13.2782i	−0.431480	+	0.578957i
$527$	−3.84596	−	7.54813i	−0.167533	−	0.328802i
$528$	1.67572	−	1.52028i	0.0729265	−	0.0661617i
$529$	32.2554	−	44.3957i	1.40241	−	1.93025i
$530$	−0.0421141	+	29.1699i	−0.00182932	+	1.26706i
$531$	−21.1758	−	29.1460i	−0.918952	−	1.26483i
$532$	−13.5735	+	25.1118i	−0.588487	+	1.08874i
$533$	−1.62166	+	10.2388i	−0.0702419	+	0.443490i
$534$	−1.36454	+	4.03226i	−0.0590494	+	0.174493i
$535$	5.96110	+	5.83481i	0.257721	+	0.252261i
$536$	8.98553	−	11.4645i	0.388116	−	0.495189i
$537$	4.56137	−	8.95219i	0.196837	−	0.386315i
$538$	−3.13350	−	6.33907i	−0.135095	−	0.273297i
$539$	1.89638	−	5.83644i	0.0816827	−	0.251393i
$540$	18.1437	−	2.62138i	0.780779	−	0.112806i
$541$	−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	$-0.263851\pi$
$542$	−25.6117	+	24.9968i	−1.10012	+	1.07370i
$543$	−8.15961	−	8.15961i	−0.350163	−	0.350163i
$544$	−13.9001	−	21.8025i	−0.595960	−	0.934773i
$545$	−2.08974	−	6.20473i	−0.0895145	−	0.265781i
$546$	−2.05291	−	6.58958i	−0.0878566	−	0.282008i
$547$	−24.3192	+	3.85178i	−1.03981	+	0.164690i	−0.652914	−	0.757432i	$-0.726454\pi$
$547$	−24.3192	+	3.85178i	−1.03981	+	0.164690i	−0.386899	+	0.922122i	$0.626454\pi$
$548$	10.9107	−	10.3930i	0.466084	−	0.443966i
$549$			4.47499i			0.190988i
$550$	4.74298	+	2.36159i	0.202242	+	0.100699i
$551$			0.0230973i			0.000983978i
$552$	−2.26744	−	18.7053i	−0.0965088	−	0.796151i
$553$	13.8451	−	2.19286i	0.588756	−	0.0932497i
$554$	−20.7005	+	6.44902i	−0.879479	+	0.273993i
$555$	−1.82526	+	5.82921i	−0.0774782	+	0.247436i
$556$	−15.3853	+	20.1288i	−0.652482	+	0.853650i
$557$	2.83685	+	2.83685i	0.120201	+	0.120201i	0.764649	−	0.644447i	$-0.222913\pi$
$557$	2.83685	+	2.83685i	0.120201	+	0.120201i	−0.644447	+	0.764649i	$0.722913\pi$
$558$	4.44890	+	4.55834i	0.188337	+	0.192970i
$559$	−4.42671	−	13.6240i	−0.187230	−	0.576235i
$560$	4.14499	+	34.6124i	0.175158	+	1.46264i
$561$	0.798955	−	2.45893i	0.0337319	−	0.103816i
$562$	27.9133	−	13.7979i	1.17745	−	0.582031i
$563$	−9.99243	+	19.6112i	−0.421131	+	0.826515i	0.578808	+	0.815464i	$0.303518\pi$
$563$	−9.99243	+	19.6112i	−0.421131	+	0.826515i	−0.999939	+	0.0110516i	$0.996482\pi$
$564$	0.0433099	−	1.78200i	0.00182368	−	0.0750357i
$565$	−14.9170	+	30.0677i	−0.627562	+	1.26496i
$566$	3.44466	+	1.16569i	0.144790	+	0.0489977i
$567$	2.55825	−	16.1522i	0.107436	−	0.678327i
$568$	27.3590	−	12.7064i	1.14796	−	0.533148i
$569$	2.34646	+	3.22963i	0.0983688	+	0.135393i	0.855364	−	0.518027i	$-0.173333\pi$
$569$	2.34646	+	3.22963i	0.0983688	+	0.135393i	−0.756995	+	0.653420i	$0.773333\pi$
$570$	7.07990	−	5.12825i	0.296544	−	0.214799i
$571$	13.9597	−	19.2139i	0.584197	−	0.804078i	−0.409951	−	0.912108i	$-0.634454\pi$
$571$	13.9597	−	19.2139i	0.584197	−	0.804078i	0.994148	+	0.108029i	$0.0344541\pi$
$572$	−1.07442	−	2.24171i	−0.0449239	−	0.0937308i
$573$	−3.26770	−	6.41323i	−0.136510	−	0.267917i
$574$	27.6186	+	20.5834i	1.15278	+	0.859135i
$575$	38.8766	−	20.8689i	1.62127	−	0.870293i
$576$	14.8541	+	12.5424i	0.618921	+	0.522599i
$577$	10.9464	−	5.57748i	0.455706	−	0.232194i	−0.211042	−	0.977477i	$-0.567686\pi$
$577$	10.9464	−	5.57748i	0.455706	−	0.232194i	0.666748	+	0.745283i	$0.267686\pi$
$578$	−4.87408	−	2.55853i	−0.202735	−	0.106421i
$579$	−5.93000	−	4.30839i	−0.246442	−	0.179051i
$580$	0.0162676	+	0.0230427i	0.000675474	+	0.000956796i
$581$	6.21235	−	4.51354i	0.257732	−	0.187253i
$582$	−6.88187	+	1.00443i	−0.285262	+	0.0416350i
$583$	−6.82676	−	1.08125i	−0.282736	−	0.0447809i
$584$	−0.724806	+	19.8767i	−0.0299927	+	0.822502i
$585$	1.31468	−	8.91742i	0.0543553	−	0.368690i
$586$	−21.1833	+	15.0007i	−0.875073	+	0.619675i
$587$	−17.0258	−	8.67508i	−0.702730	−	0.358059i	0.0658352	−	0.997831i	$-0.479029\pi$
$587$	−17.0258	−	8.67508i	−0.702730	−	0.358059i	−0.768565	+	0.639772i	$0.779029\pi$
$588$	−12.1623	−	2.23049i	−0.501564	−	0.0919840i
$589$	6.45504	+	2.09737i	0.265975	+	0.0864206i
$590$	−46.3137	+	7.26684i	−1.90671	+	0.299171i
$591$	−9.44990	+	3.07046i	−0.388717	+	0.126302i
$592$	−13.2010	+	5.93708i	−0.542560	+	0.244012i
$593$	−19.5284	+	19.5284i	−0.801936	+	0.801936i	−0.983398	−	0.181462i	$-0.941917\pi$
$593$	−19.5284	+	19.5284i	−0.801936	+	0.801936i	0.181462	+	0.983398i	$0.441917\pi$
$594$	−0.0527746	+	4.34349i	−0.00216537	+	0.178216i
$595$	23.7578	+	31.9742i	0.973973	+	1.31081i
$596$	−10.4025	+	29.5524i	−0.426104	+	1.21051i
$597$	3.04879	+	19.2493i	0.124779	+	0.787822i
$598$	−20.4062	−	3.48667i	−0.834470	−	0.142581i
$599$	13.5371			0.553109			0.276555	−	0.960998i	$-0.410807\pi$
$599$	13.5371			0.553109			0.276555	+	0.960998i	$0.410807\pi$
$600$	3.45130	−	10.1025i	0.140899	−	0.412434i
$601$	−20.0981			−0.819819			−0.409910	−	0.912126i	$-0.634440\pi$
$601$	−20.0981			−0.819819			−0.409910	+	0.912126i	$0.634440\pi$
$602$	−46.9192	−	8.01678i	−1.91228	−	0.326740i
$603$	1.95778	+	12.3609i	0.0797270	+	0.503376i
$604$	8.73717	−	24.8212i	0.355510	−	1.00996i
$605$	13.5167	−	19.0293i	0.549533	−	0.773651i
$606$	−0.107172	+	8.82052i	−0.00435355	+	0.358309i
$607$	13.9387	−	13.9387i	0.565753	−	0.565753i	−0.365182	−	0.930936i	$-0.618993\pi$
$607$	13.9387	−	13.9387i	0.565753	−	0.565753i	0.930936	+	0.365182i	$0.118993\pi$
$608$	20.2264	+	4.47691i	0.820288	+	0.181562i
$609$	−0.0176483	+	0.00573428i	−0.000715145	+	0.000232365i
$610$	5.18469	+	2.65117i	0.209922	+	0.107343i
$611$	−1.86260	−	0.605195i	−0.0753527	−	0.0244836i
$612$	21.8510	+	4.00736i	0.883276	+	0.161988i
$613$	−14.8272	−	7.55485i	−0.598866	−	0.305137i	0.128153	−	0.991754i	$-0.459095\pi$
$613$	−14.8272	−	7.55485i	−0.598866	−	0.305137i	−0.727019	+	0.686617i	$0.759095\pi$
$614$	−9.53782	+	6.75412i	−0.384915	+	0.272574i
$615$	−4.88942	−	9.34728i	−0.197161	−	0.376919i
$616$	−8.25457	−	0.301004i	−0.332586	−	0.0121278i
$617$	16.2602	+	2.57536i	0.654610	+	0.103680i	0.474900	−	0.880040i	$-0.342484\pi$
$617$	16.2602	+	2.57536i	0.654610	+	0.103680i	0.179710	+	0.983720i	$0.442484\pi$
$618$	−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	$0.319090\pi$
$620$	7.91696	−	2.45391i	0.317953	−	0.0985515i
$621$	29.2655	+	21.2626i	1.17438	+	0.853240i
$622$	−19.1366	−	10.0453i	−0.767308	−	0.402779i
$623$	13.8468	−	7.05531i	0.554762	−	0.282665i
$624$	−4.19049	+	2.74380i	−0.167754	+	0.109840i
$625$	24.9771	−	1.07027i	0.999083	−	0.0428106i
$626$	−30.4201	−	22.6713i	−1.21583	−	0.906126i
$627$	0.940418	+	1.84568i	0.0375567	+	0.0737092i
$628$	−13.1720	−	27.4825i	−0.525618	−	1.09667i
$629$	−9.72216	+	13.3814i	−0.387648	+	0.533552i
$630$	−24.2053	−	17.6396i	−0.964362	−	0.702780i
$631$	10.9928	+	15.1303i	0.437618	+	0.602329i	0.969681	−	0.244376i	$-0.0785830\pi$
$631$	10.9928	+	15.1303i	0.437618	+	0.602329i	−0.532063	+	0.846705i	$0.678583\pi$
$632$	−4.28502	−	9.22639i	−0.170449	−	0.367006i
$633$	2.92442	−	18.4641i	0.116235	−	0.733881i
$634$	4.91374	+	1.66284i	0.195150	+	0.0660398i
$635$	−22.2385	+	11.6326i	−0.882509	+	0.461627i
$636$	−0.338379	+	13.9227i	−0.0134176	+	0.552070i
$637$	−6.16769	+	12.1048i	−0.244373	+	0.479608i
$638$	−0.00599151	+	0.00296169i	−0.000237206	+	0.000117254i
$639$	−8.00905	+	24.6493i	−0.316833	+	0.975112i
$640$	23.3317	−	9.77924i	0.922265	−	0.386558i
$641$	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	$0.763555\pi$
$642$	2.78164	+	2.85006i	0.109782	+	0.112483i
$643$	−16.6982	−	16.6982i	−0.658511	−	0.658511i	0.296516	−	0.955028i	$-0.404175\pi$
$643$	−16.6982	−	16.6982i	−0.658511	−	0.658511i	−0.955028	+	0.296516i	$0.904175\pi$
$644$	−41.7726	+	54.6516i	−1.64607	+	2.15357i
$645$	11.8843	+	8.44157i	0.467945	+	0.332386i
$646$	22.6008	−	7.04105i	0.889218	−	0.277027i
$647$	5.68755	−	0.900819i	0.223601	−	0.0354149i	−0.0436287	−	0.999048i	$-0.513892\pi$
$647$	5.68755	−	0.900819i	0.223601	−	0.0354149i	0.267229	+	0.963633i	$0.413892\pi$
$648$	−11.7817	+	1.42817i	−0.462831	+	0.0561039i
$649$		−	11.1084i		−	0.436042i
$650$	−9.55278	−	6.80622i	−0.374691	−	0.266962i
$651$			5.45290i			0.213716i
$652$	16.3064	−	15.5326i	0.638607	−	0.608302i
$653$	4.08000	−	0.646208i	0.159663	−	0.0252881i	−0.0760913	−	0.997101i	$-0.524244\pi$
$653$	4.08000	−	0.646208i	0.159663	−	0.0252881i	0.235754	+	0.971813i	$0.424244\pi$
$654$	−0.929756	−	2.98439i	−0.0363563	−	0.116699i
$655$	−1.97816	+	1.46983i	−0.0772932	+	0.0574310i
$656$	8.87042	−	23.3706i	0.346332	−	0.912468i
$657$	−12.0838	−	12.0838i	−0.471433	−	0.471433i
$658$	−4.65706	+	4.54524i	−0.181551	+	0.177192i
$659$	−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	$-0.268901\pi$
$660$	2.23811	+	1.17897i	0.0871185	+	0.0458913i
$661$	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	$0.0866562\pi$
$662$	9.55981	+	19.3395i	0.371553	+	0.751652i
$663$	−2.59849	+	5.09982i	−0.100917	+	0.198060i
$664$	−4.38604	−	3.43766i	−0.170212	−	0.133407i
$665$	−31.5736	−	4.65483i	−1.22437	−	0.180507i
$666$	3.98648	−	11.7802i	0.154473	−	0.456472i
$667$	−0.00870697	+	0.0549736i	−0.000337135	+	0.00212859i
$668$	4.17165	−	7.71780i	0.161406	−	0.298611i
$669$	0.342640	+	0.471604i	0.0132472	+	0.0182333i
$670$	15.4811	+	5.05485i	0.598089	+	0.195286i
$671$	−0.811036	+	1.11629i	−0.0313097	+	0.0430941i
$672$	1.60079	+	16.5661i	0.0617518	+	0.639052i
$673$	−12.1142	−	23.7755i	−0.466969	−	0.916479i	−0.997624	−	0.0688909i	$-0.978054\pi$
$673$	−12.1142	−	23.7755i	−0.466969	−	0.916479i	0.530655	−	0.847588i	$-0.321946\pi$
$674$	24.7009	−	33.1435i	0.951444	−	1.27664i
$675$	9.69379	+	18.0585i	0.373114	+	0.695074i
$676$	−5.85835	−	19.6417i	−0.225321	−	0.755452i
$677$	8.89777	−	4.53364i	0.341969	−	0.174242i	−0.274568	−	0.961568i	$-0.588535\pi$
$677$	8.89777	−	4.53364i	0.341969	−	0.174242i	0.616537	+	0.787326i	$0.288535\pi$
$678$	−7.44812	+	14.1889i	−0.286043	+	0.544922i
$679$	20.5409	+	14.9238i	0.788286	+	0.572723i
$680$	17.5883	−	22.9423i	0.674482	−	0.879797i
$681$	−5.14876	+	3.74080i	−0.197301	+	0.143348i
$682$	0.283645	+	1.94339i	0.0108613	+	0.0744164i
$683$	−39.5771	−	6.26839i	−1.51437	−	0.239853i	−0.656741	−	0.754116i	$-0.728066\pi$
$683$	−39.5771	−	6.26839i	−1.51437	−	0.239853i	−0.857633	+	0.514263i	$0.828066\pi$
$684$	−14.6494	+	10.1089i	−0.560135	+	0.386523i
$685$	15.0918	+	7.48725i	0.576629	+	0.286073i
$686$	3.79047	+	5.35270i	0.144721	+	0.204367i
$687$	15.7936	+	8.04723i	0.602562	+	0.307021i
$688$	3.73996	+	34.3404i	0.142585	+	1.30922i
$689$	14.5524	+	4.72836i	0.554402	+	0.180136i
$690$	18.7840	−	9.53678i	0.715094	−	0.363059i
$691$	−10.3709	+	3.36971i	−0.394528	+	0.128190i	−0.499561	−	0.866279i	$-0.666505\pi$
$691$	−10.3709	+	3.36971i	−0.394528	+	0.128190i	0.105033	+	0.994469i	$0.466505\pi$
$692$	−4.33503	−	32.4561i	−0.164793	−	1.23379i
$693$	5.01827	−	5.01827i	0.190628	−	0.190628i
$694$	−3.56047	−	0.0432607i	−0.135154	−	0.00164215i
$695$	−27.0315	−	8.46420i	−1.02536	−	0.321065i
$696$	0.00751328	+	0.0111760i	0.000284790	+	0.000423627i
$697$	−4.46850	−	28.2130i	−0.169256	−	1.06864i
$698$	−4.48939	+	26.2747i	−0.169926	+	0.994513i
$699$	−1.67811			−0.0634720
$700$	−34.7773	+	17.5936i	−1.31446	+	0.664976i
$701$	−11.2244			−0.423940			−0.211970	−	0.977276i	$-0.567988\pi$
$701$	−11.2244			−0.423940			−0.211970	+	0.977276i	$0.567988\pi$
$702$	1.61959	−	9.47885i	0.0611275	−	0.357756i
$703$	−2.07305	−	13.0888i	−0.0781867	−	0.493652i
$704$	1.43224	+	5.82084i	0.0539796	+	0.219381i
$705$	1.88868	−	0.636103i	0.0711318	−	0.0239570i
$706$	31.6613	+	0.384693i	1.19159	+	0.0144781i
$707$	22.7714	−	22.7714i	0.856405	−	0.856405i
$708$	−22.1854	+	2.96321i	−0.833777	+	0.111364i
$709$	−40.0107	+	13.0003i	−1.50263	+	0.488235i	−0.940784	−	0.339006i	$-0.889909\pi$
$709$	−40.0107	+	13.0003i	−1.50263	+	0.488235i	−0.561848	+	0.827240i	$0.689909\pi$
$710$	23.8136	+	23.8825i	0.893708	+	0.896293i
$711$	8.31258	+	2.70092i	0.311746	+	0.101293i
$712$	−7.67892	−	8.26014i	−0.287780	−	0.309562i
$713$	14.5729	+	7.42527i	0.545760	+	0.278079i
$714$	10.9910	+	15.5209i	0.411327	+	0.580855i
$715$	1.94412	−	1.98620i	0.0727060	−	0.0742796i
$716$	15.1184	+	21.9091i	0.565002	+	0.818780i
$717$	−0.622840	−	0.0986482i	−0.0232604	−	0.00368408i
$718$	−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	$0.413625\pi$
$720$	−7.49504	+	20.4027i	−0.279324	+	0.760363i
$721$	17.8108	+	12.9403i	0.663309	+	0.481922i
$722$	3.67372	−	6.99855i	0.136722	−	0.260459i
$723$	8.18215	−	4.16902i	0.304298	−	0.155047i
$724$	29.2970	−	8.73813i	1.08881	−	0.324750i
$725$	−0.0179857	+	0.0259039i	−0.000667973	+	0.000962048i
$726$	6.65932	−	8.93542i	0.247151	−	0.331625i
$727$	−15.7672	−	30.9449i	−0.584773	−	1.14768i	−0.974002	−	0.226540i	$-0.927258\pi$
$727$	−15.7672	−	30.9449i	−0.584773	−	1.14768i	0.389229	−	0.921141i	$-0.372742\pi$
$728$	17.9445	+	3.51680i	0.665069	+	0.130341i
$729$	0.536916	−	0.739001i	0.0198858	−	0.0273704i
$730$	−21.1591	+	6.84124i	−0.783133	+	0.253206i
$731$	23.2017	+	31.9344i	0.858146	+	1.18114i
$732$	2.44578	+	1.32200i	0.0903988	+	0.0488627i
$733$	−4.77141	+	30.1255i	−0.176236	+	1.11271i	0.727968	+	0.685611i	$0.240465\pi$
$733$	−4.77141	+	30.1255i	−0.176236	+	1.11271i	−0.904204	+	0.427100i	$0.859535\pi$
$734$	−3.49237	+	10.3201i	−0.128906	+	0.380921i
$735$	−2.30870	−	13.6305i	−0.0851578	−	0.502768i
$736$	46.4529	+	18.2801i	1.71228	+	0.673815i
$737$	−1.75189	+	3.43828i	−0.0645318	+	0.126651i
$738$	9.51728	+	19.2535i	0.350336	+	0.708730i
$739$	−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	$0.142145\pi$
$740$	−11.2866	−	11.5977i	−0.414905	−	0.426341i
$741$	−1.41707	−	4.36128i	−0.0520572	−	0.160216i
$742$	36.3854	−	35.5118i	1.33575	−	1.30368i
$743$	−29.7687	−	29.7687i	−1.09211	−	1.09211i	−0.995303	−	0.0968046i	$-0.969138\pi$
$743$	−29.7687	−	29.7687i	−1.09211	−	1.09211i	−0.0968046	−	0.995303i	$-0.530862\pi$
$744$	3.80564	−	1.08490i	0.139521	−	0.0397743i
$745$	−35.0257	+	0.374997i	−1.28324	+	0.0137388i
$746$	−4.03226	−	12.9430i	−0.147632	−	0.473877i
$747$	4.72901	−	0.749002i	0.173026	−	0.0274046i
$748$	4.72450	+	4.95987i	0.172745	+	0.181351i
$749$		−	14.5390i		−	0.531244i
$750$	11.9335	−	0.238322i	0.435751	−	0.00870228i
$751$			31.2660i			1.14091i	0.821327	+	0.570457i	$0.193234\pi$
$751$			31.2660i			1.14091i	−0.821327	+	0.570457i	$0.806766\pi$
$752$	4.09873	+	2.34589i	0.149465	+	0.0855460i
$753$	−4.12670	+	0.653605i	−0.150385	+	0.0238187i
$754$	0.0141262	−	0.00440087i	0.000514446	−	0.000160270i
$755$	29.4184	−	0.314963i	1.07064	−	0.0114627i
$756$	−25.3862	−	19.4037i	−0.923286	−	0.705707i
$757$	4.53335	+	4.53335i	0.164767	+	0.164767i	0.784675	−	0.619908i	$-0.212830\pi$
$757$	4.53335	+	4.53335i	0.164767	+	0.164767i	−0.619908	+	0.784675i	$0.712830\pi$
$758$	18.0583	+	18.5025i	0.655906	+	0.672041i
$759$	1.54252	+	4.74738i	0.0559898	+	0.172319i
$760$	3.03316	+	22.9616i	0.110024	+	0.832906i
$761$	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	$-0.0768718\pi$
$762$	−10.7416	+	5.30975i	−0.389128	+	0.192352i
$763$	−5.18078	+	10.1678i	−0.187557	+	0.368101i
$764$	19.0639	+	0.463332i	0.689708	+	0.0167628i
$765$	4.14787	+	24.4889i	0.149967	+	0.885396i
$766$	−21.4359	−	7.25405i	−0.774512	−	0.262099i
$767$	−3.84695	+	24.2887i	−0.138905	+	0.877013i
$768$	11.2432	−	4.41317i	0.405703	−	0.159247i
$769$	−21.5371	−	29.6433i	−0.776649	−	1.06897i	−0.995644	−	0.0932401i	$-0.970278\pi$
$769$	−21.5371	−	29.6433i	−0.776649	−	1.06897i	0.218994	−	0.975726i	$-0.429722\pi$
$770$	−2.84110	−	8.78714i	−0.102386	−	0.316667i
$771$	8.21222	−	11.3031i	0.295756	−	0.407073i
$772$	17.5121	−	8.39332i	0.630275	−	0.302082i
$773$	11.0820	+	21.7496i	0.398591	+	0.782279i	0.999859	−	0.0167684i	$-0.00533778\pi$
$773$	11.0820	+	21.7496i	0.398591	+	0.782279i	−0.601268	+	0.799047i	$0.705338\pi$
$774$	−23.7972	−	17.7354i	−0.855374	−	0.637486i
$775$	5.60620	+	7.37872i	0.201381	+	0.265052i
$776$	6.32871	−	17.3049i	0.227188	−	0.621210i
$777$	9.48624	−	4.83348i	0.340317	−	0.173400i
$778$	−19.1921	−	10.0744i	−0.688070	−	0.361186i
$779$	18.5149	+	13.4518i	0.663364	+	0.481962i
$780$	−4.48539	−	3.35292i	−0.160603	−	0.120054i
$781$	−6.46525	+	4.69728i	−0.231345	+	0.168082i
$782$	56.4462	−	8.23851i	2.01851	−	0.294609i
$783$	−0.0255357	−	0.00404446i	−0.000912573	−	0.000144537i
$784$	20.5206	−	25.5366i	0.732877	−	0.912021i
$785$	23.8341	−	24.3499i	0.850674	−	0.869087i
$786$	−0.960237	+	0.679983i	−0.0342505	+	0.0242542i
$787$	−3.08909	−	1.57397i	−0.110114	−	0.0561060i	0.398066	−	0.917357i	$-0.369682\pi$
$787$	−3.08909	−	1.57397i	−0.110114	−	0.0561060i	−0.508180	+	0.861251i	$0.669682\pi$
$788$	4.74863	−	25.8930i	0.169163	−	0.922399i
$789$	−8.40701	−	2.73160i	−0.299297	−	0.0972476i
$790$	8.05398	−	8.03075i	0.286548	−	0.285721i
$791$	55.6393	−	18.0783i	1.97830	−	0.642790i
$792$	−4.50072	−	2.50388i	−0.159926	−	0.0889713i
$793$	2.15993	−	2.15993i	0.0767014	−	0.0767014i
$794$	−0.191585	+	15.7679i	−0.00679909	+	0.559583i
$795$	−14.7562	+	4.96985i	−0.523348	+	0.176262i
$796$	−48.7051	−	17.1444i	−1.72631	−	0.607666i
$797$	−1.93413	−	12.2116i	−0.0685103	−	0.432557i	−0.997973	−	0.0636405i	$-0.979729\pi$
$797$	−1.93413	−	12.2116i	−0.0685103	−	0.432557i	0.929463	−	0.368916i	$-0.120271\pi$
$798$	−15.0196	−	2.56631i	−0.531689	−	0.0908463i
$799$	5.39653			0.190916
$800$	19.1980	+	20.7711i	0.678752	+	0.734368i
$801$	9.68995			0.342378
$802$	14.1385	+	2.41575i	0.499248	+	0.0853033i
$803$	−0.824288	−	5.20435i	−0.0290885	−	0.183658i
$804$	7.33418	+	2.58166i	0.258656	+	0.0910480i
$805$	−73.3931	−	22.9811i	−2.58677	−	0.809979i
$806$	0.0528233	−	4.34750i	0.00186062	−	0.153134i
$807$	2.66902	−	2.66902i	0.0939540	−	0.0939540i
$808$	−20.4229	−	11.3618i	−0.718476	−	0.399707i
$809$	−13.3278	+	4.33048i	−0.468582	+	0.152251i	−0.533784	−	0.845621i	$-0.679231\pi$
$809$	−13.3278	+	4.33048i	−0.468582	+	0.152251i	0.0652027	+	0.997872i	$0.479231\pi$
$810$	−6.00684	−	11.8313i	−0.211059	−	0.415709i
$811$	−15.0031	−	4.87481i	−0.526831	−	0.171178i	0.0335122	−	0.999438i	$-0.489331\pi$
$811$	−15.0031	−	4.87481i	−0.526831	−	0.171178i	−0.560343	+	0.828261i	$0.689331\pi$
$812$	0.00886837	−	0.0483568i	0.000311219	−	0.00169699i
$813$	−17.0213	−	8.67277i	−0.596962	−	0.304167i
$814$	3.12944	−	2.21608i	0.109687	−	0.0776737i
$815$	22.5551	+	11.1899i	0.790072	+	0.391965i
$816$	8.64545	−	10.7587i	0.302651	−	0.376631i
$817$	−31.2360	−	4.94729i	−1.09281	−	0.173084i
$818$	1.59389	−	0.232634i	0.0557291	−	0.00813384i
$819$	−12.7104	+	9.23466i	−0.444138	+	0.322685i
$820$	27.9453	+	0.379896i	0.975893	+	0.0132665i
$821$	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	$0.657023\pi$
$822$	7.12182	+	3.73842i	0.248402	+	0.130392i
$823$	−6.26212	+	3.19071i	−0.218284	+	0.111221i	−0.559714	−	0.828686i	$-0.689089\pi$
$823$	−6.26212	+	3.19071i	−0.218284	+	0.111221i	0.341430	+	0.939907i	$0.389089\pi$
$824$	5.48757	−	15.0049i	0.191169	−	0.522721i
$825$	−0.382524	+	2.80225i	−0.0133178	+	0.0975617i
$826$	65.5178	+	48.8285i	2.27965	+	1.69896i
$827$	6.18514	+	12.1390i	0.215078	+	0.422115i	0.973188	−	0.230012i	$-0.0738767\pi$
$827$	6.18514	+	12.1390i	0.215078	+	0.422115i	−0.758109	+	0.652128i	$0.773877\pi$
$828$	−38.6777	+	18.5377i	−1.34414	+	0.644229i
$829$	−21.4059	+	29.4626i	−0.743456	+	1.02328i	0.254956	+	0.966953i	$0.417939\pi$
$829$	−21.4059	+	29.4626i	−0.743456	+	1.02328i	−0.998412	+	0.0563271i	$0.982061\pi$
$830$	1.93387	−	5.92273i	0.0671256	−	0.205581i
$831$	−6.80275	−	9.36318i	−0.235985	−	0.324805i
$832$	−1.11580	−	13.2234i	−0.0386835	−	0.458438i
$833$	5.85612	−	36.9741i	0.202902	−	1.28108i
$834$	−12.8101	−	4.33501i	−0.443577	−	0.150109i
$835$	9.70372	+	1.43060i	0.335811	+	0.0495080i
$836$	−5.48644	−	0.133343i	−0.189752	−	0.00461177i
$837$	−3.44911	+	6.76925i	−0.119219	+	0.233980i
$838$	9.90122	−	4.89432i	0.342032	−	0.169071i
$839$	−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	$0.978882\pi$
$840$	−16.7916	+	8.01818i	−0.579365	+	0.276654i
$841$	8.96148	+	27.5806i	0.309017	+	0.951055i
$842$	19.3169	+	19.7921i	0.665705	+	0.682081i
$843$	11.7527	+	11.7527i	0.404784	+	0.404784i
$844$	39.3500	+	30.0769i	1.35448	+	1.03529i
$845$	18.3943	−	13.6675i	0.632782	−	0.470175i
$846$	−3.87392	+	1.20688i	−0.133188	+	0.0414934i
$847$	−40.1826	+	6.36430i	−1.38069	+	0.218680i
$848$	−32.0232	−	18.3284i	−1.09968	−	0.629399i
$849$			1.94116i			0.0666203i
$850$	30.8299	+	9.70250i	1.05746	+	0.332793i
$851$		−	31.9339i		−	1.09468i
$852$	11.1059	+	11.6592i	0.380483	+	0.399438i
$853$	32.3819	−	5.12879i	1.10873	−	0.175606i	0.424898	−	0.905241i	$-0.360310\pi$
$853$	32.3819	−	5.12879i	1.10873	−	0.175606i	0.683837	+	0.729635i	$0.260310\pi$
$854$	−3.01893	−	9.69038i	−0.103306	−	0.331598i
$855$	−16.2234	−	11.5237i	−0.554829	−	0.394101i
$856$	−10.1469	+	2.89265i	−0.346815	+	0.0988688i
$857$	−9.60872	−	9.60872i	−0.328228	−	0.328228i	0.523685	−	0.851912i	$-0.324557\pi$
$857$	−9.60872	−	9.60872i	−0.328228	−	0.328228i	−0.851912	+	0.523685i	$0.824557\pi$
$858$	0.949623	−	0.926824i	0.0324196	−	0.0316412i
$859$	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	$0.510365\pi$
$860$	−34.6465	+	17.0641i	−1.18144	+	0.581881i
$861$	−5.68173	+	17.4866i	−0.193633	+	0.595941i
$862$	−10.1206	−	20.4740i	−0.344709	−	0.697346i
$863$	−1.37935	+	2.70712i	−0.0469535	+	0.0921515i	−0.913291	−	0.407307i	$-0.866468\pi$
$863$	−1.37935	+	2.70712i	−0.0469535	+	0.0921515i	0.866338	+	0.499459i	$0.166468\pi$
$864$	−8.49129	+	21.5778i	−0.288880	+	0.734091i
$865$	32.4393	−	16.9685i	1.10297	−	0.576947i
$866$	−2.85539	+	8.43777i	−0.0970301	+	0.286727i
$867$	0.459668	−	2.90223i	0.0156111	−	0.0985648i
$868$	−12.7090	−	6.86953i	−0.431373	−	0.233167i
$869$	1.58408	+	2.18030i	0.0537363	+	0.0739616i
$870$	−0.00886744	+	0.0121680i	−0.000300634	+	0.000412534i
$871$	5.02126	−	6.91117i	0.170139	−	0.234176i
$872$	8.12700	+	1.59274i	0.275215	+	0.0539371i
$873$	7.18720	+	14.1057i	0.243250	+	0.477405i
$874$	−27.3109	+	36.6455i	−0.923804	+	1.23955i
$875$	−31.7855	−	29.8066i	−1.07454	−	1.00765i
$876$	−10.1741	+	3.03454i	−0.343752	+	0.102527i
$877$	−24.2129	+	12.3371i	−0.817613	+	0.416595i	−0.812192	−	0.583391i	$-0.801726\pi$
$877$	−24.2129	+	12.3371i	−0.817613	+	0.416595i	−0.00542141	+	0.999985i	$0.501726\pi$
$878$	−19.2928	+	36.7534i	−0.651100	+	1.24037i
$879$	−11.2093	−	8.14404i	−0.378081	−	0.274692i
$880$	−5.56738	+	3.73110i	−0.187676	+	0.125775i
$881$	−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
$883$	−22.6146	−	3.58180i	−0.761041	−	0.120537i	−0.236162	−	0.971714i	$-0.575890\pi$
$883$	−22.6146	−	3.58180i	−0.761041	−	0.120537i	−0.524879	+	0.851177i	$0.675890\pi$
$884$	−8.61255	−	12.4810i	−0.289672	−	0.419781i
$885$	−11.5988	−	22.1739i	−0.389890	−	0.745367i
$886$	−2.10181	−	2.96807i	−0.0706118	−	0.0997143i
$887$	−41.7627	−	21.2791i	−1.40225	−	0.714484i	−0.420974	−	0.907073i	$-0.638312\pi$
$887$	−41.7627	−	21.2791i	−1.40225	−	0.714484i	−0.981279	+	0.192589i	$0.938312\pi$
$888$	−5.26070	−	5.65889i	−0.176538	−	0.189900i
$889$	41.6031	+	13.5177i	1.39532	+	0.453368i
$890$	5.74072	−	11.2267i	0.192429	−	0.376320i
$891$	2.99019	−	0.971570i	0.100175	−	0.0325488i
$892$	−1.53082	+	0.204466i	−0.0512557	+	0.00684602i
$893$	−3.05727	+	3.05727i	−0.102308	+	0.102308i
$894$	−16.7223	−	0.203180i	−0.559277	−	0.00679537i
$895$	−17.2343	+	24.2631i	−0.576080	+	0.811024i
$896$	−40.6272	−	17.1390i	−1.35726	−	0.572572i
$897$	−1.72867	−	10.9144i	−0.0577188	−	0.364422i
$898$	4.60292	−	26.9391i	0.153601	−	0.898971i
$899$	−0.0116895			−0.000389866
$900$	−24.3013	−	0.0701701i	−0.810042	−	0.00233900i
$901$	−42.1629			−1.40465
$902$	−1.11535	+	6.52770i	−0.0371369	+	0.217349i
$903$	−3.97468	−	25.0952i	−0.132269	−	0.835115i
$904$	−23.6869	−	35.2344i	−0.787815	−	1.17188i
$905$	20.3859	+	27.4363i	0.677652	+	0.912013i
$906$	14.0452	+	0.170653i	0.466620	+	0.00566956i
$907$	−37.7459	+	37.7459i	−1.25333	+	1.25333i	−0.299114	+	0.954217i	$0.596691\pi$
$907$	−37.7459	+	37.7459i	−1.25333	+	1.25333i	−0.954217	+	0.299114i	$0.903309\pi$
$908$	−2.23227	−	16.7128i	−0.0740804	−	0.554635i
$909$	19.0969	−	6.20495i	0.633403	−	0.205805i
$910$	3.16903	+	20.1972i	0.105052	+	0.669529i
$911$	−38.7405	−	12.5875i	−1.28353	−	0.417044i	−0.413707	−	0.910410i	$-0.635766\pi$
$911$	−38.7405	−	12.5875i	−1.28353	−	0.417044i	−0.869822	+	0.493366i	$0.835766\pi$
$912$	1.19723	+	10.9930i	0.0396441	+	0.364013i
$913$	1.31541	+	0.670234i	0.0435337	+	0.0221815i
$914$	−18.4267	−	26.0212i	−0.609500	−	0.860704i
$915$	−0.453360	+	3.07513i	−0.0149876	+	0.101661i
$916$	−38.6523	+	26.6721i	−1.27711	+	0.881272i
$917$	4.24262	+	0.671964i	0.140104	+	0.0221902i
$918$	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	$0.302890\pi$
$920$	−1.43663	+	55.7941i	−0.0473643	+	1.83948i
$921$	−5.04702	−	3.66687i	−0.166305	−	0.120828i
$922$	−10.9965	+	20.9488i	−0.362152	+	0.689910i
$923$	15.7631	−	8.03170i	0.518849	−	0.264367i
$924$	−1.26021	−	4.22521i	−0.0414579	−	0.138999i
$925$	7.86717	−	16.2935i	0.258671	−	0.535726i
$926$	23.4107	−	31.4122i	0.769322	−	1.03227i
$927$	6.23196	+	12.2309i	0.204684	+	0.401716i
$928$	−0.0355131	+	0.00343165i	−0.00116578	+	0.000112649i
$929$	0.175529	−	0.241595i	0.00575892	−	0.00792648i	−0.806128	−	0.591741i	$-0.798441\pi$
$929$	0.175529	−	0.241595i	0.00575892	−	0.00792648i	0.811887	+	0.583815i	$0.198441\pi$
$930$	2.59539	+	3.58312i	0.0851063	+	0.117495i
$931$	17.6291	+	24.2644i	0.577771	+	0.795233i
$932$	2.11408	−	3.91117i	0.0692489	−	0.128115i
$933$	1.80475	−	11.3947i	0.0590847	−	0.373046i
$934$	4.69285	−	13.8675i	0.153555	−	0.453759i
$935$	−3.40360	+	6.86054i	−0.111310	+	0.224364i
$936$	8.97380	+	7.03342i	0.293318	+	0.229895i
$937$	−2.37464	+	4.66050i	−0.0775762	+	0.152252i	−0.926537	−	0.376205i	$-0.877229\pi$
$937$	−2.37464	+	4.66050i	−0.0775762	+	0.152252i	0.848960	+	0.528456i	$0.177229\pi$
$938$	−12.5785	−	25.4462i	−0.410701	−	0.830849i
$939$	6.25805	−	19.2603i	0.204224	−	0.628536i
$940$	−0.896787	+	5.20330i	−0.0292500	+	0.169713i
$941$	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	$0.523982\pi$
$942$	11.6420	−	11.3625i	0.379316	−	0.370209i
$943$	38.9961	+	38.9961i	1.26989	+	1.26989i
$944$	21.0427	−	55.4404i	0.684880	−	1.80443i
$945$	10.6750	−	34.0918i	0.347256	−	1.10901i
$946$	−2.72194	−	8.73708i	−0.0884980	−	0.284067i
$947$	51.5107	−	8.15849i	1.67387	−	0.265115i	0.753868	−	0.657026i	$-0.228186\pi$
$947$	51.5107	−	8.15849i	1.67387	−	0.265115i	0.920003	+	0.391911i	$0.128186\pi$
$948$	3.93188	−	3.74530i	0.127702	−	0.121642i
$949$			11.6649i			0.378658i
$950$	−22.9626	+	11.9692i	−0.745007	+	0.388333i
$951$			2.76902i			0.0897917i
$952$	−50.0208	+	6.06348i	−1.62118	+	0.196519i
$953$	48.6871	−	7.71129i	1.57713	−	0.249793i	0.694371	−	0.719617i	$-0.255683\pi$
$953$	48.6871	−	7.71129i	1.57713	−	0.249793i	0.882760	+	0.469824i	$0.155683\pi$
$954$	30.2668	−	9.42930i	0.979923	−	0.305285i
$955$	6.80507	+	20.2052i	0.220207	+	0.653825i
$956$	1.01457	−	1.32737i	0.0328135	−	0.0429303i
$957$	−0.00252268	−	0.00252268i	−8.15467e−5	−	8.15467e-5i
$958$	23.5071	+	24.0854i	0.759481	+	0.778164i
$959$	−9.07401	−	27.9269i	−0.293015	−	0.901807i
$960$	8.93680	+	10.1237i	0.288434	+	0.326742i
$961$	8.51805	−	26.2159i	0.274776	−	0.845673i
$962$	−7.61003	+	3.76175i	−0.245357	+	0.121284i
$963$	4.11560	−	8.07732i	0.132623	−	0.260288i
$964$	−0.591130	+	24.3222i	−0.0190390	+	0.783365i
$965$	15.5160	+	15.1873i	0.499479	+	0.488897i
$966$	−34.7806	−	11.7700i	−1.11905	−	0.378693i
$967$	−6.72570	+	42.4644i	−0.216284	+	1.36556i	0.605537	+	0.795817i	$0.292959\pi$
$967$	−6.72570	+	42.4644i	−0.216284	+	1.36556i	−0.821821	+	0.569746i	$0.807041\pi$
$968$	12.4364	+	26.7776i	0.399720	+	0.860666i
$969$	7.42726	+	10.2227i	0.238598	+	0.328402i
$970$	20.6007	+	0.0297423i	0.661449	+	0.000954969i
$971$	21.5829	−	29.7063i	0.692627	−	0.953319i	−0.307372	−	0.951590i	$-0.599449\pi$
$971$	21.5829	−	29.7063i	0.692627	−	0.953319i	0.999999	−	0.00172953i	$-0.000550527\pi$
$972$	−13.3682	−	27.8919i	−0.428786	−	0.894634i
$973$	22.4140	+	43.9900i	0.718561	+	1.41026i
$974$	−27.5246	−	20.5133i	−0.881945	−	0.657289i
$975$	1.80684	−	5.99469i	0.0578653	−	0.191984i
$976$	−6.16237	+	4.03492i	−0.197253	+	0.129155i
$977$	−2.26941	+	1.15632i	−0.0726048	+	0.0369940i	−0.489916	−	0.871770i	$-0.662973\pi$
$977$	−2.26941	+	1.15632i	−0.0726048	+	0.0369940i	0.417311	+	0.908764i	$0.362973\pi$
$978$	10.6437	+	5.58717i	0.340349	+	0.178658i
$979$	2.41718	+	1.75618i	0.0772533	+	0.0561278i
$980$	34.6770	+	11.7907i	1.10771	+	0.376641i
$981$	−5.75649	+	4.18234i	−0.183791	+	0.133532i
$982$	−30.5984	+	4.46594i	−0.976435	+	0.142514i
$983$	35.5444	+	5.62969i	1.13369	+	0.179559i	0.694953	−	0.719055i	$-0.255425\pi$
$983$	35.5444	+	5.62969i	1.13369	+	0.179559i	0.438739	+	0.898615i	$0.355425\pi$
$984$	13.3345	+	0.486244i	0.425088	+	0.0155009i
$985$	29.0187	−	4.91513i	0.924613	−	0.156609i
$986$	−0.0332725	+	0.0235616i	−0.00105961	+	0.000750354i
$987$	−3.09503	−	1.57700i	−0.0985159	−	0.0501964i
$988$	11.9500	+	2.19157i	0.380181	+	0.0697231i
$989$	−72.4794	−	23.5500i	−2.30471	−	0.748846i
$990$	0.908998	−	5.68605i	0.0288899	−	0.180714i
$991$	14.2120	−	4.61776i	0.451459	−	0.146688i	−0.0744574	−	0.997224i	$-0.523722\pi$
$991$	14.2120	−	4.61776i	0.451459	−	0.146688i	0.525916	+	0.850536i	$0.323722\pi$
$992$	−2.26575	+	10.2365i	−0.0719377	+	0.325010i
$993$	−8.14277	+	8.14277i	−0.258403	+	0.258403i
$994$	0.714193	−	58.7800i	0.0226528	−	1.86439i
$995$	−0.618031	−	57.7258i	−0.0195929	−	1.83003i
$996$	0.987683	−	2.80589i	0.0312959	−	0.0889080i
$997$	−4.09586	−	25.8603i	−0.129717	−	0.819003i	−0.963656	−	0.267146i	$-0.913919\pi$
$997$	−4.09586	−	25.8603i	−0.129717	−	0.819003i	0.833939	−	0.551857i	$-0.186081\pi$
$998$	−13.6849	−	2.33825i	−0.433187	−	0.0740159i
$999$	14.8336			0.469313

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.2.l.b.47.1	✓	96	1.1	even	1	trivial
100.2.l.b.47.4	yes	96	4.3	odd	2	inner
100.2.l.b.83.1	yes	96	100.83	even	20	inner
100.2.l.b.83.4	yes	96	25.8	odd	20	inner
500.2.l.d.107.3		96	25.19	even	10
500.2.l.d.107.6		96	100.19	odd	10
500.2.l.d.243.3		96	20.7	even	4
500.2.l.d.243.6		96	5.2	odd	4
500.2.l.e.107.7		96	100.31	odd	10
500.2.l.e.107.10		96	25.6	even	5
500.2.l.e.243.7		96	5.3	odd	4
500.2.l.e.243.10		96	20.3	even	4
500.2.l.f.7.9		96	20.19	odd	2
500.2.l.f.7.12		96	5.4	even	2
500.2.l.f.143.9		96	25.17	odd	20
500.2.l.f.143.12		96	100.67	even	20
900.2.bj.d.847.9		96	12.11	even	2
900.2.bj.d.847.12		96	3.2	odd	2
900.2.bj.d.883.9		96	75.8	even	20
900.2.bj.d.883.12		96	300.83	odd	20

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39401 - 0.238186i) q^{2} +(-0.118091 - 0.745599i) q^{3} +(1.88654 + 0.664067i) q^{4} +(0.0239387 + 2.23594i) q^{5} +(-0.0129704 + 1.06750i) q^{6} +(2.75590 - 2.75590i) q^{7} +(-2.47168 - 1.37506i) q^{8} +(2.31120 - 0.750953i) q^{9} +(0.499198 - 3.12263i) q^{10} +(0.712633 + 0.231549i) q^{11} +(0.272345 - 1.48502i) q^{12} +(-1.47800 - 0.753078i) q^{13} +(-4.49817 + 3.18534i) q^{14} +(1.66429 - 0.281894i) q^{15} +(3.11803 + 2.50557i) q^{16} +(4.51455 + 0.715035i) q^{17} +(-3.40070 + 0.496343i) q^{18} +(-2.96269 + 2.15252i) q^{19} +(-1.43965 + 4.23408i) q^{20} +(-2.38025 - 1.72935i) q^{21} +(-0.938267 - 0.492520i) q^{22} +(-7.86291 + 4.00635i) q^{23} +(-0.733362 + 2.00527i) q^{24} +(-4.99885 + 0.107051i) q^{25} +(1.88097 + 1.40184i) q^{26} +(-1.86099 - 3.65239i) q^{27} +(7.02921 - 3.36900i) q^{28} +(0.00370724 - 0.00510258i) q^{29} +(-2.38718 - 0.00344650i) q^{30} +(-1.08939 - 1.49941i) q^{31} +(-3.74978 - 4.23547i) q^{32} +(0.0884866 - 0.558683i) q^{33} +(-6.12303 - 2.07207i) q^{34} +(6.22800 + 6.09605i) q^{35} +(4.85884 + 0.118090i) q^{36} +(-1.64284 + 3.22426i) q^{37} +(4.64273 - 2.29497i) q^{38} +(-0.386956 + 1.19093i) q^{39} +(3.01539 - 5.55945i) q^{40} +(-1.93115 - 5.94348i) q^{41} +(2.90618 + 2.97767i) q^{42} +(6.10648 + 6.10648i) q^{43} +(1.19064 + 0.910061i) q^{44} +(1.73441 + 5.14972i) q^{45} +(11.9152 - 3.71207i) q^{46} +(1.16611 - 0.184694i) q^{47} +(1.49994 - 2.62069i) q^{48} -8.18997i q^{49} +(6.99396 + 1.04143i) q^{50} -3.45049i q^{51} +(-2.28820 - 2.40220i) q^{52} +(-9.11077 + 1.44300i) q^{53} +(1.72429 + 5.53473i) q^{54} +(-0.500669 + 1.59895i) q^{55} +(-10.6012 + 3.02217i) q^{56} +(1.95479 + 1.95479i) q^{57} +(-0.00638330 + 0.00623004i) q^{58} +(-4.58114 - 14.0993i) q^{59} +(3.32694 + 0.573397i) q^{60} +(-0.569042 + 1.75133i) q^{61} +(1.16148 + 2.34967i) q^{62} +(4.29987 - 8.43898i) q^{63} +(4.21840 + 6.79743i) q^{64} +(1.64846 - 3.32274i) q^{65} +(-0.256422 + 0.757734i) q^{66} +(-0.805626 + 5.08652i) q^{67} +(8.04203 + 4.34691i) q^{68} +(3.91567 + 5.38946i) q^{69} +(-7.22991 - 9.98139i) q^{70} +(-6.26883 + 8.62831i) q^{71} +(-6.74515 - 1.32192i) q^{72} +(-3.19252 - 6.26568i) q^{73} +(3.05811 - 4.10335i) q^{74} +(0.670139 + 3.71450i) q^{75} +(-7.01865 + 2.09338i) q^{76} +(2.60207 - 1.32582i) q^{77} +(0.823082 - 1.56800i) q^{78} +(2.90976 + 2.11406i) q^{79} +(-5.52767 + 7.03171i) q^{80} +(3.39461 - 2.46633i) q^{81} +(1.27640 + 8.74525i) q^{82} +(1.94599 + 0.308214i) q^{83} +(-3.34201 - 4.84312i) q^{84} +(-1.49070 + 10.1114i) q^{85} +(-7.05803 - 9.96698i) q^{86} +(-0.00424227 - 0.00216155i) q^{87} +(-1.44301 - 1.55223i) q^{88} +(3.79225 + 1.23218i) q^{89} +(-1.19120 - 7.59188i) q^{90} +(-6.14862 + 1.99781i) q^{91} +(-17.4941 + 2.33662i) q^{92} +(-0.989314 + 0.989314i) q^{93} +(-1.66956 - 0.0202857i) q^{94} +(-4.88383 - 6.57288i) q^{95} +(-2.71514 + 3.29600i) q^{96} +(1.01910 + 6.43432i) q^{97} +(-1.95073 + 11.4169i) q^{98} +1.82092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 10 q^{2} - 10 q^{4} - 20 q^{5} - 6 q^{6} - 10 q^{8} - 20 q^{9} - 10 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{14} - 14 q^{16} - 20 q^{17} + 20 q^{18} + 10 q^{20} - 12 q^{21} - 10 q^{22} - 20 q^{25}+ \cdots - 130 q^{98}+O(q^{100}) \) 96 * q - 10 * q^2 - 10 * q^4 - 20 * q^5 - 6 * q^6 - 10 * q^8 - 20 * q^9 - 10 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^14 - 14 * q^16 - 20 * q^17 + 20 * q^18 + 10 * q^20 - 12 * q^21 - 10 * q^22 - 20 * q^25 - 12 * q^26 - 10 * q^28 - 20 * q^29 - 10 * q^30 - 50 * q^32 - 20 * q^33 - 60 * q^34 - 10 * q^36 + 40 * q^37 + 20 * q^38 + 40 * q^40 - 28 * q^41 + 90 * q^42 + 60 * q^44 - 20 * q^45 - 6 * q^46 + 120 * q^48 + 80 * q^50 + 80 * q^52 - 40 * q^53 + 120 * q^54 - 6 * q^56 - 20 * q^57 + 60 * q^58 + 90 * q^60 + 12 * q^61 + 40 * q^62 + 20 * q^64 - 100 * q^65 - 30 * q^66 - 10 * q^68 - 20 * q^69 - 10 * q^70 - 40 * q^72 - 20 * q^73 - 20 * q^77 + 20 * q^78 - 10 * q^80 - 36 * q^81 - 50 * q^82 - 90 * q^84 + 100 * q^85 - 6 * q^86 - 130 * q^88 + 160 * q^89 - 160 * q^90 - 110 * q^92 + 60 * q^93 - 170 * q^94 + 14 * q^96 + 180 * q^97 - 130 * q^98

Introduction

L-functions

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