LMFDB - Embedded newform 936.2.j.a.755.46

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

$q$-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	$-0.994646\pi$
$7$		−	0.0889956i		−	0.0336372i	0.999859	−	0.0168186i	$-0.00535377\pi$
$8$	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	$-0.967143\pi$
$11$		−	0.683486i		−	0.206079i	0.994677	−	0.103039i	$-0.0328568\pi$
$12$		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	$-0.996803\pi$
$17$		−	0.0828094i		−	0.0200842i	0.999950	−	0.0100421i	$-0.00319656\pi$
$18$		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	$-0.784032\pi$
$31$		−	6.98879i		−	1.25522i	0.778526	−	0.627612i	$-0.215968\pi$
$32$	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	$-0.959952\pi$
$37$		−	1.52658i		−	0.250968i	0.992096	−	0.125484i	$-0.0400484\pi$
$38$	−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	$0.179836\pi$
$41$			6.85637i			1.07079i	−0.844603	+	0.535393i	$0.820164\pi$
$42$		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	$0.172705\pi$
$59$			7.93214i			1.03268i	−0.856385	+	0.516338i	$0.827295\pi$
$60$		0			0
$61$		−	5.65426i		−	0.723953i	−0.932187	−	0.361977i	$-0.882102\pi$
$61$		−	5.65426i		−	0.723953i	0.932187	−	0.361977i	$-0.117898\pi$
$62$	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	$-0.968538\pi$
$79$		−	1.75418i		−	0.197361i	0.995119	−	0.0986806i	$-0.0314622\pi$
$80$	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	$-0.685593\pi$
$83$		−	15.2105i		−	1.66957i	0.550579	−	0.834783i	$-0.314407\pi$
$84$		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	$0.330148\pi$
$89$			16.2449i			1.72196i	−0.508640	+	0.860979i	$0.669852\pi$
$90$		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	$-0.788510\pi$
$103$		−	12.5156i		−	1.23320i	0.787278	−	0.616598i	$-0.211490\pi$
$104$	−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	$0.0952780\pi$
$107$			6.10042i			0.589750i	−0.955536	+	0.294875i	$0.904722\pi$
$108$		0			0
$109$		−	16.4324i		−	1.57394i	−0.616990	−	0.786971i	$-0.711648\pi$
$109$		−	16.4324i		−	1.57394i	0.616990	−	0.786971i	$-0.288352\pi$
$110$	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	$0.148662\pi$
$113$			9.57224i			0.900480i	−0.892908	+	0.450240i	$0.851338\pi$
$114$		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	$0.0525393\pi$
$127$			3.70333i			0.328617i	−0.986409	+	0.164309i	$0.947461\pi$
$128$	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	$0.0970787\pi$
$131$			6.87363i			0.600551i	−0.953852	+	0.300276i	$0.902921\pi$
$132$		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	$-0.893032\pi$
$137$		−	7.71953i		−	0.659524i	0.944064	−	0.329762i	$-0.106968\pi$
$138$		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	$0.248263\pi$
$151$			17.2831i			1.40648i	−0.710955	+	0.703238i	$0.751737\pi$
$152$	−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	$0.00272042\pi$
$157$			0.214171i			0.0170927i	−0.999963	+	0.00854634i	$0.997280\pi$
$158$	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	$-0.727455\pi$
$179$		−	20.2124i		−	1.51075i	0.655294	−	0.755374i	$-0.272545\pi$
$180$		0			0
$181$		−	22.7895i		−	1.69393i	−0.531646	−	0.846966i	$-0.678426\pi$
$181$		−	22.7895i		−	1.69393i	0.531646	−	0.846966i	$-0.321574\pi$
$182$	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	$0.150428\pi$
$199$			12.8425i			0.910378i	−0.890395	+	0.455189i	$0.849572\pi$
$200$	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	$0.189763\pi$
$223$			16.7690i			1.12294i	−0.827499	+	0.561468i	$0.810237\pi$
$224$	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	$-0.725674\pi$
$227$		−	22.8718i		−	1.51806i	0.651058	−	0.759028i	$-0.274326\pi$
$228$		0			0
$229$			18.1712i			1.20078i	0.799705	+	0.600392i	$0.204989\pi$
$229$			18.1712i			1.20078i	−0.799705	+	0.600392i	$0.795011\pi$
$230$	−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	$-0.817171\pi$
$233$		−	16.5865i		−	1.08662i	0.839533	−	0.543308i	$-0.182829\pi$
$234$		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	$0.0396187\pi$
$251$			3.93364i			0.248289i	−0.992264	+	0.124145i	$0.960381\pi$
$252$		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	$0.132157\pi$
$257$			12.9326i			0.806714i	−0.915043	+	0.403357i	$0.867843\pi$
$258$		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	$-0.722186\pi$
$271$		−	25.2238i		−	1.53224i	0.642700	−	0.766118i	$-0.277814\pi$
$272$	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	$0.143638\pi$
$277$			14.5161i			0.872187i	−0.899901	+	0.436093i	$0.856362\pi$
$278$	−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	$0.0955449\pi$
$281$			9.91287i			0.591352i	−0.955288	+	0.295676i	$0.904455\pi$
$282$		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	$0.0843003\pi$
$347$			9.75181i			0.523504i	−0.965135	+	0.261752i	$0.915700\pi$
$348$		0			0
$349$			8.19014i			0.438408i	0.975679	+	0.219204i	$0.0703460\pi$
$349$			8.19014i			0.438408i	−0.975679	+	0.219204i	$0.929654\pi$
$350$	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	$0.152812\pi$
$353$			17.3545i			0.923687i	−0.886961	+	0.461843i	$0.847188\pi$
$354$		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	$0.0655767\pi$
$367$			7.83765i			0.409122i	−0.978854	+	0.204561i	$0.934423\pi$
$368$	−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	$-0.980549\pi$
$373$		−	2.35883i		−	0.122136i	0.998134	−	0.0610678i	$-0.0194506\pi$
$374$	−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	$-0.792051\pi$
$397$		−	24.2208i		−	1.21561i	0.794088	−	0.607803i	$-0.207949\pi$
$398$	−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	$0.294636\pi$
$401$			31.9999i			1.59800i	−0.601333	+	0.798998i	$0.705364\pi$
$402$		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	$0.324372\pi$
$419$			34.8640i			1.70322i	−0.524179	+	0.851608i	$0.675628\pi$
$420$		0			0
$421$		−	5.59480i		−	0.272674i	−0.990663	−	0.136337i	$-0.956467\pi$
$421$		−	5.59480i		−	0.272674i	0.990663	−	0.136337i	$-0.0435330\pi$
$422$	−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	$0.0162876\pi$
$439$			2.14328i			0.102293i	−0.998691	+	0.0511465i	$0.983712\pi$
$440$	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	$0.311276\pi$
$443$			34.9106i			1.65865i	−0.558765	+	0.829326i	$0.688724\pi$
$444$		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	$-0.709499\pi$
$449$		−	33.5270i		−	1.58224i	0.611662	−	0.791119i	$-0.290501\pi$
$450$		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	$-0.902702\pi$
$463$		−	12.9506i		−	0.601864i	0.953646	−	0.300932i	$-0.0972978\pi$
$464$	−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	$-0.888980\pi$
$467$		−	14.7706i		−	0.683500i	0.939791	−	0.341750i	$-0.111020\pi$
$468$		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	$0.146029\pi$
$487$			19.5452i			0.885677i	−0.896601	+	0.442839i	$0.853971\pi$
$488$	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	$0.0392222\pi$
$491$			5.44694i			0.245817i	−0.992418	+	0.122908i	$0.960778\pi$
$492$		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	$0.0379424\pi$
$521$			5.42869i			0.237835i	−0.992904	+	0.118918i	$0.962058\pi$
$522$		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	$-0.896513\pi$
$541$		−	14.8589i		−	0.638833i	0.947614	−	0.319416i	$-0.103487\pi$
$542$	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	$0.245527\pi$
$563$			33.0810i			1.39420i	−0.716974	+	0.697100i	$0.754473\pi$
$564$		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	$0.229042\pi$
$569$			31.4417i			1.31810i	−0.752098	+	0.659051i	$0.770958\pi$
$570$		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	$-0.915512\pi$
$587$		−	12.7111i		−	0.524645i	0.964980	−	0.262323i	$-0.0844885\pi$
$588$		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	$-0.812165\pi$
$593$		−	27.1007i		−	1.11289i	0.830884	−	0.556446i	$-0.187835\pi$
$594$		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	$0.148112\pi$
$607$			22.1095i			0.897395i	−0.893684	+	0.448698i	$0.851888\pi$
$608$	−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	$-0.614184\pi$
$613$		−	46.3657i		−	1.87269i	0.351076	−	0.936347i	$-0.385816\pi$
$614$	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	$-0.812442\pi$
$617$		−	27.6077i		−	1.11145i	0.831368	−	0.555723i	$-0.187558\pi$
$618$		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	$-0.970783\pi$
$631$		−	4.60487i		−	0.183317i	0.995791	−	0.0916585i	$-0.0292168\pi$
$632$	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	$0.0291051\pi$
$641$			4.62353i			0.182618i	−0.995823	+	0.0913091i	$0.970895\pi$
$642$		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	$0.0854855\pi$
$659$			13.6233i			0.530688i	−0.964154	+	0.265344i	$0.914515\pi$
$660$		0			0
$661$			23.0462i			0.896394i	0.893935	+	0.448197i	$0.147934\pi$
$661$			23.0462i			0.896394i	−0.893935	+	0.448197i	$0.852066\pi$
$662$	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	$0.0891293\pi$
$683$			14.4451i			0.552727i	−0.961053	+	0.276363i	$0.910871\pi$
$684$		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	$-0.833524\pi$
$709$		−	26.5994i		−	0.998963i	0.866324	−	0.499482i	$-0.166476\pi$
$710$	−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	$-0.872458\pi$
$727$		−	21.0337i		−	0.780098i	0.920794	−	0.390049i	$-0.127542\pi$
$728$	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	$-0.860583\pi$
$733$		−	22.9654i		−	0.848245i	0.905605	−	0.424122i	$-0.139417\pi$
$734$	−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	$-0.855117\pi$
$751$		−	24.0944i		−	0.879216i	0.898190	−	0.439608i	$-0.144883\pi$
$752$	−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	$0.142075\pi$
$757$			23.7535i			0.863337i	−0.902032	+	0.431668i	$0.857925\pi$
$758$	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	$-0.824508\pi$
$761$		−	28.9002i		−	1.04763i	0.851832	−	0.523816i	$-0.175492\pi$
$762$		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	$-0.812463\pi$
$809$		−	31.6096i		−	1.11133i	0.831405	−	0.555666i	$-0.187537\pi$
$810$		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	$0.272579\pi$
$823$			43.3444i			1.51089i	−0.655212	+	0.755445i	$0.727421\pi$
$824$	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	$-0.900772\pi$
$827$		−	17.6404i		−	0.613416i	0.951804	−	0.306708i	$-0.0992276\pi$
$828$		0			0
$829$			10.3644i			0.359972i	0.983669	+	0.179986i	$0.0576052\pi$
$829$			10.3644i			0.359972i	−0.983669	+	0.179986i	$0.942395\pi$
$830$	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	$-0.842547\pi$
$853$		−	27.7299i		−	0.949455i	0.880133	−	0.474728i	$-0.157453\pi$
$854$	−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	$0.0102357\pi$
$857$			1.88241i			0.0643020i	−0.999483	+	0.0321510i	$0.989764\pi$
$858$		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	$0.0121974\pi$
$877$			2.26903i			0.0766195i	−0.999266	+	0.0383098i	$0.987803\pi$
$878$	−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	$0.0565727\pi$
$881$			10.4951i			0.353588i	−0.984248	+	0.176794i	$0.943427\pi$
$882$		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	$0.320067\pi$
$919$			51.1984i			1.68888i	−0.535650	+	0.844440i	$0.679933\pi$
$920$	−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	$0.169064\pi$
$929$			30.8763i			1.01302i	−0.862235	+	0.506509i	$0.830936\pi$
$930$		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	$0.0872925\pi$
$947$			16.6676i			0.541626i	−0.962632	+	0.270813i	$0.912708\pi$
$948$		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	$-0.898969\pi$
$953$		−	19.2692i		−	0.624192i	0.950051	−	0.312096i	$-0.101031\pi$
$954$		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	$0.326573\pi$
$967$			53.1884i			1.71042i	−0.518279	+	0.855211i	$0.673427\pi$
$968$	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	$0.172778\pi$
$971$			32.1913i			1.03307i	−0.856266	+	0.516534i	$0.827222\pi$
$972$		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	$-0.764367\pi$
$977$		−	42.1645i		−	1.34896i	0.738292	−	0.674481i	$-0.235633\pi$
$978$		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	$-0.739734\pi$
$991$		−	45.9321i		−	1.45908i	0.683937	−	0.729541i	$-0.260266\pi$
$992$	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	$-0.936942\pi$
$997$		−	12.4285i		−	0.393616i	0.980442	−	0.196808i	$-0.0630576\pi$
$998$	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.755.46	yes	48
3.2	odd	2	inner	936.2.j.a.755.3	✓	48
4.3	odd	2		3744.2.j.a.2159.39		48
8.3	odd	2	inner	936.2.j.a.755.4	yes	48
8.5	even	2		3744.2.j.a.2159.10		48
12.11	even	2		3744.2.j.a.2159.9		48
24.5	odd	2		3744.2.j.a.2159.40		48
24.11	even	2	inner	936.2.j.a.755.45	yes	48

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

Groups

Database

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