LMFDB - Embedded newform 288.2.w.b.107.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,2,Mod(35,288)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("288.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.w (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	288.107
Dual form			288.2.w.b.35.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.345448 - 1.37137i) q^{2} +(-1.76133 - 0.947475i) q^{4} +(1.64859 + 0.682869i) q^{5} +(2.51270 - 2.51270i) q^{7} +(-1.90779 + 2.08814i) q^{8} +(1.50597 - 2.02494i) q^{10} +(2.69097 + 1.11464i) q^{11} +(-1.76057 - 4.25040i) q^{13} +(-2.57784 - 4.31386i) q^{14} +(2.20458 + 3.33764i) q^{16} -6.10169 q^{17} +(3.43292 - 1.42196i) q^{19} +(-2.25672 - 2.76476i) q^{20} +(2.45817 - 3.30527i) q^{22} +(0.525502 - 0.525502i) q^{23} +(-1.28399 - 1.28399i) q^{25} +(-6.43707 + 0.946113i) q^{26} +(-6.80642 + 2.04498i) q^{28} +(1.46544 + 3.53788i) q^{29} +7.55322i q^{31} +(5.33872 - 1.87033i) q^{32} +(-2.10781 + 8.36770i) q^{34} +(5.85826 - 2.42657i) q^{35} +(2.30333 - 5.56073i) q^{37} +(-0.764149 - 5.19904i) q^{38} +(-4.57109 + 2.13972i) q^{40} +(3.04402 + 3.04402i) q^{41} +(-3.31422 + 8.00123i) q^{43} +(-3.68360 - 4.51287i) q^{44} +(-0.539126 - 0.902192i) q^{46} +8.59875i q^{47} -5.62732i q^{49} +(-2.20438 + 1.31728i) q^{50} +(-0.926194 + 9.15446i) q^{52} +(-3.78946 + 9.14856i) q^{53} +(3.67516 + 3.67516i) q^{55} +(0.453168 + 10.0406i) q^{56} +(5.35798 - 0.787511i) q^{58} +(3.73387 - 9.01437i) q^{59} +(3.41173 - 1.41318i) q^{61} +(10.3583 + 2.60924i) q^{62} +(-0.720670 - 7.96747i) q^{64} -8.20941i q^{65} +(0.0538792 + 0.130076i) q^{67} +(10.7471 + 5.78120i) q^{68} +(-1.30401 - 8.87212i) q^{70} +(1.31641 + 1.31641i) q^{71} +(-10.9226 + 10.9226i) q^{73} +(-6.83016 - 5.07966i) q^{74} +(-7.39380 - 0.748061i) q^{76} +(9.56234 - 3.96085i) q^{77} +11.8735 q^{79} +(1.35528 + 7.00784i) q^{80} +(5.22604 - 3.12294i) q^{82} +(-4.38490 - 10.5861i) q^{83} +(-10.0592 - 4.16666i) q^{85} +(9.82779 + 7.30904i) q^{86} +(-7.46132 + 3.49263i) q^{88} +(-5.97566 + 5.97566i) q^{89} +(-15.1038 - 6.25618i) q^{91} +(-1.42348 + 0.427683i) q^{92} +(11.7921 + 2.97042i) q^{94} +6.63051 q^{95} -3.21530 q^{97} +(-7.71716 - 1.94394i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52}+ \cdots + 44 q^{98}+O(q^{100}) $ 32 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^11 - 12 * q^14 + 8 * q^16 - 32 * q^20 + 16 * q^22 + 36 * q^26 + 16 * q^29 + 24 * q^32 - 24 * q^35 - 32 * q^38 - 32 * q^40 - 8 * q^44 - 32 * q^46 - 8 * q^50 - 56 * q^52 + 16 * q^53 - 32 * q^55 - 40 * q^56 - 32 * q^58 - 32 * q^59 + 32 * q^61 + 68 * q^62 - 48 * q^64 - 16 * q^67 + 72 * q^68 - 48 * q^70 - 16 * q^71 - 60 * q^74 - 8 * q^76 + 16 * q^77 - 32 * q^79 - 96 * q^80 + 40 * q^82 + 40 * q^83 + 40 * q^86 + 40 * q^88 - 48 * q^91 + 16 * q^92 + 72 * q^94 + 80 * q^95 + 44 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.345448	−	1.37137i	0.244268	−	0.969708i
$2$	0.345448	−	1.37137i	0.244268	−	0.969708i
$3$		0			0
$3$		0			0
$4$	−1.76133	−	0.947475i	−0.880666	−	0.473738i
$5$	1.64859	+	0.682869i	0.737273	+	0.305388i	0.719537	−	0.694454i	$-0.244354\pi$
$5$	1.64859	+	0.682869i	0.737273	+	0.305388i	0.0177359	+	0.999843i	$0.494354\pi$
$6$		0			0
$7$	2.51270	−	2.51270i	0.949711	−	0.949711i	−0.0490835	−	0.998795i	$-0.515630\pi$
$7$	2.51270	−	2.51270i	0.949711	−	0.949711i	0.998795	+	0.0490835i	$0.0156300\pi$
$8$	−1.90779	+	2.08814i	−0.674506	+	0.738270i
$9$		0			0
$10$	1.50597	−	2.02494i	0.476230	−	0.640342i
$11$	2.69097	+	1.11464i	0.811357	+	0.336075i	0.749495	−	0.662010i	$-0.230296\pi$
$11$	2.69097	+	1.11464i	0.811357	+	0.336075i	0.0618618	+	0.998085i	$0.480296\pi$
$12$		0			0
$13$	−1.76057	−	4.25040i	−0.488295	−	1.17885i	−0.955577	−	0.294740i	$-0.904767\pi$
$13$	−1.76057	−	4.25040i	−0.488295	−	1.17885i	0.467283	−	0.884108i	$-0.345233\pi$
$14$	−2.57784	−	4.31386i	−0.688958	−	1.15293i
$15$		0			0
$16$	2.20458	+	3.33764i	0.551145	+	0.834409i
$17$	−6.10169			−1.47988			−0.739939	−	0.672674i	$-0.765146\pi$
$17$	−6.10169			−1.47988			−0.739939	+	0.672674i	$0.765146\pi$
$18$		0			0
$19$	3.43292	−	1.42196i	0.787567	−	0.326221i	0.0476020	−	0.998866i	$-0.484842\pi$
$19$	3.43292	−	1.42196i	0.787567	−	0.326221i	0.739965	+	0.672645i	$0.234842\pi$
$20$	−2.25672	−	2.76476i	−0.504617	−	0.618219i
$21$		0			0
$22$	2.45817	−	3.30527i	0.524083	−	0.704687i
$23$	0.525502	−	0.525502i	0.109575	−	0.109575i	−0.650194	−	0.759768i	$-0.725312\pi$
$23$	0.525502	−	0.525502i	0.109575	−	0.109575i	0.759768	+	0.650194i	$0.225312\pi$
$24$		0			0
$25$	−1.28399	−	1.28399i	−0.256798	−	0.256798i
$26$	−6.43707	+	0.946113i	−1.26241	+	0.185548i
$27$		0			0
$28$	−6.80642	+	2.04498i	−1.28629	+	0.386464i
$29$	1.46544	+	3.53788i	0.272125	+	0.656967i	0.999574	−	0.0291945i	$-0.00929421\pi$
$29$	1.46544	+	3.53788i	0.272125	+	0.656967i	−0.727449	+	0.686162i	$0.759294\pi$
$30$		0			0
$31$			7.55322i			1.35660i	0.734786	+	0.678299i	$0.237283\pi$
$31$			7.55322i			1.35660i	−0.734786	+	0.678299i	$0.762717\pi$
$32$	5.33872	−	1.87033i	0.943760	−	0.330630i
$33$		0			0
$34$	−2.10781	+	8.36770i	−0.361487	+	1.43505i
$35$	5.85826	−	2.42657i	0.990227	−	0.410165i
$36$		0			0
$37$	2.30333	−	5.56073i	0.378665	−	0.914178i	−0.613552	−	0.789655i	$-0.710260\pi$
$37$	2.30333	−	5.56073i	0.378665	−	0.914178i	0.992217	−	0.124523i	$-0.0397402\pi$
$38$	−0.764149	−	5.19904i	−0.123961	−	0.843395i
$39$		0			0
$40$	−4.57109	+	2.13972i	−0.722754	+	0.338320i
$41$	3.04402	+	3.04402i	0.475396	+	0.475396i	0.903656	−	0.428260i	$-0.140873\pi$
$41$	3.04402	+	3.04402i	0.475396	+	0.475396i	−0.428260	+	0.903656i	$0.640873\pi$
$42$		0			0
$43$	−3.31422	+	8.00123i	−0.505414	+	1.22018i	0.441084	+	0.897466i	$0.354594\pi$
$43$	−3.31422	+	8.00123i	−0.505414	+	1.22018i	−0.946498	+	0.322711i	$0.895406\pi$
$44$	−3.68360	−	4.51287i	−0.555323	−	0.680340i
$45$		0			0
$46$	−0.539126	−	0.902192i	−0.0794898	−	0.133021i
$47$			8.59875i			1.25426i	0.778916	+	0.627128i	$0.215770\pi$
$47$			8.59875i			1.25426i	−0.778916	+	0.627128i	$0.784230\pi$
$48$		0			0
$49$		−	5.62732i		−	0.803903i
$50$	−2.20438	+	1.31728i	−0.311746	+	0.186291i
$51$		0			0
$52$	−0.926194	+	9.15446i	−0.128440	+	1.26950i
$53$	−3.78946	+	9.14856i	−0.520522	+	1.25665i	0.417058	+	0.908880i	$0.363061\pi$
$53$	−3.78946	+	9.14856i	−0.520522	+	1.25665i	−0.937580	+	0.347771i	$0.886939\pi$
$54$		0			0
$55$	3.67516	+	3.67516i	0.495558	+	0.495558i
$56$	0.453168	+	10.0406i	0.0605571	+	1.34173i
$57$		0			0
$58$	5.35798	−	0.787511i	0.703538	−	0.103405i
$59$	3.73387	−	9.01437i	0.486109	−	1.17357i	−0.470553	−	0.882372i	$-0.655946\pi$
$59$	3.73387	−	9.01437i	0.486109	−	1.17357i	0.956662	−	0.291199i	$-0.0940543\pi$
$60$		0			0
$61$	3.41173	−	1.41318i	0.436827	−	0.180940i	−0.153422	−	0.988161i	$-0.549030\pi$
$61$	3.41173	−	1.41318i	0.436827	−	0.180940i	0.590249	+	0.807221i	$0.299030\pi$
$62$	10.3583	+	2.60924i	1.31550	+	0.331374i
$63$		0			0
$64$	−0.720670	−	7.96747i	−0.0900838	−	0.995934i
$65$		−	8.20941i		−	1.01825i
$66$		0			0
$67$	0.0538792	+	0.130076i	0.00658239	+	0.0158913i	0.927137	−	0.374724i	$-0.122262\pi$
$67$	0.0538792	+	0.130076i	0.00658239	+	0.0158913i	−0.920554	+	0.390615i	$0.872262\pi$
$68$	10.7471	+	5.78120i	1.30328	+	0.701074i
$69$		0			0
$70$	−1.30401	−	8.87212i	−0.155860	−	1.06042i
$71$	1.31641	+	1.31641i	0.156229	+	0.156229i	0.780893	−	0.624664i	$-0.214764\pi$
$71$	1.31641	+	1.31641i	0.156229	+	0.156229i	−0.624664	+	0.780893i	$0.714764\pi$
$72$		0			0
$73$	−10.9226	+	10.9226i	−1.27839	+	1.27839i	−0.336829	+	0.941566i	$0.609354\pi$
$73$	−10.9226	+	10.9226i	−1.27839	+	1.27839i	−0.941566	+	0.336829i	$0.890646\pi$
$74$	−6.83016	−	5.07966i	−0.793990	−	0.590499i
$75$		0			0
$76$	−7.39380	−	0.748061i	−0.848127	−	0.0858085i
$77$	9.56234	−	3.96085i	1.08973	−	0.451381i
$78$		0			0
$79$	11.8735			1.33588			0.667939	−	0.744216i	$-0.267177\pi$
$79$	11.8735			1.33588			0.667939	+	0.744216i	$0.267177\pi$
$80$	1.35528	+	7.00784i	0.151525	+	0.783500i
$81$		0			0
$82$	5.22604	−	3.12294i	0.577119	−	0.344871i
$83$	−4.38490	−	10.5861i	−0.481305	−	1.16197i	−0.958989	−	0.283442i	$-0.908524\pi$
$83$	−4.38490	−	10.5861i	−0.481305	−	1.16197i	0.477684	−	0.878532i	$-0.341476\pi$
$84$		0			0
$85$	−10.0592	−	4.16666i	−1.09107	−	0.451937i
$86$	9.82779	+	7.30904i	1.05976	+	0.788154i
$87$		0			0
$88$	−7.46132	+	3.49263i	−0.795379	+	0.372316i
$89$	−5.97566	+	5.97566i	−0.633418	+	0.633418i	−0.948924	−	0.315506i	$-0.897826\pi$
$89$	−5.97566	+	5.97566i	−0.633418	+	0.633418i	0.315506	+	0.948924i	$0.397826\pi$
$90$		0			0
$91$	−15.1038	−	6.25618i	−1.58330	−	0.655826i
$92$	−1.42348	+	0.427683i	−0.148408	+	0.0445890i
$93$		0			0
$94$	11.7921	+	2.97042i	1.21626	+	0.306375i
$95$	6.63051			0.680276
$96$		0			0
$97$	−3.21530			−0.326464			−0.163232	−	0.986588i	$-0.552192\pi$
$97$	−3.21530			−0.326464			−0.163232	+	0.986588i	$0.552192\pi$
$98$	−7.71716	−	1.94394i	−0.779551	−	0.196368i
$99$		0			0
$100$	1.04498	+	3.47808i	0.104498	+	0.347808i
$101$	1.62739	+	0.674085i	0.161931	+	0.0670740i	0.462177	−	0.886788i	$-0.347069\pi$
$101$	1.62739	+	0.674085i	0.161931	+	0.0670740i	−0.300246	+	0.953862i	$0.597069\pi$
$102$		0			0
$103$	0.111372	−	0.111372i	0.0109738	−	0.0109738i	−0.701599	−	0.712572i	$-0.747530\pi$
$103$	0.111372	−	0.111372i	0.0109738	−	0.0109738i	0.712572	+	0.701599i	$0.247530\pi$
$104$	12.2342	+	4.43254i	1.19967	+	0.434647i
$105$		0			0
$106$	11.2370	+	8.35711i	1.09144	+	0.811714i
$107$	−3.59142	−	1.48762i	−0.347196	−	0.143813i	0.202269	−	0.979330i	$-0.435168\pi$
$107$	−3.59142	−	1.48762i	−0.347196	−	0.143813i	−0.549465	+	0.835517i	$0.685168\pi$
$108$		0			0
$109$	5.90637	+	14.2592i	0.565727	+	1.36579i	0.905126	+	0.425144i	$0.139777\pi$
$109$	5.90637	+	14.2592i	0.565727	+	1.36579i	−0.339398	+	0.940643i	$0.610223\pi$
$110$	6.30959	−	3.77044i	0.601596	−	0.359497i
$111$		0			0
$112$	13.9259	+	2.84703i	1.31588	+	0.269019i
$113$	−16.6022			−1.56180			−0.780902	−	0.624653i	$-0.785240\pi$
$113$	−16.6022			−1.56180			−0.780902	+	0.624653i	$0.785240\pi$
$114$		0			0
$115$	1.22519	−	0.507489i	0.114249	−	0.0473236i
$116$	0.770931	−	7.61984i	0.0715791	−	0.707485i
$117$		0			0
$118$	−11.0722	−	8.23453i	−1.01928	−	0.758050i
$119$	−15.3317	+	15.3317i	−1.40546	+	1.40546i
$120$		0			0
$121$	−1.77928	−	1.77928i	−0.161753	−	0.161753i
$122$	−0.759430	−	5.16693i	−0.0687556	−	0.467792i
$123$		0			0
$124$	7.15649	−	13.3037i	0.642672	−	1.19471i
$125$	−4.65432	−	11.2365i	−0.416295	−	1.00503i
$126$		0			0
$127$			19.5462i			1.73444i	0.497923	+	0.867221i	$0.334096\pi$
$127$			19.5462i			1.73444i	−0.497923	+	0.867221i	$0.665904\pi$
$128$	−11.1753	−	1.76404i	−0.987770	−	0.155920i
$129$		0			0
$130$	−11.2582	−	2.83592i	−0.987407	−	0.248727i
$131$	5.97269	−	2.47397i	0.521837	−	0.216152i	−0.106187	−	0.994346i	$-0.533864\pi$
$131$	5.97269	−	2.47397i	0.521837	−	0.216152i	0.628023	+	0.778194i	$0.283864\pi$
$132$		0			0
$133$	5.05294	−	12.1989i	0.438145	−	1.05778i
$134$	0.196995	−	0.0289541i	0.0170178	−	0.00250126i
$135$		0			0
$136$	11.6407	−	12.7412i	0.998186	−	1.09255i
$137$	−13.9438	−	13.9438i	−1.19130	−	1.19130i	−0.976703	−	0.214594i	$-0.931157\pi$
$137$	−13.9438	−	13.9438i	−1.19130	−	1.19130i	−0.214594	−	0.976703i	$-0.568843\pi$
$138$		0			0
$139$	5.10923	−	12.3348i	0.433359	−	1.04622i	−0.544838	−	0.838542i	$-0.683409\pi$
$139$	5.10923	−	12.3348i	0.433359	−	1.04622i	0.978197	−	0.207680i	$-0.0665913\pi$
$140$	−12.6175	−	1.27656i	−1.06637	−	0.107889i
$141$		0			0
$142$	2.26004	−	1.35054i	0.189658	−	0.113335i
$143$		−	13.4001i		−	1.12057i
$144$		0			0
$145$			6.83322i			0.567468i
$146$	11.2058	+	18.7522i	0.927398	+	1.55194i
$147$		0			0
$148$	−9.32558	+	7.61194i	−0.766558	+	0.625698i
$149$	−1.29028	+	3.11502i	−0.105704	+	0.255192i	−0.967878	−	0.251420i	$-0.919102\pi$
$149$	−1.29028	+	3.11502i	−0.105704	+	0.255192i	0.862174	+	0.506612i	$0.169102\pi$
$150$		0			0
$151$	−10.0537	−	10.0537i	−0.818159	−	0.818159i	0.167682	−	0.985841i	$-0.446372\pi$
$151$	−10.0537	−	10.0537i	−0.818159	−	0.818159i	−0.985841	+	0.167682i	$0.946372\pi$
$152$	−3.58004	+	9.88124i	−0.290380	+	0.801475i
$153$		0			0
$154$	−2.12852	−	14.4818i	−0.171521	−	1.16698i
$155$	−5.15786	+	12.4522i	−0.414289	+	1.00018i
$156$		0			0
$157$	15.3765	−	6.36916i	1.22718	−	0.508315i	0.327494	−	0.944853i	$-0.393796\pi$
$157$	15.3765	−	6.36916i	1.22718	−	0.508315i	0.899686	+	0.436539i	$0.143796\pi$
$158$	4.10169	−	16.2831i	0.326313	−	1.29541i
$159$		0			0
$160$	10.0785	+	0.562239i	0.796779	+	0.0444489i
$161$		−	2.64086i		−	0.208129i
$162$		0			0
$163$	4.22080	+	10.1899i	0.330599	+	0.798136i	0.998545	+	0.0539266i	$0.0171737\pi$
$163$	4.22080	+	10.1899i	0.330599	+	0.798136i	−0.667946	+	0.744210i	$0.732826\pi$
$164$	−2.47740	−	8.24566i	−0.193452	−	0.643878i
$165$		0			0
$166$	−16.0322	+	2.35640i	−1.24434	+	0.182892i
$167$	−11.1209	−	11.1209i	−0.860562	−	0.860562i	0.130842	−	0.991403i	$-0.458232\pi$
$167$	−11.1209	−	11.1209i	−0.860562	−	0.860562i	−0.991403	+	0.130842i	$0.958232\pi$
$168$		0			0
$169$	−5.77387	+	5.77387i	−0.444144	+	0.444144i
$170$	−9.18897	+	12.3556i	−0.704762	+	0.947628i
$171$		0			0
$172$	13.4184	−	10.9527i	1.02314	−	0.835134i
$173$	9.66463	−	4.00322i	0.734788	−	0.304359i	0.0162700	−	0.999868i	$-0.494821\pi$
$173$	9.66463	−	4.00322i	0.734788	−	0.304359i	0.718518	+	0.695509i	$0.244821\pi$
$174$		0			0
$175$	−6.45256			−0.487768
$176$	2.21221	+	11.4388i	0.166751	+	0.862230i
$177$		0			0
$178$	6.13058	+	10.2591i	0.459507	+	0.768955i
$179$	−6.65549	−	16.0678i	−0.497455	−	1.20096i	−0.950850	−	0.309652i	$-0.899787\pi$
$179$	−6.65549	−	16.0678i	−0.497455	−	1.20096i	0.453395	−	0.891310i	$-0.350213\pi$
$180$		0			0
$181$	−16.5604	−	6.85953i	−1.23092	−	0.509865i	−0.330056	−	0.943961i	$-0.607068\pi$
$181$	−16.5604	−	6.85953i	−1.23092	−	0.509865i	−0.900867	+	0.434096i	$0.857068\pi$
$182$	−13.7971	+	18.5517i	−1.02271	+	1.37514i
$183$		0			0
$184$	0.0947747	+	2.09987i	0.00698688	+	0.154804i
$185$	7.59450	−	7.59450i	0.558359	−	0.558359i
$186$		0			0
$187$	−16.4195	−	6.80116i	−1.20071	−	0.497350i
$188$	8.14710	−	15.1453i	0.594189	−	1.10458i
$189$		0			0
$190$	2.29049	−	9.09290i	0.166170	−	0.659668i
$191$	−0.545506			−0.0394715			−0.0197357	−	0.999805i	$-0.506282\pi$
$191$	−0.545506			−0.0394715			−0.0197357	+	0.999805i	$0.506282\pi$
$192$		0			0
$193$	13.7484			0.989632			0.494816	−	0.868998i	$-0.335235\pi$
$193$	13.7484			0.989632			0.494816	+	0.868998i	$0.335235\pi$
$194$	−1.11072	+	4.40938i	−0.0797448	+	0.316575i
$195$		0			0
$196$	−5.33175	+	9.91158i	−0.380839	+	0.707970i
$197$	3.74434	+	1.55095i	0.266773	+	0.110501i	0.512060	−	0.858949i	$-0.328882\pi$
$197$	3.74434	+	1.55095i	0.266773	+	0.110501i	−0.245288	+	0.969450i	$0.578882\pi$
$198$		0			0
$199$	9.72904	−	9.72904i	0.689673	−	0.689673i	−0.272486	−	0.962160i	$-0.587846\pi$
$199$	9.72904	−	9.72904i	0.689673	−	0.689673i	0.962160	+	0.272486i	$0.0878460\pi$
$200$	5.13074	−	0.231569i	0.362798	−	0.0163744i
$201$		0			0
$202$	1.48660	−	1.99889i	0.104597	−	0.140642i
$203$	12.5718	+	5.20742i	0.882369	+	0.365489i
$204$		0			0
$205$	2.93968	+	7.09701i	0.205316	+	0.495677i
$206$	−0.114259	−	0.191205i	−0.00796080	−	0.0133219i
$207$		0			0
$208$	10.3050	−	15.2465i	0.714520	−	1.05715i
$209$	10.8229			0.748633
$210$		0			0
$211$	12.8221	−	5.31108i	0.882708	−	0.365630i	0.105162	−	0.994455i	$-0.466464\pi$
$211$	12.8221	−	5.31108i	0.882708	−	0.365630i	0.777546	+	0.628826i	$0.216464\pi$
$212$	15.3425	−	12.5232i	1.05373	−	0.860099i
$213$		0			0
$214$	−3.28073	+	4.41129i	−0.224266	+	0.301550i
$215$	−10.9276	+	10.9276i	−0.745255	+	0.745255i
$216$		0			0
$217$	18.9790	+	18.9790i	1.28838	+	1.28838i
$218$	21.5951	−	3.17402i	1.46260	−	0.214972i
$219$		0			0
$220$	−2.99105	−	9.95529i	−0.201657	−	0.671186i
$221$	10.7425	+	25.9346i	0.722616	+	1.74455i
$222$		0			0
$223$		−	11.9519i		−	0.800361i	−0.916436	−	0.400180i	$-0.868947\pi$
$223$		−	11.9519i		−	0.800361i	0.916436	−	0.400180i	$-0.131053\pi$
$224$	8.71502	−	18.1142i	0.582297	−	1.21030i
$225$		0			0
$226$	−5.73519	+	22.7678i	−0.381499	+	1.51449i
$227$	7.57146	−	3.13620i	0.502536	−	0.208157i	−0.116991	−	0.993133i	$-0.537325\pi$
$227$	7.57146	−	3.13620i	0.502536	−	0.208157i	0.619526	+	0.784976i	$0.287325\pi$
$228$		0			0
$229$	−4.36683	+	10.5425i	−0.288568	+	0.696665i	−0.999981	−	0.00610879i	$-0.998055\pi$
$229$	−4.36683	+	10.5425i	−0.288568	+	0.696665i	0.711413	+	0.702774i	$0.248055\pi$
$230$	−0.272719	−	1.85550i	−0.0179826	−	0.122348i
$231$		0			0
$232$	−10.1833	−	3.68949i	−0.668569	−	0.242227i
$233$	16.6048	+	16.6048i	1.08782	+	1.08782i	0.995753	+	0.0920662i	$0.0293472\pi$
$233$	16.6048	+	16.6048i	1.08782	+	1.08782i	0.0920662	+	0.995753i	$0.470653\pi$
$234$		0			0
$235$	−5.87182	+	14.1758i	−0.383035	+	0.924729i
$236$	−15.1175	+	12.3395i	−0.984065	+	0.803236i
$237$		0			0
$238$	15.7292	+	26.3218i	1.01957	+	1.70619i
$239$			19.8212i			1.28213i	0.767488	+	0.641063i	$0.221506\pi$
$239$			19.8212i			1.28213i	−0.767488	+	0.641063i	$0.778494\pi$
$240$		0			0
$241$		−	7.78762i		−	0.501645i	−0.968033	−	0.250823i	$-0.919299\pi$
$241$		−	7.78762i		−	0.501645i	0.968033	−	0.250823i	$-0.0807011\pi$
$242$	−3.05471	+	1.82541i	−0.196364	+	0.117342i
$243$		0			0
$244$	−7.34814	−	0.743441i	−0.470416	−	0.0475940i
$245$	3.84272	−	9.27715i	0.245503	−	0.592695i
$246$		0			0
$247$	−12.0878	−	12.0878i	−0.769130	−	0.769130i
$248$	−15.7722	−	14.4100i	−1.00153	−	0.915033i
$249$		0			0
$250$	−17.0173	+	2.50119i	−1.07627	+	0.158189i
$251$	−11.1471	+	26.9114i	−0.703597	+	1.69863i	0.0118144	+	0.999930i	$0.496239\pi$
$251$	−11.1471	+	26.9114i	−0.703597	+	1.69863i	−0.715412	+	0.698703i	$0.753761\pi$
$252$		0			0
$253$	1.99985	−	0.828365i	0.125729	−	0.0520789i
$254$	26.8051	+	6.75218i	1.68190	+	0.423669i
$255$		0			0
$256$	−6.27965	+	14.7162i	−0.392478	+	0.919761i
$257$		−	6.18232i		−	0.385643i	−0.981234	−	0.192821i	$-0.938236\pi$
$257$		−	6.18232i		−	0.385643i	0.981234	−	0.192821i	$-0.0617638\pi$
$258$		0			0
$259$	−8.18487	−	19.7600i	−0.508583	−	1.22783i
$260$	−7.77821	+	14.4595i	−0.482384	+	0.896740i
$261$		0			0
$262$	−1.32949	−	9.04542i	−0.0821359	−	0.558828i
$263$	2.98771	+	2.98771i	0.184230	+	0.184230i	0.793196	−	0.608966i	$-0.208416\pi$
$263$	2.98771	+	2.98771i	0.184230	+	0.184230i	−0.608966	+	0.793196i	$0.708416\pi$
$264$		0			0
$265$	−12.4945	+	12.4945i	−0.767533	+	0.767533i
$266$	−14.9837	−	11.1435i	−0.918709	−	0.683254i
$267$		0			0
$268$	0.0283445	−	0.280156i	0.00173142	−	0.0171133i
$269$	14.2963	−	5.92170i	0.871658	−	0.361053i	0.0984022	−	0.995147i	$-0.468627\pi$
$269$	14.2963	−	5.92170i	0.871658	−	0.361053i	0.773256	+	0.634094i	$0.218627\pi$
$270$		0			0
$271$	−4.23625			−0.257334			−0.128667	−	0.991688i	$-0.541070\pi$
$271$	−4.23625			−0.257334			−0.128667	+	0.991688i	$0.541070\pi$
$272$	−13.4517	−	20.3652i	−0.815627	−	1.23482i
$273$		0			0
$274$	−23.9390	+	14.3053i	−1.44621	+	0.864214i
$275$	−2.02399	−	4.88635i	−0.122051	−	0.294658i
$276$		0			0
$277$	1.63206	+	0.676023i	0.0980612	+	0.0406183i	0.431175	−	0.902268i	$-0.358099\pi$
$277$	1.63206	+	0.676023i	0.0980612	+	0.0406183i	−0.333114	+	0.942887i	$0.608099\pi$
$278$	−15.1506	−	11.2677i	−0.908673	−	0.675791i
$279$		0			0
$280$	−6.10931	+	16.8623i	−0.365101	+	1.00771i
$281$	−0.648281	+	0.648281i	−0.0386732	+	0.0386732i	−0.726179	−	0.687506i	$-0.758706\pi$
$281$	−0.648281	+	0.648281i	−0.0386732	+	0.0386732i	0.687506	+	0.726179i	$0.258706\pi$
$282$		0			0
$283$	−0.905971	−	0.375265i	−0.0538544	−	0.0223072i	0.355594	−	0.934641i	$-0.384279\pi$
$283$	−0.905971	−	0.375265i	−0.0538544	−	0.0223072i	−0.409448	+	0.912333i	$0.634279\pi$
$284$	−1.07137	−	3.56589i	−0.0635739	−	0.211597i
$285$		0			0
$286$	−18.3765	−	4.62902i	−1.08663	−	0.273720i
$287$	15.2974			0.902978
$288$		0			0
$289$	20.2306			1.19004
$290$	9.37089	+	2.36052i	0.550278	+	0.138614i
$291$		0			0
$292$	29.5872	−	8.88944i	1.73146	−	0.520215i
$293$	−3.85498	−	1.59678i	−0.225210	−	0.0932851i	0.267225	−	0.963634i	$-0.413893\pi$
$293$	−3.85498	−	1.59678i	−0.225210	−	0.0932851i	−0.492435	+	0.870349i	$0.663893\pi$
$294$		0			0
$295$	12.3113	−	12.3113i	0.716790	−	0.716790i
$296$	7.21732	+	15.4184i	0.419498	+	0.896175i
$297$		0			0
$298$	3.82613	+	2.84554i	0.221642	+	0.164838i
$299$	−3.15877	−	1.30841i	−0.182677	−	0.0756671i
$300$		0			0
$301$	11.7771	+	28.4323i	0.678818	+	1.63881i
$302$	−17.2604	+	10.3144i	−0.993226	+	0.593525i
$303$		0			0
$304$	12.3142	+	8.32302i	0.706266	+	0.477358i
$305$	6.58956			0.377317
$306$		0			0
$307$	−4.77567	+	1.97815i	−0.272562	+	0.112899i	−0.514778	−	0.857323i	$-0.672126\pi$
$307$	−4.77567	+	1.97815i	−0.272562	+	0.112899i	0.242216	+	0.970222i	$0.422126\pi$
$308$	−20.5953	−	2.08371i	−1.17352	−	0.118730i
$309$		0			0
$310$	15.2948	+	11.3749i	0.868687	+	0.646052i
$311$	5.85083	−	5.85083i	0.331770	−	0.331770i	−0.521488	−	0.853258i	$-0.674623\pi$
$311$	5.85083	−	5.85083i	0.331770	−	0.331770i	0.853258	+	0.521488i	$0.174623\pi$
$312$		0			0
$313$	−9.37980	−	9.37980i	−0.530178	−	0.530178i	0.390448	−	0.920625i	$-0.372320\pi$
$313$	−9.37980	−	9.37980i	−0.530178	−	0.530178i	−0.920625	+	0.390448i	$0.872320\pi$
$314$	−3.42272	−	23.2872i	−0.193155	−	1.31417i
$315$		0			0
$316$	−20.9133	−	11.2499i	−1.17646	−	0.632856i
$317$	−7.45951	−	18.0089i	−0.418968	−	1.01148i	−0.982647	−	0.185484i	$-0.940615\pi$
$317$	−7.45951	−	18.0089i	−0.418968	−	1.01148i	0.563679	−	0.825994i	$-0.309385\pi$
$318$		0			0
$319$			11.1537i			0.624490i
$320$	4.25265	−	13.6272i	0.237730	−	0.761786i
$321$		0			0
$322$	−3.62160	−	0.912277i	−0.201824	−	0.0508392i
$323$	−20.9466	+	8.67638i	−1.16550	+	0.482767i
$324$		0			0
$325$	−3.19691	+	7.71802i	−0.177333	+	0.428119i
$326$	15.4323	−	2.26822i	0.854714	−	0.125625i
$327$		0			0
$328$	−12.1637	+	0.548992i	−0.671628	+	0.0303130i
$329$	21.6061	+	21.6061i	1.19118	+	1.19118i
$330$		0			0
$331$	−2.04504	+	4.93715i	−0.112405	+	0.271370i	−0.970064	−	0.242849i	$-0.921918\pi$
$331$	−2.04504	+	4.93715i	−0.112405	+	0.271370i	0.857659	+	0.514219i	$0.171918\pi$
$332$	−2.30679	+	22.8002i	−0.126601	+	1.25132i
$333$		0			0
$334$	−19.0926	+	11.4092i	−1.04470	+	0.624285i
$335$			0.251234i			0.0137264i
$336$		0			0
$337$		−	32.7329i		−	1.78308i	−0.452946	−	0.891538i	$-0.649627\pi$
$337$		−	32.7329i		−	1.78308i	0.452946	−	0.891538i	$-0.350373\pi$
$338$	5.92357	+	9.91271i	0.322200	+	0.539180i
$339$		0			0
$340$	13.7698	+	16.8697i	0.746771	+	0.914888i
$341$	−8.41908	+	20.3255i	−0.455919	+	1.10069i
$342$		0			0
$343$	3.44913	+	3.44913i	0.186236	+	0.186236i
$344$	−10.3849	−	22.1852i	−0.559915	−	1.19615i
$345$		0			0
$346$	−2.15129	−	14.6367i	−0.115654	−	0.786875i
$347$	10.0545	−	24.2737i	0.539755	−	1.30308i	−0.385140	−	0.922858i	$-0.625847\pi$
$347$	10.0545	−	24.2737i	0.539755	−	1.30308i	0.924894	−	0.380225i	$-0.124153\pi$
$348$		0			0
$349$	−7.53157	+	3.11968i	−0.403156	+	0.166993i	−0.575041	−	0.818124i	$-0.695014\pi$
$349$	−7.53157	+	3.11968i	−0.403156	+	0.166993i	0.171886	+	0.985117i	$0.445014\pi$
$350$	−2.22902	+	8.84887i	−0.119146	+	0.472992i
$351$		0			0
$352$	16.4510	+	0.917733i	0.876843	+	0.0489154i
$353$		−	14.4403i		−	0.768579i	−0.923213	−	0.384290i	$-0.874446\pi$
$353$		−	14.4403i		−	0.768579i	0.923213	−	0.384290i	$-0.125554\pi$
$354$		0			0
$355$	1.27128	+	3.06915i	0.0674728	+	0.162894i
$356$	16.1869	−	4.86333i	0.857904	−	0.257756i
$357$		0			0
$358$	−24.3340	+	3.57659i	−1.28609	+	0.189029i
$359$	1.26776	+	1.26776i	0.0669099	+	0.0669099i	0.739770	−	0.672860i	$-0.234934\pi$
$359$	1.26776	+	1.26776i	0.0669099	+	0.0669099i	−0.672860	+	0.739770i	$0.734934\pi$
$360$		0			0
$361$	−3.67204	+	3.67204i	−0.193265	+	0.193265i
$362$	−15.1277	+	20.3409i	−0.795095	+	1.06909i
$363$		0			0
$364$	20.6752	+	25.3297i	1.08367	+	1.32763i
$365$	−25.4656	+	10.5482i	−1.33293	+	0.552119i
$366$		0			0
$367$	−0.516344			−0.0269529			−0.0134765	−	0.999909i	$-0.504290\pi$
$367$	−0.516344			−0.0269529			−0.0134765	+	0.999909i	$0.504290\pi$
$368$	2.91244	+	0.595423i	0.151822	+	0.0310386i
$369$		0			0
$370$	−7.79139	−	13.0384i	−0.405055	−	0.677834i
$371$	13.4658	+	32.5093i	0.699110	+	1.68780i
$372$		0			0
$373$	15.7829	+	6.53747i	0.817205	+	0.338498i	0.751825	−	0.659363i	$-0.229174\pi$
$373$	15.7829	+	6.53747i	0.817205	+	0.338498i	0.0653805	+	0.997860i	$0.479174\pi$
$374$	−14.9990	+	20.1678i	−0.775579	+	1.04285i
$375$		0			0
$376$	−17.9554	−	16.4046i	−0.925980	−	0.846003i
$377$	12.4574	−	12.4574i	0.641587	−	0.641587i
$378$		0			0
$379$	10.1190	+	4.19144i	0.519780	+	0.215300i	0.627120	−	0.778922i	$-0.284233\pi$
$379$	10.1190	+	4.19144i	0.519780	+	0.215300i	−0.107340	+	0.994222i	$0.534233\pi$
$380$	−11.6785	−	6.28224i	−0.599096	−	0.322272i
$381$		0			0
$382$	−0.188444	+	0.748093i	−0.00964162	+	0.0382758i
$383$	10.5915			0.541201			0.270601	−	0.962692i	$-0.412778\pi$
$383$	10.5915			0.541201			0.270601	+	0.962692i	$0.412778\pi$
$384$		0			0
$385$	18.4691			0.941274
$386$	4.74935	−	18.8542i	0.241736	−	0.959654i
$387$		0			0
$388$	5.66321	+	3.04642i	0.287506	+	0.154658i
$389$	−9.74428	−	4.03621i	−0.494054	−	0.204644i	0.121723	−	0.992564i	$-0.461158\pi$
$389$	−9.74428	−	4.03621i	−0.494054	−	0.204644i	−0.615778	+	0.787920i	$0.711158\pi$
$390$		0			0
$391$	−3.20645	+	3.20645i	−0.162157	+	0.162157i
$392$	11.7506	+	10.7357i	0.593497	+	0.542237i
$393$		0			0
$394$	3.42041	−	4.59911i	0.172318	−	0.231700i
$395$	19.5746	+	8.10808i	0.984906	+	0.407962i
$396$		0			0
$397$	−6.26413	−	15.1230i	−0.314388	−	0.759000i	−0.999532	−	0.0305919i	$-0.990261\pi$
$397$	−6.26413	−	15.1230i	−0.314388	−	0.759000i	0.685144	−	0.728408i	$-0.259739\pi$
$398$	−9.98128	−	16.7030i	−0.500316	−	0.837247i
$399$		0			0
$400$	1.45483	−	7.11615i	0.0727416	−	0.355808i
$401$	−9.54016			−0.476413			−0.238207	−	0.971215i	$-0.576560\pi$
$401$	−9.54016			−0.476413			−0.238207	+	0.971215i	$0.576560\pi$
$402$		0			0
$403$	32.1042	−	13.2980i	1.59922	−	0.662420i
$404$	−2.22769	−	2.72919i	−0.110832	−	0.135783i
$405$		0			0
$406$	11.4842	−	15.4418i	0.569953	−	0.766363i
$407$	12.3964	−	12.3964i	0.614465	−	0.614465i
$408$		0			0
$409$	−9.43887	−	9.43887i	−0.466722	−	0.466722i	0.434129	−	0.900851i	$-0.357056\pi$
$409$	−9.43887	−	9.43887i	−0.466722	−	0.466722i	−0.900851	+	0.434129i	$0.857056\pi$
$410$	10.7482	−	1.57975i	0.530814	−	0.0780185i
$411$		0			0
$412$	−0.301684	+	0.0906405i	−0.0148629	+	0.00446554i
$413$	−13.2683	−	32.0325i	−0.652890	−	1.57622i
$414$		0			0
$415$		−	20.4464i		−	1.00368i
$416$	−17.3488	−	19.3988i	−0.850596	−	0.951105i
$417$		0			0
$418$	3.73873	−	14.8422i	0.182867	−	0.725955i
$419$	−18.2081	+	7.54205i	−0.889525	+	0.368453i	−0.780183	−	0.625551i	$-0.784874\pi$
$419$	−18.2081	+	7.54205i	−0.889525	+	0.368453i	−0.109342	+	0.994004i	$0.534874\pi$
$420$		0			0
$421$	7.63758	−	18.4387i	0.372233	−	0.898649i	−0.621139	−	0.783701i	$-0.713330\pi$
$421$	7.63758	−	18.4387i	0.372233	−	0.898649i	0.993371	−	0.114949i	$-0.0366704\pi$
$422$	−2.85412	−	19.4186i	−0.138936	−	0.945280i
$423$		0			0
$424$	−11.8740	−	25.3665i	−0.576652	−	1.23190i
$425$	7.83451	+	7.83451i	0.380029	+	0.380029i
$426$		0			0
$427$	5.02174	−	12.1235i	0.243019	−	0.586700i
$428$	4.91621	+	6.02297i	0.237634	+	0.291131i
$429$		0			0
$430$	11.2109	+	18.7607i	0.540638	+	0.904722i
$431$		−	15.7171i		−	0.757067i	−0.925588	−	0.378534i	$-0.876428\pi$
$431$		−	15.7171i		−	0.757067i	0.925588	−	0.378534i	$-0.123572\pi$
$432$		0			0
$433$			2.04349i			0.0982041i	0.998794	+	0.0491020i	$0.0156360\pi$
$433$			2.04349i			0.0982041i	−0.998794	+	0.0491020i	$0.984364\pi$
$434$	32.5835	−	19.4710i	1.56406	−	0.934639i
$435$		0			0
$436$	3.10720	−	30.7114i	0.148808	−	1.47081i
$437$	1.05676	−	2.55125i	0.0505518	−	0.122043i
$438$		0			0
$439$	−8.47375	−	8.47375i	−0.404430	−	0.404430i	0.475361	−	0.879791i	$-0.342318\pi$
$439$	−8.47375	−	8.47375i	−0.404430	−	0.404430i	−0.879791	+	0.475361i	$0.842318\pi$
$440$	−14.6857	+	0.662818i	−0.700112	+	0.0315986i
$441$		0			0
$442$	39.2770	−	5.77289i	1.86822	−	0.274588i
$443$	−12.8153	+	30.9388i	−0.608873	+	1.46995i	0.255355	+	0.966847i	$0.417808\pi$
$443$	−12.8153	+	30.9388i	−0.608873	+	1.46995i	−0.864228	+	0.503101i	$0.832192\pi$
$444$		0			0
$445$	−13.9320	+	5.77083i	−0.660440	+	0.273563i
$446$	−16.3906	−	4.12877i	−0.776116	−	0.195503i
$447$		0			0
$448$	−21.8307	−	18.2090i	−1.03140	−	0.860296i
$449$			19.7880i			0.933851i	0.884297	+	0.466926i	$0.154638\pi$
$449$			19.7880i			0.933851i	−0.884297	+	0.466926i	$0.845362\pi$
$450$		0			0
$451$	4.79839	+	11.5843i	0.225947	+	0.545485i
$452$	29.2420	+	15.7302i	1.37543	+	0.739885i
$453$		0			0
$454$	−1.68536	−	11.4667i	−0.0790980	−	0.538159i
$455$	−20.6278	−	20.6278i	−0.967045	−	0.967045i
$456$		0			0
$457$	9.46165	−	9.46165i	0.442597	−	0.442597i	−0.450287	−	0.892884i	$-0.648678\pi$
$457$	9.46165	−	9.46165i	0.442597	−	0.442597i	0.892884	+	0.450287i	$0.148678\pi$
$458$	12.9491	+	9.63042i	0.605074	+	0.450000i
$459$		0			0
$460$	−2.63879	−	0.266978i	−0.123034	−	0.0124479i
$461$	8.16779	−	3.38321i	0.380412	−	0.157572i	−0.184280	−	0.982874i	$-0.558995\pi$
$461$	8.16779	−	3.38321i	0.380412	−	0.157572i	0.564691	+	0.825302i	$0.308995\pi$
$462$		0			0
$463$	−39.2301			−1.82318			−0.911590	−	0.411101i	$-0.865144\pi$
$463$	−39.2301			−1.82318			−0.911590	+	0.411101i	$0.865144\pi$
$464$	−8.57748	+	12.6906i	−0.398199	+	0.589148i
$465$		0			0
$466$	28.5075	−	17.0353i	1.32059	−	0.789147i
$467$	−6.94459	−	16.7657i	−0.321357	−	0.775825i	−0.999176	−	0.0405959i	$-0.987074\pi$
$467$	−6.94459	−	16.7657i	−0.321357	−	0.775825i	0.677818	−	0.735230i	$-0.262926\pi$
$468$		0			0
$469$	0.462224	+	0.191459i	0.0213435	+	0.00884078i
$470$	17.4120	+	12.9495i	0.803154	+	0.597314i
$471$		0			0
$472$	11.6998	+	24.9944i	0.538528	+	1.15046i
$473$	−17.8369	+	17.8369i	−0.820142	+	0.820142i
$474$		0			0
$475$	−6.23363	−	2.58205i	−0.286018	−	0.118473i
$476$	41.5307	−	12.4778i	1.90356	−	0.571920i
$477$		0			0
$478$	27.1823	+	6.84718i	1.24329	+	0.313183i
$479$	−10.6817			−0.488058			−0.244029	−	0.969768i	$-0.578469\pi$
$479$	−10.6817			−0.488058			−0.244029	+	0.969768i	$0.578469\pi$
$480$		0			0
$481$	−27.6905			−1.26258
$482$	−10.6797	−	2.69022i	−0.486449	−	0.122536i
$483$		0			0
$484$	1.44808	+	4.81973i	0.0658218	+	0.219079i
$485$	−5.30071	−	2.19563i	−0.240693	−	0.0996983i
$486$		0			0
$487$	−7.67417	+	7.67417i	−0.347750	+	0.347750i	−0.859271	−	0.511521i	$-0.829082\pi$
$487$	−7.67417	+	7.67417i	−0.347750	+	0.347750i	0.511521	+	0.859271i	$0.329082\pi$
$488$	−3.55793	+	9.82022i	−0.161060	+	0.444541i
$489$		0			0
$490$	−11.3950	−	8.47458i	−0.514773	−	0.382842i
$491$	−38.6885	−	16.0253i	−1.74599	−	0.723212i	−0.998245	−	0.0592250i	$-0.981137\pi$
$491$	−38.6885	−	16.0253i	−1.74599	−	0.723212i	−0.747744	−	0.663987i	$-0.768863\pi$
$492$		0			0
$493$	−8.94164	−	21.5870i	−0.402711	−	0.972231i
$494$	−20.7526	+	12.4012i	−0.933705	+	0.557957i
$495$		0			0
$496$	−25.2099	+	16.6517i	−1.13196	+	0.747683i
$497$	6.61547			0.296745
$498$		0			0
$499$	18.1565	−	7.52067i	0.812797	−	0.336671i	0.0627275	−	0.998031i	$-0.480020\pi$
$499$	18.1565	−	7.52067i	0.812797	−	0.336671i	0.750069	+	0.661359i	$0.230020\pi$
$500$	−2.44853	+	24.2011i	−0.109501	+	1.08231i
$501$		0			0
$502$	33.0549	+	24.5833i	1.47531	+	1.09721i
$503$	20.9341	−	20.9341i	0.933405	−	0.933405i	−0.0645124	−	0.997917i	$-0.520549\pi$
$503$	20.9341	−	20.9341i	0.933405	−	0.933405i	0.997917	+	0.0645124i	$0.0205492\pi$
$504$		0			0
$505$	2.22258	+	2.22258i	0.0989036	+	0.0989036i
$506$	−0.445155	−	3.02870i	−0.0197895	−	0.134642i
$507$		0			0
$508$	18.5195	−	34.4273i	0.821671	−	1.52746i
$509$	−0.399075	−	0.963453i	−0.0176887	−	0.0427043i	0.914788	−	0.403933i	$-0.132357\pi$
$509$	−0.399075	−	0.963453i	−0.0176887	−	0.0427043i	−0.932477	+	0.361229i	$0.882357\pi$
$510$		0			0
$511$			54.8905i			2.42821i
$512$	18.0121	+	13.6954i	0.796030	+	0.605257i
$513$		0			0
$514$	−8.47828	−	2.13567i	−0.373961	−	0.0942003i
$515$	0.259658	−	0.107554i	0.0114419	−	0.00473940i
$516$		0			0
$517$	−9.58447	+	23.1390i	−0.421525	+	1.01765i
$518$	−29.9258	+	4.39846i	−1.31486	+	0.193257i
$519$		0			0
$520$	17.1424	+	15.6618i	0.751744	+	0.686817i
$521$	−3.86359	−	3.86359i	−0.169267	−	0.169267i	0.617390	−	0.786657i	$-0.288190\pi$
$521$	−3.86359	−	3.86359i	−0.169267	−	0.169267i	−0.786657	+	0.617390i	$0.788190\pi$
$522$		0			0
$523$	−8.40221	+	20.2847i	−0.367403	+	0.886989i	0.626771	+	0.779203i	$0.284376\pi$
$523$	−8.40221	+	20.2847i	−0.367403	+	0.886989i	−0.994174	+	0.107786i	$0.965624\pi$
$524$	−12.8639	−	1.30150i	−0.561963	−	0.0568561i
$525$		0			0
$526$	5.12936	−	3.06517i	0.223651	−	0.133648i
$527$		−	46.0874i		−	2.00760i
$528$		0			0
$529$			22.4477i			0.975987i
$530$	12.8185	+	21.4509i	0.556799	+	0.931767i
$531$		0			0
$532$	−20.4580	+	16.6987i	−0.886969	+	0.723982i
$533$	7.57908	−	18.2975i	0.328286	−	0.792553i
$534$		0			0
$535$	−4.90494	−	4.90494i	−0.212059	−	0.212059i
$536$	−0.374407	−	0.135650i	−0.0161719	−	0.00585920i
$537$		0			0
$538$	−3.18226	−	21.6511i	−0.137197	−	0.933447i
$539$	6.27241	−	15.1429i	0.270172	−	0.652252i
$540$		0			0
$541$	0.504857	−	0.209119i	0.0217055	−	0.00899071i	−0.371804	−	0.928311i	$-0.621261\pi$
$541$	0.504857	−	0.209119i	0.0217055	−	0.00899071i	0.393510	+	0.919320i	$0.371261\pi$
$542$	−1.46340	+	5.80948i	−0.0628585	+	0.249538i
$543$		0			0
$544$	−32.5752	+	11.4122i	−1.39665	+	0.489292i
$545$			27.5409i			1.17972i
$546$		0			0
$547$	11.9972	+	28.9639i	0.512964	+	1.23841i	0.942151	+	0.335190i	$0.108800\pi$
$547$	11.9972	+	28.9639i	0.512964	+	1.23841i	−0.429186	+	0.903216i	$0.641200\pi$
$548$	11.3482	+	37.7710i	0.484773	+	1.61350i
$549$		0			0
$550$	−7.40020	+	1.08767i	−0.315546	+	0.0463786i
$551$	10.0615	+	10.0615i	0.428633	+	0.428633i
$552$		0			0
$553$	29.8347	−	29.8347i	1.26870	−	1.26870i
$554$	1.49087	−	2.00464i	0.0633411	−	0.0851689i
$555$		0			0
$556$	−20.6859	+	16.8848i	−0.877279	+	0.716073i
$557$	−3.31995	+	1.37517i	−0.140671	+	0.0582677i	−0.451908	−	0.892064i	$-0.649257\pi$
$557$	−3.31995	+	1.37517i	−0.140671	+	0.0582677i	0.311238	+	0.950332i	$0.399257\pi$
$558$		0			0
$559$	39.8433			1.68519
$560$	21.0140	+	14.2032i	0.888005	+	0.600194i
$561$		0			0
$562$	0.665088	+	1.11298i	0.0280551	+	0.0469483i
$563$	3.47196	+	8.38204i	0.146325	+	0.353261i	0.980001	−	0.198994i	$-0.0637675\pi$
$563$	3.47196	+	8.38204i	0.146325	+	0.353261i	−0.833675	+	0.552255i	$0.813767\pi$
$564$		0			0
$565$	−27.3703	−	11.3371i	−1.15148	−	0.476957i
$566$	−0.827594	+	1.11279i	−0.0347864	+	0.0467741i
$567$		0			0
$568$	−5.26028	+	0.237415i	−0.220716	+	0.00996173i
$569$	2.72691	−	2.72691i	0.114318	−	0.114318i	−0.647634	−	0.761952i	$-0.724241\pi$
$569$	2.72691	−	2.72691i	0.114318	−	0.114318i	0.761952	+	0.647634i	$0.224241\pi$
$570$		0			0
$571$	30.8517	+	12.7792i	1.29110	+	0.534792i	0.919314	−	0.393525i	$-0.128745\pi$
$571$	30.8517	+	12.7792i	1.29110	+	0.534792i	0.371789	+	0.928317i	$0.378745\pi$
$572$	−12.6962	+	23.6020i	−0.530856	+	0.986848i
$573$		0			0
$574$	5.28445	−	20.9785i	0.220569	−	0.875625i
$575$	−1.34948			−0.0562771
$576$		0			0
$577$	−45.9313			−1.91214			−0.956072	−	0.293131i	$-0.905303\pi$
$577$	−45.9313			−1.91214			−0.956072	+	0.293131i	$0.905303\pi$
$578$	6.98862	−	27.7438i	0.290688	−	1.15399i
$579$		0			0
$580$	6.47430	−	12.0356i	0.268831	−	0.499750i
$581$	−37.6176	−	15.5817i	−1.56064	−	0.646438i
$582$		0			0
$583$	−20.3946	+	20.3946i	−0.844658	+	0.844658i
$584$	−1.96990	−	43.6460i	−0.0815152	−	1.80608i
$585$		0			0
$586$	−3.52148	+	4.73501i	−0.145471	+	0.195601i
$587$	−11.3774	−	4.71269i	−0.469597	−	0.194514i	0.135320	−	0.990802i	$-0.456794\pi$
$587$	−11.3774	−	4.71269i	−0.469597	−	0.194514i	−0.604917	+	0.796288i	$0.706794\pi$
$588$		0			0
$589$	10.7404	+	25.9296i	0.442551	+	1.06841i
$590$	−12.6305	−	21.1362i	−0.519988	−	0.870166i
$591$		0			0
$592$	23.6376	−	4.57140i	0.971498	−	0.187883i
$593$	−14.4266			−0.592431			−0.296216	−	0.955121i	$-0.595725\pi$
$593$	−14.4266			−0.592431			−0.296216	+	0.955121i	$0.595725\pi$
$594$		0			0
$595$	−35.7453	+	14.8062i	−1.46541	+	0.606994i
$596$	5.22402	−	4.26407i	0.213984	−	0.174663i
$597$		0			0
$598$	−2.88551	+	3.87987i	−0.117997	+	0.158660i
$599$	11.4738	−	11.4738i	0.468808	−	0.468808i	−0.432720	−	0.901528i	$-0.642446\pi$
$599$	11.4738	−	11.4738i	0.468808	−	0.468808i	0.901528	+	0.432720i	$0.142446\pi$
$600$		0			0
$601$	−5.94470	−	5.94470i	−0.242489	−	0.242489i	0.575390	−	0.817879i	$-0.304850\pi$
$601$	−5.94470	−	5.94470i	−0.242489	−	0.242489i	−0.817879	+	0.575390i	$0.804850\pi$
$602$	43.0597	−	6.32887i	1.75498	−	0.257945i
$603$		0			0
$604$	8.18228	+	27.2336i	0.332932	+	1.10812i
$605$	−1.71829	−	4.14832i	−0.0698585	−	0.168653i
$606$		0			0
$607$		−	22.8701i		−	0.928269i	−0.885765	−	0.464135i	$-0.846365\pi$
$607$		−	22.8701i		−	0.928269i	0.885765	−	0.464135i	$-0.153635\pi$
$608$	15.6679	−	14.0121i	0.635416	−	0.568268i
$609$		0			0
$610$	2.27635	−	9.03675i	0.0921666	−	0.365887i
$611$	36.5481	−	15.1387i	1.47858	−	0.612447i
$612$		0			0
$613$	−5.36341	+	12.9484i	−0.216626	+	0.522982i	−0.994415	−	0.105544i	$-0.966342\pi$
$613$	−5.36341	+	12.9484i	−0.216626	+	0.522982i	0.777788	+	0.628526i	$0.216342\pi$
$614$	1.06304	+	7.23258i	0.0429007	+	0.291883i
$615$		0			0
$616$	−9.97212	+	27.5240i	−0.401788	+	1.10897i
$617$	−20.5540	−	20.5540i	−0.827474	−	0.827474i	0.159693	−	0.987167i	$-0.448950\pi$
$617$	−20.5540	−	20.5540i	−0.827474	−	0.827474i	−0.987167	+	0.159693i	$0.948950\pi$
$618$		0			0
$619$	−4.42844	+	10.6912i	−0.177994	+	0.429716i	−0.987546	−	0.157333i	$-0.949710\pi$
$619$	−4.42844	+	10.6912i	−0.177994	+	0.429716i	0.809551	+	0.587049i	$0.199710\pi$
$620$	20.8828	−	17.0455i	0.838675	−	0.684562i
$621$		0			0
$622$	−6.00252	−	10.0448i	−0.240679	−	0.402761i
$623$			30.0301i			1.20313i
$624$		0			0
$625$		−	12.6236i		−	0.504943i
$626$	−16.1034	+	9.62298i	−0.643623	+	0.384612i
$627$		0			0
$628$	−33.1178	−	3.35066i	−1.32154	−	0.133706i
$629$	−14.0542	+	33.9298i	−0.560378	+	1.35287i
$630$		0			0
$631$	0.402845	+	0.402845i	0.0160370	+	0.0160370i	0.715080	−	0.699043i	$-0.246390\pi$
$631$	0.402845	+	0.402845i	0.0160370	+	0.0160370i	−0.699043	+	0.715080i	$0.746390\pi$
$632$	−22.6522	+	24.7936i	−0.901058	+	0.986238i
$633$		0			0
$634$	−27.2737	+	4.00866i	−1.08318	+	0.159204i
$635$	−13.3475	+	32.2237i	−0.529678	+	1.27876i
$636$		0			0
$637$	−23.9183	+	9.90730i	−0.947679	+	0.392542i
$638$	15.2959	+	3.85303i	0.605572	+	0.152543i
$639$		0			0
$640$	−17.2190	−	10.5395i	−0.680639	−	0.416609i
$641$		−	11.0551i		−	0.436649i	−0.975876	−	0.218324i	$-0.929941\pi$
$641$		−	11.0551i		−	0.436649i	0.975876	−	0.218324i	$-0.0700591\pi$
$642$		0			0
$643$	10.8771	+	26.2596i	0.428950	+	1.03558i	0.979621	+	0.200854i	$0.0643717\pi$
$643$	10.8771	+	26.2596i	0.428950	+	1.03558i	−0.550671	+	0.834722i	$0.685628\pi$
$644$	−2.50215	+	4.65142i	−0.0985983	+	0.183292i
$645$		0			0
$646$	4.66260	+	31.7229i	0.183448	+	1.24812i
$647$	3.60517	+	3.60517i	0.141734	+	0.141734i	0.774414	−	0.632680i	$-0.218045\pi$
$647$	3.60517	+	3.60517i	0.141734	+	0.141734i	−0.632680	+	0.774414i	$0.718045\pi$
$648$		0			0
$649$	20.0955	−	20.0955i	0.788816	−	0.788816i
$650$	9.47993	+	7.05033i	0.371833	+	0.276537i
$651$		0			0
$652$	2.22046	−	21.9469i	0.0869600	−	0.859509i
$653$	−34.1322	+	14.1380i	−1.33570	+	0.553264i	−0.932275	−	0.361749i	$-0.882180\pi$
$653$	−34.1322	+	14.1380i	−1.33570	+	0.553264i	−0.403423	+	0.915014i	$0.632180\pi$
$654$		0			0
$655$	11.5359			0.450746
$656$	−3.44905	+	16.8706i	−0.134663	+	0.658687i
$657$		0			0
$658$	37.0938	−	22.1662i	1.44607	−	0.864130i
$659$	17.8965	+	43.2060i	0.697150	+	1.68307i	0.729854	+	0.683603i	$0.239588\pi$
$659$	17.8965	+	43.2060i	0.697150	+	1.68307i	−0.0327038	+	0.999465i	$0.510412\pi$
$660$		0			0
$661$	−3.26994	−	1.35446i	−0.127186	−	0.0526822i	0.318183	−	0.948029i	$-0.396927\pi$
$661$	−3.26994	−	1.35446i	−0.127186	−	0.0526822i	−0.445369	+	0.895347i	$0.646927\pi$
$662$	6.06423	+	4.51004i	0.235693	+	0.175288i
$663$		0			0
$664$	30.4707	+	11.0397i	1.18249	+	0.428425i
$665$	16.6605	−	16.6605i	0.646065	−	0.646065i
$666$		0			0
$667$	2.62925	+	1.08907i	0.101805	+	0.0421690i
$668$	9.05083	+	30.1244i	0.350187	+	1.16555i
$669$		0			0
$670$	0.344536	+	0.0867883i	0.0133106	+	0.00335293i
$671$	10.7560			0.415232
$672$		0			0
$673$	31.8698			1.22849			0.614245	−	0.789115i	$-0.289461\pi$
$673$	31.8698			1.22849			0.614245	+	0.789115i	$0.289461\pi$
$674$	−44.8891	−	11.3075i	−1.72906	−	0.435549i
$675$		0			0
$676$	15.6403	−	4.69910i	0.601550	−	0.180735i
$677$	−13.6153	−	5.63965i	−0.523279	−	0.216749i	0.105378	−	0.994432i	$-0.466395\pi$
$677$	−13.6153	−	5.63965i	−0.523279	−	0.216749i	−0.628657	+	0.777683i	$0.716395\pi$
$678$		0			0
$679$	−8.07908	+	8.07908i	−0.310047	+	0.310047i
$680$	27.8914	−	13.0559i	1.06959	−	0.500672i
$681$		0			0
$682$	24.9655	+	18.5671i	0.955977	+	0.710971i
$683$	24.0468	+	9.96050i	0.920124	+	0.381128i	0.791923	−	0.610621i	$-0.209080\pi$
$683$	24.0468	+	9.96050i	0.920124	+	0.381128i	0.128200	+	0.991748i	$0.459080\pi$
$684$		0			0
$685$	−13.4658	−	32.5094i	−0.514503	−	1.24212i
$686$	5.92155	−	3.53856i	0.226086	−	0.135103i
$687$		0			0
$688$	−34.0117	+	6.57770i	−1.29668	+	0.250773i
$689$	45.5566			1.73557
$690$		0			0
$691$	−37.6111	+	15.5790i	−1.43079	+	0.592653i	−0.957547	−	0.288278i	$-0.906917\pi$
$691$	−37.6111	+	15.5790i	−1.43079	+	0.592653i	−0.473245	+	0.880931i	$0.656917\pi$
$692$	−20.8156	−	2.10600i	−0.791289	−	0.0800580i
$693$		0			0
$694$	−29.8151	−	22.1738i	−1.13176	−	0.841706i
$695$	16.8461	−	16.8461i	0.639008	−	0.639008i
$696$		0			0
$697$	−18.5737	−	18.5737i	−0.703528	−	0.703528i
$698$	1.67648	+	11.4063i	0.0634558	+	0.431734i
$699$		0			0
$700$	11.3651	+	6.11364i	0.429560	+	0.231074i
$701$	9.53278	+	23.0142i	0.360048	+	0.869233i	0.995292	+	0.0969216i	$0.0308996\pi$
$701$	9.53278	+	23.0142i	0.360048	+	0.869233i	−0.635244	+	0.772312i	$0.719100\pi$
$702$		0			0
$703$		−	22.3648i		−	0.843505i
$704$	6.94153	−	22.2435i	0.261619	−	0.838333i
$705$		0			0
$706$	−19.8030	−	4.98836i	−0.745297	−	0.187740i
$707$	5.78290	−	2.39536i	0.217488	−	0.0900867i
$708$		0			0
$709$	−1.93081	+	4.66140i	−0.0725132	+	0.175062i	−0.955980	−	0.293431i	$-0.905203\pi$
$709$	−1.93081	+	4.66140i	−0.0725132	+	0.175062i	0.883467	+	0.468493i	$0.155203\pi$
$710$	4.64812	−	0.683175i	0.174441	−	0.0256391i
$711$		0			0
$712$	−1.07772	−	23.8783i	−0.0403891	−	0.894878i
$713$	3.96923	+	3.96923i	0.148649	+	0.148649i
$714$		0			0
$715$	9.15050	−	22.0913i	0.342209	−	0.826166i
$716$	−3.50129	+	34.6066i	−0.130849	+	1.29331i
$717$		0			0
$718$	2.17652	−	1.30063i	0.0812270	−	0.0485391i
$719$		−	39.1090i		−	1.45852i	−0.684237	−	0.729260i	$-0.739865\pi$
$719$		−	39.1090i		−	1.45852i	0.684237	−	0.729260i	$-0.260135\pi$
$720$		0			0
$721$		−	0.559686i		−	0.0208438i
$722$	3.76724	+	6.30423i	0.140202	+	0.234619i
$723$		0			0
$724$	22.6691	+	27.7725i	0.842490	+	1.03216i
$725$	2.66099	−	6.42420i	0.0988268	−	0.238589i
$726$		0			0
$727$	17.8274	+	17.8274i	0.661183	+	0.661183i	0.955659	−	0.294476i	$-0.0951450\pi$
$727$	17.8274	+	17.8274i	0.661183	+	0.661183i	−0.294476	+	0.955659i	$0.595145\pi$
$728$	41.8786	−	19.6033i	1.55212	−	0.726547i
$729$		0			0
$730$	5.66850	+	38.5668i	0.209801	+	1.42742i
$731$	20.2223	−	48.8210i	0.747950	−	1.80571i
$732$		0			0
$733$	3.09283	−	1.28109i	0.114236	−	0.0473182i	−0.324833	−	0.945771i	$-0.605308\pi$
$733$	3.09283	−	1.28109i	0.114236	−	0.0473182i	0.439070	+	0.898453i	$0.355308\pi$
$734$	−0.178370	+	0.708101i	−0.00658375	+	0.0261365i
$735$		0			0
$736$	1.82264	−	3.78836i	0.0671835	−	0.139641i
$737$			0.410086i			0.0151057i
$738$		0			0
$739$	−8.57114	−	20.6926i	−0.315295	−	0.761188i	−0.999491	−	0.0318910i	$-0.989847\pi$
$739$	−8.57114	−	20.6926i	−0.315295	−	0.761188i	0.684197	−	0.729297i	$-0.260153\pi$
$740$	−20.5720	+	6.18083i	−0.756243	+	0.227212i
$741$		0			0
$742$	49.2342	−	7.23639i	1.80744	−	0.265656i
$743$	30.6030	+	30.6030i	1.12272	+	1.12272i	0.991332	+	0.131384i	$0.0419421\pi$
$743$	30.6030	+	30.6030i	1.12272	+	1.12272i	0.131384	+	0.991332i	$0.458058\pi$
$744$		0			0
$745$	−4.25430	+	4.25430i	−0.155866	+	0.155866i
$746$	14.4175	−	19.3858i	0.527861	−	0.709766i
$747$		0			0
$748$	22.4762	+	27.5361i	0.821810	+	1.00682i
$749$	−12.7621	+	5.28623i	−0.466317	+	0.193155i
$750$		0			0
$751$	−9.79523			−0.357433			−0.178716	−	0.983901i	$-0.557194\pi$
$751$	−9.79523			−0.357433			−0.178716	+	0.983901i	$0.557194\pi$
$752$	−28.6995	+	18.9566i	−1.04656	+	0.691278i
$753$		0			0
$754$	−12.7803	−	21.3871i	−0.465433	−	0.778872i
$755$	−9.70910	−	23.4398i	−0.353350	−	0.853063i
$756$		0			0
$757$	10.1531	+	4.20556i	0.369021	+	0.152854i	0.559485	−	0.828841i	$-0.310999\pi$
$757$	10.1531	+	4.20556i	0.369021	+	0.152854i	−0.190463	+	0.981694i	$0.560999\pi$
$758$	9.24363	−	12.4291i	0.335744	−	0.451444i
$759$		0			0
$760$	−12.6496	+	13.8454i	−0.458850	+	0.502227i
$761$	−19.7195	+	19.7195i	−0.714832	+	0.714832i	−0.967542	−	0.252710i	$-0.918678\pi$
$761$	−19.7195	+	19.7195i	−0.714832	+	0.714832i	0.252710	+	0.967542i	$0.418678\pi$
$762$		0			0
$763$	50.6701	+	20.9882i	1.83438	+	0.759825i
$764$	0.960818	+	0.516854i	0.0347612	+	0.0186991i
$765$		0			0
$766$	3.65881	−	14.5249i	0.132198	−	0.524807i
$767$	−44.8884			−1.62083
$768$		0			0
$769$	−11.6440			−0.419894			−0.209947	−	0.977713i	$-0.567329\pi$
$769$	−11.6440			−0.419894			−0.209947	+	0.977713i	$0.567329\pi$
$770$	6.38011	−	25.3281i	0.229923	−	0.912761i
$771$		0			0
$772$	−24.2155	−	13.0263i	−0.871535	−	0.468826i
$773$	32.6494	+	13.5238i	1.17432	+	0.486418i	0.882617	−	0.470092i	$-0.155779\pi$
$773$	32.6494	+	13.5238i	1.17432	+	0.486418i	0.291700	+	0.956510i	$0.405779\pi$
$774$		0			0
$775$	9.69825	−	9.69825i	0.348372	−	0.348372i
$776$	6.13411	−	6.71400i	0.220202	−	0.241018i
$777$		0			0
$778$	−8.90129	+	11.9687i	−0.319127	+	0.429100i
$779$	14.7784	+	6.12140i	0.529490	+	0.219322i
$780$		0			0
$781$	2.07510	+	5.00972i	0.0742528	+	0.179262i
$782$	3.28958	+	5.50490i	0.117635	+	0.196855i
$783$		0			0
$784$	18.7820	−	12.4059i	0.670784	−	0.443067i
$785$	29.6989			1.06000
$786$		0			0
$787$	4.72873	−	1.95870i	0.168561	−	0.0698203i	−0.296807	−	0.954937i	$-0.595922\pi$
$787$	4.72873	−	1.95870i	0.168561	−	0.0698203i	0.465368	+	0.885117i	$0.345922\pi$
$788$	−5.12553	−	6.27941i	−0.182589	−	0.223695i
$789$		0			0
$790$	17.8812	−	24.0432i	0.636185	−	0.855419i
$791$	−41.7164	+	41.7164i	−1.48326	+	1.48326i
$792$		0			0
$793$	−12.0132	−	12.0132i	−0.426600	−	0.426600i
$794$	−22.9032	+	3.36628i	−0.812803	+	0.119465i
$795$		0			0
$796$	−26.3541	+	7.91804i	−0.934096	+	0.280648i
$797$	−1.47493	−	3.56079i	−0.0522447	−	0.126130i	0.895602	−	0.444856i	$-0.146745\pi$
$797$	−1.47493	−	3.56079i	−0.0522447	−	0.126130i	−0.947847	+	0.318726i	$0.896745\pi$
$798$		0			0
$799$		−	52.4669i		−	1.85615i
$800$	−9.25633	−	4.45338i	−0.327261	−	0.157451i
$801$		0			0
$802$	−3.29563	+	13.0831i	−0.116373	+	0.461981i
$803$	−41.5671	+	17.2177i	−1.46687	+	0.607598i
$804$		0			0
$805$	1.80336	−	4.35369i	0.0635600	−	0.153447i
$806$	−7.14620	−	48.6206i	−0.251714	−	1.71259i
$807$		0			0
$808$	−4.51230	+	2.11220i	−0.158742	+	0.0743069i
$809$	0.851642	+	0.851642i	0.0299421	+	0.0299421i	0.721919	−	0.691977i	$-0.243260\pi$
$809$	0.851642	+	0.851642i	0.0299421	+	0.0299421i	−0.691977	+	0.721919i	$0.743260\pi$
$810$		0			0
$811$	11.0808	−	26.7515i	0.389100	−	0.939371i	−0.601031	−	0.799226i	$-0.705243\pi$
$811$	11.0808	−	26.7515i	0.389100	−	0.939371i	0.990131	−	0.140145i	$-0.0447568\pi$
$812$	−17.2093	−	21.0835i	−0.603926	−	0.739885i
$813$		0			0
$814$	−12.7178	−	21.2823i	−0.445757	−	0.745946i
$815$			19.6813i			0.689405i
$816$		0			0
$817$			32.1803i			1.12585i
$818$	−16.2049	+	9.68358i	−0.566589	+	0.338579i
$819$		0			0
$820$	1.54649	−	15.2855i	0.0540059	−	0.533792i
$821$	14.6802	−	35.4411i	0.512342	−	1.23690i	−0.430176	−	0.902745i	$-0.641548\pi$
$821$	14.6802	−	35.4411i	0.512342	−	1.23690i	0.942517	−	0.334157i	$-0.108452\pi$
$822$		0			0
$823$	23.7916	+	23.7916i	0.829322	+	0.829322i	0.987423	−	0.158101i	$-0.0505370\pi$
$823$	23.7916	+	23.7916i	0.829322	+	0.829322i	−0.158101	+	0.987423i	$0.550537\pi$
$824$	0.0200860	+	0.445033i	0.000699728	+	0.0155035i
$825$		0			0
$826$	−48.5120	+	7.13025i	−1.68795	+	0.248093i
$827$	6.95203	−	16.7837i	0.241746	−	0.583626i	−0.755711	−	0.654906i	$-0.772708\pi$
$827$	6.95203	−	16.7837i	0.241746	−	0.583626i	0.997456	+	0.0712800i	$0.0227084\pi$
$828$		0			0
$829$	17.6000	−	7.29015i	0.611272	−	0.253197i	−0.0555001	−	0.998459i	$-0.517675\pi$
$829$	17.6000	−	7.29015i	0.611272	−	0.253197i	0.666772	+	0.745261i	$0.267675\pi$
$830$	−28.0397	−	7.06317i	−0.973273	−	0.245166i
$831$		0			0
$832$	−32.5961	+	17.0904i	−1.13007	+	0.592505i
$833$			34.3362i			1.18968i
$834$		0			0
$835$	−10.7397	−	25.9280i	−0.371663	−	0.897274i
$836$	−19.0626	−	10.2544i	−0.659295	−	0.354656i
$837$		0			0
$838$	4.05302	+	27.5755i	0.140009	+	0.952581i
$839$	4.74463	+	4.74463i	0.163803	+	0.163803i	0.784249	−	0.620446i	$-0.213048\pi$
$839$	4.74463	+	4.74463i	0.163803	+	0.163803i	−0.620446	+	0.784249i	$0.713048\pi$
$840$		0			0
$841$	10.1370	−	10.1370i	0.349553	−	0.349553i
$842$	−22.6480	−	16.8436i	−0.780503	−	0.580469i
$843$		0			0
$844$	−27.6160	−	2.79403i	−0.950583	−	0.0961744i
$845$	−13.4616	+	5.57596i	−0.463092	+	0.191819i
$846$		0			0
$847$	−8.94160			−0.307237
$848$	−38.8887	+	7.52090i	−1.33544	+	0.258269i
$849$		0			0
$850$	13.4504	−	8.03763i	0.461347	−	0.275688i
$851$	−1.71177	−	4.13257i	−0.0586787	−	0.141663i
$852$		0			0
$853$	21.3984	+	8.86349i	0.732666	+	0.303480i	0.717647	−	0.696407i	$-0.245219\pi$
$853$	21.3984	+	8.86349i	0.732666	+	0.303480i	0.0150190	+	0.999887i	$0.495219\pi$
$854$	−14.8912	−	11.0747i	−0.509565	−	0.378969i
$855$		0			0
$856$	9.95804	−	4.66134i	0.340359	−	0.159321i
$857$	14.9755	−	14.9755i	0.511554	−	0.511554i	−0.403448	−	0.915003i	$-0.632188\pi$
$857$	14.9755	−	14.9755i	0.511554	−	0.511554i	0.915003	+	0.403448i	$0.132188\pi$
$858$		0			0
$859$	−3.68023	−	1.52440i	−0.125568	−	0.0520119i	0.319015	−	0.947750i	$-0.396648\pi$
$859$	−3.68023	−	1.52440i	−0.125568	−	0.0520119i	−0.444583	+	0.895738i	$0.646648\pi$
$860$	29.6007	−	8.89349i	1.00938	−	0.303265i
$861$		0			0
$862$	−21.5541	−	5.42944i	−0.734134	−	0.184928i
$863$	52.6581			1.79250			0.896252	−	0.443545i	$-0.146279\pi$
$863$	52.6581			1.79250			0.896252	+	0.443545i	$0.146279\pi$
$864$		0			0
$865$	18.6667			0.634687
$866$	2.80239	+	0.705920i	0.0952292	+	0.0239881i
$867$		0			0
$868$	−15.4462	−	51.4104i	−0.524277	−	1.74498i
$869$	31.9513	+	13.2347i	1.08387	+	0.448955i
$870$		0			0
$871$	0.458016	−	0.458016i	0.0155193	−	0.0155193i
$872$	−41.0434	−	14.8703i	−1.38991	−	0.503572i
$873$		0			0
$874$	−3.13366	−	2.33054i	−0.105998	−	0.0788317i
$875$	−39.9289	−	16.5391i	−1.34984	−	0.559124i
$876$		0			0
$877$	−4.99743	−	12.0649i	−0.168751	−	0.407401i	0.816768	−	0.576966i	$-0.195764\pi$
$877$	−4.99743	−	12.0649i	−0.168751	−	0.407401i	−0.985519	+	0.169565i	$0.945764\pi$
$878$	−14.5479	+	8.69344i	−0.490968	+	0.293390i
$879$		0			0
$880$	−4.16416	+	20.3685i	−0.140374	+	0.686623i
$881$	−38.6516			−1.30221			−0.651103	−	0.758989i	$-0.725694\pi$
$881$	−38.6516			−1.30221			−0.651103	+	0.758989i	$0.725694\pi$
$882$		0			0
$883$	−10.8231	+	4.48306i	−0.364226	+	0.150867i	−0.557288	−	0.830319i	$-0.688158\pi$
$883$	−10.8231	+	4.48306i	−0.364226	+	0.150867i	0.193062	+	0.981186i	$0.438158\pi$
$884$	5.65135	−	55.8577i	0.190076	−	1.87870i
$885$		0			0
$886$	38.0017	+	28.2623i	1.27669	+	0.949490i
$887$	3.30593	−	3.30593i	0.111002	−	0.111002i	−0.649424	−	0.760426i	$-0.724990\pi$
$887$	3.30593	−	3.30593i	0.111002	−	0.111002i	0.760426	+	0.649424i	$0.224990\pi$
$888$		0			0
$889$	49.1137	+	49.1137i	1.64722	+	1.64722i
$890$	3.10118	+	21.0995i	0.103952	+	0.707257i
$891$		0			0
$892$	−11.3242	+	21.0513i	−0.379161	+	0.704850i
$893$	12.2271	+	29.5189i	0.409165	+	0.987811i
$894$		0			0
$895$		−	31.0340i		−	1.03735i
$896$	−32.5128	+	23.6478i	−1.08618	+	0.790017i
$897$		0			0
$898$	27.1367	+	6.83570i	0.905563	+	0.228110i
$899$	−26.7224	+	11.0688i	−0.891241	+	0.369164i
$900$		0			0
$901$	23.1221	−	55.8217i	0.770309	−	1.85969i
$902$	17.5440	−	2.57860i	0.584153	−	0.0858581i
$903$		0			0
$904$	31.6735	−	34.6678i	1.05345	−	1.15303i
$905$	−22.6171	−	22.6171i	−0.751819	−	0.751819i
$906$		0			0
$907$	14.0586	−	33.9405i	0.466809	−	1.12698i	−0.498739	−	0.866752i	$-0.666203\pi$
$907$	14.0586	−	33.9405i	0.466809	−	1.12698i	0.965548	−	0.260225i	$-0.0837967\pi$
$908$	−16.3073	−	1.64988i	−0.541178	−	0.0547532i
$909$		0			0
$910$	−35.4142	+	21.1626i	−1.17397	+	0.701533i
$911$			28.5526i			0.945990i	0.881065	+	0.472995i	$0.156827\pi$
$911$			28.5526i			0.945990i	−0.881065	+	0.472995i	$0.843173\pi$
$912$		0			0
$913$		−	33.3744i		−	1.10453i
$914$	−9.70695	−	16.2440i	−0.321077	−	0.537302i
$915$		0			0
$916$	17.6802	−	14.4313i	0.584169	−	0.476824i
$917$	8.79124	−	21.2239i	0.290312	−	0.700876i
$918$		0			0
$919$	14.1101	+	14.1101i	0.465448	+	0.465448i	0.900436	−	0.434988i	$-0.143247\pi$
$919$	14.1101	+	14.1101i	0.465448	+	0.465448i	−0.434988	+	0.900436i	$0.643247\pi$
$920$	−1.27769	+	3.52654i	−0.0421242	+	0.116267i
$921$		0			0
$922$	−1.81810	−	12.3698i	−0.0598760	−	0.407378i
$923$	3.27762	−	7.91289i	0.107884	−	0.260456i
$924$		0			0
$925$	−10.0974	+	4.18247i	−0.331999	+	0.137519i
$926$	−13.5520	+	53.7992i	−0.445345	+	1.76795i
$927$		0			0
$928$	14.4405	+	16.1469i	0.474034	+	0.530047i
$929$			1.88348i			0.0617951i	0.999523	+	0.0308975i	$0.00983656\pi$
$929$			1.88348i			0.0617951i	−0.999523	+	0.0308975i	$0.990163\pi$
$930$		0			0
$931$	−8.00185	−	19.3182i	−0.262250	−	0.633127i
$932$	−13.5140	−	44.9793i	−0.442664	−	1.47335i
$933$		0			0
$934$	−25.3911	+	3.73195i	−0.830821	+	0.122113i
$935$	−22.4247	−	22.4247i	−0.733365	−	0.733365i
$936$		0			0
$937$	−15.2871	+	15.2871i	−0.499409	+	0.499409i	−0.911254	−	0.411845i	$-0.864885\pi$
$937$	−15.2871	+	15.2871i	−0.499409	+	0.499409i	0.411845	+	0.911254i	$0.364885\pi$
$938$	0.422237	−	0.567743i	0.0137865	−	0.0185375i
$939$		0			0
$940$	23.7735	−	19.4049i	0.775405	−	0.632919i
$941$	35.4271	−	14.6744i	1.15489	−	0.478372i	0.278721	−	0.960372i	$-0.410090\pi$
$941$	35.4271	−	14.6744i	1.15489	−	0.478372i	0.876171	+	0.482000i	$0.160090\pi$
$942$		0			0
$943$	3.19927			0.104183
$944$	38.3183	−	7.41059i	1.24716	−	0.241194i
$945$		0			0
$946$	18.2994	+	30.6228i	0.594963	+	0.995633i
$947$	8.28542	+	20.0028i	0.269240	+	0.650003i	0.999448	−	0.0332221i	$-0.0105769\pi$
$947$	8.28542	+	20.0028i	0.269240	+	0.650003i	−0.730208	+	0.683225i	$0.760577\pi$
$948$		0			0
$949$	65.6555	+	27.1954i	2.13127	+	0.882800i
$950$	−5.69435	+	7.65667i	−0.184749	+	0.248415i
$951$		0			0
$952$	−2.76509	−	61.2645i	−0.0896171	−	1.98559i
$953$	−27.6252	+	27.6252i	−0.894867	+	0.894867i	−0.994976	−	0.100110i	$-0.968081\pi$
$953$	−27.6252	+	27.6252i	−0.894867	+	0.894867i	0.100110	+	0.994976i	$0.468081\pi$
$954$		0			0
$955$	−0.899317	−	0.372509i	−0.0291012	−	0.0120541i
$956$	18.7801	−	34.9117i	0.607392	−	1.12913i
$957$		0			0
$958$	−3.68995	+	14.6486i	−0.119217	+	0.473273i
$959$	−70.0731			−2.26278
$960$		0			0
$961$	−26.0511			−0.840358
$962$	−9.56561	+	37.9740i	−0.308408	+	1.22433i
$963$		0			0
$964$	−7.37858	+	13.7166i	−0.237648	+	0.441782i
$965$	22.6655	+	9.38836i	0.729629	+	0.302222i
$966$		0			0
$967$	−32.5133	+	32.5133i	−1.04556	+	1.04556i	−0.0466463	+	0.998911i	$0.514853\pi$
$967$	−32.5133	+	32.5133i	−1.04556	+	1.04556i	−0.998911	+	0.0466463i	$0.985147\pi$
$968$	7.10989	−	0.320895i	0.228520	−	0.0103140i
$969$		0			0
$970$	−4.84214	+	6.51079i	−0.155472	+	0.209049i
$971$	49.5609	+	20.5288i	1.59048	+	0.658800i	0.990030	−	0.140859i	$-0.0449863\pi$
$971$	49.5609	+	20.5288i	1.59048	+	0.658800i	0.600455	+	0.799659i	$0.294986\pi$
$972$		0			0
$973$	−18.1556	−	43.8315i	−0.582042	−	1.40517i
$974$	7.87313	+	13.1752i	0.252271	+	0.422160i
$975$		0			0
$976$	12.2381	+	8.27163i	0.391733	+	0.264768i
$977$	29.2129			0.934603			0.467301	−	0.884098i	$-0.345226\pi$
$977$	29.2129			0.934603			0.467301	+	0.884098i	$0.345226\pi$
$978$		0			0
$979$	−22.7410	+	9.41962i	−0.726805	+	0.301052i
$980$	−15.5582	+	12.6993i	−0.496988	+	0.405663i
$981$		0			0
$982$	−35.3415	+	47.5205i	−1.12779	+	1.51644i
$983$	33.7320	−	33.7320i	1.07588	−	1.07588i	0.0790094	−	0.996874i	$-0.474824\pi$
$983$	33.7320	−	33.7320i	1.07588	−	1.07588i	0.996874	−	0.0790094i	$-0.0251757\pi$
$984$		0			0
$985$	5.11378	+	5.11378i	0.162939	+	0.162939i
$986$	−32.6928	+	4.80515i	−1.04115	+	0.153027i
$987$		0			0
$988$	9.83776	+	32.7436i	0.312981	+	1.04171i
$989$	2.46303	+	5.94629i	0.0783199	+	0.189081i
$990$		0			0
$991$			2.34392i			0.0744571i	0.999307	+	0.0372285i	$0.0118530\pi$
$991$			2.34392i			0.0744571i	−0.999307	+	0.0372285i	$0.988147\pi$
$992$	14.1270	+	40.3245i	0.448532	+	1.28030i
$993$		0			0
$994$	2.28530	−	9.07229i	0.0724853	−	0.287755i
$995$	22.6829	−	9.39555i	0.719095	−	0.297859i
$996$		0			0
$997$	−14.7502	+	35.6102i	−0.467145	+	1.12779i	0.498259	+	0.867028i	$0.333973\pi$
$997$	−14.7502	+	35.6102i	−0.467145	+	1.12779i	−0.965404	+	0.260759i	$0.916027\pi$
$998$	−4.04153	−	27.4974i	−0.127932	−	0.870413i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.b.107.5	yes	32
3.2	odd	2		288.2.w.a.107.4	yes	32
4.3	odd	2		1152.2.w.a.719.6		32
12.11	even	2		1152.2.w.b.719.3		32
32.3	odd	8		288.2.w.a.35.4	✓	32
32.29	even	8		1152.2.w.b.431.3		32
96.29	odd	8		1152.2.w.a.431.6		32
96.35	even	8	inner	288.2.w.b.35.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.4	✓	32	32.3	odd	8
288.2.w.a.107.4	yes	32	3.2	odd	2
288.2.w.b.35.5	yes	32	96.35	even	8	inner
288.2.w.b.107.5	yes	32	1.1	even	1	trivial
1152.2.w.a.431.6		32	96.29	odd	8
1152.2.w.a.719.6		32	4.3	odd	2
1152.2.w.b.431.3		32	32.29	even	8
1152.2.w.b.719.3		32	12.11	even	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.345448 - 1.37137i) q^{2} +(-1.76133 - 0.947475i) q^{4} +(1.64859 + 0.682869i) q^{5} +(2.51270 - 2.51270i) q^{7} +(-1.90779 + 2.08814i) q^{8} +(1.50597 - 2.02494i) q^{10} +(2.69097 + 1.11464i) q^{11} +(-1.76057 - 4.25040i) q^{13} +(-2.57784 - 4.31386i) q^{14} +(2.20458 + 3.33764i) q^{16} -6.10169 q^{17} +(3.43292 - 1.42196i) q^{19} +(-2.25672 - 2.76476i) q^{20} +(2.45817 - 3.30527i) q^{22} +(0.525502 - 0.525502i) q^{23} +(-1.28399 - 1.28399i) q^{25} +(-6.43707 + 0.946113i) q^{26} +(-6.80642 + 2.04498i) q^{28} +(1.46544 + 3.53788i) q^{29} +7.55322i q^{31} +(5.33872 - 1.87033i) q^{32} +(-2.10781 + 8.36770i) q^{34} +(5.85826 - 2.42657i) q^{35} +(2.30333 - 5.56073i) q^{37} +(-0.764149 - 5.19904i) q^{38} +(-4.57109 + 2.13972i) q^{40} +(3.04402 + 3.04402i) q^{41} +(-3.31422 + 8.00123i) q^{43} +(-3.68360 - 4.51287i) q^{44} +(-0.539126 - 0.902192i) q^{46} +8.59875i q^{47} -5.62732i q^{49} +(-2.20438 + 1.31728i) q^{50} +(-0.926194 + 9.15446i) q^{52} +(-3.78946 + 9.14856i) q^{53} +(3.67516 + 3.67516i) q^{55} +(0.453168 + 10.0406i) q^{56} +(5.35798 - 0.787511i) q^{58} +(3.73387 - 9.01437i) q^{59} +(3.41173 - 1.41318i) q^{61} +(10.3583 + 2.60924i) q^{62} +(-0.720670 - 7.96747i) q^{64} -8.20941i q^{65} +(0.0538792 + 0.130076i) q^{67} +(10.7471 + 5.78120i) q^{68} +(-1.30401 - 8.87212i) q^{70} +(1.31641 + 1.31641i) q^{71} +(-10.9226 + 10.9226i) q^{73} +(-6.83016 - 5.07966i) q^{74} +(-7.39380 - 0.748061i) q^{76} +(9.56234 - 3.96085i) q^{77} +11.8735 q^{79} +(1.35528 + 7.00784i) q^{80} +(5.22604 - 3.12294i) q^{82} +(-4.38490 - 10.5861i) q^{83} +(-10.0592 - 4.16666i) q^{85} +(9.82779 + 7.30904i) q^{86} +(-7.46132 + 3.49263i) q^{88} +(-5.97566 + 5.97566i) q^{89} +(-15.1038 - 6.25618i) q^{91} +(-1.42348 + 0.427683i) q^{92} +(11.7921 + 2.97042i) q^{94} +6.63051 q^{95} -3.21530 q^{97} +(-7.71716 - 1.94394i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52}+ \cdots + 44 q^{98}+O(q^{100}) \) 32 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^11 - 12 * q^14 + 8 * q^16 - 32 * q^20 + 16 * q^22 + 36 * q^26 + 16 * q^29 + 24 * q^32 - 24 * q^35 - 32 * q^38 - 32 * q^40 - 8 * q^44 - 32 * q^46 - 8 * q^50 - 56 * q^52 + 16 * q^53 - 32 * q^55 - 40 * q^56 - 32 * q^58 - 32 * q^59 + 32 * q^61 + 68 * q^62 - 48 * q^64 - 16 * q^67 + 72 * q^68 - 48 * q^70 - 16 * q^71 - 60 * q^74 - 8 * q^76 + 16 * q^77 - 32 * q^79 - 96 * q^80 + 40 * q^82 + 40 * q^83 + 40 * q^86 + 40 * q^88 - 48 * q^91 + 16 * q^92 + 72 * q^94 + 80 * q^95 + 44 * q^98

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