LMFDB - Embedded newform 936.2.j.a.755.45

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(755,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.755"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.j (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			755.45
Character	$\chi$	$=$	936.755
Dual form			936.2.j.a.755.46

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40416 - 0.168324i) q^{2} +(1.94333 - 0.472708i) q^{4} +2.74521 q^{5} +0.0889956i q^{7} +(2.64918 - 0.990868i) q^{8} +(3.85471 - 0.462085i) q^{10} +0.683486i q^{11} -1.00000i q^{13} +(0.0149801 + 0.124964i) q^{14} +(3.55309 - 1.83726i) q^{16} +0.0828094i q^{17} -1.60411 q^{19} +(5.33485 - 1.29768i) q^{20} +(0.115047 + 0.959725i) q^{22} -4.13521 q^{23} +2.53616 q^{25} +(-0.168324 - 1.40416i) q^{26} +(0.0420689 + 0.172948i) q^{28} -1.05035 q^{29} +6.98879i q^{31} +(4.67986 - 3.17788i) q^{32} +(0.0139388 + 0.116278i) q^{34} +0.244311i q^{35} +1.52658i q^{37} +(-2.25243 + 0.270010i) q^{38} +(7.27256 - 2.72014i) q^{40} -6.85637i q^{41} +0.580391 q^{43} +(0.323090 + 1.32824i) q^{44} +(-5.80650 + 0.696056i) q^{46} -7.69506 q^{47} +6.99208 q^{49} +(3.56118 - 0.426897i) q^{50} +(-0.472708 - 1.94333i) q^{52} -2.24587 q^{53} +1.87631i q^{55} +(0.0881829 + 0.235766i) q^{56} +(-1.47485 + 0.176798i) q^{58} -7.93214i q^{59} +5.65426i q^{61} +(1.17638 + 9.81339i) q^{62} +(6.03636 - 5.24999i) q^{64} -2.74521i q^{65} -5.72816 q^{67} +(0.0391447 + 0.160926i) q^{68} +(0.0411235 + 0.343052i) q^{70} -3.71930 q^{71} +6.94518 q^{73} +(0.256960 + 2.14356i) q^{74} +(-3.11732 + 0.758276i) q^{76} -0.0608273 q^{77} +1.75418i q^{79} +(9.75398 - 5.04366i) q^{80} +(-1.15409 - 9.62744i) q^{82} +15.2105i q^{83} +0.227329i q^{85} +(0.814962 - 0.0976938i) q^{86} +(0.677245 + 1.81068i) q^{88} -16.2449i q^{89} +0.0889956 q^{91} +(-8.03610 + 1.95475i) q^{92} +(-10.8051 + 1.29527i) q^{94} -4.40361 q^{95} +4.85412 q^{97} +(9.81800 - 1.17694i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) $ 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	1.40416	−	0.168324i	0.992891	−	0.119023i
$2$	1.40416	−	0.168324i	0.992891	−	0.119023i
$3$		0			0
$3$		0			0
$4$	1.94333	−	0.472708i	0.971667	−	0.236354i
$5$	2.74521			1.22769			0.613847	−	0.789425i	$-0.289621\pi$
$5$	2.74521			1.22769			0.613847	+	0.789425i	$0.289621\pi$
$6$		0			0
$7$			0.0889956i			0.0336372i	0.999859	+	0.0168186i	$0.00535377\pi$
$7$			0.0889956i			0.0336372i	−0.999859	+	0.0168186i	$0.994646\pi$
$8$	2.64918	−	0.990868i	0.936628	−	0.350325i
$9$		0			0
$10$	3.85471	−	0.462085i	1.21897	−	0.146124i
$11$			0.683486i			0.206079i	0.994677	+	0.103039i	$0.0328568\pi$
$11$			0.683486i			0.206079i	−0.994677	+	0.103039i	$0.967143\pi$
$12$		0			0
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.0149801	+	0.124964i	0.00400360	+	0.0333981i
$15$		0			0
$16$	3.55309	−	1.83726i	0.888273	−	0.459315i
$17$			0.0828094i			0.0200842i	0.999950	+	0.0100421i	$0.00319656\pi$
$17$			0.0828094i			0.0200842i	−0.999950	+	0.0100421i	$0.996803\pi$
$18$		0			0
$19$	−1.60411			−0.368008			−0.184004	−	0.982926i	$-0.558906\pi$
$19$	−1.60411			−0.368008			−0.184004	+	0.982926i	$0.558906\pi$
$20$	5.33485	−	1.29768i	1.19291	−	0.290171i
$21$		0			0
$22$	0.115047	+	0.959725i	0.0245282	+	0.204614i
$23$	−4.13521			−0.862252			−0.431126	−	0.902292i	$-0.641884\pi$
$23$	−4.13521			−0.862252			−0.431126	+	0.902292i	$0.641884\pi$
$24$		0			0
$25$	2.53616			0.507233
$26$	−0.168324	−	1.40416i	−0.0330111	−	0.275379i
$27$		0			0
$28$	0.0420689	+	0.172948i	0.00795028	+	0.0326841i
$29$	−1.05035			−0.195044			−0.0975221	−	0.995233i	$-0.531092\pi$
$29$	−1.05035			−0.195044			−0.0975221	+	0.995233i	$0.531092\pi$
$30$		0			0
$31$			6.98879i			1.25522i	0.778526	+	0.627612i	$0.215968\pi$
$31$			6.98879i			1.25522i	−0.778526	+	0.627612i	$0.784032\pi$
$32$	4.67986	−	3.17788i	0.827290	−	0.561775i
$33$		0			0
$34$	0.0139388	+	0.116278i	0.00239049	+	0.0199415i
$35$			0.244311i			0.0412961i
$36$		0			0
$37$			1.52658i			0.250968i	0.992096	+	0.125484i	$0.0400484\pi$
$37$			1.52658i			0.250968i	−0.992096	+	0.125484i	$0.959952\pi$
$38$	−2.25243	+	0.270010i	−0.365392	+	0.0438014i
$39$		0			0
$40$	7.27256	−	2.72014i	1.14989	−	0.430092i
$41$		−	6.85637i		−	1.07079i	−0.844603	−	0.535393i	$-0.820164\pi$
$41$		−	6.85637i		−	1.07079i	0.844603	−	0.535393i	$-0.179836\pi$
$42$		0			0
$43$	0.580391			0.0885088			0.0442544	−	0.999020i	$-0.485909\pi$
$43$	0.580391			0.0885088			0.0442544	+	0.999020i	$0.485909\pi$
$44$	0.323090	+	1.32824i	0.0487076	+	0.200240i
$45$		0			0
$46$	−5.80650	+	0.696056i	−0.856122	+	0.102628i
$47$	−7.69506			−1.12244			−0.561220	−	0.827667i	$-0.689668\pi$
$47$	−7.69506			−1.12244			−0.561220	+	0.827667i	$0.689668\pi$
$48$		0			0
$49$	6.99208			0.998869
$50$	3.56118	−	0.426897i	0.503627	−	0.0603724i
$51$		0			0
$52$	−0.472708	−	1.94333i	−0.0655528	−	0.269492i
$53$	−2.24587			−0.308493			−0.154247	−	0.988032i	$-0.549295\pi$
$53$	−2.24587			−0.308493			−0.154247	+	0.988032i	$0.549295\pi$
$54$		0			0
$55$			1.87631i			0.253002i
$56$	0.0881829	+	0.235766i	0.0117839	+	0.0315055i
$57$		0			0
$58$	−1.47485	+	0.176798i	−0.193658	+	0.0232148i
$59$		−	7.93214i		−	1.03268i	−0.856385	−	0.516338i	$-0.827295\pi$
$59$		−	7.93214i		−	1.03268i	0.856385	−	0.516338i	$-0.172705\pi$
$60$		0			0
$61$			5.65426i			0.723953i	0.932187	+	0.361977i	$0.117898\pi$
$61$			5.65426i			0.723953i	−0.932187	+	0.361977i	$0.882102\pi$
$62$	1.17638	+	9.81339i	0.149401	+	1.24630i
$63$		0			0
$64$	6.03636	−	5.24999i	0.754545	−	0.656248i
$65$		−	2.74521i		−	0.340501i
$66$		0			0
$67$	−5.72816			−0.699806			−0.349903	−	0.936786i	$-0.613785\pi$
$67$	−5.72816			−0.699806			−0.349903	+	0.936786i	$0.613785\pi$
$68$	0.0391447	+	0.160926i	0.00474699	+	0.0195152i
$69$		0			0
$70$	0.0411235	+	0.343052i	0.00491520	+	0.0410026i
$71$	−3.71930			−0.441400			−0.220700	−	0.975342i	$-0.570834\pi$
$71$	−3.71930			−0.441400			−0.220700	+	0.975342i	$0.570834\pi$
$72$		0			0
$73$	6.94518			0.812872			0.406436	−	0.913679i	$-0.366771\pi$
$73$	6.94518			0.812872			0.406436	+	0.913679i	$0.366771\pi$
$74$	0.256960	+	2.14356i	0.0298710	+	0.249184i
$75$		0			0
$76$	−3.11732	+	0.758276i	−0.357581	+	0.0869802i
$77$	−0.0608273			−0.00693191
$78$		0			0
$79$			1.75418i			0.197361i	0.995119	+	0.0986806i	$0.0314622\pi$
$79$			1.75418i			0.197361i	−0.995119	+	0.0986806i	$0.968538\pi$
$80$	9.75398	−	5.04366i	1.09053	−	0.563898i
$81$		0			0
$82$	−1.15409	−	9.62744i	−0.127448	−	1.06317i
$83$			15.2105i			1.66957i	0.550579	+	0.834783i	$0.314407\pi$
$83$			15.2105i			1.66957i	−0.550579	+	0.834783i	$0.685593\pi$
$84$		0			0
$85$			0.227329i			0.0246573i
$86$	0.814962	−	0.0976938i	0.0878796	−	0.0105346i
$87$		0			0
$88$	0.677245	+	1.81068i	0.0721946	+	0.193019i
$89$		−	16.2449i		−	1.72196i	−0.508640	−	0.860979i	$-0.669852\pi$
$89$		−	16.2449i		−	1.72196i	0.508640	−	0.860979i	$-0.330148\pi$
$90$		0			0
$91$	0.0889956			0.00932927
$92$	−8.03610	+	1.95475i	−0.837822	+	0.203797i
$93$		0			0
$94$	−10.8051	+	1.29527i	−1.11446	+	0.133596i
$95$	−4.40361			−0.451801
$96$		0			0
$97$	4.85412			0.492861			0.246431	−	0.969160i	$-0.420742\pi$
$97$	4.85412			0.492861			0.246431	+	0.969160i	$0.420742\pi$
$98$	9.81800	−	1.17694i	0.991768	−	0.118888i
$99$		0			0
$100$	4.92861	−	1.19887i	0.492861	−	0.119887i
$101$	−11.8637			−1.18048			−0.590240	−	0.807228i	$-0.700967\pi$
$101$	−11.8637			−1.18048			−0.590240	+	0.807228i	$0.700967\pi$
$102$		0			0
$103$			12.5156i			1.23320i	0.787278	+	0.616598i	$0.211490\pi$
$103$			12.5156i			1.23320i	−0.787278	+	0.616598i	$0.788510\pi$
$104$	−0.990868	−	2.64918i	−0.0971626	−	0.259774i
$105$		0			0
$106$	−3.15356	+	0.378033i	−0.306300	+	0.0367178i
$107$		−	6.10042i		−	0.589750i	−0.955536	−	0.294875i	$-0.904722\pi$
$107$		−	6.10042i		−	0.589750i	0.955536	−	0.294875i	$-0.0952780\pi$
$108$		0			0
$109$			16.4324i			1.57394i	0.616990	+	0.786971i	$0.288352\pi$
$109$			16.4324i			1.57394i	−0.616990	+	0.786971i	$0.711648\pi$
$110$	0.315829	+	2.63464i	0.0301131	+	0.251203i
$111$		0			0
$112$	0.163508	+	0.316210i	0.0154501	+	0.0298790i
$113$		−	9.57224i		−	0.900480i	−0.892908	−	0.450240i	$-0.851338\pi$
$113$		−	9.57224i		−	0.900480i	0.892908	−	0.450240i	$-0.148662\pi$
$114$		0			0
$115$	−11.3520			−1.05858
$116$	−2.04117	+	0.496507i	−0.189518	+	0.0460995i
$117$		0			0
$118$	−1.33517	−	11.1380i	−0.122912	−	1.02534i
$119$	−0.00736967			−0.000675577
$120$		0			0
$121$	10.5328			0.957531
$122$	0.951748	+	7.93948i	0.0861672	+	0.718807i
$123$		0			0
$124$	3.30366	+	13.5816i	0.296678	+	1.21966i
$125$	−6.76374			−0.604968
$126$		0			0
$127$		−	3.70333i		−	0.328617i	−0.986409	−	0.164309i	$-0.947461\pi$
$127$		−	3.70333i		−	0.328617i	0.986409	−	0.164309i	$-0.0525393\pi$
$128$	7.59232	−	8.38789i	0.671072	−	0.741392i
$129$		0			0
$130$	−0.462085	−	3.85471i	−0.0405275	−	0.338081i
$131$		−	6.87363i		−	0.600551i	−0.953852	−	0.300276i	$-0.902921\pi$
$131$		−	6.87363i		−	0.600551i	0.953852	−	0.300276i	$-0.0970787\pi$
$132$		0			0
$133$		−	0.142759i		−	0.0123787i
$134$	−8.04325	+	0.964187i	−0.694831	+	0.0832931i
$135$		0			0
$136$	0.0820533	+	0.219378i	0.00703601	+	0.0188115i
$137$			7.71953i			0.659524i	0.944064	+	0.329762i	$0.106968\pi$
$137$			7.71953i			0.659524i	−0.944064	+	0.329762i	$0.893032\pi$
$138$		0			0
$139$	−5.47680			−0.464536			−0.232268	−	0.972652i	$-0.574615\pi$
$139$	−5.47680			−0.464536			−0.232268	+	0.972652i	$0.574615\pi$
$140$	0.115488	+	0.474778i	0.00976052	+	0.0401261i
$141$		0			0
$142$	−5.22250	+	0.626049i	−0.438262	+	0.0525368i
$143$	0.683486			0.0571560
$144$		0			0
$145$	−2.88342			−0.239455
$146$	9.75215	−	1.16904i	0.807094	−	0.0967506i
$147$		0			0
$148$	0.721626	+	2.96665i	0.0593173	+	0.243857i
$149$	−7.11749			−0.583088			−0.291544	−	0.956557i	$-0.594169\pi$
$149$	−7.11749			−0.583088			−0.291544	+	0.956557i	$0.594169\pi$
$150$		0			0
$151$		−	17.2831i		−	1.40648i	−0.710955	−	0.703238i	$-0.751737\pi$
$151$		−	17.2831i		−	1.40648i	0.710955	−	0.703238i	$-0.248263\pi$
$152$	−4.24958	+	1.58946i	−0.344687	+	0.128922i
$153$		0			0
$154$	−0.0854113	+	0.0102387i	−0.00688264	+	0.000825058i
$155$			19.1857i			1.54103i
$156$		0			0
$157$		−	0.214171i		−	0.0170927i	−0.999963	−	0.00854634i	$-0.997280\pi$
$157$		−	0.214171i		−	0.0170927i	0.999963	−	0.00854634i	$-0.00272042\pi$
$158$	0.295272	+	2.46316i	0.0234905	+	0.195958i
$159$		0			0
$160$	12.8472	−	8.72394i	1.01566	−	0.689688i
$161$		−	0.368016i		−	0.0290037i
$162$		0			0
$163$	−18.3321			−1.43588			−0.717939	−	0.696106i	$-0.754914\pi$
$163$	−18.3321			−1.43588			−0.717939	+	0.696106i	$0.754914\pi$
$164$	−3.24106	−	13.3242i	−0.253084	−	1.04045i
$165$		0			0
$166$	2.56029	+	21.3579i	0.198717	+	1.65770i
$167$	11.0312			0.853617			0.426808	−	0.904342i	$-0.359638\pi$
$167$	11.0312			0.853617			0.426808	+	0.904342i	$0.359638\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	0.0382650	+	0.319207i	0.00293479	+	0.0244820i
$171$		0			0
$172$	1.12789	−	0.274356i	0.0860011	−	0.0209194i
$173$	−12.5569			−0.954682			−0.477341	−	0.878718i	$-0.658399\pi$
$173$	−12.5569			−0.954682			−0.477341	+	0.878718i	$0.658399\pi$
$174$		0			0
$175$			0.225707i			0.0170619i
$176$	1.25574	+	2.42849i	0.0946551	+	0.183054i
$177$		0			0
$178$	−2.73441	−	22.8105i	−0.204953	−	1.70972i
$179$			20.2124i			1.51075i	0.655294	+	0.755374i	$0.272545\pi$
$179$			20.2124i			1.51075i	−0.655294	+	0.755374i	$0.727455\pi$
$180$		0			0
$181$			22.7895i			1.69393i	0.531646	+	0.846966i	$0.321574\pi$
$181$			22.7895i			1.69393i	−0.531646	+	0.846966i	$0.678426\pi$
$182$	0.124964	−	0.0149801i	0.00926295	−	0.00111040i
$183$		0			0
$184$	−10.9549	+	4.09745i	−0.807609	+	0.302068i
$185$			4.19078i			0.308112i
$186$		0			0
$187$	−0.0565991			−0.00413894
$188$	−14.9541	+	3.63752i	−1.09064	+	0.265293i
$189$		0			0
$190$	−6.18338	+	0.741234i	−0.448589	+	0.0537748i
$191$	−9.29602			−0.672636			−0.336318	−	0.941748i	$-0.609182\pi$
$191$	−9.29602			−0.672636			−0.336318	+	0.941748i	$0.609182\pi$
$192$		0			0
$193$	−19.5645			−1.40828			−0.704141	−	0.710061i	$-0.748668\pi$
$193$	−19.5645			−1.40828			−0.704141	+	0.710061i	$0.748668\pi$
$194$	6.81597	−	0.817066i	0.489358	−	0.0586619i
$195$		0			0
$196$	13.5879	−	3.30521i	0.970568	−	0.236087i
$197$	1.34800			0.0960410			0.0480205	−	0.998846i	$-0.484709\pi$
$197$	1.34800			0.0960410			0.0480205	+	0.998846i	$0.484709\pi$
$198$		0			0
$199$		−	12.8425i		−	0.910378i	−0.890395	−	0.455189i	$-0.849572\pi$
$199$		−	12.8425i		−	0.910378i	0.890395	−	0.455189i	$-0.150428\pi$
$200$	6.71876	−	2.51300i	0.475088	−	0.177696i
$201$		0			0
$202$	−16.6585	+	1.99694i	−1.17209	+	0.140504i
$203$		−	0.0934761i		−	0.00656074i
$204$		0			0
$205$		−	18.8222i		−	1.31460i
$206$	2.10667	+	17.5739i	0.146779	+	1.22443i
$207$		0			0
$208$	−1.83726	−	3.55309i	−0.127391	−	0.246363i
$209$		−	1.09639i		−	0.0758386i
$210$		0			0
$211$	−26.5080			−1.82489			−0.912443	−	0.409203i	$-0.865807\pi$
$211$	−26.5080			−1.82489			−0.912443	+	0.409203i	$0.865807\pi$
$212$	−4.36447	+	1.06164i	−0.299753	+	0.0729137i
$213$		0			0
$214$	−1.02685	−	8.56597i	−0.0701939	−	0.585558i
$215$	1.59329			0.108662
$216$		0			0
$217$	−0.621972			−0.0422222
$218$	2.76598	+	23.0738i	0.187336	+	1.56275i
$219$		0			0
$220$	0.886948	+	3.64630i	0.0597980	+	0.245834i
$221$	0.0828094			0.00557037
$222$		0			0
$223$		−	16.7690i		−	1.12294i	−0.827499	−	0.561468i	$-0.810237\pi$
$223$		−	16.7690i		−	1.12294i	0.827499	−	0.561468i	$-0.189763\pi$
$224$	0.282817	+	0.416487i	0.0188965	+	0.0278277i
$225$		0			0
$226$	−1.61124	−	13.4410i	−0.107178	−	0.894079i
$227$			22.8718i			1.51806i	0.651058	+	0.759028i	$0.274326\pi$
$227$			22.8718i			1.51806i	−0.651058	+	0.759028i	$0.725674\pi$
$228$		0			0
$229$		−	18.1712i		−	1.20078i	−0.799705	−	0.600392i	$-0.795011\pi$
$229$		−	18.1712i		−	1.20078i	0.799705	−	0.600392i	$-0.204989\pi$
$230$	−15.9401	+	1.91082i	−1.05106	+	0.125996i
$231$		0			0
$232$	−2.78256	+	1.04075i	−0.182684	+	0.0683289i
$233$			16.5865i			1.08662i	0.839533	+	0.543308i	$0.182829\pi$
$233$			16.5865i			1.08662i	−0.839533	+	0.543308i	$0.817171\pi$
$234$		0			0
$235$	−21.1245			−1.37801
$236$	−3.74959	−	15.4148i	−0.244077	−	1.00342i
$237$		0			0
$238$	−0.0103482	+	0.00124049i	−0.000670775	+	8.04093e-5i
$239$	2.21652			0.143375			0.0716874	−	0.997427i	$-0.477162\pi$
$239$	2.21652			0.143375			0.0716874	+	0.997427i	$0.477162\pi$
$240$		0			0
$241$	21.0982			1.35905			0.679526	−	0.733651i	$-0.262185\pi$
$241$	21.0982			1.35905			0.679526	+	0.733651i	$0.262185\pi$
$242$	14.7898	−	1.77293i	0.950725	−	0.113968i
$243$		0			0
$244$	2.67281	+	10.9881i	0.171109	+	0.703441i
$245$	19.1947			1.22630
$246$		0			0
$247$			1.60411i			0.102067i
$248$	6.92498	+	18.5146i	0.439736	+	1.17568i
$249$		0			0
$250$	−9.49738	+	1.13850i	−0.600667	+	0.0720052i
$251$		−	3.93364i		−	0.248289i	−0.992264	−	0.124145i	$-0.960381\pi$
$251$		−	3.93364i		−	0.248289i	0.992264	−	0.124145i	$-0.0396187\pi$
$252$		0			0
$253$		−	2.82636i		−	0.177692i
$254$	−0.623360	−	5.20007i	−0.0391131	−	0.326281i
$255$		0			0
$256$	9.24895	−	13.0559i	0.578059	−	0.815995i
$257$		−	12.9326i		−	0.806714i	−0.915043	−	0.403357i	$-0.867843\pi$
$257$		−	12.9326i		−	0.806714i	0.915043	−	0.403357i	$-0.132157\pi$
$258$		0			0
$259$	−0.135859			−0.00844185
$260$	−1.29768	−	5.33485i	−0.0804788	−	0.330854i
$261$		0			0
$262$	−1.15700	−	9.65167i	−0.0714795	−	0.596282i
$263$	15.7884			0.973555			0.486777	−	0.873526i	$-0.338172\pi$
$263$	15.7884			0.973555			0.486777	+	0.873526i	$0.338172\pi$
$264$		0			0
$265$	−6.16537			−0.378735
$266$	−0.0240297	−	0.200456i	−0.00147336	−	0.0122907i
$267$		0			0
$268$	−11.1317	+	2.70775i	−0.679978	+	0.165402i
$269$	14.1225			0.861064			0.430532	−	0.902575i	$-0.358326\pi$
$269$	14.1225			0.861064			0.430532	+	0.902575i	$0.358326\pi$
$270$		0			0
$271$			25.2238i			1.53224i	0.642700	+	0.766118i	$0.277814\pi$
$271$			25.2238i			1.53224i	−0.642700	+	0.766118i	$0.722186\pi$
$272$	0.152143	+	0.294230i	0.00922499	+	0.0178403i
$273$		0			0
$274$	1.29938	+	10.8395i	0.0784986	+	0.654835i
$275$			1.73343i			0.104530i
$276$		0			0
$277$		−	14.5161i		−	0.872187i	−0.899901	−	0.436093i	$-0.856362\pi$
$277$		−	14.5161i		−	0.872187i	0.899901	−	0.436093i	$-0.143638\pi$
$278$	−7.69031	+	0.921878i	−0.461234	+	0.0552906i
$279$		0			0
$280$	0.242080	+	0.647226i	0.0144671	+	0.0386791i
$281$		−	9.91287i		−	0.591352i	−0.955288	−	0.295676i	$-0.904455\pi$
$281$		−	9.91287i		−	0.591352i	0.955288	−	0.295676i	$-0.0955449\pi$
$282$		0			0
$283$	20.8428			1.23897			0.619487	−	0.785007i	$-0.287341\pi$
$283$	20.8428			1.23897			0.619487	+	0.785007i	$0.287341\pi$
$284$	−7.22785	+	1.75815i	−0.428894	+	0.104327i
$285$		0			0
$286$	0.959725	−	0.115047i	0.0567497	−	0.00680289i
$287$	0.610187			0.0360182
$288$		0			0
$289$	16.9931			0.999597
$290$	−4.04878	+	0.485349i	−0.237752	+	0.0285006i
$291$		0			0
$292$	13.4968	−	3.28305i	0.789841	−	0.192126i
$293$	3.18526			0.186085			0.0930425	−	0.995662i	$-0.470341\pi$
$293$	3.18526			0.186085			0.0930425	+	0.995662i	$0.470341\pi$
$294$		0			0
$295$		−	21.7754i		−	1.26781i
$296$	1.51264	+	4.04419i	0.0879203	+	0.235064i
$297$		0			0
$298$	−9.99410	+	1.19805i	−0.578943	+	0.0694010i
$299$			4.13521i			0.239146i
$300$		0			0
$301$			0.0516522i			0.00297718i
$302$	−2.90916	−	24.2682i	−0.167403	−	1.39648i
$303$		0			0
$304$	−5.69955	+	2.94717i	−0.326892	+	0.169032i
$305$			15.5221i			0.888793i
$306$		0			0
$307$	3.05148			0.174157			0.0870786	−	0.996201i	$-0.472247\pi$
$307$	3.05148			0.174157			0.0870786	+	0.996201i	$0.472247\pi$
$308$	−0.118208	+	0.0287536i	−0.00673551	+	0.00163839i
$309$		0			0
$310$	3.22942	+	26.9398i	0.183418	+	1.53008i
$311$	27.8964			1.58186			0.790930	−	0.611907i	$-0.209597\pi$
$311$	27.8964			1.58186			0.790930	+	0.611907i	$0.209597\pi$
$312$		0			0
$313$	12.9375			0.731273			0.365636	−	0.930758i	$-0.380851\pi$
$313$	12.9375			0.731273			0.365636	+	0.930758i	$0.380851\pi$
$314$	−0.0360501	−	0.300730i	−0.00203442	−	0.0169712i
$315$		0			0
$316$	0.829217	+	3.40897i	0.0466471	+	0.191769i
$317$	24.3152			1.36568			0.682838	−	0.730570i	$-0.260745\pi$
$317$	24.3152			1.36568			0.682838	+	0.730570i	$0.260745\pi$
$318$		0			0
$319$		−	0.717897i		−	0.0401945i
$320$	16.5711	−	14.4123i	0.926350	−	0.805672i
$321$		0			0
$322$	−0.0619459	−	0.516753i	−0.00345211	−	0.0287975i
$323$		−	0.132835i		−	0.00739116i
$324$		0			0
$325$		−	2.53616i		−	0.140681i
$326$	−25.7412	+	3.08573i	−1.42567	+	0.170903i
$327$		0			0
$328$	−6.79376	−	18.1638i	−0.375123	−	1.00293i
$329$		−	0.684827i		−	0.0377557i
$330$		0			0
$331$	20.9383			1.15087			0.575436	−	0.817847i	$-0.304833\pi$
$331$	20.9383			1.15087			0.575436	+	0.817847i	$0.304833\pi$
$332$	7.19012	+	29.5590i	0.394609	+	1.62226i
$333$		0			0
$334$	15.4895	−	1.85681i	0.847549	−	0.101600i
$335$	−15.7250			−0.859147
$336$		0			0
$337$	13.0390			0.710280			0.355140	−	0.934813i	$-0.384433\pi$
$337$	13.0390			0.710280			0.355140	+	0.934813i	$0.384433\pi$
$338$	−1.40416	+	0.168324i	−0.0763763	+	0.00915563i
$339$		0			0
$340$	0.107460	+	0.441776i	0.00582786	+	0.0239587i
$341$	−4.77675			−0.258675
$342$		0			0
$343$			1.24523i			0.0672363i
$344$	1.53756	−	0.575091i	0.0828998	−	0.0310068i
$345$		0			0
$346$	−17.6319	+	2.11363i	−0.947895	+	0.113629i
$347$		−	9.75181i		−	0.523504i	−0.965135	−	0.261752i	$-0.915700\pi$
$347$		−	9.75181i		−	0.523504i	0.965135	−	0.261752i	$-0.0843003\pi$
$348$		0			0
$349$		−	8.19014i		−	0.438408i	−0.975679	−	0.219204i	$-0.929654\pi$
$349$		−	8.19014i		−	0.438408i	0.975679	−	0.219204i	$-0.0703460\pi$
$350$	0.0379920	+	0.316929i	0.00203076	+	0.0169406i
$351$		0			0
$352$	2.17204	+	3.19862i	0.115770	+	0.170487i
$353$		−	17.3545i		−	0.923687i	−0.886961	−	0.461843i	$-0.847188\pi$
$353$		−	17.3545i		−	0.923687i	0.886961	−	0.461843i	$-0.152812\pi$
$354$		0			0
$355$	−10.2103			−0.541904
$356$	−7.67911	−	31.5693i	−0.406992	−	1.67317i
$357$		0			0
$358$	3.40224	+	28.3815i	0.179814	+	1.50001i
$359$	2.69754			0.142371			0.0711855	−	0.997463i	$-0.477322\pi$
$359$	2.69754			0.142371			0.0711855	+	0.997463i	$0.477322\pi$
$360$		0			0
$361$	−16.4268			−0.864570
$362$	3.83603	+	32.0002i	0.201617	+	1.68189i
$363$		0			0
$364$	0.172948	−	0.0420689i	0.00906495	−	0.00220501i
$365$	19.0660			0.997958
$366$		0			0
$367$		−	7.83765i		−	0.409122i	−0.978854	−	0.204561i	$-0.934423\pi$
$367$		−	7.83765i		−	0.409122i	0.978854	−	0.204561i	$-0.0655767\pi$
$368$	−14.6928	+	7.59746i	−0.765915	+	0.396045i
$369$		0			0
$370$	0.705409	+	5.88452i	0.0366725	+	0.305922i
$371$		−	0.199872i		−	0.0103768i
$372$		0			0
$373$			2.35883i			0.122136i	0.998134	+	0.0610678i	$0.0194506\pi$
$373$			2.35883i			0.122136i	−0.998134	+	0.0610678i	$0.980549\pi$
$374$	−0.0794743	+	0.00952700i	−0.00410952	+	0.000492630i
$375$		0			0
$376$	−20.3856	+	7.62479i	−1.05131	+	0.393219i
$377$			1.05035i			0.0540955i
$378$		0			0
$379$	18.8503			0.968273			0.484136	−	0.874993i	$-0.339134\pi$
$379$	18.8503			0.968273			0.484136	+	0.874993i	$0.339134\pi$
$380$	−8.55769	+	2.08162i	−0.439000	+	0.106785i
$381$		0			0
$382$	−13.0531	+	1.56474i	−0.667855	+	0.0800593i
$383$	−18.9471			−0.968151			−0.484075	−	0.875026i	$-0.660844\pi$
$383$	−18.9471			−0.968151			−0.484075	+	0.875026i	$0.660844\pi$
$384$		0			0
$385$	−0.166983			−0.00851027
$386$	−27.4717	+	3.29317i	−1.39827	+	0.167618i
$387$		0			0
$388$	9.43318	−	2.29458i	0.478897	−	0.116490i
$389$	14.7733			0.749035			0.374518	−	0.927220i	$-0.377808\pi$
$389$	14.7733			0.749035			0.374518	+	0.927220i	$0.377808\pi$
$390$		0			0
$391$		−	0.342435i		−	0.0173177i
$392$	18.5233	−	6.92823i	0.935568	−	0.349929i
$393$		0			0
$394$	1.89281	−	0.226901i	0.0953583	−	0.0114311i
$395$			4.81560i			0.242299i
$396$		0			0
$397$			24.2208i			1.21561i	0.794088	+	0.607803i	$0.207949\pi$
$397$			24.2208i			1.21561i	−0.794088	+	0.607803i	$0.792051\pi$
$398$	−2.16170	−	18.0329i	−0.108356	−	0.903907i
$399$		0			0
$400$	9.01122	−	4.65959i	0.450561	−	0.232980i
$401$		−	31.9999i		−	1.59800i	−0.601333	−	0.798998i	$-0.705364\pi$
$401$		−	31.9999i		−	1.59800i	0.601333	−	0.798998i	$-0.294636\pi$
$402$		0			0
$403$	6.98879			0.348137
$404$	−23.0551	+	5.60806i	−1.14703	+	0.279011i
$405$		0			0
$406$	−0.0157343	−	0.131255i	−0.000780879	−	0.00651410i
$407$	−1.04340			−0.0517192
$408$		0			0
$409$	36.5920			1.80936			0.904678	−	0.426096i	$-0.140111\pi$
$409$	36.5920			1.80936			0.904678	+	0.426096i	$0.140111\pi$
$410$	−3.16822	−	26.4293i	−0.156467	−	1.30525i
$411$		0			0
$412$	5.91622	+	24.3219i	0.291471	+	1.19826i
$413$	0.705925			0.0347363
$414$		0			0
$415$			41.7559i			2.04972i
$416$	−3.17788	−	4.67986i	−0.155808	−	0.229449i
$417$		0			0
$418$	−0.184548	−	1.53950i	−0.00902656	−	0.0752995i
$419$		−	34.8640i		−	1.70322i	−0.524179	−	0.851608i	$-0.675628\pi$
$419$		−	34.8640i		−	1.70322i	0.524179	−	0.851608i	$-0.324372\pi$
$420$		0			0
$421$			5.59480i			0.272674i	0.990663	+	0.136337i	$0.0435330\pi$
$421$			5.59480i			0.272674i	−0.990663	+	0.136337i	$0.956467\pi$
$422$	−37.2215	+	4.46194i	−1.81191	+	0.217204i
$423$		0			0
$424$	−5.94971	+	2.22536i	−0.288944	+	0.108073i
$425$			0.210018i			0.0101874i
$426$		0			0
$427$	−0.503204			−0.0243517
$428$	−2.88372	−	11.8552i	−0.139390	−	0.573041i
$429$		0			0
$430$	2.23724	−	0.268190i	0.107889	−	0.0129333i
$431$	−17.1684			−0.826974			−0.413487	−	0.910510i	$-0.635689\pi$
$431$	−17.1684			−0.826974			−0.413487	+	0.910510i	$0.635689\pi$
$432$		0			0
$433$	2.73858			0.131608			0.0658039	−	0.997833i	$-0.479039\pi$
$433$	2.73858			0.131608			0.0658039	+	0.997833i	$0.479039\pi$
$434$	−0.873348	+	0.104693i	−0.0419221	+	0.00502542i
$435$		0			0
$436$	7.76775	+	31.9337i	0.372008	+	1.52935i
$437$	6.63333			0.317315
$438$		0			0
$439$		−	2.14328i		−	0.102293i	−0.998691	−	0.0511465i	$-0.983712\pi$
$439$		−	2.14328i		−	0.102293i	0.998691	−	0.0511465i	$-0.0162876\pi$
$440$	1.85918	+	4.97070i	0.0886328	+	0.236969i
$441$		0			0
$442$	0.116278	−	0.0139388i	0.00553077	−	0.000663003i
$443$		−	34.9106i		−	1.65865i	−0.558765	−	0.829326i	$-0.688724\pi$
$443$		−	34.9106i		−	1.65865i	0.558765	−	0.829326i	$-0.311276\pi$
$444$		0			0
$445$		−	44.5957i		−	2.11404i
$446$	−2.82263	−	23.5464i	−0.133655	−	1.11495i
$447$		0			0
$448$	0.467226	+	0.537209i	0.0220743	+	0.0253808i
$449$			33.5270i			1.58224i	0.611662	+	0.791119i	$0.290501\pi$
$449$			33.5270i			1.58224i	−0.611662	+	0.791119i	$0.709499\pi$
$450$		0			0
$451$	4.68624			0.220666
$452$	−4.52488	−	18.6021i	−0.212832	−	0.874967i
$453$		0			0
$454$	3.84988	+	32.1157i	0.180684	+	1.50727i
$455$	0.244311			0.0114535
$456$		0			0
$457$	−18.5231			−0.866475			−0.433237	−	0.901280i	$-0.642629\pi$
$457$	−18.5231			−0.866475			−0.433237	+	0.901280i	$0.642629\pi$
$458$	−3.05865	−	25.5152i	−0.142921	−	1.19225i
$459$		0			0
$460$	−22.0608	+	5.36619i	−1.02859	+	0.250200i
$461$	−25.1536			−1.17152			−0.585761	−	0.810484i	$-0.699204\pi$
$461$	−25.1536			−1.17152			−0.585761	+	0.810484i	$0.699204\pi$
$462$		0			0
$463$			12.9506i			0.601864i	0.953646	+	0.300932i	$0.0972978\pi$
$463$			12.9506i			0.601864i	−0.953646	+	0.300932i	$0.902702\pi$
$464$	−3.73198	+	1.92976i	−0.173253	+	0.0895868i
$465$		0			0
$466$	2.79191	+	23.2901i	0.129333	+	1.07889i
$467$			14.7706i			0.683500i	0.939791	+	0.341750i	$0.111020\pi$
$467$			14.7706i			0.683500i	−0.939791	+	0.341750i	$0.888980\pi$
$468$		0			0
$469$		−	0.509781i		−	0.0235395i
$470$	−29.6623	+	3.55577i	−1.36822	+	0.164015i
$471$		0			0
$472$	−7.85970	−	21.0137i	−0.361772	−	0.967234i
$473$			0.396689i			0.0182398i
$474$		0			0
$475$	−4.06828			−0.186666
$476$	−0.0143217	+	0.00348371i	−0.000656436	+	0.000159675i
$477$		0			0
$478$	3.11235	−	0.373094i	0.142356	−	0.0170649i
$479$	33.2576			1.51958			0.759790	−	0.650168i	$-0.225302\pi$
$479$	33.2576			1.51958			0.759790	+	0.650168i	$0.225302\pi$
$480$		0			0
$481$	1.52658			0.0696060
$482$	29.6252	−	3.55133i	1.34939	−	0.161759i
$483$		0			0
$484$	20.4688	−	4.97896i	0.930402	−	0.226317i
$485$	13.3256			0.605083
$486$		0			0
$487$		−	19.5452i		−	0.885677i	−0.896601	−	0.442839i	$-0.853971\pi$
$487$		−	19.5452i		−	0.885677i	0.896601	−	0.442839i	$-0.146029\pi$
$488$	5.60262	+	14.9792i	0.253619	+	0.678075i
$489$		0			0
$490$	26.9525	−	3.23093i	1.21759	−	0.145959i
$491$		−	5.44694i		−	0.245817i	−0.992418	−	0.122908i	$-0.960778\pi$
$491$		−	5.44694i		−	0.245817i	0.992418	−	0.122908i	$-0.0392222\pi$
$492$		0			0
$493$		−	0.0869785i		−	0.00391732i
$494$	0.270010	+	2.25243i	0.0121483	+	0.101341i
$495$		0			0
$496$	12.8402	+	24.8318i	0.576544	+	1.11498i
$497$		−	0.331002i		−	0.0148475i
$498$		0			0
$499$	20.3074			0.909082			0.454541	−	0.890726i	$-0.349803\pi$
$499$	20.3074			0.909082			0.454541	+	0.890726i	$0.349803\pi$
$500$	−13.1442	+	3.19728i	−0.587827	+	0.142987i
$501$		0			0
$502$	−0.662127	−	5.52346i	−0.0295522	−	0.246524i
$503$	−0.606110			−0.0270251			−0.0135126	−	0.999909i	$-0.504301\pi$
$503$	−0.606110			−0.0270251			−0.0135126	+	0.999909i	$0.504301\pi$
$504$		0			0
$505$	−32.5682			−1.44927
$506$	−0.475745	−	3.96867i	−0.0211495	−	0.176429i
$507$		0			0
$508$	−1.75059	−	7.19680i	−0.0776700	−	0.319306i
$509$	34.6953			1.53784			0.768922	−	0.639343i	$-0.220794\pi$
$509$	34.6953			1.53784			0.768922	+	0.639343i	$0.220794\pi$
$510$		0			0
$511$			0.618091i			0.0273427i
$512$	10.7894	−	19.8894i	0.476828	−	0.878997i
$513$		0			0
$514$	−2.17687	−	18.1595i	−0.0960177	−	0.800980i
$515$			34.3578i			1.51399i
$516$		0			0
$517$		−	5.25947i		−	0.231311i
$518$	−0.190768	+	0.0228683i	−0.00838184	+	0.00100478i
$519$		0			0
$520$	−2.72014	−	7.27256i	−0.119286	−	0.318923i
$521$		−	5.42869i		−	0.237835i	−0.992904	−	0.118918i	$-0.962058\pi$
$521$		−	5.42869i		−	0.237835i	0.992904	−	0.118918i	$-0.0379424\pi$
$522$		0			0
$523$	9.02542			0.394654			0.197327	−	0.980338i	$-0.436774\pi$
$523$	9.02542			0.394654			0.197327	+	0.980338i	$0.436774\pi$
$524$	−3.24922	−	13.3577i	−0.141943	−	0.583536i
$525$		0			0
$526$	22.1695	−	2.65757i	0.966634	−	0.115876i
$527$	−0.578738			−0.0252102
$528$		0			0
$529$	−5.90000			−0.256522
$530$	−8.65716	+	1.03778i	−0.376043	+	0.0450783i
$531$		0			0
$532$	−0.0674832	−	0.277428i	−0.00292577	−	0.0120280i
$533$	−6.85637			−0.296982
$534$		0			0
$535$		−	16.7469i		−	0.724033i
$536$	−15.1749	+	5.67585i	−0.655458	+	0.245159i
$537$		0			0
$538$	19.8303	−	2.37716i	0.854943	−	0.102487i
$539$			4.77899i			0.205846i
$540$		0			0
$541$			14.8589i			0.638833i	0.947614	+	0.319416i	$0.103487\pi$
$541$			14.8589i			0.638833i	−0.947614	+	0.319416i	$0.896513\pi$
$542$	4.24577	+	35.4182i	0.182371	+	1.52134i
$543$		0			0
$544$	0.263158	+	0.387537i	0.0112828	+	0.0166155i
$545$			45.1104i			1.93232i
$546$		0			0
$547$	−23.6294			−1.01032			−0.505160	−	0.863026i	$-0.668567\pi$
$547$	−23.6294			−1.01032			−0.505160	+	0.863026i	$0.668567\pi$
$548$	3.64908	+	15.0016i	0.155881	+	0.640837i
$549$		0			0
$550$	0.291779	+	2.43402i	0.0124415	+	0.103787i
$551$	1.68487			0.0717778
$552$		0			0
$553$	−0.156115			−0.00663867
$554$	−2.44341	−	20.3829i	−0.103810	−	0.865987i
$555$		0			0
$556$	−10.6433	+	2.58893i	−0.451375	+	0.109795i
$557$	−21.2040			−0.898440			−0.449220	−	0.893421i	$-0.648298\pi$
$557$	−21.2040			−0.898440			−0.449220	+	0.893421i	$0.648298\pi$
$558$		0			0
$559$		−	0.580391i		−	0.0245479i
$560$	0.448863	+	0.868061i	0.0189679	+	0.0366823i
$561$		0			0
$562$	−1.66858	−	13.9193i	−0.0703846	−	0.587149i
$563$		−	33.0810i		−	1.39420i	−0.716974	−	0.697100i	$-0.754473\pi$
$563$		−	33.0810i		−	1.39420i	0.716974	−	0.697100i	$-0.245527\pi$
$564$		0			0
$565$		−	26.2778i		−	1.10551i
$566$	29.2666	−	3.50834i	1.23017	−	0.147466i
$567$		0			0
$568$	−9.85312	+	3.68534i	−0.413428	+	0.154633i
$569$		−	31.4417i		−	1.31810i	−0.752098	−	0.659051i	$-0.770958\pi$
$569$		−	31.4417i		−	1.31810i	0.752098	−	0.659051i	$-0.229042\pi$
$570$		0			0
$571$	0.634572			0.0265560			0.0132780	−	0.999912i	$-0.495773\pi$
$571$	0.634572			0.0265560			0.0132780	+	0.999912i	$0.495773\pi$
$572$	1.32824	−	0.323090i	0.0555366	−	0.0135091i
$573$		0			0
$574$	0.856800	−	0.102709i	0.0357621	−	0.00428700i
$575$	−10.4876			−0.437362
$576$		0			0
$577$	−7.64474			−0.318255			−0.159127	−	0.987258i	$-0.550868\pi$
$577$	−7.64474			−0.318255			−0.159127	+	0.987258i	$0.550868\pi$
$578$	23.8611	−	2.86036i	0.992491	−	0.118975i
$579$		0			0
$580$	−5.60344	+	1.36301i	−0.232670	+	0.0565961i
$581$	−1.35366			−0.0561595
$582$		0			0
$583$		−	1.53502i		−	0.0635740i
$584$	18.3991	−	6.88176i	0.761359	−	0.284769i
$585$		0			0
$586$	4.47262	−	0.536157i	0.184762	−	0.0221484i
$587$			12.7111i			0.524645i	0.964980	+	0.262323i	$0.0844885\pi$
$587$			12.7111i			0.524645i	−0.964980	+	0.262323i	$0.915512\pi$
$588$		0			0
$589$		−	11.2108i		−	0.461932i
$590$	−3.66532	−	30.5761i	−0.150899	−	1.25880i
$591$		0			0
$592$	2.80472	+	5.42408i	0.115273	+	0.222928i
$593$			27.1007i			1.11289i	0.830884	+	0.556446i	$0.187835\pi$
$593$			27.1007i			1.11289i	−0.830884	+	0.556446i	$0.812165\pi$
$594$		0			0
$595$	−0.0202313			−0.000829402
$596$	−13.8317	+	3.36450i	−0.566567	+	0.137815i
$597$		0			0
$598$	0.696056	+	5.80650i	0.0284639	+	0.237446i
$599$	41.6624			1.70228			0.851140	−	0.524939i	$-0.175912\pi$
$599$	41.6624			1.70228			0.851140	+	0.524939i	$0.175912\pi$
$600$		0			0
$601$	16.2944			0.664664			0.332332	−	0.943163i	$-0.392165\pi$
$601$	16.2944			0.664664			0.332332	+	0.943163i	$0.392165\pi$
$602$	0.00869432	+	0.0725280i	0.000354354	+	0.00295602i
$603$		0			0
$604$	−8.16985	−	33.5868i	−0.332426	−	1.36663i
$605$	28.9148			1.17556
$606$		0			0
$607$		−	22.1095i		−	0.897395i	−0.893684	−	0.448698i	$-0.851888\pi$
$607$		−	22.1095i		−	0.897395i	0.893684	−	0.448698i	$-0.148112\pi$
$608$	−7.50700	+	5.09767i	−0.304449	+	0.206738i
$609$		0			0
$610$	2.61274	+	21.7955i	0.105787	+	0.882475i
$611$			7.69506i			0.311309i
$612$		0			0
$613$			46.3657i			1.87269i	0.351076	+	0.936347i	$0.385816\pi$
$613$			46.3657i			1.87269i	−0.351076	+	0.936347i	$0.614184\pi$
$614$	4.28477	−	0.513638i	0.172919	−	0.0207287i
$615$		0			0
$616$	−0.161143	+	0.0602718i	−0.00649262	+	0.00242842i
$617$			27.6077i			1.11145i	0.831368	+	0.555723i	$0.187558\pi$
$617$			27.6077i			1.11145i	−0.831368	+	0.555723i	$0.812442\pi$
$618$		0			0
$619$	40.2262			1.61683			0.808414	−	0.588615i	$-0.200327\pi$
$619$	40.2262			1.61683			0.808414	+	0.588615i	$0.200327\pi$
$620$	9.06923	+	37.2842i	0.364229	+	1.49737i
$621$		0			0
$622$	39.1710	−	4.69564i	1.57062	−	0.188278i
$623$	1.44573			0.0579218
$624$		0			0
$625$	−31.2487			−1.24995
$626$	18.1664	−	2.17770i	0.726075	−	0.0870384i
$627$		0			0
$628$	−0.101240	−	0.416205i	−0.00403992	−	0.0166084i
$629$	−0.126415			−0.00504050
$630$		0			0
$631$			4.60487i			0.183317i	0.995791	+	0.0916585i	$0.0292168\pi$
$631$			4.60487i			0.183317i	−0.995791	+	0.0916585i	$0.970783\pi$
$632$	1.73817	+	4.64716i	0.0691405	+	0.184854i
$633$		0			0
$634$	34.1424	−	4.09283i	1.35597	−	0.162547i
$635$		−	10.1664i		−	0.403441i
$636$		0			0
$637$		−	6.99208i		−	0.277036i
$638$	−0.120839	−	1.00804i	−0.00478408	−	0.0399088i
$639$		0			0
$640$	20.8425	−	23.0265i	0.823872	−	0.910202i
$641$		−	4.62353i		−	0.182618i	−0.995823	−	0.0913091i	$-0.970895\pi$
$641$		−	4.62353i		−	0.182618i	0.995823	−	0.0913091i	$-0.0291051\pi$
$642$		0			0
$643$	40.8652			1.61157			0.805784	−	0.592210i	$-0.201744\pi$
$643$	40.8652			1.61157			0.805784	+	0.592210i	$0.201744\pi$
$644$	−0.173964	−	0.715178i	−0.00685515	−	0.0281819i
$645$		0			0
$646$	−0.0223594	−	0.186522i	−0.000879719	−	0.00733862i
$647$	43.8609			1.72435			0.862175	−	0.506610i	$-0.169102\pi$
$647$	43.8609			1.72435			0.862175	+	0.506610i	$0.169102\pi$
$648$		0			0
$649$	5.42151			0.212813
$650$	−0.426897	−	3.56118i	−0.0167443	−	0.139681i
$651$		0			0
$652$	−35.6253	+	8.66572i	−1.39520	+	0.339376i
$653$	−38.5643			−1.50914			−0.754568	−	0.656221i	$-0.772154\pi$
$653$	−38.5643			−1.50914			−0.754568	+	0.656221i	$0.772154\pi$
$654$		0			0
$655$		−	18.8695i		−	0.737293i
$656$	−12.5969	−	24.3613i	−0.491828	−	0.951150i
$657$		0			0
$658$	−0.115273	−	0.961607i	−0.00449380	−	0.0374873i
$659$		−	13.6233i		−	0.530688i	−0.964154	−	0.265344i	$-0.914515\pi$
$659$		−	13.6233i		−	0.530688i	0.964154	−	0.265344i	$-0.0854855\pi$
$660$		0			0
$661$		−	23.0462i		−	0.896394i	−0.893935	−	0.448197i	$-0.852066\pi$
$661$		−	23.0462i		−	0.896394i	0.893935	−	0.448197i	$-0.147934\pi$
$662$	29.4007	−	3.52442i	1.14269	−	0.136980i
$663$		0			0
$664$	15.0716	+	40.2953i	0.584891	+	1.56376i
$665$		−	0.391902i		−	0.0151973i
$666$		0			0
$667$	4.34340			0.168177
$668$	21.4372	−	5.21452i	0.829431	−	0.201756i
$669$		0			0
$670$	−22.0804	+	2.64689i	−0.853040	+	0.102258i
$671$	−3.86461			−0.149191
$672$		0			0
$673$	−28.5978			−1.10236			−0.551182	−	0.834385i	$-0.685823\pi$
$673$	−28.5978			−1.10236			−0.551182	+	0.834385i	$0.685823\pi$
$674$	18.3089	−	2.19478i	0.705231	−	0.0845397i
$675$		0			0
$676$	−1.94333	+	0.472708i	−0.0747436	+	0.0181811i
$677$	−21.4731			−0.825277			−0.412639	−	0.910895i	$-0.635393\pi$
$677$	−21.4731			−0.825277			−0.412639	+	0.910895i	$0.635393\pi$
$678$		0			0
$679$			0.431995i			0.0165785i
$680$	0.225253	+	0.602237i	0.00863807	+	0.0230947i
$681$		0			0
$682$	−6.70732	+	0.804042i	−0.256837	+	0.0307884i
$683$		−	14.4451i		−	0.552727i	−0.961053	−	0.276363i	$-0.910871\pi$
$683$		−	14.4451i		−	0.552727i	0.961053	−	0.276363i	$-0.0891293\pi$
$684$		0			0
$685$			21.1917i			0.809693i
$686$	0.209603	+	1.74851i	0.00800267	+	0.0667583i
$687$		0			0
$688$	2.06218	−	1.06633i	0.0786200	−	0.0406534i
$689$			2.24587i			0.0855607i
$690$		0			0
$691$	0.206894			0.00787064			0.00393532	−	0.999992i	$-0.498747\pi$
$691$	0.206894			0.00787064			0.00393532	+	0.999992i	$0.498747\pi$
$692$	−24.4022	+	5.93574i	−0.927633	+	0.225643i
$693$		0			0
$694$	−1.64146	−	13.6931i	−0.0623091	−	0.519783i
$695$	−15.0350			−0.570309
$696$		0			0
$697$	0.567772			0.0215059
$698$	−1.37860	−	11.5003i	−0.0521807	−	0.435292i
$699$		0			0
$700$	0.106694	+	0.438625i	0.00403264	+	0.0165785i
$701$	−24.9967			−0.944114			−0.472057	−	0.881568i	$-0.656488\pi$
$701$	−24.9967			−0.944114			−0.472057	+	0.881568i	$0.656488\pi$
$702$		0			0
$703$		−	2.44880i		−	0.0923582i
$704$	3.58829	+	4.12577i	0.135239	+	0.155496i
$705$		0			0
$706$	−2.92118	−	24.3685i	−0.109940	−	0.917121i
$707$		−	1.05581i		−	0.0397080i
$708$		0			0
$709$			26.5994i			0.998963i	0.866324	+	0.499482i	$0.166476\pi$
$709$			26.5994i			0.998963i	−0.866324	+	0.499482i	$0.833524\pi$
$710$	−14.3368	+	1.71863i	−0.538052	+	0.0644992i
$711$		0			0
$712$	−16.0966	−	43.0358i	−0.603245	−	1.61284i
$713$		−	28.9002i		−	1.08232i
$714$		0			0
$715$	1.87631			0.0701701
$716$	9.55459	+	39.2795i	0.357072	+	1.46794i
$717$		0			0
$718$	3.78779	−	0.454062i	0.141359	−	0.0169454i
$719$	7.23300			0.269745			0.134873	−	0.990863i	$-0.456937\pi$
$719$	7.23300			0.269745			0.134873	+	0.990863i	$0.456937\pi$
$720$		0			0
$721$	−1.11383			−0.0414812
$722$	−23.0659	+	2.76503i	−0.858424	+	0.102904i
$723$		0			0
$724$	10.7728	+	44.2877i	0.400368	+	1.64594i
$725$	−2.66385			−0.0989328
$726$		0			0
$727$			21.0337i			0.780098i	0.920794	+	0.390049i	$0.127542\pi$
$727$			21.0337i			0.780098i	−0.920794	+	0.390049i	$0.872458\pi$
$728$	0.235766	−	0.0881829i	0.00873806	−	0.00326828i
$729$		0			0
$730$	26.7717	−	3.20926i	0.990864	−	0.118780i
$731$			0.0480619i			0.00177763i
$732$		0			0
$733$			22.9654i			0.848245i	0.905605	+	0.424122i	$0.139417\pi$
$733$			22.9654i			0.848245i	−0.905605	+	0.424122i	$0.860583\pi$
$734$	−1.31927	−	11.0053i	−0.0486950	−	0.406214i
$735$		0			0
$736$	−19.3522	+	13.1412i	−0.713332	+	0.484392i
$737$		−	3.91512i		−	0.144215i
$738$		0			0
$739$	2.84081			0.104501			0.0522505	−	0.998634i	$-0.483361\pi$
$739$	2.84081			0.104501			0.0522505	+	0.998634i	$0.483361\pi$
$740$	1.98101	+	8.14408i	0.0728235	+	0.299382i
$741$		0			0
$742$	−0.0336433	−	0.280653i	−0.00123508	−	0.0103031i
$743$	11.2838			0.413964			0.206982	−	0.978345i	$-0.433636\pi$
$743$	11.2838			0.413964			0.206982	+	0.978345i	$0.433636\pi$
$744$		0			0
$745$	−19.5390			−0.715853
$746$	0.397048	+	3.31218i	0.0145370	+	0.121267i
$747$		0			0
$748$	−0.109991	+	0.0267549i	−0.00402167	+	0.000978255i
$749$	0.542911			0.0198375
$750$		0			0
$751$			24.0944i			0.879216i	0.898190	+	0.439608i	$0.144883\pi$
$751$			24.0944i			0.879216i	−0.898190	+	0.439608i	$0.855117\pi$
$752$	−27.3413	+	14.1378i	−0.997034	+	0.515554i
$753$		0			0
$754$	0.176798	+	1.47485i	0.00643862	+	0.0537110i
$755$		−	47.4456i		−	1.72672i
$756$		0			0
$757$		−	23.7535i		−	0.863337i	−0.902032	−	0.431668i	$-0.857925\pi$
$757$		−	23.7535i		−	0.863337i	0.902032	−	0.431668i	$-0.142075\pi$
$758$	26.4688	−	3.17295i	0.961390	−	0.115247i
$759$		0			0
$760$	−11.6660	+	4.36340i	−0.423170	+	0.158277i
$761$			28.9002i			1.04763i	0.851832	+	0.523816i	$0.175492\pi$
$761$			28.9002i			1.04763i	−0.851832	+	0.523816i	$0.824508\pi$
$762$		0			0
$763$	−1.46241			−0.0529429
$764$	−18.0653	+	4.39430i	−0.653578	+	0.158980i
$765$		0			0
$766$	−26.6047	+	3.18925i	−0.961269	+	0.115232i
$767$	−7.93214			−0.286413
$768$		0			0
$769$	−16.4576			−0.593476			−0.296738	−	0.954959i	$-0.595899\pi$
$769$	−16.4576			−0.593476			−0.296738	+	0.954959i	$0.595899\pi$
$770$	−0.234472	+	0.0281074i	−0.00844977	+	0.00101292i
$771$		0			0
$772$	−38.0203	+	9.24829i	−1.36838	+	0.332853i
$773$	−1.00884			−0.0362855			−0.0181428	−	0.999835i	$-0.505775\pi$
$773$	−1.00884			−0.0362855			−0.0181428	+	0.999835i	$0.505775\pi$
$774$		0			0
$775$			17.7247i			0.636691i
$776$	12.8595	−	4.80980i	0.461628	−	0.172662i
$777$		0			0
$778$	20.7441	−	2.48670i	0.743711	−	0.0891525i
$779$			10.9984i			0.394057i
$780$		0			0
$781$		−	2.54209i		−	0.0909633i
$782$	−0.0576401	−	0.480833i	−0.00206120	−	0.0171946i
$783$		0			0
$784$	24.8435	−	12.8463i	0.887268	−	0.458795i
$785$		−	0.587943i		−	0.0209846i
$786$		0			0
$787$	4.83938			0.172505			0.0862526	−	0.996273i	$-0.472511\pi$
$787$	4.83938			0.172505			0.0862526	+	0.996273i	$0.472511\pi$
$788$	2.61961	−	0.637211i	0.0933199	−	0.0226997i
$789$		0			0
$790$	0.810582	+	6.76187i	0.0288392	+	0.240577i
$791$	0.851887			0.0302896
$792$		0			0
$793$	5.65426			0.200789
$794$	4.07694	+	34.0099i	0.144685	+	1.20697i
$795$		0			0
$796$	−6.07074	−	24.9572i	−0.215172	−	0.884584i
$797$	−33.8113			−1.19766			−0.598829	−	0.800877i	$-0.704367\pi$
$797$	−33.8113			−1.19766			−0.598829	+	0.800877i	$0.704367\pi$
$798$		0			0
$799$		−	0.637224i		−	0.0225434i
$800$	11.8689	−	8.05962i	0.419628	−	0.284951i
$801$		0			0
$802$	−5.38635	−	44.9329i	−0.190199	−	1.58664i
$803$			4.74694i			0.167516i
$804$		0			0
$805$		−	1.01028i		−	0.0356077i
$806$	9.81339	−	1.17638i	0.345662	−	0.0414363i
$807$		0			0
$808$	−31.4291	+	11.7553i	−1.10567	+	0.413551i
$809$			31.6096i			1.11133i	0.831405	+	0.555666i	$0.187537\pi$
$809$			31.6096i			1.11133i	−0.831405	+	0.555666i	$0.812463\pi$
$810$		0			0
$811$	8.46809			0.297355			0.148677	−	0.988886i	$-0.452498\pi$
$811$	8.46809			0.297355			0.148677	+	0.988886i	$0.452498\pi$
$812$	−0.0441869	−	0.181655i	−0.00155066	−	0.00637485i
$813$		0			0
$814$	−1.46510	+	0.175629i	−0.0513516	+	0.00615578i
$815$	−50.3253			−1.76282
$816$		0			0
$817$	−0.931010			−0.0325719
$818$	51.3810	−	6.15931i	1.79649	−	0.215355i
$819$		0			0
$820$	−8.89739	−	36.5777i	−0.310710	−	1.27735i
$821$	9.61153			0.335445			0.167722	−	0.985834i	$-0.446359\pi$
$821$	9.61153			0.335445			0.167722	+	0.985834i	$0.446359\pi$
$822$		0			0
$823$		−	43.3444i		−	1.51089i	−0.655212	−	0.755445i	$-0.727421\pi$
$823$		−	43.3444i		−	1.51089i	0.655212	−	0.755445i	$-0.272579\pi$
$824$	12.4013	+	33.1561i	0.432019	+	1.15505i
$825$		0			0
$826$	0.991232	−	0.118824i	0.0344894	−	0.00413442i
$827$			17.6404i			0.613416i	0.951804	+	0.306708i	$0.0992276\pi$
$827$			17.6404i			0.613416i	−0.951804	+	0.306708i	$0.900772\pi$
$828$		0			0
$829$		−	10.3644i		−	0.359972i	−0.983669	−	0.179986i	$-0.942395\pi$
$829$		−	10.3644i		−	0.359972i	0.983669	−	0.179986i	$-0.0576052\pi$
$830$	7.02853	+	58.6320i	0.243964	+	2.03515i
$831$		0			0
$832$	−5.24999	−	6.03636i	−0.182011	−	0.209273i
$833$			0.579010i			0.0200615i
$834$		0			0
$835$	30.2828			1.04798
$836$	−0.518271	−	2.13065i	−0.0179248	−	0.0736899i
$837$		0			0
$838$	−5.86845	−	48.9546i	−0.202722	−	1.69111i
$839$	35.7509			1.23426			0.617129	−	0.786862i	$-0.288296\pi$
$839$	35.7509			1.23426			0.617129	+	0.786862i	$0.288296\pi$
$840$		0			0
$841$	−27.8968			−0.961958
$842$	0.941740	+	7.85600i	0.0324545	+	0.270736i
$843$		0			0
$844$	−51.5139	+	12.5306i	−1.77318	+	0.431320i
$845$	−2.74521			−0.0944380
$846$		0			0
$847$			0.937377i			0.0322086i
$848$	−7.97977	+	4.12624i	−0.274026	+	0.141696i
$849$		0			0
$850$	0.0353511	+	0.294899i	0.00121253	+	0.0101150i
$851$		−	6.31273i		−	0.216398i
$852$		0			0
$853$			27.7299i			0.949455i	0.880133	+	0.474728i	$0.157453\pi$
$853$			27.7299i			0.949455i	−0.880133	+	0.474728i	$0.842547\pi$
$854$	−0.706579	+	0.0847013i	−0.0241786	+	0.00289842i
$855$		0			0
$856$	−6.04471	−	16.1611i	−0.206604	−	0.552376i
$857$		−	1.88241i		−	0.0643020i	−0.999483	−	0.0321510i	$-0.989764\pi$
$857$		−	1.88241i		−	0.0643020i	0.999483	−	0.0321510i	$-0.0102357\pi$
$858$		0			0
$859$	6.50488			0.221944			0.110972	−	0.993824i	$-0.464604\pi$
$859$	6.50488			0.221944			0.110972	+	0.993824i	$0.464604\pi$
$860$	3.09630	−	0.753163i	0.105583	−	0.0256826i
$861$		0			0
$862$	−24.1072	+	2.88986i	−0.821095	+	0.0984290i
$863$	−56.4785			−1.92255			−0.961274	−	0.275593i	$-0.911126\pi$
$863$	−56.4785			−1.92255			−0.961274	+	0.275593i	$0.911126\pi$
$864$		0			0
$865$	−34.4712			−1.17206
$866$	3.84541	−	0.460969i	0.130672	−	0.0156644i
$867$		0			0
$868$	−1.20870	+	0.294011i	−0.0410259	+	0.00997939i
$869$	−1.19896			−0.0406720
$870$		0			0
$871$			5.72816i			0.194091i
$872$	16.2824	+	43.5326i	0.551391	+	1.47420i
$873$		0			0
$874$	9.31427	−	1.11655i	0.315060	−	0.0377679i
$875$		−	0.601943i		−	0.0203494i
$876$		0			0
$877$		−	2.26903i		−	0.0766195i	−0.999266	−	0.0383098i	$-0.987803\pi$
$877$		−	2.26903i		−	0.0766195i	0.999266	−	0.0383098i	$-0.0121974\pi$
$878$	−0.360765	−	3.00951i	−0.0121752	−	0.101566i
$879$		0			0
$880$	3.44727	+	6.66671i	0.116208	+	0.224735i
$881$		−	10.4951i		−	0.353588i	−0.984248	−	0.176794i	$-0.943427\pi$
$881$		−	10.4951i		−	0.353588i	0.984248	−	0.176794i	$-0.0565727\pi$
$882$		0			0
$883$	28.9867			0.975482			0.487741	−	0.872989i	$-0.337821\pi$
$883$	28.9867			0.975482			0.487741	+	0.872989i	$0.337821\pi$
$884$	0.160926	−	0.0391447i	0.00541254	−	0.00131658i
$885$		0			0
$886$	−5.87630	−	49.0201i	−0.197418	−	1.64686i
$887$	12.2815			0.412372			0.206186	−	0.978513i	$-0.433895\pi$
$887$	12.2815			0.412372			0.206186	+	0.978513i	$0.433895\pi$
$888$		0			0
$889$	0.329580			0.0110538
$890$	−7.50653	−	62.6195i	−0.251620	−	2.09901i
$891$		0			0
$892$	−7.92685	−	32.5878i	−0.265411	−	1.09112i
$893$	12.3437			0.413067
$894$		0			0
$895$			55.4873i			1.85474i
$896$	0.746485	+	0.675683i	0.0249383	+	0.0225730i
$897$		0			0
$898$	5.64341	+	47.0773i	0.188323	+	1.57099i
$899$		−	7.34065i		−	0.244824i
$900$		0			0
$901$		−	0.185979i		−	0.00619585i
$902$	6.58023	−	0.788807i	0.219098	−	0.0262644i
$903$		0			0
$904$	−9.48483	−	25.3586i	−0.315461	−	0.843415i
$905$			62.5620i			2.07963i
$906$		0			0
$907$	−35.7757			−1.18791			−0.593956	−	0.804497i	$-0.702435\pi$
$907$	−35.7757			−1.18791			−0.593956	+	0.804497i	$0.702435\pi$
$908$	10.8117	+	44.4476i	0.358799	+	1.47505i
$909$		0			0
$910$	0.343052	−	0.0411235i	0.0113721	−	0.00136323i
$911$	−37.6040			−1.24588			−0.622938	−	0.782271i	$-0.714061\pi$
$911$	−37.6040			−1.24588			−0.622938	+	0.782271i	$0.714061\pi$
$912$		0			0
$913$	−10.3962			−0.344062
$914$	−26.0094	+	3.11789i	−0.860315	+	0.103131i
$915$		0			0
$916$	−8.58966	−	35.3127i	−0.283811	−	1.16676i
$917$	0.611722			0.0202008
$918$		0			0
$919$		−	51.1984i		−	1.68888i	−0.535650	−	0.844440i	$-0.679933\pi$
$919$		−	51.1984i		−	1.68888i	0.535650	−	0.844440i	$-0.320067\pi$
$920$	−30.0736	+	11.2484i	−0.991497	+	0.370847i
$921$		0			0
$922$	−35.3197	+	4.23396i	−1.16319	+	0.139438i
$923$			3.71930i			0.122422i
$924$		0			0
$925$			3.87165i			0.127299i
$926$	2.17990	+	18.1847i	0.0716358	+	0.597586i
$927$		0			0
$928$	−4.91547	+	3.33787i	−0.161358	+	0.109571i
$929$		−	30.8763i		−	1.01302i	−0.862235	−	0.506509i	$-0.830936\pi$
$929$		−	30.8763i		−	1.01302i	0.862235	−	0.506509i	$-0.169064\pi$
$930$		0			0
$931$	−11.2161			−0.367591
$932$	7.84057	+	32.2331i	0.256826	+	1.05583i
$933$		0			0
$934$	2.48624	+	20.7403i	0.0813524	+	0.678642i
$935$	−0.155376			−0.00508135
$936$		0			0
$937$	−46.2602			−1.51125			−0.755627	−	0.655002i	$-0.772668\pi$
$937$	−46.2602			−1.51125			−0.755627	+	0.655002i	$0.772668\pi$
$938$	−0.0858084	−	0.715814i	−0.00280174	−	0.0233722i
$939$		0			0
$940$	−41.0520	+	9.98575i	−1.33897	+	0.325699i
$941$	−16.2868			−0.530936			−0.265468	−	0.964120i	$-0.585526\pi$
$941$	−16.2868			−0.530936			−0.265468	+	0.964120i	$0.585526\pi$
$942$		0			0
$943$			28.3526i			0.923286i
$944$	−14.5734	−	28.1836i	−0.474324	−	0.917299i
$945$		0			0
$946$	0.0667724	+	0.557016i	0.00217096	+	0.0181101i
$947$		−	16.6676i		−	0.541626i	−0.962632	−	0.270813i	$-0.912708\pi$
$947$		−	16.6676i		−	0.541626i	0.962632	−	0.270813i	$-0.0872925\pi$
$948$		0			0
$949$		−	6.94518i		−	0.225450i
$950$	−5.71252	+	0.684790i	−0.185339	+	0.0222175i
$951$		0			0
$952$	−0.0195236	+	0.00730238i	−0.000632764	+	0.000236671i
$953$			19.2692i			0.624192i	0.950051	+	0.312096i	$0.101031\pi$
$953$			19.2692i			0.624192i	−0.950051	+	0.312096i	$0.898969\pi$
$954$		0			0
$955$	−25.5195			−0.825791
$956$	4.30744	−	1.04777i	0.139313	−	0.0338872i
$957$		0			0
$958$	46.6991	−	5.59807i	1.50878	−	0.180865i
$959$	−0.687004			−0.0221845
$960$		0			0
$961$	−17.8433			−0.575589
$962$	2.14356	−	0.256960i	0.0691112	−	0.00828473i
$963$		0			0
$964$	41.0008	−	9.97328i	1.32055	−	0.321218i
$965$	−53.7085			−1.72894
$966$		0			0
$967$		−	53.1884i		−	1.71042i	−0.518279	−	0.855211i	$-0.673427\pi$
$967$		−	53.1884i		−	1.71042i	0.518279	−	0.855211i	$-0.326573\pi$
$968$	27.9035	−	10.4367i	0.896851	−	0.335447i
$969$		0			0
$970$	18.7112	−	2.24302i	0.600782	−	0.0720189i
$971$		−	32.1913i		−	1.03307i	−0.856266	−	0.516534i	$-0.827222\pi$
$971$		−	32.1913i		−	1.03307i	0.856266	−	0.516534i	$-0.172778\pi$
$972$		0			0
$973$		−	0.487411i		−	0.0156257i
$974$	−3.28993	−	27.4446i	−0.105416	−	0.879382i
$975$		0			0
$976$	10.3883	+	20.0901i	0.332523	+	0.643068i
$977$			42.1645i			1.34896i	0.738292	+	0.674481i	$0.235633\pi$
$977$			42.1645i			1.34896i	−0.738292	+	0.674481i	$0.764367\pi$
$978$		0			0
$979$	11.1032			0.354859
$980$	37.3017	−	9.07350i	1.19156	−	0.289842i
$981$		0			0
$982$	−0.916852	−	7.64838i	−0.0292579	−	0.244070i
$983$	0.948296			0.0302459			0.0151230	−	0.999886i	$-0.495186\pi$
$983$	0.948296			0.0302459			0.0151230	+	0.999886i	$0.495186\pi$
$984$		0			0
$985$	3.70054			0.117909
$986$	−0.0146406	−	0.122132i	−0.000466251	−	0.00388947i
$987$		0			0
$988$	0.758276	+	3.11732i	0.0241240	+	0.0991751i
$989$	−2.40004			−0.0763169
$990$		0			0
$991$			45.9321i			1.45908i	0.683937	+	0.729541i	$0.260266\pi$
$991$			45.9321i			1.45908i	−0.683937	+	0.729541i	$0.739734\pi$
$992$	22.2095	+	32.7066i	0.705154	+	1.03843i
$993$		0			0
$994$	−0.0557156	−	0.464779i	−0.00176719	−	0.0147419i
$995$		−	35.2552i		−	1.11767i
$996$		0			0
$997$			12.4285i			0.393616i	0.980442	+	0.196808i	$0.0630576\pi$
$997$			12.4285i			0.393616i	−0.980442	+	0.196808i	$0.936942\pi$
$998$	28.5148	−	3.41822i	0.902620	−	0.108202i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.j.a.755.45	yes	48
3.2	odd	2	inner	936.2.j.a.755.4	yes	48
4.3	odd	2		3744.2.j.a.2159.40		48
8.3	odd	2	inner	936.2.j.a.755.3	✓	48
8.5	even	2		3744.2.j.a.2159.9		48
12.11	even	2		3744.2.j.a.2159.10		48
24.5	odd	2		3744.2.j.a.2159.39		48
24.11	even	2	inner	936.2.j.a.755.46	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.j.a.755.3	✓	48	8.3	odd	2	inner
936.2.j.a.755.4	yes	48	3.2	odd	2	inner
936.2.j.a.755.45	yes	48	1.1	even	1	trivial
936.2.j.a.755.46	yes	48	24.11	even	2	inner
3744.2.j.a.2159.9		48	8.5	even	2
3744.2.j.a.2159.10		48	12.11	even	2
3744.2.j.a.2159.39		48	24.5	odd	2
3744.2.j.a.2159.40		48	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40416 - 0.168324i) q^{2} +(1.94333 - 0.472708i) q^{4} +2.74521 q^{5} +0.0889956i q^{7} +(2.64918 - 0.990868i) q^{8} +(3.85471 - 0.462085i) q^{10} +0.683486i q^{11} -1.00000i q^{13} +(0.0149801 + 0.124964i) q^{14} +(3.55309 - 1.83726i) q^{16} +0.0828094i q^{17} -1.60411 q^{19} +(5.33485 - 1.29768i) q^{20} +(0.115047 + 0.959725i) q^{22} -4.13521 q^{23} +2.53616 q^{25} +(-0.168324 - 1.40416i) q^{26} +(0.0420689 + 0.172948i) q^{28} -1.05035 q^{29} +6.98879i q^{31} +(4.67986 - 3.17788i) q^{32} +(0.0139388 + 0.116278i) q^{34} +0.244311i q^{35} +1.52658i q^{37} +(-2.25243 + 0.270010i) q^{38} +(7.27256 - 2.72014i) q^{40} -6.85637i q^{41} +0.580391 q^{43} +(0.323090 + 1.32824i) q^{44} +(-5.80650 + 0.696056i) q^{46} -7.69506 q^{47} +6.99208 q^{49} +(3.56118 - 0.426897i) q^{50} +(-0.472708 - 1.94333i) q^{52} -2.24587 q^{53} +1.87631i q^{55} +(0.0881829 + 0.235766i) q^{56} +(-1.47485 + 0.176798i) q^{58} -7.93214i q^{59} +5.65426i q^{61} +(1.17638 + 9.81339i) q^{62} +(6.03636 - 5.24999i) q^{64} -2.74521i q^{65} -5.72816 q^{67} +(0.0391447 + 0.160926i) q^{68} +(0.0411235 + 0.343052i) q^{70} -3.71930 q^{71} +6.94518 q^{73} +(0.256960 + 2.14356i) q^{74} +(-3.11732 + 0.758276i) q^{76} -0.0608273 q^{77} +1.75418i q^{79} +(9.75398 - 5.04366i) q^{80} +(-1.15409 - 9.62744i) q^{82} +15.2105i q^{83} +0.227329i q^{85} +(0.814962 - 0.0976938i) q^{86} +(0.677245 + 1.81068i) q^{88} -16.2449i q^{89} +0.0889956 q^{91} +(-8.03610 + 1.95475i) q^{92} +(-10.8051 + 1.29527i) q^{94} -4.40361 q^{95} +4.85412 q^{97} +(9.81800 - 1.17694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{4} + 16 q^{10} + 8 q^{16} + 32 q^{19} + 48 q^{25} - 24 q^{28} + 32 q^{34} - 32 q^{40} - 32 q^{43} + 24 q^{46} - 48 q^{49} + 8 q^{52} - 40 q^{58} + 40 q^{64} + 32 q^{67} - 40 q^{70} + 40 q^{76}+ \cdots - 32 q^{97}+O(q^{100}) \) 48 * q - 8 * q^4 + 16 * q^10 + 8 * q^16 + 32 * q^19 + 48 * q^25 - 24 * q^28 + 32 * q^34 - 32 * q^40 - 32 * q^43 + 24 * q^46 - 48 * q^49 + 8 * q^52 - 40 * q^58 + 40 * q^64 + 32 * q^67 - 40 * q^70 + 40 * q^76 + 16 * q^82 + 48 * q^88 + 32 * q^94 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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