LMFDB - Embedded newform 640.2.o.k.63.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(63,640)] 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("640.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,20] 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:	$5.11042572936$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.6
Root			$-0.219986 - 0.219986i$ of defining polynomial
Character	$\chi$	$=$	640.63
Dual form			640.2.o.k.447.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

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

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	$0.0663248\pi$
$3$	2.05288	+	2.05288i	1.18523	+	1.18523i	0.206861	+	0.978370i	$0.433675\pi$
$4$		0			0
$5$	2.21432	−	0.311108i	0.990274	−	0.139132i
$5$	2.21432	−	0.311108i	0.990274	−	0.139132i
$6$		0			0
$7$	1.07864	+	1.07864i	0.407688	+	0.407688i	0.880931	−	0.473244i	$-0.156917\pi$
$7$	1.07864	+	1.07864i	0.407688	+	0.407688i	−0.473244	+	0.880931i	$0.656917\pi$
$8$		0			0
$9$			5.42864i			1.80955i
$10$		0			0
$11$	−4.98571			−1.50325			−0.751624	−	0.659592i	$-0.770729\pi$
$11$	−4.98571			−1.50325			−0.751624	+	0.659592i	$0.770729\pi$
$12$		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	−0.751434	−	0.659808i	$-0.770638\pi$
$17$	−0.377784	+	0.377784i	−0.0916262	+	0.0916262i	0.659808	+	0.751434i	$0.270638\pi$
$18$		0			0
$19$			3.43461i			0.787955i	0.919120	+	0.393977i	$0.128901\pi$
$19$			3.43461i			0.787955i	−0.919120	+	0.393977i	$0.871099\pi$
$20$		0			0
$21$			4.42864i			0.966408i
$22$		0			0
$23$	0.198694	−	0.198694i	0.0414306	−	0.0414306i	−0.686088	−	0.727519i	$-0.740673\pi$
$23$	0.198694	−	0.198694i	0.0414306	−	0.0414306i	0.727519	+	0.686088i	$0.240673\pi$
$24$		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
$29$	−7.80642			−1.44962			−0.724808	−	0.688951i	$-0.758072\pi$
$29$	−7.80642			−1.44962			−0.724808	+	0.688951i	$0.758072\pi$
$30$		0			0
$31$		−	6.05424i		−	1.08737i	−0.839288	−	0.543687i	$-0.817028\pi$
$31$		−	6.05424i		−	1.08737i	0.839288	−	0.543687i	$-0.182972\pi$
$32$		0			0
$33$	−10.2351	−	10.2351i	−1.78170	−	1.78170i
$34$		0			0
$35$	2.72403	+	2.05288i	0.460445	+	0.347000i
$36$		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	$-0.420015\pi$
$41$	3.18421			0.497290			0.248645	+	0.968595i	$0.420015\pi$
$42$		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
$45$	1.68889	+	12.0207i	0.251765	+	1.79195i
$46$		0			0
$47$	2.35597	+	2.35597i	0.343654	+	0.343654i	0.857739	−	0.514085i	$-0.171868\pi$
$47$	2.35597	+	2.35597i	0.343654	+	0.343654i	−0.514085	+	0.857739i	$0.671868\pi$
$48$		0			0
$49$		−	4.67307i		−	0.667582i
$50$		0			0
$51$	−1.55109			−0.217196
$52$		0			0
$53$	−0.719004	+	0.719004i	−0.0987628	+	0.0987628i	−0.754762	−	0.655999i	$-0.772248\pi$
$53$	−0.719004	+	0.719004i	−0.0987628	+	0.0987628i	0.655999	+	0.754762i	$0.272248\pi$
$54$		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
$59$		−	6.53680i		−	0.851019i	−0.904954	−	0.425509i	$-0.860095\pi$
$59$		−	6.53680i		−	0.851019i	0.904954	−	0.425509i	$-0.139905\pi$
$60$		0			0
$61$			3.37778i			0.432481i	0.976340	+	0.216240i	$0.0693795\pi$
$61$			3.37778i			0.432481i	−0.976340	+	0.216240i	$0.930620\pi$
$62$		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
$69$	0.815792			0.0982098
$70$		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	$-0.195710\pi$
$73$	2.05086	+	2.05086i	0.240034	+	0.240034i	−0.576830	+	0.816864i	$0.695710\pi$
$74$		0			0
$75$	12.6954	+	7.03859i	1.46594	+	0.812746i
$76$		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	0.338600	−	0.940931i	$-0.390047\pi$
$83$	−5.48750	−	5.48750i	−0.602331	−	0.602331i	−0.940931	+	0.338600i	$0.890047\pi$
$84$		0			0
$85$	−0.719004	+	0.954067i	−0.0779869	+	0.103483i
$86$		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
$91$	8.42032			0.882690
$92$		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	−0.835079	−	0.550130i	$-0.814578\pi$
$97$	−2.80642	+	2.80642i	−0.284949	+	0.284949i	0.550130	+	0.835079i	$0.314578\pi$
$98$		0			0
$99$		−	27.0656i		−	2.72020i
$100$		0			0
$101$		−	14.1017i		−	1.40317i	−0.712584	−	0.701586i	$-0.752475\pi$
$101$		−	14.1017i		−	1.40317i	0.712584	−	0.701586i	$-0.247525\pi$
$102$		0			0
$103$	10.1701	−	10.1701i	1.00209	−	1.00209i	0.00209284	−	0.999998i	$-0.499334\pi$
$103$	10.1701	−	10.1701i	1.00209	−	1.00209i	0.999998	−	0.00209284i	$-0.000666171\pi$
$104$		0			0
$105$	1.37778	+	9.80642i	0.134458	+	0.957009i
$106$		0			0
$107$	2.26168	−	2.26168i	0.218645	−	0.218645i	−0.589282	−	0.807927i	$-0.700589\pi$
$107$	2.26168	−	2.26168i	0.218645	−	0.218645i	0.807927	+	0.589282i	$0.200589\pi$
$108$		0			0
$109$	−0.815792			−0.0781387			−0.0390693	−	0.999237i	$-0.512439\pi$
$109$	−0.815792			−0.0781387			−0.0390693	+	0.999237i	$0.512439\pi$
$110$		0			0
$111$		−	25.9971i		−	2.46753i
$112$		0			0
$113$	7.42864	+	7.42864i	0.698828	+	0.698828i	0.964158	−	0.265330i	$-0.0854809\pi$
$113$	7.42864	+	7.42864i	0.698828	+	0.698828i	−0.265330	+	0.964158i	$0.585481\pi$
$114$		0			0
$115$	0.378158	−	0.501788i	0.0352634	−	0.0467920i
$116$		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
$125$	10.2143	−	4.54617i	0.913597	−	0.406622i
$126$		0			0
$127$	−8.89277	−	8.89277i	−0.789106	−	0.789106i	0.192241	−	0.981348i	$-0.438424\pi$
$127$	−8.89277	−	8.89277i	−0.789106	−	0.789106i	−0.981348	+	0.192241i	$0.938424\pi$
$128$		0			0
$129$			8.42864i			0.742100i
$130$		0			0
$131$	−17.0942			−1.49353			−0.746763	−	0.665090i	$-0.768393\pi$
$131$	−17.0942			−1.49353			−0.746763	+	0.665090i	$0.768393\pi$
$132$		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	$-0.652325\pi$
$137$	5.00000	−	5.00000i	0.427179	−	0.427179i	0.887666	+	0.460487i	$0.152325\pi$
$138$		0			0
$139$		−	18.6453i		−	1.58147i	−0.612157	−	0.790736i	$-0.709698\pi$
$139$		−	18.6453i		−	1.58147i	0.612157	−	0.790736i	$-0.290302\pi$
$140$		0			0
$141$			9.67307i			0.814620i
$142$		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
$149$	9.93978			0.814298			0.407149	−	0.913362i	$-0.366523\pi$
$149$	9.93978			0.814298			0.407149	+	0.913362i	$0.366523\pi$
$150$		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
$155$	−1.88352	−	13.4060i	−0.151288	−	1.07680i
$156$		0			0
$157$	−10.9541	−	10.9541i	−0.874230	−	0.874230i	0.118700	−	0.992930i	$-0.462127\pi$
$157$	−10.9541	−	10.9541i	−0.874230	−	0.874230i	−0.992930	+	0.118700i	$0.962127\pi$
$158$		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	0.998398	−	0.0565824i	$-0.0180204\pi$
$163$	12.0243	+	12.0243i	0.941816	+	0.941816i	−0.0565824	+	0.998398i	$0.518020\pi$
$164$		0			0
$165$	−25.8479	−	19.4795i	−2.01226	−	1.51648i
$166$		0			0
$167$	−7.61544	−	7.61544i	−0.589300	−	0.589300i	0.348142	−	0.937442i	$-0.386813\pi$
$167$	−7.61544	−	7.61544i	−0.589300	−	0.589300i	−0.937442	+	0.348142i	$0.886813\pi$
$168$		0			0
$169$		−	17.4701i		−	1.34386i
$170$		0			0
$171$	−18.6453			−1.42584
$172$		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
$179$			5.57169i			0.416447i	0.978081	+	0.208224i	$0.0667682\pi$
$179$			5.57169i			0.416447i	−0.978081	+	0.208224i	$0.933232\pi$
$180$		0			0
$181$			3.34614i			0.248717i	0.992237	+	0.124358i	$0.0396872\pi$
$181$			3.34614i			0.248717i	−0.992237	+	0.124358i	$0.960313\pi$
$182$		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
$189$	−10.7556			−0.782353
$190$		0			0
$191$		−	9.15643i		−	0.662536i	−0.943537	−	0.331268i	$-0.892524\pi$
$191$		−	9.15643i		−	0.662536i	0.943537	−	0.331268i	$-0.107476\pi$
$192$		0			0
$193$	5.99063	+	5.99063i	0.431215	+	0.431215i	0.889042	−	0.457826i	$-0.151372\pi$
$193$	5.99063	+	5.99063i	0.431215	+	0.431215i	−0.457826	+	0.889042i	$0.651372\pi$
$194$		0			0
$195$	35.4859	−	4.98571i	2.54120	−	0.357034i
$196$		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	$-0.464930\pi$
$199$	3.10219			0.219908			0.109954	+	0.993937i	$0.464930\pi$
$200$		0			0
$201$	−31.6543			−2.23272
$202$		0			0
$203$	−8.42032	−	8.42032i	−0.590991	−	0.590991i
$204$		0			0
$205$	7.05086	−	0.990632i	0.492453	−	0.0691887i
$206$		0			0
$207$	1.07864	+	1.07864i	0.0749707	+	0.0749707i
$208$		0			0
$209$		−	17.1240i		−	1.18449i
$210$		0			0
$211$	17.0942			1.17681			0.588406	−	0.808565i	$-0.299756\pi$
$211$	17.0942			1.17681			0.588406	+	0.808565i	$0.299756\pi$
$212$		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
$219$			8.42032i			0.568993i
$220$		0			0
$221$			2.94914i			0.198381i
$222$		0			0
$223$	3.23592	−	3.23592i	0.216693	−	0.216693i	−0.590410	−	0.807103i	$-0.701034\pi$
$223$	3.23592	−	3.23592i	0.216693	−	0.216693i	0.807103	+	0.590410i	$0.201034\pi$
$224$		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
$229$	12.1936			0.805774			0.402887	−	0.915250i	$-0.368007\pi$
$229$	12.1936			0.805774			0.402887	+	0.915250i	$0.368007\pi$
$230$		0			0
$231$		−	22.0799i		−	1.45275i
$232$		0			0
$233$	1.13335	+	1.13335i	0.0742484	+	0.0742484i	0.743256	−	0.669007i	$-0.233281\pi$
$233$	1.13335	+	1.13335i	0.0742484	+	0.0742484i	−0.669007	+	0.743256i	$0.733281\pi$
$234$		0			0
$235$	5.94984	+	4.48392i	0.388125	+	0.292499i
$236$		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
$245$	−1.45383	−	10.3477i	−0.0928817	−	0.661089i
$246$		0			0
$247$	13.4060	+	13.4060i	0.853005	+	0.853005i
$248$		0			0
$249$		−	22.5303i		−	1.42780i
$250$		0			0
$251$	−14.9571			−0.944085			−0.472043	−	0.881576i	$-0.656483\pi$
$251$	−14.9571			−0.944085			−0.472043	+	0.881576i	$0.656483\pi$
$252$		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	−0.883911	−	0.467656i	$-0.845099\pi$
$257$	−6.67307	+	6.67307i	−0.416255	+	0.416255i	0.467656	+	0.883911i	$0.345099\pi$
$258$		0			0
$259$		−	13.6596i		−	0.848765i
$260$		0			0
$261$		−	42.3783i		−	2.62315i
$262$		0			0
$263$	−16.7069	+	16.7069i	−1.03019	+	1.03019i	−0.0306624	+	0.999530i	$0.509762\pi$
$263$	−16.7069	+	16.7069i	−1.03019	+	1.03019i	−0.999530	+	0.0306624i	$0.990238\pi$
$264$		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
$269$	16.8988			1.03034			0.515168	−	0.857089i	$-0.327730\pi$
$269$	16.8988			1.03034			0.515168	+	0.857089i	$0.327730\pi$
$270$		0			0
$271$			19.1278i			1.16193i	0.813927	+	0.580967i	$0.197325\pi$
$271$			19.1278i			1.16193i	−0.813927	+	0.580967i	$0.802675\pi$
$272$		0			0
$273$	17.2859	+	17.2859i	1.04619	+	1.04619i
$274$		0			0
$275$	−23.9634	+	6.86923i	−1.44505	+	0.414230i
$276$		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	$-0.625708\pi$
$281$	−12.8988			−0.769476			−0.384738	+	0.923026i	$0.625708\pi$
$282$		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
$285$	−13.4193	+	17.8064i	−0.794889	+	1.05476i
$286$		0			0
$287$	3.43461	+	3.43461i	0.202739	+	0.202739i
$288$		0			0
$289$			16.7146i			0.983209i
$290$		0			0
$291$	−11.5225			−0.675461
$292$		0			0
$293$	−12.4652	+	12.4652i	−0.728225	+	0.728225i	−0.970266	−	0.242041i	$-0.922183\pi$
$293$	−12.4652	+	12.4652i	−0.728225	+	0.728225i	0.242041	+	0.970266i	$0.422183\pi$
$294$		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
$299$		−	1.55109i		−	0.0897020i
$300$		0			0
$301$			4.42864i			0.255263i
$302$		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
$309$	41.7560			2.37542
$310$		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	$-0.0178386\pi$
$313$	16.6731	+	16.6731i	0.942418	+	0.942418i	−0.0560124	+	0.998430i	$0.517839\pi$
$314$		0			0
$315$	−11.1443	+	14.7878i	−0.627913	+	0.833196i
$316$		0			0
$317$	−6.85236	−	6.85236i	−0.384867	−	0.384867i	0.487985	−	0.872852i	$-0.337732\pi$
$317$	−6.85236	−	6.85236i	−0.384867	−	0.384867i	−0.872852	+	0.487985i	$0.837732\pi$
$318$		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
$325$	13.3827	−	24.1383i	0.742339	−	1.33895i
$326$		0			0
$327$	−1.67472	−	1.67472i	−0.0926124	−	0.0926124i
$328$		0			0
$329$			5.08250i			0.280207i
$330$		0			0
$331$	27.0656			1.48766			0.743830	−	0.668369i	$-0.233007\pi$
$331$	27.0656			1.48766			0.743830	+	0.668369i	$0.233007\pi$
$332$		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	−0.456632	+	0.889656i	$0.650944\pi$
$337$	−24.7146	+	24.7146i	−1.34629	+	1.34629i	−0.889656	+	0.456632i	$0.849056\pi$
$338$		0			0
$339$			30.5002i			1.65654i
$340$		0			0
$341$			30.1847i			1.63459i
$342$		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	−0.582984	−	0.812484i	$-0.698115\pi$
$347$	4.27512	−	4.27512i	0.229500	−	0.229500i	0.812484	+	0.582984i	$0.198115\pi$
$348$		0			0
$349$	−6.29529			−0.336979			−0.168489	−	0.985703i	$-0.553889\pi$
$349$	−6.29529			−0.336979			−0.168489	+	0.985703i	$0.553889\pi$
$350$		0			0
$351$			38.9205i			2.07743i
$352$		0			0
$353$	9.85728	+	9.85728i	0.524650	+	0.524650i	0.918972	−	0.394322i	$-0.129021\pi$
$353$	9.85728	+	9.85728i	0.524650	+	0.524650i	−0.394322	+	0.918972i	$0.629021\pi$
$354$		0			0
$355$	4.02059	+	28.6167i	0.213391	+	1.51882i
$356$		0			0
$357$	−1.67307	−	1.67307i	−0.0885483	−	0.0885483i
$358$		0			0
$359$	−25.1821			−1.32906			−0.664530	−	0.747262i	$-0.731368\pi$
$359$	−25.1821			−1.32906			−0.664530	+	0.747262i	$0.731368\pi$
$360$		0			0
$361$	7.20342			0.379127
$362$		0			0
$363$	28.4473	+	28.4473i	1.49310	+	1.49310i
$364$		0			0
$365$	5.17929	+	3.90321i	0.271096	+	0.204303i
$366$		0			0
$367$	−21.0013	−	21.0013i	−1.09626	−	1.09626i	−0.994844	−	0.101412i	$-0.967664\pi$
$367$	−21.0013	−	21.0013i	−1.09626	−	1.09626i	−0.101412	−	0.994844i	$-0.532336\pi$
$368$		0			0
$369$			17.2859i			0.899869i
$370$		0			0
$371$	−1.55109			−0.0805287
$372$		0			0
$373$	−10.7190	+	10.7190i	−0.555009	+	0.555009i	−0.927882	−	0.372873i	$-0.878373\pi$
$373$	−10.7190	+	10.7190i	−0.555009	+	0.555009i	0.372873	+	0.927882i	$0.378373\pi$
$374$		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
$379$			15.5431i			0.798395i	0.916865	+	0.399198i	$0.130711\pi$
$379$			15.5431i			0.798395i	−0.916865	+	0.399198i	$0.869289\pi$
$380$		0			0
$381$		−	36.5116i		−	1.87055i
$382$		0			0
$383$	15.3444	−	15.3444i	0.784063	−	0.784063i	−0.196451	−	0.980514i	$-0.562942\pi$
$383$	15.3444	−	15.3444i	0.784063	−	0.784063i	0.980514	+	0.196451i	$0.0629417\pi$
$384$		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
$389$	−13.5526			−0.687145			−0.343573	−	0.939126i	$-0.611637\pi$
$389$	−13.5526			−0.687145			−0.343573	+	0.939126i	$0.611637\pi$
$390$		0			0
$391$			0.150127i			0.00759226i
$392$		0			0
$393$	−35.0923	−	35.0923i	−1.77017	−	1.77017i
$394$		0			0
$395$	6.86923	−	0.965114i	0.345628	−	0.0485602i
$396$		0			0
$397$	11.8716	+	11.8716i	0.595817	+	0.595817i	0.939197	−	0.343380i	$-0.111572\pi$
$397$	11.8716	+	11.8716i	0.595817	+	0.595817i	−0.343380	+	0.939197i	$0.611572\pi$
$398$		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
$405$	−9.26517	+	1.30174i	−0.460390	+	0.0646840i
$406$		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
$411$	20.5288			1.01261
$412$		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
$419$		−	22.4123i		−	1.09491i	−0.836834	−	0.547457i	$-0.815596\pi$
$419$		−	22.4123i		−	1.09491i	0.836834	−	0.547457i	$-0.184404\pi$
$420$		0			0
$421$			29.3590i			1.43087i	0.698678	+	0.715436i	$0.253772\pi$
$421$			29.3590i			1.43087i	−0.698678	+	0.715436i	$0.746228\pi$
$422$		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
$429$	−79.8992			−3.85757
$430$		0			0
$431$			12.9235i			0.622502i	0.950328	+	0.311251i	$0.100748\pi$
$431$			12.9235i			0.622502i	−0.950328	+	0.311251i	$0.899252\pi$
$432$		0			0
$433$	−16.9081	−	16.9081i	−0.812553	−	0.812553i	0.172463	−	0.985016i	$-0.444827\pi$
$433$	−16.9081	−	16.9081i	−0.812553	−	0.812553i	−0.985016	+	0.172463i	$0.944827\pi$
$434$		0			0
$435$	−40.4716	−	30.5002i	−1.94047	−	1.46237i
$436$		0			0
$437$	0.682439	+	0.682439i	0.0326455	+	0.0326455i
$438$		0			0
$439$	−18.9777			−0.905757			−0.452878	−	0.891572i	$-0.649603\pi$
$439$	−18.9777			−0.905757			−0.452878	+	0.891572i	$0.649603\pi$
$440$		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
$445$	2.75557	+	19.6128i	0.130626	+	0.929738i
$446$		0			0
$447$	20.4052	+	20.4052i	0.965132	+	0.965132i
$448$		0			0
$449$		−	12.1432i		−	0.573073i	−0.958069	−	0.286536i	$-0.907496\pi$
$449$		−	12.1432i		−	0.573073i	0.958069	−	0.286536i	$-0.0925040\pi$
$450$		0			0
$451$	−15.8755			−0.747550
$452$		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	$-0.722894\pi$
$457$	2.57136	−	2.57136i	0.120283	−	0.120283i	0.764686	+	0.644403i	$0.222894\pi$
$458$		0			0
$459$		−	3.76704i		−	0.175831i
$460$		0			0
$461$			35.6128i			1.65866i	0.558762	+	0.829328i	$0.311276\pi$
$461$			35.6128i			1.65866i	−0.558762	+	0.829328i	$0.688724\pi$
$462$		0			0
$463$	−6.67054	+	6.67054i	−0.310006	+	0.310006i	−0.844912	−	0.534906i	$-0.820347\pi$
$463$	−6.67054	+	6.67054i	−0.310006	+	0.310006i	0.534906	+	0.844912i	$0.320347\pi$
$464$		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
$469$	−16.6321			−0.767997
$470$		0			0
$471$		−	44.9748i		−	2.07233i
$472$		0			0
$473$	−10.2351	−	10.2351i	−0.470609	−	0.470609i
$474$		0			0
$475$	4.73216	+	16.5082i	0.217126	+	0.757449i
$476$		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
$485$	−5.34122	+	7.08742i	−0.242532	+	0.321823i
$486$		0			0
$487$	−8.89277	−	8.89277i	−0.402970	−	0.402970i	0.476308	−	0.879278i	$-0.341975\pi$
$487$	−8.89277	−	8.89277i	−0.402970	−	0.402970i	−0.879278	+	0.476308i	$0.841975\pi$
$488$		0			0
$489$			49.3689i			2.23254i
$490$		0			0
$491$	−30.8327			−1.39146			−0.695729	−	0.718304i	$-0.744919\pi$
$491$	−30.8327			−1.39146			−0.695729	+	0.718304i	$0.744919\pi$
$492$		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
$499$			35.4859i			1.58857i	0.607546	+	0.794284i	$0.292154\pi$
$499$			35.4859i			1.58857i	−0.607546	+	0.794284i	$0.707846\pi$
$500$		0			0
$501$		−	31.2672i		−	1.39691i
$502$		0			0
$503$	−8.80761	+	8.80761i	−0.392712	+	0.392712i	−0.875653	−	0.482941i	$-0.839569\pi$
$503$	−8.80761	+	8.80761i	−0.392712	+	0.392712i	0.482941	+	0.875653i	$0.339569\pi$
$504$		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
$509$	21.9081			0.971061			0.485530	−	0.874220i	$-0.338626\pi$
$509$	21.9081			0.971061			0.485530	+	0.874220i	$0.338626\pi$
$510$		0			0
$511$			4.42427i			0.195718i
$512$		0			0
$513$	−17.1240	−	17.1240i	−0.756042	−	0.756042i
$514$		0			0
$515$	19.3559	−	25.6839i	0.852922	−	1.13177i
$516$		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	$-0.358790\pi$
$521$	19.5941			0.858434			0.429217	+	0.903201i	$0.358790\pi$
$522$		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
$525$	6.10171	+	21.2859i	0.266300	+	0.928994i
$526$		0			0
$527$	2.28720	+	2.28720i	0.0996319	+	0.0996319i
$528$		0			0
$529$			22.9210i			0.996567i
$530$		0			0
$531$	35.4859			1.53996
$532$		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
$539$			23.2986i			1.00354i
$540$		0			0
$541$			26.8385i			1.15388i	0.816787	+	0.576940i	$0.195753\pi$
$541$			26.8385i			1.15388i	−0.816787	+	0.576940i	$0.804247\pi$
$542$		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
$549$	−18.3368			−0.782594
$550$		0			0
$551$		−	26.8121i		−	1.14223i
$552$		0			0
$553$	3.34614	+	3.34614i	0.142292	+	0.142292i
$554$		0			0
$555$	−8.08789	−	57.5658i	−0.343312	−	2.44353i
$556$		0			0
$557$	−29.6780	−	29.6780i	−1.25750	−	1.25750i	−0.952284	−	0.305213i	$-0.901272\pi$
$557$	−29.6780	−	29.6780i	−1.25750	−	1.25750i	−0.305213	−	0.952284i	$-0.598728\pi$
$558$		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	0.807343	−	0.590083i	$-0.200905\pi$
$563$	5.15507	+	5.15507i	0.217260	+	0.217260i	−0.590083	+	0.807343i	$0.700905\pi$
$564$		0			0
$565$	18.7605	+	14.1383i	0.789260	+	0.594802i
$566$		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
$571$	1.21866			0.0509995			0.0254997	−	0.999675i	$-0.491882\pi$
$571$	1.21866			0.0509995			0.0254997	+	0.999675i	$0.491882\pi$
$572$		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	−0.984338	−	0.176293i	$-0.943589\pi$
$577$	−19.4099	+	19.4099i	−0.808045	+	0.808045i	0.176293	+	0.984338i	$0.443589\pi$
$578$		0			0
$579$			24.5961i			1.02218i
$580$		0			0
$581$		−	11.8381i		−	0.491126i
$582$		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	−0.895805	−	0.444447i	$-0.853400\pi$
$587$	−10.9356	+	10.9356i	−0.451358	+	0.451358i	0.444447	+	0.895805i	$0.353400\pi$
$588$		0			0
$589$	20.7940			0.856802
$590$		0			0
$591$			15.0605i			0.619508i
$592$		0			0
$593$	−20.3274	−	20.3274i	−0.834747	−	0.834747i	0.153415	−	0.988162i	$-0.450973\pi$
$593$	−20.3274	−	20.3274i	−0.834747	−	0.834747i	−0.988162	+	0.153415i	$0.950973\pi$
$594$		0			0
$595$	−1.80464	+	0.253549i	−0.0739831	+	0.0103945i
$596$		0			0
$597$	6.36842	+	6.36842i	0.260642	+	0.260642i
$598$		0			0
$599$	−47.2620			−1.93107			−0.965536	−	0.260269i	$-0.916189\pi$
$599$	−47.2620			−1.93107			−0.965536	+	0.260269i	$0.916189\pi$
$600$		0			0
$601$	28.0415			1.14384			0.571918	−	0.820311i	$-0.306200\pi$
$601$	28.0415			1.14384			0.571918	+	0.820311i	$0.306200\pi$
$602$		0			0
$603$	−41.8534	−	41.8534i	−1.70440	−	1.70440i
$604$		0			0
$605$	30.6844	−	4.31111i	1.24750	−	0.175271i
$606$		0			0
$607$	−16.6217	−	16.6217i	−0.674656	−	0.674656i	0.284130	−	0.958786i	$-0.408295\pi$
$607$	−16.6217	−	16.6217i	−0.674656	−	0.674656i	−0.958786	+	0.284130i	$0.908295\pi$
$608$		0			0
$609$		−	34.5718i		−	1.40092i
$610$		0			0
$611$	18.3917			0.744050
$612$		0			0
$613$	5.41435	−	5.41435i	0.218684	−	0.218684i	−0.589260	−	0.807943i	$-0.700581\pi$
$613$	5.41435	−	5.41435i	0.218684	−	0.218684i	0.807943	+	0.589260i	$0.200581\pi$
$614$		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	$-0.889927\pi$
$617$	−14.9496	+	14.9496i	−0.601849	+	0.601849i	0.338954	+	0.940803i	$0.389927\pi$
$618$		0			0
$619$		−	20.2753i		−	0.814931i	−0.913220	−	0.407466i	$-0.866413\pi$
$619$		−	20.2753i		−	0.814931i	0.913220	−	0.407466i	$-0.133587\pi$
$620$		0			0
$621$			1.98126i			0.0795054i
$622$		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
$629$	4.78415			0.190757
$630$		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
$635$	−22.4581	−	16.9248i	−0.891221	−	0.671642i
$636$		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	0.801305	−	0.598257i	$-0.204140\pi$
$643$	5.14878	+	5.14878i	0.203048	+	0.203048i	−0.598257	+	0.801305i	$0.704140\pi$
$644$		0			0
$645$	2.62222	+	18.6637i	0.103250	+	0.734883i
$646$		0			0
$647$	16.2893	+	16.2893i	0.640399	+	0.640399i	0.950654	−	0.310255i	$-0.100414\pi$
$647$	16.2893	+	16.2893i	0.640399	+	0.640399i	−0.310255	+	0.950654i	$0.600414\pi$
$648$		0			0
$649$			32.5906i			1.27929i
$650$		0			0
$651$	26.8121			1.05085
$652$		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
$659$			1.80464i			0.0702988i	0.999382	+	0.0351494i	$0.0111907\pi$
$659$			1.80464i			0.0702988i	−0.999382	+	0.0351494i	$0.988809\pi$
$660$		0			0
$661$		−	23.3145i		−	0.906829i	−0.891300	−	0.453414i	$-0.850206\pi$
$661$		−	23.3145i		−	0.906829i	0.891300	−	0.453414i	$-0.149794\pi$
$662$		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
$669$	13.2859			0.513663
$670$		0			0
$671$		−	16.8406i		−	0.650126i
$672$		0			0
$673$	−6.15257	−	6.15257i	−0.237164	−	0.237164i	0.578511	−	0.815675i	$-0.303634\pi$
$673$	−6.15257	−	6.15257i	−0.237164	−	0.237164i	−0.815675	+	0.578511i	$0.803634\pi$
$674$		0			0
$675$	−17.0942	+	30.8327i	−0.657956	+	1.18675i
$676$		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
$685$	9.51606	−	12.6271i	0.363590	−	0.482458i
$686$		0			0
$687$	25.0320	+	25.0320i	0.955029	+	0.955029i
$688$		0			0
$689$			5.61285i			0.213832i
$690$		0			0
$691$	43.2414			1.64498			0.822490	−	0.568779i	$-0.192584\pi$
$691$	43.2414			1.64498			0.822490	+	0.568779i	$0.192584\pi$
$692$		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
$699$			4.65328i			0.176003i
$700$		0			0
$701$			24.8256i			0.937651i	0.883291	+	0.468826i	$0.155323\pi$
$701$			24.8256i			0.937651i	−0.883291	+	0.468826i	$0.844677\pi$
$702$		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
$709$	42.8484			1.60920			0.804602	−	0.593814i	$-0.202378\pi$
$709$	42.8484			1.60920			0.804602	+	0.593814i	$0.202378\pi$
$710$		0			0
$711$			16.8406i			0.631574i
$712$		0			0
$713$	−1.20294	−	1.20294i	−0.0450506	−	0.0450506i
$714$		0			0
$715$	−37.0370	+	49.1455i	−1.38511	+	1.83794i
$716$		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
$725$	−37.5210	+	10.7556i	−1.39349	+	0.399452i
$726$		0			0
$727$	−22.6312	−	22.6312i	−0.839346	−	0.839346i	0.149427	−	0.988773i	$-0.452257\pi$
$727$	−22.6312	−	22.6312i	−0.839346	−	0.839346i	−0.988773	+	0.149427i	$0.952257\pi$
$728$		0			0
$729$			38.6958i			1.43318i
$730$		0			0
$731$	−1.55109			−0.0573692
$732$		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
$739$		−	52.3266i		−	1.92486i	−0.271522	−	0.962432i	$-0.587527\pi$
$739$		−	52.3266i		−	1.92486i	0.271522	−	0.962432i	$-0.412473\pi$
$740$		0			0
$741$			55.0420i			2.02202i
$742$		0			0
$743$	30.5551	−	30.5551i	1.12096	−	1.12096i	0.129359	−	0.991598i	$-0.458708\pi$
$743$	30.5551	−	30.5551i	1.12096	−	1.12096i	0.991598	−	0.129359i	$-0.0412921\pi$
$744$		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
$749$	4.87908			0.178278
$750$		0			0
$751$			36.9336i			1.34773i	0.738856	+	0.673863i	$0.235366\pi$
$751$			36.9336i			1.34773i	−0.738856	+	0.673863i	$0.764634\pi$
$752$		0			0
$753$	−30.7052	−	30.7052i	−1.11896	−	1.11896i
$754$		0			0
$755$	−1.21866	−	8.67387i	−0.0443517	−	0.315674i
$756$		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	$-0.458083\pi$
$761$	7.24443			0.262610			0.131305	+	0.991342i	$0.458083\pi$
$762$		0			0
$763$	−0.879946	−	0.879946i	−0.0318562	−	0.0318562i
$764$		0			0
$765$	−5.17929	−	3.90321i	−0.187257	−	0.141121i
$766$		0			0
$767$	−25.5145	−	25.5145i	−0.921276	−	0.921276i
$768$		0			0
$769$		−	29.3274i		−	1.05757i	−0.848755	−	0.528787i	$-0.822647\pi$
$769$		−	29.3274i		−	1.05757i	0.848755	−	0.528787i	$-0.177353\pi$
$770$		0			0
$771$	−27.3980			−0.986716
$772$		0			0
$773$	−0.954067	+	0.954067i	−0.0343154	+	0.0343154i	−0.724056	−	0.689741i	$-0.757724\pi$
$773$	−0.954067	+	0.954067i	−0.0343154	+	0.0343154i	0.689741	+	0.724056i	$0.257724\pi$
$774$		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
$779$			10.9365i			0.391842i
$780$		0			0
$781$		−	64.4327i		−	2.30558i
$782$		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
$789$	−68.5946			−2.44203
$790$		0			0
$791$			16.0257i			0.569807i
$792$		0			0
$793$	13.1842	+	13.1842i	0.468185	+	0.468185i
$794$		0			0
$795$	−6.53680	+	0.918408i	−0.231836	+	0.0325726i
$796$		0			0
$797$	−6.85236	−	6.85236i	−0.242723	−	0.242723i	0.575253	−	0.817976i	$-0.304904\pi$
$797$	−6.85236	−	6.85236i	−0.242723	−	0.242723i	−0.817976	+	0.575253i	$0.804904\pi$
$798$		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
$805$	0.949145	−	0.133353i	0.0334530	−	0.00470008i
$806$		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
$811$	11.1901			0.392937			0.196468	−	0.980510i	$-0.437053\pi$
$811$	11.1901			0.392937			0.196468	+	0.980510i	$0.437053\pi$
$812$		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
$819$			45.7109i			1.59727i
$820$		0			0
$821$		−	6.33677i		−	0.221155i	−0.993868	−	0.110577i	$-0.964730\pi$
$821$		−	6.33677i		−	0.221155i	0.993868	−	0.110577i	$-0.0352700\pi$
$822$		0			0
$823$	9.20500	−	9.20500i	0.320866	−	0.320866i	−0.528233	−	0.849099i	$-0.677145\pi$
$823$	9.20500	−	9.20500i	0.320866	−	0.320866i	0.849099	+	0.528233i	$0.177145\pi$
$824$		0			0
$825$	−63.2958	−	35.0923i	−2.20368	−	1.22176i
$826$		0			0
$827$	7.37731	−	7.37731i	0.256534	−	0.256534i	−0.567109	−	0.823643i	$-0.691938\pi$
$827$	7.37731	−	7.37731i	0.256534	−	0.256534i	0.823643	+	0.567109i	$0.191938\pi$
$828$		0			0
$829$	−52.2449			−1.81454			−0.907270	−	0.420548i	$-0.861838\pi$
$829$	−52.2449			−1.81454			−0.907270	+	0.420548i	$0.861838\pi$
$830$		0			0
$831$			19.1278i			0.663538i
$832$		0			0
$833$	1.76541	+	1.76541i	0.0611679	+	0.0611679i
$834$		0			0
$835$	−19.2322	−	14.4938i	−0.665559	−	0.501579i
$836$		0			0
$837$	30.1847	+	30.1847i	1.04334	+	1.04334i
$838$		0			0
$839$	53.6241			1.85131			0.925655	−	0.378368i	$-0.123515\pi$
$839$	53.6241			1.85131			0.925655	+	0.378368i	$0.123515\pi$
$840$		0			0
$841$	31.9403			1.10139
$842$		0			0
$843$	−26.4796	−	26.4796i	−0.912007	−	0.912007i
$844$		0			0
$845$	−5.43509	−	38.6844i	−0.186973	−	1.33079i
$846$		0			0
$847$	14.9470	+	14.9470i	0.513586	+	0.513586i
$848$		0			0
$849$		−	35.2672i		−	1.21037i
$850$		0			0
$851$	−2.51621			−0.0862545
$852$		0			0
$853$	−27.7926	+	27.7926i	−0.951601	+	0.951601i	−0.998882	−	0.0472808i	$-0.984944\pi$
$853$	−27.7926	+	27.7926i	−0.951601	+	0.951601i	0.0472808	+	0.998882i	$0.484944\pi$
$854$		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	$-0.828785\pi$
$857$	−10.1427	+	10.1427i	−0.346469	+	0.346469i	0.512324	+	0.858792i	$0.328785\pi$
$858$		0			0
$859$			27.1445i			0.926158i	0.886317	+	0.463079i	$0.153255\pi$
$859$			27.1445i			0.926158i	−0.886317	+	0.463079i	$0.846745\pi$
$860$		0			0
$861$			14.1017i			0.480585i
$862$		0			0
$863$	−15.0120	+	15.0120i	−0.511014	+	0.511014i	−0.914837	−	0.403823i	$-0.867681\pi$
$863$	−15.0120	+	15.0120i	−0.511014	+	0.511014i	0.403823	+	0.914837i	$0.367681\pi$
$864$		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
$869$	−15.4666			−0.524668
$870$		0			0
$871$			60.1855i			2.03931i
$872$		0			0
$873$	−15.2351	−	15.2351i	−0.515629	−	0.515629i
$874$		0			0
$875$	15.9213	+	6.11389i	0.538237	+	0.206687i
$876$		0			0
$877$	13.9032	+	13.9032i	0.469478	+	0.469478i	0.901745	−	0.432267i	$-0.142286\pi$
$877$	13.9032	+	13.9032i	0.469478	+	0.469478i	−0.432267	+	0.901745i	$0.642286\pi$
$878$		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	$-0.986331\pi$
$883$	−30.9635	−	30.9635i	−1.04201	−	1.04201i	−0.0429282	−	0.999078i	$-0.513669\pi$
$884$		0			0
$885$	25.5397	−	33.8894i	0.858508	−	1.13918i
$886$		0			0
$887$	−13.1669	−	13.1669i	−0.442102	−	0.442102i	0.450616	−	0.892718i	$-0.351204\pi$
$887$	−13.1669	−	13.1669i	−0.442102	−	0.442102i	−0.892718	+	0.450616i	$0.851204\pi$
$888$		0			0
$889$		−	19.1842i		−	0.643418i
$890$		0			0
$891$	20.8612			0.698878
$892$		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
$899$			47.2620i			1.57628i
$900$		0			0
$901$		−	0.543257i		−	0.0180985i
$902$		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	−0.927893	−	0.372846i	$-0.878382\pi$
$907$	−16.7160	+	16.7160i	−0.555047	+	0.555047i	0.372846	+	0.927893i	$0.378382\pi$
$908$		0			0
$909$	76.5531			2.53911
$910$		0			0
$911$		−	30.2712i		−	1.00293i	−0.865178	−	0.501465i	$-0.832795\pi$
$911$		−	30.2712i		−	1.00293i	0.865178	−	0.501465i	$-0.167205\pi$
$912$		0			0
$913$	27.3590	+	27.3590i	0.905452	+	0.905452i
$914$		0			0
$915$	−13.1972	+	17.5118i	−0.436287	+	0.578922i
$916$		0			0
$917$	−18.4385	−	18.4385i	−0.608892	−	0.608892i
$918$		0			0
$919$	16.8406			0.555522			0.277761	−	0.960650i	$-0.410408\pi$
$919$	16.8406			0.555522			0.277761	+	0.960650i	$0.410408\pi$
$920$		0			0
$921$	18.0602			0.595105
$922$		0			0
$923$	50.4431	+	50.4431i	1.66035	+	1.66035i
$924$		0			0
$925$	−39.1575	−	21.7096i	−1.28749	−	0.713808i
$926$		0			0
$927$	55.2099	+	55.2099i	1.81333	+	1.81333i
$928$		0			0
$929$			33.6543i			1.10416i	0.833790	+	0.552081i	$0.186166\pi$
$929$			33.6543i			1.10416i	−0.833790	+	0.552081i	$0.813834\pi$
$930$		0			0
$931$	16.0502			0.526024
$932$		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	$-0.502410\pi$
$937$	30.3778	−	30.3778i	0.992399	−	0.992399i	0.999971	+	0.00757237i	$0.00241038\pi$
$938$		0			0
$939$			68.4557i			2.23397i
$940$		0			0
$941$			9.39069i			0.306128i	0.988216	+	0.153064i	$0.0489140\pi$
$941$			9.39069i			0.306128i	−0.988216	+	0.153064i	$0.951086\pi$
$942$		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
$949$	16.0098			0.519702
$950$		0			0
$951$		−	28.1341i		−	0.912312i
$952$		0			0
$953$	33.7971	+	33.7971i	1.09479	+	1.09479i	0.995009	+	0.0997850i	$0.0318155\pi$
$953$	33.7971	+	33.7971i	1.09479	+	1.09479i	0.0997850	+	0.995009i	$0.468184\pi$
$954$		0			0
$955$	−2.84864	−	20.2753i	−0.0921797	−	0.656092i
$956$		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
$965$	15.1289	+	11.4014i	0.487017	+	0.367025i
$966$		0			0
$967$	35.0722	+	35.0722i	1.12784	+	1.12784i	0.990527	+	0.137317i	$0.0438480\pi$
$967$	35.0722	+	35.0722i	1.12784	+	1.12784i	0.137317	+	0.990527i	$0.456152\pi$
$968$		0			0
$969$		−	5.32741i		−	0.171141i
$970$		0			0
$971$	55.0496			1.76663			0.883313	−	0.468783i	$-0.155307\pi$
$971$	55.0496			1.76663			0.883313	+	0.468783i	$0.155307\pi$
$972$		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	−0.294002	−	0.955805i	$-0.594987\pi$
$977$	20.6860	−	20.6860i	0.661803	−	0.661803i	0.955805	+	0.294002i	$0.0949872\pi$
$978$		0			0
$979$		−	44.1598i		−	1.41135i
$980$		0			0
$981$		−	4.42864i		−	0.141396i
$982$		0			0
$983$	−9.83768	+	9.83768i	−0.313773	+	0.313773i	−0.846369	−	0.532596i	$-0.821216\pi$
$983$	−9.83768	+	9.83768i	−0.313773	+	0.313773i	0.532596	+	0.846369i	$0.321216\pi$
$984$		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
$989$	0.815792			0.0259407
$990$		0			0
$991$		−	41.8726i		−	1.33013i	−0.746787	−	0.665064i	$-0.768404\pi$
$991$		−	41.8726i		−	1.33013i	0.746787	−	0.665064i	$-0.231596\pi$
$992$		0			0
$993$	55.5625	+	55.5625i	1.76322	+	1.76322i
$994$		0			0
$995$	6.86923	−	0.965114i	0.217769	−	0.0305962i
$996$		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	640.2.o.k.63.6	yes	12
4.3	odd	2	inner	640.2.o.k.63.1	yes	12
5.2	odd	4		640.2.o.j.447.6	yes	12
8.3	odd	2		640.2.o.j.63.6	yes	12
8.5	even	2		640.2.o.j.63.1	✓	12
16.3	odd	4		1280.2.n.r.1023.6		12
16.5	even	4		1280.2.n.s.1023.6		12
16.11	odd	4		1280.2.n.s.1023.1		12
16.13	even	4		1280.2.n.r.1023.1		12
20.7	even	4		640.2.o.j.447.1	yes	12
40.27	even	4	inner	640.2.o.k.447.6	yes	12
40.37	odd	4	inner	640.2.o.k.447.1	yes	12
80.27	even	4		1280.2.n.s.767.6		12
80.37	odd	4		1280.2.n.s.767.1		12
80.67	even	4		1280.2.n.r.767.1		12
80.77	odd	4		1280.2.n.r.767.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.o.j.63.1	✓	12	8.5	even	2
640.2.o.j.63.6	yes	12	8.3	odd	2
640.2.o.j.447.1	yes	12	20.7	even	4
640.2.o.j.447.6	yes	12	5.2	odd	4
640.2.o.k.63.1	yes	12	4.3	odd	2	inner
640.2.o.k.63.6	yes	12	1.1	even	1	trivial
640.2.o.k.447.1	yes	12	40.37	odd	4	inner
640.2.o.k.447.6	yes	12	40.27	even	4	inner
1280.2.n.r.767.1		12	80.67	even	4
1280.2.n.r.767.6		12	80.77	odd	4
1280.2.n.r.1023.1		12	16.13	even	4
1280.2.n.r.1023.6		12	16.3	odd	4
1280.2.n.s.767.1		12	80.37	odd	4
1280.2.n.s.767.6		12	80.27	even	4
1280.2.n.s.1023.1		12	16.11	odd	4
1280.2.n.s.1023.6		12	16.5	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.o (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

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