LMFDB - Embedded newform 288.2.w.a.35.4

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			35.4
Character	$\chi$	$=$	288.35
Dual form			288.2.w.a.107.4

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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	$-0.755646\pi$
$5$	−1.64859	+	0.682869i	−0.737273	+	0.305388i	−0.0177359	+	0.999843i	$0.505646\pi$
$6$		0			0
$7$	2.51270	+	2.51270i	0.949711	+	0.949711i	0.998795	−	0.0490835i	$-0.0156300\pi$
$7$	2.51270	+	2.51270i	0.949711	+	0.949711i	−0.0490835	+	0.998795i	$0.515630\pi$
$8$	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	$-0.769704\pi$
$11$	−2.69097	+	1.11464i	−0.811357	+	0.336075i	−0.0618618	+	0.998085i	$0.519704\pi$
$12$		0			0
$13$	−1.76057	+	4.25040i	−0.488295	+	1.17885i	0.467283	+	0.884108i	$0.345233\pi$
$13$	−1.76057	+	4.25040i	−0.488295	+	1.17885i	−0.955577	+	0.294740i	$0.904767\pi$
$14$	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	$-0.234854\pi$
$17$	6.10169			1.47988			0.739939	+	0.672674i	$0.234854\pi$
$18$		0			0
$19$	3.43292	+	1.42196i	0.787567	+	0.326221i	0.739965	−	0.672645i	$-0.234842\pi$
$19$	3.43292	+	1.42196i	0.787567	+	0.326221i	0.0476020	+	0.998866i	$0.484842\pi$
$20$	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	$-0.274688\pi$
$23$	−0.525502	−	0.525502i	−0.109575	−	0.109575i	−0.759768	+	0.650194i	$0.774688\pi$
$24$		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	$-0.990706\pi$
$29$	−1.46544	+	3.53788i	−0.272125	+	0.656967i	0.727449	+	0.686162i	$0.240706\pi$
$30$		0			0
$31$		−	7.55322i		−	1.35660i	−0.734786	−	0.678299i	$-0.762717\pi$
$31$		−	7.55322i		−	1.35660i	0.734786	−	0.678299i	$-0.237283\pi$
$32$	−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	0.992217	+	0.124523i	$0.0397402\pi$
$37$	2.30333	+	5.56073i	0.378665	+	0.914178i	−0.613552	+	0.789655i	$0.710260\pi$
$38$	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	$-0.859127\pi$
$41$	−3.04402	+	3.04402i	−0.475396	+	0.475396i	0.428260	+	0.903656i	$0.359127\pi$
$42$		0			0
$43$	−3.31422	−	8.00123i	−0.505414	−	1.22018i	−0.946498	−	0.322711i	$-0.895406\pi$
$43$	−3.31422	−	8.00123i	−0.505414	−	1.22018i	0.441084	−	0.897466i	$-0.354594\pi$
$44$	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	0.937580	+	0.347771i	$0.113061\pi$
$53$	3.78946	+	9.14856i	0.520522	+	1.25665i	−0.417058	+	0.908880i	$0.636939\pi$
$54$		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	−0.956662	−	0.291199i	$-0.905946\pi$
$59$	−3.73387	−	9.01437i	−0.486109	−	1.17357i	0.470553	−	0.882372i	$-0.344054\pi$
$60$		0			0
$61$	3.41173	+	1.41318i	0.436827	+	0.180940i	0.590249	−	0.807221i	$-0.299030\pi$
$61$	3.41173	+	1.41318i	0.436827	+	0.180940i	−0.153422	+	0.988161i	$0.549030\pi$
$62$	−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	−0.920554	−	0.390615i	$-0.872262\pi$
$67$	0.0538792	−	0.130076i	0.00658239	−	0.0158913i	0.927137	+	0.374724i	$0.122262\pi$
$68$	−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	$-0.785236\pi$
$71$	−1.31641	+	1.31641i	−0.156229	+	0.156229i	0.624664	+	0.780893i	$0.285236\pi$
$72$		0			0
$73$	−10.9226	−	10.9226i	−1.27839	−	1.27839i	−0.941566	−	0.336829i	$-0.890646\pi$
$73$	−10.9226	−	10.9226i	−1.27839	−	1.27839i	−0.336829	−	0.941566i	$-0.609354\pi$
$74$	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	−0.477684	−	0.878532i	$-0.658524\pi$
$83$	4.38490	−	10.5861i	0.481305	−	1.16197i	0.958989	−	0.283442i	$-0.0914763\pi$
$84$		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	$-0.102174\pi$
$89$	5.97566	+	5.97566i	0.633418	+	0.633418i	−0.315506	+	0.948924i	$0.602174\pi$
$90$		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	$-0.652931\pi$
$101$	−1.62739	+	0.674085i	−0.161931	+	0.0670740i	0.300246	+	0.953862i	$0.402931\pi$
$102$		0			0
$103$	0.111372	+	0.111372i	0.0109738	+	0.0109738i	0.712572	−	0.701599i	$-0.247530\pi$
$103$	0.111372	+	0.111372i	0.0109738	+	0.0109738i	−0.701599	+	0.712572i	$0.747530\pi$
$104$	−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	$-0.564832\pi$
$107$	3.59142	−	1.48762i	0.347196	−	0.143813i	0.549465	+	0.835517i	$0.314832\pi$
$108$		0			0
$109$	5.90637	−	14.2592i	0.565727	−	1.36579i	−0.339398	−	0.940643i	$-0.610223\pi$
$109$	5.90637	−	14.2592i	0.565727	−	1.36579i	0.905126	−	0.425144i	$-0.139777\pi$
$110$	−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	$-0.214760\pi$
$113$	16.6022			1.56180			0.780902	+	0.624653i	$0.214760\pi$
$114$		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	$-0.665904\pi$
$127$		−	19.5462i		−	1.73444i	0.497923	−	0.867221i	$-0.334096\pi$
$128$	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	$-0.466136\pi$
$131$	−5.97269	−	2.47397i	−0.521837	−	0.216152i	−0.628023	+	0.778194i	$0.716136\pi$
$132$		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	0.214594	−	0.976703i	$-0.431157\pi$
$137$	13.9438	−	13.9438i	1.19130	−	1.19130i	0.976703	−	0.214594i	$-0.0688429\pi$
$138$		0			0
$139$	5.10923	+	12.3348i	0.433359	+	1.04622i	0.978197	+	0.207680i	$0.0665913\pi$
$139$	5.10923	+	12.3348i	0.433359	+	1.04622i	−0.544838	+	0.838542i	$0.683409\pi$
$140$	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	$-0.0808975\pi$
$149$	1.29028	+	3.11502i	0.105704	+	0.255192i	−0.862174	+	0.506612i	$0.830898\pi$
$150$		0			0
$151$	−10.0537	+	10.0537i	−0.818159	+	0.818159i	−0.985841	−	0.167682i	$-0.946372\pi$
$151$	−10.0537	+	10.0537i	−0.818159	+	0.818159i	0.167682	+	0.985841i	$0.446372\pi$
$152$	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	0.899686	−	0.436539i	$-0.143796\pi$
$157$	15.3765	+	6.36916i	1.22718	+	0.508315i	0.327494	+	0.944853i	$0.393796\pi$
$158$	−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	−0.667946	−	0.744210i	$-0.732826\pi$
$163$	4.22080	−	10.1899i	0.330599	−	0.798136i	0.998545	−	0.0539266i	$-0.0171737\pi$
$164$	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	$-0.541768\pi$
$167$	11.1209	−	11.1209i	0.860562	−	0.860562i	0.991403	+	0.130842i	$0.0417679\pi$
$168$		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	$-0.505179\pi$
$173$	−9.66463	−	4.00322i	−0.734788	−	0.304359i	−0.718518	+	0.695509i	$0.755179\pi$
$174$		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	−0.453395	−	0.891310i	$-0.649787\pi$
$179$	6.65549	−	16.0678i	0.497455	−	1.20096i	0.950850	−	0.309652i	$-0.100213\pi$
$180$		0			0
$181$	−16.5604	+	6.85953i	−1.23092	+	0.509865i	−0.900867	−	0.434096i	$-0.857068\pi$
$181$	−16.5604	+	6.85953i	−1.23092	+	0.509865i	−0.330056	+	0.943961i	$0.607068\pi$
$182$	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	$-0.493718\pi$
$191$	0.545506			0.0394715			0.0197357	+	0.999805i	$0.493718\pi$
$192$		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	$-0.671118\pi$
$197$	−3.74434	+	1.55095i	−0.266773	+	0.110501i	0.245288	+	0.969450i	$0.421118\pi$
$198$		0			0
$199$	9.72904	+	9.72904i	0.689673	+	0.689673i	0.962160	−	0.272486i	$-0.0878460\pi$
$199$	9.72904	+	9.72904i	0.689673	+	0.689673i	−0.272486	+	0.962160i	$0.587846\pi$
$200$	−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	0.777546	−	0.628826i	$-0.216464\pi$
$211$	12.8221	+	5.31108i	0.882708	+	0.365630i	0.105162	+	0.994455i	$0.466464\pi$
$212$	−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	$0.131053\pi$
$223$			11.9519i			0.800361i	−0.916436	+	0.400180i	$0.868947\pi$
$224$	−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	$-0.462675\pi$
$227$	−7.57146	−	3.13620i	−0.502536	−	0.208157i	−0.619526	+	0.784976i	$0.712675\pi$
$228$		0			0
$229$	−4.36683	−	10.5425i	−0.288568	−	0.696665i	0.711413	−	0.702774i	$-0.248055\pi$
$229$	−4.36683	−	10.5425i	−0.288568	−	0.696665i	−0.999981	+	0.00610879i	$0.998055\pi$
$230$	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	−0.0920662	+	0.995753i	$0.529347\pi$
$233$	−16.6048	+	16.6048i	−1.08782	+	1.08782i	−0.995753	+	0.0920662i	$0.970653\pi$
$234$		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	$0.0807011\pi$
$241$			7.78762i			0.501645i	−0.968033	+	0.250823i	$0.919299\pi$
$242$	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	0.715412	+	0.698703i	$0.246239\pi$
$251$	11.1471	+	26.9114i	0.703597	+	1.69863i	−0.0118144	+	0.999930i	$0.503761\pi$
$252$		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	$-0.791584\pi$
$263$	−2.98771	+	2.98771i	−0.184230	+	0.184230i	0.608966	+	0.793196i	$0.291584\pi$
$264$		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	$-0.531373\pi$
$269$	−14.2963	−	5.92170i	−0.871658	−	0.361053i	−0.773256	+	0.634094i	$0.781373\pi$
$270$		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	−0.333114	−	0.942887i	$-0.608099\pi$
$277$	1.63206	−	0.676023i	0.0980612	−	0.0406183i	0.431175	+	0.902268i	$0.358099\pi$
$278$	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	$-0.241294\pi$
$281$	0.648281	+	0.648281i	0.0386732	+	0.0386732i	−0.687506	+	0.726179i	$0.741294\pi$
$282$		0			0
$283$	−0.905971	+	0.375265i	−0.0538544	+	0.0223072i	−0.409448	−	0.912333i	$-0.634279\pi$
$283$	−0.905971	+	0.375265i	−0.0538544	+	0.0223072i	0.355594	+	0.934641i	$0.384279\pi$
$284$	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	$-0.586107\pi$
$293$	3.85498	−	1.59678i	0.225210	−	0.0932851i	0.492435	+	0.870349i	$0.336107\pi$
$294$		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	0.242216	−	0.970222i	$-0.422126\pi$
$307$	−4.77567	−	1.97815i	−0.272562	−	0.112899i	−0.514778	+	0.857323i	$0.672126\pi$
$308$	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	$-0.325377\pi$
$311$	−5.85083	−	5.85083i	−0.331770	−	0.331770i	−0.853258	+	0.521488i	$0.825377\pi$
$312$		0			0
$313$	−9.37980	+	9.37980i	−0.530178	+	0.530178i	−0.920625	−	0.390448i	$-0.872320\pi$
$313$	−9.37980	+	9.37980i	−0.530178	+	0.530178i	0.390448	+	0.920625i	$0.372320\pi$
$314$	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	−0.563679	−	0.825994i	$-0.690615\pi$
$317$	7.45951	−	18.0089i	0.418968	−	1.01148i	0.982647	−	0.185484i	$-0.0593853\pi$
$318$		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	0.857659	−	0.514219i	$-0.171918\pi$
$331$	−2.04504	−	4.93715i	−0.112405	−	0.271370i	−0.970064	+	0.242849i	$0.921918\pi$
$332$	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	$0.350373\pi$
$337$			32.7329i			1.78308i	−0.452946	+	0.891538i	$0.649627\pi$
$338$	−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	−0.924894	−	0.380225i	$-0.875847\pi$
$347$	−10.0545	−	24.2737i	−0.539755	−	1.30308i	0.385140	−	0.922858i	$-0.374153\pi$
$348$		0			0
$349$	−7.53157	−	3.11968i	−0.403156	−	0.166993i	0.171886	−	0.985117i	$-0.445014\pi$
$349$	−7.53157	−	3.11968i	−0.403156	−	0.166993i	−0.575041	+	0.818124i	$0.695014\pi$
$350$	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	$-0.765066\pi$
$359$	−1.26776	+	1.26776i	−0.0669099	+	0.0669099i	0.672860	+	0.739770i	$0.265066\pi$
$360$		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	0.0653805	−	0.997860i	$-0.479174\pi$
$373$	15.7829	−	6.53747i	0.817205	−	0.338498i	0.751825	+	0.659363i	$0.229174\pi$
$374$	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	−0.107340	−	0.994222i	$-0.534233\pi$
$379$	10.1190	−	4.19144i	0.519780	−	0.215300i	0.627120	+	0.778922i	$0.284233\pi$
$380$	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	$-0.587222\pi$
$383$	−10.5915			−0.541201			−0.270601	+	0.962692i	$0.587222\pi$
$384$		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	$-0.538842\pi$
$389$	9.74428	−	4.03621i	0.494054	−	0.204644i	0.615778	+	0.787920i	$0.288842\pi$
$390$		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	0.685144	+	0.728408i	$0.259739\pi$
$397$	−6.26413	+	15.1230i	−0.314388	+	0.759000i	−0.999532	+	0.0305919i	$0.990261\pi$
$398$	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	$-0.423440\pi$
$401$	9.54016			0.476413			0.238207	+	0.971215i	$0.423440\pi$
$402$		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	−0.900851	−	0.434129i	$-0.857056\pi$
$409$	−9.43887	+	9.43887i	−0.466722	+	0.466722i	0.434129	+	0.900851i	$0.357056\pi$
$410$	−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	$-0.215126\pi$
$419$	18.2081	+	7.54205i	0.889525	+	0.368453i	0.109342	+	0.994004i	$0.465126\pi$
$420$		0			0
$421$	7.63758	+	18.4387i	0.372233	+	0.898649i	0.993371	+	0.114949i	$0.0366704\pi$
$421$	7.63758	+	18.4387i	0.372233	+	0.898649i	−0.621139	+	0.783701i	$0.713330\pi$
$422$	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	$-0.984364\pi$
$433$		−	2.04349i		−	0.0982041i	0.998794	−	0.0491020i	$-0.0156360\pi$
$434$	−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	−0.879791	−	0.475361i	$-0.842318\pi$
$439$	−8.47375	+	8.47375i	−0.404430	+	0.404430i	0.475361	+	0.879791i	$0.342318\pi$
$440$	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	0.864228	+	0.503101i	$0.167808\pi$
$443$	12.8153	+	30.9388i	0.608873	+	1.46995i	−0.255355	+	0.966847i	$0.582192\pi$
$444$		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	0.892884	−	0.450287i	$-0.148678\pi$
$457$	9.46165	+	9.46165i	0.442597	+	0.442597i	−0.450287	+	0.892884i	$0.648678\pi$
$458$	−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	$-0.441005\pi$
$461$	−8.16779	−	3.38321i	−0.380412	−	0.157572i	−0.564691	+	0.825302i	$0.691005\pi$
$462$		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	−0.677818	−	0.735230i	$-0.737074\pi$
$467$	6.94459	−	16.7657i	0.321357	−	0.775825i	0.999176	−	0.0405959i	$-0.0129256\pi$
$468$		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	$-0.421531\pi$
$479$	10.6817			0.488058			0.244029	+	0.969768i	$0.421531\pi$
$480$		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	0.511521	−	0.859271i	$-0.329082\pi$
$487$	−7.67417	−	7.67417i	−0.347750	−	0.347750i	−0.859271	+	0.511521i	$0.829082\pi$
$488$	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	0.747744	−	0.663987i	$-0.231137\pi$
$491$	38.6885	−	16.0253i	1.74599	−	0.723212i	0.998245	−	0.0592250i	$-0.0188629\pi$
$492$		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	0.750069	−	0.661359i	$-0.230020\pi$
$499$	18.1565	+	7.52067i	0.812797	+	0.336671i	0.0627275	+	0.998031i	$0.480020\pi$
$500$	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	$-0.479451\pi$
$503$	−20.9341	−	20.9341i	−0.933405	−	0.933405i	−0.997917	+	0.0645124i	$0.979451\pi$
$504$		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	$-0.867643\pi$
$509$	0.399075	−	0.963453i	0.0176887	−	0.0427043i	0.932477	+	0.361229i	$0.117643\pi$
$510$		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	$-0.711810\pi$
$521$	3.86359	−	3.86359i	0.169267	−	0.169267i	0.786657	+	0.617390i	$0.211810\pi$
$522$		0			0
$523$	−8.40221	−	20.2847i	−0.367403	−	0.886989i	−0.994174	−	0.107786i	$-0.965624\pi$
$523$	−8.40221	−	20.2847i	−0.367403	−	0.886989i	0.626771	−	0.779203i	$-0.284376\pi$
$524$	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	0.393510	−	0.919320i	$-0.371261\pi$
$541$	0.504857	+	0.209119i	0.0217055	+	0.00899071i	−0.371804	+	0.928311i	$0.621261\pi$
$542$	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	−0.429186	−	0.903216i	$-0.641200\pi$
$547$	11.9972	−	28.9639i	0.512964	−	1.23841i	0.942151	−	0.335190i	$-0.108800\pi$
$548$	−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	$-0.350743\pi$
$557$	3.31995	+	1.37517i	0.140671	+	0.0582677i	−0.311238	+	0.950332i	$0.600743\pi$
$558$		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	$-0.936233\pi$
$563$	−3.47196	+	8.38204i	−0.146325	+	0.353261i	0.833675	+	0.552255i	$0.186233\pi$
$564$		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	$-0.275759\pi$
$569$	−2.72691	−	2.72691i	−0.114318	−	0.114318i	−0.761952	+	0.647634i	$0.775759\pi$
$570$		0			0
$571$	30.8517	−	12.7792i	1.29110	−	0.534792i	0.371789	−	0.928317i	$-0.378745\pi$
$571$	30.8517	−	12.7792i	1.29110	−	0.534792i	0.919314	+	0.393525i	$0.128745\pi$
$572$	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	$-0.543206\pi$
$587$	11.3774	−	4.71269i	0.469597	−	0.194514i	0.604917	+	0.796288i	$0.293206\pi$
$588$		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	$-0.404275\pi$
$593$	14.4266			0.592431			0.296216	+	0.955121i	$0.404275\pi$
$594$		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	$-0.357554\pi$
$599$	−11.4738	−	11.4738i	−0.468808	−	0.468808i	−0.901528	+	0.432720i	$0.857554\pi$
$600$		0			0
$601$	−5.94470	+	5.94470i	−0.242489	+	0.242489i	−0.817879	−	0.575390i	$-0.804850\pi$
$601$	−5.94470	+	5.94470i	−0.242489	+	0.242489i	0.575390	+	0.817879i	$0.304850\pi$
$602$	−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	$0.153635\pi$
$607$			22.8701i			0.928269i	−0.885765	+	0.464135i	$0.846365\pi$
$608$	−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	0.777788	−	0.628526i	$-0.216342\pi$
$613$	−5.36341	−	12.9484i	−0.216626	−	0.522982i	−0.994415	+	0.105544i	$0.966342\pi$
$614$	−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	$-0.551050\pi$
$617$	20.5540	−	20.5540i	0.827474	−	0.827474i	0.987167	+	0.159693i	$0.0510505\pi$
$618$		0			0
$619$	−4.42844	−	10.6912i	−0.177994	−	0.429716i	0.809551	−	0.587049i	$-0.199710\pi$
$619$	−4.42844	−	10.6912i	−0.177994	−	0.429716i	−0.987546	+	0.157333i	$0.949710\pi$
$620$	−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	−0.699043	−	0.715080i	$-0.746390\pi$
$631$	0.402845	−	0.402845i	0.0160370	−	0.0160370i	0.715080	+	0.699043i	$0.246390\pi$
$632$	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	−0.550671	−	0.834722i	$-0.685628\pi$
$643$	10.8771	−	26.2596i	0.428950	−	1.03558i	0.979621	−	0.200854i	$-0.0643717\pi$
$644$	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	$-0.781955\pi$
$647$	−3.60517	+	3.60517i	−0.141734	+	0.141734i	0.632680	+	0.774414i	$0.281955\pi$
$648$		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	$-0.117820\pi$
$653$	34.1322	+	14.1380i	1.33570	+	0.553264i	0.403423	+	0.915014i	$0.367820\pi$
$654$		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	0.0327038	+	0.999465i	$0.489588\pi$
$659$	−17.8965	+	43.2060i	−0.697150	+	1.68307i	−0.729854	+	0.683603i	$0.760412\pi$
$660$		0			0
$661$	−3.26994	+	1.35446i	−0.127186	+	0.0526822i	−0.445369	−	0.895347i	$-0.646927\pi$
$661$	−3.26994	+	1.35446i	−0.127186	+	0.0526822i	0.318183	+	0.948029i	$0.396927\pi$
$662$	−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	$-0.533605\pi$
$677$	13.6153	−	5.63965i	0.523279	−	0.216749i	0.628657	+	0.777683i	$0.283605\pi$
$678$		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	$-0.790920\pi$
$683$	−24.0468	+	9.96050i	−0.920124	+	0.381128i	−0.128200	+	0.991748i	$0.540920\pi$
$684$		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	−0.473245	−	0.880931i	$-0.656917\pi$
$691$	−37.6111	−	15.5790i	−1.43079	−	0.592653i	−0.957547	+	0.288278i	$0.906917\pi$
$692$	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	0.635244	+	0.772312i	$0.280900\pi$
$701$	−9.53278	+	23.0142i	−0.360048	+	0.869233i	−0.995292	+	0.0969216i	$0.969100\pi$
$702$		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	0.883467	−	0.468493i	$-0.155203\pi$
$709$	−1.93081	−	4.66140i	−0.0725132	−	0.175062i	−0.955980	+	0.293431i	$0.905203\pi$
$710$	−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	−0.294476	−	0.955659i	$-0.595145\pi$
$727$	17.8274	−	17.8274i	0.661183	−	0.661183i	0.955659	+	0.294476i	$0.0951450\pi$
$728$	−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	0.439070	−	0.898453i	$-0.355308\pi$
$733$	3.09283	+	1.28109i	0.114236	+	0.0473182i	−0.324833	+	0.945771i	$0.605308\pi$
$734$	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	0.684197	+	0.729297i	$0.260153\pi$
$739$	−8.57114	+	20.6926i	−0.315295	+	0.761188i	−0.999491	+	0.0318910i	$0.989847\pi$
$740$	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	−0.131384	+	0.991332i	$0.541942\pi$
$743$	−30.6030	+	30.6030i	−1.12272	+	1.12272i	−0.991332	+	0.131384i	$0.958058\pi$
$744$		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	−0.190463	−	0.981694i	$-0.560999\pi$
$757$	10.1531	−	4.20556i	0.369021	−	0.152854i	0.559485	+	0.828841i	$0.310999\pi$
$758$	−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	$-0.0813219\pi$
$761$	19.7195	+	19.7195i	0.714832	+	0.714832i	−0.252710	+	0.967542i	$0.581322\pi$
$762$		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	$-0.844221\pi$
$773$	−32.6494	+	13.5238i	−1.17432	+	0.486418i	−0.291700	+	0.956510i	$0.594221\pi$
$774$		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	0.465368	−	0.885117i	$-0.345922\pi$
$787$	4.72873	+	1.95870i	0.168561	+	0.0698203i	−0.296807	+	0.954937i	$0.595922\pi$
$788$	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	$-0.853255\pi$
$797$	1.47493	−	3.56079i	0.0522447	−	0.126130i	0.947847	+	0.318726i	$0.103255\pi$
$798$		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	$-0.756740\pi$
$809$	−0.851642	+	0.851642i	−0.0299421	+	0.0299421i	0.691977	+	0.721919i	$0.256740\pi$
$810$		0			0
$811$	11.0808	+	26.7515i	0.389100	+	0.939371i	0.990131	+	0.140145i	$0.0447568\pi$
$811$	11.0808	+	26.7515i	0.389100	+	0.939371i	−0.601031	+	0.799226i	$0.705243\pi$
$812$	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	−0.942517	−	0.334157i	$-0.891548\pi$
$821$	−14.6802	−	35.4411i	−0.512342	−	1.23690i	0.430176	−	0.902745i	$-0.358452\pi$
$822$		0			0
$823$	23.7916	−	23.7916i	0.829322	−	0.829322i	−0.158101	−	0.987423i	$-0.550537\pi$
$823$	23.7916	−	23.7916i	0.829322	−	0.829322i	0.987423	+	0.158101i	$0.0505370\pi$
$824$	−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	$-0.227292\pi$
$827$	−6.95203	−	16.7837i	−0.241746	−	0.583626i	−0.997456	+	0.0712800i	$0.977292\pi$
$828$		0			0
$829$	17.6000	+	7.29015i	0.611272	+	0.253197i	0.666772	−	0.745261i	$-0.267675\pi$
$829$	17.6000	+	7.29015i	0.611272	+	0.253197i	−0.0555001	+	0.998459i	$0.517675\pi$
$830$	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	$-0.786952\pi$
$839$	−4.74463	+	4.74463i	−0.163803	+	0.163803i	0.620446	+	0.784249i	$0.286952\pi$
$840$		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	0.0150190	−	0.999887i	$-0.495219\pi$
$853$	21.3984	−	8.86349i	0.732666	−	0.303480i	0.717647	+	0.696407i	$0.245219\pi$
$854$	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	$-0.367812\pi$
$857$	−14.9755	−	14.9755i	−0.511554	−	0.511554i	−0.915003	+	0.403448i	$0.867812\pi$
$858$		0			0
$859$	−3.68023	+	1.52440i	−0.125568	+	0.0520119i	−0.444583	−	0.895738i	$-0.646648\pi$
$859$	−3.68023	+	1.52440i	−0.125568	+	0.0520119i	0.319015	+	0.947750i	$0.396648\pi$
$860$	−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	$-0.853721\pi$
$863$	−52.6581			−1.79250			−0.896252	+	0.443545i	$0.853721\pi$
$864$		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	−0.985519	−	0.169565i	$-0.945764\pi$
$877$	−4.99743	+	12.0649i	−0.168751	+	0.407401i	0.816768	+	0.576966i	$0.195764\pi$
$878$	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	$-0.274306\pi$
$881$	38.6516			1.30221			0.651103	+	0.758989i	$0.274306\pi$
$882$		0			0
$883$	−10.8231	−	4.48306i	−0.364226	−	0.150867i	0.193062	−	0.981186i	$-0.438158\pi$
$883$	−10.8231	−	4.48306i	−0.364226	−	0.150867i	−0.557288	+	0.830319i	$0.688158\pi$
$884$	−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	$-0.275010\pi$
$887$	−3.30593	−	3.30593i	−0.111002	−	0.111002i	−0.760426	+	0.649424i	$0.775010\pi$
$888$		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	0.965548	+	0.260225i	$0.0837967\pi$
$907$	14.0586	+	33.9405i	0.466809	+	1.12698i	−0.498739	+	0.866752i	$0.666203\pi$
$908$	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	−0.434988	−	0.900436i	$-0.643247\pi$
$919$	14.1101	−	14.1101i	0.465448	−	0.465448i	0.900436	+	0.434988i	$0.143247\pi$
$920$	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	0.411845	−	0.911254i	$-0.364885\pi$
$937$	−15.2871	−	15.2871i	−0.499409	−	0.499409i	−0.911254	+	0.411845i	$0.864885\pi$
$938$	−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	$-0.589910\pi$
$941$	−35.4271	−	14.6744i	−1.15489	−	0.478372i	−0.876171	+	0.482000i	$0.839910\pi$
$942$		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	$-0.989423\pi$
$947$	−8.28542	+	20.0028i	−0.269240	+	0.650003i	0.730208	+	0.683225i	$0.239423\pi$
$948$		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	$-0.0319194\pi$
$953$	27.6252	+	27.6252i	0.894867	+	0.894867i	−0.100110	+	0.994976i	$0.531919\pi$
$954$		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	−0.998911	−	0.0466463i	$-0.985147\pi$
$967$	−32.5133	−	32.5133i	−1.04556	−	1.04556i	−0.0466463	−	0.998911i	$-0.514853\pi$
$968$	−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	$-0.955014\pi$
$971$	−49.5609	+	20.5288i	−1.59048	+	0.658800i	−0.600455	+	0.799659i	$0.705014\pi$
$972$		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	$-0.654774\pi$
$977$	−29.2129			−0.934603			−0.467301	+	0.884098i	$0.654774\pi$
$978$		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	−0.996874	−	0.0790094i	$-0.974824\pi$
$983$	−33.7320	−	33.7320i	−1.07588	−	1.07588i	−0.0790094	−	0.996874i	$-0.525176\pi$
$984$		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	$-0.988147\pi$
$991$		−	2.34392i		−	0.0744571i	0.999307	−	0.0372285i	$-0.0118530\pi$
$992$	−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	−0.965404	−	0.260759i	$-0.916027\pi$
$997$	−14.7502	−	35.6102i	−0.467145	−	1.12779i	0.498259	−	0.867028i	$-0.333973\pi$
$998$	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.a.35.4	✓	32
3.2	odd	2		288.2.w.b.35.5	yes	32
4.3	odd	2		1152.2.w.b.431.3		32
12.11	even	2		1152.2.w.a.431.6		32
32.11	odd	8		288.2.w.b.107.5	yes	32
32.21	even	8		1152.2.w.a.719.6		32
96.11	even	8	inner	288.2.w.a.107.4	yes	32
96.53	odd	8		1152.2.w.b.719.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.4	✓	32	1.1	even	1	trivial
288.2.w.a.107.4	yes	32	96.11	even	8	inner
288.2.w.b.35.5	yes	32	3.2	odd	2
288.2.w.b.107.5	yes	32	32.11	odd	8
1152.2.w.a.431.6		32	12.11	even	2
1152.2.w.a.719.6		32	32.21	even	8
1152.2.w.b.431.3		32	4.3	odd	2
1152.2.w.b.719.3		32	96.53	odd	8

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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