LMFDB - Embedded newform 288.2.w.b.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.b.107.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.349793 - 1.37027i) q^{2} +(-1.75529 + 0.958624i) q^{4} +(2.97412 - 1.23192i) q^{5} +(0.237717 + 0.237717i) q^{7} +(1.92756 + 2.06990i) q^{8} +(-2.72839 - 3.64443i) q^{10} +(2.12394 - 0.879764i) q^{11} +(0.0390635 - 0.0943077i) q^{13} +(0.242585 - 0.408888i) q^{14} +(2.16208 - 3.36532i) q^{16} +4.16112 q^{17} +(-4.25390 - 1.76202i) q^{19} +(-4.03949 + 5.01343i) q^{20} +(-1.94845 - 2.60264i) q^{22} +(-4.84847 - 4.84847i) q^{23} +(3.79221 - 3.79221i) q^{25} +(-0.142891 - 0.0205395i) q^{26} +(-0.645142 - 0.189381i) q^{28} +(2.90419 - 7.01132i) q^{29} +9.88480i q^{31} +(-5.36769 - 1.78547i) q^{32} +(-1.45553 - 5.70186i) q^{34} +(0.999845 + 0.414149i) q^{35} +(0.175641 + 0.424034i) q^{37} +(-0.926465 + 6.44535i) q^{38} +(8.28275 + 3.78153i) q^{40} +(-7.67919 + 7.67919i) q^{41} +(2.99581 + 7.23252i) q^{43} +(-2.88476 + 3.58030i) q^{44} +(-4.94776 + 8.33968i) q^{46} -6.10937i q^{47} -6.88698i q^{49} +(-6.52284 - 3.86986i) q^{50} +(0.0218378 + 0.202984i) q^{52} +(4.28258 + 10.3391i) q^{53} +(5.23304 - 5.23304i) q^{55} +(-0.0338366 + 0.950265i) q^{56} +(-10.6233 - 1.52701i) q^{58} +(1.19303 + 2.88024i) q^{59} +(6.29246 + 2.60642i) q^{61} +(13.5449 - 3.45764i) q^{62} +(-0.569000 + 7.97974i) q^{64} -0.328605i q^{65} +(-5.66771 + 13.6831i) q^{67} +(-7.30396 + 3.98894i) q^{68} +(0.217758 - 1.51493i) q^{70} +(3.49288 - 3.49288i) q^{71} +(-1.42542 - 1.42542i) q^{73} +(0.519604 - 0.389000i) q^{74} +(9.15595 - 0.985029i) q^{76} +(0.714030 + 0.295761i) q^{77} +1.53778 q^{79} +(2.28447 - 12.6724i) q^{80} +(13.2087 + 7.83645i) q^{82} +(-2.95890 + 7.14340i) q^{83} +(12.3756 - 5.12616i) q^{85} +(8.86261 - 6.63496i) q^{86} +(5.91505 + 2.70055i) q^{88} +(-1.92767 - 1.92767i) q^{89} +(0.0317046 - 0.0131325i) q^{91} +(13.1583 + 3.86261i) q^{92} +(-8.37149 + 2.13702i) q^{94} -14.8223 q^{95} -12.9791 q^{97} +(-9.43704 + 2.40902i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.349793	−	1.37027i	−0.247341	−	0.968928i
$2$	−0.349793	−	1.37027i	−0.247341	−	0.968928i
$3$		0			0
$3$		0			0
$4$	−1.75529	+	0.958624i	−0.877645	+	0.479312i
$5$	2.97412	−	1.23192i	1.33007	−	0.550931i	0.399391	−	0.916781i	$-0.369222\pi$
$5$	2.97412	−	1.23192i	1.33007	−	0.550931i	0.930674	+	0.365850i	$0.119222\pi$
$6$		0			0
$7$	0.237717	+	0.237717i	0.0898485	+	0.0898485i	0.750603	−	0.660754i	$-0.229763\pi$
$7$	0.237717	+	0.237717i	0.0898485	+	0.0898485i	−0.660754	+	0.750603i	$0.729763\pi$
$8$	1.92756	+	2.06990i	0.681497	+	0.731821i
$9$		0			0
$10$	−2.72839	−	3.64443i	−0.862793	−	1.15247i
$11$	2.12394	−	0.879764i	0.640391	−	0.265259i	−0.0387695	−	0.999248i	$-0.512344\pi$
$11$	2.12394	−	0.879764i	0.640391	−	0.265259i	0.679161	+	0.733989i	$0.262344\pi$
$12$		0			0
$13$	0.0390635	−	0.0943077i	0.0108343	−	0.0261562i	−0.918370	−	0.395723i	$-0.870494\pi$
$13$	0.0390635	−	0.0943077i	0.0108343	−	0.0261562i	0.929204	+	0.369567i	$0.120494\pi$
$14$	0.242585	−	0.408888i	0.0648335	−	0.109280i
$15$		0			0
$16$	2.16208	−	3.36532i	0.540520	−	0.841331i
$17$	4.16112			1.00922			0.504609	−	0.863348i	$-0.331636\pi$
$17$	4.16112			1.00922			0.504609	+	0.863348i	$0.331636\pi$
$18$		0			0
$19$	−4.25390	−	1.76202i	−0.975912	−	0.404236i	−0.163002	−	0.986626i	$-0.552118\pi$
$19$	−4.25390	−	1.76202i	−0.975912	−	0.404236i	−0.812910	+	0.582390i	$0.802118\pi$
$20$	−4.03949	+	5.01343i	−0.903257	+	1.12104i
$21$		0			0
$22$	−1.94845	−	2.60264i	−0.415412	−	0.554884i
$23$	−4.84847	−	4.84847i	−1.01098	−	1.01098i	−0.999939	−	0.0110368i	$-0.996487\pi$
$23$	−4.84847	−	4.84847i	−1.01098	−	1.01098i	−0.0110368	−	0.999939i	$-0.503513\pi$
$24$		0			0
$25$	3.79221	−	3.79221i	0.758441	−	0.758441i
$26$	−0.142891	−	0.0205395i	−0.0280233	−	0.00402812i
$27$		0			0
$28$	−0.645142	−	0.189381i	−0.121920	−	0.0357896i
$29$	2.90419	−	7.01132i	0.539294	−	1.30197i	−0.385923	−	0.922531i	$-0.626117\pi$
$29$	2.90419	−	7.01132i	0.539294	−	1.30197i	0.925217	−	0.379439i	$-0.123883\pi$
$30$		0			0
$31$			9.88480i			1.77536i	0.460459	+	0.887681i	$0.347685\pi$
$31$			9.88480i			1.77536i	−0.460459	+	0.887681i	$0.652315\pi$
$32$	−5.36769	−	1.78547i	−0.948882	−	0.315630i
$33$		0			0
$34$	−1.45553	−	5.70186i	−0.249621	−	0.977861i
$35$	0.999845	+	0.414149i	0.169005	+	0.0700040i
$36$		0			0
$37$	0.175641	+	0.424034i	0.0288752	+	0.0697108i	0.937659	−	0.347556i	$-0.112988\pi$
$37$	0.175641	+	0.424034i	0.0288752	+	0.0697108i	−0.908784	+	0.417266i	$0.862988\pi$
$38$	−0.926465	+	6.44535i	−0.150293	+	1.04557i
$39$		0			0
$40$	8.28275	+	3.78153i	1.30962	+	0.597912i
$41$	−7.67919	+	7.67919i	−1.19929	+	1.19929i	−0.224907	+	0.974380i	$0.572208\pi$
$41$	−7.67919	+	7.67919i	−1.19929	+	1.19929i	−0.974380	+	0.224907i	$0.927792\pi$
$42$		0			0
$43$	2.99581	+	7.23252i	0.456857	+	1.10295i	0.969663	+	0.244445i	$0.0786058\pi$
$43$	2.99581	+	7.23252i	0.456857	+	1.10295i	−0.512807	+	0.858504i	$0.671394\pi$
$44$	−2.88476	+	3.58030i	−0.434894	+	0.539750i
$45$		0			0
$46$	−4.94776	+	8.33968i	−0.729507	+	1.22962i
$47$		−	6.10937i		−	0.891143i	−0.895246	−	0.445571i	$-0.853001\pi$
$47$		−	6.10937i		−	0.891143i	0.895246	−	0.445571i	$-0.146999\pi$
$48$		0			0
$49$		−	6.88698i		−	0.983855i
$50$	−6.52284	−	3.86986i	−0.922469	−	0.547282i
$51$		0			0
$52$	0.0218378	+	0.202984i	0.00302836	+	0.0281489i
$53$	4.28258	+	10.3391i	0.588258	+	1.42018i	0.885167	+	0.465274i	$0.154044\pi$
$53$	4.28258	+	10.3391i	0.588258	+	1.42018i	−0.296909	+	0.954906i	$0.595956\pi$
$54$		0			0
$55$	5.23304	−	5.23304i	0.705623	−	0.705623i
$56$	−0.0338366	+	0.950265i	−0.00452161	+	0.126984i
$57$		0			0
$58$	−10.6233	−	1.52701i	−1.39491	−	0.200506i
$59$	1.19303	+	2.88024i	0.155320	+	0.374975i	0.982316	−	0.187233i	$-0.0599519\pi$
$59$	1.19303	+	2.88024i	0.155320	+	0.374975i	−0.826996	+	0.562208i	$0.809952\pi$
$60$		0			0
$61$	6.29246	+	2.60642i	0.805667	+	0.333718i	0.747224	−	0.664573i	$-0.231386\pi$
$61$	6.29246	+	2.60642i	0.805667	+	0.333718i	0.0584431	+	0.998291i	$0.481386\pi$
$62$	13.5449	−	3.45764i	1.72020	−	0.439120i
$63$		0			0
$64$	−0.569000	+	7.97974i	−0.0711250	+	0.997467i
$65$		−	0.328605i		−	0.0407584i
$66$		0			0
$67$	−5.66771	+	13.6831i	−0.692420	+	1.67165i	0.0474259	+	0.998875i	$0.484898\pi$
$67$	−5.66771	+	13.6831i	−0.692420	+	1.67165i	−0.739846	+	0.672776i	$0.765102\pi$
$68$	−7.30396	+	3.98894i	−0.885736	+	0.483731i
$69$		0			0
$70$	0.217758	−	1.51493i	0.0260271	−	0.181068i
$71$	3.49288	−	3.49288i	0.414528	−	0.414528i	−0.468784	−	0.883313i	$-0.655308\pi$
$71$	3.49288	−	3.49288i	0.414528	−	0.414528i	0.883313	+	0.468784i	$0.155308\pi$
$72$		0			0
$73$	−1.42542	−	1.42542i	−0.166833	−	0.166833i	0.618753	−	0.785586i	$-0.287638\pi$
$73$	−1.42542	−	1.42542i	−0.166833	−	0.166833i	−0.785586	+	0.618753i	$0.787638\pi$
$74$	0.519604	−	0.389000i	0.0604028	−	0.0452203i
$75$		0			0
$76$	9.15595	−	0.985029i	1.05026	−	0.112991i
$77$	0.714030	+	0.295761i	0.0813713	+	0.0337051i
$78$		0			0
$79$	1.53778			0.173014			0.0865070	−	0.996251i	$-0.472430\pi$
$79$	1.53778			0.173014			0.0865070	+	0.996251i	$0.472430\pi$
$80$	2.28447	−	12.6724i	0.255412	−	1.41681i
$81$		0			0
$82$	13.2087	+	7.83645i	1.45866	+	0.865391i
$83$	−2.95890	+	7.14340i	−0.324781	+	0.784091i	0.674182	+	0.738565i	$0.264496\pi$
$83$	−2.95890	+	7.14340i	−0.324781	+	0.784091i	−0.998963	+	0.0455255i	$0.985504\pi$
$84$		0			0
$85$	12.3756	−	5.12616i	1.34233	−	0.556010i
$86$	8.86261	−	6.63496i	0.955680	−	0.715466i
$87$		0			0
$88$	5.91505	+	2.70055i	0.630547	+	0.287879i
$89$	−1.92767	−	1.92767i	−0.204333	−	0.204333i	0.597521	−	0.801853i	$-0.296153\pi$
$89$	−1.92767	−	1.92767i	−0.204333	−	0.204333i	−0.801853	+	0.597521i	$0.796153\pi$
$90$		0			0
$91$	0.0317046	−	0.0131325i	0.00332354	−	0.00137666i
$92$	13.1583	+	3.86261i	1.37185	+	0.402705i
$93$		0			0
$94$	−8.37149	+	2.13702i	−0.863454	+	0.220416i
$95$	−14.8223			−1.52073
$96$		0			0
$97$	−12.9791			−1.31783			−0.658915	−	0.752218i	$-0.728984\pi$
$97$	−12.9791			−1.31783			−0.658915	+	0.752218i	$0.728984\pi$
$98$	−9.43704	+	2.40902i	−0.953285	+	0.243348i
$99$		0			0
$100$	−3.02112	+	10.2917i	−0.302112	+	1.02917i
$101$	10.2765	−	4.25666i	1.02255	−	0.423554i	0.192532	−	0.981291i	$-0.438330\pi$
$101$	10.2765	−	4.25666i	1.02255	−	0.423554i	0.830018	+	0.557737i	$0.188330\pi$
$102$		0			0
$103$	−6.66422	−	6.66422i	−0.656645	−	0.656645i	0.297940	−	0.954585i	$-0.403701\pi$
$103$	−6.66422	−	6.66422i	−0.656645	−	0.656645i	−0.954585	+	0.297940i	$0.903701\pi$
$104$	0.270505	−	0.100926i	0.0265252	−	0.00989664i
$105$		0			0
$106$	12.6693	−	9.48483i	1.23055	−	0.921248i
$107$	−11.1377	+	4.61340i	−1.07673	+	0.445994i	−0.849359	−	0.527815i	$-0.823011\pi$
$107$	−11.1377	+	4.61340i	−1.07673	+	0.445994i	−0.227366	+	0.973809i	$0.573011\pi$
$108$		0			0
$109$	−3.68462	+	8.89546i	−0.352922	+	0.852030i	0.643334	+	0.765585i	$0.277551\pi$
$109$	−3.68462	+	8.89546i	−0.352922	+	0.852030i	−0.996257	+	0.0864447i	$0.972449\pi$
$110$	−9.00117	−	5.34020i	−0.858228	−	0.509169i
$111$		0			0
$112$	1.31396	−	0.286031i	0.124157	−	0.0270274i
$113$	−7.16123			−0.673672			−0.336836	−	0.941563i	$-0.609357\pi$
$113$	−7.16123			−0.673672			−0.336836	+	0.941563i	$0.609357\pi$
$114$		0			0
$115$	−20.3928	−	8.44699i	−1.90164	−	0.787686i
$116$	1.62353	+	15.0909i	0.150741	+	1.40116i
$117$		0			0
$118$	3.52940	−	2.64227i	0.324907	−	0.243241i
$119$	0.989167	+	0.989167i	0.0906768	+	0.0906768i
$120$		0			0
$121$	−4.04105	+	4.04105i	−0.367368	+	0.367368i
$122$	1.37045	−	9.53409i	0.124074	−	0.863176i
$123$		0			0
$124$	−9.47580	−	17.3507i	−0.850952	−	1.55814i
$125$	0.447173	−	1.07957i	0.0399964	−	0.0965599i
$126$		0			0
$127$		−	9.41925i		−	0.835823i	−0.908488	−	0.417911i	$-0.862762\pi$
$127$		−	9.41925i		−	0.835823i	0.908488	−	0.417911i	$-0.137238\pi$
$128$	11.1334	−	2.01157i	0.984067	−	0.177800i
$129$		0			0
$130$	−0.450278	+	0.114944i	−0.0394920	+	0.0100812i
$131$	−3.15026	−	1.30488i	−0.275240	−	0.114008i	0.240794	−	0.970576i	$-0.422592\pi$
$131$	−3.15026	−	1.30488i	−0.275240	−	0.114008i	−0.516034	+	0.856568i	$0.672592\pi$
$132$		0			0
$133$	−0.592361	−	1.43009i	−0.0513642	−	0.124004i
$134$	20.7320	+	2.98006i	1.79097	+	0.257438i
$135$		0			0
$136$	8.02081	+	8.61311i	0.687779	+	0.738568i
$137$	−8.26376	+	8.26376i	−0.706021	+	0.706021i	−0.965696	−	0.259675i	$-0.916384\pi$
$137$	−8.26376	+	8.26376i	−0.706021	+	0.706021i	0.259675	+	0.965696i	$0.416384\pi$
$138$		0			0
$139$	0.429473	+	1.03684i	0.0364274	+	0.0879436i	0.941046	−	0.338278i	$-0.109844\pi$
$139$	0.429473	+	1.03684i	0.0364274	+	0.0879436i	−0.904619	+	0.426222i	$0.859844\pi$
$140$	−2.15203	+	0.231523i	−0.181880	+	0.0195673i
$141$		0			0
$142$	−6.00798	−	3.56441i	−0.504178	−	0.299118i
$143$		−	0.234670i		−	0.0196241i
$144$		0			0
$145$		−	24.4302i		−	2.02882i
$146$	−1.45461	+	2.45182i	−0.120385	+	0.202914i
$147$		0			0
$148$	−0.714790	−	0.575930i	−0.0587554	−	0.0473411i
$149$	0.253180	+	0.611230i	0.0207413	+	0.0500739i	0.933911	−	0.357506i	$-0.116373\pi$
$149$	0.253180	+	0.611230i	0.0207413	+	0.0500739i	−0.913170	+	0.407580i	$0.866373\pi$
$150$		0			0
$151$	11.4878	−	11.4878i	0.934862	−	0.934862i	−0.0631423	−	0.998005i	$-0.520112\pi$
$151$	11.4878	−	11.4878i	0.934862	−	0.934862i	0.998005	+	0.0631423i	$0.0201122\pi$
$152$	−4.55245	−	12.2016i	−0.369252	−	0.989679i
$153$		0			0
$154$	0.155510	−	1.08187i	0.0125314	−	0.0871796i
$155$	12.1773	+	29.3985i	0.978102	+	2.36135i
$156$		0			0
$157$	−13.7120	−	5.67968i	−1.09433	−	0.453288i	−0.238818	−	0.971064i	$-0.576760\pi$
$157$	−13.7120	−	5.67968i	−1.09433	−	0.453288i	−0.855516	+	0.517777i	$0.826760\pi$
$158$	−0.537906	−	2.10718i	−0.0427935	−	0.167638i
$159$		0			0
$160$	−18.1637	+	1.30236i	−1.43597	+	0.102961i
$161$		−	2.30512i		−	0.181669i
$162$		0			0
$163$	2.66632	−	6.43706i	0.208842	−	0.504189i	−0.784399	−	0.620256i	$-0.787029\pi$
$163$	2.66632	−	6.43706i	0.208842	−	0.504189i	0.993241	+	0.116067i	$0.0370287\pi$
$164$	6.11775	−	20.8406i	0.477716	−	1.62738i
$165$		0			0
$166$	10.8234	+	1.55578i	0.840059	+	0.120752i
$167$	6.53445	−	6.53445i	0.505651	−	0.505651i	−0.407538	−	0.913188i	$-0.633613\pi$
$167$	6.53445	−	6.53445i	0.505651	−	0.505651i	0.913188	+	0.407538i	$0.133613\pi$
$168$		0			0
$169$	9.18502	+	9.18502i	0.706540	+	0.706540i
$170$	−11.3531	−	15.1649i	−0.870747	−	1.16309i
$171$		0			0
$172$	−12.1918	−	9.82332i	−0.929614	−	0.749021i
$173$	−3.24361	−	1.34355i	−0.246607	−	0.102148i	0.255956	−	0.966688i	$-0.417610\pi$
$173$	−3.24361	−	1.34355i	−0.246607	−	0.102148i	−0.502563	+	0.864540i	$0.667610\pi$
$174$		0			0
$175$	1.80294			0.136290
$176$	1.63144	−	9.04986i	0.122974	−	0.682159i
$177$		0			0
$178$	−1.96715	+	3.31572i	−0.147444	+	0.248524i
$179$	9.86789	−	23.8232i	0.737560	−	1.78063i	0.122013	−	0.992528i	$-0.461065\pi$
$179$	9.86789	−	23.8232i	0.737560	−	1.78063i	0.615547	−	0.788100i	$-0.288935\pi$
$180$		0			0
$181$	12.1863	−	5.04772i	0.905799	−	0.375194i	0.119352	−	0.992852i	$-0.461918\pi$
$181$	12.1863	−	5.04772i	0.905799	−	0.375194i	0.786447	+	0.617658i	$0.211918\pi$
$182$	−0.0290851	−	0.0388502i	−0.00215593	−	0.00287977i
$183$		0			0
$184$	0.690132	−	19.3816i	0.0508772	−	1.42883i
$185$	1.04475	+	1.04475i	0.0768117	+	0.0768117i
$186$		0			0
$187$	8.83795	−	3.66080i	0.646295	−	0.267704i
$188$	5.85658	+	10.7237i	0.427135	+	0.782107i
$189$		0			0
$190$	5.18473	+	20.3105i	0.376140	+	1.47348i
$191$	−12.7590			−0.923208			−0.461604	−	0.887086i	$-0.652726\pi$
$191$	−12.7590			−0.923208			−0.461604	+	0.887086i	$0.652726\pi$
$192$		0			0
$193$	−12.6078			−0.907531			−0.453766	−	0.891121i	$-0.649920\pi$
$193$	−12.6078			−0.907531			−0.453766	+	0.891121i	$0.649920\pi$
$194$	4.54001	+	17.7849i	0.325953	+	1.27688i
$195$		0			0
$196$	6.60202	+	12.0886i	0.471573	+	0.863475i
$197$	−0.666855	+	0.276221i	−0.0475115	+	0.0196799i	−0.406313	−	0.913734i	$-0.633186\pi$
$197$	−0.666855	+	0.276221i	−0.0475115	+	0.0196799i	0.358801	+	0.933414i	$0.383186\pi$
$198$		0			0
$199$	−4.26928	−	4.26928i	−0.302641	−	0.302641i	0.539405	−	0.842046i	$-0.318649\pi$
$199$	−4.26928	−	4.26928i	−0.302641	−	0.302641i	−0.842046	+	0.539405i	$0.818649\pi$
$200$	15.1592	+	0.539783i	1.07192	+	0.0381684i
$201$		0			0
$202$	−9.42744	−	12.5926i	−0.663312	−	0.886015i
$203$	2.35708	−	0.976336i	0.165435	−	0.0685253i
$204$		0			0
$205$	−13.3787	+	32.2989i	−0.934406	+	2.25586i
$206$	−6.80069	+	11.4629i	−0.473827	+	0.798658i
$207$		0			0
$208$	−0.232917	−	0.335362i	−0.0161499	−	0.0232532i
$209$	−10.5852			−0.732193
$210$		0			0
$211$	15.6370	+	6.47704i	1.07649	+	0.445898i	0.849278	−	0.527947i	$-0.177038\pi$
$211$	15.6370	+	6.47704i	1.07649	+	0.445898i	0.227215	+	0.973845i	$0.427038\pi$
$212$	−17.4284	−	14.0427i	−1.19699	−	0.964454i
$213$		0			0
$214$	10.2175	+	13.6480i	0.698455	+	0.932957i
$215$	17.8198	+	17.8198i	1.21530	+	1.21530i
$216$		0			0
$217$	−2.34978	+	2.34978i	−0.159514	+	0.159514i
$218$	13.4780	+	1.93736i	0.912849	+	0.131214i
$219$		0			0
$220$	−4.16898	+	14.2020i	−0.281073	+	0.957500i
$221$	0.162548	−	0.392425i	0.0109342	−	0.0263974i
$222$		0			0
$223$			29.4910i			1.97487i	0.158038	+	0.987433i	$0.449483\pi$
$223$			29.4910i			1.97487i	−0.158038	+	0.987433i	$0.550517\pi$
$224$	−0.851553	−	1.70043i	−0.0568968	−	0.113614i
$225$		0			0
$226$	2.50495	+	9.81283i	0.166627	+	0.652740i
$227$	18.5140	+	7.66873i	1.22881	+	0.508992i	0.900202	−	0.435473i	$-0.143419\pi$
$227$	18.5140	+	7.66873i	1.22881	+	0.508992i	0.328613	+	0.944465i	$0.393419\pi$
$228$		0			0
$229$	2.09503	+	5.05785i	0.138444	+	0.334232i	0.977861	−	0.209255i	$-0.0671037\pi$
$229$	2.09503	+	5.05785i	0.138444	+	0.334232i	−0.839418	+	0.543487i	$0.817104\pi$
$230$	−4.44139	+	30.8984i	−0.292857	+	2.03738i
$231$		0			0
$232$	20.1108	−	7.50339i	1.32034	−	0.492622i
$233$	−0.699144	+	0.699144i	−0.0458024	+	0.0458024i	−0.729637	−	0.683835i	$-0.760311\pi$
$233$	−0.699144	+	0.699144i	−0.0458024	+	0.0458024i	0.683835	+	0.729637i	$0.260311\pi$
$234$		0			0
$235$	−7.52625	−	18.1700i	−0.490958	−	1.18528i
$236$	−4.85519	−	3.91199i	−0.316046	−	0.254649i
$237$		0			0
$238$	1.00942	−	1.70143i	0.0654312	−	0.110287i
$239$		−	22.1034i		−	1.42975i	−0.699253	−	0.714875i	$-0.746484\pi$
$239$		−	22.1034i		−	1.42975i	0.699253	−	0.714875i	$-0.253516\pi$
$240$		0			0
$241$			9.09381i			0.585784i	0.956146	+	0.292892i	$0.0946176\pi$
$241$			9.09381i			0.585784i	−0.956146	+	0.292892i	$0.905382\pi$
$242$	6.95086	+	4.12380i	0.446818	+	0.265088i
$243$		0			0
$244$	−13.5437	+	1.45707i	−0.867044	+	0.0932797i
$245$	−8.48420	−	20.4827i	−0.542036	−	1.30859i
$246$		0			0
$247$	−0.332345	+	0.332345i	−0.0211466	+	0.0211466i
$248$	−20.4606	+	19.0536i	−1.29925	+	1.20990i
$249$		0			0
$250$	−1.63573	−	0.235122i	−0.103452	−	0.0148704i
$251$	1.43019	+	3.45279i	0.0902728	+	0.217938i	0.962567	−	0.271043i	$-0.0873687\pi$
$251$	1.43019	+	3.45279i	0.0902728	+	0.217938i	−0.872294	+	0.488981i	$0.837369\pi$
$252$		0			0
$253$	−14.5634	−	6.03234i	−0.915591	−	0.379250i
$254$	−12.9069	+	3.29479i	−0.809853	+	0.206733i
$255$		0			0
$256$	−6.65081	−	14.5522i	−0.415675	−	0.909513i
$257$			3.05245i			0.190406i	0.995458	+	0.0952032i	$0.0303501\pi$
$257$			3.05245i			0.190406i	−0.995458	+	0.0952032i	$0.969650\pi$
$258$		0			0
$259$	−0.0590473	+	0.142553i	−0.00366902	+	0.00885780i
$260$	0.315009	+	0.576797i	0.0195360	+	0.0357714i
$261$		0			0
$262$	−0.686102	+	4.77316i	−0.0423875	+	0.294887i
$263$	2.44480	−	2.44480i	0.150753	−	0.150753i	−0.627701	−	0.778454i	$-0.716004\pi$
$263$	2.44480	−	2.44480i	0.150753	−	0.150753i	0.778454	+	0.627701i	$0.216004\pi$
$264$		0			0
$265$	25.4738	+	25.4738i	1.56484	+	1.56484i
$266$	−1.75240	+	1.31193i	−0.107447	+	0.0804396i
$267$		0			0
$268$	−3.16843	−	29.4509i	−0.193543	−	1.79900i
$269$	−13.7507	−	5.69573i	−0.838395	−	0.347275i	−0.0781745	−	0.996940i	$-0.524909\pi$
$269$	−13.7507	−	5.69573i	−0.838395	−	0.347275i	−0.760221	+	0.649665i	$0.774909\pi$
$270$		0			0
$271$	24.0583			1.46144			0.730720	−	0.682677i	$-0.239184\pi$
$271$	24.0583			1.46144			0.730720	+	0.682677i	$0.239184\pi$
$272$	8.99667	−	14.0035i	0.545503	−	0.849087i
$273$		0			0
$274$	14.2142	+	8.43299i	0.858711	+	0.509455i
$275$	4.71816	−	11.3907i	0.284516	−	0.686882i
$276$		0			0
$277$	−6.48199	+	2.68493i	−0.389465	+	0.161322i	−0.568819	−	0.822463i	$-0.692599\pi$
$277$	−6.48199	+	2.68493i	−0.389465	+	0.161322i	0.179354	+	0.983785i	$0.442599\pi$
$278$	1.27053	−	0.951174i	0.0762010	−	0.0570476i
$279$		0			0
$280$	1.07002	+	2.86788i	0.0639456	+	0.171389i
$281$	−4.59744	−	4.59744i	−0.274260	−	0.274260i	0.556552	−	0.830813i	$-0.312124\pi$
$281$	−4.59744	−	4.59744i	−0.274260	−	0.274260i	−0.830813	+	0.556552i	$0.812124\pi$
$282$		0			0
$283$	17.9590	−	7.43884i	1.06755	−	0.442193i	0.221424	−	0.975178i	$-0.428930\pi$
$283$	17.9590	−	7.43884i	1.06755	−	0.442193i	0.846125	+	0.532984i	$0.178930\pi$
$284$	−2.78266	+	9.47937i	−0.165120	+	0.562497i
$285$		0			0
$286$	−0.321562	+	0.0820861i	−0.0190144	+	0.00485385i
$287$	−3.65094			−0.215508
$288$		0			0
$289$	0.314890			0.0185229
$290$	−33.4760	+	8.54552i	−1.96578	+	0.501810i
$291$		0			0
$292$	3.86847	+	1.13559i	0.226385	+	0.0664551i
$293$	−0.0302145	+	0.0125153i	−0.00176515	+	0.000731150i	−0.383566	−	0.923514i	$-0.625304\pi$
$293$	−0.0302145	+	0.0125153i	−0.00176515	+	0.000731150i	0.381801	+	0.924245i	$0.375304\pi$
$294$		0			0
$295$	7.09645	+	7.09645i	0.413171	+	0.413171i
$296$	−0.539152	+	1.18091i	−0.0313375	+	0.0686392i
$297$		0			0
$298$	0.748990	−	0.560729i	0.0433878	−	0.0324821i
$299$	−0.646646	+	0.267850i	−0.0373965	+	0.0154901i
$300$		0			0
$301$	−1.00714	+	2.43145i	−0.0580504	+	0.140146i
$302$	−19.7597	−	11.7230i	−1.13704	−	0.674585i
$303$		0			0
$304$	−15.1271	+	10.5061i	−0.867597	+	0.602567i
$305$	21.9254			1.25544
$306$		0			0
$307$	−21.7209	−	8.99707i	−1.23967	−	0.513490i	−0.336062	−	0.941840i	$-0.609095\pi$
$307$	−21.7209	−	8.99707i	−1.23967	−	0.513490i	−0.903613	+	0.428350i	$0.859095\pi$
$308$	−1.53685	+	0.165340i	−0.0875703	+	0.00942112i
$309$		0			0
$310$	36.0244	−	26.9696i	2.04605	−	1.53177i
$311$	3.59830	+	3.59830i	0.204041	+	0.204041i	0.801729	−	0.597688i	$-0.203914\pi$
$311$	3.59830	+	3.59830i	0.204041	+	0.204041i	−0.597688	+	0.801729i	$0.703914\pi$
$312$		0			0
$313$	1.24094	−	1.24094i	0.0701421	−	0.0701421i	−0.671165	−	0.741308i	$-0.734206\pi$
$313$	1.24094	−	1.24094i	0.0701421	−	0.0701421i	0.741308	+	0.671165i	$0.234206\pi$
$314$	−2.98635	+	20.7758i	−0.168530	+	1.17245i
$315$		0			0
$316$	−2.69925	+	1.47415i	−0.151845	+	0.0829276i
$317$	2.92298	−	7.05670i	0.164171	−	0.396344i	−0.820290	−	0.571948i	$-0.806188\pi$
$317$	2.92298	−	7.05670i	0.164171	−	0.396344i	0.984461	+	0.175604i	$0.0561879\pi$
$318$		0			0
$319$		−	17.4466i		−	0.976823i
$320$	8.13812	+	24.4336i	0.454935	+	1.36588i
$321$		0			0
$322$	−3.15865	+	0.806317i	−0.176025	+	0.0449343i
$323$	−17.7010	−	7.33199i	−0.984909	−	0.407963i
$324$		0			0
$325$	−0.209497	−	0.505771i	−0.0116208	−	0.0280551i
$326$	−9.75318	−	1.40194i	−0.540178	−	0.0776462i
$327$		0			0
$328$	−30.6973	−	1.09306i	−1.69497	−	0.0603540i
$329$	1.45230	−	1.45230i	0.0800678	−	0.0800678i
$330$		0			0
$331$	11.2439	+	27.1453i	0.618023	+	1.49204i	0.853996	+	0.520280i	$0.174172\pi$
$331$	11.2439	+	27.1453i	0.618023	+	1.49204i	−0.235973	+	0.971760i	$0.575828\pi$
$332$	−1.65412	−	15.3752i	−0.0907816	−	0.843824i
$333$		0			0
$334$	−11.2397	−	6.66826i	−0.615008	−	0.364871i
$335$			47.6771i			2.60488i
$336$		0			0
$337$			13.3438i			0.726882i	0.931617	+	0.363441i	$0.118398\pi$
$337$			13.3438i			0.726882i	−0.931617	+	0.363441i	$0.881602\pi$
$338$	9.37312	−	15.7988i	0.509830	−	0.859343i
$339$		0			0
$340$	−16.8088	+	20.8615i	−0.911584	+	1.13137i
$341$	8.69629	+	20.9947i	0.470930	+	1.13693i
$342$		0			0
$343$	3.30117	−	3.30117i	0.178246	−	0.178246i
$344$	−9.19601	+	20.1422i	−0.495816	+	1.08599i
$345$		0			0
$346$	−0.706432	+	4.91459i	−0.0379780	+	0.264210i
$347$	−3.38445	−	8.17078i	−0.181687	−	0.438631i	0.806628	−	0.591060i	$-0.201290\pi$
$347$	−3.38445	−	8.17078i	−0.181687	−	0.438631i	−0.988314	+	0.152429i	$0.951290\pi$
$348$		0			0
$349$	17.9607	+	7.43958i	0.961416	+	0.398232i	0.807510	−	0.589854i	$-0.200815\pi$
$349$	17.9607	+	7.43958i	0.961416	+	0.398232i	0.153906	+	0.988085i	$0.450815\pi$
$350$	−0.630657	−	2.47052i	−0.0337100	−	0.132055i
$351$		0			0
$352$	−12.9714	+	0.930068i	−0.691380	+	0.0495728i
$353$		−	30.1730i		−	1.60594i	−0.596016	−	0.802972i	$-0.703251\pi$
$353$		−	30.1730i		−	1.60594i	0.596016	−	0.802972i	$-0.296749\pi$
$354$		0			0
$355$	6.08528	−	14.6912i	0.322973	−	0.779726i
$356$	5.23153	+	1.53571i	0.277270	+	0.0813924i
$357$		0			0
$358$	−36.0960	−	5.18850i	−1.90773	−	0.274221i
$359$	5.24818	−	5.24818i	0.276988	−	0.276988i	−0.554917	−	0.831905i	$-0.687250\pi$
$359$	5.24818	−	5.24818i	0.276988	−	0.276988i	0.831905	+	0.554917i	$0.187250\pi$
$360$		0			0
$361$	1.55592	+	1.55592i	0.0818907	+	0.0818907i
$362$	−11.1794	−	14.9329i	−0.587578	−	0.784853i
$363$		0			0
$364$	−0.0430616	+	0.0534440i	−0.00225704	+	0.00280123i
$365$	−5.99538	−	2.48337i	−0.313812	−	0.129985i
$366$		0			0
$367$	−31.3373			−1.63580			−0.817898	−	0.575363i	$-0.804861\pi$
$367$	−31.3373			−1.63580			−0.817898	+	0.575363i	$0.804861\pi$
$368$	−26.7995	+	5.83388i	−1.39702	+	0.304112i
$369$		0			0
$370$	1.06615	−	1.79704i	0.0554264	−	0.0934237i
$371$	−1.43973	+	3.47581i	−0.0747469	+	0.180455i
$372$		0			0
$373$	12.2609	−	5.07863i	0.634845	−	0.262962i	−0.0419649	−	0.999119i	$-0.513362\pi$
$373$	12.2609	−	5.07863i	0.634845	−	0.262962i	0.676810	+	0.736158i	$0.263362\pi$
$374$	−8.10775	−	10.8299i	−0.419242	−	0.560000i
$375$		0			0
$376$	12.6458	−	11.7762i	0.652157	−	0.607311i
$377$	−0.547774	−	0.547774i	−0.0282118	−	0.0282118i
$378$		0			0
$379$	23.5487	−	9.75417i	1.20961	−	0.501038i	0.315520	−	0.948919i	$-0.397821\pi$
$379$	23.5487	−	9.75417i	1.20961	−	0.501038i	0.894093	+	0.447881i	$0.147821\pi$
$380$	26.0174	−	14.2090i	1.33466	−	0.728905i
$381$		0			0
$382$	4.46301	+	17.4833i	0.228347	+	0.894523i
$383$	16.6719			0.851896			0.425948	−	0.904748i	$-0.359941\pi$
$383$	16.6719			0.851896			0.425948	+	0.904748i	$0.359941\pi$
$384$		0			0
$385$	2.48796			0.126798
$386$	4.41013	+	17.2762i	0.224470	+	0.879333i
$387$		0			0
$388$	22.7821	−	12.4421i	1.15659	−	0.631651i
$389$	−1.38281	+	0.572777i	−0.0701110	+	0.0290409i	−0.417463	−	0.908694i	$-0.637081\pi$
$389$	−1.38281	+	0.572777i	−0.0701110	+	0.0290409i	0.347352	+	0.937735i	$0.387081\pi$
$390$		0			0
$391$	−20.1750	−	20.1750i	−1.02030	−	1.02030i
$392$	14.2554	−	13.2751i	0.720006	−	0.670493i
$393$		0			0
$394$	0.611759	+	0.817153i	0.0308200	+	0.0411676i
$395$	4.57354	−	1.89442i	0.230120	−	0.0953187i
$396$		0			0
$397$	4.37989	−	10.5740i	0.219821	−	0.530694i	−0.775044	−	0.631907i	$-0.782272\pi$
$397$	4.37989	−	10.5740i	0.219821	−	0.530694i	0.994865	+	0.101213i	$0.0322724\pi$
$398$	−4.35671	+	7.34344i	−0.218382	+	0.368093i
$399$		0			0
$400$	−4.56294	−	20.9611i	−0.228147	−	1.04805i
$401$	23.7727			1.18715			0.593576	−	0.804778i	$-0.297716\pi$
$401$	23.7727			1.18715			0.593576	+	0.804778i	$0.297716\pi$
$402$		0			0
$403$	0.932212	+	0.386135i	0.0464368	+	0.0192348i
$404$	−13.9577	+	17.3230i	−0.694421	+	0.861850i
$405$		0			0
$406$	−2.16234	−	2.88833i	−0.107315	−	0.143345i
$407$	0.746100	+	0.746100i	0.0369828	+	0.0369828i
$408$		0			0
$409$	−24.1735	+	24.1735i	−1.19530	+	1.19530i	−0.219743	+	0.975558i	$0.570522\pi$
$409$	−24.1735	+	24.1735i	−1.19530	+	1.19530i	−0.975558	+	0.219743i	$0.929478\pi$
$410$	48.9381	+	7.03445i	2.41688	+	0.347406i
$411$		0			0
$412$	18.0861	+	5.30916i	0.891039	+	0.261563i
$413$	−0.401077	+	0.968286i	−0.0197357	+	0.0476462i
$414$		0			0
$415$			24.8904i			1.22182i
$416$	−0.378065	+	0.436468i	−0.0185361	+	0.0213996i
$417$		0			0
$418$	3.70263	+	14.5046i	0.181101	+	0.709442i
$419$	−6.78167	−	2.80906i	−0.331306	−	0.137232i	0.210828	−	0.977523i	$-0.432384\pi$
$419$	−6.78167	−	2.80906i	−0.331306	−	0.137232i	−0.542135	+	0.840291i	$0.682384\pi$
$420$		0			0
$421$	−9.06067	−	21.8744i	−0.441590	−	1.06609i	−0.975391	−	0.220482i	$-0.929237\pi$
$421$	−9.06067	−	21.8744i	−0.441590	−	1.06609i	0.533801	−	0.845610i	$-0.320763\pi$
$422$	3.40560	−	23.6925i	0.165782	−	1.15333i
$423$		0			0
$424$	−13.1459	+	28.7937i	−0.638422	+	1.39835i
$425$	15.7798	−	15.7798i	0.765433	−	0.765433i
$426$		0			0
$427$	0.876233	+	2.11541i	0.0424039	+	0.102372i
$428$	15.1274	−	18.7748i	0.731212	−	0.907512i
$429$		0			0
$430$	18.1847	−	30.6512i	0.876943	−	1.47813i
$431$		−	22.9164i		−	1.10384i	−0.833896	−	0.551922i	$-0.813895\pi$
$431$		−	22.9164i		−	1.10384i	0.833896	−	0.551922i	$-0.186105\pi$
$432$		0			0
$433$		−	17.6486i		−	0.848139i	−0.905630	−	0.424070i	$-0.860601\pi$
$433$		−	17.6486i		−	0.848139i	0.905630	−	0.424070i	$-0.139399\pi$
$434$	4.04178	+	2.39790i	0.194011	+	0.115103i
$435$		0			0
$436$	−2.05982	−	19.1463i	−0.0986476	−	0.916940i
$437$	12.0818	+	29.1680i	0.577951	+	1.39530i
$438$		0			0
$439$	11.5122	−	11.5122i	0.549449	−	0.549449i	−0.376832	−	0.926281i	$-0.622987\pi$
$439$	11.5122	−	11.5122i	0.549449	−	0.549449i	0.926281	+	0.376832i	$0.122987\pi$
$440$	20.9189	+	0.744872i	0.997270	+	0.0355104i
$441$		0			0
$442$	−0.594587	−	0.0854670i	−0.0282816	−	0.00406525i
$443$	−13.4242	−	32.4089i	−0.637804	−	1.53980i	−0.829598	−	0.558360i	$-0.811431\pi$
$443$	−13.4242	−	32.4089i	−0.637804	−	1.53980i	0.191794	−	0.981435i	$-0.438569\pi$
$444$		0			0
$445$	−8.10785	−	3.35838i	−0.384349	−	0.159202i
$446$	40.4107	−	10.3158i	1.91350	−	0.488466i
$447$		0			0
$448$	−2.03218	+	1.76166i	−0.0960114	+	0.0832304i
$449$		−	16.3232i		−	0.770339i	−0.922846	−	0.385170i	$-0.874143\pi$
$449$		−	16.3232i		−	0.770339i	0.922846	−	0.385170i	$-0.125857\pi$
$450$		0			0
$451$	−9.55425	+	23.0660i	−0.449892	+	1.08614i
$452$	12.5700	−	6.86493i	0.591245	−	0.322899i
$453$		0			0
$454$	4.03219	−	28.0516i	0.189240	−	1.31653i
$455$	0.0781149	−	0.0781149i	0.00366208	−	0.00366208i
$456$		0			0
$457$	−22.1907	−	22.1907i	−1.03804	−	1.03804i	−0.999247	−	0.0387901i	$-0.987650\pi$
$457$	−22.1907	−	22.1907i	−1.03804	−	1.03804i	−0.0387901	−	0.999247i	$-0.512350\pi$
$458$	6.19781	−	4.63996i	0.289604	−	0.216811i
$459$		0			0
$460$	43.8928	−	4.72214i	2.04651	−	0.220171i
$461$	−15.6722	−	6.49164i	−0.729927	−	0.302346i	−0.0134051	−	0.999910i	$-0.504267\pi$
$461$	−15.6722	−	6.49164i	−0.729927	−	0.302346i	−0.716522	+	0.697564i	$0.754267\pi$
$462$		0			0
$463$	−21.1826			−0.984441			−0.492220	−	0.870471i	$-0.663815\pi$
$463$	−21.1826			−0.984441			−0.492220	+	0.870471i	$0.663815\pi$
$464$	−17.3163	−	24.9326i	−0.803889	−	1.15747i
$465$		0			0
$466$	1.20257	+	0.713461i	0.0557081	+	0.0330505i
$467$	−4.30158	+	10.3849i	−0.199053	+	0.480557i	−0.991614	−	0.129236i	$-0.958747\pi$
$467$	−4.30158	+	10.3849i	−0.199053	+	0.480557i	0.792561	+	0.609793i	$0.208747\pi$
$468$		0			0
$469$	−4.60000	+	1.90538i	−0.212408	+	0.0879824i
$470$	−22.2652	+	16.6687i	−1.02702	+	0.768871i
$471$		0			0
$472$	−3.66217	+	8.02131i	−0.168565	+	0.369211i
$473$	12.7258	+	12.7258i	0.585134	+	0.585134i
$474$		0			0
$475$	−22.8136	+	9.44971i	−1.04676	+	0.433583i
$476$	−2.68451	−	0.788035i	−0.123044	−	0.0361195i
$477$		0			0
$478$	−30.2877	+	7.73162i	−1.38532	+	0.353636i
$479$	36.0607			1.64766			0.823828	−	0.566840i	$-0.191834\pi$
$479$	36.0607			1.64766			0.823828	+	0.566840i	$0.191834\pi$
$480$		0			0
$481$	0.0468509			0.00213622
$482$	12.4610	−	3.18095i	0.567583	−	0.144888i
$483$		0			0
$484$	3.21936	−	10.9670i	0.146335	−	0.498502i
$485$	−38.6014	+	15.9892i	−1.75280	+	0.726033i
$486$		0			0
$487$	−6.99084	−	6.99084i	−0.316785	−	0.316785i	0.530746	−	0.847531i	$-0.321912\pi$
$487$	−6.99084	−	6.99084i	−0.316785	−	0.316785i	−0.847531	+	0.530746i	$0.821912\pi$
$488$	6.73407	+	18.0488i	0.304837	+	0.817032i
$489$		0			0
$490$	−25.0991	+	18.7904i	−1.13386	+	0.848862i
$491$	−6.37664	+	2.64129i	−0.287774	+	0.119200i	−0.521901	−	0.853006i	$-0.674777\pi$
$491$	−6.37664	+	2.64129i	−0.287774	+	0.119200i	0.234127	+	0.972206i	$0.424777\pi$
$492$		0			0
$493$	12.0847	−	29.1749i	0.544266	−	1.31397i
$494$	0.571655	+	0.339151i	0.0257200	+	0.0152591i
$495$		0			0
$496$	33.2655	+	21.3717i	1.49367	+	0.959619i
$497$	1.66063			0.0744895
$498$		0			0
$499$	7.43198	+	3.07843i	0.332701	+	0.137809i	0.542779	−	0.839875i	$-0.317372\pi$
$499$	7.43198	+	3.07843i	0.332701	+	0.137809i	−0.210078	+	0.977685i	$0.567372\pi$
$500$	0.249985	+	2.32363i	0.0111797	+	0.103916i
$501$		0			0
$502$	4.23098	−	3.16751i	0.188838	−	0.141373i
$503$	2.67081	+	2.67081i	0.119086	+	0.119086i	0.764138	−	0.645053i	$-0.223165\pi$
$503$	2.67081	+	2.67081i	0.119086	+	0.119086i	−0.645053	+	0.764138i	$0.723165\pi$
$504$		0			0
$505$	25.3196	−	25.3196i	1.12671	−	1.12671i
$506$	−3.17178	+	22.0658i	−0.141003	+	0.980946i
$507$		0			0
$508$	9.02951	+	16.5335i	0.400620	+	0.733556i
$509$	−9.36796	+	22.6162i	−0.415227	+	1.00245i	0.568484	+	0.822694i	$0.307530\pi$
$509$	−9.36796	+	22.6162i	−0.415227	+	1.00245i	−0.983712	+	0.179753i	$0.942470\pi$
$510$		0			0
$511$		−	0.677694i		−	0.0299794i
$512$	−17.6141	+	14.2037i	−0.778439	+	0.627720i
$513$		0			0
$514$	4.18268	−	1.06773i	0.184490	−	0.0470954i
$515$	−28.0299	−	11.6104i	−1.23515	−	0.511615i
$516$		0			0
$517$	−5.37480	−	12.9759i	−0.236384	−	0.570680i
$518$	0.215990	+	0.0310469i	0.00949008	+	0.00136412i
$519$		0			0
$520$	0.680181	−	0.633407i	0.0298279	−	0.0277767i
$521$	−22.3821	+	22.3821i	−0.980579	+	0.980579i	−0.999815	−	0.0192357i	$-0.993877\pi$
$521$	−22.3821	+	22.3821i	−0.980579	+	0.980579i	0.0192357	+	0.999815i	$0.493877\pi$
$522$		0			0
$523$	2.70300	+	6.52561i	0.118194	+	0.285345i	0.971894	−	0.235420i	$-0.0756467\pi$
$523$	2.70300	+	6.52561i	0.118194	+	0.285345i	−0.853700	+	0.520765i	$0.825647\pi$
$524$	6.78051	−	0.729472i	0.296208	−	0.0318671i
$525$		0			0
$526$	−4.20522	−	2.49487i	−0.183356	−	0.108782i
$527$			41.1318i			1.79173i
$528$		0			0
$529$			24.0153i			1.04414i
$530$	25.9954	−	43.8166i	1.12917	−	1.90327i
$531$		0			0
$532$	2.41068	+	1.94236i	0.104516	+	0.0842121i
$533$	0.424230	+	1.02418i	0.0183755	+	0.0443623i
$534$		0			0
$535$	−27.4416	+	27.4416i	−1.18640	+	1.18640i
$536$	−39.2475	+	14.6433i	−1.69523	+	0.632496i
$537$		0			0
$538$	−2.99479	+	20.8345i	−0.129115	+	0.898240i
$539$	−6.05892	−	14.6275i	−0.260976	−	0.630052i
$540$		0			0
$541$	−3.90965	−	1.61943i	−0.168089	−	0.0696246i	0.297052	−	0.954861i	$-0.403996\pi$
$541$	−3.90965	−	1.61943i	−0.168089	−	0.0696246i	−0.465141	+	0.885237i	$0.653996\pi$
$542$	−8.41545	−	32.9665i	−0.361474	−	1.41603i
$543$		0			0
$544$	−22.3356	−	7.42956i	−0.957630	−	0.318540i
$545$			30.9953i			1.32769i
$546$		0			0
$547$	6.81941	−	16.4635i	0.291577	−	0.703929i	−0.708421	−	0.705790i	$-0.750592\pi$
$547$	6.81941	−	16.4635i	0.291577	−	0.703929i	0.999998	+	0.00186067i	$0.000592269\pi$
$548$	6.58345	−	22.4271i	0.281231	−	0.958039i
$549$		0			0
$550$	−17.2587	−	2.48079i	−0.735913	−	0.105781i
$551$	−24.7082	+	24.7082i	−1.05261	+	1.05261i
$552$		0			0
$553$	0.365556	+	0.365556i	0.0155450	+	0.0155450i
$554$	5.94644	+	7.94292i	0.252640	+	0.337462i
$555$		0			0
$556$	−1.74779	−	1.40825i	−0.0741227	−	0.0597231i
$557$	−3.65431	−	1.51367i	−0.154838	−	0.0641361i	0.303918	−	0.952698i	$-0.401705\pi$
$557$	−3.65431	−	1.51367i	−0.154838	−	0.0641361i	−0.458757	+	0.888562i	$0.651705\pi$
$558$		0			0
$559$	0.799109			0.0337987
$560$	3.55549	−	2.46938i	0.150247	−	0.104350i
$561$		0			0
$562$	−4.69159	+	7.90789i	−0.197903	+	0.333574i
$563$	−1.27091	+	3.06826i	−0.0535626	+	0.129312i	−0.948396	−	0.317089i	$-0.897294\pi$
$563$	−1.27091	+	3.06826i	−0.0535626	+	0.129312i	0.894833	+	0.446401i	$0.147294\pi$
$564$		0			0
$565$	−21.2983	+	8.82206i	−0.896028	+	0.371147i
$566$	−16.4752	−	22.0066i	−0.692503	−	0.925006i
$567$		0			0
$568$	13.9627	+	0.497177i	0.585860	+	0.0208611i
$569$	−8.04933	−	8.04933i	−0.337446	−	0.337446i	0.517960	−	0.855405i	$-0.326692\pi$
$569$	−8.04933	−	8.04933i	−0.337446	−	0.337446i	−0.855405	+	0.517960i	$0.826692\pi$
$570$		0			0
$571$	24.5752	−	10.1794i	1.02844	−	0.425994i	0.196292	−	0.980546i	$-0.437110\pi$
$571$	24.5752	−	10.1794i	1.02844	−	0.425994i	0.832150	+	0.554551i	$0.187110\pi$
$572$	0.224961	+	0.411914i	0.00940607	+	0.0172230i
$573$		0			0
$574$	1.27707	+	5.00278i	0.0533041	+	0.208812i
$575$	−36.7728			−1.53353
$576$		0			0
$577$	6.56790			0.273425			0.136713	−	0.990611i	$-0.456346\pi$
$577$	6.56790			0.273425			0.136713	+	0.990611i	$0.456346\pi$
$578$	−0.110146	−	0.431485i	−0.00458148	−	0.0179474i
$579$		0			0
$580$	23.4194	+	42.8821i	0.972437	+	1.78058i
$581$	−2.40149	+	0.994728i	−0.0996304	+	0.0412683i
$582$		0			0
$583$	18.1919	+	18.1919i	0.753430	+	0.753430i
$584$	0.202895	−	5.69808i	0.00839585	−	0.235788i
$585$		0			0
$586$	0.0277182	+	0.0370244i	0.00114503	+	0.00152946i
$587$	16.5921	−	6.87268i	0.684830	−	0.283666i	−0.0130142	−	0.999915i	$-0.504143\pi$
$587$	16.5921	−	6.87268i	0.684830	−	0.283666i	0.697844	+	0.716249i	$0.254143\pi$
$588$		0			0
$589$	17.4172	−	42.0490i	0.717665	−	1.73260i
$590$	7.24177	−	12.2064i	0.298139	−	0.502528i
$591$		0			0
$592$	1.80676	+	0.325709i	0.0742575	+	0.0133866i
$593$	28.8208			1.18353			0.591765	−	0.806111i	$-0.298431\pi$
$593$	28.8208			1.18353			0.591765	+	0.806111i	$0.298431\pi$
$594$		0			0
$595$	4.16047	+	1.72332i	0.170563	+	0.0706494i
$596$	−1.03034	−	0.830181i	−0.0422045	−	0.0340055i
$597$		0			0
$598$	0.593219	+	0.792389i	0.0242585	+	0.0324032i
$599$	−17.4840	−	17.4840i	−0.714377	−	0.714377i	0.253071	−	0.967448i	$-0.418560\pi$
$599$	−17.4840	−	17.4840i	−0.714377	−	0.714377i	−0.967448	+	0.253071i	$0.918560\pi$
$600$		0			0
$601$	33.1960	−	33.1960i	1.35409	−	1.35409i	0.473065	−	0.881028i	$-0.343148\pi$
$601$	33.1960	−	33.1960i	1.35409	−	1.35409i	0.881028	−	0.473065i	$-0.156852\pi$
$602$	3.68403	+	0.529549i	0.150150	+	0.0215828i
$603$		0			0
$604$	−9.15192	+	31.1768i	−0.372386	+	1.26857i
$605$	−7.04030	+	16.9968i	−0.286229	+	0.691017i
$606$		0			0
$607$			15.7874i			0.640790i	0.947284	+	0.320395i	$0.103816\pi$
$607$			15.7874i			0.640790i	−0.947284	+	0.320395i	$0.896184\pi$
$608$	19.6876	+	17.0532i	0.798437	+	0.691599i
$609$		0			0
$610$	−7.66936	−	30.0438i	−0.310523	−	1.21644i
$611$	−0.576160	−	0.238653i	−0.0233090	−	0.00965488i
$612$		0			0
$613$	−1.45651	−	3.51632i	−0.0588278	−	0.142023i	0.891733	−	0.452563i	$-0.149490\pi$
$613$	−1.45651	−	3.51632i	−0.0588278	−	0.142023i	−0.950560	+	0.310540i	$0.899490\pi$
$614$	−4.73063	+	32.9106i	−0.190913	+	1.32816i
$615$		0			0
$616$	0.764142	+	2.04807i	0.0307881	+	0.0825192i
$617$	5.98815	−	5.98815i	0.241074	−	0.241074i	−0.576220	−	0.817294i	$-0.695473\pi$
$617$	5.98815	−	5.98815i	0.241074	−	0.241074i	0.817294	+	0.576220i	$0.195473\pi$
$618$		0			0
$619$	−7.03768	−	16.9905i	−0.282868	−	0.682905i	0.717032	−	0.697041i	$-0.245500\pi$
$619$	−7.03768	−	16.9905i	−0.282868	−	0.682905i	−0.999900	+	0.0141358i	$0.995500\pi$
$620$	−49.5568	−	39.9295i	−1.99025	−	1.60361i
$621$		0			0
$622$	3.67199	−	6.18931i	0.147233	−	0.248169i
$623$		−	0.916479i		−	0.0367179i
$624$		0			0
$625$			23.0533i			0.922132i
$626$	−2.13450	−	1.26635i	−0.0853117	−	0.0506136i
$627$		0			0
$628$	29.5131	−	3.17513i	1.17770	−	0.126701i
$629$	0.730862	+	1.76446i	0.0291414	+	0.0703535i
$630$		0			0
$631$	−19.0530	+	19.0530i	−0.758486	+	0.758486i	−0.976047	−	0.217561i	$-0.930190\pi$
$631$	−19.0530	+	19.0530i	−0.758486	+	0.758486i	0.217561	+	0.976047i	$0.430190\pi$
$632$	2.96417	+	3.18306i	0.117908	+	0.126615i
$633$		0			0
$634$	−10.6920	−	1.53689i	−0.424635	−	0.0610378i
$635$	−11.6037	−	28.0139i	−0.460481	−	1.11170i
$636$		0			0
$637$	−0.649495	−	0.269030i	−0.0257339	−	0.0106593i
$638$	−23.9066	+	6.10271i	−0.946472	+	0.241609i
$639$		0			0
$640$	30.6341	−	19.6982i	1.21092	−	0.778638i
$641$			4.84179i			0.191239i	0.995418	+	0.0956197i	$0.0304833\pi$
$641$			4.84179i			0.191239i	−0.995418	+	0.0956197i	$0.969517\pi$
$642$		0			0
$643$	−1.99669	+	4.82043i	−0.0787417	+	0.190099i	−0.958348	−	0.285603i	$-0.907806\pi$
$643$	−1.99669	+	4.82043i	−0.0787417	+	0.190099i	0.879606	+	0.475702i	$0.157806\pi$
$644$	2.20975	+	4.04616i	0.0870762	+	0.159441i
$645$		0			0
$646$	−3.85513	+	26.8198i	−0.151678	+	1.05521i
$647$	−23.0278	+	23.0278i	−0.905316	+	0.905316i	−0.995890	−	0.0905742i	$-0.971130\pi$
$647$	−23.0278	+	23.0278i	−0.905316	+	0.905316i	0.0905742	+	0.995890i	$0.471130\pi$
$648$		0			0
$649$	5.06786	+	5.06786i	0.198931	+	0.198931i
$650$	−0.619763	+	0.463983i	−0.0243091	+	0.0181989i
$651$		0			0
$652$	1.49056	+	13.8549i	0.0583747	+	0.542599i
$653$	25.3058	+	10.4820i	0.990294	+	0.410193i	0.818229	−	0.574893i	$-0.194956\pi$
$653$	25.3058	+	10.4820i	0.990294	+	0.410193i	0.172065	+	0.985086i	$0.444956\pi$
$654$		0			0
$655$	−10.9768			−0.428897
$656$	9.23992	+	42.4460i	0.360758	+	1.65724i
$657$		0			0
$658$	−2.49805	−	1.48204i	−0.0973841	−	0.0577759i
$659$	−8.74923	+	21.1225i	−0.340821	+	0.822816i	0.656812	+	0.754055i	$0.271905\pi$
$659$	−8.74923	+	21.1225i	−0.340821	+	0.822816i	−0.997633	+	0.0687611i	$0.978095\pi$
$660$		0			0
$661$	14.1409	−	5.85735i	0.550017	−	0.227824i	−0.0903280	−	0.995912i	$-0.528792\pi$
$661$	14.1409	−	5.85735i	0.550017	−	0.227824i	0.640345	+	0.768088i	$0.278792\pi$
$662$	33.2634	−	24.9025i	1.29282	−	0.967863i
$663$		0			0
$664$	−20.4896	+	7.64474i	−0.795151	+	0.296673i
$665$	−3.52350	−	3.52350i	−0.136635	−	0.136635i
$666$		0			0
$667$	−48.0751	+	19.9133i	−1.86147	+	0.771048i
$668$	−5.20577	+	17.7339i	−0.201417	+	0.686146i
$669$		0			0
$670$	65.3306	−	16.6771i	2.52394	−	0.644294i
$671$	15.6578			0.604464
$672$		0			0
$673$	38.4339			1.48152			0.740758	−	0.671772i	$-0.234466\pi$
$673$	38.4339			1.48152			0.740758	+	0.671772i	$0.234466\pi$
$674$	18.2846	−	4.66756i	0.704296	−	0.179788i
$675$		0			0
$676$	−24.9273	−	7.31739i	−0.958744	−	0.281438i
$677$	11.0186	−	4.56407i	0.423481	−	0.175412i	−0.160757	−	0.986994i	$-0.551394\pi$
$677$	11.0186	−	4.56407i	0.423481	−	0.175412i	0.584238	+	0.811583i	$0.301394\pi$
$678$		0			0
$679$	−3.08535	−	3.08535i	−0.118405	−	0.118405i
$680$	34.4655	+	15.7354i	1.32169	+	0.603425i
$681$		0			0
$682$	25.7265	−	19.2601i	0.985120	−	0.737507i
$683$	−44.4586	+	18.4153i	−1.70116	+	0.704643i	−0.999965	−	0.00832649i	$-0.997350\pi$
$683$	−44.4586	+	18.4153i	−1.70116	+	0.704643i	−0.701195	+	0.712970i	$0.747350\pi$
$684$		0			0
$685$	−14.3971	+	34.7577i	−0.550085	+	1.32802i
$686$	−5.67822	−	3.36877i	−0.216796	−	0.128620i
$687$		0			0
$688$	30.8170	+	5.55544i	1.17489	+	0.211799i
$689$	1.14235			0.0435199
$690$		0			0
$691$	−2.14643	−	0.889080i	−0.0816540	−	0.0338222i	0.341483	−	0.939888i	$-0.389071\pi$
$691$	−2.14643	−	0.889080i	−0.0816540	−	0.0338222i	−0.423137	+	0.906066i	$0.639071\pi$
$692$	6.98143	−	0.751086i	0.265394	−	0.0285520i
$693$		0			0
$694$	−10.0123	+	7.49570i	−0.380063	+	0.284533i
$695$	2.55461	+	2.55461i	0.0969017	+	0.0969017i
$696$		0			0
$697$	−31.9540	+	31.9540i	−1.21034	+	1.21034i
$698$	3.91170	−	27.2134i	0.148060	−	1.03004i
$699$		0			0
$700$	−3.16468	+	1.72834i	−0.119614	+	0.0653252i
$701$	11.0073	−	26.5740i	0.415740	−	1.00368i	−0.567828	−	0.823147i	$-0.692216\pi$
$701$	11.0073	−	26.5740i	0.415740	−	1.00368i	0.983568	−	0.180537i	$-0.0577837\pi$
$702$		0			0
$703$		−	2.11328i		−	0.0797040i
$704$	5.81177	+	17.4491i	0.219039	+	0.657636i
$705$		0			0
$706$	−41.3452	+	10.5543i	−1.55605	+	0.397216i
$707$	3.45478	+	1.43101i	0.129930	+	0.0538189i
$708$		0			0
$709$	2.62019	+	6.32569i	0.0984031	+	0.237566i	0.965413	−	0.260724i	$-0.0839613\pi$
$709$	2.62019	+	6.32569i	0.0984031	+	0.237566i	−0.867010	+	0.498290i	$0.833961\pi$
$710$	−22.2595	−	3.19962i	−0.835383	−	0.120079i
$711$		0			0
$712$	0.274385	−	7.70580i	0.0102830	−	0.288787i
$713$	47.9261	−	47.9261i	1.79485	−	1.79485i
$714$		0			0
$715$	−0.289095	−	0.697937i	−0.0108115	−	0.0261014i
$716$	5.51647	+	51.2762i	0.206160	+	1.91628i
$717$		0			0
$718$	−9.02720	−	5.35565i	−0.336892	−	0.199871i
$719$		−	17.1528i		−	0.639691i	−0.947470	−	0.319845i	$-0.896369\pi$
$719$		−	17.1528i		−	0.639691i	0.947470	−	0.319845i	$-0.103631\pi$
$720$		0			0
$721$		−	3.16839i		−	0.117997i
$722$	1.58779	−	2.67629i	0.0590913	−	0.0996012i
$723$		0			0
$724$	−16.5516	+	20.5423i	−0.615135	+	0.763447i
$725$	−15.5751	−	37.6017i	−0.578445	−	1.39649i
$726$		0			0
$727$	−7.52775	+	7.52775i	−0.279189	+	0.279189i	−0.832785	−	0.553596i	$-0.813255\pi$
$727$	−7.52775	+	7.52775i	−0.279189	+	0.279189i	0.553596	+	0.832785i	$0.313255\pi$
$728$	0.0882955	+	0.0403117i	0.00327245	+	0.00149405i
$729$		0			0
$730$	−1.30574	+	9.08396i	−0.0483278	+	0.336212i
$731$	12.4659	+	30.0954i	0.461068	+	1.11312i
$732$		0			0
$733$	−7.56986	−	3.13554i	−0.279599	−	0.115814i	0.238477	−	0.971148i	$-0.423352\pi$
$733$	−7.56986	−	3.13554i	−0.279599	−	0.115814i	−0.518076	+	0.855334i	$0.673352\pi$
$734$	10.9616	+	42.9407i	0.404600	+	1.58497i
$735$		0			0
$736$	17.3683	+	34.6819i	0.640203	+	1.27839i
$737$			34.0482i			1.25418i
$738$		0			0
$739$	3.52118	−	8.50088i	0.129529	−	0.312710i	−0.845789	−	0.533518i	$-0.820870\pi$
$739$	3.52118	−	8.50088i	0.129529	−	0.312710i	0.975317	+	0.220808i	$0.0708696\pi$
$740$	−2.83537	−	0.832318i	−0.104230	−	0.0305966i
$741$		0			0
$742$	5.26641	+	0.757003i	0.193336	+	0.0277905i
$743$	6.66625	−	6.66625i	0.244561	−	0.244561i	−0.574173	−	0.818734i	$-0.694676\pi$
$743$	6.66625	−	6.66625i	0.244561	−	0.244561i	0.818734	+	0.574173i	$0.194676\pi$
$744$		0			0
$745$	1.50597	+	1.50597i	0.0551745	+	0.0551745i
$746$	−11.2479	−	15.0243i	−0.411814	−	0.550078i
$747$		0			0
$748$	−12.0038	+	14.8980i	−0.438904	+	0.544726i
$749$	−3.74431	−	1.55094i	−0.136814	−	0.0566702i
$750$		0			0
$751$	8.17302			0.298238			0.149119	−	0.988819i	$-0.452356\pi$
$751$	8.17302			0.298238			0.149119	+	0.988819i	$0.452356\pi$
$752$	−20.5600	−	13.2090i	−0.749746	−	0.481681i
$753$		0			0
$754$	−0.558992	+	0.942207i	−0.0203573	+	0.0343132i
$755$	20.0140	−	48.3180i	0.728383	−	1.75847i
$756$		0			0
$757$	−17.8950	+	7.41237i	−0.650406	+	0.269407i	−0.683395	−	0.730049i	$-0.739497\pi$
$757$	−17.8950	+	7.41237i	−0.650406	+	0.269407i	0.0329891	+	0.999456i	$0.489497\pi$
$758$	−21.6030	−	28.8561i	−0.784657	−	1.04810i
$759$		0			0
$760$	−28.5709	−	30.6807i	−1.03637	−	1.11290i
$761$	30.8536	+	30.8536i	1.11844	+	1.11844i	0.991970	+	0.126471i	$0.0403650\pi$
$761$	30.8536	+	30.8536i	1.11844	+	1.11844i	0.126471	+	0.991970i	$0.459635\pi$
$762$		0			0
$763$	−2.99049	+	1.23870i	−0.108263	+	0.0448441i
$764$	22.3957	−	12.2311i	0.810249	−	0.442505i
$765$		0			0
$766$	−5.83173	−	22.8451i	−0.210709	−	0.825426i
$767$	0.318233			0.0114907
$768$		0			0
$769$	36.0834			1.30120			0.650599	−	0.759421i	$-0.274518\pi$
$769$	36.0834			1.30120			0.650599	+	0.759421i	$0.274518\pi$
$770$	−0.870272	−	3.40918i	−0.0313624	−	0.122858i
$771$		0			0
$772$	22.1304	−	12.0862i	0.796490	−	0.434991i
$773$	14.9974	−	6.21213i	0.539419	−	0.223435i	−0.0963038	−	0.995352i	$-0.530702\pi$
$773$	14.9974	−	6.21213i	0.539419	−	0.223435i	0.635723	+	0.771917i	$0.280702\pi$
$774$		0			0
$775$	37.4852	+	37.4852i	1.34651	+	1.34651i
$776$	−25.0181	−	26.8655i	−0.898096	−	0.964416i
$777$		0			0
$778$	1.26856	+	1.69447i	0.0454799	+	0.0607495i
$779$	46.1974	−	19.1356i	1.65519	−	0.685604i
$780$		0			0
$781$	4.34575	−	10.4916i	0.155503	−	0.375418i
$782$	−20.5882	+	34.7024i	−0.736233	+	1.24096i
$783$		0			0
$784$	−23.1769	−	14.8902i	−0.827747	−	0.531793i
$785$	−47.7779			−1.70527
$786$		0			0
$787$	43.7262	+	18.1120i	1.55867	+	0.645623i	0.984858	−	0.173364i	$-0.0554636\pi$
$787$	43.7262	+	18.1120i	1.55867	+	0.645623i	0.573813	+	0.818986i	$0.305464\pi$
$788$	0.905733	−	1.12411i	0.0322654	−	0.0400448i
$789$		0			0
$790$	−4.19567	−	5.60434i	−0.149275	−	0.199393i
$791$	−1.70234	−	1.70234i	−0.0605284	−	0.0605284i
$792$		0			0
$793$	0.491611	−	0.491611i	0.0174576	−	0.0174576i
$794$	−16.0213	−	2.30293i	−0.568575	−	0.0817280i
$795$		0			0
$796$	11.5865	+	3.40119i	0.410671	+	0.120552i
$797$	−10.6617	+	25.7396i	−0.377656	+	0.911742i	0.614748	+	0.788723i	$0.289258\pi$
$797$	−10.6617	+	25.7396i	−0.377656	+	0.911742i	−0.992404	+	0.123019i	$0.960742\pi$
$798$		0			0
$799$		−	25.4218i		−	0.899358i
$800$	−27.1263	+	13.5845i	−0.959058	+	0.480285i
$801$		0			0
$802$	−8.31553	−	32.5751i	−0.293632	−	1.15027i
$803$	−4.28155	−	1.77347i	−0.151092	−	0.0625845i
$804$		0			0
$805$	−2.83973	−	6.85571i	−0.100087	−	0.241632i
$806$	0.203028	−	1.41245i	0.00715137	−	0.0497515i
$807$		0			0
$808$	28.6195	+	13.0664i	1.00683	+	0.459673i
$809$	−7.10579	+	7.10579i	−0.249826	+	0.249826i	−0.820899	−	0.571073i	$-0.806527\pi$
$809$	−7.10579	+	7.10579i	−0.249826	+	0.249826i	0.571073	+	0.820899i	$0.306527\pi$
$810$		0			0
$811$	−12.7431	−	30.7646i	−0.447471	−	1.08029i	−0.973266	−	0.229680i	$-0.926232\pi$
$811$	−12.7431	−	30.7646i	−0.447471	−	1.08029i	0.525795	−	0.850611i	$-0.323768\pi$
$812$	−3.20142	+	3.97331i	−0.112348	+	0.139436i
$813$		0			0
$814$	0.761379	−	1.28334i	0.0266863	−	0.0449811i
$815$		−	22.4292i		−	0.785662i
$816$		0			0
$817$		−	36.0451i		−	1.26106i
$818$	41.5799	+	24.6685i	1.45381	+	0.862514i
$819$		0			0
$820$	−7.47911	−	69.5191i	−0.261182	−	2.42771i
$821$	−17.6756	−	42.6728i	−0.616884	−	1.48929i	−0.855303	−	0.518128i	$-0.826629\pi$
$821$	−17.6756	−	42.6728i	−0.616884	−	1.48929i	0.238419	−	0.971162i	$-0.423371\pi$
$822$		0			0
$823$	−26.0687	+	26.0687i	−0.908697	+	0.908697i	−0.996167	−	0.0874705i	$-0.972122\pi$
$823$	−26.0687	+	26.0687i	−0.908697	+	0.908697i	0.0874705	+	0.996167i	$0.472122\pi$
$824$	0.948587	−	26.6400i	0.0330456	−	0.928048i
$825$		0			0
$826$	1.46711	+	0.210885i	0.0510472	+	0.00733762i
$827$	−0.996651	−	2.40613i	−0.0346569	−	0.0836693i	0.905603	−	0.424126i	$-0.139418\pi$
$827$	−0.996651	−	2.40613i	−0.0346569	−	0.0836693i	−0.940260	+	0.340456i	$0.889418\pi$
$828$		0			0
$829$	15.8506	+	6.56553i	0.550514	+	0.228030i	0.640561	−	0.767907i	$-0.278702\pi$
$829$	15.8506	+	6.56553i	0.550514	+	0.228030i	−0.0900472	+	0.995938i	$0.528702\pi$
$830$	34.1067	−	8.70650i	1.18386	−	0.302207i
$831$		0			0
$832$	0.730324	+	0.365378i	0.0253194	+	0.0126672i
$833$		−	28.6575i		−	0.992925i
$834$		0			0
$835$	11.3843	−	27.4841i	0.393970	−	0.951127i
$836$	18.5801	−	10.1472i	0.642605	−	0.350949i
$837$		0			0
$838$	−1.47699	+	10.2753i	−0.0510219	+	0.354955i
$839$	22.7964	−	22.7964i	0.787019	−	0.787019i	−0.193985	−	0.981004i	$-0.562141\pi$
$839$	22.7964	−	22.7964i	0.787019	−	0.787019i	0.981004	+	0.193985i	$0.0621414\pi$
$840$		0			0
$841$	−20.2183	−	20.2183i	−0.697182	−	0.697182i
$842$	−26.8045	+	20.0671i	−0.923744	+	0.691557i
$843$		0			0
$844$	−33.6564	+	3.62088i	−1.15850	+	0.124636i
$845$	38.6325	+	16.0021i	1.32900	+	0.550489i
$846$		0			0
$847$	−1.92125			−0.0660149
$848$	44.0536	+	7.94163i	1.51281	+	0.272717i
$849$		0			0
$850$	−27.1423	−	16.1030i	−0.930973	−	0.552327i
$851$	1.20433	−	2.90751i	0.0412839	−	0.0996681i
$852$		0			0
$853$	−12.7603	+	5.28551i	−0.436906	+	0.180972i	−0.590285	−	0.807195i	$-0.700985\pi$
$853$	−12.7603	+	5.28551i	−0.436906	+	0.180972i	0.153379	+	0.988167i	$0.450985\pi$
$854$	2.59219	−	1.94063i	0.0887029	−	0.0664071i
$855$		0			0
$856$	−31.0180	−	14.1614i	−1.06017	−	0.484027i
$857$	18.2677	+	18.2677i	0.624014	+	0.624014i	0.946555	−	0.322542i	$-0.104537\pi$
$857$	18.2677	+	18.2677i	0.624014	+	0.624014i	−0.322542	+	0.946555i	$0.604537\pi$
$858$		0			0
$859$	−11.7109	+	4.85082i	−0.399572	+	0.165508i	−0.573414	−	0.819265i	$-0.694382\pi$
$859$	−11.7109	+	4.85082i	−0.399572	+	0.165508i	0.173843	+	0.984773i	$0.444382\pi$
$860$	−48.3613	−	14.1964i	−1.64911	−	0.484093i
$861$		0			0
$862$	−31.4017	+	8.01600i	−1.06955	+	0.273026i
$863$	12.2378			0.416579			0.208290	−	0.978067i	$-0.433210\pi$
$863$	12.2378			0.416579			0.208290	+	0.978067i	$0.433210\pi$
$864$		0			0
$865$	−11.3020			−0.384280
$866$	−24.1834	+	6.17337i	−0.821786	+	0.209780i
$867$		0			0
$868$	1.87199	−	6.37710i	0.0635395	−	0.216453i
$869$	3.26615	−	1.35288i	0.110797	−	0.0458935i
$870$		0			0
$871$	1.06902	+	1.06902i	0.0362222	+	0.0362222i
$872$	−25.5151	+	9.51975i	−0.864049	+	0.322379i
$873$		0			0
$874$	35.7420	−	26.7581i	1.20899	−	0.905107i
$875$	0.362933	−	0.150332i	0.0122694	−	0.00508214i
$876$		0			0
$877$	11.9105	−	28.7545i	0.402189	−	0.970971i	−0.584944	−	0.811073i	$-0.698884\pi$
$877$	11.9105	−	28.7545i	0.402189	−	0.970971i	0.987134	−	0.159897i	$-0.0511164\pi$
$878$	−19.8018	−	11.7480i	−0.668278	−	0.396475i
$879$		0			0
$880$	−6.29661	−	28.9251i	−0.212259	−	0.975066i
$881$	−27.8002			−0.936611			−0.468306	−	0.883567i	$-0.655135\pi$
$881$	−27.8002			−0.936611			−0.468306	+	0.883567i	$0.655135\pi$
$882$		0			0
$883$	39.6413	+	16.4200i	1.33404	+	0.552576i	0.931804	−	0.362962i	$-0.118235\pi$
$883$	39.6413	+	16.4200i	1.33404	+	0.552576i	0.402232	+	0.915538i	$0.368235\pi$
$884$	0.0908696	+	0.844642i	0.00305627	+	0.0284084i
$885$		0			0
$886$	−39.7134	+	29.7313i	−1.33420	+	0.998842i
$887$	−0.491398	−	0.491398i	−0.0164995	−	0.0164995i	0.698809	−	0.715308i	$-0.253714\pi$
$887$	−0.491398	−	0.491398i	−0.0164995	−	0.0164995i	−0.715308	+	0.698809i	$0.753714\pi$
$888$		0			0
$889$	2.23911	−	2.23911i	0.0750974	−	0.0750974i
$890$	−1.76582	+	12.2847i	−0.0591905	+	0.411784i
$891$		0			0
$892$	−28.2708	−	51.7653i	−0.946577	−	1.73323i
$893$	−10.7649	+	25.9887i	−0.360232	+	0.869677i
$894$		0			0
$895$		−	83.0093i		−	2.77470i
$896$	3.12479	+	2.16842i	0.104392	+	0.0724419i
$897$		0			0
$898$	−22.3672	+	5.70974i	−0.746404	+	0.190537i
$899$	69.3055	+	28.7073i	2.31147	+	0.957442i
$900$		0			0
$901$	17.8203	+	43.0220i	0.593681	+	1.43327i
$902$	34.9487	+	5.02359i	1.16366	+	0.167267i
$903$		0			0
$904$	−13.8037	−	14.8231i	−0.459105	−	0.493008i
$905$	30.0250	−	30.0250i	0.998065	−	0.998065i
$906$		0			0
$907$	0.533580	+	1.28817i	0.0177172	+	0.0427731i	0.932491	−	0.361194i	$-0.117631\pi$
$907$	0.533580	+	1.28817i	0.0177172	+	0.0427731i	−0.914773	+	0.403967i	$0.867631\pi$
$908$	−39.8488	+	4.28707i	−1.32243	+	0.142271i
$909$		0			0
$910$	−0.134363	−	0.0797146i	−0.00445408	−	0.00264251i
$911$			19.5482i			0.647661i	0.946115	+	0.323830i	$0.104971\pi$
$911$			19.5482i			0.647661i	−0.946115	+	0.323830i	$0.895029\pi$
$912$		0			0
$913$			17.7753i			0.588276i
$914$	−22.6451	+	38.1695i	−0.749035	+	1.26253i
$915$		0			0
$916$	−8.52596	−	6.86965i	−0.281706	−	0.226980i
$917$	−0.438678	−	1.05906i	−0.0144864	−	0.0349733i
$918$		0			0
$919$	13.3357	−	13.3357i	0.439905	−	0.439905i	−0.452075	−	0.891980i	$-0.649316\pi$
$919$	13.3357	−	13.3357i	0.439905	−	0.439905i	0.891980	+	0.452075i	$0.149316\pi$
$920$	−21.8240	−	58.4933i	−0.719517	−	1.92847i
$921$		0			0
$922$	−3.41328	+	23.7459i	−0.112410	+	0.782030i
$923$	−0.192961	−	0.465849i	−0.00635139	−	0.0153336i
$924$		0			0
$925$	2.27409	+	0.941960i	0.0747717	+	0.0309714i
$926$	7.40954	+	29.0260i	0.243493	+	0.953853i
$927$		0			0
$928$	−28.1073	+	32.4493i	−0.922667	+	1.06520i
$929$		−	10.1690i		−	0.333632i	−0.985988	−	0.166816i	$-0.946651\pi$
$929$		−	10.1690i		−	0.333632i	0.985988	−	0.166816i	$-0.0533487\pi$
$930$		0			0
$931$	−12.1350	+	29.2965i	−0.397709	+	0.960155i
$932$	0.556984	−	1.89742i	0.0182446	−	0.0621519i
$933$		0			0
$934$	15.7348	+	2.26175i	0.514859	+	0.0740068i
$935$	21.7753	−	21.7753i	0.712128	−	0.712128i
$936$		0			0
$937$	−19.7470	−	19.7470i	−0.645107	−	0.645107i	0.306699	−	0.951806i	$-0.400775\pi$
$937$	−19.7470	−	19.7470i	−0.645107	−	0.645107i	−0.951806	+	0.306699i	$0.900775\pi$
$938$	4.21994	+	5.63676i	0.137786	+	0.184047i
$939$		0			0
$940$	30.6289	+	24.6787i	0.999005	+	0.804931i
$941$	30.2481	+	12.5292i	0.986059	+	0.408439i	0.816667	−	0.577109i	$-0.195819\pi$
$941$	30.2481	+	12.5292i	0.986059	+	0.408439i	0.169393	+	0.985549i	$0.445819\pi$
$942$		0			0
$943$	74.4646			2.42490
$944$	12.2724	+	2.21237i	0.399432	+	0.0720064i
$945$		0			0
$946$	12.9864	−	21.8892i	0.422225	−	0.711681i
$947$	−21.4716	+	51.8370i	−0.697732	+	1.68448i	0.0308563	+	0.999524i	$0.490177\pi$
$947$	−21.4716	+	51.8370i	−0.697732	+	1.68448i	−0.728589	+	0.684951i	$0.759823\pi$
$948$		0			0
$949$	−0.190110	+	0.0787463i	−0.00617124	+	0.00255621i
$950$	20.9287	+	27.9554i	0.679018	+	0.906994i
$951$		0			0
$952$	−0.140798	+	3.95416i	−0.00456330	+	0.128155i
$953$	−39.2913	−	39.2913i	−1.27277	−	1.27277i	−0.944628	−	0.328143i	$-0.893577\pi$
$953$	−39.2913	−	39.2913i	−1.27277	−	1.27277i	−0.328143	−	0.944628i	$-0.606423\pi$
$954$		0			0
$955$	−37.9467	+	15.7180i	−1.22793	+	0.508624i
$956$	21.1888	+	38.7978i	0.685296	+	1.25481i
$957$		0			0
$958$	−12.6138	−	49.4130i	−0.407533	−	1.59646i
$959$	−3.92887			−0.126870
$960$		0			0
$961$	−66.7092			−2.15191
$962$	−0.0163881	−	0.0641984i	−0.000528374	−	0.00206984i
$963$		0			0
$964$	−8.71754	−	15.9623i	−0.280773	−	0.514110i
$965$	−37.4971	+	15.5318i	−1.20708	+	0.499987i
$966$		0			0
$967$	−6.93096	−	6.93096i	−0.222885	−	0.222885i	0.586827	−	0.809712i	$-0.300377\pi$
$967$	−6.93096	−	6.93096i	−0.222885	−	0.222885i	−0.809712	+	0.586827i	$0.800377\pi$
$968$	−16.1539	−	0.575203i	−0.519208	−	0.0184877i
$969$		0			0
$970$	35.4121	+	47.3015i	1.13701	+	1.51876i
$971$	10.2938	−	4.26384i	0.330345	−	0.136833i	−0.211346	−	0.977411i	$-0.567785\pi$
$971$	10.2938	−	4.26384i	0.330345	−	0.136833i	0.541690	+	0.840578i	$0.317785\pi$
$972$		0			0
$973$	−0.144381	+	0.348567i	−0.00462865	+	0.0111745i
$974$	−7.13400	+	12.0247i	−0.228588	+	0.385296i
$975$		0			0
$976$	22.3763	−	15.5409i	0.716247	−	0.497451i
$977$	−59.9974			−1.91949			−0.959743	−	0.280879i	$-0.909374\pi$
$977$	−59.9974			−1.91949			−0.959743	+	0.280879i	$0.909374\pi$
$978$		0			0
$979$	−5.79015	−	2.39836i	−0.185054	−	0.0766518i
$980$	34.5274	+	27.8199i	1.10294	+	0.888673i
$981$		0			0
$982$	5.84979	+	7.81382i	0.186674	+	0.249349i
$983$	8.59392	+	8.59392i	0.274104	+	0.274104i	0.830750	−	0.556646i	$-0.187912\pi$
$983$	8.59392	+	8.59392i	0.274104	+	0.274104i	−0.556646	+	0.830750i	$0.687912\pi$
$984$		0			0
$985$	−1.64302	+	1.64302i	−0.0523511	+	0.0523511i
$986$	−44.2047	−	6.35407i	−1.40777	−	0.202355i
$987$		0			0
$988$	0.264768	−	0.901955i	0.00842338	−	0.0286950i
$989$	20.5416	−	49.5918i	0.653184	−	1.57693i
$990$		0			0
$991$		−	17.4869i		−	0.555488i	−0.960655	−	0.277744i	$-0.910413\pi$
$991$		−	17.4869i		−	0.555488i	0.960655	−	0.277744i	$-0.0895867\pi$
$992$	17.6490	−	53.0585i	0.560357	−	1.68461i
$993$		0			0
$994$	−0.580877	−	2.27552i	−0.0184243	−	0.0721750i
$995$	−17.9567	−	7.43792i	−0.569267	−	0.235798i
$996$		0			0
$997$	19.1891	+	46.3265i	0.607724	+	1.46718i	0.865469	+	0.500963i	$0.167021\pi$
$997$	19.1891	+	46.3265i	0.607724	+	1.46718i	−0.257745	+	0.966213i	$0.582979\pi$
$998$	1.61862	−	11.2606i	0.0512367	−	0.356449i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.w.b.35.4	yes	32
3.2	odd	2		288.2.w.a.35.5	✓	32
4.3	odd	2		1152.2.w.a.431.8		32
12.11	even	2		1152.2.w.b.431.1		32
32.11	odd	8		288.2.w.a.107.5	yes	32
32.21	even	8		1152.2.w.b.719.1		32
96.11	even	8	inner	288.2.w.b.107.4	yes	32
96.53	odd	8		1152.2.w.a.719.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.w.a.35.5	✓	32	3.2	odd	2
288.2.w.a.107.5	yes	32	32.11	odd	8
288.2.w.b.35.4	yes	32	1.1	even	1	trivial
288.2.w.b.107.4	yes	32	96.11	even	8	inner
1152.2.w.a.431.8		32	4.3	odd	2
1152.2.w.a.719.8		32	96.53	odd	8
1152.2.w.b.431.1		32	12.11	even	2
1152.2.w.b.719.1		32	32.21	even	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)

\(f(q)\)	\(=\)	\(q+(-0.349793 - 1.37027i) q^{2} +(-1.75529 + 0.958624i) q^{4} +(2.97412 - 1.23192i) q^{5} +(0.237717 + 0.237717i) q^{7} +(1.92756 + 2.06990i) q^{8} +(-2.72839 - 3.64443i) q^{10} +(2.12394 - 0.879764i) q^{11} +(0.0390635 - 0.0943077i) q^{13} +(0.242585 - 0.408888i) q^{14} +(2.16208 - 3.36532i) q^{16} +4.16112 q^{17} +(-4.25390 - 1.76202i) q^{19} +(-4.03949 + 5.01343i) q^{20} +(-1.94845 - 2.60264i) q^{22} +(-4.84847 - 4.84847i) q^{23} +(3.79221 - 3.79221i) q^{25} +(-0.142891 - 0.0205395i) q^{26} +(-0.645142 - 0.189381i) q^{28} +(2.90419 - 7.01132i) q^{29} +9.88480i q^{31} +(-5.36769 - 1.78547i) q^{32} +(-1.45553 - 5.70186i) q^{34} +(0.999845 + 0.414149i) q^{35} +(0.175641 + 0.424034i) q^{37} +(-0.926465 + 6.44535i) q^{38} +(8.28275 + 3.78153i) q^{40} +(-7.67919 + 7.67919i) q^{41} +(2.99581 + 7.23252i) q^{43} +(-2.88476 + 3.58030i) q^{44} +(-4.94776 + 8.33968i) q^{46} -6.10937i q^{47} -6.88698i q^{49} +(-6.52284 - 3.86986i) q^{50} +(0.0218378 + 0.202984i) q^{52} +(4.28258 + 10.3391i) q^{53} +(5.23304 - 5.23304i) q^{55} +(-0.0338366 + 0.950265i) q^{56} +(-10.6233 - 1.52701i) q^{58} +(1.19303 + 2.88024i) q^{59} +(6.29246 + 2.60642i) q^{61} +(13.5449 - 3.45764i) q^{62} +(-0.569000 + 7.97974i) q^{64} -0.328605i q^{65} +(-5.66771 + 13.6831i) q^{67} +(-7.30396 + 3.98894i) q^{68} +(0.217758 - 1.51493i) q^{70} +(3.49288 - 3.49288i) q^{71} +(-1.42542 - 1.42542i) q^{73} +(0.519604 - 0.389000i) q^{74} +(9.15595 - 0.985029i) q^{76} +(0.714030 + 0.295761i) q^{77} +1.53778 q^{79} +(2.28447 - 12.6724i) q^{80} +(13.2087 + 7.83645i) q^{82} +(-2.95890 + 7.14340i) q^{83} +(12.3756 - 5.12616i) q^{85} +(8.86261 - 6.63496i) q^{86} +(5.91505 + 2.70055i) q^{88} +(-1.92767 - 1.92767i) q^{89} +(0.0317046 - 0.0131325i) q^{91} +(13.1583 + 3.86261i) q^{92} +(-8.37149 + 2.13702i) q^{94} -14.8223 q^{95} -12.9791 q^{97} +(-9.43704 + 2.40902i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{11} - 12 q^{14} + 8 q^{16} - 32 q^{20} + 16 q^{22} + 36 q^{26} + 16 q^{29} + 24 q^{32} - 24 q^{35} - 32 q^{38} - 32 q^{40} - 8 q^{44} - 32 q^{46} - 8 q^{50} - 56 q^{52}+ \cdots + 44 q^{98}+O(q^{100}) \) 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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