LMFDB - Embedded newform 1280.2.j.d.63.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(63,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,-32,0,0,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.6
Character	$\chi$	$=$	1280.63
Dual form			1280.2.j.d.447.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.939635i q^{3} +(-0.792335 + 2.09098i) q^{5} +(1.01861 - 1.01861i) q^{7} +2.11709 q^{9} +(-3.22205 + 3.22205i) q^{11} +5.40928 q^{13} +(1.96476 + 0.744506i) q^{15} +(-3.10743 + 3.10743i) q^{17} +(-5.93316 + 5.93316i) q^{19} +(-0.957123 - 0.957123i) q^{21} +(-2.19117 - 2.19117i) q^{23} +(-3.74441 - 3.31352i) q^{25} -4.80819i q^{27} +(2.79693 + 2.79693i) q^{29} -1.58447i q^{31} +(3.02755 + 3.02755i) q^{33} +(1.32282 + 2.93698i) q^{35} -1.28350 q^{37} -5.08275i q^{39} +2.45299i q^{41} +6.78310 q^{43} +(-1.67744 + 4.42679i) q^{45} +(4.21863 + 4.21863i) q^{47} +4.92486i q^{49} +(2.91985 + 2.91985i) q^{51} +13.6734i q^{53} +(-4.18430 - 9.29019i) q^{55} +(5.57500 + 5.57500i) q^{57} +(1.51289 + 1.51289i) q^{59} +(0.215294 - 0.215294i) q^{61} +(2.15649 - 2.15649i) q^{63} +(-4.28597 + 11.3107i) q^{65} -10.0394 q^{67} +(-2.05890 + 2.05890i) q^{69} -2.01032 q^{71} +(0.130678 - 0.130678i) q^{73} +(-3.11350 + 3.51838i) q^{75} +6.56403i q^{77} +13.2101 q^{79} +1.83331 q^{81} +8.24281i q^{83} +(-4.03546 - 8.95972i) q^{85} +(2.62809 - 2.62809i) q^{87} -1.49612 q^{89} +(5.50996 - 5.50996i) q^{91} -1.48882 q^{93} +(-7.70508 - 17.1072i) q^{95} +(6.11613 - 6.11613i) q^{97} +(-6.82135 + 6.82135i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) $ 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	0.939635i		−	0.542499i	−0.962509	−	0.271249i	$-0.912563\pi$
$3$		−	0.939635i		−	0.542499i	0.962509	−	0.271249i	$-0.0874368\pi$
$4$		0			0
$5$	−0.792335	+	2.09098i	−0.354343	+	0.935115i
$5$	−0.792335	+	2.09098i	−0.354343	+	0.935115i
$6$		0			0
$7$	1.01861	−	1.01861i	0.384999	−	0.384999i	−0.487900	−	0.872899i	$-0.662237\pi$
$7$	1.01861	−	1.01861i	0.384999	−	0.384999i	0.872899	+	0.487900i	$0.162237\pi$
$8$		0			0
$9$	2.11709			0.705695
$10$		0			0
$11$	−3.22205	+	3.22205i	−0.971484	+	0.971484i	−0.999605	−	0.0281203i	$-0.991048\pi$
$11$	−3.22205	+	3.22205i	−0.971484	+	0.971484i	0.0281203	+	0.999605i	$0.491048\pi$
$12$		0			0
$13$	5.40928			1.50027			0.750133	−	0.661287i	$-0.229990\pi$
$13$	5.40928			1.50027			0.750133	+	0.661287i	$0.229990\pi$
$14$		0			0
$15$	1.96476	+	0.744506i	0.507299	+	0.192231i
$16$		0			0
$17$	−3.10743	+	3.10743i	−0.753664	+	0.753664i	−0.975161	−	0.221497i	$-0.928906\pi$
$17$	−3.10743	+	3.10743i	−0.753664	+	0.753664i	0.221497	+	0.975161i	$0.428906\pi$
$18$		0			0
$19$	−5.93316	+	5.93316i	−1.36116	+	1.36116i	−0.488718	+	0.872442i	$0.662535\pi$
$19$	−5.93316	+	5.93316i	−1.36116	+	1.36116i	−0.872442	+	0.488718i	$0.837465\pi$
$20$		0			0
$21$	−0.957123	−	0.957123i	−0.208861	−	0.208861i
$22$		0			0
$23$	−2.19117	−	2.19117i	−0.456890	−	0.456890i	0.440743	−	0.897633i	$-0.354715\pi$
$23$	−2.19117	−	2.19117i	−0.456890	−	0.456890i	−0.897633	+	0.440743i	$0.854715\pi$
$24$		0			0
$25$	−3.74441	−	3.31352i	−0.748882	−	0.662703i
$26$		0			0
$27$		−	4.80819i		−	0.925337i
$28$		0			0
$29$	2.79693	+	2.79693i	0.519377	+	0.519377i	0.917383	−	0.398006i	$-0.130298\pi$
$29$	2.79693	+	2.79693i	0.519377	+	0.519377i	−0.398006	+	0.917383i	$0.630298\pi$
$30$		0			0
$31$		−	1.58447i		−	0.284578i	−0.989825	−	0.142289i	$-0.954554\pi$
$31$		−	1.58447i		−	0.284578i	0.989825	−	0.142289i	$-0.0454463\pi$
$32$		0			0
$33$	3.02755	+	3.02755i	0.527029	+	0.527029i
$34$		0			0
$35$	1.32282	+	2.93698i	0.223597	+	0.496440i
$36$		0			0
$37$	−1.28350			−0.211006			−0.105503	−	0.994419i	$-0.533645\pi$
$37$	−1.28350			−0.211006			−0.105503	+	0.994419i	$0.533645\pi$
$38$		0			0
$39$		−	5.08275i		−	0.813892i
$40$		0			0
$41$			2.45299i			0.383092i	0.981484	+	0.191546i	$0.0613502\pi$
$41$			2.45299i			0.383092i	−0.981484	+	0.191546i	$0.938650\pi$
$42$		0			0
$43$	6.78310			1.03441			0.517207	−	0.855860i	$-0.326972\pi$
$43$	6.78310			1.03441			0.517207	+	0.855860i	$0.326972\pi$
$44$		0			0
$45$	−1.67744	+	4.42679i	−0.250058	+	0.659907i
$46$		0			0
$47$	4.21863	+	4.21863i	0.615351	+	0.615351i	0.944335	−	0.328985i	$-0.106706\pi$
$47$	4.21863	+	4.21863i	0.615351	+	0.615351i	−0.328985	+	0.944335i	$0.606706\pi$
$48$		0			0
$49$			4.92486i			0.703552i
$50$		0			0
$51$	2.91985	+	2.91985i	0.408861	+	0.408861i
$52$		0			0
$53$			13.6734i			1.87818i	0.343665	+	0.939092i	$0.388332\pi$
$53$			13.6734i			1.87818i	−0.343665	+	0.939092i	$0.611668\pi$
$54$		0			0
$55$	−4.18430	−	9.29019i	−0.564211	−	1.25269i
$56$		0			0
$57$	5.57500	+	5.57500i	0.738427	+	0.738427i
$58$		0			0
$59$	1.51289	+	1.51289i	0.196961	+	0.196961i	0.798696	−	0.601735i	$-0.205524\pi$
$59$	1.51289	+	1.51289i	0.196961	+	0.196961i	−0.601735	+	0.798696i	$0.705524\pi$
$60$		0			0
$61$	0.215294	−	0.215294i	0.0275656	−	0.0275656i	−0.693190	−	0.720755i	$-0.743795\pi$
$61$	0.215294	−	0.215294i	0.0275656	−	0.0275656i	0.720755	+	0.693190i	$0.243795\pi$
$62$		0			0
$63$	2.15649	−	2.15649i	0.271692	−	0.271692i
$64$		0			0
$65$	−4.28597	+	11.3107i	−0.531609	+	1.40292i
$66$		0			0
$67$	−10.0394			−1.22651			−0.613253	−	0.789887i	$-0.710139\pi$
$67$	−10.0394			−1.22651			−0.613253	+	0.789887i	$0.710139\pi$
$68$		0			0
$69$	−2.05890	+	2.05890i	−0.247862	+	0.247862i
$70$		0			0
$71$	−2.01032			−0.238582			−0.119291	−	0.992859i	$-0.538062\pi$
$71$	−2.01032			−0.238582			−0.119291	+	0.992859i	$0.538062\pi$
$72$		0			0
$73$	0.130678	−	0.130678i	0.0152947	−	0.0152947i	−0.699418	−	0.714713i	$-0.746557\pi$
$73$	0.130678	−	0.130678i	0.0152947	−	0.0152947i	0.714713	+	0.699418i	$0.246557\pi$
$74$		0			0
$75$	−3.11350	+	3.51838i	−0.359516	+	0.406267i
$76$		0			0
$77$			6.56403i			0.748041i
$78$		0			0
$79$	13.2101			1.48626			0.743128	−	0.669150i	$-0.233341\pi$
$79$	13.2101			1.48626			0.743128	+	0.669150i	$0.233341\pi$
$80$		0			0
$81$	1.83331			0.203701
$82$		0			0
$83$			8.24281i			0.904766i	0.891824	+	0.452383i	$0.149426\pi$
$83$			8.24281i			0.904766i	−0.891824	+	0.452383i	$0.850574\pi$
$84$		0			0
$85$	−4.03546	−	8.95972i	−0.437707	−	0.971818i
$86$		0			0
$87$	2.62809	−	2.62809i	0.281761	−	0.281761i
$88$		0			0
$89$	−1.49612			−0.158588			−0.0792942	−	0.996851i	$-0.525267\pi$
$89$	−1.49612			−0.158588			−0.0792942	+	0.996851i	$0.525267\pi$
$90$		0			0
$91$	5.50996	−	5.50996i	0.577601	−	0.577601i
$92$		0			0
$93$	−1.48882			−0.154383
$94$		0			0
$95$	−7.70508	−	17.1072i	−0.790524	−	1.75516i
$96$		0			0
$97$	6.11613	−	6.11613i	0.620999	−	0.620999i	−0.324788	−	0.945787i	$-0.605293\pi$
$97$	6.11613	−	6.11613i	0.620999	−	0.620999i	0.945787	+	0.324788i	$0.105293\pi$
$98$		0			0
$99$	−6.82135	+	6.82135i	−0.685572	+	0.685572i
$100$		0			0
$101$	−8.76147	−	8.76147i	−0.871799	−	0.871799i	0.120869	−	0.992668i	$-0.461432\pi$
$101$	−8.76147	−	8.76147i	−0.871799	−	0.871799i	−0.992668	+	0.120869i	$0.961432\pi$
$102$		0			0
$103$	5.89018	+	5.89018i	0.580377	+	0.580377i	0.935007	−	0.354630i	$-0.115393\pi$
$103$	5.89018	+	5.89018i	0.580377	+	0.580377i	−0.354630	+	0.935007i	$0.615393\pi$
$104$		0			0
$105$	2.75969	−	1.24296i	0.269318	−	0.121301i
$106$		0			0
$107$			7.97349i			0.770827i	0.922744	+	0.385413i	$0.125941\pi$
$107$			7.97349i			0.770827i	−0.922744	+	0.385413i	$0.874059\pi$
$108$		0			0
$109$	2.76833	+	2.76833i	0.265158	+	0.265158i	0.827146	−	0.561988i	$-0.189963\pi$
$109$	2.76833	+	2.76833i	0.265158	+	0.265158i	−0.561988	+	0.827146i	$0.689963\pi$
$110$		0			0
$111$			1.20602i			0.114471i
$112$		0			0
$113$	11.8837	+	11.8837i	1.11793	+	1.11793i	0.992045	+	0.125881i	$0.0401758\pi$
$113$	11.8837	+	11.8837i	1.11793	+	1.11793i	0.125881	+	0.992045i	$0.459824\pi$
$114$		0			0
$115$	6.31783	−	2.84555i	0.589141	−	0.265349i
$116$		0			0
$117$	11.4519			1.05873
$118$		0			0
$119$			6.33054i			0.580319i
$120$		0			0
$121$		−	9.76320i		−	0.887563i
$122$		0			0
$123$	2.30491			0.207827
$124$		0			0
$125$	9.89533	−	5.20408i	0.885065	−	0.465467i
$126$		0			0
$127$	7.30101	+	7.30101i	0.647860	+	0.647860i	0.952476	−	0.304615i	$-0.0985279\pi$
$127$	7.30101	+	7.30101i	0.647860	+	0.647860i	−0.304615	+	0.952476i	$0.598528\pi$
$128$		0			0
$129$		−	6.37364i		−	0.561168i
$130$		0			0
$131$	−7.57527	−	7.57527i	−0.661854	−	0.661854i	0.293963	−	0.955817i	$-0.405026\pi$
$131$	−7.57527	−	7.57527i	−0.661854	−	0.661854i	−0.955817	+	0.293963i	$0.905026\pi$
$132$		0			0
$133$			12.0872i			1.04809i
$134$		0			0
$135$	10.0538	+	3.80970i	0.865297	+	0.327887i
$136$		0			0
$137$	−6.67718	−	6.67718i	−0.570470	−	0.570470i	0.361790	−	0.932260i	$-0.382166\pi$
$137$	−6.67718	−	6.67718i	−0.570470	−	0.570470i	−0.932260	+	0.361790i	$0.882166\pi$
$138$		0			0
$139$	−6.78143	−	6.78143i	−0.575193	−	0.575193i	0.358382	−	0.933575i	$-0.383329\pi$
$139$	−6.78143	−	6.78143i	−0.575193	−	0.575193i	−0.933575	+	0.358382i	$0.883329\pi$
$140$		0			0
$141$	3.96397	−	3.96397i	0.333827	−	0.333827i
$142$		0			0
$143$	−17.4290	+	17.4290i	−1.45748	+	1.45748i
$144$		0			0
$145$	−8.06443	+	3.63222i	−0.669715	+	0.301640i
$146$		0			0
$147$	4.62757			0.381676
$148$		0			0
$149$	3.92575	−	3.92575i	0.321610	−	0.321610i	−0.527775	−	0.849384i	$-0.676973\pi$
$149$	3.92575	−	3.92575i	0.321610	−	0.321610i	0.849384	+	0.527775i	$0.176973\pi$
$150$		0			0
$151$	−16.4839			−1.34144			−0.670722	−	0.741709i	$-0.734016\pi$
$151$	−16.4839			−1.34144			−0.670722	+	0.741709i	$0.734016\pi$
$152$		0			0
$153$	−6.57871	+	6.57871i	−0.531857	+	0.531857i
$154$		0			0
$155$	3.31309	+	1.25543i	0.266114	+	0.100838i
$156$		0			0
$157$		−	7.11211i		−	0.567608i	−0.958882	−	0.283804i	$-0.908403\pi$
$157$		−	7.11211i		−	0.567608i	0.958882	−	0.283804i	$-0.0915965\pi$
$158$		0			0
$159$	12.8480			1.01891
$160$		0			0
$161$	−4.46390			−0.351804
$162$		0			0
$163$		−	19.9435i		−	1.56210i	−0.624470	−	0.781048i	$-0.714685\pi$
$163$		−	19.9435i		−	1.56210i	0.624470	−	0.781048i	$-0.285315\pi$
$164$		0			0
$165$	−8.72939	+	3.93172i	−0.679582	+	0.306084i
$166$		0			0
$167$	13.9919	−	13.9919i	1.08273	−	1.08273i	0.0864749	−	0.996254i	$-0.472440\pi$
$167$	13.9919	−	13.9919i	1.08273	−	1.08273i	0.996254	−	0.0864749i	$-0.0275602\pi$
$168$		0			0
$169$	16.2604			1.25080
$170$		0			0
$171$	−12.5610	+	12.5610i	−0.960564	+	0.960564i
$172$		0			0
$173$	−10.4459			−0.794185			−0.397093	−	0.917779i	$-0.629981\pi$
$173$	−10.4459			−0.794185			−0.397093	+	0.917779i	$0.629981\pi$
$174$		0			0
$175$	−7.18928	+	0.438912i	−0.543459	+	0.0331786i
$176$		0			0
$177$	1.42156	−	1.42156i	0.106851	−	0.106851i
$178$		0			0
$179$	6.42941	−	6.42941i	0.480557	−	0.480557i	−0.424753	−	0.905309i	$-0.639639\pi$
$179$	6.42941	−	6.42941i	0.480557	−	0.480557i	0.905309	+	0.424753i	$0.139639\pi$
$180$		0			0
$181$	−4.96413	−	4.96413i	−0.368981	−	0.368981i	0.498125	−	0.867105i	$-0.334022\pi$
$181$	−4.96413	−	4.96413i	−0.368981	−	0.368981i	−0.867105	+	0.498125i	$0.834022\pi$
$182$		0			0
$183$	−0.202298	−	0.202298i	−0.0149543	−	0.0149543i
$184$		0			0
$185$	1.01696	−	2.68378i	0.0747687	−	0.197315i
$186$		0			0
$187$		−	20.0246i		−	1.46434i
$188$		0			0
$189$	−4.89768	−	4.89768i	−0.356254	−	0.356254i
$190$		0			0
$191$		−	24.2722i		−	1.75628i	−0.478408	−	0.878138i	$-0.658786\pi$
$191$		−	24.2722i		−	1.75628i	0.478408	−	0.878138i	$-0.341214\pi$
$192$		0			0
$193$	−3.89887	−	3.89887i	−0.280647	−	0.280647i	0.552720	−	0.833367i	$-0.313590\pi$
$193$	−3.89887	−	3.89887i	−0.280647	−	0.280647i	−0.833367	+	0.552720i	$0.813590\pi$
$194$		0			0
$195$	10.6279	+	4.02725i	0.761083	+	0.288397i
$196$		0			0
$197$	18.2875			1.30293			0.651466	−	0.758678i	$-0.274154\pi$
$197$	18.2875			1.30293			0.651466	+	0.758678i	$0.274154\pi$
$198$		0			0
$199$			0.848017i			0.0601143i	0.999548	+	0.0300572i	$0.00956893\pi$
$199$			0.848017i			0.0601143i	−0.999548	+	0.0300572i	$0.990431\pi$
$200$		0			0
$201$			9.43335i			0.665377i
$202$		0			0
$203$	5.69797			0.399919
$204$		0			0
$205$	−5.12915	−	1.94359i	−0.358236	−	0.135746i
$206$		0			0
$207$	−4.63889	−	4.63889i	−0.322425	−	0.322425i
$208$		0			0
$209$		−	38.2339i		−	2.64469i
$210$		0			0
$211$	14.9631	+	14.9631i	1.03011	+	1.03011i	0.999533	+	0.0305732i	$0.00973327\pi$
$211$	14.9631	+	14.9631i	1.03011	+	1.03011i	0.0305732	+	0.999533i	$0.490267\pi$
$212$		0			0
$213$			1.88897i			0.129430i
$214$		0			0
$215$	−5.37449	+	14.1833i	−0.366537	+	0.967296i
$216$		0			0
$217$	−1.61395	−	1.61395i	−0.109562	−	0.109562i
$218$		0			0
$219$	−0.122790	−	0.122790i	−0.00829737	−	0.00829737i
$220$		0			0
$221$	−16.8090	+	16.8090i	−1.13070	+	1.13070i
$222$		0			0
$223$	−15.6462	+	15.6462i	−1.04775	+	1.04775i	−0.0489455	+	0.998801i	$0.515586\pi$
$223$	−15.6462	+	15.6462i	−1.04775	+	1.04775i	−0.998801	+	0.0489455i	$0.984414\pi$
$224$		0			0
$225$	−7.92724	−	7.01500i	−0.528482	−	0.467667i
$226$		0			0
$227$	−7.18645			−0.476981			−0.238491	−	0.971145i	$-0.576653\pi$
$227$	−7.18645			−0.476981			−0.238491	+	0.971145i	$0.576653\pi$
$228$		0			0
$229$	19.3337	−	19.3337i	1.27761	−	1.27761i	0.335603	−	0.942004i	$-0.391060\pi$
$229$	19.3337	−	19.3337i	1.27761	−	1.27761i	0.942004	−	0.335603i	$-0.108940\pi$
$230$		0			0
$231$	6.16779			0.405811
$232$		0			0
$233$	−14.5796	+	14.5796i	−0.955143	+	0.955143i	−0.999036	−	0.0438933i	$-0.986024\pi$
$233$	−14.5796	+	14.5796i	−0.955143	+	0.955143i	0.0438933	+	0.999036i	$0.486024\pi$
$234$		0			0
$235$	−12.1637	+	5.47851i	−0.793469	+	0.357379i
$236$		0			0
$237$		−	12.4127i		−	0.806291i
$238$		0			0
$239$	−5.38456			−0.348298			−0.174149	−	0.984719i	$-0.555717\pi$
$239$	−5.38456			−0.348298			−0.174149	+	0.984719i	$0.555717\pi$
$240$		0			0
$241$	−19.4003			−1.24968			−0.624841	−	0.780752i	$-0.714836\pi$
$241$	−19.4003			−1.24968			−0.624841	+	0.780752i	$0.714836\pi$
$242$		0			0
$243$		−	16.1472i		−	1.03584i
$244$		0			0
$245$	−10.2978	−	3.90214i	−0.657902	−	0.249299i
$246$		0			0
$247$	−32.0941	+	32.0941i	−2.04210	+	2.04210i
$248$		0			0
$249$	7.74523			0.490834
$250$		0			0
$251$	−6.79393	+	6.79393i	−0.428829	+	0.428829i	−0.888229	−	0.459400i	$-0.848064\pi$
$251$	−6.79393	+	6.79393i	−0.428829	+	0.428829i	0.459400	+	0.888229i	$0.348064\pi$
$252$		0			0
$253$	14.1201			0.887723
$254$		0			0
$255$	−8.41887	+	3.79186i	−0.527210	+	0.237455i
$256$		0			0
$257$	9.57720	−	9.57720i	0.597409	−	0.597409i	−0.342213	−	0.939622i	$-0.611177\pi$
$257$	9.57720	−	9.57720i	0.597409	−	0.597409i	0.939622	+	0.342213i	$0.111177\pi$
$258$		0			0
$259$	−1.30739	+	1.30739i	−0.0812372	+	0.0812372i
$260$		0			0
$261$	5.92134	+	5.92134i	0.366522	+	0.366522i
$262$		0			0
$263$	1.36034	+	1.36034i	0.0838820	+	0.0838820i	0.747803	−	0.663921i	$-0.231109\pi$
$263$	1.36034	+	1.36034i	0.0838820	+	0.0838820i	−0.663921	+	0.747803i	$0.731109\pi$
$264$		0			0
$265$	−28.5908	−	10.8339i	−1.75632	−	0.665522i
$266$		0			0
$267$			1.40581i			0.0860340i
$268$		0			0
$269$	−12.2019	−	12.2019i	−0.743961	−	0.743961i	0.229377	−	0.973338i	$-0.426331\pi$
$269$	−12.2019	−	12.2019i	−0.743961	−	0.743961i	−0.973338	+	0.229377i	$0.926331\pi$
$270$		0			0
$271$			20.2941i			1.23278i	0.787442	+	0.616388i	$0.211405\pi$
$271$			20.2941i			1.23278i	−0.787442	+	0.616388i	$0.788595\pi$
$272$		0			0
$273$	−5.17735	−	5.17735i	−0.313347	−	0.313347i
$274$		0			0
$275$	22.7410	−	1.38836i	1.37133	−	0.0837210i
$276$		0			0
$277$	−3.35288			−0.201455			−0.100728	−	0.994914i	$-0.532117\pi$
$277$	−3.35288			−0.201455			−0.100728	+	0.994914i	$0.532117\pi$
$278$		0			0
$279$		−	3.35445i		−	0.200826i
$280$		0			0
$281$			6.11851i			0.365000i	0.983206	+	0.182500i	$0.0584189\pi$
$281$			6.11851i			0.365000i	−0.983206	+	0.182500i	$0.941581\pi$
$282$		0			0
$283$	28.6325			1.70203			0.851013	−	0.525145i	$-0.175989\pi$
$283$	28.6325			1.70203			0.851013	+	0.525145i	$0.175989\pi$
$284$		0			0
$285$	−16.0745	+	7.23996i	−0.952171	+	0.428858i
$286$		0			0
$287$	2.49864	+	2.49864i	0.147490	+	0.147490i
$288$		0			0
$289$		−	2.31230i		−	0.136017i
$290$		0			0
$291$	−5.74693	−	5.74693i	−0.336891	−	0.336891i
$292$		0			0
$293$			8.82401i			0.515504i	0.966211	+	0.257752i	$0.0829818\pi$
$293$			8.82401i			0.515504i	−0.966211	+	0.257752i	$0.917018\pi$
$294$		0			0
$295$	−4.36213	+	1.96470i	−0.253973	+	0.114389i
$296$		0			0
$297$	15.4922	+	15.4922i	0.898951	+	0.898951i
$298$		0			0
$299$	−11.8526	−	11.8526i	−0.685456	−	0.685456i
$300$		0			0
$301$	6.90935	−	6.90935i	0.398248	−	0.398248i
$302$		0			0
$303$	−8.23259	+	8.23259i	−0.472950	+	0.472950i
$304$		0			0
$305$	0.279591	+	0.620762i	0.0160093	+	0.0355447i
$306$		0			0
$307$	−10.6320			−0.606800			−0.303400	−	0.952863i	$-0.598122\pi$
$307$	−10.6320			−0.606800			−0.303400	+	0.952863i	$0.598122\pi$
$308$		0			0
$309$	5.53462	−	5.53462i	0.314854	−	0.314854i
$310$		0			0
$311$	21.0188			1.19187			0.595934	−	0.803033i	$-0.296782\pi$
$311$	21.0188			1.19187			0.595934	+	0.803033i	$0.296782\pi$
$312$		0			0
$313$	5.56786	−	5.56786i	0.314714	−	0.314714i	−0.532018	−	0.846733i	$-0.678566\pi$
$313$	5.56786	−	5.56786i	0.314714	−	0.314714i	0.846733	+	0.532018i	$0.178566\pi$
$314$		0			0
$315$	2.80052	+	6.21784i	0.157791	+	0.350335i
$316$		0			0
$317$		−	1.15926i		−	0.0651107i	−0.999470	−	0.0325553i	$-0.989635\pi$
$317$		−	1.15926i		−	0.0651107i	0.999470	−	0.0325553i	$-0.0103645\pi$
$318$		0			0
$319$	−18.0237			−1.00913
$320$		0			0
$321$	7.49217			0.418172
$322$		0			0
$323$		−	36.8738i		−	2.05171i
$324$		0			0
$325$	−20.2546	−	17.9238i	−1.12352	−	0.994231i
$326$		0			0
$327$	2.60122	−	2.60122i	0.143848	−	0.143848i
$328$		0			0
$329$	8.59429			0.473819
$330$		0			0
$331$	10.2111	−	10.2111i	0.561251	−	0.561251i	−0.368412	−	0.929663i	$-0.620098\pi$
$331$	10.2111	−	10.2111i	0.561251	−	0.561251i	0.929663	+	0.368412i	$0.120098\pi$
$332$		0			0
$333$	−2.71728			−0.148906
$334$		0			0
$335$	7.95455	−	20.9922i	0.434604	−	1.14692i
$336$		0			0
$337$	20.8943	−	20.8943i	1.13819	−	1.13819i	0.149412	−	0.988775i	$-0.452262\pi$
$337$	20.8943	−	20.8943i	1.13819	−	1.13819i	0.988775	−	0.149412i	$-0.0477380\pi$
$338$		0			0
$339$	11.1664	−	11.1664i	0.606473	−	0.606473i
$340$		0			0
$341$	5.10522	+	5.10522i	0.276463	+	0.276463i
$342$		0			0
$343$	12.1468	+	12.1468i	0.655865	+	0.655865i
$344$		0			0
$345$	−2.67378	−	5.93646i	−0.143951	−	0.319608i
$346$		0			0
$347$		−	8.32389i		−	0.446850i	−0.974721	−	0.223425i	$-0.928276\pi$
$347$		−	8.32389i		−	0.446850i	0.974721	−	0.223425i	$-0.0717237\pi$
$348$		0			0
$349$	−20.1777	−	20.1777i	−1.08009	−	1.08009i	−0.996501	−	0.0835867i	$-0.973362\pi$
$349$	−20.1777	−	20.1777i	−1.08009	−	1.08009i	−0.0835867	−	0.996501i	$-0.526638\pi$
$350$		0			0
$351$		−	26.0089i		−	1.38825i
$352$		0			0
$353$	0.383759	+	0.383759i	0.0204254	+	0.0204254i	0.717246	−	0.696820i	$-0.245403\pi$
$353$	0.383759	+	0.383759i	0.0204254	+	0.0204254i	−0.696820	+	0.717246i	$0.745403\pi$
$354$		0			0
$355$	1.59285	−	4.20355i	0.0845397	−	0.223101i
$356$		0			0
$357$	5.94839			0.314822
$358$		0			0
$359$			18.0846i			0.954469i	0.878776	+	0.477235i	$0.158361\pi$
$359$			18.0846i			0.954469i	−0.878776	+	0.477235i	$0.841639\pi$
$360$		0			0
$361$		−	51.4047i		−	2.70551i
$362$		0			0
$363$	−9.17384			−0.481502
$364$		0			0
$365$	0.169705	+	0.376787i	0.00888276	+	0.0197219i
$366$		0			0
$367$	13.2373	+	13.2373i	0.690979	+	0.690979i	0.962447	−	0.271468i	$-0.0875092\pi$
$367$	13.2373	+	13.2373i	0.690979	+	0.690979i	−0.271468	+	0.962447i	$0.587509\pi$
$368$		0			0
$369$			5.19319i			0.270347i
$370$		0			0
$371$	13.9279	+	13.9279i	0.723099	+	0.723099i
$372$		0			0
$373$		−	6.42208i		−	0.332523i	−0.986082	−	0.166261i	$-0.946830\pi$
$373$		−	6.42208i		−	0.332523i	0.986082	−	0.166261i	$-0.0531695\pi$
$374$		0			0
$375$	−4.88993	−	9.29800i	−0.252515	−	0.480147i
$376$		0			0
$377$	15.1294	+	15.1294i	0.779203	+	0.779203i
$378$		0			0
$379$	−8.86295	−	8.86295i	−0.455259	−	0.455259i	0.441837	−	0.897096i	$-0.354327\pi$
$379$	−8.86295	−	8.86295i	−0.455259	−	0.455259i	−0.897096	+	0.441837i	$0.854327\pi$
$380$		0			0
$381$	6.86029	−	6.86029i	0.351463	−	0.351463i
$382$		0			0
$383$	10.4938	−	10.4938i	0.536208	−	0.536208i	−0.386205	−	0.922413i	$-0.626214\pi$
$383$	10.4938	−	10.4938i	0.536208	−	0.536208i	0.922413	+	0.386205i	$0.126214\pi$
$384$		0			0
$385$	−13.7253	−	5.20091i	−0.699504	−	0.265063i
$386$		0			0
$387$	14.3604			0.729981
$388$		0			0
$389$	19.2034	−	19.2034i	0.973649	−	0.973649i	−0.0260124	−	0.999662i	$-0.508281\pi$
$389$	19.2034	−	19.2034i	0.973649	−	0.973649i	0.999662	+	0.0260124i	$0.00828093\pi$
$390$		0			0
$391$	13.6178			0.688683
$392$		0			0
$393$	−7.11799	+	7.11799i	−0.359055	+	0.359055i
$394$		0			0
$395$	−10.4669	+	27.6221i	−0.526644	+	1.38982i
$396$		0			0
$397$		−	7.01030i		−	0.351837i	−0.984405	−	0.175918i	$-0.943711\pi$
$397$		−	7.01030i		−	0.351837i	0.984405	−	0.175918i	$-0.0562895\pi$
$398$		0			0
$399$	11.3575			0.568587
$400$		0			0
$401$	−2.47101			−0.123396			−0.0616981	−	0.998095i	$-0.519652\pi$
$401$	−2.47101			−0.123396			−0.0616981	+	0.998095i	$0.519652\pi$
$402$		0			0
$403$		−	8.57082i		−	0.426943i
$404$		0			0
$405$	−1.45260	+	3.83342i	−0.0721801	+	0.190484i
$406$		0			0
$407$	4.13551	−	4.13551i	0.204989	−	0.204989i
$408$		0			0
$409$	−24.3365			−1.20336			−0.601680	−	0.798737i	$-0.705502\pi$
$409$	−24.3365			−1.20336			−0.601680	+	0.798737i	$0.705502\pi$
$410$		0			0
$411$	−6.27411	+	6.27411i	−0.309479	+	0.309479i
$412$		0			0
$413$	3.08208			0.151659
$414$		0			0
$415$	−17.2356	−	6.53107i	−0.846061	−	0.320598i
$416$		0			0
$417$	−6.37206	+	6.37206i	−0.312041	+	0.312041i
$418$		0			0
$419$	−16.9042	+	16.9042i	−0.825824	+	0.825824i	−0.986936	−	0.161112i	$-0.948492\pi$
$419$	−16.9042	+	16.9042i	−0.825824	+	0.825824i	0.161112	+	0.986936i	$0.448492\pi$
$420$		0			0
$421$	−12.9762	−	12.9762i	−0.632422	−	0.632422i	0.316253	−	0.948675i	$-0.397575\pi$
$421$	−12.9762	−	12.9762i	−0.632422	−	0.632422i	−0.948675	+	0.316253i	$0.897575\pi$
$422$		0			0
$423$	8.93120	+	8.93120i	0.434250	+	0.434250i
$424$		0			0
$425$	21.9320	−	1.33897i	1.06386	−	0.0649496i
$426$		0			0
$427$		−	0.438602i		−	0.0212255i
$428$		0			0
$429$	16.3769	+	16.3769i	0.790683	+	0.790683i
$430$		0			0
$431$			12.4393i			0.599182i	0.954068	+	0.299591i	$0.0968502\pi$
$431$			12.4393i			0.599182i	−0.954068	+	0.299591i	$0.903150\pi$
$432$		0			0
$433$	27.0966	+	27.0966i	1.30218	+	1.30218i	0.926919	+	0.375261i	$0.122447\pi$
$433$	27.0966	+	27.0966i	1.30218	+	1.30218i	0.375261	+	0.926919i	$0.377553\pi$
$434$		0			0
$435$	3.41296	+	7.57762i	0.163639	+	0.363319i
$436$		0			0
$437$	26.0011			1.24380
$438$		0			0
$439$		−	15.5428i		−	0.741816i	−0.928670	−	0.370908i	$-0.879047\pi$
$439$		−	15.5428i		−	0.741816i	0.928670	−	0.370908i	$-0.120953\pi$
$440$		0			0
$441$			10.4264i			0.496493i
$442$		0			0
$443$	−16.7942			−0.797917			−0.398959	−	0.916969i	$-0.630628\pi$
$443$	−16.7942			−0.797917			−0.398959	+	0.916969i	$0.630628\pi$
$444$		0			0
$445$	1.18543	−	3.12836i	0.0561947	−	0.148298i
$446$		0			0
$447$	−3.68877	−	3.68877i	−0.174473	−	0.174473i
$448$		0			0
$449$			4.54035i			0.214272i	0.994244	+	0.107136i	$0.0341681\pi$
$449$			4.54035i			0.214272i	−0.994244	+	0.107136i	$0.965832\pi$
$450$		0			0
$451$	−7.90365	−	7.90365i	−0.372168	−	0.372168i
$452$		0			0
$453$			15.4889i			0.727731i
$454$		0			0
$455$	7.15549	+	15.8870i	0.335454	+	0.744792i
$456$		0			0
$457$	−4.83585	−	4.83585i	−0.226212	−	0.226212i	0.584896	−	0.811108i	$-0.301135\pi$
$457$	−4.83585	−	4.83585i	−0.226212	−	0.226212i	−0.811108	+	0.584896i	$0.801135\pi$
$458$		0			0
$459$	14.9411	+	14.9411i	0.697393	+	0.697393i
$460$		0			0
$461$	−7.74413	+	7.74413i	−0.360680	+	0.360680i	−0.864063	−	0.503383i	$-0.832088\pi$
$461$	−7.74413	+	7.74413i	−0.360680	+	0.360680i	0.503383	+	0.864063i	$0.332088\pi$
$462$		0			0
$463$	−16.6931	+	16.6931i	−0.775795	+	0.775795i	−0.979113	−	0.203318i	$-0.934828\pi$
$463$	−16.6931	+	16.6931i	−0.775795	+	0.775795i	0.203318	+	0.979113i	$0.434828\pi$
$464$		0			0
$465$	1.17964	−	3.11309i	0.0547047	−	0.144366i
$466$		0			0
$467$	−23.9174			−1.10677			−0.553383	−	0.832927i	$-0.686663\pi$
$467$	−23.9174			−1.10677			−0.553383	+	0.832927i	$0.686663\pi$
$468$		0			0
$469$	−10.2262	+	10.2262i	−0.472203	+	0.472203i
$470$		0			0
$471$	−6.68279			−0.307927
$472$		0			0
$473$	−21.8555	+	21.8555i	−1.00492	+	1.00492i
$474$		0			0
$475$	41.8758	−	2.55655i	1.92139	−	0.117303i
$476$		0			0
$477$			28.9477i			1.32543i
$478$		0			0
$479$	25.0247			1.14341			0.571703	−	0.820460i	$-0.306283\pi$
$479$	25.0247			1.14341			0.571703	+	0.820460i	$0.306283\pi$
$480$		0			0
$481$	−6.94283			−0.316566
$482$		0			0
$483$			4.19443i			0.190853i
$484$		0			0
$485$	7.94269	+	17.6347i	0.360659	+	0.800753i
$486$		0			0
$487$	11.3049	−	11.3049i	0.512274	−	0.512274i	−0.402949	−	0.915223i	$-0.632015\pi$
$487$	11.3049	−	11.3049i	0.512274	−	0.512274i	0.915223	+	0.402949i	$0.132015\pi$
$488$		0			0
$489$	−18.7396			−0.847435
$490$		0			0
$491$	17.0233	−	17.0233i	0.768250	−	0.768250i	−0.209548	−	0.977798i	$-0.567199\pi$
$491$	17.0233	−	17.0233i	0.768250	−	0.768250i	0.977798	+	0.209548i	$0.0671993\pi$
$492$		0			0
$493$	−17.3825			−0.782870
$494$		0			0
$495$	−8.85853	−	19.6681i	−0.398161	−	0.884017i
$496$		0			0
$497$	−2.04774	+	2.04774i	−0.0918536	+	0.0918536i
$498$		0			0
$499$	−11.4673	+	11.4673i	−0.513347	+	0.513347i	−0.915550	−	0.402204i	$-0.868244\pi$
$499$	−11.4673	+	11.4673i	−0.513347	+	0.513347i	0.402204	+	0.915550i	$0.368244\pi$
$500$		0			0
$501$	−13.1473	−	13.1473i	−0.587379	−	0.587379i
$502$		0			0
$503$	−14.5339	−	14.5339i	−0.648033	−	0.648033i	0.304484	−	0.952517i	$-0.401516\pi$
$503$	−14.5339	−	14.5339i	−0.648033	−	0.648033i	−0.952517	+	0.304484i	$0.901516\pi$
$504$		0			0
$505$	25.2621	−	11.3781i	1.12415	−	0.506317i
$506$		0			0
$507$		−	15.2788i		−	0.678556i
$508$		0			0
$509$	12.9000	+	12.9000i	0.571783	+	0.571783i	0.932627	−	0.360843i	$-0.117511\pi$
$509$	12.9000	+	12.9000i	0.571783	+	0.571783i	−0.360843	+	0.932627i	$0.617511\pi$
$510$		0			0
$511$		−	0.266221i		−	0.0117769i
$512$		0			0
$513$	28.5278	+	28.5278i	1.25953	+	1.25953i
$514$		0			0
$515$	−16.9833	+	7.64927i	−0.748372	+	0.337067i
$516$		0			0
$517$	−27.1853			−1.19561
$518$		0			0
$519$			9.81531i			0.430844i
$520$		0			0
$521$			16.8361i			0.737601i	0.929509	+	0.368801i	$0.120231\pi$
$521$			16.8361i			0.737601i	−0.929509	+	0.368801i	$0.879769\pi$
$522$		0			0
$523$	5.88217			0.257209			0.128605	−	0.991696i	$-0.458950\pi$
$523$	5.88217			0.257209			0.128605	+	0.991696i	$0.458950\pi$
$524$		0			0
$525$	0.412417	+	6.75530i	0.0179993	+	0.294826i
$526$		0			0
$527$	4.92362	+	4.92362i	0.214476	+	0.214476i
$528$		0			0
$529$		−	13.3976i		−	0.582503i
$530$		0			0
$531$	3.20291	+	3.20291i	0.138994	+	0.138994i
$532$		0			0
$533$			13.2689i			0.574741i
$534$		0			0
$535$	−16.6724	−	6.31768i	−0.720812	−	0.273137i
$536$		0			0
$537$	−6.04130	−	6.04130i	−0.260701	−	0.260701i
$538$		0			0
$539$	−15.8681	−	15.8681i	−0.683489	−	0.683489i
$540$		0			0
$541$	25.5334	−	25.5334i	1.09777	−	1.09777i	0.103097	−	0.994671i	$-0.467125\pi$
$541$	25.5334	−	25.5334i	1.09777	−	1.09777i	0.994671	−	0.103097i	$-0.0328752\pi$
$542$		0			0
$543$	−4.66447	+	4.66447i	−0.200171	+	0.200171i
$544$		0			0
$545$	−7.98197	+	3.59508i	−0.341910	+	0.153996i
$546$		0			0
$547$	33.9517			1.45167			0.725835	−	0.687869i	$-0.241454\pi$
$547$	33.9517			1.45167			0.725835	+	0.687869i	$0.241454\pi$
$548$		0			0
$549$	0.455797	−	0.455797i	0.0194529	−	0.0194529i
$550$		0			0
$551$	−33.1892			−1.41391
$552$		0			0
$553$	13.4560	−	13.4560i	0.572207	−	0.572207i
$554$		0			0
$555$	−2.52177	−	0.955575i	−0.107043	−	0.0405619i
$556$		0			0
$557$		−	16.0858i		−	0.681576i	−0.940140	−	0.340788i	$-0.889306\pi$
$557$		−	16.0858i		−	0.681576i	0.940140	−	0.340788i	$-0.110694\pi$
$558$		0			0
$559$	36.6917			1.55190
$560$		0			0
$561$	−18.8158			−0.794405
$562$		0			0
$563$			25.0409i			1.05535i	0.849447	+	0.527675i	$0.176936\pi$
$563$			25.0409i			1.05535i	−0.849447	+	0.527675i	$0.823064\pi$
$564$		0			0
$565$	−34.2645	+	15.4328i	−1.44152	+	0.649261i
$566$		0			0
$567$	1.86743	−	1.86743i	0.0784248	−	0.0784248i
$568$		0			0
$569$	35.9948			1.50898			0.754490	−	0.656311i	$-0.227884\pi$
$569$	35.9948			1.50898			0.754490	+	0.656311i	$0.227884\pi$
$570$		0			0
$571$	2.90471	−	2.90471i	0.121558	−	0.121558i	−0.643711	−	0.765269i	$-0.722606\pi$
$571$	2.90471	−	2.90471i	0.121558	−	0.121558i	0.765269	+	0.643711i	$0.222606\pi$
$572$		0			0
$573$	−22.8070			−0.952777
$574$		0			0
$575$	0.944157	+	15.4651i	0.0393741	+	0.644939i
$576$		0			0
$577$	−16.2961	+	16.2961i	−0.678417	+	0.678417i	−0.959642	−	0.281225i	$-0.909259\pi$
$577$	−16.2961	+	16.2961i	−0.678417	+	0.678417i	0.281225	+	0.959642i	$0.409259\pi$
$578$		0			0
$579$	−3.66352	+	3.66352i	−0.152251	+	0.152251i
$580$		0			0
$581$	8.39622	+	8.39622i	0.348334	+	0.348334i
$582$		0			0
$583$	−44.0563	−	44.0563i	−1.82463	−	1.82463i
$584$		0			0
$585$	−9.07376	+	23.9458i	−0.375154	+	0.990035i
$586$		0			0
$587$			42.0558i			1.73583i	0.496716	+	0.867913i	$0.334539\pi$
$587$			42.0558i			1.73583i	−0.496716	+	0.867913i	$0.665461\pi$
$588$		0			0
$589$	9.40088	+	9.40088i	0.387357	+	0.387357i
$590$		0			0
$591$		−	17.1836i		−	0.706839i
$592$		0			0
$593$	−19.7600	−	19.7600i	−0.811446	−	0.811446i	0.173404	−	0.984851i	$-0.444523\pi$
$593$	−19.7600	−	19.7600i	−0.811446	−	0.811446i	−0.984851	+	0.173404i	$0.944523\pi$
$594$		0			0
$595$	−13.2370	−	5.01591i	−0.542665	−	0.205632i
$596$		0			0
$597$	0.796826			0.0326119
$598$		0			0
$599$		−	38.3344i		−	1.56630i	−0.621833	−	0.783150i	$-0.713612\pi$
$599$		−	38.3344i		−	1.56630i	0.621833	−	0.783150i	$-0.286388\pi$
$600$		0			0
$601$		−	1.37984i		−	0.0562849i	−0.999604	−	0.0281424i	$-0.991041\pi$
$601$		−	1.37984i		−	0.0562849i	0.999604	−	0.0281424i	$-0.00895920\pi$
$602$		0			0
$603$	−21.2542			−0.865539
$604$		0			0
$605$	20.4147	+	7.73573i	0.829974	+	0.314502i
$606$		0			0
$607$	24.1264	+	24.1264i	0.979261	+	0.979261i	0.999789	−	0.0205286i	$-0.00653491\pi$
$607$	24.1264	+	24.1264i	0.979261	+	0.979261i	−0.0205286	+	0.999789i	$0.506535\pi$
$608$		0			0
$609$		−	5.35401i		−	0.216955i
$610$		0			0
$611$	22.8198	+	22.8198i	0.923189	+	0.923189i
$612$		0			0
$613$			8.45490i			0.341490i	0.985315	+	0.170745i	$0.0546174\pi$
$613$			8.45490i			0.341490i	−0.985315	+	0.170745i	$0.945383\pi$
$614$		0			0
$615$	−1.82626	+	4.81953i	−0.0736421	+	0.194342i
$616$		0			0
$617$	2.55138	+	2.55138i	0.102715	+	0.102715i	0.756597	−	0.653882i	$-0.226861\pi$
$617$	2.55138	+	2.55138i	0.102715	+	0.102715i	−0.653882	+	0.756597i	$0.726861\pi$
$618$		0			0
$619$	−1.07954	−	1.07954i	−0.0433905	−	0.0433905i	0.685079	−	0.728469i	$-0.259768\pi$
$619$	−1.07954	−	1.07954i	−0.0433905	−	0.0433905i	−0.728469	+	0.685079i	$0.759768\pi$
$620$		0			0
$621$	−10.5356	+	10.5356i	−0.422777	+	0.422777i
$622$		0			0
$623$	−1.52396	+	1.52396i	−0.0610564	+	0.0610564i
$624$		0			0
$625$	3.04121	+	24.8143i	0.121648	+	0.992573i
$626$		0			0
$627$	−35.9259			−1.43474
$628$		0			0
$629$	3.98840	−	3.98840i	0.159028	−	0.159028i
$630$		0			0
$631$	10.8929			0.433638			0.216819	−	0.976212i	$-0.430432\pi$
$631$	10.8929			0.433638			0.216819	+	0.976212i	$0.430432\pi$
$632$		0			0
$633$	14.0599	−	14.0599i	0.558831	−	0.558831i
$634$		0			0
$635$	−21.0511	+	9.48144i	−0.835389	+	0.376259i
$636$		0			0
$637$			26.6400i			1.05551i
$638$		0			0
$639$	−4.25603			−0.168366
$640$		0			0
$641$	−5.90389			−0.233190			−0.116595	−	0.993180i	$-0.537198\pi$
$641$	−5.90389			−0.233190			−0.116595	+	0.993180i	$0.537198\pi$
$642$		0			0
$643$			18.5260i			0.730595i	0.930891	+	0.365297i	$0.119033\pi$
$643$			18.5260i			0.730595i	−0.930891	+	0.365297i	$0.880967\pi$
$644$		0			0
$645$	13.3272	+	5.05006i	0.524757	+	0.198846i
$646$		0			0
$647$	14.1074	−	14.1074i	0.554618	−	0.554618i	−0.373152	−	0.927770i	$-0.621723\pi$
$647$	14.1074	−	14.1074i	0.554618	−	0.554618i	0.927770	+	0.373152i	$0.121723\pi$
$648$		0			0
$649$	−9.74918			−0.382689
$650$		0			0
$651$	−1.51653	+	1.51653i	−0.0594374	+	0.0594374i
$652$		0			0
$653$	37.3232			1.46057			0.730285	−	0.683143i	$-0.239387\pi$
$653$	37.3232			1.46057			0.730285	+	0.683143i	$0.239387\pi$
$654$		0			0
$655$	21.8419	−	9.83760i	0.853434	−	0.384387i
$656$		0			0
$657$	0.276657	−	0.276657i	0.0107934	−	0.0107934i
$658$		0			0
$659$	−15.7382	+	15.7382i	−0.613075	+	0.613075i	−0.943746	−	0.330671i	$-0.892725\pi$
$659$	−15.7382	+	15.7382i	−0.613075	+	0.613075i	0.330671	+	0.943746i	$0.392725\pi$
$660$		0			0
$661$	8.03703	+	8.03703i	0.312604	+	0.312604i	0.845918	−	0.533313i	$-0.179053\pi$
$661$	8.03703	+	8.03703i	0.312604	+	0.312604i	−0.533313	+	0.845918i	$0.679053\pi$
$662$		0			0
$663$	15.7943	+	15.7943i	0.613401	+	0.613401i
$664$		0			0
$665$	−25.2740	−	9.57709i	−0.980085	−	0.371383i
$666$		0			0
$667$		−	12.2571i		−	0.474596i
$668$		0			0
$669$	14.7017	+	14.7017i	0.568401	+	0.568401i
$670$		0			0
$671$			1.38738i			0.0535591i
$672$		0			0
$673$	8.84337	+	8.84337i	0.340887	+	0.340887i	0.856701	−	0.515814i	$-0.172510\pi$
$673$	8.84337	+	8.84337i	0.340887	+	0.340887i	−0.515814	+	0.856701i	$0.672510\pi$
$674$		0			0
$675$	−15.9320	+	18.0038i	−0.613224	+	0.692968i
$676$		0			0
$677$	−20.3288			−0.781299			−0.390650	−	0.920539i	$-0.627750\pi$
$677$	−20.3288			−0.781299			−0.390650	+	0.920539i	$0.627750\pi$
$678$		0			0
$679$		−	12.4599i		−	0.478168i
$680$		0			0
$681$			6.75264i			0.258762i
$682$		0			0
$683$	34.6127			1.32442			0.662208	−	0.749320i	$-0.269619\pi$
$683$	34.6127			1.32442			0.662208	+	0.749320i	$0.269619\pi$
$684$		0			0
$685$	19.2524	−	8.67129i	0.735597	−	0.331313i
$686$		0			0
$687$	−18.1666	−	18.1666i	−0.693100	−	0.693100i
$688$		0			0
$689$			73.9633i			2.81778i
$690$		0			0
$691$	−5.37721	−	5.37721i	−0.204559	−	0.204559i	0.597391	−	0.801950i	$-0.296204\pi$
$691$	−5.37721	−	5.37721i	−0.204559	−	0.204559i	−0.801950	+	0.597391i	$0.796204\pi$
$692$		0			0
$693$			13.8966i			0.527889i
$694$		0			0
$695$	19.5530	−	8.80667i	0.741688	−	0.334056i
$696$		0			0
$697$	−7.62250	−	7.62250i	−0.288723	−	0.288723i
$698$		0			0
$699$	13.6995	+	13.6995i	0.518164	+	0.518164i
$700$		0			0
$701$	−18.8920	+	18.8920i	−0.713541	+	0.713541i	−0.967274	−	0.253733i	$-0.918341\pi$
$701$	−18.8920	+	18.8920i	−0.713541	+	0.713541i	0.253733	+	0.967274i	$0.418341\pi$
$702$		0			0
$703$	7.61522	−	7.61522i	0.287213	−	0.287213i
$704$		0			0
$705$	5.14780	+	11.4294i	0.193877	+	0.430456i
$706$		0			0
$707$	−17.8491			−0.671283
$708$		0			0
$709$	−15.8819	+	15.8819i	−0.596456	+	0.596456i	−0.939368	−	0.342911i	$-0.888587\pi$
$709$	−15.8819	+	15.8819i	−0.596456	+	0.596456i	0.342911	+	0.939368i	$0.388587\pi$
$710$		0			0
$711$	27.9670			1.04884
$712$		0			0
$713$	−3.47183	+	3.47183i	−0.130021	+	0.130021i
$714$		0			0
$715$	−22.6341	−	50.2533i	−0.846467	−	1.87937i
$716$		0			0
$717$			5.05952i			0.188951i
$718$		0			0
$719$	−21.7427			−0.810865			−0.405433	−	0.914125i	$-0.632879\pi$
$719$	−21.7427			−0.810865			−0.405433	+	0.914125i	$0.632879\pi$
$720$		0			0
$721$	11.9996			0.446889
$722$		0			0
$723$			18.2292i			0.677951i
$724$		0			0
$725$	−1.20517	−	19.7405i	−0.0447591	−	0.733144i
$726$		0			0
$727$	−7.65957	+	7.65957i	−0.284078	+	0.284078i	−0.834733	−	0.550655i	$-0.814378\pi$
$727$	−7.65957	+	7.65957i	−0.284078	+	0.284078i	0.550655	+	0.834733i	$0.314378\pi$
$728$		0			0
$729$	−9.67256			−0.358243
$730$		0			0
$731$	−21.0781	+	21.0781i	−0.779600	+	0.779600i
$732$		0			0
$733$	47.8143			1.76606			0.883030	−	0.469316i	$-0.155499\pi$
$733$	47.8143			1.76606			0.883030	+	0.469316i	$0.155499\pi$
$734$		0			0
$735$	−3.66659	+	9.67617i	−0.135244	+	0.356911i
$736$		0			0
$737$	32.3474	−	32.3474i	1.19153	−	1.19153i
$738$		0			0
$739$	4.22084	−	4.22084i	0.155266	−	0.155266i	−0.625199	−	0.780465i	$-0.714982\pi$
$739$	4.22084	−	4.22084i	0.155266	−	0.155266i	0.780465	+	0.625199i	$0.214982\pi$
$740$		0			0
$741$	30.1568	+	30.1568i	1.10784	+	1.10784i
$742$		0			0
$743$	−10.6484	−	10.6484i	−0.390650	−	0.390650i	0.484269	−	0.874919i	$-0.339086\pi$
$743$	−10.6484	−	10.6484i	−0.390650	−	0.390650i	−0.874919	+	0.484269i	$0.839086\pi$
$744$		0			0
$745$	5.09816	+	11.3192i	0.186782	+	0.414703i
$746$		0			0
$747$			17.4507i			0.638489i
$748$		0			0
$749$	8.12189	+	8.12189i	0.296767	+	0.296767i
$750$		0			0
$751$			7.38006i			0.269302i	0.990893	+	0.134651i	$0.0429914\pi$
$751$			7.38006i			0.269302i	−0.990893	+	0.134651i	$0.957009\pi$
$752$		0			0
$753$	6.38382	+	6.38382i	0.232639	+	0.232639i
$754$		0			0
$755$	13.0608	−	34.4676i	0.475331	−	1.25440i
$756$		0			0
$757$	−7.66297			−0.278516			−0.139258	−	0.990256i	$-0.544472\pi$
$757$	−7.66297			−0.278516			−0.139258	+	0.990256i	$0.544472\pi$
$758$		0			0
$759$		−	13.2677i		−	0.481588i
$760$		0			0
$761$		−	0.144605i		−	0.00524192i	−0.999997	−	0.00262096i	$-0.999166\pi$
$761$		−	0.144605i		−	0.00524192i	0.999997	−	0.00262096i	$-0.000834278\pi$
$762$		0			0
$763$	5.63970			0.204171
$764$		0			0
$765$	−8.54341	−	18.9685i	−0.308888	−	0.685807i
$766$		0			0
$767$	8.18363	+	8.18363i	0.295494	+	0.295494i
$768$		0			0
$769$			18.5898i			0.670365i	0.942153	+	0.335182i	$0.108798\pi$
$769$			18.5898i			0.670365i	−0.942153	+	0.335182i	$0.891202\pi$
$770$		0			0
$771$	−8.99907	−	8.99907i	−0.324094	−	0.324094i
$772$		0			0
$773$		−	11.9451i		−	0.429636i	−0.976654	−	0.214818i	$-0.931084\pi$
$773$		−	11.9451i		−	0.429636i	0.976654	−	0.214818i	$-0.0689158\pi$
$774$		0			0
$775$	−5.25015	+	5.93289i	−0.188591	+	0.213116i
$776$		0			0
$777$	1.22847	+	1.22847i	0.0440711	+	0.0440711i
$778$		0			0
$779$	−14.5540	−	14.5540i	−0.521450	−	0.521450i
$780$		0			0
$781$	6.47736	−	6.47736i	0.231778	−	0.231778i
$782$		0			0
$783$	13.4482	−	13.4482i	0.480598	−	0.480598i
$784$		0			0
$785$	14.8713	+	5.63517i	0.530779	+	0.201128i
$786$		0			0
$787$	−24.9168			−0.888189			−0.444095	−	0.895980i	$-0.646475\pi$
$787$	−24.9168			−0.888189			−0.444095	+	0.895980i	$0.646475\pi$
$788$		0			0
$789$	1.27822	−	1.27822i	0.0455059	−	0.0455059i
$790$		0			0
$791$	24.2098			0.860801
$792$		0			0
$793$	1.16459	−	1.16459i	0.0413557	−	0.0413557i
$794$		0			0
$795$	−10.1799	+	26.8649i	−0.361045	+	0.952801i
$796$		0			0
$797$		−	47.9617i		−	1.69889i	−0.527677	−	0.849445i	$-0.676937\pi$
$797$		−	47.9617i		−	1.69889i	0.527677	−	0.849445i	$-0.323063\pi$
$798$		0			0
$799$	−26.2182			−0.927535
$800$		0			0
$801$	−3.16741			−0.111915
$802$		0			0
$803$			0.842104i			0.0297172i
$804$		0			0
$805$	3.53690	−	9.33392i	0.124659	−	0.328978i
$806$		0			0
$807$	−11.4653	+	11.4653i	−0.403598	+	0.403598i
$808$		0			0
$809$	38.5831			1.35651			0.678255	−	0.734827i	$-0.262737\pi$
$809$	38.5831			1.35651			0.678255	+	0.734827i	$0.262737\pi$
$810$		0			0
$811$	4.26398	−	4.26398i	0.149729	−	0.149729i	−0.628268	−	0.777997i	$-0.716236\pi$
$811$	4.26398	−	4.26398i	0.149729	−	0.149729i	0.777997	+	0.628268i	$0.216236\pi$
$812$		0			0
$813$	19.0690			0.668779
$814$		0			0
$815$	41.7015	+	15.8020i	1.46074	+	0.553518i
$816$		0			0
$817$	−40.2452	+	40.2452i	−1.40800	+	1.40800i
$818$		0			0
$819$	11.6651	−	11.6651i	0.407610	−	0.407610i
$820$		0			0
$821$	17.3718	+	17.3718i	0.606279	+	0.606279i	0.941972	−	0.335692i	$-0.108970\pi$
$821$	17.3718	+	17.3718i	0.606279	+	0.606279i	−0.335692	+	0.941972i	$0.608970\pi$
$822$		0			0
$823$	20.0408	+	20.0408i	0.698580	+	0.698580i	0.964104	−	0.265524i	$-0.0855451\pi$
$823$	20.0408	+	20.0408i	0.698580	+	0.698580i	−0.265524	+	0.964104i	$0.585545\pi$
$824$		0			0
$825$	−1.30455	−	21.3682i	−0.0454185	−	0.743946i
$826$		0			0
$827$			9.01022i			0.313316i	0.987653	+	0.156658i	$0.0500720\pi$
$827$			9.01022i			0.313316i	−0.987653	+	0.156658i	$0.949928\pi$
$828$		0			0
$829$	−4.96517	−	4.96517i	−0.172447	−	0.172447i	0.615606	−	0.788054i	$-0.288911\pi$
$829$	−4.96517	−	4.96517i	−0.172447	−	0.172447i	−0.788054	+	0.615606i	$0.788911\pi$
$830$		0			0
$831$			3.15048i			0.109289i
$832$		0			0
$833$	−15.3037	−	15.3037i	−0.530241	−	0.530241i
$834$		0			0
$835$	18.1706	+	40.3432i	0.628819	+	1.39613i
$836$		0			0
$837$	−7.61842			−0.263331
$838$		0			0
$839$		−	4.47707i		−	0.154566i	−0.997009	−	0.0772828i	$-0.975376\pi$
$839$		−	4.47707i		−	0.154566i	0.997009	−	0.0772828i	$-0.0246244\pi$
$840$		0			0
$841$		−	13.3544i		−	0.460496i
$842$		0			0
$843$	5.74917			0.198012
$844$		0			0
$845$	−12.8837	+	34.0001i	−0.443211	+	1.16964i
$846$		0			0
$847$	−9.94490	−	9.94490i	−0.341711	−	0.341711i
$848$		0			0
$849$		−	26.9041i		−	0.923347i
$850$		0			0
$851$	2.81237	+	2.81237i	0.0964067	+	0.0964067i
$852$		0			0
$853$		−	44.4073i		−	1.52048i	−0.649644	−	0.760239i	$-0.725082\pi$
$853$		−	44.4073i		−	1.52048i	0.649644	−	0.760239i	$-0.274918\pi$
$854$		0			0
$855$	−16.3123	−	36.2174i	−0.557869	−	1.23861i
$856$		0			0
$857$	−10.8581	−	10.8581i	−0.370905	−	0.370905i	0.496902	−	0.867807i	$-0.334471\pi$
$857$	−10.8581	−	10.8581i	−0.370905	−	0.370905i	−0.867807	+	0.496902i	$0.834471\pi$
$858$		0			0
$859$	29.5319	+	29.5319i	1.00762	+	1.00762i	0.999971	+	0.00764439i	$0.00243331\pi$
$859$	29.5319	+	29.5319i	1.00762	+	1.00762i	0.00764439	+	0.999971i	$0.497567\pi$
$860$		0			0
$861$	2.34781	−	2.34781i	0.0800132	−	0.0800132i
$862$		0			0
$863$	35.5938	−	35.5938i	1.21163	−	1.21163i	0.241136	−	0.970491i	$-0.422480\pi$
$863$	35.5938	−	35.5938i	1.21163	−	1.21163i	0.970491	−	0.241136i	$-0.0775201\pi$
$864$		0			0
$865$	8.27664	−	21.8421i	0.281414	−	0.742655i
$866$		0			0
$867$	−2.17272			−0.0737893
$868$		0			0
$869$	−42.5637	+	42.5637i	−1.44387	+	1.44387i
$870$		0			0
$871$	−54.3059			−1.84008
$872$		0			0
$873$	12.9484	−	12.9484i	0.438236	−	0.438236i
$874$		0			0
$875$	4.77857	−	15.3804i	0.161545	−	0.519953i
$876$		0			0
$877$			19.0764i			0.644165i	0.946712	+	0.322083i	$0.104383\pi$
$877$			19.0764i			0.644165i	−0.946712	+	0.322083i	$0.895617\pi$
$878$		0			0
$879$	8.29135			0.279660
$880$		0			0
$881$	45.9584			1.54838			0.774189	−	0.632954i	$-0.218158\pi$
$881$	45.9584			1.54838			0.774189	+	0.632954i	$0.218158\pi$
$882$		0			0
$883$			0.280016i			0.00942327i	0.999989	+	0.00471164i	$0.00149977\pi$
$883$			0.280016i			0.00942327i	−0.999989	+	0.00471164i	$0.998500\pi$
$884$		0			0
$885$	1.84610	+	4.09881i	0.0620561	+	0.137780i
$886$		0			0
$887$	13.6733	−	13.6733i	0.459105	−	0.459105i	−0.439257	−	0.898362i	$-0.644758\pi$
$887$	13.6733	−	13.6733i	0.459105	−	0.459105i	0.898362	+	0.439257i	$0.144758\pi$
$888$		0			0
$889$	14.8738			0.498851
$890$		0			0
$891$	−5.90702	+	5.90702i	−0.197893	+	0.197893i
$892$		0			0
$893$	−50.0596			−1.67518
$894$		0			0
$895$	8.34953	+	18.5380i	0.279094	+	0.619658i
$896$		0			0
$897$	−11.1372	+	11.1372i	−0.371859	+	0.371859i
$898$		0			0
$899$	4.43164	−	4.43164i	0.147803	−	0.147803i
$900$		0			0
$901$	−42.4892	−	42.4892i	−1.41552	−	1.41552i
$902$		0			0
$903$	−6.49226	−	6.49226i	−0.216049	−	0.216049i
$904$		0			0
$905$	14.3131	−	6.44665i	0.475785	−	0.214294i
$906$		0			0
$907$		−	55.4174i		−	1.84011i	−0.391794	−	0.920053i	$-0.628145\pi$
$907$		−	55.4174i		−	1.84011i	0.391794	−	0.920053i	$-0.371855\pi$
$908$		0			0
$909$	−18.5488	−	18.5488i	−0.615225	−	0.615225i
$910$		0			0
$911$		−	23.4625i		−	0.777348i	−0.921375	−	0.388674i	$-0.872933\pi$
$911$		−	23.4625i		−	0.777348i	0.921375	−	0.388674i	$-0.127067\pi$
$912$		0			0
$913$	−26.5587	−	26.5587i	−0.878966	−	0.878966i
$914$		0			0
$915$	0.583290	−	0.262714i	0.0192830	−	0.00868505i
$916$		0			0
$917$	−15.4325			−0.509626
$918$		0			0
$919$			37.3241i			1.23121i	0.788055	+	0.615604i	$0.211088\pi$
$919$			37.3241i			1.23121i	−0.788055	+	0.615604i	$0.788912\pi$
$920$		0			0
$921$			9.99019i			0.329188i
$922$		0			0
$923$	−10.8744			−0.357936
$924$		0			0
$925$	4.80596	+	4.25291i	0.158019	+	0.139835i
$926$		0			0
$927$	12.4700	+	12.4700i	0.409569	+	0.409569i
$928$		0			0
$929$			24.2664i			0.796153i	0.917352	+	0.398077i	$0.130322\pi$
$929$			24.2664i			0.796153i	−0.917352	+	0.398077i	$0.869678\pi$
$930$		0			0
$931$	−29.2200	−	29.2200i	−0.957646	−	0.957646i
$932$		0			0
$933$		−	19.7500i		−	0.646587i
$934$		0			0
$935$	41.8711	+	15.8662i	1.36933	+	0.518880i
$936$		0			0
$937$	−1.52618	−	1.52618i	−0.0498582	−	0.0498582i	0.681738	−	0.731596i	$-0.261224\pi$
$937$	−1.52618	−	1.52618i	−0.0498582	−	0.0498582i	−0.731596	+	0.681738i	$0.761224\pi$
$938$		0			0
$939$	−5.23176	−	5.23176i	−0.170732	−	0.170732i
$940$		0			0
$941$	−16.7475	+	16.7475i	−0.545953	+	0.545953i	−0.925268	−	0.379315i	$-0.876160\pi$
$941$	−16.7475	+	16.7475i	−0.545953	+	0.545953i	0.379315	+	0.925268i	$0.376160\pi$
$942$		0			0
$943$	5.37491	−	5.37491i	0.175031	−	0.175031i
$944$		0			0
$945$	14.1216	−	6.36035i	0.459374	−	0.206902i
$946$		0			0
$947$	24.3522			0.791339			0.395670	−	0.918393i	$-0.370513\pi$
$947$	24.3522			0.791339			0.395670	+	0.918393i	$0.370513\pi$
$948$		0			0
$949$	0.706876	−	0.706876i	0.0229462	−	0.0229462i
$950$		0			0
$951$	−1.08928			−0.0353224
$952$		0			0
$953$	−5.88082	+	5.88082i	−0.190498	+	0.190498i	−0.795911	−	0.605413i	$-0.793008\pi$
$953$	−5.88082	+	5.88082i	−0.190498	+	0.190498i	0.605413	+	0.795911i	$0.293008\pi$
$954$		0			0
$955$	50.7528	+	19.2317i	1.64232	+	0.622324i
$956$		0			0
$957$			16.9357i			0.547453i
$958$		0			0
$959$	−13.6029			−0.439260
$960$		0			0
$961$	28.4895			0.919015
$962$		0			0
$963$			16.8806i			0.543969i
$964$		0			0
$965$	11.2417	−	5.06325i	0.361883	−	0.162992i
$966$		0			0
$967$	−3.31683	+	3.31683i	−0.106662	+	0.106662i	−0.758424	−	0.651762i	$-0.774030\pi$
$967$	−3.31683	+	3.31683i	−0.106662	+	0.106662i	0.651762	+	0.758424i	$0.274030\pi$
$968$		0			0
$969$	−34.6479			−1.11305
$970$		0			0
$971$	31.1533	−	31.1533i	0.999758	−	0.999758i	−0.000242242	−	1.00000i	$-0.500077\pi$
$971$	31.1533	−	31.1533i	0.999758	−	0.999758i	1.00000		0.000242242i	$7.71079e-5\pi$
$972$		0			0
$973$	−13.8153			−0.442897
$974$		0			0
$975$	−16.8418	+	19.0319i	−0.539369	+	0.609509i
$976$		0			0
$977$	−2.89478	+	2.89478i	−0.0926121	+	0.0926121i	−0.751895	−	0.659283i	$-0.770860\pi$
$977$	−2.89478	+	2.89478i	−0.0926121	+	0.0926121i	0.659283	+	0.751895i	$0.270860\pi$
$978$		0			0
$979$	4.82057	−	4.82057i	0.154066	−	0.154066i
$980$		0			0
$981$	5.86079	+	5.86079i	0.187121	+	0.187121i
$982$		0			0
$983$	16.3487	+	16.3487i	0.521442	+	0.521442i	0.918007	−	0.396565i	$-0.129798\pi$
$983$	16.3487	+	16.3487i	0.521442	+	0.521442i	−0.396565	+	0.918007i	$0.629798\pi$
$984$		0			0
$985$	−14.4899	+	38.2389i	−0.461685	+	1.21839i
$986$		0			0
$987$		−	8.07550i		−	0.257046i
$988$		0			0
$989$	−14.8629	−	14.8629i	−0.472613	−	0.472613i
$990$		0			0
$991$			55.1842i			1.75298i	0.481416	+	0.876492i	$0.340123\pi$
$991$			55.1842i			1.75298i	−0.481416	+	0.876492i	$0.659877\pi$
$992$		0			0
$993$	−9.59467	−	9.59467i	−0.304478	−	0.304478i
$994$		0			0
$995$	−1.77319	−	0.671914i	−0.0562138	−	0.0213011i
$996$		0			0
$997$	50.7136			1.60612			0.803058	−	0.595901i	$-0.203205\pi$
$997$	50.7136			1.60612			0.803058	+	0.595901i	$0.203205\pi$
$998$		0			0
$999$			6.17133i			0.195252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.j.d.63.6	yes	32
4.3	odd	2	inner	1280.2.j.d.63.11	yes	32
5.2	odd	4		1280.2.s.c.1087.6	yes	32
8.3	odd	2		1280.2.j.c.63.6	✓	32
8.5	even	2		1280.2.j.c.63.11	yes	32
16.3	odd	4		1280.2.s.c.703.6	yes	32
16.5	even	4		1280.2.s.d.703.6	yes	32
16.11	odd	4		1280.2.s.d.703.11	yes	32
16.13	even	4		1280.2.s.c.703.11	yes	32
20.7	even	4		1280.2.s.c.1087.11	yes	32
40.27	even	4		1280.2.s.d.1087.6	yes	32
40.37	odd	4		1280.2.s.d.1087.11	yes	32
80.27	even	4		1280.2.j.c.447.6	yes	32
80.37	odd	4		1280.2.j.c.447.11	yes	32
80.67	even	4	inner	1280.2.j.d.447.11	yes	32
80.77	odd	4	inner	1280.2.j.d.447.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.j.c.63.6	✓	32	8.3	odd	2
1280.2.j.c.63.11	yes	32	8.5	even	2
1280.2.j.c.447.6	yes	32	80.27	even	4
1280.2.j.c.447.11	yes	32	80.37	odd	4
1280.2.j.d.63.6	yes	32	1.1	even	1	trivial
1280.2.j.d.63.11	yes	32	4.3	odd	2	inner
1280.2.j.d.447.6	yes	32	80.77	odd	4	inner
1280.2.j.d.447.11	yes	32	80.67	even	4	inner
1280.2.s.c.703.6	yes	32	16.3	odd	4
1280.2.s.c.703.11	yes	32	16.13	even	4
1280.2.s.c.1087.6	yes	32	5.2	odd	4
1280.2.s.c.1087.11	yes	32	20.7	even	4
1280.2.s.d.703.6	yes	32	16.5	even	4
1280.2.s.d.703.11	yes	32	16.11	odd	4
1280.2.s.d.1087.6	yes	32	40.27	even	4
1280.2.s.d.1087.11	yes	32	40.37	odd	4

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:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.939635i q^{3} +(-0.792335 + 2.09098i) q^{5} +(1.01861 - 1.01861i) q^{7} +2.11709 q^{9} +(-3.22205 + 3.22205i) q^{11} +5.40928 q^{13} +(1.96476 + 0.744506i) q^{15} +(-3.10743 + 3.10743i) q^{17} +(-5.93316 + 5.93316i) q^{19} +(-0.957123 - 0.957123i) q^{21} +(-2.19117 - 2.19117i) q^{23} +(-3.74441 - 3.31352i) q^{25} -4.80819i q^{27} +(2.79693 + 2.79693i) q^{29} -1.58447i q^{31} +(3.02755 + 3.02755i) q^{33} +(1.32282 + 2.93698i) q^{35} -1.28350 q^{37} -5.08275i q^{39} +2.45299i q^{41} +6.78310 q^{43} +(-1.67744 + 4.42679i) q^{45} +(4.21863 + 4.21863i) q^{47} +4.92486i q^{49} +(2.91985 + 2.91985i) q^{51} +13.6734i q^{53} +(-4.18430 - 9.29019i) q^{55} +(5.57500 + 5.57500i) q^{57} +(1.51289 + 1.51289i) q^{59} +(0.215294 - 0.215294i) q^{61} +(2.15649 - 2.15649i) q^{63} +(-4.28597 + 11.3107i) q^{65} -10.0394 q^{67} +(-2.05890 + 2.05890i) q^{69} -2.01032 q^{71} +(0.130678 - 0.130678i) q^{73} +(-3.11350 + 3.51838i) q^{75} +6.56403i q^{77} +13.2101 q^{79} +1.83331 q^{81} +8.24281i q^{83} +(-4.03546 - 8.95972i) q^{85} +(2.62809 - 2.62809i) q^{87} -1.49612 q^{89} +(5.50996 - 5.50996i) q^{91} -1.48882 q^{93} +(-7.70508 - 17.1072i) q^{95} +(6.11613 - 6.11613i) q^{97} +(-6.82135 + 6.82135i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) \) 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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