LMFDB - Embedded newform 1280.2.n.r.767.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(767,1280)] 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("1280.767"); 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, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1280 = 2^{8} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1280.n (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-4,0,0,0,0,0,0,0,20] 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:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.125772815663104.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 27x^{8} + 107x^{4} + 1 $ x^12 + 27x^8 + 107x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	no (minimal twist has level 640)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			767.1
Root			$0.219986 + 0.219986i$ of defining polynomial
Character	$\chi$	$=$	1280.767
Dual form			1280.2.n.r.1023.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05288 - 2.05288i) q^{3} +(-0.311108 + 2.21432i) q^{5} +(-1.07864 + 1.07864i) q^{7} +5.42864i q^{9} -4.98571i q^{11} +(3.90321 - 3.90321i) q^{13} +(5.18440 - 3.90707i) q^{15} +(-0.377784 - 0.377784i) q^{17} -3.43461 q^{19} +4.42864 q^{21} +(-0.198694 - 0.198694i) q^{23} +(-4.80642 - 1.37778i) q^{25} +(4.98571 - 4.98571i) q^{27} +7.80642i q^{29} +6.05424i q^{31} +(-10.2351 + 10.2351i) q^{33} +(-2.05288 - 2.72403i) q^{35} +(-6.33185 - 6.33185i) q^{37} -16.0257 q^{39} -3.18421 q^{41} +(2.05288 + 2.05288i) q^{43} +(-12.0207 - 1.68889i) q^{45} +(2.35597 - 2.35597i) q^{47} +4.67307i q^{49} +1.55109i q^{51} +(0.719004 - 0.719004i) q^{53} +(11.0400 + 1.55109i) q^{55} +(7.05086 + 7.05086i) q^{57} -6.53680 q^{59} -3.37778 q^{61} +(-5.85555 - 5.85555i) q^{63} +(7.42864 + 9.85728i) q^{65} +(-7.70974 + 7.70974i) q^{67} +0.815792i q^{69} +12.9235i q^{71} +(-2.05086 + 2.05086i) q^{73} +(7.03859 + 12.6954i) q^{75} +(5.37778 + 5.37778i) q^{77} +3.10219 q^{79} -4.18421 q^{81} +(5.48750 + 5.48750i) q^{83} +(0.954067 - 0.719004i) q^{85} +(16.0257 - 16.0257i) q^{87} +8.85728i q^{89} +8.42032i q^{91} +(12.4286 - 12.4286i) q^{93} +(1.06854 - 7.60534i) q^{95} +(-2.80642 - 2.80642i) q^{97} +27.0656 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} + 20 q^{13} - 4 q^{17} - 4 q^{25} - 16 q^{33} + 4 q^{37} + 16 q^{41} - 64 q^{45} + 36 q^{53} + 32 q^{57} - 40 q^{61} + 36 q^{65} + 28 q^{73} + 64 q^{77} + 4 q^{81} - 68 q^{85} + 96 q^{93}+ \cdots + 20 q^{97}+O(q^{100}) $ 12 * q - 4 * q^5 + 20 * q^13 - 4 * q^17 - 4 * q^25 - 16 * q^33 + 4 * q^37 + 16 * q^41 - 64 * q^45 + 36 * q^53 + 32 * q^57 - 40 * q^61 + 36 * q^65 + 28 * q^73 + 64 * q^77 + 4 * q^81 - 68 * q^85 + 96 * q^93 + 20 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.05288	−	2.05288i	−1.18523	−	1.18523i	−0.978370	−	0.206861i	$-0.933675\pi$
$3$	−2.05288	−	2.05288i	−1.18523	−	1.18523i	−0.206861	−	0.978370i	$-0.566325\pi$
$4$		0			0
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$5$	−0.311108	+	2.21432i	−0.139132	+	0.990274i
$6$		0			0
$7$	−1.07864	+	1.07864i	−0.407688	+	0.407688i	−0.880931	−	0.473244i	$-0.843083\pi$
$7$	−1.07864	+	1.07864i	−0.407688	+	0.407688i	0.473244	+	0.880931i	$0.343083\pi$
$8$		0			0
$9$			5.42864i			1.80955i
$10$		0			0
$11$		−	4.98571i		−	1.50325i	−0.659592	−	0.751624i	$-0.729271\pi$
$11$		−	4.98571i		−	1.50325i	0.659592	−	0.751624i	$-0.270729\pi$
$12$		0			0
$13$	3.90321	−	3.90321i	1.08256	−	1.08256i	0.0862858	−	0.996270i	$-0.472500\pi$
$13$	3.90321	−	3.90321i	1.08256	−	1.08256i	0.996270	−	0.0862858i	$-0.0274998\pi$
$14$		0			0
$15$	5.18440	−	3.90707i	1.33861	−	1.00880i
$16$		0			0
$17$	−0.377784	−	0.377784i	−0.0916262	−	0.0916262i	0.659808	−	0.751434i	$-0.270638\pi$
$17$	−0.377784	−	0.377784i	−0.0916262	−	0.0916262i	−0.751434	+	0.659808i	$0.770638\pi$
$18$		0			0
$19$	−3.43461			−0.787955			−0.393977	−	0.919120i	$-0.628901\pi$
$19$	−3.43461			−0.787955			−0.393977	+	0.919120i	$0.628901\pi$
$20$		0			0
$21$	4.42864			0.966408
$22$		0			0
$23$	−0.198694	−	0.198694i	−0.0414306	−	0.0414306i	0.686088	−	0.727519i	$-0.259327\pi$
$23$	−0.198694	−	0.198694i	−0.0414306	−	0.0414306i	−0.727519	+	0.686088i	$0.759327\pi$
$24$		0			0
$25$	−4.80642	−	1.37778i	−0.961285	−	0.275557i
$26$		0			0
$27$	4.98571	−	4.98571i	0.959500	−	0.959500i
$28$		0			0
$29$			7.80642i			1.44962i	0.688951	+	0.724808i	$0.258072\pi$
$29$			7.80642i			1.44962i	−0.688951	+	0.724808i	$0.741928\pi$
$30$		0			0
$31$			6.05424i			1.08737i	0.839288	+	0.543687i	$0.182972\pi$
$31$			6.05424i			1.08737i	−0.839288	+	0.543687i	$0.817028\pi$
$32$		0			0
$33$	−10.2351	+	10.2351i	−1.78170	+	1.78170i
$34$		0			0
$35$	−2.05288	−	2.72403i	−0.347000	−	0.460445i
$36$		0			0
$37$	−6.33185	−	6.33185i	−1.04095	−	1.04095i	−0.999125	−	0.0418250i	$-0.986683\pi$
$37$	−6.33185	−	6.33185i	−1.04095	−	1.04095i	−0.0418250	−	0.999125i	$-0.513317\pi$
$38$		0			0
$39$	−16.0257			−2.56616
$40$		0			0
$41$	−3.18421			−0.497290			−0.248645	−	0.968595i	$-0.579985\pi$
$41$	−3.18421			−0.497290			−0.248645	+	0.968595i	$0.579985\pi$
$42$		0			0
$43$	2.05288	+	2.05288i	0.313061	+	0.313061i	0.846094	−	0.533033i	$-0.178948\pi$
$43$	2.05288	+	2.05288i	0.313061	+	0.313061i	−0.533033	+	0.846094i	$0.678948\pi$
$44$		0			0
$45$	−12.0207	−	1.68889i	−1.79195	−	0.251765i
$46$		0			0
$47$	2.35597	−	2.35597i	0.343654	−	0.343654i	−0.514085	−	0.857739i	$-0.671868\pi$
$47$	2.35597	−	2.35597i	0.343654	−	0.343654i	0.857739	+	0.514085i	$0.171868\pi$
$48$		0			0
$49$			4.67307i			0.667582i
$50$		0			0
$51$			1.55109i			0.217196i
$52$		0			0
$53$	0.719004	−	0.719004i	0.0987628	−	0.0987628i	−0.655999	−	0.754762i	$-0.727752\pi$
$53$	0.719004	−	0.719004i	0.0987628	−	0.0987628i	0.754762	+	0.655999i	$0.227752\pi$
$54$		0			0
$55$	11.0400	+	1.55109i	1.48863	+	0.209149i
$56$		0			0
$57$	7.05086	+	7.05086i	0.933909	+	0.933909i
$58$		0			0
$59$	−6.53680			−0.851019			−0.425509	−	0.904954i	$-0.639905\pi$
$59$	−6.53680			−0.851019			−0.425509	+	0.904954i	$0.639905\pi$
$60$		0			0
$61$	−3.37778			−0.432481			−0.216240	−	0.976340i	$-0.569380\pi$
$61$	−3.37778			−0.432481			−0.216240	+	0.976340i	$0.569380\pi$
$62$		0			0
$63$	−5.85555	−	5.85555i	−0.737730	−	0.737730i
$64$		0			0
$65$	7.42864	+	9.85728i	0.921409	+	1.22264i
$66$		0			0
$67$	−7.70974	+	7.70974i	−0.941894	+	0.941894i	−0.998402	−	0.0565081i	$-0.982003\pi$
$67$	−7.70974	+	7.70974i	−0.941894	+	0.941894i	0.0565081	+	0.998402i	$0.482003\pi$
$68$		0			0
$69$			0.815792i			0.0982098i
$70$		0			0
$71$			12.9235i			1.53373i	0.641806	+	0.766867i	$0.278185\pi$
$71$			12.9235i			1.53373i	−0.641806	+	0.766867i	$0.721815\pi$
$72$		0			0
$73$	−2.05086	+	2.05086i	−0.240034	+	0.240034i	−0.816864	−	0.576830i	$-0.804290\pi$
$73$	−2.05086	+	2.05086i	−0.240034	+	0.240034i	0.576830	+	0.816864i	$0.304290\pi$
$74$		0			0
$75$	7.03859	+	12.6954i	0.812746	+	1.46594i
$76$		0			0
$77$	5.37778	+	5.37778i	0.612855	+	0.612855i
$78$		0			0
$79$	3.10219			0.349023			0.174512	−	0.984655i	$-0.444165\pi$
$79$	3.10219			0.349023			0.174512	+	0.984655i	$0.444165\pi$
$80$		0			0
$81$	−4.18421			−0.464912
$82$		0			0
$83$	5.48750	+	5.48750i	0.602331	+	0.602331i	0.940931	−	0.338600i	$-0.109953\pi$
$83$	5.48750	+	5.48750i	0.602331	+	0.602331i	−0.338600	+	0.940931i	$0.609953\pi$
$84$		0			0
$85$	0.954067	−	0.719004i	0.103483	−	0.0779869i
$86$		0			0
$87$	16.0257	−	16.0257i	1.71813	−	1.71813i
$88$		0			0
$89$			8.85728i			0.938870i	0.882967	+	0.469435i	$0.155542\pi$
$89$			8.85728i			0.938870i	−0.882967	+	0.469435i	$0.844458\pi$
$90$		0			0
$91$			8.42032i			0.882690i
$92$		0			0
$93$	12.4286	−	12.4286i	1.28879	−	1.28879i
$94$		0			0
$95$	1.06854	−	7.60534i	0.109629	−	0.780291i
$96$		0			0
$97$	−2.80642	−	2.80642i	−0.284949	−	0.284949i	0.550130	−	0.835079i	$-0.314578\pi$
$97$	−2.80642	−	2.80642i	−0.284949	−	0.284949i	−0.835079	+	0.550130i	$0.814578\pi$
$98$		0			0
$99$	27.0656			2.72020
$100$		0			0
$101$	−14.1017			−1.40317			−0.701586	−	0.712584i	$-0.747525\pi$
$101$	−14.1017			−1.40317			−0.701586	+	0.712584i	$0.747525\pi$
$102$		0			0
$103$	−10.1701	−	10.1701i	−1.00209	−	1.00209i	−0.999998	−	0.00209284i	$-0.999334\pi$
$103$	−10.1701	−	10.1701i	−1.00209	−	1.00209i	−0.00209284	−	0.999998i	$-0.500666\pi$
$104$		0			0
$105$	−1.37778	+	9.80642i	−0.134458	+	0.957009i
$106$		0			0
$107$	−2.26168	+	2.26168i	−0.218645	+	0.218645i	−0.807927	−	0.589282i	$-0.799411\pi$
$107$	−2.26168	+	2.26168i	−0.218645	+	0.218645i	0.589282	+	0.807927i	$0.299411\pi$
$108$		0			0
$109$			0.815792i			0.0781387i	0.999237	+	0.0390693i	$0.0124393\pi$
$109$			0.815792i			0.0781387i	−0.999237	+	0.0390693i	$0.987561\pi$
$110$		0			0
$111$			25.9971i			2.46753i
$112$		0			0
$113$	7.42864	−	7.42864i	0.698828	−	0.698828i	−0.265330	−	0.964158i	$-0.585481\pi$
$113$	7.42864	−	7.42864i	0.698828	−	0.698828i	0.964158	+	0.265330i	$0.0854809\pi$
$114$		0			0
$115$	0.501788	−	0.378158i	0.0467920	−	0.0352634i
$116$		0			0
$117$	21.1891	+	21.1891i	1.95894	+	1.95894i
$118$		0			0
$119$	0.814987			0.0747097
$120$		0			0
$121$	−13.8573			−1.25975
$122$		0			0
$123$	6.53680	+	6.53680i	0.589403	+	0.589403i
$124$		0			0
$125$	4.54617	−	10.2143i	0.406622	−	0.913597i
$126$		0			0
$127$	−8.89277	+	8.89277i	−0.789106	+	0.789106i	−0.981348	−	0.192241i	$-0.938424\pi$
$127$	−8.89277	+	8.89277i	−0.789106	+	0.789106i	0.192241	+	0.981348i	$0.438424\pi$
$128$		0			0
$129$		−	8.42864i		−	0.742100i
$130$		0			0
$131$			17.0942i			1.49353i	0.665090	+	0.746763i	$0.268393\pi$
$131$			17.0942i			1.49353i	−0.665090	+	0.746763i	$0.731607\pi$
$132$		0			0
$133$	3.70471	−	3.70471i	0.321239	−	0.321239i
$134$		0			0
$135$	9.48886	+	12.5910i	0.816671	+	1.08366i
$136$		0			0
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	0.460487	−	0.887666i	$-0.347675\pi$
$137$	−5.00000	−	5.00000i	−0.427179	−	0.427179i	−0.887666	+	0.460487i	$0.847675\pi$
$138$		0			0
$139$	−18.6453			−1.58147			−0.790736	−	0.612157i	$-0.790302\pi$
$139$	−18.6453			−1.58147			−0.790736	+	0.612157i	$0.790302\pi$
$140$		0			0
$141$	−9.67307			−0.814620
$142$		0			0
$143$	−19.4603	−	19.4603i	−1.62735	−	1.62735i
$144$		0			0
$145$	−17.2859	−	2.42864i	−1.43552	−	0.201688i
$146$		0			0
$147$	9.59326	−	9.59326i	0.791239	−	0.791239i
$148$		0			0
$149$			9.93978i			0.814298i	0.913362	+	0.407149i	$0.133477\pi$
$149$			9.93978i			0.814298i	−0.913362	+	0.407149i	$0.866523\pi$
$150$		0			0
$151$		−	3.91717i		−	0.318775i	−0.987216	−	0.159387i	$-0.949048\pi$
$151$		−	3.91717i		−	0.318775i	0.987216	−	0.159387i	$-0.0509519\pi$
$152$		0			0
$153$	2.05086	−	2.05086i	0.165802	−	0.165802i
$154$		0			0
$155$	−13.4060	−	1.88352i	−1.07680	−	0.151288i
$156$		0			0
$157$	10.9541	+	10.9541i	0.874230	+	0.874230i	0.992930	−	0.118700i	$-0.0378728\pi$
$157$	10.9541	+	10.9541i	0.874230	+	0.874230i	−0.118700	+	0.992930i	$0.537873\pi$
$158$		0			0
$159$	−2.95206			−0.234113
$160$		0			0
$161$	0.428639			0.0337815
$162$		0			0
$163$	−12.0243	−	12.0243i	−0.941816	−	0.941816i	0.0565824	−	0.998398i	$-0.481980\pi$
$163$	−12.0243	−	12.0243i	−0.941816	−	0.941816i	−0.998398	+	0.0565824i	$0.981980\pi$
$164$		0			0
$165$	−19.4795	−	25.8479i	−1.51648	−	2.01226i
$166$		0			0
$167$	7.61544	−	7.61544i	0.589300	−	0.589300i	−0.348142	−	0.937442i	$-0.613187\pi$
$167$	7.61544	−	7.61544i	0.589300	−	0.589300i	0.937442	+	0.348142i	$0.113187\pi$
$168$		0			0
$169$		−	17.4701i		−	1.34386i
$170$		0			0
$171$		−	18.6453i		−	1.42584i
$172$		0			0
$173$	−11.1891	+	11.1891i	−0.850694	+	0.850694i	−0.990219	−	0.139525i	$-0.955443\pi$
$173$	−11.1891	+	11.1891i	−0.850694	+	0.850694i	0.139525	+	0.990219i	$0.455443\pi$
$174$		0			0
$175$	6.67054	−	3.69827i	0.504245	−	0.279563i
$176$		0			0
$177$	13.4193	+	13.4193i	1.00865	+	1.00865i
$178$		0			0
$179$	−5.57169			−0.416447			−0.208224	−	0.978081i	$-0.566768\pi$
$179$	−5.57169			−0.416447			−0.208224	+	0.978081i	$0.566768\pi$
$180$		0			0
$181$	3.34614			0.248717			0.124358	−	0.992237i	$-0.460313\pi$
$181$	3.34614			0.248717			0.124358	+	0.992237i	$0.460313\pi$
$182$		0			0
$183$	6.93419	+	6.93419i	0.512590	+	0.512590i
$184$		0			0
$185$	15.9906	−	12.0509i	1.17565	−	0.885996i
$186$		0			0
$187$	−1.88352	+	1.88352i	−0.137737	+	0.137737i
$188$		0			0
$189$			10.7556i			0.782353i
$190$		0			0
$191$			9.15643i			0.662536i	0.943537	+	0.331268i	$0.107476\pi$
$191$			9.15643i			0.662536i	−0.943537	+	0.331268i	$0.892524\pi$
$192$		0			0
$193$	5.99063	−	5.99063i	0.431215	−	0.431215i	−0.457826	−	0.889042i	$-0.651372\pi$
$193$	5.99063	−	5.99063i	0.431215	−	0.431215i	0.889042	+	0.457826i	$0.151372\pi$
$194$		0			0
$195$	4.98571	−	35.4859i	0.357034	−	2.54120i
$196$		0			0
$197$	3.66815	+	3.66815i	0.261345	+	0.261345i	0.825600	−	0.564255i	$-0.190837\pi$
$197$	3.66815	+	3.66815i	0.261345	+	0.261345i	−0.564255	+	0.825600i	$0.690837\pi$
$198$		0			0
$199$	−3.10219			−0.219908			−0.109954	−	0.993937i	$-0.535070\pi$
$199$	−3.10219			−0.219908			−0.109954	+	0.993937i	$0.535070\pi$
$200$		0			0
$201$	31.6543			2.23272
$202$		0			0
$203$	−8.42032	−	8.42032i	−0.590991	−	0.590991i
$204$		0			0
$205$	0.990632	−	7.05086i	0.0691887	−	0.492453i
$206$		0			0
$207$	1.07864	−	1.07864i	0.0749707	−	0.0749707i
$208$		0			0
$209$			17.1240i			1.18449i
$210$		0			0
$211$		−	17.0942i		−	1.17681i	−0.808565	−	0.588406i	$-0.799756\pi$
$211$		−	17.0942i		−	1.17681i	0.808565	−	0.588406i	$-0.200244\pi$
$212$		0			0
$213$	26.5303	−	26.5303i	1.81783	−	1.81783i
$214$		0			0
$215$	−5.18440	+	3.90707i	−0.353573	+	0.266460i
$216$		0			0
$217$	−6.53035	−	6.53035i	−0.443309	−	0.443309i
$218$		0			0
$219$	8.42032			0.568993
$220$		0			0
$221$	−2.94914			−0.198381
$222$		0			0
$223$	3.23592	+	3.23592i	0.216693	+	0.216693i	0.807103	−	0.590410i	$-0.201034\pi$
$223$	3.23592	+	3.23592i	0.216693	+	0.216693i	−0.590410	+	0.807103i	$0.701034\pi$
$224$		0			0
$225$	7.47949	−	26.0923i	0.498633	−	1.73949i
$226$		0			0
$227$	−17.8048	+	17.8048i	−1.18174	+	1.18174i	−0.202453	+	0.979292i	$0.564891\pi$
$227$	−17.8048	+	17.8048i	−1.18174	+	1.18174i	−0.979292	+	0.202453i	$0.935109\pi$
$228$		0			0
$229$			12.1936i			0.805774i	0.915250	+	0.402887i	$0.131993\pi$
$229$			12.1936i			0.805774i	−0.915250	+	0.402887i	$0.868007\pi$
$230$		0			0
$231$		−	22.0799i		−	1.45275i
$232$		0			0
$233$	−1.13335	+	1.13335i	−0.0742484	+	0.0742484i	−0.743256	−	0.669007i	$-0.766719\pi$
$233$	−1.13335	+	1.13335i	−0.0742484	+	0.0742484i	0.669007	+	0.743256i	$0.266719\pi$
$234$		0			0
$235$	4.48392	+	5.94984i	0.292499	+	0.388125i
$236$		0			0
$237$	−6.36842	−	6.36842i	−0.413673	−	0.413673i
$238$		0			0
$239$	2.13707			0.138236			0.0691178	−	0.997609i	$-0.477982\pi$
$239$	2.13707			0.138236			0.0691178	+	0.997609i	$0.477982\pi$
$240$		0			0
$241$	−0.161933			−0.0104310			−0.00521552	−	0.999986i	$-0.501660\pi$
$241$	−0.161933			−0.0104310			−0.00521552	+	0.999986i	$0.501660\pi$
$242$		0			0
$243$	−6.36744	−	6.36744i	−0.408472	−	0.408472i
$244$		0			0
$245$	−10.3477	−	1.45383i	−0.661089	−	0.0928817i
$246$		0			0
$247$	−13.4060	+	13.4060i	−0.853005	+	0.853005i
$248$		0			0
$249$		−	22.5303i		−	1.42780i
$250$		0			0
$251$		−	14.9571i		−	0.944085i	−0.881576	−	0.472043i	$-0.843517\pi$
$251$		−	14.9571i		−	0.944085i	0.881576	−	0.472043i	$-0.156483\pi$
$252$		0			0
$253$	−0.990632	+	0.990632i	−0.0622805	+	0.0622805i
$254$		0			0
$255$	−3.43461	−	0.482557i	−0.215084	−	0.0302189i
$256$		0			0
$257$	−6.67307	−	6.67307i	−0.416255	−	0.416255i	0.467656	−	0.883911i	$-0.345099\pi$
$257$	−6.67307	−	6.67307i	−0.416255	−	0.416255i	−0.883911	+	0.467656i	$0.845099\pi$
$258$		0			0
$259$	13.6596			0.848765
$260$		0			0
$261$	−42.3783			−2.62315
$262$		0			0
$263$	16.7069	+	16.7069i	1.03019	+	1.03019i	0.999530	+	0.0306624i	$0.00976166\pi$
$263$	16.7069	+	16.7069i	1.03019	+	1.03019i	0.0306624	+	0.999530i	$0.490238\pi$
$264$		0			0
$265$	1.36842	+	1.81579i	0.0840612	+	0.111543i
$266$		0			0
$267$	18.1829	−	18.1829i	1.11278	−	1.11278i
$268$		0			0
$269$		−	16.8988i		−	1.03034i	−0.857089	−	0.515168i	$-0.827730\pi$
$269$		−	16.8988i		−	1.03034i	0.857089	−	0.515168i	$-0.172270\pi$
$270$		0			0
$271$		−	19.1278i		−	1.16193i	−0.813927	−	0.580967i	$-0.802675\pi$
$271$		−	19.1278i		−	1.16193i	0.813927	−	0.580967i	$-0.197325\pi$
$272$		0			0
$273$	17.2859	−	17.2859i	1.04619	−	1.04619i
$274$		0			0
$275$	−6.86923	+	23.9634i	−0.414230	+	1.44505i
$276$		0			0
$277$	4.65878	+	4.65878i	0.279919	+	0.279919i	0.833077	−	0.553158i	$-0.186577\pi$
$277$	4.65878	+	4.65878i	0.279919	+	0.279919i	−0.553158	+	0.833077i	$0.686577\pi$
$278$		0			0
$279$	−32.8663			−1.96765
$280$		0			0
$281$	12.8988			0.769476			0.384738	−	0.923026i	$-0.374292\pi$
$281$	12.8988			0.769476			0.384738	+	0.923026i	$0.374292\pi$
$282$		0			0
$283$	−8.58968	−	8.58968i	−0.510604	−	0.510604i	0.404108	−	0.914711i	$-0.367582\pi$
$283$	−8.58968	−	8.58968i	−0.510604	−	0.510604i	−0.914711	+	0.404108i	$0.867582\pi$
$284$		0			0
$285$	−17.8064	+	13.4193i	−1.05476	+	0.794889i
$286$		0			0
$287$	3.43461	−	3.43461i	0.202739	−	0.202739i
$288$		0			0
$289$		−	16.7146i		−	0.983209i
$290$		0			0
$291$			11.5225i			0.675461i
$292$		0			0
$293$	12.4652	−	12.4652i	0.728225	−	0.728225i	−0.242041	−	0.970266i	$-0.577817\pi$
$293$	12.4652	−	12.4652i	0.728225	−	0.728225i	0.970266	+	0.242041i	$0.0778169\pi$
$294$		0			0
$295$	2.03365	−	14.4746i	0.118404	−	0.842742i
$296$		0			0
$297$	−24.8573	−	24.8573i	−1.44237	−	1.44237i
$298$		0			0
$299$	−1.55109			−0.0897020
$300$		0			0
$301$	−4.42864			−0.255263
$302$		0			0
$303$	28.9491	+	28.9491i	1.66308	+	1.66308i
$304$		0			0
$305$	1.05086	−	7.47949i	0.0601718	−	0.428275i
$306$		0			0
$307$	4.39875	−	4.39875i	0.251050	−	0.251050i	−0.570351	−	0.821401i	$-0.693193\pi$
$307$	4.39875	−	4.39875i	0.251050	−	0.251050i	0.821401	+	0.570351i	$0.193193\pi$
$308$		0			0
$309$			41.7560i			2.37542i
$310$		0			0
$311$			10.7864i			0.611641i	0.952089	+	0.305820i	$0.0989307\pi$
$311$			10.7864i			0.611641i	−0.952089	+	0.305820i	$0.901069\pi$
$312$		0			0
$313$	−16.6731	+	16.6731i	−0.942418	+	0.942418i	−0.998430	−	0.0560124i	$-0.982161\pi$
$313$	−16.6731	+	16.6731i	−0.942418	+	0.942418i	0.0560124	+	0.998430i	$0.482161\pi$
$314$		0			0
$315$	14.7878	−	11.1443i	0.833196	−	0.627913i
$316$		0			0
$317$	6.85236	+	6.85236i	0.384867	+	0.384867i	0.872852	−	0.487985i	$-0.162268\pi$
$317$	6.85236	+	6.85236i	0.384867	+	0.384867i	−0.487985	+	0.872852i	$0.662268\pi$
$318$		0			0
$319$	38.9205			2.17913
$320$		0			0
$321$	9.28592			0.518289
$322$		0			0
$323$	1.29754	+	1.29754i	0.0721973	+	0.0721973i
$324$		0			0
$325$	−24.1383	+	13.3827i	−1.33895	+	0.742339i
$326$		0			0
$327$	1.67472	−	1.67472i	0.0926124	−	0.0926124i
$328$		0			0
$329$			5.08250i			0.280207i
$330$		0			0
$331$			27.0656i			1.48766i	0.668369	+	0.743830i	$0.266993\pi$
$331$			27.0656i			1.48766i	−0.668369	+	0.743830i	$0.733007\pi$
$332$		0			0
$333$	34.3733	−	34.3733i	1.88365	−	1.88365i
$334$		0			0
$335$	−14.6733	−	19.4704i	−0.801686	−	1.06378i
$336$		0			0
$337$	−24.7146	−	24.7146i	−1.34629	−	1.34629i	−0.889656	−	0.456632i	$-0.849056\pi$
$337$	−24.7146	−	24.7146i	−1.34629	−	1.34629i	−0.456632	−	0.889656i	$-0.650944\pi$
$338$		0			0
$339$	−30.5002			−1.65654
$340$		0			0
$341$	30.1847			1.63459
$342$		0			0
$343$	−12.5910	−	12.5910i	−0.679852	−	0.679852i
$344$		0			0
$345$	−1.80642	−	0.253799i	−0.0972546	−	0.0136641i
$346$		0			0
$347$	−4.27512	+	4.27512i	−0.229500	+	0.229500i	−0.812484	−	0.582984i	$-0.801885\pi$
$347$	−4.27512	+	4.27512i	−0.229500	+	0.229500i	0.582984	+	0.812484i	$0.301885\pi$
$348$		0			0
$349$			6.29529i			0.336979i	0.985703	+	0.168489i	$0.0538889\pi$
$349$			6.29529i			0.336979i	−0.985703	+	0.168489i	$0.946111\pi$
$350$		0			0
$351$		−	38.9205i		−	2.07743i
$352$		0			0
$353$	9.85728	−	9.85728i	0.524650	−	0.524650i	−0.394322	−	0.918972i	$-0.629021\pi$
$353$	9.85728	−	9.85728i	0.524650	−	0.524650i	0.918972	+	0.394322i	$0.129021\pi$
$354$		0			0
$355$	−28.6167	−	4.02059i	−1.51882	−	0.213391i
$356$		0			0
$357$	−1.67307	−	1.67307i	−0.0885483	−	0.0885483i
$358$		0			0
$359$	25.1821			1.32906			0.664530	−	0.747262i	$-0.268632\pi$
$359$	25.1821			1.32906			0.664530	+	0.747262i	$0.268632\pi$
$360$		0			0
$361$	−7.20342			−0.379127
$362$		0			0
$363$	28.4473	+	28.4473i	1.49310	+	1.49310i
$364$		0			0
$365$	−3.90321	−	5.17929i	−0.204303	−	0.271096i
$366$		0			0
$367$	−21.0013	+	21.0013i	−1.09626	+	1.09626i	−0.101412	+	0.994844i	$0.532336\pi$
$367$	−21.0013	+	21.0013i	−1.09626	+	1.09626i	−0.994844	+	0.101412i	$0.967664\pi$
$368$		0			0
$369$		−	17.2859i		−	0.899869i
$370$		0			0
$371$			1.55109i			0.0805287i
$372$		0			0
$373$	10.7190	−	10.7190i	0.555009	−	0.555009i	−0.372873	−	0.927882i	$-0.621627\pi$
$373$	10.7190	−	10.7190i	0.555009	−	0.555009i	0.927882	+	0.372873i	$0.121627\pi$
$374$		0			0
$375$	−30.3015	+	11.6360i	−1.56476	+	0.600882i
$376$		0			0
$377$	30.4701	+	30.4701i	1.56929	+	1.56929i
$378$		0			0
$379$	15.5431			0.798395			0.399198	−	0.916865i	$-0.369289\pi$
$379$	15.5431			0.798395			0.399198	+	0.916865i	$0.369289\pi$
$380$		0			0
$381$	36.5116			1.87055
$382$		0			0
$383$	15.3444	+	15.3444i	0.784063	+	0.784063i	0.980514	−	0.196451i	$-0.0629417\pi$
$383$	15.3444	+	15.3444i	0.784063	+	0.784063i	−0.196451	+	0.980514i	$0.562942\pi$
$384$		0			0
$385$	−13.5812	+	10.2351i	−0.692162	+	0.521627i
$386$		0			0
$387$	−11.1443	+	11.1443i	−0.566499	+	0.566499i
$388$		0			0
$389$		−	13.5526i		−	0.687145i	−0.939126	−	0.343573i	$-0.888363\pi$
$389$		−	13.5526i		−	0.687145i	0.939126	−	0.343573i	$-0.111637\pi$
$390$		0			0
$391$			0.150127i			0.00759226i
$392$		0			0
$393$	35.0923	−	35.0923i	1.77017	−	1.77017i
$394$		0			0
$395$	−0.965114	+	6.86923i	−0.0485602	+	0.345628i
$396$		0			0
$397$	−11.8716	−	11.8716i	−0.595817	−	0.595817i	0.343380	−	0.939197i	$-0.388428\pi$
$397$	−11.8716	−	11.8716i	−0.595817	−	0.595817i	−0.939197	+	0.343380i	$0.888428\pi$
$398$		0			0
$399$	−15.2107			−0.761486
$400$		0			0
$401$	20.9590			1.04664			0.523321	−	0.852136i	$-0.324693\pi$
$401$	20.9590			1.04664			0.523321	+	0.852136i	$0.324693\pi$
$402$		0			0
$403$	23.6310	+	23.6310i	1.17714	+	1.17714i
$404$		0			0
$405$	1.30174	−	9.26517i	0.0646840	−	0.460390i
$406$		0			0
$407$	−31.5688	+	31.5688i	−1.56481	+	1.56481i
$408$		0			0
$409$		−	19.5526i		−	0.966815i	−0.875395	−	0.483408i	$-0.839399\pi$
$409$		−	19.5526i		−	0.966815i	0.875395	−	0.483408i	$-0.160601\pi$
$410$		0			0
$411$			20.5288i			1.01261i
$412$		0			0
$413$	7.05086	−	7.05086i	0.346950	−	0.346950i
$414$		0			0
$415$	−13.8583	+	10.4439i	−0.680276	+	0.512669i
$416$		0			0
$417$	38.2766	+	38.2766i	1.87441	+	1.87441i
$418$		0			0
$419$	22.4123			1.09491			0.547457	−	0.836834i	$-0.315596\pi$
$419$	22.4123			1.09491			0.547457	+	0.836834i	$0.315596\pi$
$420$		0			0
$421$	29.3590			1.43087			0.715436	−	0.698678i	$-0.246228\pi$
$421$	29.3590			1.43087			0.715436	+	0.698678i	$0.246228\pi$
$422$		0			0
$423$	12.7897	+	12.7897i	0.621858	+	0.621858i
$424$		0			0
$425$	1.29529	+	2.33630i	0.0628306	+	0.113327i
$426$		0			0
$427$	3.64341	−	3.64341i	0.176317	−	0.176317i
$428$		0			0
$429$			79.8992i			3.85757i
$430$		0			0
$431$		−	12.9235i		−	0.622502i	−0.950328	−	0.311251i	$-0.899252\pi$
$431$		−	12.9235i		−	0.622502i	0.950328	−	0.311251i	$-0.100748\pi$
$432$		0			0
$433$	−16.9081	+	16.9081i	−0.812553	+	0.812553i	−0.985016	−	0.172463i	$-0.944827\pi$
$433$	−16.9081	+	16.9081i	−0.812553	+	0.812553i	0.172463	+	0.985016i	$0.444827\pi$
$434$		0			0
$435$	30.5002	+	40.4716i	1.46237	+	1.94047i
$436$		0			0
$437$	0.682439	+	0.682439i	0.0326455	+	0.0326455i
$438$		0			0
$439$	18.9777			0.905757			0.452878	−	0.891572i	$-0.350397\pi$
$439$	18.9777			0.905757			0.452878	+	0.891572i	$0.350397\pi$
$440$		0			0
$441$	−25.3684			−1.20802
$442$		0			0
$443$	1.38173	+	1.38173i	0.0656482	+	0.0656482i	0.739169	−	0.673520i	$-0.235219\pi$
$443$	1.38173	+	1.38173i	0.0656482	+	0.0656482i	−0.673520	+	0.739169i	$0.735219\pi$
$444$		0			0
$445$	−19.6128	−	2.75557i	−0.929738	−	0.130626i
$446$		0			0
$447$	20.4052	−	20.4052i	0.965132	−	0.965132i
$448$		0			0
$449$			12.1432i			0.573073i	0.958069	+	0.286536i	$0.0925040\pi$
$449$			12.1432i			0.573073i	−0.958069	+	0.286536i	$0.907496\pi$
$450$		0			0
$451$			15.8755i			0.747550i
$452$		0			0
$453$	−8.04149	+	8.04149i	−0.377822	+	0.377822i
$454$		0			0
$455$	−18.6453	−	2.61963i	−0.874104	−	0.122810i
$456$		0			0
$457$	−2.57136	−	2.57136i	−0.120283	−	0.120283i	0.644403	−	0.764686i	$-0.277106\pi$
$457$	−2.57136	−	2.57136i	−0.120283	−	0.120283i	−0.764686	+	0.644403i	$0.777106\pi$
$458$		0			0
$459$	−3.76704			−0.175831
$460$		0			0
$461$	−35.6128			−1.65866			−0.829328	−	0.558762i	$-0.811276\pi$
$461$	−35.6128			−1.65866			−0.829328	+	0.558762i	$0.811276\pi$
$462$		0			0
$463$	−6.67054	−	6.67054i	−0.310006	−	0.310006i	0.534906	−	0.844912i	$-0.320347\pi$
$463$	−6.67054	−	6.67054i	−0.310006	−	0.310006i	−0.844912	+	0.534906i	$0.820347\pi$
$464$		0			0
$465$	23.6543	+	31.3876i	1.09694	+	1.45557i
$466$		0			0
$467$	11.1443	−	11.1443i	0.515699	−	0.515699i	−0.400568	−	0.916267i	$-0.631187\pi$
$467$	11.1443	−	11.1443i	0.515699	−	0.515699i	0.916267	+	0.400568i	$0.131187\pi$
$468$		0			0
$469$		−	16.6321i		−	0.767997i
$470$		0			0
$471$		−	44.9748i		−	2.07233i
$472$		0			0
$473$	10.2351	−	10.2351i	0.470609	−	0.470609i
$474$		0			0
$475$	16.5082	+	4.73216i	0.757449	+	0.217126i
$476$		0			0
$477$	3.90321	+	3.90321i	0.178716	+	0.178716i
$478$		0			0
$479$	−0.965114			−0.0440972			−0.0220486	−	0.999757i	$-0.507019\pi$
$479$	−0.965114			−0.0440972			−0.0220486	+	0.999757i	$0.507019\pi$
$480$		0			0
$481$	−49.4291			−2.25377
$482$		0			0
$483$	−0.879946	−	0.879946i	−0.0400389	−	0.0400389i
$484$		0			0
$485$	7.08742	−	5.34122i	0.321823	−	0.242532i
$486$		0			0
$487$	8.89277	−	8.89277i	0.402970	−	0.402970i	−0.476308	−	0.879278i	$-0.658025\pi$
$487$	8.89277	−	8.89277i	0.402970	−	0.402970i	0.879278	+	0.476308i	$0.158025\pi$
$488$		0			0
$489$			49.3689i			2.23254i
$490$		0			0
$491$		−	30.8327i		−	1.39146i	−0.718304	−	0.695729i	$-0.755081\pi$
$491$		−	30.8327i		−	1.39146i	0.718304	−	0.695729i	$-0.244919\pi$
$492$		0			0
$493$	2.94914	−	2.94914i	0.132823	−	0.132823i
$494$		0			0
$495$	−8.42032	+	59.9319i	−0.378465	+	2.69374i
$496$		0			0
$497$	−13.9398	−	13.9398i	−0.625284	−	0.625284i
$498$		0			0
$499$	−35.4859			−1.58857			−0.794284	−	0.607546i	$-0.792154\pi$
$499$	−35.4859			−1.58857			−0.794284	+	0.607546i	$0.792154\pi$
$500$		0			0
$501$	−31.2672			−1.39691
$502$		0			0
$503$	8.80761	+	8.80761i	0.392712	+	0.392712i	0.875653	−	0.482941i	$-0.160431\pi$
$503$	8.80761	+	8.80761i	0.392712	+	0.392712i	−0.482941	+	0.875653i	$0.660431\pi$
$504$		0			0
$505$	4.38715	−	31.2257i	0.195226	−	1.38953i
$506$		0			0
$507$	−35.8641	+	35.8641i	−1.59278	+	1.59278i
$508$		0			0
$509$		−	21.9081i		−	0.971061i	−0.874220	−	0.485530i	$-0.838626\pi$
$509$		−	21.9081i		−	0.971061i	0.874220	−	0.485530i	$-0.161374\pi$
$510$		0			0
$511$		−	4.42427i		−	0.195718i
$512$		0			0
$513$	−17.1240	+	17.1240i	−0.756042	+	0.756042i
$514$		0			0
$515$	25.6839	−	19.3559i	1.13177	−	0.852922i
$516$		0			0
$517$	−11.7462	−	11.7462i	−0.516597	−	0.516597i
$518$		0			0
$519$	45.9399			2.01654
$520$		0			0
$521$	−19.5941			−0.858434			−0.429217	−	0.903201i	$-0.641210\pi$
$521$	−19.5941			−0.858434			−0.429217	+	0.903201i	$0.641210\pi$
$522$		0			0
$523$	−10.7268	−	10.7268i	−0.469048	−	0.469048i	0.432558	−	0.901606i	$-0.357611\pi$
$523$	−10.7268	−	10.7268i	−0.469048	−	0.469048i	−0.901606	+	0.432558i	$0.857611\pi$
$524$		0			0
$525$	−21.2859	−	6.10171i	−0.928994	−	0.266300i
$526$		0			0
$527$	2.28720	−	2.28720i	0.0996319	−	0.0996319i
$528$		0			0
$529$		−	22.9210i		−	0.996567i
$530$		0			0
$531$		−	35.4859i		−	1.53996i
$532$		0			0
$533$	−12.4286	+	12.4286i	−0.538344	+	0.538344i
$534$		0			0
$535$	−4.30446	−	5.71171i	−0.186098	−	0.246939i
$536$		0			0
$537$	11.4380	+	11.4380i	0.493586	+	0.493586i
$538$		0			0
$539$	23.2986			1.00354
$540$		0			0
$541$	−26.8385			−1.15388			−0.576940	−	0.816787i	$-0.695753\pi$
$541$	−26.8385			−1.15388			−0.576940	+	0.816787i	$0.695753\pi$
$542$		0			0
$543$	−6.86923	−	6.86923i	−0.294787	−	0.294787i
$544$		0			0
$545$	−1.80642	−	0.253799i	−0.0773787	−	0.0108716i
$546$		0			0
$547$	18.9787	−	18.9787i	0.811470	−	0.811470i	−0.173384	−	0.984854i	$-0.555470\pi$
$547$	18.9787	−	18.9787i	0.811470	−	0.811470i	0.984854	+	0.173384i	$0.0554702\pi$
$548$		0			0
$549$		−	18.3368i		−	0.782594i
$550$		0			0
$551$		−	26.8121i		−	1.14223i
$552$		0			0
$553$	−3.34614	+	3.34614i	−0.142292	+	0.142292i
$554$		0			0
$555$	−57.5658	−	8.08789i	−2.44353	−	0.343312i
$556$		0			0
$557$	29.6780	+	29.6780i	1.25750	+	1.25750i	0.952284	+	0.305213i	$0.0987276\pi$
$557$	29.6780	+	29.6780i	1.25750	+	1.25750i	0.305213	+	0.952284i	$0.401272\pi$
$558$		0			0
$559$	16.0257			0.677813
$560$		0			0
$561$	7.73329			0.326500
$562$		0			0
$563$	−5.15507	−	5.15507i	−0.217260	−	0.217260i	0.590083	−	0.807343i	$-0.299095\pi$
$563$	−5.15507	−	5.15507i	−0.217260	−	0.217260i	−0.807343	+	0.590083i	$0.799095\pi$
$564$		0			0
$565$	14.1383	+	18.7605i	0.594802	+	0.789260i
$566$		0			0
$567$	4.51326	−	4.51326i	0.189539	−	0.189539i
$568$		0			0
$569$		−	1.95851i		−	0.0821051i	−0.999157	−	0.0410526i	$-0.986929\pi$
$569$		−	1.95851i		−	0.0821051i	0.999157	−	0.0410526i	$-0.0130711\pi$
$570$		0			0
$571$			1.21866i			0.0509995i	0.999675	+	0.0254997i	$0.00811769\pi$
$571$			1.21866i			0.0509995i	−0.999675	+	0.0254997i	$0.991882\pi$
$572$		0			0
$573$	18.7971	−	18.7971i	0.785258	−	0.785258i
$574$		0			0
$575$	0.681251	+	1.22877i	0.0284101	+	0.0512431i
$576$		0			0
$577$	−19.4099	−	19.4099i	−0.808045	−	0.808045i	0.176293	−	0.984338i	$-0.443589\pi$
$577$	−19.4099	−	19.4099i	−0.808045	−	0.808045i	−0.984338	+	0.176293i	$0.943589\pi$
$578$		0			0
$579$	−24.5961			−1.02218
$580$		0			0
$581$	−11.8381			−0.491126
$582$		0			0
$583$	−3.58474	−	3.58474i	−0.148465	−	0.148465i
$584$		0			0
$585$	−53.5116	+	40.3274i	−2.21243	+	1.66733i
$586$		0			0
$587$	10.9356	−	10.9356i	0.451358	−	0.451358i	−0.444447	−	0.895805i	$-0.646600\pi$
$587$	10.9356	−	10.9356i	0.451358	−	0.451358i	0.895805	+	0.444447i	$0.146600\pi$
$588$		0			0
$589$		−	20.7940i		−	0.856802i
$590$		0			0
$591$		−	15.0605i		−	0.619508i
$592$		0			0
$593$	−20.3274	+	20.3274i	−0.834747	+	0.834747i	−0.988162	−	0.153415i	$-0.950973\pi$
$593$	−20.3274	+	20.3274i	−0.834747	+	0.834747i	0.153415	+	0.988162i	$0.450973\pi$
$594$		0			0
$595$	−0.253549	+	1.80464i	−0.0103945	+	0.0739831i
$596$		0			0
$597$	6.36842	+	6.36842i	0.260642	+	0.260642i
$598$		0			0
$599$	47.2620			1.93107			0.965536	−	0.260269i	$-0.0838112\pi$
$599$	47.2620			1.93107			0.965536	+	0.260269i	$0.0838112\pi$
$600$		0			0
$601$	−28.0415			−1.14384			−0.571918	−	0.820311i	$-0.693800\pi$
$601$	−28.0415			−1.14384			−0.571918	+	0.820311i	$0.693800\pi$
$602$		0			0
$603$	−41.8534	−	41.8534i	−1.70440	−	1.70440i
$604$		0			0
$605$	4.31111	−	30.6844i	0.175271	−	1.24750i
$606$		0			0
$607$	−16.6217	+	16.6217i	−0.674656	+	0.674656i	−0.958786	−	0.284130i	$-0.908295\pi$
$607$	−16.6217	+	16.6217i	−0.674656	+	0.674656i	0.284130	+	0.958786i	$0.408295\pi$
$608$		0			0
$609$			34.5718i			1.40092i
$610$		0			0
$611$		−	18.3917i		−	0.744050i
$612$		0			0
$613$	−5.41435	+	5.41435i	−0.218684	+	0.218684i	−0.807943	−	0.589260i	$-0.799419\pi$
$613$	−5.41435	+	5.41435i	−0.218684	+	0.218684i	0.589260	+	0.807943i	$0.299419\pi$
$614$		0			0
$615$	−16.5082	+	12.4409i	−0.665675	+	0.501666i
$616$		0			0
$617$	14.9496	+	14.9496i	0.601849	+	0.601849i	0.940803	−	0.338954i	$-0.110073\pi$
$617$	14.9496	+	14.9496i	0.601849	+	0.601849i	−0.338954	+	0.940803i	$0.610073\pi$
$618$		0			0
$619$	−20.2753			−0.814931			−0.407466	−	0.913220i	$-0.633587\pi$
$619$	−20.2753			−0.814931			−0.407466	+	0.913220i	$0.633587\pi$
$620$		0			0
$621$	−1.98126			−0.0795054
$622$		0			0
$623$	−9.55382	−	9.55382i	−0.382766	−	0.382766i
$624$		0			0
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$		0			0
$627$	35.1535	−	35.1535i	1.40390	−	1.40390i
$628$		0			0
$629$			4.78415i			0.190757i
$630$		0			0
$631$			41.2077i			1.64045i	0.572038	+	0.820227i	$0.306153\pi$
$631$			41.2077i			1.64045i	−0.572038	+	0.820227i	$0.693847\pi$
$632$		0			0
$633$	−35.0923	+	35.0923i	−1.39480	+	1.39480i
$634$		0			0
$635$	−16.9248	−	22.4581i	−0.671642	−	0.891221i
$636$		0			0
$637$	18.2400	+	18.2400i	0.722695	+	0.722695i
$638$		0			0
$639$	−70.1569			−2.77536
$640$		0			0
$641$	28.0415			1.10757			0.553786	−	0.832659i	$-0.313183\pi$
$641$	28.0415			1.10757			0.553786	+	0.832659i	$0.313183\pi$
$642$		0			0
$643$	−5.14878	−	5.14878i	−0.203048	−	0.203048i	0.598257	−	0.801305i	$-0.295860\pi$
$643$	−5.14878	−	5.14878i	−0.203048	−	0.203048i	−0.801305	+	0.598257i	$0.795860\pi$
$644$		0			0
$645$	18.6637	+	2.62222i	0.734883	+	0.103250i
$646$		0			0
$647$	−16.2893	+	16.2893i	−0.640399	+	0.640399i	−0.950654	−	0.310255i	$-0.899586\pi$
$647$	−16.2893	+	16.2893i	−0.640399	+	0.640399i	0.310255	+	0.950654i	$0.399586\pi$
$648$		0			0
$649$			32.5906i			1.27929i
$650$		0			0
$651$			26.8121i			1.05085i
$652$		0			0
$653$	4.13828	−	4.13828i	0.161943	−	0.161943i	−0.621484	−	0.783427i	$-0.713470\pi$
$653$	4.13828	−	4.13828i	0.161943	−	0.161943i	0.783427	+	0.621484i	$0.213470\pi$
$654$		0			0
$655$	−37.8520	−	5.31814i	−1.47900	−	0.207797i
$656$		0			0
$657$	−11.1334	−	11.1334i	−0.434353	−	0.434353i
$658$		0			0
$659$	−1.80464			−0.0702988			−0.0351494	−	0.999382i	$-0.511191\pi$
$659$	−1.80464			−0.0702988			−0.0351494	+	0.999382i	$0.511191\pi$
$660$		0			0
$661$	−23.3145			−0.906829			−0.453414	−	0.891300i	$-0.649794\pi$
$661$	−23.3145			−0.906829			−0.453414	+	0.891300i	$0.649794\pi$
$662$		0			0
$663$	6.05424	+	6.05424i	0.235127	+	0.235127i
$664$		0			0
$665$	7.05086	+	9.35599i	0.273420	+	0.362810i
$666$		0			0
$667$	1.55109	−	1.55109i	0.0600585	−	0.0600585i
$668$		0			0
$669$		−	13.2859i		−	0.513663i
$670$		0			0
$671$			16.8406i			0.650126i
$672$		0			0
$673$	−6.15257	+	6.15257i	−0.237164	+	0.237164i	−0.815675	−	0.578511i	$-0.803634\pi$
$673$	−6.15257	+	6.15257i	−0.237164	+	0.237164i	0.578511	+	0.815675i	$0.303634\pi$
$674$		0			0
$675$	−30.8327	+	17.0942i	−1.18675	+	0.657956i
$676$		0			0
$677$	10.0366	+	10.0366i	0.385737	+	0.385737i	0.873164	−	0.487427i	$-0.162065\pi$
$677$	10.0366	+	10.0366i	0.385737	+	0.385737i	−0.487427	+	0.873164i	$0.662065\pi$
$678$		0			0
$679$	6.05424			0.232341
$680$		0			0
$681$	73.1022			2.80128
$682$		0			0
$683$	12.0243	+	12.0243i	0.460097	+	0.460097i	0.898687	−	0.438590i	$-0.144522\pi$
$683$	12.0243	+	12.0243i	0.460097	+	0.460097i	−0.438590	+	0.898687i	$0.644522\pi$
$684$		0			0
$685$	12.6271	−	9.51606i	0.482458	−	0.363590i
$686$		0			0
$687$	25.0320	−	25.0320i	0.955029	−	0.955029i
$688$		0			0
$689$		−	5.61285i		−	0.213832i
$690$		0			0
$691$		−	43.2414i		−	1.64498i	−0.568779	−	0.822490i	$-0.692584\pi$
$691$		−	43.2414i		−	1.64498i	0.568779	−	0.822490i	$-0.307416\pi$
$692$		0			0
$693$	−29.1941	+	29.1941i	−1.10899	+	1.10899i
$694$		0			0
$695$	5.80069	−	41.2866i	0.220033	−	1.56609i
$696$		0			0
$697$	1.20294	+	1.20294i	0.0455648	+	0.0455648i
$698$		0			0
$699$	4.65328			0.176003
$700$		0			0
$701$	−24.8256			−0.937651			−0.468826	−	0.883291i	$-0.655323\pi$
$701$	−24.8256			−0.937651			−0.468826	+	0.883291i	$0.655323\pi$
$702$		0			0
$703$	21.7475	+	21.7475i	0.820221	+	0.820221i
$704$		0			0
$705$	3.00937	−	21.4193i	0.113339	−	0.806696i
$706$		0			0
$707$	15.2107	−	15.2107i	0.572056	−	0.572056i
$708$		0			0
$709$			42.8484i			1.60920i	0.593814	+	0.804602i	$0.297622\pi$
$709$			42.8484i			1.60920i	−0.593814	+	0.804602i	$0.702378\pi$
$710$		0			0
$711$			16.8406i			0.631574i
$712$		0			0
$713$	1.20294	−	1.20294i	0.0450506	−	0.0450506i
$714$		0			0
$715$	49.1455	−	37.0370i	1.83794	−	1.38511i
$716$		0			0
$717$	−4.38715	−	4.38715i	−0.163841	−	0.163841i
$718$		0			0
$719$	11.6014			0.432659			0.216329	−	0.976320i	$-0.430591\pi$
$719$	11.6014			0.432659			0.216329	+	0.976320i	$0.430591\pi$
$720$		0			0
$721$	21.9398			0.817080
$722$		0			0
$723$	0.332430	+	0.332430i	0.0123632	+	0.0123632i
$724$		0			0
$725$	10.7556	−	37.5210i	0.399452	−	1.39349i
$726$		0			0
$727$	22.6312	−	22.6312i	0.839346	−	0.839346i	−0.149427	−	0.988773i	$-0.547743\pi$
$727$	22.6312	−	22.6312i	0.839346	−	0.839346i	0.988773	+	0.149427i	$0.0477428\pi$
$728$		0			0
$729$			38.6958i			1.43318i
$730$		0			0
$731$		−	1.55109i		−	0.0573692i
$732$		0			0
$733$	−25.2908	+	25.2908i	−0.934139	+	0.934139i	−0.997961	−	0.0638227i	$-0.979671\pi$
$733$	−25.2908	+	25.2908i	−0.934139	+	0.934139i	0.0638227	+	0.997961i	$0.479671\pi$
$734$		0			0
$735$	18.2580	+	24.2271i	0.673457	+	0.893629i
$736$		0			0
$737$	38.4385	+	38.4385i	1.41590	+	1.41590i
$738$		0			0
$739$	52.3266			1.92486			0.962432	−	0.271522i	$-0.0875271\pi$
$739$	52.3266			1.92486			0.962432	+	0.271522i	$0.0875271\pi$
$740$		0			0
$741$	55.0420			2.02202
$742$		0			0
$743$	−30.5551	−	30.5551i	−1.12096	−	1.12096i	−0.991598	−	0.129359i	$-0.958708\pi$
$743$	−30.5551	−	30.5551i	−1.12096	−	1.12096i	−0.129359	−	0.991598i	$-0.541292\pi$
$744$		0			0
$745$	−22.0098	−	3.09234i	−0.806378	−	0.113295i
$746$		0			0
$747$	−29.7896	+	29.7896i	−1.08995	+	1.08995i
$748$		0			0
$749$		−	4.87908i		−	0.178278i
$750$		0			0
$751$		−	36.9336i		−	1.34773i	−0.738856	−	0.673863i	$-0.764634\pi$
$751$		−	36.9336i		−	1.34773i	0.738856	−	0.673863i	$-0.235366\pi$
$752$		0			0
$753$	−30.7052	+	30.7052i	−1.11896	+	1.11896i
$754$		0			0
$755$	8.67387	+	1.21866i	0.315674	+	0.0443517i
$756$		0			0
$757$	−12.4652	−	12.4652i	−0.453056	−	0.453056i	0.443312	−	0.896367i	$-0.353803\pi$
$757$	−12.4652	−	12.4652i	−0.453056	−	0.453056i	−0.896367	+	0.443312i	$0.853803\pi$
$758$		0			0
$759$	4.06730			0.147634
$760$		0			0
$761$	−7.24443			−0.262610			−0.131305	−	0.991342i	$-0.541917\pi$
$761$	−7.24443			−0.262610			−0.131305	+	0.991342i	$0.541917\pi$
$762$		0			0
$763$	−0.879946	−	0.879946i	−0.0318562	−	0.0318562i
$764$		0			0
$765$	3.90321	+	5.17929i	0.141121	+	0.187257i
$766$		0			0
$767$	−25.5145	+	25.5145i	−0.921276	+	0.921276i
$768$		0			0
$769$			29.3274i			1.05757i	0.848755	+	0.528787i	$0.177353\pi$
$769$			29.3274i			1.05757i	−0.848755	+	0.528787i	$0.822647\pi$
$770$		0			0
$771$			27.3980i			0.986716i
$772$		0			0
$773$	0.954067	−	0.954067i	0.0343154	−	0.0343154i	−0.689741	−	0.724056i	$-0.742276\pi$
$773$	0.954067	−	0.954067i	0.0343154	−	0.0343154i	0.724056	+	0.689741i	$0.242276\pi$
$774$		0			0
$775$	8.34144	−	29.0993i	0.299633	−	1.04528i
$776$		0			0
$777$	−28.0415	−	28.0415i	−1.00598	−	1.00598i
$778$		0			0
$779$	10.9365			0.391842
$780$		0			0
$781$	64.4327			2.30558
$782$		0			0
$783$	38.9205	+	38.9205i	1.39091	+	1.39091i
$784$		0			0
$785$	−27.6637	+	20.8479i	−0.987360	+	0.744094i
$786$		0			0
$787$	−34.5218	+	34.5218i	−1.23057	+	1.23057i	−0.266824	+	0.963745i	$0.585974\pi$
$787$	−34.5218	+	34.5218i	−1.23057	+	1.23057i	−0.963745	+	0.266824i	$0.914026\pi$
$788$		0			0
$789$		−	68.5946i		−	2.44203i
$790$		0			0
$791$			16.0257i			0.569807i
$792$		0			0
$793$	−13.1842	+	13.1842i	−0.468185	+	0.468185i
$794$		0			0
$795$	0.918408	−	6.53680i	0.0325726	−	0.231836i
$796$		0			0
$797$	6.85236	+	6.85236i	0.242723	+	0.242723i	0.817976	−	0.575253i	$-0.195096\pi$
$797$	6.85236	+	6.85236i	0.242723	+	0.242723i	−0.575253	+	0.817976i	$0.695096\pi$
$798$		0			0
$799$	−1.78010			−0.0629754
$800$		0			0
$801$	−48.0830			−1.69893
$802$		0			0
$803$	10.2250	+	10.2250i	0.360831	+	0.360831i
$804$		0			0
$805$	−0.133353	+	0.949145i	−0.00470008	+	0.0334530i
$806$		0			0
$807$	−34.6912	+	34.6912i	−1.22119	+	1.22119i
$808$		0			0
$809$		−	28.7368i		−	1.01033i	−0.863022	−	0.505167i	$-0.831431\pi$
$809$		−	28.7368i		−	1.01033i	0.863022	−	0.505167i	$-0.168569\pi$
$810$		0			0
$811$			11.1901i			0.392937i	0.980510	+	0.196468i	$0.0629473\pi$
$811$			11.1901i			0.392937i	−0.980510	+	0.196468i	$0.937053\pi$
$812$		0			0
$813$	−39.2672	+	39.2672i	−1.37716	+	1.37716i
$814$		0			0
$815$	30.3665	−	22.8848i	1.06369	−	0.801619i
$816$		0			0
$817$	−7.05086	−	7.05086i	−0.246678	−	0.246678i
$818$		0			0
$819$	−45.7109			−1.59727
$820$		0			0
$821$	−6.33677			−0.221155			−0.110577	−	0.993868i	$-0.535270\pi$
$821$	−6.33677			−0.221155			−0.110577	+	0.993868i	$0.535270\pi$
$822$		0			0
$823$	−9.20500	−	9.20500i	−0.320866	−	0.320866i	0.528233	−	0.849099i	$-0.322855\pi$
$823$	−9.20500	−	9.20500i	−0.320866	−	0.320866i	−0.849099	+	0.528233i	$0.822855\pi$
$824$		0			0
$825$	63.2958	−	35.0923i	2.20368	−	1.22176i
$826$		0			0
$827$	−7.37731	+	7.37731i	−0.256534	+	0.256534i	−0.823643	−	0.567109i	$-0.808062\pi$
$827$	−7.37731	+	7.37731i	−0.256534	+	0.256534i	0.567109	+	0.823643i	$0.308062\pi$
$828$		0			0
$829$			52.2449i			1.81454i	0.420548	+	0.907270i	$0.361838\pi$
$829$			52.2449i			1.81454i	−0.420548	+	0.907270i	$0.638162\pi$
$830$		0			0
$831$		−	19.1278i		−	0.663538i
$832$		0			0
$833$	1.76541	−	1.76541i	0.0611679	−	0.0611679i
$834$		0			0
$835$	14.4938	+	19.2322i	0.501579	+	0.665559i
$836$		0			0
$837$	30.1847	+	30.1847i	1.04334	+	1.04334i
$838$		0			0
$839$	−53.6241			−1.85131			−0.925655	−	0.378368i	$-0.876485\pi$
$839$	−53.6241			−1.85131			−0.925655	+	0.378368i	$0.876485\pi$
$840$		0			0
$841$	−31.9403			−1.10139
$842$		0			0
$843$	−26.4796	−	26.4796i	−0.912007	−	0.912007i
$844$		0			0
$845$	38.6844	+	5.43509i	1.33079	+	0.186973i
$846$		0			0
$847$	14.9470	−	14.9470i	0.513586	−	0.513586i
$848$		0			0
$849$			35.2672i			1.21037i
$850$		0			0
$851$			2.51621i			0.0862545i
$852$		0			0
$853$	27.7926	−	27.7926i	0.951601	−	0.951601i	−0.0472808	−	0.998882i	$-0.515056\pi$
$853$	27.7926	−	27.7926i	0.951601	−	0.951601i	0.998882	+	0.0472808i	$0.0150556\pi$
$854$		0			0
$855$	41.2866	+	5.80069i	1.41197	+	0.198380i
$856$		0			0
$857$	10.1427	+	10.1427i	0.346469	+	0.346469i	0.858792	−	0.512324i	$-0.171215\pi$
$857$	10.1427	+	10.1427i	0.346469	+	0.346469i	−0.512324	+	0.858792i	$0.671215\pi$
$858$		0			0
$859$	27.1445			0.926158			0.463079	−	0.886317i	$-0.346745\pi$
$859$	27.1445			0.926158			0.463079	+	0.886317i	$0.346745\pi$
$860$		0			0
$861$	−14.1017			−0.480585
$862$		0			0
$863$	−15.0120	−	15.0120i	−0.511014	−	0.511014i	0.403823	−	0.914837i	$-0.367681\pi$
$863$	−15.0120	−	15.0120i	−0.511014	−	0.511014i	−0.914837	+	0.403823i	$0.867681\pi$
$864$		0			0
$865$	−21.2953	−	28.2573i	−0.724061	−	0.960778i
$866$		0			0
$867$	−34.3130	+	34.3130i	−1.16533	+	1.16533i
$868$		0			0
$869$		−	15.4666i		−	0.524668i
$870$		0			0
$871$			60.1855i			2.03931i
$872$		0			0
$873$	15.2351	−	15.2351i	0.515629	−	0.515629i
$874$		0			0
$875$	6.11389	+	15.9213i	0.206687	+	0.538237i
$876$		0			0
$877$	−13.9032	−	13.9032i	−0.469478	−	0.469478i	0.432267	−	0.901745i	$-0.357714\pi$
$877$	−13.9032	−	13.9032i	−0.469478	−	0.469478i	−0.901745	+	0.432267i	$0.857714\pi$
$878$		0			0
$879$	−51.1792			−1.72623
$880$		0			0
$881$	−9.55262			−0.321836			−0.160918	−	0.986968i	$-0.551445\pi$
$881$	−9.55262			−0.321836			−0.160918	+	0.986968i	$0.551445\pi$
$882$		0			0
$883$	30.9635	+	30.9635i	1.04201	+	1.04201i	0.999078	+	0.0429282i	$0.0136687\pi$
$883$	30.9635	+	30.9635i	1.04201	+	1.04201i	0.0429282	+	0.999078i	$0.486331\pi$
$884$		0			0
$885$	−33.8894	+	25.5397i	−1.13918	+	0.858508i
$886$		0			0
$887$	13.1669	−	13.1669i	0.442102	−	0.442102i	−0.450616	−	0.892718i	$-0.648796\pi$
$887$	13.1669	−	13.1669i	0.442102	−	0.442102i	0.892718	+	0.450616i	$0.148796\pi$
$888$		0			0
$889$		−	19.1842i		−	0.643418i
$890$		0			0
$891$			20.8612i			0.698878i
$892$		0			0
$893$	−8.09187	+	8.09187i	−0.270784	+	0.270784i
$894$		0			0
$895$	1.73340	−	12.3375i	0.0579410	−	0.412397i
$896$		0			0
$897$	3.18421	+	3.18421i	0.106318	+	0.106318i
$898$		0			0
$899$	−47.2620			−1.57628
$900$		0			0
$901$	−0.543257			−0.0180985
$902$		0			0
$903$	9.09147	+	9.09147i	0.302545	+	0.302545i
$904$		0			0
$905$	−1.04101	+	7.40943i	−0.0346044	+	0.246298i
$906$		0			0
$907$	16.7160	−	16.7160i	0.555047	−	0.555047i	−0.372846	−	0.927893i	$-0.621618\pi$
$907$	16.7160	−	16.7160i	0.555047	−	0.555047i	0.927893	+	0.372846i	$0.121618\pi$
$908$		0			0
$909$		−	76.5531i		−	2.53911i
$910$		0			0
$911$			30.2712i			1.00293i	0.865178	+	0.501465i	$0.167205\pi$
$911$			30.2712i			1.00293i	−0.865178	+	0.501465i	$0.832795\pi$
$912$		0			0
$913$	27.3590	−	27.3590i	0.905452	−	0.905452i
$914$		0			0
$915$	−17.5118	+	13.1972i	−0.578922	+	0.436287i
$916$		0			0
$917$	−18.4385	−	18.4385i	−0.608892	−	0.608892i
$918$		0			0
$919$	−16.8406			−0.555522			−0.277761	−	0.960650i	$-0.589592\pi$
$919$	−16.8406			−0.555522			−0.277761	+	0.960650i	$0.589592\pi$
$920$		0			0
$921$	−18.0602			−0.595105
$922$		0			0
$923$	50.4431	+	50.4431i	1.66035	+	1.66035i
$924$		0			0
$925$	21.7096	+	39.1575i	0.713808	+	1.28749i
$926$		0			0
$927$	55.2099	−	55.2099i	1.81333	−	1.81333i
$928$		0			0
$929$		−	33.6543i		−	1.10416i	−0.833790	−	0.552081i	$-0.813834\pi$
$929$		−	33.6543i		−	1.10416i	0.833790	−	0.552081i	$-0.186166\pi$
$930$		0			0
$931$		−	16.0502i		−	0.526024i
$932$		0			0
$933$	22.1432	−	22.1432i	0.724936	−	0.724936i
$934$		0			0
$935$	−3.58474	−	4.75670i	−0.117234	−	0.155561i
$936$		0			0
$937$	−30.3778	−	30.3778i	−0.992399	−	0.992399i	0.00757237	−	0.999971i	$-0.497590\pi$
$937$	−30.3778	−	30.3778i	−0.992399	−	0.992399i	−0.999971	+	0.00757237i	$0.997590\pi$
$938$		0			0
$939$	68.4557			2.23397
$940$		0			0
$941$	−9.39069			−0.306128			−0.153064	−	0.988216i	$-0.548914\pi$
$941$	−9.39069			−0.306128			−0.153064	+	0.988216i	$0.548914\pi$
$942$		0			0
$943$	0.632684	+	0.632684i	0.0206030	+	0.0206030i
$944$		0			0
$945$	−23.8163	−	3.34614i	−0.774743	−	0.108850i
$946$		0			0
$947$	14.3702	−	14.3702i	0.466968	−	0.466968i	−0.433963	−	0.900931i	$-0.642885\pi$
$947$	14.3702	−	14.3702i	0.466968	−	0.466968i	0.900931	+	0.433963i	$0.142885\pi$
$948$		0			0
$949$			16.0098i			0.519702i
$950$		0			0
$951$		−	28.1341i		−	0.912312i
$952$		0			0
$953$	−33.7971	+	33.7971i	−1.09479	+	1.09479i	−0.0997850	+	0.995009i	$0.531816\pi$
$953$	−33.7971	+	33.7971i	−1.09479	+	1.09479i	−0.995009	+	0.0997850i	$0.968184\pi$
$954$		0			0
$955$	−20.2753	−	2.84864i	−0.656092	−	0.0921797i
$956$		0			0
$957$	−79.8992	−	79.8992i	−2.58278	−	2.58278i
$958$		0			0
$959$	10.7864			0.348311
$960$		0			0
$961$	−5.65386			−0.182383
$962$		0			0
$963$	−12.2778	−	12.2778i	−0.395648	−	0.395648i
$964$		0			0
$965$	11.4014	+	15.1289i	0.367025	+	0.487017i
$966$		0			0
$967$	−35.0722	+	35.0722i	−1.12784	+	1.12784i	−0.137317	+	0.990527i	$0.543848\pi$
$967$	−35.0722	+	35.0722i	−1.12784	+	1.12784i	−0.990527	+	0.137317i	$0.956152\pi$
$968$		0			0
$969$		−	5.32741i		−	0.171141i
$970$		0			0
$971$			55.0496i			1.76663i	0.468783	+	0.883313i	$0.344693\pi$
$971$			55.0496i			1.76663i	−0.468783	+	0.883313i	$0.655307\pi$
$972$		0			0
$973$	20.1116	−	20.1116i	0.644747	−	0.644747i
$974$		0			0
$975$	77.0261	+	22.0799i	2.46681	+	0.707123i
$976$		0			0
$977$	20.6860	+	20.6860i	0.661803	+	0.661803i	0.955805	−	0.294002i	$-0.0949872\pi$
$977$	20.6860	+	20.6860i	0.661803	+	0.661803i	−0.294002	+	0.955805i	$0.594987\pi$
$978$		0			0
$979$	44.1598			1.41135
$980$		0			0
$981$	−4.42864			−0.141396
$982$		0			0
$983$	9.83768	+	9.83768i	0.313773	+	0.313773i	0.846369	−	0.532596i	$-0.178784\pi$
$983$	9.83768	+	9.83768i	0.313773	+	0.313773i	−0.532596	+	0.846369i	$0.678784\pi$
$984$		0			0
$985$	−9.26364	+	6.98126i	−0.295164	+	0.222442i
$986$		0			0
$987$	10.4338	−	10.4338i	0.332110	−	0.332110i
$988$		0			0
$989$		−	0.815792i		−	0.0259407i
$990$		0			0
$991$			41.8726i			1.33013i	0.746787	+	0.665064i	$0.231596\pi$
$991$			41.8726i			1.33013i	−0.746787	+	0.665064i	$0.768404\pi$
$992$		0			0
$993$	55.5625	−	55.5625i	1.76322	−	1.76322i
$994$		0			0
$995$	0.965114	−	6.86923i	0.0305962	−	0.217769i
$996$		0			0
$997$	−6.38223	−	6.38223i	−0.202127	−	0.202127i	0.598784	−	0.800911i	$-0.295651\pi$
$997$	−6.38223	−	6.38223i	−0.202127	−	0.202127i	−0.800911	+	0.598784i	$0.795651\pi$
$998$		0			0
$999$	−63.1375			−1.99758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.r.767.1		12
4.3	odd	2	inner	1280.2.n.r.767.6		12
5.3	odd	4	inner	1280.2.n.r.1023.6		12
8.3	odd	2		1280.2.n.s.767.1		12
8.5	even	2		1280.2.n.s.767.6		12
16.3	odd	4		640.2.o.k.447.1	yes	12
16.5	even	4		640.2.o.j.447.1	yes	12
16.11	odd	4		640.2.o.j.447.6	yes	12
16.13	even	4		640.2.o.k.447.6	yes	12
20.3	even	4	inner	1280.2.n.r.1023.1		12
40.3	even	4		1280.2.n.s.1023.6		12
40.13	odd	4		1280.2.n.s.1023.1		12
80.3	even	4		640.2.o.j.63.1	✓	12
80.13	odd	4		640.2.o.j.63.6	yes	12
80.43	even	4		640.2.o.k.63.6	yes	12
80.53	odd	4		640.2.o.k.63.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.o.j.63.1	✓	12	80.3	even	4
640.2.o.j.63.6	yes	12	80.13	odd	4
640.2.o.j.447.1	yes	12	16.5	even	4
640.2.o.j.447.6	yes	12	16.11	odd	4
640.2.o.k.63.1	yes	12	80.53	odd	4
640.2.o.k.63.6	yes	12	80.43	even	4
640.2.o.k.447.1	yes	12	16.3	odd	4
640.2.o.k.447.6	yes	12	16.13	even	4
1280.2.n.r.767.1		12	1.1	even	1	trivial
1280.2.n.r.767.6		12	4.3	odd	2	inner
1280.2.n.r.1023.1		12	20.3	even	4	inner
1280.2.n.r.1023.6		12	5.3	odd	4	inner
1280.2.n.s.767.1		12	8.3	odd	2
1280.2.n.s.767.6		12	8.5	even	2
1280.2.n.s.1023.1		12	40.13	odd	4
1280.2.n.s.1023.6		12	40.3	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.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.05288 - 2.05288i) q^{3} +(-0.311108 + 2.21432i) q^{5} +(-1.07864 + 1.07864i) q^{7} +5.42864i q^{9} -4.98571i q^{11} +(3.90321 - 3.90321i) q^{13} +(5.18440 - 3.90707i) q^{15} +(-0.377784 - 0.377784i) q^{17} -3.43461 q^{19} +4.42864 q^{21} +(-0.198694 - 0.198694i) q^{23} +(-4.80642 - 1.37778i) q^{25} +(4.98571 - 4.98571i) q^{27} +7.80642i q^{29} +6.05424i q^{31} +(-10.2351 + 10.2351i) q^{33} +(-2.05288 - 2.72403i) q^{35} +(-6.33185 - 6.33185i) q^{37} -16.0257 q^{39} -3.18421 q^{41} +(2.05288 + 2.05288i) q^{43} +(-12.0207 - 1.68889i) q^{45} +(2.35597 - 2.35597i) q^{47} +4.67307i q^{49} +1.55109i q^{51} +(0.719004 - 0.719004i) q^{53} +(11.0400 + 1.55109i) q^{55} +(7.05086 + 7.05086i) q^{57} -6.53680 q^{59} -3.37778 q^{61} +(-5.85555 - 5.85555i) q^{63} +(7.42864 + 9.85728i) q^{65} +(-7.70974 + 7.70974i) q^{67} +0.815792i q^{69} +12.9235i q^{71} +(-2.05086 + 2.05086i) q^{73} +(7.03859 + 12.6954i) q^{75} +(5.37778 + 5.37778i) q^{77} +3.10219 q^{79} -4.18421 q^{81} +(5.48750 + 5.48750i) q^{83} +(0.954067 - 0.719004i) q^{85} +(16.0257 - 16.0257i) q^{87} +8.85728i q^{89} +8.42032i q^{91} +(12.4286 - 12.4286i) q^{93} +(1.06854 - 7.60534i) q^{95} +(-2.80642 - 2.80642i) q^{97} +27.0656 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} + 20 q^{13} - 4 q^{17} - 4 q^{25} - 16 q^{33} + 4 q^{37} + 16 q^{41} - 64 q^{45} + 36 q^{53} + 32 q^{57} - 40 q^{61} + 36 q^{65} + 28 q^{73} + 64 q^{77} + 4 q^{81} - 68 q^{85} + 96 q^{93}+ \cdots + 20 q^{97}+O(q^{100}) \) 12 * q - 4 * q^5 + 20 * q^13 - 4 * q^17 - 4 * q^25 - 16 * q^33 + 4 * q^37 + 16 * q^41 - 64 * q^45 + 36 * q^53 + 32 * q^57 - 40 * q^61 + 36 * q^65 + 28 * q^73 + 64 * q^77 + 4 * q^81 - 68 * q^85 + 96 * q^93 + 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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