LMFDB - Embedded newform 1280.2.j.d.447.1

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			447.1
Character	$\chi$	$=$	1280.447
Dual form			1280.2.j.d.63.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.97565i q^{3} +(2.23290 - 0.119064i) q^{5} +(3.13319 + 3.13319i) q^{7} -5.85447 q^{9} +(2.21241 + 2.21241i) q^{11} +1.39508 q^{13} +(-0.354293 - 6.64431i) q^{15} +(-3.70925 - 3.70925i) q^{17} +(2.34851 + 2.34851i) q^{19} +(9.32327 - 9.32327i) q^{21} +(-0.674307 + 0.674307i) q^{23} +(4.97165 - 0.531716i) q^{25} +8.49391i q^{27} +(3.36055 - 3.36055i) q^{29} +5.35793i q^{31} +(6.58335 - 6.58335i) q^{33} +(7.36914 + 6.62304i) q^{35} -1.39898 q^{37} -4.15127i q^{39} -0.0613778i q^{41} +9.38196 q^{43} +(-13.0724 + 0.697059i) q^{45} +(7.45692 - 7.45692i) q^{47} +12.6338i q^{49} +(-11.0374 + 11.0374i) q^{51} -1.38273i q^{53} +(5.20350 + 4.67666i) q^{55} +(6.98833 - 6.98833i) q^{57} +(0.326364 - 0.326364i) q^{59} +(-3.51712 - 3.51712i) q^{61} +(-18.3432 - 18.3432i) q^{63} +(3.11507 - 0.166104i) q^{65} -10.4618 q^{67} +(2.00650 + 2.00650i) q^{69} -12.5032 q^{71} +(-10.9895 - 10.9895i) q^{73} +(-1.58220 - 14.7939i) q^{75} +13.8638i q^{77} -0.452069 q^{79} +7.71145 q^{81} -5.30840i q^{83} +(-8.72400 - 7.84072i) q^{85} +(-9.99982 - 9.99982i) q^{87} -11.1169 q^{89} +(4.37105 + 4.37105i) q^{91} +15.9433 q^{93} +(5.52359 + 4.96435i) q^{95} +(10.5598 + 10.5598i) q^{97} +(-12.9525 - 12.9525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times$.

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

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
$3$		−	2.97565i		−	1.71799i	−0.511984	−	0.858995i	$-0.671089\pi$
$3$		−	2.97565i		−	1.71799i	0.511984	−	0.858995i	$-0.328911\pi$
$4$		0			0
$5$	2.23290	−	0.119064i	0.998581	−	0.0532472i
$5$	2.23290	−	0.119064i	0.998581	−	0.0532472i
$6$		0			0
$7$	3.13319	+	3.13319i	1.18423	+	1.18423i	0.978636	+	0.205598i	$0.0659140\pi$
$7$	3.13319	+	3.13319i	1.18423	+	1.18423i	0.205598	+	0.978636i	$0.434086\pi$
$8$		0			0
$9$	−5.85447			−1.95149
$10$		0			0
$11$	2.21241	+	2.21241i	0.667067	+	0.667067i	0.957036	−	0.289969i	$-0.0936450\pi$
$11$	2.21241	+	2.21241i	0.667067	+	0.667067i	−0.289969	+	0.957036i	$0.593645\pi$
$12$		0			0
$13$	1.39508			0.386926			0.193463	−	0.981108i	$-0.438028\pi$
$13$	1.39508			0.386926			0.193463	+	0.981108i	$0.438028\pi$
$14$		0			0
$15$	−0.354293	−	6.64431i	−0.0914781	−	1.71555i
$16$		0			0
$17$	−3.70925	−	3.70925i	−0.899624	−	0.899624i	0.0957783	−	0.995403i	$-0.469466\pi$
$17$	−3.70925	−	3.70925i	−0.899624	−	0.899624i	−0.995403	+	0.0957783i	$0.969466\pi$
$18$		0			0
$19$	2.34851	+	2.34851i	0.538784	+	0.538784i	0.923172	−	0.384387i	$-0.125587\pi$
$19$	2.34851	+	2.34851i	0.538784	+	0.538784i	−0.384387	+	0.923172i	$0.625587\pi$
$20$		0			0
$21$	9.32327	−	9.32327i	2.03450	−	2.03450i
$22$		0			0
$23$	−0.674307	+	0.674307i	−0.140603	+	0.140603i	−0.773905	−	0.633302i	$-0.781699\pi$
$23$	−0.674307	+	0.674307i	−0.140603	+	0.140603i	0.633302	+	0.773905i	$0.281699\pi$
$24$		0			0
$25$	4.97165	−	0.531716i	0.994329	−	0.106343i
$26$		0			0
$27$			8.49391i			1.63465i
$28$		0			0
$29$	3.36055	−	3.36055i	0.624039	−	0.624039i	−0.322523	−	0.946562i	$-0.604531\pi$
$29$	3.36055	−	3.36055i	0.624039	−	0.624039i	0.946562	+	0.322523i	$0.104531\pi$
$30$		0			0
$31$			5.35793i			0.962312i	0.876635	+	0.481156i	$0.159783\pi$
$31$			5.35793i			0.962312i	−0.876635	+	0.481156i	$0.840217\pi$
$32$		0			0
$33$	6.58335	−	6.58335i	1.14601	−	1.14601i
$34$		0			0
$35$	7.36914	+	6.62304i	1.24561	+	1.11950i
$36$		0			0
$37$	−1.39898			−0.229991			−0.114995	−	0.993366i	$-0.536685\pi$
$37$	−1.39898			−0.229991			−0.114995	+	0.993366i	$0.536685\pi$
$38$		0			0
$39$		−	4.15127i		−	0.664735i
$40$		0			0
$41$		−	0.0613778i		−	0.00958560i	−0.999989	−	0.00479280i	$-0.998474\pi$
$41$		−	0.0613778i		−	0.00958560i	0.999989	−	0.00479280i	$-0.00152560\pi$
$42$		0			0
$43$	9.38196			1.43074			0.715368	−	0.698748i	$-0.246259\pi$
$43$	9.38196			1.43074			0.715368	+	0.698748i	$0.246259\pi$
$44$		0			0
$45$	−13.0724	+	0.697059i	−1.94872	+	0.103911i
$46$		0			0
$47$	7.45692	−	7.45692i	1.08770	−	1.08770i	0.0919394	−	0.995765i	$-0.470693\pi$
$47$	7.45692	−	7.45692i	1.08770	−	1.08770i	0.995765	−	0.0919394i	$-0.0293066\pi$
$48$		0			0
$49$			12.6338i			1.80482i
$50$		0			0
$51$	−11.0374	+	11.0374i	−1.54555	+	1.54555i
$52$		0			0
$53$		−	1.38273i		−	0.189932i	−0.995480	−	0.0949662i	$-0.969726\pi$
$53$		−	1.38273i		−	0.189932i	0.995480	−	0.0949662i	$-0.0302743\pi$
$54$		0			0
$55$	5.20350	+	4.67666i	0.701640	+	0.630601i
$56$		0			0
$57$	6.98833	−	6.98833i	0.925627	−	0.925627i
$58$		0			0
$59$	0.326364	−	0.326364i	0.0424889	−	0.0424889i	−0.685543	−	0.728032i	$-0.740435\pi$
$59$	0.326364	−	0.326364i	0.0424889	−	0.0424889i	0.728032	+	0.685543i	$0.240435\pi$
$60$		0			0
$61$	−3.51712	−	3.51712i	−0.450321	−	0.450321i	0.445140	−	0.895461i	$-0.353154\pi$
$61$	−3.51712	−	3.51712i	−0.450321	−	0.450321i	−0.895461	+	0.445140i	$0.853154\pi$
$62$		0			0
$63$	−18.3432	−	18.3432i	−2.31102	−	2.31102i
$64$		0			0
$65$	3.11507	−	0.166104i	0.386377	−	0.0206027i
$66$		0			0
$67$	−10.4618			−1.27811			−0.639056	−	0.769160i	$-0.720675\pi$
$67$	−10.4618			−1.27811			−0.639056	+	0.769160i	$0.720675\pi$
$68$		0			0
$69$	2.00650	+	2.00650i	0.241554	+	0.241554i
$70$		0			0
$71$	−12.5032			−1.48386			−0.741930	−	0.670478i	$-0.766089\pi$
$71$	−12.5032			−1.48386			−0.741930	+	0.670478i	$0.766089\pi$
$72$		0			0
$73$	−10.9895	−	10.9895i	−1.28622	−	1.28622i	−0.937066	−	0.349153i	$-0.886469\pi$
$73$	−10.9895	−	10.9895i	−1.28622	−	1.28622i	−0.349153	−	0.937066i	$-0.613531\pi$
$74$		0			0
$75$	−1.58220	−	14.7939i	−0.182697	−	1.70825i
$76$		0			0
$77$			13.8638i			1.57993i
$78$		0			0
$79$	−0.452069			−0.0508618			−0.0254309	−	0.999677i	$-0.508096\pi$
$79$	−0.452069			−0.0508618			−0.0254309	+	0.999677i	$0.508096\pi$
$80$		0			0
$81$	7.71145			0.856827
$82$		0			0
$83$		−	5.30840i		−	0.582673i	−0.956621	−	0.291336i	$-0.905900\pi$
$83$		−	5.30840i		−	0.582673i	0.956621	−	0.291336i	$-0.0940999\pi$
$84$		0			0
$85$	−8.72400	−	7.84072i	−0.946251	−	0.850446i
$86$		0			0
$87$	−9.99982	−	9.99982i	−1.07209	−	1.07209i
$88$		0			0
$89$	−11.1169			−1.17839			−0.589197	−	0.807990i	$-0.700556\pi$
$89$	−11.1169			−1.17839			−0.589197	+	0.807990i	$0.700556\pi$
$90$		0			0
$91$	4.37105	+	4.37105i	0.458211	+	0.458211i
$92$		0			0
$93$	15.9433			1.65324
$94$		0			0
$95$	5.52359	+	4.96435i	0.566709	+	0.509331i
$96$		0			0
$97$	10.5598	+	10.5598i	1.07219	+	1.07219i	0.997183	+	0.0750042i	$0.0238970\pi$
$97$	10.5598	+	10.5598i	1.07219	+	1.07219i	0.0750042	+	0.997183i	$0.476103\pi$
$98$		0			0
$99$	−12.9525	−	12.9525i	−1.30178	−	1.30178i
$100$		0			0
$101$	−1.59553	+	1.59553i	−0.158761	+	0.158761i	−0.782018	−	0.623256i	$-0.785809\pi$
$101$	−1.59553	+	1.59553i	−0.158761	+	0.158761i	0.623256	+	0.782018i	$0.285809\pi$
$102$		0			0
$103$	−0.461391	+	0.461391i	−0.0454622	+	0.0454622i	−0.729472	−	0.684010i	$-0.760234\pi$
$103$	−0.461391	+	0.461391i	−0.0454622	+	0.0454622i	0.684010	+	0.729472i	$0.260234\pi$
$104$		0			0
$105$	19.7078	−	21.9280i	1.92329	−	2.13995i
$106$		0			0
$107$			1.60137i			0.154810i	0.997000	+	0.0774051i	$0.0246635\pi$
$107$			1.60137i			0.154810i	−0.997000	+	0.0774051i	$0.975337\pi$
$108$		0			0
$109$	3.45952	−	3.45952i	0.331362	−	0.331362i	−0.521742	−	0.853104i	$-0.674717\pi$
$109$	3.45952	−	3.45952i	0.331362	−	0.331362i	0.853104	+	0.521742i	$0.174717\pi$
$110$		0			0
$111$			4.16287i			0.395122i
$112$		0			0
$113$	−6.08214	+	6.08214i	−0.572159	+	0.572159i	−0.932731	−	0.360572i	$-0.882582\pi$
$113$	−6.08214	+	6.08214i	−0.572159	+	0.572159i	0.360572	+	0.932731i	$0.382582\pi$
$114$		0			0
$115$	−1.42537	+	1.58594i	−0.132917	+	0.147890i
$116$		0			0
$117$	−8.16746			−0.755082
$118$		0			0
$119$		−	23.2436i		−	2.13073i
$120$		0			0
$121$		−	1.21048i		−	0.110044i
$122$		0			0
$123$	−0.182639			−0.0164680
$124$		0			0
$125$	11.0379	−	1.77921i	0.987256	−	0.159138i
$126$		0			0
$127$	0.227630	−	0.227630i	0.0201989	−	0.0201989i	−0.696935	−	0.717134i	$-0.745453\pi$
$127$	0.227630	−	0.227630i	0.0201989	−	0.0201989i	0.717134	+	0.696935i	$0.245453\pi$
$128$		0			0
$129$		−	27.9174i		−	2.45799i
$130$		0			0
$131$	−12.7235	+	12.7235i	−1.11166	+	1.11166i	−0.118732	+	0.992926i	$0.537883\pi$
$131$	−12.7235	+	12.7235i	−1.11166	+	1.11166i	−0.992926	+	0.118732i	$0.962117\pi$
$132$		0			0
$133$			14.7166i			1.27609i
$134$		0			0
$135$	1.01132	+	18.9660i	0.0870406	+	1.63233i
$136$		0			0
$137$	−5.82981	+	5.82981i	−0.498075	+	0.498075i	−0.910838	−	0.412764i	$-0.864564\pi$
$137$	−5.82981	+	5.82981i	−0.498075	+	0.498075i	0.412764	+	0.910838i	$0.364564\pi$
$138$		0			0
$139$	−4.03357	+	4.03357i	−0.342123	+	0.342123i	−0.857165	−	0.515042i	$-0.827776\pi$
$139$	−4.03357	+	4.03357i	−0.342123	+	0.342123i	0.515042	+	0.857165i	$0.327776\pi$
$140$		0			0
$141$	−22.1892	−	22.1892i	−1.86867	−	1.86867i
$142$		0			0
$143$	3.08649	+	3.08649i	0.258105	+	0.258105i
$144$		0			0
$145$	7.10364	−	7.90388i	0.589925	−	0.656382i
$146$		0			0
$147$	37.5936			3.10067
$148$		0			0
$149$	−9.98681	−	9.98681i	−0.818151	−	0.818151i	0.167689	−	0.985840i	$-0.446370\pi$
$149$	−9.98681	−	9.98681i	−0.818151	−	0.818151i	−0.985840	+	0.167689i	$0.946370\pi$
$150$		0			0
$151$	3.89073			0.316623			0.158312	−	0.987389i	$-0.449395\pi$
$151$	3.89073			0.316623			0.158312	+	0.987389i	$0.449395\pi$
$152$		0			0
$153$	21.7157	+	21.7157i	1.75561	+	1.75561i
$154$		0			0
$155$	0.637937	+	11.9637i	0.0512404	+	0.960947i
$156$		0			0
$157$			6.30365i			0.503086i	0.967846	+	0.251543i	$0.0809380\pi$
$157$			6.30365i			0.503086i	−0.967846	+	0.251543i	$0.919062\pi$
$158$		0			0
$159$	−4.11451			−0.326302
$160$		0			0
$161$	−4.22546			−0.333013
$162$		0			0
$163$		−	2.20424i		−	0.172650i	−0.996267	−	0.0863248i	$-0.972488\pi$
$163$		−	2.20424i		−	0.172650i	0.996267	−	0.0863248i	$-0.0275123\pi$
$164$		0			0
$165$	13.9161	−	15.4838i	1.08337	−	1.20541i
$166$		0			0
$167$	0.246540	+	0.246540i	0.0190778	+	0.0190778i	0.716581	−	0.697504i	$-0.245706\pi$
$167$	0.246540	+	0.246540i	0.0190778	+	0.0190778i	−0.697504	+	0.716581i	$0.745706\pi$
$168$		0			0
$169$	−11.0538			−0.850289
$170$		0			0
$171$	−13.7493	−	13.7493i	−1.05143	−	1.05143i
$172$		0			0
$173$	19.2382			1.46265			0.731326	−	0.682029i	$-0.238902\pi$
$173$	19.2382			1.46265			0.731326	+	0.682029i	$0.238902\pi$
$174$		0			0
$175$	17.2431	+	13.9112i	1.30345	+	1.05158i
$176$		0			0
$177$	−0.971143	−	0.971143i	−0.0729956	−	0.0729956i
$178$		0			0
$179$	1.50544	+	1.50544i	0.112522	+	0.112522i	0.761126	−	0.648604i	$-0.224647\pi$
$179$	1.50544	+	1.50544i	0.112522	+	0.112522i	−0.648604	+	0.761126i	$0.724647\pi$
$180$		0			0
$181$	12.1599	−	12.1599i	0.903837	−	0.903837i	−0.0919290	−	0.995766i	$-0.529303\pi$
$181$	12.1599	−	12.1599i	0.903837	−	0.903837i	0.995766	+	0.0919290i	$0.0293033\pi$
$182$		0			0
$183$	−10.4657	+	10.4657i	−0.773646	+	0.773646i
$184$		0			0
$185$	−3.12378	+	0.166568i	−0.229665	+	0.0122464i
$186$		0			0
$187$		−	16.4128i		−	1.20022i
$188$		0			0
$189$	−26.6130	+	26.6130i	−1.93581	+	1.93581i
$190$		0			0
$191$			4.96940i			0.359573i	0.983706	+	0.179787i	$0.0575407\pi$
$191$			4.96940i			0.359573i	−0.983706	+	0.179787i	$0.942459\pi$
$192$		0			0
$193$	−15.3547	+	15.3547i	−1.10525	+	1.10525i	−0.111486	+	0.993766i	$0.535561\pi$
$193$	−15.3547	+	15.3547i	−1.10525	+	1.10525i	−0.993766	+	0.111486i	$0.964439\pi$
$194$		0			0
$195$	−0.494267	−	9.26934i	−0.0353952	−	0.663792i
$196$		0			0
$197$	4.11449			0.293145			0.146572	−	0.989200i	$-0.453176\pi$
$197$	4.11449			0.293145			0.146572	+	0.989200i	$0.453176\pi$
$198$		0			0
$199$			25.7162i			1.82297i	0.411334	+	0.911485i	$0.365063\pi$
$199$			25.7162i			1.82297i	−0.411334	+	0.911485i	$0.634937\pi$
$200$		0			0
$201$			31.1306i			2.19579i
$202$		0			0
$203$	21.0585			1.47802
$204$		0			0
$205$	−0.00730790	−	0.137050i	−0.000510406	−	0.00957201i
$206$		0			0
$207$	3.94771	−	3.94771i	0.274385	−	0.274385i
$208$		0			0
$209$			10.3917i			0.718810i
$210$		0			0
$211$	9.76624	−	9.76624i	0.672336	−	0.672336i	−0.285918	−	0.958254i	$-0.592299\pi$
$211$	9.76624	−	9.76624i	0.672336	−	0.672336i	0.958254	+	0.285918i	$0.0922986\pi$
$212$		0			0
$213$			37.2052i			2.54926i
$214$		0			0
$215$	20.9489	−	1.11706i	1.42871	−	0.0761826i
$216$		0			0
$217$	−16.7874	+	16.7874i	−1.13960	+	1.13960i
$218$		0			0
$219$	−32.7007	+	32.7007i	−2.20971	+	2.20971i
$220$		0			0
$221$	−5.17470	−	5.17470i	−0.348088	−	0.348088i
$222$		0			0
$223$	−2.32868	−	2.32868i	−0.155940	−	0.155940i	0.624825	−	0.780765i	$-0.285170\pi$
$223$	−2.32868	−	2.32868i	−0.155940	−	0.155940i	−0.780765	+	0.624825i	$0.785170\pi$
$224$		0			0
$225$	−29.1064	+	3.11292i	−1.94043	+	0.207528i
$226$		0			0
$227$	9.73288			0.645994			0.322997	−	0.946400i	$-0.395310\pi$
$227$	9.73288			0.645994			0.322997	+	0.946400i	$0.395310\pi$
$228$		0			0
$229$	7.39128	+	7.39128i	0.488429	+	0.488429i	0.907810	−	0.419381i	$-0.137753\pi$
$229$	7.39128	+	7.39128i	0.488429	+	0.488429i	−0.419381	+	0.907810i	$0.637753\pi$
$230$		0			0
$231$	41.2538			2.71430
$232$		0			0
$233$	8.55716	+	8.55716i	0.560598	+	0.560598i	0.929477	−	0.368879i	$-0.120258\pi$
$233$	8.55716	+	8.55716i	0.560598	+	0.560598i	−0.368879	+	0.929477i	$0.620258\pi$
$234$		0			0
$235$	15.7627	−	17.5384i	1.02824	−	1.14408i
$236$		0			0
$237$			1.34520i			0.0873801i
$238$		0			0
$239$	0.446382			0.0288741			0.0144370	−	0.999896i	$-0.495404\pi$
$239$	0.446382			0.0288741			0.0144370	+	0.999896i	$0.495404\pi$
$240$		0			0
$241$	−23.2902			−1.50025			−0.750127	−	0.661294i	$-0.770008\pi$
$241$	−23.2902			−1.50025			−0.750127	+	0.661294i	$0.770008\pi$
$242$		0			0
$243$			2.53518i			0.162632i
$244$		0			0
$245$	1.50423	+	28.2099i	0.0961017	+	1.80226i
$246$		0			0
$247$	3.27636	+	3.27636i	0.208469	+	0.208469i
$248$		0			0
$249$	−15.7959			−1.00103
$250$		0			0
$251$	−11.7889	−	11.7889i	−0.744107	−	0.744107i	0.229259	−	0.973365i	$-0.426370\pi$
$251$	−11.7889	−	11.7889i	−0.744107	−	0.744107i	−0.973365	+	0.229259i	$0.926370\pi$
$252$		0			0
$253$	−2.98369			−0.187583
$254$		0			0
$255$	−23.3312	+	25.9595i	−1.46106	+	1.62565i
$256$		0			0
$257$	−2.36238	−	2.36238i	−0.147361	−	0.147361i	0.629577	−	0.776938i	$-0.283228\pi$
$257$	−2.36238	−	2.36238i	−0.147361	−	0.147361i	−0.776938	+	0.629577i	$0.783228\pi$
$258$		0			0
$259$	−4.38327	−	4.38327i	−0.272363	−	0.272363i
$260$		0			0
$261$	−19.6743	+	19.6743i	−1.21781	+	1.21781i
$262$		0			0
$263$	6.30062	−	6.30062i	0.388513	−	0.388513i	−0.485644	−	0.874157i	$-0.661415\pi$
$263$	6.30062	−	6.30062i	0.388513	−	0.388513i	0.874157	+	0.485644i	$0.161415\pi$
$264$		0			0
$265$	−0.164634	−	3.08749i	−0.0101134	−	0.189663i
$266$		0			0
$267$			33.0801i			2.02447i
$268$		0			0
$269$	10.2072	−	10.2072i	0.622342	−	0.622342i	−0.323788	−	0.946130i	$-0.604956\pi$
$269$	10.2072	−	10.2072i	0.622342	−	0.622342i	0.946130	+	0.323788i	$0.104956\pi$
$270$		0			0
$271$			5.65243i			0.343361i	0.985153	+	0.171680i	$0.0549197\pi$
$271$			5.65243i			0.343361i	−0.985153	+	0.171680i	$0.945080\pi$
$272$		0			0
$273$	13.0067	−	13.0067i	0.787202	−	0.787202i
$274$		0			0
$275$	12.1757	+	9.82295i	0.734222	+	0.592346i
$276$		0			0
$277$	7.27360			0.437028			0.218514	−	0.975834i	$-0.429879\pi$
$277$	7.27360			0.437028			0.218514	+	0.975834i	$0.429879\pi$
$278$		0			0
$279$		−	31.3678i		−	1.87794i
$280$		0			0
$281$		−	22.2329i		−	1.32630i	−0.748484	−	0.663152i	$-0.769218\pi$
$281$		−	22.2329i		−	1.32630i	0.748484	−	0.663152i	$-0.230782\pi$
$282$		0			0
$283$	16.2661			0.966918			0.483459	−	0.875367i	$-0.339380\pi$
$283$	16.2661			0.966918			0.483459	+	0.875367i	$0.339380\pi$
$284$		0			0
$285$	14.7721	−	16.4363i	0.875026	−	0.973600i
$286$		0			0
$287$	0.192308	−	0.192308i	0.0113516	−	0.0113516i
$288$		0			0
$289$			10.5170i			0.618648i
$290$		0			0
$291$	31.4223	−	31.4223i	1.84201	−	1.84201i
$292$		0			0
$293$		−	25.3926i		−	1.48345i	−0.670703	−	0.741726i	$-0.734008\pi$
$293$		−	25.3926i		−	1.48345i	0.670703	−	0.741726i	$-0.265992\pi$
$294$		0			0
$295$	0.689878	−	0.767594i	0.0401662	−	0.0446911i
$296$		0			0
$297$	−18.7920	+	18.7920i	−1.09042	+	1.09042i
$298$		0			0
$299$	−0.940712	+	0.940712i	−0.0544028	+	0.0544028i
$300$		0			0
$301$	29.3955	+	29.3955i	1.69433	+	1.69433i
$302$		0			0
$303$	4.74773	+	4.74773i	0.272750	+	0.272750i
$304$		0			0
$305$	−8.27212	−	7.43459i	−0.473660	−	0.425703i
$306$		0			0
$307$	−19.6772			−1.12304			−0.561520	−	0.827463i	$-0.689783\pi$
$307$	−19.6772			−1.12304			−0.561520	+	0.827463i	$0.689783\pi$
$308$		0			0
$309$	1.37294	+	1.37294i	0.0781037	+	0.0781037i
$310$		0			0
$311$	−28.1914			−1.59859			−0.799294	−	0.600940i	$-0.794793\pi$
$311$	−28.1914			−1.59859			−0.799294	+	0.600940i	$0.794793\pi$
$312$		0			0
$313$	4.45325	+	4.45325i	0.251712	+	0.251712i	0.821672	−	0.569960i	$-0.193041\pi$
$313$	4.45325	+	4.45325i	0.251712	+	0.251712i	−0.569960	+	0.821672i	$0.693041\pi$
$314$		0			0
$315$	−43.1424	−	38.7744i	−2.43080	−	2.18469i
$316$		0			0
$317$		−	30.9996i		−	1.74111i	−0.492071	−	0.870555i	$-0.663760\pi$
$317$		−	30.9996i		−	1.74111i	0.492071	−	0.870555i	$-0.336240\pi$
$318$		0			0
$319$	14.8698			0.832551
$320$		0			0
$321$	4.76511			0.265962
$322$		0			0
$323$		−	17.4224i		−	0.969407i
$324$		0			0
$325$	6.93585	−	0.741787i	0.384732	−	0.0411469i
$326$		0			0
$327$	−10.2943	−	10.2943i	−0.569277	−	0.569277i
$328$		0			0
$329$	46.7279			2.57619
$330$		0			0
$331$	−21.3401	−	21.3401i	−1.17296	−	1.17296i	−0.981501	−	0.191456i	$-0.938679\pi$
$331$	−21.3401	−	21.3401i	−1.17296	−	1.17296i	−0.191456	−	0.981501i	$-0.561321\pi$
$332$		0			0
$333$	8.19029			0.448825
$334$		0			0
$335$	−23.3601	+	1.24563i	−1.27630	+	0.0680559i
$336$		0			0
$337$	−8.55232	−	8.55232i	−0.465874	−	0.465874i	0.434701	−	0.900575i	$-0.356854\pi$
$337$	−8.55232	−	8.55232i	−0.465874	−	0.465874i	−0.900575	+	0.434701i	$0.856854\pi$
$338$		0			0
$339$	18.0983	+	18.0983i	0.982964	+	0.982964i
$340$		0			0
$341$	−11.8539	+	11.8539i	−0.641926	+	0.641926i
$342$		0			0
$343$	−17.6517	+	17.6517i	−0.953100	+	0.953100i
$344$		0			0
$345$	4.71921	+	4.24140i	0.254074	+	0.228349i
$346$		0			0
$347$			8.06806i			0.433116i	0.976270	+	0.216558i	$0.0694830\pi$
$347$			8.06806i			0.433116i	−0.976270	+	0.216558i	$0.930517\pi$
$348$		0			0
$349$	−24.4770	+	24.4770i	−1.31022	+	1.31022i	−0.388973	+	0.921249i	$0.627170\pi$
$349$	−24.4770	+	24.4770i	−1.31022	+	1.31022i	−0.921249	+	0.388973i	$0.872830\pi$
$350$		0			0
$351$			11.8497i			0.632489i
$352$		0			0
$353$	9.63289	−	9.63289i	0.512707	−	0.512707i	−0.402648	−	0.915355i	$-0.631910\pi$
$353$	9.63289	−	9.63289i	0.512707	−	0.512707i	0.915355	+	0.402648i	$0.131910\pi$
$354$		0			0
$355$	−27.9184	+	1.48869i	−1.48175	+	0.0790113i
$356$		0			0
$357$	−69.1646			−3.66058
$358$		0			0
$359$			6.93152i			0.365832i	0.983129	+	0.182916i	$0.0585536\pi$
$359$			6.93152i			0.365832i	−0.983129	+	0.182916i	$0.941446\pi$
$360$		0			0
$361$		−	7.96903i		−	0.419423i
$362$		0			0
$363$	−3.60196			−0.189054
$364$		0			0
$365$	−25.8468	−	23.2299i	−1.35288	−	1.21591i
$366$		0			0
$367$	5.75329	−	5.75329i	0.300319	−	0.300319i	−0.540820	−	0.841139i	$-0.681886\pi$
$367$	5.75329	−	5.75329i	0.300319	−	0.300319i	0.841139	+	0.540820i	$0.181886\pi$
$368$		0			0
$369$			0.359335i			0.0187062i
$370$		0			0
$371$	4.33235	−	4.33235i	0.224925	−	0.224925i
$372$		0			0
$373$			19.9960i			1.03536i	0.855576	+	0.517678i	$0.173203\pi$
$373$			19.9960i			1.03536i	−0.855576	+	0.517678i	$0.826797\pi$
$374$		0			0
$375$	−5.29431	−	32.8448i	−0.273397	−	1.69610i
$376$		0			0
$377$	4.68824	−	4.68824i	0.241457	−	0.241457i
$378$		0			0
$379$	12.8102	−	12.8102i	0.658018	−	0.658018i	−0.296893	−	0.954911i	$-0.595950\pi$
$379$	12.8102	−	12.8102i	0.658018	−	0.658018i	0.954911	+	0.296893i	$0.0959505\pi$
$380$		0			0
$381$	−0.677347	−	0.677347i	−0.0347015	−	0.0347015i
$382$		0			0
$383$	22.4012	+	22.4012i	1.14465	+	1.14465i	0.987589	+	0.157059i	$0.0502011\pi$
$383$	22.4012	+	22.4012i	1.14465	+	1.14465i	0.157059	+	0.987589i	$0.449799\pi$
$384$		0			0
$385$	1.65068	+	30.9564i	0.0841266	+	1.57769i
$386$		0			0
$387$	−54.9265			−2.79207
$388$		0			0
$389$	−19.2181	−	19.2181i	−0.974395	−	0.974395i	0.0252853	−	0.999680i	$-0.491951\pi$
$389$	−19.2181	−	19.2181i	−0.974395	−	0.974395i	−0.999680	+	0.0252853i	$0.991951\pi$
$390$		0			0
$391$	5.00234			0.252979
$392$		0			0
$393$	37.8607	+	37.8607i	1.90982	+	1.90982i
$394$		0			0
$395$	−1.00942	+	0.0538253i	−0.0507896	+	0.00270825i
$396$		0			0
$397$			39.2857i			1.97169i	0.167651	+	0.985846i	$0.446382\pi$
$397$			39.2857i			1.97169i	−0.167651	+	0.985846i	$0.553618\pi$
$398$		0			0
$399$	43.7915			2.19232
$400$		0			0
$401$	23.3346			1.16527			0.582637	−	0.812732i	$-0.302021\pi$
$401$	23.3346			1.16527			0.582637	+	0.812732i	$0.302021\pi$
$402$		0			0
$403$			7.47474i			0.372343i
$404$		0			0
$405$	17.2189	−	0.918158i	0.855612	−	0.0456236i
$406$		0			0
$407$	−3.09512	−	3.09512i	−0.153419	−	0.153419i
$408$		0			0
$409$	−23.5949			−1.16669			−0.583346	−	0.812223i	$-0.698257\pi$
$409$	−23.5949			−1.16669			−0.583346	+	0.812223i	$0.698257\pi$
$410$		0			0
$411$	17.3475	+	17.3475i	0.855687	+	0.855687i
$412$		0			0
$413$	2.04512			0.100634
$414$		0			0
$415$	−0.632041	−	11.8531i	−0.0310257	−	0.581846i
$416$		0			0
$417$	12.0025	+	12.0025i	0.587764	+	0.587764i
$418$		0			0
$419$	18.7073	+	18.7073i	0.913911	+	0.913911i	0.996577	−	0.0826667i	$-0.0263437\pi$
$419$	18.7073	+	18.7073i	0.913911	+	0.913911i	−0.0826667	+	0.996577i	$0.526344\pi$
$420$		0			0
$421$	1.46082	−	1.46082i	0.0711962	−	0.0711962i	−0.670612	−	0.741808i	$-0.733968\pi$
$421$	1.46082	−	1.46082i	0.0711962	−	0.0711962i	0.741808	+	0.670612i	$0.233968\pi$
$422$		0			0
$423$	−43.6564	+	43.6564i	−2.12265	+	2.12265i
$424$		0			0
$425$	−20.4133	−	16.4688i	−0.990192	−	0.798854i
$426$		0			0
$427$		−	22.0396i		−	1.06657i
$428$		0			0
$429$	9.18430	−	9.18430i	0.443422	−	0.443422i
$430$		0			0
$431$			21.2337i			1.02279i	0.859346	+	0.511395i	$0.170871\pi$
$431$			21.2337i			1.02279i	−0.859346	+	0.511395i	$0.829129\pi$
$432$		0			0
$433$	13.3918	−	13.3918i	0.643568	−	0.643568i	−0.307863	−	0.951431i	$-0.599614\pi$
$433$	13.3918	−	13.3918i	0.643568	−	0.643568i	0.951431	+	0.307863i	$0.0996138\pi$
$434$		0			0
$435$	−23.5192	−	21.1379i	−1.12766	−	1.01349i
$436$		0			0
$437$	−3.16723			−0.151509
$438$		0			0
$439$			19.6174i			0.936286i	0.883653	+	0.468143i	$0.155077\pi$
$439$			19.6174i			0.936286i	−0.883653	+	0.468143i	$0.844923\pi$
$440$		0			0
$441$		−	73.9641i		−	3.52210i
$442$		0			0
$443$	−2.97052			−0.141134			−0.0705668	−	0.997507i	$-0.522481\pi$
$443$	−2.97052			−0.141134			−0.0705668	+	0.997507i	$0.522481\pi$
$444$		0			0
$445$	−24.8230	+	1.32363i	−1.17672	+	0.0627461i
$446$		0			0
$447$	−29.7172	+	29.7172i	−1.40558	+	1.40558i
$448$		0			0
$449$			20.1793i			0.952318i	0.879359	+	0.476159i	$0.157971\pi$
$449$			20.1793i			0.952318i	−0.879359	+	0.476159i	$0.842029\pi$
$450$		0			0
$451$	0.135793	−	0.135793i	0.00639424	−	0.00639424i
$452$		0			0
$453$		−	11.5774i		−	0.543955i
$454$		0			0
$455$	10.2805	+	9.23967i	0.481959	+	0.433162i
$456$		0			0
$457$	−6.37301	+	6.37301i	−0.298117	+	0.298117i	−0.840276	−	0.542159i	$-0.817607\pi$
$457$	−6.37301	+	6.37301i	−0.298117	+	0.298117i	0.542159	+	0.840276i	$0.317607\pi$
$458$		0			0
$459$	31.5060	−	31.5060i	1.47057	−	1.47057i
$460$		0			0
$461$	27.4972	+	27.4972i	1.28067	+	1.28067i	0.940286	+	0.340385i	$0.110557\pi$
$461$	27.4972	+	27.4972i	1.28067	+	1.28067i	0.340385	+	0.940286i	$0.389443\pi$
$462$		0			0
$463$	7.98877	+	7.98877i	0.371269	+	0.371269i	0.867939	−	0.496670i	$-0.165444\pi$
$463$	7.98877	+	7.98877i	0.371269	+	0.371269i	−0.496670	+	0.867939i	$0.665444\pi$
$464$		0			0
$465$	35.5997	−	1.89828i	1.65090	−	0.0880305i
$466$		0			0
$467$	−0.761551			−0.0352404			−0.0176202	−	0.999845i	$-0.505609\pi$
$467$	−0.761551			−0.0352404			−0.0176202	+	0.999845i	$0.505609\pi$
$468$		0			0
$469$	−32.7788	−	32.7788i	−1.51359	−	1.51359i
$470$		0			0
$471$	18.7574			0.864297
$472$		0			0
$473$	20.7568	+	20.7568i	0.954397	+	0.954397i
$474$		0			0
$475$	12.9247	+	10.4272i	0.593025	+	0.478433i
$476$		0			0
$477$			8.09515i			0.370652i
$478$		0			0
$479$	−19.3307			−0.883241			−0.441621	−	0.897202i	$-0.645596\pi$
$479$	−19.3307			−0.883241			−0.441621	+	0.897202i	$0.645596\pi$
$480$		0			0
$481$	−1.95169			−0.0889893
$482$		0			0
$483$			12.5735i			0.572114i
$484$		0			0
$485$	24.8363	+	22.3217i	1.12776	+	1.01358i
$486$		0			0
$487$	−30.4781	−	30.4781i	−1.38109	−	1.38109i	−0.842681	−	0.538413i	$-0.819024\pi$
$487$	−30.4781	−	30.4781i	−1.38109	−	1.38109i	−0.538413	−	0.842681i	$-0.680976\pi$
$488$		0			0
$489$	−6.55905			−0.296610
$490$		0			0
$491$	−9.36598	−	9.36598i	−0.422681	−	0.422681i	0.463445	−	0.886126i	$-0.346613\pi$
$491$	−9.36598	−	9.36598i	−0.422681	−	0.422681i	−0.886126	+	0.463445i	$0.846613\pi$
$492$		0			0
$493$	−24.9302			−1.12280
$494$		0			0
$495$	−30.4638	−	27.3794i	−1.36924	−	1.23061i
$496$		0			0
$497$	−39.1750	−	39.1750i	−1.75724	−	1.75724i
$498$		0			0
$499$	−6.42506	−	6.42506i	−0.287625	−	0.287625i	0.548515	−	0.836141i	$-0.315193\pi$
$499$	−6.42506	−	6.42506i	−0.287625	−	0.287625i	−0.836141	+	0.548515i	$0.815193\pi$
$500$		0			0
$501$	0.733615	−	0.733615i	0.0327755	−	0.0327755i
$502$		0			0
$503$	22.5218	−	22.5218i	1.00420	−	1.00420i	0.00420549	−	0.999991i	$-0.498661\pi$
$503$	22.5218	−	22.5218i	1.00420	−	1.00420i	0.999991	−	0.00420549i	$-0.00133865\pi$
$504$		0			0
$505$	−3.37268	+	3.75262i	−0.150082	+	0.166989i
$506$		0			0
$507$			32.8921i			1.46079i
$508$		0			0
$509$	5.10973	−	5.10973i	0.226485	−	0.226485i	−0.584738	−	0.811222i	$-0.698803\pi$
$509$	5.10973	−	5.10973i	0.226485	−	0.226485i	0.811222	+	0.584738i	$0.198803\pi$
$510$		0			0
$511$		−	68.8641i		−	3.04637i
$512$		0			0
$513$	−19.9480	+	19.9480i	−0.880726	+	0.880726i
$514$		0			0
$515$	−0.975303	+	1.08517i	−0.0429770	+	0.0478185i
$516$		0			0
$517$	32.9955			1.45114
$518$		0			0
$519$		−	57.2460i		−	2.51282i
$520$		0			0
$521$		−	32.2312i		−	1.41208i	−0.708174	−	0.706038i	$-0.750481\pi$
$521$		−	32.2312i		−	1.41208i	0.708174	−	0.706038i	$-0.249519\pi$
$522$		0			0
$523$	−19.3381			−0.845598			−0.422799	−	0.906223i	$-0.638952\pi$
$523$	−19.3381			−0.845598			−0.422799	+	0.906223i	$0.638952\pi$
$524$		0			0
$525$	41.3947	−	51.3093i	1.80661	−	2.23932i
$526$		0			0
$527$	19.8739	−	19.8739i	0.865719	−	0.865719i
$528$		0			0
$529$			22.0906i			0.960462i
$530$		0			0
$531$	−1.91069	+	1.91069i	−0.0829168	+	0.0829168i
$532$		0			0
$533$		−	0.0856270i		−	0.00370892i
$534$		0			0
$535$	0.190666	+	3.57569i	0.00824320	+	0.154591i
$536$		0			0
$537$	4.47964	−	4.47964i	0.193311	−	0.193311i
$538$		0			0
$539$	−27.9511	+	27.9511i	−1.20394	+	1.20394i
$540$		0			0
$541$	−9.31865	−	9.31865i	−0.400640	−	0.400640i	0.477818	−	0.878459i	$-0.341428\pi$
$541$	−9.31865	−	9.31865i	−0.400640	−	0.400640i	−0.878459	+	0.477818i	$0.841428\pi$
$542$		0			0
$543$	−36.1835	−	36.1835i	−1.55278	−	1.55278i
$544$		0			0
$545$	7.31284	−	8.13665i	0.313248	−	0.348536i
$546$		0			0
$547$	10.8270			0.462928			0.231464	−	0.972843i	$-0.425648\pi$
$547$	10.8270			0.462928			0.231464	+	0.972843i	$0.425648\pi$
$548$		0			0
$549$	20.5909	+	20.5909i	0.878797	+	0.878797i
$550$		0			0
$551$	15.7846			0.672445
$552$		0			0
$553$	−1.41642	−	1.41642i	−0.0602323	−	0.0602323i
$554$		0			0
$555$	0.495649	+	9.29525i	0.0210391	+	0.394561i
$556$		0			0
$557$		−	21.8505i		−	0.925837i	−0.886401	−	0.462919i	$-0.846802\pi$
$557$		−	21.8505i		−	0.925837i	0.886401	−	0.462919i	$-0.153198\pi$
$558$		0			0
$559$	13.0886			0.553588
$560$		0			0
$561$	−48.8386			−2.06197
$562$		0			0
$563$			43.7789i			1.84506i	0.385922	+	0.922531i	$0.373883\pi$
$563$			43.7789i			1.84506i	−0.385922	+	0.922531i	$0.626117\pi$
$564$		0			0
$565$	−12.8566	+	14.3049i	−0.540882	+	0.601814i
$566$		0			0
$567$	24.1614	+	24.1614i	1.01468	+	1.01468i
$568$		0			0
$569$	−22.7808			−0.955021			−0.477511	−	0.878626i	$-0.658461\pi$
$569$	−22.7808			−0.955021			−0.477511	+	0.878626i	$0.658461\pi$
$570$		0			0
$571$	14.2769	+	14.2769i	0.597472	+	0.597472i	0.939639	−	0.342167i	$-0.111161\pi$
$571$	14.2769	+	14.2769i	0.597472	+	0.597472i	−0.342167	+	0.939639i	$0.611161\pi$
$572$		0			0
$573$	14.7872			0.617743
$574$		0			0
$575$	−2.99388	+	3.71096i	−0.124853	+	0.154758i
$576$		0			0
$577$	8.57087	+	8.57087i	0.356810	+	0.356810i	0.862636	−	0.505826i	$-0.168812\pi$
$577$	8.57087	+	8.57087i	0.356810	+	0.356810i	−0.505826	+	0.862636i	$0.668812\pi$
$578$		0			0
$579$	45.6900	+	45.6900i	1.89881	+	1.89881i
$580$		0			0
$581$	16.6322	−	16.6322i	0.690022	−	0.690022i
$582$		0			0
$583$	3.05916	−	3.05916i	0.126698	−	0.126698i
$584$		0			0
$585$	−18.2371	+	0.972453i	−0.754011	+	0.0402060i
$586$		0			0
$587$			5.32689i			0.219864i	0.993939	+	0.109932i	$0.0350634\pi$
$587$			5.32689i			0.219864i	−0.993939	+	0.109932i	$0.964937\pi$
$588$		0			0
$589$	−12.5831	+	12.5831i	−0.518479	+	0.518479i
$590$		0			0
$591$		−	12.2433i		−	0.503620i
$592$		0			0
$593$	14.1909	−	14.1909i	0.582750	−	0.582750i	−0.352908	−	0.935658i	$-0.614807\pi$
$593$	14.1909	−	14.1909i	0.582750	−	0.582750i	0.935658	+	0.352908i	$0.114807\pi$
$594$		0			0
$595$	−2.76748	−	51.9004i	−0.113455	−	2.12771i
$596$		0			0
$597$	76.5222			3.13184
$598$		0			0
$599$			19.3816i			0.791912i	0.918269	+	0.395956i	$0.129587\pi$
$599$			19.3816i			0.791912i	−0.918269	+	0.395956i	$0.870413\pi$
$600$		0			0
$601$			38.9996i			1.59083i	0.606068	+	0.795413i	$0.292746\pi$
$601$			38.9996i			1.59083i	−0.606068	+	0.795413i	$0.707254\pi$
$602$		0			0
$603$	61.2484			2.49423
$604$		0			0
$605$	−0.144125	−	2.70287i	−0.00585951	−	0.109887i
$606$		0			0
$607$	−18.5409	+	18.5409i	−0.752553	+	0.752553i	−0.974955	−	0.222402i	$-0.928610\pi$
$607$	−18.5409	+	18.5409i	−0.752553	+	0.752553i	0.222402	+	0.974955i	$0.428610\pi$
$608$		0			0
$609$		−	62.6627i		−	2.53922i
$610$		0			0
$611$	10.4030	−	10.4030i	0.420861	−	0.420861i
$612$		0			0
$613$		−	16.1206i		−	0.651104i	−0.945524	−	0.325552i	$-0.894450\pi$
$613$		−	16.1206i		−	0.651104i	0.945524	−	0.325552i	$-0.105550\pi$
$614$		0			0
$615$	−0.407813	+	0.0217457i	−0.0164446	+	0.000876873i
$616$		0			0
$617$	3.27211	−	3.27211i	0.131730	−	0.131730i	−0.638167	−	0.769898i	$-0.720307\pi$
$617$	3.27211	−	3.27211i	0.131730	−	0.131730i	0.769898	+	0.638167i	$0.220307\pi$
$618$		0			0
$619$	−20.6549	+	20.6549i	−0.830192	+	0.830192i	−0.987543	−	0.157351i	$-0.949705\pi$
$619$	−20.6549	+	20.6549i	−0.830192	+	0.830192i	0.157351	+	0.987543i	$0.449705\pi$
$620$		0			0
$621$	−5.72750	−	5.72750i	−0.229837	−	0.229837i
$622$		0			0
$623$	−34.8315	−	34.8315i	−1.39549	−	1.39549i
$624$		0			0
$625$	24.4346	−	5.28701i	0.977382	−	0.211480i
$626$		0			0
$627$	30.9221			1.23491
$628$		0			0
$629$	5.18916	+	5.18916i	0.206905	+	0.206905i
$630$		0			0
$631$	42.2426			1.68165			0.840826	−	0.541305i	$-0.182070\pi$
$631$	42.2426			1.68165			0.840826	+	0.541305i	$0.182070\pi$
$632$		0			0
$633$	−29.0609	−	29.0609i	−1.15507	−	1.15507i
$634$		0			0
$635$	0.481172	−	0.535377i	0.0190947	−	0.0212458i
$636$		0			0
$637$			17.6251i			0.698333i
$638$		0			0
$639$	73.1998			2.89574
$640$		0			0
$641$	15.6661			0.618774			0.309387	−	0.950936i	$-0.399876\pi$
$641$	15.6661			0.618774			0.309387	+	0.950936i	$0.399876\pi$
$642$		0			0
$643$		−	12.8099i		−	0.505174i	−0.967574	−	0.252587i	$-0.918719\pi$
$643$		−	12.8099i		−	0.505174i	0.967574	−	0.252587i	$-0.0812814\pi$
$644$		0			0
$645$	−3.32397	−	62.3367i	−0.130881	−	2.45450i
$646$		0			0
$647$	4.86503	+	4.86503i	0.191264	+	0.191264i	0.796242	−	0.604978i	$-0.206818\pi$
$647$	4.86503	+	4.86503i	0.191264	+	0.191264i	−0.604978	+	0.796242i	$0.706818\pi$
$648$		0			0
$649$	1.44410			0.0566859
$650$		0			0
$651$	49.9534	+	49.9534i	1.95783	+	1.95783i
$652$		0			0
$653$	−40.5285			−1.58600			−0.793002	−	0.609219i	$-0.791483\pi$
$653$	−40.5285			−1.58600			−0.793002	+	0.609219i	$0.791483\pi$
$654$		0			0
$655$	−26.8954	+	29.9252i	−1.05089	+	1.16927i
$656$		0			0
$657$	64.3375	+	64.3375i	2.51004	+	2.51004i
$658$		0			0
$659$	−26.6285	−	26.6285i	−1.03730	−	1.03730i	−0.999277	−	0.0380210i	$-0.987895\pi$
$659$	−26.6285	−	26.6285i	−1.03730	−	1.03730i	−0.0380210	−	0.999277i	$-0.512105\pi$
$660$		0			0
$661$	−7.11926	+	7.11926i	−0.276907	+	0.276907i	−0.831873	−	0.554966i	$-0.812731\pi$
$661$	−7.11926	+	7.11926i	−0.276907	+	0.276907i	0.554966	+	0.831873i	$0.312731\pi$
$662$		0			0
$663$	−15.3981	+	15.3981i	−0.598011	+	0.598011i
$664$		0			0
$665$	1.75223	+	32.8607i	0.0679484	+	1.27428i
$666$		0			0
$667$			4.53209i			0.175483i
$668$		0			0
$669$	−6.92934	+	6.92934i	−0.267904	+	0.267904i
$670$		0			0
$671$		−	15.5626i		−	0.600788i
$672$		0			0
$673$	1.30978	−	1.30978i	0.0504884	−	0.0504884i	−0.681412	−	0.731900i	$-0.738634\pi$
$673$	1.30978	−	1.30978i	0.0504884	−	0.0504884i	0.731900	+	0.681412i	$0.238634\pi$
$674$		0			0
$675$	4.51635	+	42.2287i	0.173834	+	1.62538i
$676$		0			0
$677$	35.4587			1.36279			0.681394	−	0.731916i	$-0.261374\pi$
$677$	35.4587			1.36279			0.681394	+	0.731916i	$0.261374\pi$
$678$		0			0
$679$			66.1719i			2.53944i
$680$		0			0
$681$		−	28.9616i		−	1.10981i
$682$		0			0
$683$	12.9149			0.494174			0.247087	−	0.968993i	$-0.420527\pi$
$683$	12.9149			0.494174			0.247087	+	0.968993i	$0.420527\pi$
$684$		0			0
$685$	−12.3232	+	13.7115i	−0.470847	+	0.523889i
$686$		0			0
$687$	21.9938	−	21.9938i	0.839117	−	0.839117i
$688$		0			0
$689$		−	1.92902i		−	0.0734897i
$690$		0			0
$691$	−19.5974	+	19.5974i	−0.745519	+	0.745519i	−0.973634	−	0.228115i	$-0.926744\pi$
$691$	−19.5974	+	19.5974i	−0.745519	+	0.745519i	0.228115	+	0.973634i	$0.426744\pi$
$692$		0			0
$693$		−	81.1653i		−	3.08322i
$694$		0			0
$695$	−8.52629	+	9.48680i	−0.323421	+	0.359855i
$696$		0			0
$697$	−0.227665	+	0.227665i	−0.00862344	+	0.00862344i
$698$		0			0
$699$	25.4631	−	25.4631i	0.963103	−	0.963103i
$700$		0			0
$701$	1.46152	+	1.46152i	0.0552009	+	0.0552009i	0.734168	−	0.678967i	$-0.237572\pi$
$701$	1.46152	+	1.46152i	0.0552009	+	0.0552009i	−0.678967	+	0.734168i	$0.737572\pi$
$702$		0			0
$703$	−3.28551	−	3.28551i	−0.123915	−	0.123915i
$704$		0			0
$705$	−52.1880	−	46.9042i	−1.96552	−	1.76651i
$706$		0			0
$707$	−9.99819			−0.376021
$708$		0			0
$709$	13.1164	+	13.1164i	0.492595	+	0.492595i	0.909123	−	0.416528i	$-0.136753\pi$
$709$	13.1164	+	13.1164i	0.492595	+	0.492595i	−0.416528	+	0.909123i	$0.636753\pi$
$710$		0			0
$711$	2.64663			0.0992563
$712$		0			0
$713$	−3.61289	−	3.61289i	−0.135304	−	0.135304i
$714$		0			0
$715$	7.25930	+	6.52432i	0.271482	+	0.243996i
$716$		0			0
$717$		−	1.32828i		−	0.0496054i
$718$		0			0
$719$	−34.5952			−1.29018			−0.645091	−	0.764106i	$-0.723181\pi$
$719$	−34.5952			−1.29018			−0.645091	+	0.764106i	$0.723181\pi$
$720$		0			0
$721$	−2.89125			−0.107676
$722$		0			0
$723$			69.3034i			2.57742i
$724$		0			0
$725$	14.9206	−	18.4943i	0.554138	−	0.686863i
$726$		0			0
$727$	5.08106	+	5.08106i	0.188446	+	0.188446i	0.795024	−	0.606578i	$-0.207458\pi$
$727$	5.08106	+	5.08106i	0.188446	+	0.188446i	−0.606578	+	0.795024i	$0.707458\pi$
$728$		0			0
$729$	30.6781			1.13623
$730$		0			0
$731$	−34.8000	−	34.8000i	−1.28713	−	1.28713i
$732$		0			0
$733$	−1.11460			−0.0411688			−0.0205844	−	0.999788i	$-0.506553\pi$
$733$	−1.11460			−0.0411688			−0.0205844	+	0.999788i	$0.506553\pi$
$734$		0			0
$735$	83.9427	−	4.47606i	3.09627	−	0.165102i
$736$		0			0
$737$	−23.1458	−	23.1458i	−0.852587	−	0.852587i
$738$		0			0
$739$	−24.9950	−	24.9950i	−0.919454	−	0.919454i	0.0775354	−	0.996990i	$-0.475295\pi$
$739$	−24.9950	−	24.9950i	−0.919454	−	0.919454i	−0.996990	+	0.0775354i	$0.975295\pi$
$740$		0			0
$741$	9.74928	−	9.74928i	0.358149	−	0.358149i
$742$		0			0
$743$	4.45168	−	4.45168i	0.163316	−	0.163316i	−0.620718	−	0.784034i	$-0.713159\pi$
$743$	4.45168	−	4.45168i	0.163316	−	0.163316i	0.784034	+	0.620718i	$0.213159\pi$
$744$		0			0
$745$	−23.4886	−	21.1104i	−0.860555	−	0.773426i
$746$		0			0
$747$			31.0779i			1.13708i
$748$		0			0
$749$	−5.01739	+	5.01739i	−0.183332	+	0.183332i
$750$		0			0
$751$		−	7.28572i		−	0.265860i	−0.991125	−	0.132930i	$-0.957562\pi$
$751$		−	7.28572i		−	0.265860i	0.991125	−	0.132930i	$-0.0424385\pi$
$752$		0			0
$753$	−35.0795	+	35.0795i	−1.27837	+	1.27837i
$754$		0			0
$755$	8.68759	−	0.463247i	0.316174	−	0.0168593i
$756$		0			0
$757$	−6.32260			−0.229799			−0.114899	−	0.993377i	$-0.536655\pi$
$757$	−6.32260			−0.229799			−0.114899	+	0.993377i	$0.536655\pi$
$758$		0			0
$759$			8.87840i			0.322266i
$760$		0			0
$761$			21.1584i			0.766990i	0.923543	+	0.383495i	$0.125280\pi$
$761$			21.1584i			0.766990i	−0.923543	+	0.383495i	$0.874720\pi$
$762$		0			0
$763$	21.6787			0.784821
$764$		0			0
$765$	51.0744	+	45.9033i	1.84660	+	1.65964i
$766$		0			0
$767$	0.455303	−	0.455303i	0.0164401	−	0.0164401i
$768$		0			0
$769$			8.67496i			0.312827i	0.987692	+	0.156414i	$0.0499933\pi$
$769$			8.67496i			0.312827i	−0.987692	+	0.156414i	$0.950007\pi$
$770$		0			0
$771$	−7.02960	+	7.02960i	−0.253165	+	0.253165i
$772$		0			0
$773$			30.4072i			1.09367i	0.837241	+	0.546835i	$0.184167\pi$
$773$			30.4072i			1.09367i	−0.837241	+	0.546835i	$0.815833\pi$
$774$		0			0
$775$	2.84890	+	26.6377i	0.102335	+	0.956855i
$776$		0			0
$777$	−13.0431	+	13.0431i	−0.467917	+	0.467917i
$778$		0			0
$779$	0.144146	−	0.144146i	0.00516457	−	0.00516457i
$780$		0			0
$781$	−27.6623	−	27.6623i	−0.989833	−	0.989833i
$782$		0			0
$783$	28.5442	+	28.5442i	1.02009	+	1.02009i
$784$		0			0
$785$	0.750540	+	14.0754i	0.0267879	+	0.502373i
$786$		0			0
$787$	5.43338			0.193679			0.0968395	−	0.995300i	$-0.469127\pi$
$787$	5.43338			0.193679			0.0968395	+	0.995300i	$0.469127\pi$
$788$		0			0
$789$	−18.7484	−	18.7484i	−0.667461	−	0.667461i
$790$		0			0
$791$	−38.1130			−1.35514
$792$		0			0
$793$	−4.90666	−	4.90666i	−0.174241	−	0.174241i
$794$		0			0
$795$	−9.18728	+	0.489892i	−0.325839	+	0.0173747i
$796$		0			0
$797$		−	21.9799i		−	0.778569i	−0.921118	−	0.389285i	$-0.872722\pi$
$797$		−	21.9799i		−	0.778569i	0.921118	−	0.389285i	$-0.127278\pi$
$798$		0			0
$799$	−55.3191			−1.95705
$800$		0			0
$801$	65.0838			2.29962
$802$		0			0
$803$		−	48.6264i		−	1.71599i
$804$		0			0
$805$	−9.43502	+	0.503102i	−0.332541	+	0.0177320i
$806$		0			0
$807$	−30.3729	−	30.3729i	−1.06918	−	1.06918i
$808$		0			0
$809$	37.4350			1.31614			0.658072	−	0.752955i	$-0.271372\pi$
$809$	37.4350			1.31614			0.658072	+	0.752955i	$0.271372\pi$
$810$		0			0
$811$	−5.92150	−	5.92150i	−0.207932	−	0.207932i	0.595456	−	0.803388i	$-0.296971\pi$
$811$	−5.92150	−	5.92150i	−0.207932	−	0.207932i	−0.803388	+	0.595456i	$0.796971\pi$
$812$		0			0
$813$	16.8196			0.589891
$814$		0			0
$815$	−0.262446	−	4.92184i	−0.00919310	−	0.172405i
$816$		0			0
$817$	22.0336	+	22.0336i	0.770858	+	0.770858i
$818$		0			0
$819$	−25.5902	−	25.5902i	−0.894194	−	0.894194i
$820$		0			0
$821$	17.5498	−	17.5498i	0.612494	−	0.612494i	−0.331101	−	0.943595i	$-0.607420\pi$
$821$	17.5498	−	17.5498i	0.612494	−	0.612494i	0.943595	+	0.331101i	$0.107420\pi$
$822$		0			0
$823$	−3.62807	+	3.62807i	−0.126467	+	0.126467i	−0.767507	−	0.641041i	$-0.778503\pi$
$823$	−3.62807	+	3.62807i	−0.126467	+	0.126467i	0.641041	+	0.767507i	$0.278503\pi$
$824$		0			0
$825$	29.2296	−	36.2306i	1.01765	−	1.26139i
$826$		0			0
$827$		−	35.1888i		−	1.22364i	−0.790999	−	0.611818i	$-0.790439\pi$
$827$		−	35.1888i		−	1.22364i	0.790999	−	0.611818i	$-0.209561\pi$
$828$		0			0
$829$	26.6936	−	26.6936i	0.927108	−	0.927108i	−0.0704101	−	0.997518i	$-0.522431\pi$
$829$	26.6936	−	26.6936i	0.927108	−	0.927108i	0.997518	+	0.0704101i	$0.0224308\pi$
$830$		0			0
$831$		−	21.6437i		−	0.750810i
$832$		0			0
$833$	46.8618	−	46.8618i	1.62366	−	1.62366i
$834$		0			0
$835$	0.579851	+	0.521143i	0.0200666	+	0.0180349i
$836$		0			0
$837$	−45.5097			−1.57305
$838$		0			0
$839$		−	43.8632i		−	1.51433i	−0.653226	−	0.757163i	$-0.726585\pi$
$839$		−	43.8632i		−	1.51433i	0.653226	−	0.757163i	$-0.273415\pi$
$840$		0			0
$841$			6.41338i			0.221151i
$842$		0			0
$843$	−66.1573			−2.27858
$844$		0			0
$845$	−24.6819	+	1.31611i	−0.849082	+	0.0452754i
$846$		0			0
$847$	3.79266	−	3.79266i	0.130317	−	0.130317i
$848$		0			0
$849$		−	48.4021i		−	1.66116i
$850$		0			0
$851$	0.943342	−	0.943342i	0.0323373	−	0.0323373i
$852$		0			0
$853$			32.1850i			1.10199i	0.834508	+	0.550996i	$0.185752\pi$
$853$			32.1850i			1.10199i	−0.834508	+	0.550996i	$0.814248\pi$
$854$		0			0
$855$	−32.3377	−	29.0636i	−1.10593	−	0.993956i
$856$		0			0
$857$	16.2444	−	16.2444i	0.554899	−	0.554899i	−0.372952	−	0.927851i	$-0.621654\pi$
$857$	16.2444	−	16.2444i	0.554899	−	0.554899i	0.927851	+	0.372952i	$0.121654\pi$
$858$		0			0
$859$	−5.95585	+	5.95585i	−0.203211	+	0.203211i	−0.801374	−	0.598163i	$-0.795897\pi$
$859$	−5.95585	+	5.95585i	−0.203211	+	0.203211i	0.598163	+	0.801374i	$0.295897\pi$
$860$		0			0
$861$	−0.572242	−	0.572242i	−0.0195019	−	0.0195019i
$862$		0			0
$863$	16.9034	+	16.9034i	0.575399	+	0.575399i	0.933632	−	0.358233i	$-0.116621\pi$
$863$	16.9034	+	16.9034i	0.575399	+	0.575399i	−0.358233	+	0.933632i	$0.616621\pi$
$864$		0			0
$865$	42.9568	−	2.29058i	1.46058	−	0.0778820i
$866$		0			0
$867$	31.2949			1.06283
$868$		0			0
$869$	−1.00016	−	1.00016i	−0.0339282	−	0.0339282i
$870$		0			0
$871$	−14.5951			−0.494535
$872$		0			0
$873$	−61.8222	−	61.8222i	−2.09236	−	2.09236i
$874$		0			0
$875$	40.1583	+	29.0091i	1.35760	+	0.980687i
$876$		0			0
$877$		−	7.01598i		−	0.236913i	−0.992959	−	0.118456i	$-0.962205\pi$
$877$		−	7.01598i		−	0.236913i	0.992959	−	0.118456i	$-0.0377946\pi$
$878$		0			0
$879$	−75.5594			−2.54856
$880$		0			0
$881$	−11.3834			−0.383517			−0.191759	−	0.981442i	$-0.561419\pi$
$881$	−11.3834			−0.383517			−0.191759	+	0.981442i	$0.561419\pi$
$882$		0			0
$883$		−	32.7727i		−	1.10289i	−0.834211	−	0.551445i	$-0.814077\pi$
$883$		−	32.7727i		−	1.10289i	0.834211	−	0.551445i	$-0.185923\pi$
$884$		0			0
$885$	−2.28409	−	2.05283i	−0.0767788	−	0.0690052i
$886$		0			0
$887$	−13.4104	−	13.4104i	−0.450279	−	0.450279i	0.445168	−	0.895447i	$-0.353144\pi$
$887$	−13.4104	−	13.4104i	−0.450279	−	0.450279i	−0.895447	+	0.445168i	$0.853144\pi$
$888$		0			0
$889$	1.42642			0.0478405
$890$		0			0
$891$	17.0609	+	17.0609i	0.571561	+	0.571561i
$892$		0			0
$893$	35.0253			1.17208
$894$		0			0
$895$	3.54072	+	3.18224i	0.118353	+	0.106370i
$896$		0			0
$897$	2.79923	+	2.79923i	0.0934635	+	0.0934635i
$898$		0			0
$899$	18.0056	+	18.0056i	0.600520	+	0.600520i
$900$		0			0
$901$	−5.12888	+	5.12888i	−0.170868	+	0.170868i
$902$		0			0
$903$	87.4706	−	87.4706i	2.91084	−	2.91084i
$904$		0			0
$905$	25.7039	−	28.5995i	0.854428	−	0.950681i
$906$		0			0
$907$		−	7.75207i		−	0.257403i	−0.991683	−	0.128702i	$-0.958919\pi$
$907$		−	7.75207i		−	0.257403i	0.991683	−	0.128702i	$-0.0410810\pi$
$908$		0			0
$909$	9.34098	−	9.34098i	0.309821	−	0.309821i
$910$		0			0
$911$		−	32.1640i		−	1.06564i	−0.846228	−	0.532820i	$-0.821132\pi$
$911$		−	32.1640i		−	1.06564i	0.846228	−	0.532820i	$-0.178868\pi$
$912$		0			0
$913$	11.7444	−	11.7444i	0.388682	−	0.388682i
$914$		0			0
$915$	−22.1227	+	24.6149i	−0.731354	+	0.813743i
$916$		0			0
$917$	−79.7304			−2.63293
$918$		0			0
$919$			9.75137i			0.321668i	0.986981	+	0.160834i	$0.0514184\pi$
$919$			9.75137i			0.321668i	−0.986981	+	0.160834i	$0.948582\pi$
$920$		0			0
$921$			58.5525i			1.92937i
$922$		0			0
$923$	−17.4430			−0.574143
$924$		0			0
$925$	−6.95523	+	0.743860i	−0.228687	+	0.0244580i
$926$		0			0
$927$	2.70120	−	2.70120i	0.0887191	−	0.0887191i
$928$		0			0
$929$			43.6287i			1.43141i	0.698402	+	0.715705i	$0.253895\pi$
$929$			43.6287i			1.43141i	−0.698402	+	0.715705i	$0.746105\pi$
$930$		0			0
$931$	−29.6705	+	29.6705i	−0.972411	+	0.972411i
$932$		0			0
$933$			83.8877i			2.74636i
$934$		0			0
$935$	−1.95417	−	36.6480i	−0.0639083	−	1.19852i
$936$		0			0
$937$	31.5549	−	31.5549i	1.03085	−	1.03085i	0.0313438	−	0.999509i	$-0.490021\pi$
$937$	31.5549	−	31.5549i	1.03085	−	1.03085i	0.999509	−	0.0313438i	$-0.00997868\pi$
$938$		0			0
$939$	13.2513	−	13.2513i	0.432439	−	0.432439i
$940$		0			0
$941$	14.9543	+	14.9543i	0.487497	+	0.487497i	0.907516	−	0.420018i	$-0.137976\pi$
$941$	14.9543	+	14.9543i	0.487497	+	0.487497i	−0.420018	+	0.907516i	$0.637976\pi$
$942$		0			0
$943$	0.0413875	+	0.0413875i	0.00134776	+	0.00134776i
$944$		0			0
$945$	−56.2555	+	62.5928i	−1.82999	+	2.03614i
$946$		0			0
$947$	−31.6676			−1.02906			−0.514530	−	0.857472i	$-0.672034\pi$
$947$	−31.6676			−1.02906			−0.514530	+	0.857472i	$0.672034\pi$
$948$		0			0
$949$	−15.3312	−	15.3312i	−0.497671	−	0.497671i
$950$		0			0
$951$	−92.2438			−2.99121
$952$		0			0
$953$	−0.671313	−	0.671313i	−0.0217460	−	0.0217460i	0.696150	−	0.717896i	$-0.254895\pi$
$953$	−0.671313	−	0.671313i	−0.0217460	−	0.0217460i	−0.717896	+	0.696150i	$0.754895\pi$
$954$		0			0
$955$	0.591678	+	11.0962i	0.0191462	+	0.359063i
$956$		0			0
$957$		−	44.2474i		−	1.43032i
$958$		0			0
$959$	−36.5318			−1.17967
$960$		0			0
$961$	2.29263			0.0739559
$962$		0			0
$963$		−	9.37517i		−	0.302111i
$964$		0			0
$965$	−32.4572	+	36.1135i	−1.04483	+	1.16254i
$966$		0			0
$967$	22.7926	+	22.7926i	0.732959	+	0.732959i	0.971205	−	0.238246i	$-0.0765723\pi$
$967$	22.7926	+	22.7926i	0.732959	+	0.732959i	−0.238246	+	0.971205i	$0.576572\pi$
$968$		0			0
$969$	−51.8429			−1.66543
$970$		0			0
$971$	−22.9086	−	22.9086i	−0.735173	−	0.735173i	0.236467	−	0.971640i	$-0.424011\pi$
$971$	−22.9086	−	22.9086i	−0.735173	−	0.735173i	−0.971640	+	0.236467i	$0.924011\pi$
$972$		0			0
$973$	−25.2759			−0.810308
$974$		0			0
$975$	−2.20730	−	20.6386i	−0.0706900	−	0.660965i
$976$		0			0
$977$	−33.5811	−	33.5811i	−1.07435	−	1.07435i	−0.997004	−	0.0773506i	$-0.975354\pi$
$977$	−33.5811	−	33.5811i	−1.07435	−	1.07435i	−0.0773506	−	0.997004i	$-0.524646\pi$
$978$		0			0
$979$	−24.5952	−	24.5952i	−0.786067	−	0.786067i
$980$		0			0
$981$	−20.2537	+	20.2537i	−0.646650	+	0.646650i
$982$		0			0
$983$	−8.88025	+	8.88025i	−0.283236	+	0.283236i	−0.834398	−	0.551162i	$-0.814185\pi$
$983$	−8.88025	+	8.88025i	−0.283236	+	0.283236i	0.551162	+	0.834398i	$0.314185\pi$
$984$		0			0
$985$	9.18722	−	0.489888i	0.292729	−	0.0156091i
$986$		0			0
$987$		−	139.046i		−	4.42588i
$988$		0			0
$989$	−6.32632	+	6.32632i	−0.201165	+	0.201165i
$990$		0			0
$991$			45.7111i			1.45206i	0.687663	+	0.726030i	$0.258637\pi$
$991$			45.7111i			1.45206i	−0.687663	+	0.726030i	$0.741363\pi$
$992$		0			0
$993$	−63.5006	+	63.5006i	−2.01513	+	2.01513i
$994$		0			0
$995$	3.06187	+	57.4215i	0.0970679	+	1.82038i
$996$		0			0
$997$	−9.18540			−0.290904			−0.145452	−	0.989365i	$-0.546464\pi$
$997$	−9.18540			−0.290904			−0.145452	+	0.989365i	$0.546464\pi$
$998$		0			0
$999$		−	11.8828i		−	0.375955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.j.d.447.1	yes	32
4.3	odd	2	inner	1280.2.j.d.447.16	yes	32
5.3	odd	4		1280.2.s.c.703.16	yes	32
8.3	odd	2		1280.2.j.c.447.1	yes	32
8.5	even	2		1280.2.j.c.447.16	yes	32
16.3	odd	4		1280.2.s.d.1087.1	yes	32
16.5	even	4		1280.2.s.c.1087.1	yes	32
16.11	odd	4		1280.2.s.c.1087.16	yes	32
16.13	even	4		1280.2.s.d.1087.16	yes	32
20.3	even	4		1280.2.s.c.703.1	yes	32
40.3	even	4		1280.2.s.d.703.16	yes	32
40.13	odd	4		1280.2.s.d.703.1	yes	32
80.3	even	4		1280.2.j.c.63.1	✓	32
80.13	odd	4		1280.2.j.c.63.16	yes	32
80.43	even	4	inner	1280.2.j.d.63.16	yes	32
80.53	odd	4	inner	1280.2.j.d.63.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.j.c.63.1	✓	32	80.3	even	4
1280.2.j.c.63.16	yes	32	80.13	odd	4
1280.2.j.c.447.1	yes	32	8.3	odd	2
1280.2.j.c.447.16	yes	32	8.5	even	2
1280.2.j.d.63.1	yes	32	80.53	odd	4	inner
1280.2.j.d.63.16	yes	32	80.43	even	4	inner
1280.2.j.d.447.1	yes	32	1.1	even	1	trivial
1280.2.j.d.447.16	yes	32	4.3	odd	2	inner
1280.2.s.c.703.1	yes	32	20.3	even	4
1280.2.s.c.703.16	yes	32	5.3	odd	4
1280.2.s.c.1087.1	yes	32	16.5	even	4
1280.2.s.c.1087.16	yes	32	16.11	odd	4
1280.2.s.d.703.1	yes	32	40.13	odd	4
1280.2.s.d.703.16	yes	32	40.3	even	4
1280.2.s.d.1087.1	yes	32	16.3	odd	4
1280.2.s.d.1087.16	yes	32	16.13	even	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)

\(f(q)\)	\(=\)	\(q-2.97565i q^{3} +(2.23290 - 0.119064i) q^{5} +(3.13319 + 3.13319i) q^{7} -5.85447 q^{9} +(2.21241 + 2.21241i) q^{11} +1.39508 q^{13} +(-0.354293 - 6.64431i) q^{15} +(-3.70925 - 3.70925i) q^{17} +(2.34851 + 2.34851i) q^{19} +(9.32327 - 9.32327i) q^{21} +(-0.674307 + 0.674307i) q^{23} +(4.97165 - 0.531716i) q^{25} +8.49391i q^{27} +(3.36055 - 3.36055i) q^{29} +5.35793i q^{31} +(6.58335 - 6.58335i) q^{33} +(7.36914 + 6.62304i) q^{35} -1.39898 q^{37} -4.15127i q^{39} -0.0613778i q^{41} +9.38196 q^{43} +(-13.0724 + 0.697059i) q^{45} +(7.45692 - 7.45692i) q^{47} +12.6338i q^{49} +(-11.0374 + 11.0374i) q^{51} -1.38273i q^{53} +(5.20350 + 4.67666i) q^{55} +(6.98833 - 6.98833i) q^{57} +(0.326364 - 0.326364i) q^{59} +(-3.51712 - 3.51712i) q^{61} +(-18.3432 - 18.3432i) q^{63} +(3.11507 - 0.166104i) q^{65} -10.4618 q^{67} +(2.00650 + 2.00650i) q^{69} -12.5032 q^{71} +(-10.9895 - 10.9895i) q^{73} +(-1.58220 - 14.7939i) q^{75} +13.8638i q^{77} -0.452069 q^{79} +7.71145 q^{81} -5.30840i q^{83} +(-8.72400 - 7.84072i) q^{85} +(-9.99982 - 9.99982i) q^{87} -11.1169 q^{89} +(4.37105 + 4.37105i) q^{91} +15.9433 q^{93} +(5.52359 + 4.96435i) q^{95} +(10.5598 + 10.5598i) q^{97} +(-12.9525 - 12.9525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) \) 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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