LMFDB - Embedded newform 1280.2.j.d.63.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			63.10
Character	$\chi$	$=$	1280.63
Dual form			1280.2.j.d.447.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.782176i q^{3} +(1.69250 + 1.46131i) q^{5} +(1.70686 - 1.70686i) q^{7} +2.38820 q^{9} +(-0.646047 + 0.646047i) q^{11} +0.260697 q^{13} +(-1.14301 + 1.32383i) q^{15} +(3.72262 - 3.72262i) q^{17} +(1.70356 - 1.70356i) q^{19} +(1.33507 + 1.33507i) q^{21} +(0.151537 + 0.151537i) q^{23} +(0.729119 + 4.94655i) q^{25} +4.21452i q^{27} +(-2.19762 - 2.19762i) q^{29} -9.53524i q^{31} +(-0.505323 - 0.505323i) q^{33} +(5.38312 - 0.394603i) q^{35} +6.34990 q^{37} +0.203911i q^{39} +7.94153i q^{41} -8.86040 q^{43} +(4.04203 + 3.48991i) q^{45} +(-7.80293 - 7.80293i) q^{47} +1.17325i q^{49} +(2.91174 + 2.91174i) q^{51} -0.114178i q^{53} +(-2.03751 + 0.149357i) q^{55} +(1.33248 + 1.33248i) q^{57} +(10.2731 + 10.2731i) q^{59} +(-4.14809 + 4.14809i) q^{61} +(4.07632 - 4.07632i) q^{63} +(0.441230 + 0.380961i) q^{65} +4.61532 q^{67} +(-0.118529 + 0.118529i) q^{69} -5.62379 q^{71} +(6.14095 - 6.14095i) q^{73} +(-3.86908 + 0.570299i) q^{75} +2.20542i q^{77} -11.2806 q^{79} +3.86810 q^{81} +9.37971i q^{83} +(11.7405 - 0.860618i) q^{85} +(1.71893 - 1.71893i) q^{87} -4.25350 q^{89} +(0.444974 - 0.444974i) q^{91} +7.45824 q^{93} +(5.37270 - 0.393839i) q^{95} +(1.49978 - 1.49978i) q^{97} +(-1.54289 + 1.54289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) $ 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.782176i			0.451590i	0.974175	+	0.225795i	$0.0724979\pi$
$3$			0.782176i			0.451590i	−0.974175	+	0.225795i	$0.927502\pi$
$4$		0			0
$5$	1.69250	+	1.46131i	0.756909	+	0.653520i
$5$	1.69250	+	1.46131i	0.756909	+	0.653520i
$6$		0			0
$7$	1.70686	−	1.70686i	0.645133	−	0.645133i	−0.306680	−	0.951813i	$-0.599218\pi$
$7$	1.70686	−	1.70686i	0.645133	−	0.645133i	0.951813	+	0.306680i	$0.0992181\pi$
$8$		0			0
$9$	2.38820			0.796067
$10$		0			0
$11$	−0.646047	+	0.646047i	−0.194790	+	0.194790i	−0.797762	−	0.602972i	$-0.793983\pi$
$11$	−0.646047	+	0.646047i	−0.194790	+	0.194790i	0.602972	+	0.797762i	$0.293983\pi$
$12$		0			0
$13$	0.260697			0.0723044			0.0361522	−	0.999346i	$-0.488490\pi$
$13$	0.260697			0.0723044			0.0361522	+	0.999346i	$0.488490\pi$
$14$		0			0
$15$	−1.14301	+	1.32383i	−0.295123	+	0.341813i
$16$		0			0
$17$	3.72262	−	3.72262i	0.902868	−	0.902868i	−0.0928157	−	0.995683i	$-0.529587\pi$
$17$	3.72262	−	3.72262i	0.902868	−	0.902868i	0.995683	+	0.0928157i	$0.0295867\pi$
$18$		0			0
$19$	1.70356	−	1.70356i	0.390822	−	0.390822i	−0.484158	−	0.874981i	$-0.660874\pi$
$19$	1.70356	−	1.70356i	0.390822	−	0.390822i	0.874981	+	0.484158i	$0.160874\pi$
$20$		0			0
$21$	1.33507	+	1.33507i	0.291335	+	0.291335i
$22$		0			0
$23$	0.151537	+	0.151537i	0.0315976	+	0.0315976i	0.722729	−	0.691131i	$-0.242887\pi$
$23$	0.151537	+	0.151537i	0.0315976	+	0.0315976i	−0.691131	+	0.722729i	$0.742887\pi$
$24$		0			0
$25$	0.729119	+	4.94655i	0.145824	+	0.989311i
$26$		0			0
$27$			4.21452i			0.811085i
$28$		0			0
$29$	−2.19762	−	2.19762i	−0.408088	−	0.408088i	0.472983	−	0.881071i	$-0.343177\pi$
$29$	−2.19762	−	2.19762i	−0.408088	−	0.408088i	−0.881071	+	0.472983i	$0.843177\pi$
$30$		0			0
$31$		−	9.53524i		−	1.71258i	−0.516496	−	0.856290i	$-0.672764\pi$
$31$		−	9.53524i		−	1.71258i	0.516496	−	0.856290i	$-0.327236\pi$
$32$		0			0
$33$	−0.505323	−	0.505323i	−0.0879654	−	0.0879654i
$34$		0			0
$35$	5.38312	−	0.394603i	0.909914	−	0.0667000i
$36$		0			0
$37$	6.34990			1.04392			0.521959	−	0.852971i	$-0.325201\pi$
$37$	6.34990			1.04392			0.521959	+	0.852971i	$0.325201\pi$
$38$		0			0
$39$			0.203911i			0.0326519i
$40$		0			0
$41$			7.94153i			1.24026i	0.784500	+	0.620129i	$0.212920\pi$
$41$			7.94153i			1.24026i	−0.784500	+	0.620129i	$0.787080\pi$
$42$		0			0
$43$	−8.86040			−1.35120			−0.675599	−	0.737269i	$-0.736115\pi$
$43$	−8.86040			−1.35120			−0.675599	+	0.737269i	$0.736115\pi$
$44$		0			0
$45$	4.04203	+	3.48991i	0.602550	+	0.520245i
$46$		0			0
$47$	−7.80293	−	7.80293i	−1.13817	−	1.13817i	−0.988777	−	0.149397i	$-0.952267\pi$
$47$	−7.80293	−	7.80293i	−1.13817	−	1.13817i	−0.149397	−	0.988777i	$-0.547733\pi$
$48$		0			0
$49$			1.17325i			0.167608i
$50$		0			0
$51$	2.91174	+	2.91174i	0.407726	+	0.407726i
$52$		0			0
$53$		−	0.114178i		−	0.0156835i	−0.999969	−	0.00784176i	$-0.997504\pi$
$53$		−	0.114178i		−	0.0156835i	0.999969	−	0.00784176i	$-0.00249614\pi$
$54$		0			0
$55$	−2.03751	+	0.149357i	−0.274738	+	0.0201393i
$56$		0			0
$57$	1.33248	+	1.33248i	0.176491	+	0.176491i
$58$		0			0
$59$	10.2731	+	10.2731i	1.33744	+	1.33744i	0.898532	+	0.438909i	$0.144635\pi$
$59$	10.2731	+	10.2731i	1.33744	+	1.33744i	0.438909	+	0.898532i	$0.355365\pi$
$60$		0			0
$61$	−4.14809	+	4.14809i	−0.531108	+	0.531108i	−0.920902	−	0.389794i	$-0.872546\pi$
$61$	−4.14809	+	4.14809i	−0.531108	+	0.531108i	0.389794	+	0.920902i	$0.372546\pi$
$62$		0			0
$63$	4.07632	−	4.07632i	0.513569	−	0.513569i
$64$		0			0
$65$	0.441230	+	0.380961i	0.0547279	+	0.0472524i
$66$		0			0
$67$	4.61532			0.563851			0.281925	−	0.959436i	$-0.409027\pi$
$67$	4.61532			0.563851			0.281925	+	0.959436i	$0.409027\pi$
$68$		0			0
$69$	−0.118529	+	0.118529i	−0.0142692	+	0.0142692i
$70$		0			0
$71$	−5.62379			−0.667421			−0.333710	−	0.942676i	$-0.608301\pi$
$71$	−5.62379			−0.667421			−0.333710	+	0.942676i	$0.608301\pi$
$72$		0			0
$73$	6.14095	−	6.14095i	0.718744	−	0.718744i	−0.249604	−	0.968348i	$-0.580301\pi$
$73$	6.14095	−	6.14095i	0.718744	−	0.718744i	0.968348	+	0.249604i	$0.0803005\pi$
$74$		0			0
$75$	−3.86908	+	0.570299i	−0.446762	+	0.0658525i
$76$		0			0
$77$			2.20542i			0.251331i
$78$		0			0
$79$	−11.2806			−1.26917			−0.634585	−	0.772853i	$-0.718829\pi$
$79$	−11.2806			−1.26917			−0.634585	+	0.772853i	$0.718829\pi$
$80$		0			0
$81$	3.86810			0.429789
$82$		0			0
$83$			9.37971i			1.02956i	0.857323	+	0.514779i	$0.172126\pi$
$83$			9.37971i			1.02956i	−0.857323	+	0.514779i	$0.827874\pi$
$84$		0			0
$85$	11.7405	−	0.860618i	1.27343	−	0.0933471i
$86$		0			0
$87$	1.71893	−	1.71893i	0.184288	−	0.184288i
$88$		0			0
$89$	−4.25350			−0.450870			−0.225435	−	0.974258i	$-0.572380\pi$
$89$	−4.25350			−0.450870			−0.225435	+	0.974258i	$0.572380\pi$
$90$		0			0
$91$	0.444974	−	0.444974i	0.0466459	−	0.0466459i
$92$		0			0
$93$	7.45824			0.773383
$94$		0			0
$95$	5.37270	−	0.393839i	0.551227	−	0.0404070i
$96$		0			0
$97$	1.49978	−	1.49978i	0.152280	−	0.152280i	−0.626856	−	0.779135i	$-0.715658\pi$
$97$	1.49978	−	1.49978i	0.152280	−	0.152280i	0.779135	+	0.626856i	$0.215658\pi$
$98$		0			0
$99$	−1.54289	+	1.54289i	−0.155066	+	0.155066i
$100$		0			0
$101$	8.79082	+	8.79082i	0.874719	+	0.874719i	0.992982	−	0.118263i	$-0.0377327\pi$
$101$	8.79082	+	8.79082i	0.874719	+	0.874719i	−0.118263	+	0.992982i	$0.537733\pi$
$102$		0			0
$103$	13.8635	+	13.8635i	1.36601	+	1.36601i	0.866043	+	0.499970i	$0.166655\pi$
$103$	13.8635	+	13.8635i	1.36601	+	1.36601i	0.499970	+	0.866043i	$0.333345\pi$
$104$		0			0
$105$	0.308649	+	4.21055i	0.0301210	+	0.410908i
$106$		0			0
$107$			10.6841i			1.03287i	0.856326	+	0.516436i	$0.172742\pi$
$107$			10.6841i			1.03287i	−0.856326	+	0.516436i	$0.827258\pi$
$108$		0			0
$109$	−9.10545	−	9.10545i	−0.872144	−	0.872144i	0.120562	−	0.992706i	$-0.461530\pi$
$109$	−9.10545	−	9.10545i	−0.872144	−	0.872144i	−0.992706	+	0.120562i	$0.961530\pi$
$110$		0			0
$111$			4.96675i			0.471423i
$112$		0			0
$113$	5.92583	+	5.92583i	0.557455	+	0.557455i	0.928582	−	0.371127i	$-0.121029\pi$
$113$	5.92583	+	5.92583i	0.557455	+	0.557455i	−0.371127	+	0.928582i	$0.621029\pi$
$114$		0			0
$115$	0.0350333	+	0.477920i	0.00326687	+	0.0445662i
$116$		0			0
$117$	0.622597			0.0575591
$118$		0			0
$119$		−	12.7080i		−	1.16494i
$120$		0			0
$121$			10.1652i			0.924113i
$122$		0			0
$123$	−6.21168			−0.560088
$124$		0			0
$125$	−5.99444	+	9.43752i	−0.536159	+	0.844117i
$126$		0			0
$127$	1.44106	+	1.44106i	0.127873	+	0.127873i	0.768147	−	0.640274i	$-0.221179\pi$
$127$	1.44106	+	1.44106i	0.127873	+	0.127873i	−0.640274	+	0.768147i	$0.721179\pi$
$128$		0			0
$129$		−	6.93040i		−	0.610187i
$130$		0			0
$131$	−8.31926	−	8.31926i	−0.726857	−	0.726857i	0.243136	−	0.969992i	$-0.421824\pi$
$131$	−8.31926	−	8.31926i	−0.726857	−	0.726857i	−0.969992	+	0.243136i	$0.921824\pi$
$132$		0			0
$133$		−	5.81546i		−	0.504265i
$134$		0			0
$135$	−6.15874	+	7.13308i	−0.530060	+	0.613918i
$136$		0			0
$137$	−7.09034	−	7.09034i	−0.605768	−	0.605768i	0.336069	−	0.941837i	$-0.390902\pi$
$137$	−7.09034	−	7.09034i	−0.605768	−	0.605768i	−0.941837	+	0.336069i	$0.890902\pi$
$138$		0			0
$139$	−5.53541	−	5.53541i	−0.469507	−	0.469507i	0.432248	−	0.901755i	$-0.357721\pi$
$139$	−5.53541	−	5.53541i	−0.469507	−	0.469507i	−0.901755	+	0.432248i	$0.857721\pi$
$140$		0			0
$141$	6.10327	−	6.10327i	0.513988	−	0.513988i
$142$		0			0
$143$	−0.168423	+	0.168423i	−0.0140842	+	0.0140842i
$144$		0			0
$145$	−0.508060	−	6.93089i	−0.0421921	−	0.575579i
$146$		0			0
$147$	−0.917691			−0.0756899
$148$		0			0
$149$	−2.92249	+	2.92249i	−0.239420	+	0.239420i	−0.816610	−	0.577190i	$-0.804149\pi$
$149$	−2.92249	+	2.92249i	−0.239420	+	0.239420i	0.577190	+	0.816610i	$0.304149\pi$
$150$		0			0
$151$	−2.33398			−0.189937			−0.0949683	−	0.995480i	$-0.530275\pi$
$151$	−2.33398			−0.189937			−0.0949683	+	0.995480i	$0.530275\pi$
$152$		0			0
$153$	8.89036	−	8.89036i	0.718743	−	0.718743i
$154$		0			0
$155$	13.9340	−	16.1384i	1.11920	−	1.29627i
$156$		0			0
$157$		−	13.5828i		−	1.08403i	−0.840370	−	0.542014i	$-0.817662\pi$
$157$		−	13.5828i		−	1.08403i	0.840370	−	0.542014i	$-0.182338\pi$
$158$		0			0
$159$	0.0893072			0.00708252
$160$		0			0
$161$	0.517305			0.0407693
$162$		0			0
$163$		−	23.9271i		−	1.87411i	−0.349175	−	0.937057i	$-0.613538\pi$
$163$		−	23.9271i		−	1.87411i	0.349175	−	0.937057i	$-0.386462\pi$
$164$		0			0
$165$	−0.116824	−	1.59369i	−0.00909471	−	0.124069i
$166$		0			0
$167$	6.53242	−	6.53242i	0.505493	−	0.505493i	−0.407646	−	0.913140i	$-0.633650\pi$
$167$	6.53242	−	6.53242i	0.505493	−	0.505493i	0.913140	+	0.407646i	$0.133650\pi$
$168$		0			0
$169$	−12.9320			−0.994772
$170$		0			0
$171$	4.06843	−	4.06843i	0.311121	−	0.311121i
$172$		0			0
$173$	10.5017			0.798430			0.399215	−	0.916857i	$-0.369283\pi$
$173$	10.5017			0.798430			0.399215	+	0.916857i	$0.369283\pi$
$174$		0			0
$175$	9.68758	+	7.19857i	0.732312	+	0.544161i
$176$		0			0
$177$	−8.03536	+	8.03536i	−0.603974	+	0.603974i
$178$		0			0
$179$	−13.0235	+	13.0235i	−0.973420	+	0.973420i	−0.999656	−	0.0262359i	$-0.991648\pi$
$179$	−13.0235	+	13.0235i	−0.973420	+	0.973420i	0.0262359	+	0.999656i	$0.491648\pi$
$180$		0			0
$181$	−10.5304	−	10.5304i	−0.782719	−	0.782719i	0.197570	−	0.980289i	$-0.436695\pi$
$181$	−10.5304	−	10.5304i	−0.782719	−	0.782719i	−0.980289	+	0.197570i	$0.936695\pi$
$182$		0			0
$183$	−3.24454	−	3.24454i	−0.239843	−	0.239843i
$184$		0			0
$185$	10.7472	+	9.27921i	0.790151	+	0.682221i
$186$		0			0
$187$			4.80997i			0.351740i
$188$		0			0
$189$	7.19360	+	7.19360i	0.523258	+	0.523258i
$190$		0			0
$191$			9.96706i			0.721191i	0.932722	+	0.360596i	$0.117427\pi$
$191$			9.96706i			0.721191i	−0.932722	+	0.360596i	$0.882573\pi$
$192$		0			0
$193$	−3.42094	−	3.42094i	−0.246245	−	0.246245i	0.573183	−	0.819428i	$-0.305709\pi$
$193$	−3.42094	−	3.42094i	−0.246245	−	0.246245i	−0.819428	+	0.573183i	$0.805709\pi$
$194$		0			0
$195$	−0.297978	+	0.345120i	−0.0213387	+	0.0247146i
$196$		0			0
$197$	−26.5699			−1.89303			−0.946514	−	0.322662i	$-0.895422\pi$
$197$	−26.5699			−1.89303			−0.946514	+	0.322662i	$0.895422\pi$
$198$		0			0
$199$			6.75067i			0.478542i	0.970953	+	0.239271i	$0.0769085\pi$
$199$			6.75067i			0.478542i	−0.970953	+	0.239271i	$0.923092\pi$
$200$		0			0
$201$			3.60999i			0.254629i
$202$		0			0
$203$	−7.50207			−0.526542
$204$		0			0
$205$	−11.6051	+	13.4410i	−0.810533	+	0.938763i
$206$		0			0
$207$	0.361901	+	0.361901i	0.0251538	+	0.0251538i
$208$		0			0
$209$			2.20115i			0.152257i
$210$		0			0
$211$	2.63954	+	2.63954i	0.181714	+	0.181714i	0.792102	−	0.610388i	$-0.208987\pi$
$211$	2.63954	+	2.63954i	0.181714	+	0.181714i	−0.610388	+	0.792102i	$0.708987\pi$
$212$		0			0
$213$		−	4.39879i		−	0.301400i
$214$		0			0
$215$	−14.9962	−	12.9478i	−1.02274	−	0.883035i
$216$		0			0
$217$	−16.2753	−	16.2753i	−1.10484	−	1.10484i
$218$		0			0
$219$	4.80330	+	4.80330i	0.324577	+	0.324577i
$220$		0			0
$221$	0.970476	−	0.970476i	0.0652813	−	0.0652813i
$222$		0			0
$223$	12.2892	−	12.2892i	0.822943	−	0.822943i	−0.163586	−	0.986529i	$-0.552306\pi$
$223$	12.2892	−	12.2892i	0.822943	−	0.822943i	0.986529	+	0.163586i	$0.0523063\pi$
$224$		0			0
$225$	1.74128	+	11.8134i	0.116085	+	0.787557i
$226$		0			0
$227$	9.10335			0.604211			0.302105	−	0.953275i	$-0.402311\pi$
$227$	9.10335			0.604211			0.302105	+	0.953275i	$0.402311\pi$
$228$		0			0
$229$	−12.9591	+	12.9591i	−0.856363	+	0.856363i	−0.990908	−	0.134545i	$-0.957043\pi$
$229$	−12.9591	+	12.9591i	−0.856363	+	0.856363i	0.134545	+	0.990908i	$0.457043\pi$
$230$		0			0
$231$	−1.72503			−0.113499
$232$		0			0
$233$	16.3322	−	16.3322i	1.06996	−	1.06996i	0.0725980	−	0.997361i	$-0.476871\pi$
$233$	16.3322	−	16.3322i	1.06996	−	1.06996i	0.997361	−	0.0725980i	$-0.0231290\pi$
$234$		0			0
$235$	−1.80393	−	24.6090i	−0.117675	−	1.60531i
$236$		0			0
$237$		−	8.82344i		−	0.573144i
$238$		0			0
$239$	−8.38208			−0.542192			−0.271096	−	0.962552i	$-0.587386\pi$
$239$	−8.38208			−0.542192			−0.271096	+	0.962552i	$0.587386\pi$
$240$		0			0
$241$	−21.8249			−1.40587			−0.702933	−	0.711257i	$-0.748126\pi$
$241$	−21.8249			−1.40587			−0.702933	+	0.711257i	$0.748126\pi$
$242$		0			0
$243$			15.6691i			1.00517i
$244$		0			0
$245$	−1.71449	+	1.98573i	−0.109535	+	0.126864i
$246$		0			0
$247$	0.444112	−	0.444112i	0.0282582	−	0.0282582i
$248$		0			0
$249$	−7.33659			−0.464938
$250$		0			0
$251$	12.3616	−	12.3616i	0.780259	−	0.780259i	−0.199615	−	0.979874i	$-0.563969\pi$
$251$	12.3616	−	12.3616i	0.780259	−	0.780259i	0.979874	+	0.199615i	$0.0639692\pi$
$252$		0			0
$253$	−0.195800			−0.0123098
$254$		0			0
$255$	0.673155	+	9.18310i	0.0421546	+	0.575068i
$256$		0			0
$257$	−11.3629	+	11.3629i	−0.708800	+	0.708800i	−0.966283	−	0.257483i	$-0.917107\pi$
$257$	−11.3629	+	11.3629i	−0.708800	+	0.708800i	0.257483	+	0.966283i	$0.417107\pi$
$258$		0			0
$259$	10.8384	−	10.8384i	0.673466	−	0.673466i
$260$		0			0
$261$	−5.24836	−	5.24836i	−0.324865	−	0.324865i
$262$		0			0
$263$	11.3800	+	11.3800i	0.701721	+	0.701721i	0.964780	−	0.263059i	$-0.0847313\pi$
$263$	11.3800	+	11.3800i	0.701721	+	0.701721i	−0.263059	+	0.964780i	$0.584731\pi$
$264$		0			0
$265$	0.166850	−	0.193246i	0.0102495	−	0.0118710i
$266$		0			0
$267$		−	3.32699i		−	0.203608i
$268$		0			0
$269$	−5.55401	−	5.55401i	−0.338634	−	0.338634i	0.517219	−	0.855853i	$-0.326967\pi$
$269$	−5.55401	−	5.55401i	−0.338634	−	0.338634i	−0.855853	+	0.517219i	$0.826967\pi$
$270$		0			0
$271$			27.5500i			1.67355i	0.547550	+	0.836773i	$0.315560\pi$
$271$			27.5500i			1.67355i	−0.547550	+	0.836773i	$0.684440\pi$
$272$		0			0
$273$	0.348048	+	0.348048i	0.0210648	+	0.0210648i
$274$		0			0
$275$	−3.66675	−	2.72466i	−0.221113	−	0.164303i
$276$		0			0
$277$	−21.0677			−1.26583			−0.632917	−	0.774219i	$-0.718143\pi$
$277$	−21.0677			−1.26583			−0.632917	+	0.774219i	$0.718143\pi$
$278$		0			0
$279$		−	22.7721i		−	1.36333i
$280$		0			0
$281$		−	24.7592i		−	1.47701i	−0.674249	−	0.738504i	$-0.735533\pi$
$281$		−	24.7592i		−	1.47701i	0.674249	−	0.738504i	$-0.264467\pi$
$282$		0			0
$283$	−17.8897			−1.06343			−0.531717	−	0.846922i	$-0.678453\pi$
$283$	−17.8897			−1.06343			−0.531717	+	0.846922i	$0.678453\pi$
$284$		0			0
$285$	0.308051	+	4.20240i	0.0182474	+	0.248929i
$286$		0			0
$287$	13.5551	+	13.5551i	0.800131	+	0.800131i
$288$		0			0
$289$		−	10.7158i		−	0.630340i
$290$		0			0
$291$	1.17309	+	1.17309i	0.0687680	+	0.0687680i
$292$		0			0
$293$		−	27.7548i		−	1.62145i	−0.585427	−	0.810725i	$-0.699073\pi$
$293$		−	27.7548i		−	1.62145i	0.585427	−	0.810725i	$-0.300927\pi$
$294$		0			0
$295$	2.37499	+	32.3994i	0.138277	+	1.88636i
$296$		0			0
$297$	−2.72278	−	2.72278i	−0.157992	−	0.157992i
$298$		0			0
$299$	0.0395053	+	0.0395053i	0.00228465	+	0.00228465i
$300$		0			0
$301$	−15.1235	+	15.1235i	−0.871702	+	0.871702i
$302$		0			0
$303$	−6.87597	+	6.87597i	−0.395014	+	0.395014i
$304$		0			0
$305$	−13.0823	+	0.958981i	−0.749091	+	0.0549111i
$306$		0			0
$307$	−30.6805			−1.75103			−0.875513	−	0.483194i	$-0.839476\pi$
$307$	−30.6805			−1.75103			−0.875513	+	0.483194i	$0.839476\pi$
$308$		0			0
$309$	−10.8437	+	10.8437i	−0.616877	+	0.616877i
$310$		0			0
$311$	−15.9382			−0.903774			−0.451887	−	0.892075i	$-0.649249\pi$
$311$	−15.9382			−0.903774			−0.451887	+	0.892075i	$0.649249\pi$
$312$		0			0
$313$	3.39796	−	3.39796i	0.192064	−	0.192064i	−0.604523	−	0.796587i	$-0.706636\pi$
$313$	3.39796	−	3.39796i	0.192064	−	0.192064i	0.796587	+	0.604523i	$0.206636\pi$
$314$		0			0
$315$	12.8560	−	0.942390i	0.724352	−	0.0530977i
$316$		0			0
$317$		−	8.14299i		−	0.457356i	−0.973502	−	0.228678i	$-0.926560\pi$
$317$		−	8.14299i		−	0.457356i	0.973502	−	0.228678i	$-0.0734403\pi$
$318$		0			0
$319$	2.83953			0.158983
$320$		0			0
$321$	−8.35686			−0.466435
$322$		0			0
$323$		−	12.6834i		−	0.705722i
$324$		0			0
$325$	0.190079	+	1.28955i	0.0105437	+	0.0715315i
$326$		0			0
$327$	7.12207	−	7.12207i	0.393851	−	0.393851i
$328$		0			0
$329$	−26.6370			−1.46855
$330$		0			0
$331$	10.3975	−	10.3975i	0.571497	−	0.571497i	−0.361050	−	0.932547i	$-0.617582\pi$
$331$	10.3975	−	10.3975i	0.571497	−	0.571497i	0.932547	+	0.361050i	$0.117582\pi$
$332$		0			0
$333$	15.1648			0.831028
$334$		0			0
$335$	7.81143	+	6.74443i	0.426784	+	0.368488i
$336$		0			0
$337$	16.4138	−	16.4138i	0.894116	−	0.894116i	−0.100792	−	0.994908i	$-0.532138\pi$
$337$	16.4138	−	16.4138i	0.894116	−	0.894116i	0.994908	+	0.100792i	$0.0321377\pi$
$338$		0			0
$339$	−4.63504	+	4.63504i	−0.251741	+	0.251741i
$340$		0			0
$341$	6.16021	+	6.16021i	0.333594	+	0.333594i
$342$		0			0
$343$	13.9506	+	13.9506i	0.753262	+	0.753262i
$344$		0			0
$345$	−0.373818	+	0.0274022i	−0.0201257	+	0.00147528i
$346$		0			0
$347$		−	6.70343i		−	0.359859i	−0.983680	−	0.179929i	$-0.942413\pi$
$347$		−	6.70343i		−	0.359859i	0.983680	−	0.179929i	$-0.0575869\pi$
$348$		0			0
$349$	−16.5083	−	16.5083i	−0.883668	−	0.883668i	0.110237	−	0.993905i	$-0.464839\pi$
$349$	−16.5083	−	16.5083i	−0.883668	−	0.883668i	−0.993905	+	0.110237i	$0.964839\pi$
$350$		0			0
$351$			1.09871i			0.0586450i
$352$		0			0
$353$	10.6294	+	10.6294i	0.565748	+	0.565748i	0.930935	−	0.365186i	$-0.118995\pi$
$353$	10.6294	+	10.6294i	0.565748	+	0.565748i	−0.365186	+	0.930935i	$0.618995\pi$
$354$		0			0
$355$	−9.51827	−	8.21813i	−0.505177	−	0.436173i
$356$		0			0
$357$	9.93988			0.526074
$358$		0			0
$359$		−	4.96557i		−	0.262073i	−0.991378	−	0.131036i	$-0.958170\pi$
$359$		−	4.96557i		−	0.262073i	0.991378	−	0.131036i	$-0.0418305\pi$
$360$		0			0
$361$			13.1958i			0.694516i
$362$		0			0
$363$	−7.95102			−0.417320
$364$		0			0
$365$	19.3674	−	1.41970i	1.01374	−	0.0743106i
$366$		0			0
$367$	−1.99352	−	1.99352i	−0.104061	−	0.104061i	0.653160	−	0.757220i	$-0.273443\pi$
$367$	−1.99352	−	1.99352i	−0.104061	−	0.104061i	−0.757220	+	0.653160i	$0.773443\pi$
$368$		0			0
$369$			18.9660i			0.987328i
$370$		0			0
$371$	−0.194886	−	0.194886i	−0.0101180	−	0.0101180i
$372$		0			0
$373$		−	8.86266i		−	0.458891i	−0.973322	−	0.229446i	$-0.926309\pi$
$373$		−	8.86266i		−	0.458891i	0.973322	−	0.229446i	$-0.0736913\pi$
$374$		0			0
$375$	−7.38180	−	4.68871i	−0.381195	−	0.242124i
$376$		0			0
$377$	−0.572914	−	0.572914i	−0.0295066	−	0.0295066i
$378$		0			0
$379$	17.0332	+	17.0332i	0.874937	+	0.874937i	0.993005	−	0.118068i	$-0.0376702\pi$
$379$	17.0332	+	17.0332i	0.874937	+	0.874937i	−0.118068	+	0.993005i	$0.537670\pi$
$380$		0			0
$381$	−1.12716	+	1.12716i	−0.0577463	+	0.0577463i
$382$		0			0
$383$	19.0504	−	19.0504i	0.973432	−	0.973432i	−0.0262243	−	0.999656i	$-0.508348\pi$
$383$	19.0504	−	19.0504i	0.973432	−	0.973432i	0.999656	+	0.0262243i	$0.00834842\pi$
$384$		0			0
$385$	−3.22282	+	3.73268i	−0.164250	+	0.190235i
$386$		0			0
$387$	−21.1604			−1.07564
$388$		0			0
$389$	4.66848	−	4.66848i	0.236701	−	0.236701i	−0.578781	−	0.815483i	$-0.696472\pi$
$389$	4.66848	−	4.66848i	0.236701	−	0.236701i	0.815483	+	0.578781i	$0.196472\pi$
$390$		0			0
$391$	1.12823			0.0570570
$392$		0			0
$393$	6.50713	−	6.50713i	0.328241	−	0.328241i
$394$		0			0
$395$	−19.0925	−	16.4845i	−0.960646	−	0.829427i
$396$		0			0
$397$		−	6.29671i		−	0.316023i	−0.987437	−	0.158012i	$-0.949492\pi$
$397$		−	6.29671i		−	0.316023i	0.987437	−	0.158012i	$-0.0505083\pi$
$398$		0			0
$399$	4.54872			0.227721
$400$		0			0
$401$	18.0541			0.901580			0.450790	−	0.892630i	$-0.351142\pi$
$401$	18.0541			0.901580			0.450790	+	0.892630i	$0.351142\pi$
$402$		0			0
$403$		−	2.48581i		−	0.123827i
$404$		0			0
$405$	6.54676	+	5.65251i	0.325311	+	0.280876i
$406$		0			0
$407$	−4.10234	+	4.10234i	−0.203345	+	0.203345i
$408$		0			0
$409$	−21.6420			−1.07013			−0.535064	−	0.844812i	$-0.679712\pi$
$409$	−21.6420			−1.07013			−0.535064	+	0.844812i	$0.679712\pi$
$410$		0			0
$411$	5.54589	−	5.54589i	0.273559	−	0.273559i
$412$		0			0
$413$	35.0694			1.72565
$414$		0			0
$415$	−13.7067	+	15.8752i	−0.672836	+	0.779282i
$416$		0			0
$417$	4.32966	−	4.32966i	0.212025	−	0.212025i
$418$		0			0
$419$	−7.23877	+	7.23877i	−0.353637	+	0.353637i	−0.861461	−	0.507824i	$-0.830450\pi$
$419$	−7.23877	+	7.23877i	−0.353637	+	0.353637i	0.507824	+	0.861461i	$0.330450\pi$
$420$		0			0
$421$	−0.595174	−	0.595174i	−0.0290070	−	0.0290070i	0.692455	−	0.721462i	$-0.256529\pi$
$421$	−0.595174	−	0.595174i	−0.0290070	−	0.0290070i	−0.721462	+	0.692455i	$0.756529\pi$
$422$		0			0
$423$	−18.6350	−	18.6350i	−0.906063	−	0.906063i
$424$		0			0
$425$	21.1284	+	15.6999i	1.02488	+	0.761557i
$426$		0			0
$427$			14.1604i			0.685271i
$428$		0			0
$429$	−0.131736	−	0.131736i	−0.00636028	−	0.00636028i
$430$		0			0
$431$			4.38072i			0.211012i	0.994419	+	0.105506i	$0.0336462\pi$
$431$			4.38072i			0.211012i	−0.994419	+	0.105506i	$0.966354\pi$
$432$		0			0
$433$	−25.7387	−	25.7387i	−1.23692	−	1.23692i	−0.961251	−	0.275673i	$-0.911099\pi$
$433$	−25.7387	−	25.7387i	−1.23692	−	1.23692i	−0.275673	−	0.961251i	$-0.588901\pi$
$434$		0			0
$435$	5.42118	−	0.397392i	0.259926	−	0.0190535i
$436$		0			0
$437$	0.516303			0.0246981
$438$		0			0
$439$			3.34072i			0.159444i	0.996817	+	0.0797219i	$0.0254032\pi$
$439$			3.34072i			0.159444i	−0.996817	+	0.0797219i	$0.974597\pi$
$440$		0			0
$441$			2.80197i			0.133427i
$442$		0			0
$443$	−2.79018			−0.132566			−0.0662828	−	0.997801i	$-0.521114\pi$
$443$	−2.79018			−0.132566			−0.0662828	+	0.997801i	$0.521114\pi$
$444$		0			0
$445$	−7.19906	−	6.21571i	−0.341268	−	0.294653i
$446$		0			0
$447$	−2.28590	−	2.28590i	−0.108119	−	0.108119i
$448$		0			0
$449$			17.5342i			0.827490i	0.910393	+	0.413745i	$0.135780\pi$
$449$			17.5342i			0.827490i	−0.910393	+	0.413745i	$0.864220\pi$
$450$		0			0
$451$	−5.13060	−	5.13060i	−0.241591	−	0.241591i
$452$		0			0
$453$		−	1.82558i		−	0.0857734i
$454$		0			0
$455$	1.40337	−	0.102872i	0.0657908	−	0.00482271i
$456$		0			0
$457$	−11.8607	−	11.8607i	−0.554821	−	0.554821i	0.373007	−	0.927828i	$-0.378327\pi$
$457$	−11.8607	−	11.8607i	−0.554821	−	0.554821i	−0.927828	+	0.373007i	$0.878327\pi$
$458$		0			0
$459$	15.6891	+	15.6891i	0.732303	+	0.732303i
$460$		0			0
$461$	−10.7534	+	10.7534i	−0.500836	+	0.500836i	−0.911698	−	0.410862i	$-0.865228\pi$
$461$	−10.7534	+	10.7534i	−0.500836	+	0.500836i	0.410862	+	0.911698i	$0.365228\pi$
$462$		0			0
$463$	−4.13024	+	4.13024i	−0.191949	+	0.191949i	−0.796538	−	0.604589i	$-0.793337\pi$
$463$	−4.13024	+	4.13024i	−0.191949	+	0.191949i	0.604589	+	0.796538i	$0.293337\pi$
$464$		0			0
$465$	12.6231	+	10.8988i	0.585381	+	0.505421i
$466$		0			0
$467$	−1.03647			−0.0479620			−0.0239810	−	0.999712i	$-0.507634\pi$
$467$	−1.03647			−0.0479620			−0.0239810	+	0.999712i	$0.507634\pi$
$468$		0			0
$469$	7.87770	−	7.87770i	0.363758	−	0.363758i
$470$		0			0
$471$	10.6242			0.489536
$472$		0			0
$473$	5.72424	−	5.72424i	0.263201	−	0.263201i
$474$		0			0
$475$	9.66882	+	7.18463i	0.443636	+	0.329654i
$476$		0			0
$477$		−	0.272679i		−	0.0124851i
$478$		0			0
$479$	4.45599			0.203599			0.101800	−	0.994805i	$-0.467540\pi$
$479$	4.45599			0.203599			0.101800	+	0.994805i	$0.467540\pi$
$480$		0			0
$481$	1.65540			0.0754799
$482$		0			0
$483$			0.404624i			0.0184110i
$484$		0			0
$485$	4.73004	−	0.346729i	0.214780	−	0.0157442i
$486$		0			0
$487$	4.32429	−	4.32429i	0.195952	−	0.195952i	−0.602310	−	0.798262i	$-0.705753\pi$
$487$	4.32429	−	4.32429i	0.195952	−	0.195952i	0.798262	+	0.602310i	$0.205753\pi$
$488$		0			0
$489$	18.7152			0.846331
$490$		0			0
$491$	−4.08628	+	4.08628i	−0.184411	+	0.184411i	−0.793275	−	0.608864i	$-0.791626\pi$
$491$	−4.08628	+	4.08628i	−0.184411	+	0.184411i	0.608864	+	0.793275i	$0.291626\pi$
$492$		0			0
$493$	−16.3618			−0.736899
$494$		0			0
$495$	−4.86599	+	0.356695i	−0.218710	+	0.0160322i
$496$		0			0
$497$	−9.59902	+	9.59902i	−0.430575	+	0.430575i
$498$		0			0
$499$	23.2943	−	23.2943i	1.04280	−	1.04280i	0.0437532	−	0.999042i	$-0.486068\pi$
$499$	23.2943	−	23.2943i	1.04280	−	1.04280i	0.999042	−	0.0437532i	$-0.0139315\pi$
$500$		0			0
$501$	5.10950	+	5.10950i	0.228276	+	0.228276i
$502$		0			0
$503$	16.0272	+	16.0272i	0.714615	+	0.714615i	0.967497	−	0.252882i	$-0.0813784\pi$
$503$	16.0272	+	16.0272i	0.714615	+	0.714615i	−0.252882	+	0.967497i	$0.581378\pi$
$504$		0			0
$505$	2.03232	+	27.7246i	0.0904369	+	1.23373i
$506$		0			0
$507$		−	10.1151i		−	0.449229i
$508$		0			0
$509$	7.47749	+	7.47749i	0.331434	+	0.331434i	0.853131	−	0.521697i	$-0.174701\pi$
$509$	7.47749	+	7.47749i	0.331434	+	0.331434i	−0.521697	+	0.853131i	$0.674701\pi$
$510$		0			0
$511$		−	20.9635i		−	0.927370i
$512$		0			0
$513$	7.17967	+	7.17967i	0.316990	+	0.316990i
$514$		0			0
$515$	3.20505	+	43.7230i	0.141232	+	1.92666i
$516$		0			0
$517$	10.0821			0.443411
$518$		0			0
$519$			8.21419i			0.360563i
$520$		0			0
$521$		−	13.0578i		−	0.572071i	−0.958219	−	0.286035i	$-0.907663\pi$
$521$		−	13.0578i		−	0.572071i	0.958219	−	0.286035i	$-0.0923374\pi$
$522$		0			0
$523$	−25.1919			−1.10157			−0.550783	−	0.834649i	$-0.685671\pi$
$523$	−25.1919			−1.10157			−0.550783	+	0.834649i	$0.685671\pi$
$524$		0			0
$525$	−5.63055	+	7.57740i	−0.245737	+	0.330705i
$526$		0			0
$527$	−35.4961	−	35.4961i	−1.54623	−	1.54623i
$528$		0			0
$529$		−	22.9541i		−	0.998003i
$530$		0			0
$531$	24.5342	+	24.5342i	1.06469	+	1.06469i
$532$		0			0
$533$			2.07033i			0.0896761i
$534$		0			0
$535$	−15.6129	+	18.0829i	−0.675003	+	0.781791i
$536$		0			0
$537$	−10.1867	−	10.1867i	−0.439586	−	0.439586i
$538$		0			0
$539$	−0.757977	−	0.757977i	−0.0326484	−	0.0326484i
$540$		0			0
$541$	−8.89675	+	8.89675i	−0.382501	+	0.382501i	−0.872002	−	0.489501i	$-0.837179\pi$
$541$	−8.89675	+	8.89675i	−0.382501	+	0.382501i	0.489501	+	0.872002i	$0.337179\pi$
$542$		0			0
$543$	8.23664	−	8.23664i	0.353468	−	0.353468i
$544$		0			0
$545$	−2.10505	−	28.7169i	−0.0901706	−	1.23010i
$546$		0			0
$547$	45.1122			1.92886			0.964430	−	0.264339i	$-0.0851538\pi$
$547$	45.1122			1.92886			0.964430	+	0.264339i	$0.0851538\pi$
$548$		0			0
$549$	−9.90647	+	9.90647i	−0.422798	+	0.422798i
$550$		0			0
$551$	−7.48754			−0.318980
$552$		0			0
$553$	−19.2545	+	19.2545i	−0.818783	+	0.818783i
$554$		0			0
$555$	−7.25798	+	8.40622i	−0.308084	+	0.356824i
$556$		0			0
$557$			11.9924i			0.508135i	0.967186	+	0.254068i	$0.0817686\pi$
$557$			11.9924i			0.508135i	−0.967186	+	0.254068i	$0.918231\pi$
$558$		0			0
$559$	−2.30988			−0.0976976
$560$		0			0
$561$	−3.76225			−0.158842
$562$		0			0
$563$			3.82112i			0.161041i	0.996753	+	0.0805204i	$0.0256582\pi$
$563$			3.82112i			0.161041i	−0.996753	+	0.0805204i	$0.974342\pi$
$564$		0			0
$565$	1.36997	+	18.6890i	0.0576351	+	0.786251i
$566$		0			0
$567$	6.60231	−	6.60231i	0.277271	−	0.277271i
$568$		0			0
$569$	36.6832			1.53784			0.768921	−	0.639344i	$-0.220794\pi$
$569$	36.6832			1.53784			0.768921	+	0.639344i	$0.220794\pi$
$570$		0			0
$571$	−22.1407	+	22.1407i	−0.926559	+	0.926559i	−0.997482	−	0.0709228i	$-0.977406\pi$
$571$	−22.1407	+	22.1407i	−0.926559	+	0.926559i	0.0709228	+	0.997482i	$0.477406\pi$
$572$		0			0
$573$	−7.79600			−0.325683
$574$		0			0
$575$	−0.639097	+	0.860074i	−0.0266522	+	0.0358676i
$576$		0			0
$577$	9.94802	−	9.94802i	0.414142	−	0.414142i	−0.469037	−	0.883179i	$-0.655399\pi$
$577$	9.94802	−	9.94802i	0.414142	−	0.414142i	0.883179	+	0.469037i	$0.155399\pi$
$578$		0			0
$579$	2.67578	−	2.67578i	0.111202	−	0.111202i
$580$		0			0
$581$	16.0099	+	16.0099i	0.664201	+	0.664201i
$582$		0			0
$583$	0.0737642	+	0.0737642i	0.00305500	+	0.00305500i
$584$		0			0
$585$	1.05375	+	0.909810i	0.0435671	+	0.0376160i
$586$		0			0
$587$			38.3121i			1.58131i	0.612263	+	0.790654i	$0.290259\pi$
$587$			38.3121i			1.58131i	−0.612263	+	0.790654i	$0.709741\pi$
$588$		0			0
$589$	−16.2438	−	16.2438i	−0.669314	−	0.669314i
$590$		0			0
$591$		−	20.7824i		−	0.854872i
$592$		0			0
$593$	20.1383	+	20.1383i	0.826979	+	0.826979i	0.987098	−	0.160119i	$-0.0511878\pi$
$593$	20.1383	+	20.1383i	0.826979	+	0.826979i	−0.160119	+	0.987098i	$0.551188\pi$
$594$		0			0
$595$	18.5704	−	21.5083i	0.761311	−	0.881753i
$596$		0			0
$597$	−5.28021			−0.216105
$598$		0			0
$599$		−	21.4746i		−	0.877428i	−0.898627	−	0.438714i	$-0.855434\pi$
$599$		−	21.4746i		−	0.877428i	0.898627	−	0.438714i	$-0.144566\pi$
$600$		0			0
$601$			13.0407i			0.531942i	0.963981	+	0.265971i	$0.0856925\pi$
$601$			13.0407i			0.531942i	−0.963981	+	0.265971i	$0.914308\pi$
$602$		0			0
$603$	11.0223			0.448863
$604$		0			0
$605$	−14.8546	+	17.2047i	−0.603926	+	0.699470i
$606$		0			0
$607$	−10.5677	−	10.5677i	−0.428928	−	0.428928i	0.459335	−	0.888263i	$-0.348088\pi$
$607$	−10.5677	−	10.5677i	−0.428928	−	0.428928i	−0.888263	+	0.459335i	$0.848088\pi$
$608$		0			0
$609$		−	5.86794i		−	0.237781i
$610$		0			0
$611$	−2.03420	−	2.03420i	−0.0822950	−	0.0822950i
$612$		0			0
$613$			11.0469i			0.446180i	0.974798	+	0.223090i	$0.0716143\pi$
$613$			11.0469i			0.446180i	−0.974798	+	0.223090i	$0.928386\pi$
$614$		0			0
$615$	−10.5133	−	9.07721i	−0.423936	−	0.366029i
$616$		0			0
$617$	29.4944	+	29.4944i	1.18740	+	1.18740i	0.977783	+	0.209618i	$0.0672220\pi$
$617$	29.4944	+	29.4944i	1.18740	+	1.18740i	0.209618	+	0.977783i	$0.432778\pi$
$618$		0			0
$619$	−21.0249	−	21.0249i	−0.845061	−	0.845061i	0.144451	−	0.989512i	$-0.453858\pi$
$619$	−21.0249	−	21.0249i	−0.845061	−	0.845061i	−0.989512	+	0.144451i	$0.953858\pi$
$620$		0			0
$621$	−0.638656	+	0.638656i	−0.0256284	+	0.0256284i
$622$		0			0
$623$	−7.26013	+	7.26013i	−0.290871	+	0.290871i
$624$		0			0
$625$	−23.9368	+	7.21325i	−0.957471	+	0.288530i
$626$		0			0
$627$	−1.72169			−0.0687577
$628$		0			0
$629$	23.6383	−	23.6383i	0.942520	−	0.942520i
$630$		0			0
$631$	29.7066			1.18260			0.591301	−	0.806451i	$-0.298614\pi$
$631$	29.7066			1.18260			0.591301	+	0.806451i	$0.298614\pi$
$632$		0			0
$633$	−2.06459	+	2.06459i	−0.0820600	+	0.0820600i
$634$		0			0
$635$	0.333153	+	4.54484i	0.0132208	+	0.180356i
$636$		0			0
$637$			0.305864i			0.0121188i
$638$		0			0
$639$	−13.4307			−0.531312
$640$		0			0
$641$	16.9395			0.669070			0.334535	−	0.942383i	$-0.391421\pi$
$641$	16.9395			0.669070			0.334535	+	0.942383i	$0.391421\pi$
$642$		0			0
$643$			3.35063i			0.132136i	0.997815	+	0.0660680i	$0.0210454\pi$
$643$			3.35063i			0.132136i	−0.997815	+	0.0660680i	$0.978955\pi$
$644$		0			0
$645$	10.1275	−	11.7297i	0.398770	−	0.461857i
$646$		0			0
$647$	12.6002	−	12.6002i	0.495365	−	0.495365i	−0.414627	−	0.909992i	$-0.636088\pi$
$647$	12.6002	−	12.6002i	0.495365	−	0.495365i	0.909992	+	0.414627i	$0.136088\pi$
$648$		0			0
$649$	−13.2738			−0.521041
$650$		0			0
$651$	12.7302	−	12.7302i	0.498935	−	0.498935i
$652$		0			0
$653$	40.7862			1.59609			0.798044	−	0.602599i	$-0.205868\pi$
$653$	40.7862			1.59609			0.798044	+	0.602599i	$0.205868\pi$
$654$		0			0
$655$	−1.92330	−	26.2374i	−0.0751494	−	1.02518i
$656$		0			0
$657$	14.6658	−	14.6658i	0.572168	−	0.572168i
$658$		0			0
$659$	4.80982	−	4.80982i	0.187364	−	0.187364i	−0.607192	−	0.794555i	$-0.707704\pi$
$659$	4.80982	−	4.80982i	0.187364	−	0.187364i	0.794555	+	0.607192i	$0.207704\pi$
$660$		0			0
$661$	16.0067	+	16.0067i	0.622587	+	0.622587i	0.946192	−	0.323605i	$-0.104895\pi$
$661$	16.0067	+	16.0067i	0.622587	+	0.622587i	−0.323605	+	0.946192i	$0.604895\pi$
$662$		0			0
$663$	0.759084	+	0.759084i	0.0294804	+	0.0294804i
$664$		0			0
$665$	8.49822	−	9.84268i	0.329547	−	0.381683i
$666$		0			0
$667$		−	0.666042i		−	0.0257892i
$668$		0			0
$669$	9.61229	+	9.61229i	0.371632	+	0.371632i
$670$		0			0
$671$		−	5.35972i		−	0.206910i
$672$		0			0
$673$	−11.5424	−	11.5424i	−0.444928	−	0.444928i	0.448736	−	0.893664i	$-0.351874\pi$
$673$	−11.5424	−	11.5424i	−0.444928	−	0.444928i	−0.893664	+	0.448736i	$0.851874\pi$
$674$		0			0
$675$	−20.8474	+	3.07289i	−0.802415	+	0.118275i
$676$		0			0
$677$	−8.31435			−0.319547			−0.159773	−	0.987154i	$-0.551076\pi$
$677$	−8.31435			−0.319547			−0.159773	+	0.987154i	$0.551076\pi$
$678$		0			0
$679$		−	5.11984i		−	0.196481i
$680$		0			0
$681$			7.12042i			0.272855i
$682$		0			0
$683$	24.3673			0.932388			0.466194	−	0.884682i	$-0.345625\pi$
$683$	24.3673			0.932388			0.466194	+	0.884682i	$0.345625\pi$
$684$		0			0
$685$	−1.63919	−	22.3616i	−0.0626301	−	0.854393i
$686$		0			0
$687$	−10.1363	−	10.1363i	−0.386725	−	0.386725i
$688$		0			0
$689$		−	0.0297658i		−	0.00113399i
$690$		0			0
$691$	5.77907	+	5.77907i	0.219846	+	0.219846i	0.808434	−	0.588587i	$-0.200316\pi$
$691$	5.77907	+	5.77907i	0.219846	+	0.219846i	−0.588587	+	0.808434i	$0.700316\pi$
$692$		0			0
$693$			5.26699i			0.200077i
$694$		0			0
$695$	−1.27971	−	17.4576i	−0.0485421	−	0.662206i
$696$		0			0
$697$	29.5633	+	29.5633i	1.11979	+	1.11979i
$698$		0			0
$699$	12.7747	+	12.7747i	0.483183	+	0.483183i
$700$		0			0
$701$	21.5039	−	21.5039i	0.812190	−	0.812190i	−0.172772	−	0.984962i	$-0.555272\pi$
$701$	21.5039	−	21.5039i	0.812190	−	0.812190i	0.984962	+	0.172772i	$0.0552725\pi$
$702$		0			0
$703$	10.8174	−	10.8174i	0.407987	−	0.407987i
$704$		0			0
$705$	19.2486	−	1.41099i	0.724943	−	0.0531410i
$706$		0			0
$707$	30.0094			1.12862
$708$		0			0
$709$	5.60093	−	5.60093i	0.210347	−	0.210347i	−0.594068	−	0.804415i	$-0.702479\pi$
$709$	5.60093	−	5.60093i	0.210347	−	0.210347i	0.804415	+	0.594068i	$0.202479\pi$
$710$		0			0
$711$	−26.9404			−1.01034
$712$		0			0
$713$	1.44494	−	1.44494i	0.0541135	−	0.0541135i
$714$		0			0
$715$	−0.531174	+	0.0389370i	−0.0198648	+	0.00145616i
$716$		0			0
$717$		−	6.55626i		−	0.244848i
$718$		0			0
$719$	20.8520			0.777649			0.388824	−	0.921312i	$-0.372881\pi$
$719$	20.8520			0.777649			0.388824	+	0.921312i	$0.372881\pi$
$720$		0			0
$721$	47.3262			1.76252
$722$		0			0
$723$		−	17.0709i		−	0.634874i
$724$		0			0
$725$	9.26832	−	12.4730i	0.344217	−	0.463235i
$726$		0			0
$727$	−23.1549	+	23.1549i	−0.858769	+	0.858769i	−0.991193	−	0.132424i	$-0.957724\pi$
$727$	−23.1549	+	23.1549i	−0.858769	+	0.858769i	0.132424	+	0.991193i	$0.457724\pi$
$728$		0			0
$729$	−0.651701			−0.0241371
$730$		0			0
$731$	−32.9839	+	32.9839i	−1.21995	+	1.21995i
$732$		0			0
$733$	−28.9140			−1.06796			−0.533981	−	0.845496i	$-0.679305\pi$
$733$	−28.9140			−1.06796			−0.533981	+	0.845496i	$0.679305\pi$
$734$		0			0
$735$	−1.55319	−	1.34104i	−0.0572904	−	0.0494649i
$736$		0			0
$737$	−2.98171	+	2.98171i	−0.109833	+	0.109833i
$738$		0			0
$739$	−11.5603	+	11.5603i	−0.425251	+	0.425251i	−0.887007	−	0.461756i	$-0.847220\pi$
$739$	−11.5603	+	11.5603i	−0.425251	+	0.425251i	0.461756	+	0.887007i	$0.347220\pi$
$740$		0			0
$741$	0.347374	+	0.347374i	0.0127611	+	0.0127611i
$742$		0			0
$743$	−12.8732	−	12.8732i	−0.472271	−	0.472271i	0.430378	−	0.902649i	$-0.358380\pi$
$743$	−12.8732	−	12.8732i	−0.472271	−	0.472271i	−0.902649	+	0.430378i	$0.858380\pi$
$744$		0			0
$745$	−9.21699	+	0.675639i	−0.337685	+	0.0247535i
$746$		0			0
$747$			22.4006i			0.819596i
$748$		0			0
$749$	18.2363	+	18.2363i	0.666340	+	0.666340i
$750$		0			0
$751$			23.1857i			0.846059i	0.906116	+	0.423030i	$0.139033\pi$
$751$			23.1857i			0.846059i	−0.906116	+	0.423030i	$0.860967\pi$
$752$		0			0
$753$	9.66898	+	9.66898i	0.352357	+	0.352357i
$754$		0			0
$755$	−3.95026	−	3.41068i	−0.143765	−	0.124127i
$756$		0			0
$757$	43.6722			1.58729			0.793646	−	0.608379i	$-0.208180\pi$
$757$	43.6722			1.58729			0.793646	+	0.608379i	$0.208180\pi$
$758$		0			0
$759$		−	0.153150i		−	0.00555900i
$760$		0			0
$761$			48.4215i			1.75528i	0.479322	+	0.877639i	$0.340882\pi$
$761$			48.4215i			1.75528i	−0.479322	+	0.877639i	$0.659118\pi$
$762$		0			0
$763$	−31.0835			−1.12530
$764$		0			0
$765$	28.0386	−	2.05533i	1.01374	−	0.0743106i
$766$		0			0
$767$	2.67816	+	2.67816i	0.0967028	+	0.0967028i
$768$		0			0
$769$		−	20.2823i		−	0.731400i	−0.930733	−	0.365700i	$-0.880830\pi$
$769$		−	20.2823i		−	0.731400i	0.930733	−	0.365700i	$-0.119170\pi$
$770$		0			0
$771$	−8.88782	−	8.88782i	−0.320087	−	0.320087i
$772$		0			0
$773$			48.5903i			1.74767i	0.486220	+	0.873836i	$0.338375\pi$
$773$			48.5903i			1.74767i	−0.486220	+	0.873836i	$0.661625\pi$
$774$		0			0
$775$	47.1666	−	6.95232i	1.69427	−	0.249735i
$776$		0			0
$777$	8.47754	+	8.47754i	0.304130	+	0.304130i
$778$		0			0
$779$	13.5288	+	13.5288i	0.484721	+	0.484721i
$780$		0			0
$781$	3.63323	−	3.63323i	0.130007	−	0.130007i
$782$		0			0
$783$	9.26193	−	9.26193i	0.330994	−	0.330994i
$784$		0			0
$785$	19.8488	−	22.9889i	0.708433	−	0.820511i
$786$		0			0
$787$	−27.2293			−0.970620			−0.485310	−	0.874342i	$-0.661293\pi$
$787$	−27.2293			−0.970620			−0.485310	+	0.874342i	$0.661293\pi$
$788$		0			0
$789$	−8.90117	+	8.90117i	−0.316890	+	0.316890i
$790$		0			0
$791$	20.2291			0.719265
$792$		0			0
$793$	−1.08140	+	1.08140i	−0.0384015	+	0.0384015i
$794$		0			0
$795$	0.151152	+	0.130506i	0.00536083	+	0.00462857i
$796$		0			0
$797$			17.9989i			0.637554i	0.947830	+	0.318777i	$0.103272\pi$
$797$			17.9989i			0.637554i	−0.947830	+	0.318777i	$0.896728\pi$
$798$		0			0
$799$	−58.0947			−2.05524
$800$		0			0
$801$	−10.1582			−0.358923
$802$		0			0
$803$			7.93468i			0.280009i
$804$		0			0
$805$	0.875539	+	0.755945i	0.0308587	+	0.0266436i
$806$		0			0
$807$	4.34421	−	4.34421i	0.152923	−	0.152923i
$808$		0			0
$809$	−9.27856			−0.326217			−0.163108	−	0.986608i	$-0.552152\pi$
$809$	−9.27856			−0.326217			−0.163108	+	0.986608i	$0.552152\pi$
$810$		0			0
$811$	9.68248	−	9.68248i	0.339998	−	0.339998i	−0.516369	−	0.856366i	$-0.672717\pi$
$811$	9.68248	−	9.68248i	0.339998	−	0.339998i	0.856366	+	0.516369i	$0.172717\pi$
$812$		0			0
$813$	−21.5490			−0.755756
$814$		0			0
$815$	34.9650	−	40.4966i	1.22477	−	1.41854i
$816$		0			0
$817$	−15.0942	+	15.0942i	−0.528079	+	0.528079i
$818$		0			0
$819$	1.06269	−	1.06269i	0.0371333	−	0.0371333i
$820$		0			0
$821$	8.15143	+	8.15143i	0.284487	+	0.284487i	0.834895	−	0.550409i	$-0.185528\pi$
$821$	8.15143	+	8.15143i	0.284487	+	0.284487i	−0.550409	+	0.834895i	$0.685528\pi$
$822$		0			0
$823$	9.84275	+	9.84275i	0.343097	+	0.343097i	0.857530	−	0.514434i	$-0.171998\pi$
$823$	9.84275	+	9.84275i	0.343097	+	0.343097i	−0.514434	+	0.857530i	$0.671998\pi$
$824$		0			0
$825$	2.13116	−	2.86805i	0.0741976	−	0.0998525i
$826$		0			0
$827$		−	27.9185i		−	0.970821i	−0.874286	−	0.485410i	$-0.838670\pi$
$827$		−	27.9185i		−	0.970821i	0.874286	−	0.485410i	$-0.161330\pi$
$828$		0			0
$829$	−13.4622	−	13.4622i	−0.467560	−	0.467560i	0.433563	−	0.901123i	$-0.357256\pi$
$829$	−13.4622	−	13.4622i	−0.467560	−	0.467560i	−0.901123	+	0.433563i	$0.857256\pi$
$830$		0			0
$831$		−	16.4786i		−	0.571638i
$832$		0			0
$833$	4.36758	+	4.36758i	0.151328	+	0.151328i
$834$		0			0
$835$	20.6020	−	1.51020i	0.712963	−	0.0522628i
$836$		0			0
$837$	40.1865			1.38905
$838$		0			0
$839$			3.34964i			0.115642i	0.998327	+	0.0578211i	$0.0184153\pi$
$839$			3.34964i			0.115642i	−0.998327	+	0.0578211i	$0.981585\pi$
$840$		0			0
$841$		−	19.3409i		−	0.666928i
$842$		0			0
$843$	19.3660			0.667002
$844$		0			0
$845$	−21.8875	−	18.8978i	−0.752952	−	0.650103i
$846$		0			0
$847$	17.3507	+	17.3507i	0.596176	+	0.596176i
$848$		0			0
$849$		−	13.9929i		−	0.480236i
$850$		0			0
$851$	0.962245	+	0.962245i	0.0329853	+	0.0329853i
$852$		0			0
$853$		−	36.5317i		−	1.25082i	−0.780295	−	0.625411i	$-0.784931\pi$
$853$		−	36.5317i		−	1.25082i	0.780295	−	0.625411i	$-0.215069\pi$
$854$		0			0
$855$	12.8311	−	0.940565i	0.438814	−	0.0321667i
$856$		0			0
$857$	−23.0064	−	23.0064i	−0.785883	−	0.785883i	0.194933	−	0.980817i	$-0.437551\pi$
$857$	−23.0064	−	23.0064i	−0.785883	−	0.785883i	−0.980817	+	0.194933i	$0.937551\pi$
$858$		0			0
$859$	−24.2440	−	24.2440i	−0.827194	−	0.827194i	0.159934	−	0.987128i	$-0.448872\pi$
$859$	−24.2440	−	24.2440i	−0.827194	−	0.827194i	−0.987128	+	0.159934i	$0.948872\pi$
$860$		0			0
$861$	−10.6025	+	10.6025i	−0.361331	+	0.361331i
$862$		0			0
$863$	−32.5729	+	32.5729i	−1.10879	+	1.10879i	−0.115483	+	0.993309i	$0.536842\pi$
$863$	−32.5729	+	32.5729i	−1.10879	+	1.10879i	−0.993309	+	0.115483i	$0.963158\pi$
$864$		0			0
$865$	17.7741	+	15.3463i	0.604339	+	0.521790i
$866$		0			0
$867$	8.38163			0.284655
$868$		0			0
$869$	7.28781	−	7.28781i	0.247222	−	0.247222i
$870$		0			0
$871$	1.20320			0.0407689
$872$		0			0
$873$	3.58178	−	3.58178i	0.121225	−	0.121225i
$874$		0			0
$875$	5.87686	+	26.3402i	0.198674	+	0.890461i
$876$		0			0
$877$		−	10.2642i		−	0.346596i	−0.984869	−	0.173298i	$-0.944558\pi$
$877$		−	10.2642i		−	0.346596i	0.984869	−	0.173298i	$-0.0554424\pi$
$878$		0			0
$879$	21.7091			0.732230
$880$		0			0
$881$	−27.6098			−0.930198			−0.465099	−	0.885259i	$-0.653981\pi$
$881$	−27.6098			−0.930198			−0.465099	+	0.885259i	$0.653981\pi$
$882$		0			0
$883$		−	4.66123i		−	0.156863i	−0.996920	−	0.0784315i	$-0.975009\pi$
$883$		−	4.66123i		−	0.156863i	0.996920	−	0.0784315i	$-0.0249912\pi$
$884$		0			0
$885$	−25.3420	+	1.85766i	−0.851863	+	0.0624447i
$886$		0			0
$887$	−38.1939	+	38.1939i	−1.28242	+	1.28242i	−0.343141	+	0.939284i	$0.611491\pi$
$887$	−38.1939	+	38.1939i	−1.28242	+	1.28242i	−0.939284	+	0.343141i	$0.888509\pi$
$888$		0			0
$889$	4.91938			0.164991
$890$		0			0
$891$	−2.49897	+	2.49897i	−0.0837188	+	0.0837188i
$892$		0			0
$893$	−26.5854			−0.889648
$894$		0			0
$895$	−41.0736	+	3.01085i	−1.37294	+	0.100642i
$896$		0			0
$897$	−0.0309001	+	0.0309001i	−0.00103172	+	0.00103172i
$898$		0			0
$899$	−20.9548	+	20.9548i	−0.698883	+	0.698883i
$900$		0			0
$901$	−0.425040	−	0.425040i	−0.0141601	−	0.0141601i
$902$		0			0
$903$	−11.8292	−	11.8292i	−0.393652	−	0.393652i
$904$		0			0
$905$	−2.43449	−	33.2110i	−0.0809250	−	1.10397i
$906$		0			0
$907$			0.648260i			0.0215251i	0.999942	+	0.0107626i	$0.00342589\pi$
$907$			0.648260i			0.0215251i	−0.999942	+	0.0107626i	$0.996574\pi$
$908$		0			0
$909$	20.9942	+	20.9942i	0.696335	+	0.696335i
$910$		0			0
$911$			14.1895i			0.470119i	0.971981	+	0.235059i	$0.0755285\pi$
$911$			14.1895i			0.470119i	−0.971981	+	0.235059i	$0.924472\pi$
$912$		0			0
$913$	−6.05974	−	6.05974i	−0.200548	−	0.200548i
$914$		0			0
$915$	−0.750092	−	10.2327i	−0.0247973	−	0.338282i
$916$		0			0
$917$	−28.3996			−0.937838
$918$		0			0
$919$			35.3001i			1.16444i	0.813031	+	0.582221i	$0.197816\pi$
$919$			35.3001i			1.16444i	−0.813031	+	0.582221i	$0.802184\pi$
$920$		0			0
$921$		−	23.9975i		−	0.790745i
$922$		0			0
$923$	−1.46611			−0.0482575
$924$		0			0
$925$	4.62983	+	31.4101i	0.152228	+	1.03276i
$926$		0			0
$927$	33.1088	+	33.1088i	1.08744	+	1.08744i
$928$		0			0
$929$			3.23832i			0.106246i	0.998588	+	0.0531229i	$0.0169175\pi$
$929$			3.23832i			0.106246i	−0.998588	+	0.0531229i	$0.983082\pi$
$930$		0			0
$931$	1.99870	+	1.99870i	0.0655049	+	0.0655049i
$932$		0			0
$933$		−	12.4665i		−	0.408135i
$934$		0			0
$935$	−7.02888	+	8.14088i	−0.229869	+	0.266235i
$936$		0			0
$937$	6.27461	+	6.27461i	0.204983	+	0.204983i	0.802131	−	0.597148i	$-0.203700\pi$
$937$	6.27461	+	6.27461i	0.204983	+	0.204983i	−0.597148	+	0.802131i	$0.703700\pi$
$938$		0			0
$939$	2.65781	+	2.65781i	0.0867342	+	0.0867342i
$940$		0			0
$941$	14.5002	−	14.5002i	0.472692	−	0.472692i	−0.430093	−	0.902785i	$-0.641519\pi$
$941$	14.5002	−	14.5002i	0.472692	−	0.472692i	0.902785	+	0.430093i	$0.141519\pi$
$942$		0			0
$943$	−1.20344	+	1.20344i	−0.0391892	+	0.0391892i
$944$		0			0
$945$	1.66306	+	22.6873i	0.0540994	+	0.738018i
$946$		0			0
$947$	18.0520			0.586612			0.293306	−	0.956019i	$-0.405245\pi$
$947$	18.0520			0.586612			0.293306	+	0.956019i	$0.405245\pi$
$948$		0			0
$949$	1.60093	−	1.60093i	0.0519683	−	0.0519683i
$950$		0			0
$951$	6.36926			0.206537
$952$		0			0
$953$	−19.7572	+	19.7572i	−0.639998	+	0.639998i	−0.950555	−	0.310557i	$-0.899485\pi$
$953$	−19.7572	+	19.7572i	−0.639998	+	0.639998i	0.310557	+	0.950555i	$0.399485\pi$
$954$		0			0
$955$	−14.5650	+	16.8693i	−0.471313	+	0.545876i
$956$		0			0
$957$			2.22102i			0.0717952i
$958$		0			0
$959$	−24.2044			−0.781602
$960$		0			0
$961$	−59.9208			−1.93293
$962$		0			0
$963$			25.5158i			0.822235i
$964$		0			0
$965$	−0.790875	−	10.7890i	−0.0254592	−	0.347311i
$966$		0			0
$967$	19.5896	−	19.5896i	0.629959	−	0.629959i	−0.318099	−	0.948058i	$-0.603044\pi$
$967$	19.5896	−	19.5896i	0.629959	−	0.629959i	0.948058	+	0.318099i	$0.103044\pi$
$968$		0			0
$969$	9.92064			0.318697
$970$		0			0
$971$	12.7228	−	12.7228i	0.408293	−	0.408293i	−0.472850	−	0.881143i	$-0.656775\pi$
$971$	12.7228	−	12.7228i	0.408293	−	0.408293i	0.881143	+	0.472850i	$0.156775\pi$
$972$		0			0
$973$	−18.8963			−0.605789
$974$		0			0
$975$	−1.00866	+	0.148675i	−0.0323029	+	0.00476143i
$976$		0			0
$977$	−0.180025	+	0.180025i	−0.00575950	+	0.00575950i	−0.709981	−	0.704221i	$-0.751296\pi$
$977$	−0.180025	+	0.180025i	−0.00575950	+	0.00575950i	0.704221	+	0.709981i	$0.251296\pi$
$978$		0			0
$979$	2.74796	−	2.74796i	0.0878252	−	0.0878252i
$980$		0			0
$981$	−21.7456	−	21.7456i	−0.694285	−	0.694285i
$982$		0			0
$983$	−1.16197	−	1.16197i	−0.0370610	−	0.0370610i	0.688333	−	0.725394i	$-0.258343\pi$
$983$	−1.16197	−	1.16197i	−0.0370610	−	0.0370610i	−0.725394	+	0.688333i	$0.758343\pi$
$984$		0			0
$985$	−44.9696	−	38.8270i	−1.43285	−	1.23713i
$986$		0			0
$987$		−	20.8349i		−	0.663181i
$988$		0			0
$989$	−1.34268	−	1.34268i	−0.0426947	−	0.0426947i
$990$		0			0
$991$		−	32.3198i		−	1.02667i	−0.858188	−	0.513335i	$-0.828410\pi$
$991$		−	32.3198i		−	1.02667i	0.858188	−	0.513335i	$-0.171590\pi$
$992$		0			0
$993$	8.13266	+	8.13266i	0.258082	+	0.258082i
$994$		0			0
$995$	−9.86485	+	11.4255i	−0.312737	+	0.362213i
$996$		0			0
$997$	−15.5529			−0.492565			−0.246282	−	0.969198i	$-0.579209\pi$
$997$	−15.5529			−0.492565			−0.246282	+	0.969198i	$0.579209\pi$
$998$		0			0
$999$			26.7618i			0.846706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.j.d.63.10	yes	32
4.3	odd	2	inner	1280.2.j.d.63.7	yes	32
5.2	odd	4		1280.2.s.c.1087.10	yes	32
8.3	odd	2		1280.2.j.c.63.10	yes	32
8.5	even	2		1280.2.j.c.63.7	✓	32
16.3	odd	4		1280.2.s.c.703.10	yes	32
16.5	even	4		1280.2.s.d.703.10	yes	32
16.11	odd	4		1280.2.s.d.703.7	yes	32
16.13	even	4		1280.2.s.c.703.7	yes	32
20.7	even	4		1280.2.s.c.1087.7	yes	32
40.27	even	4		1280.2.s.d.1087.10	yes	32
40.37	odd	4		1280.2.s.d.1087.7	yes	32
80.27	even	4		1280.2.j.c.447.10	yes	32
80.37	odd	4		1280.2.j.c.447.7	yes	32
80.67	even	4	inner	1280.2.j.d.447.7	yes	32
80.77	odd	4	inner	1280.2.j.d.447.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1280.2.j.c.63.7	✓	32	8.5	even	2
1280.2.j.c.63.10	yes	32	8.3	odd	2
1280.2.j.c.447.7	yes	32	80.37	odd	4
1280.2.j.c.447.10	yes	32	80.27	even	4
1280.2.j.d.63.7	yes	32	4.3	odd	2	inner
1280.2.j.d.63.10	yes	32	1.1	even	1	trivial
1280.2.j.d.447.7	yes	32	80.67	even	4	inner
1280.2.j.d.447.10	yes	32	80.77	odd	4	inner
1280.2.s.c.703.7	yes	32	16.13	even	4
1280.2.s.c.703.10	yes	32	16.3	odd	4
1280.2.s.c.1087.7	yes	32	20.7	even	4
1280.2.s.c.1087.10	yes	32	5.2	odd	4
1280.2.s.d.703.7	yes	32	16.11	odd	4
1280.2.s.d.703.10	yes	32	16.5	even	4
1280.2.s.d.1087.7	yes	32	40.37	odd	4
1280.2.s.d.1087.10	yes	32	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+0.782176i q^{3} +(1.69250 + 1.46131i) q^{5} +(1.70686 - 1.70686i) q^{7} +2.38820 q^{9} +(-0.646047 + 0.646047i) q^{11} +0.260697 q^{13} +(-1.14301 + 1.32383i) q^{15} +(3.72262 - 3.72262i) q^{17} +(1.70356 - 1.70356i) q^{19} +(1.33507 + 1.33507i) q^{21} +(0.151537 + 0.151537i) q^{23} +(0.729119 + 4.94655i) q^{25} +4.21452i q^{27} +(-2.19762 - 2.19762i) q^{29} -9.53524i q^{31} +(-0.505323 - 0.505323i) q^{33} +(5.38312 - 0.394603i) q^{35} +6.34990 q^{37} +0.203911i q^{39} +7.94153i q^{41} -8.86040 q^{43} +(4.04203 + 3.48991i) q^{45} +(-7.80293 - 7.80293i) q^{47} +1.17325i q^{49} +(2.91174 + 2.91174i) q^{51} -0.114178i q^{53} +(-2.03751 + 0.149357i) q^{55} +(1.33248 + 1.33248i) q^{57} +(10.2731 + 10.2731i) q^{59} +(-4.14809 + 4.14809i) q^{61} +(4.07632 - 4.07632i) q^{63} +(0.441230 + 0.380961i) q^{65} +4.61532 q^{67} +(-0.118529 + 0.118529i) q^{69} -5.62379 q^{71} +(6.14095 - 6.14095i) q^{73} +(-3.86908 + 0.570299i) q^{75} +2.20542i q^{77} -11.2806 q^{79} +3.86810 q^{81} +9.37971i q^{83} +(11.7405 - 0.860618i) q^{85} +(1.71893 - 1.71893i) q^{87} -4.25350 q^{89} +(0.444974 - 0.444974i) q^{91} +7.45824 q^{93} +(5.37270 - 0.393839i) q^{95} +(1.49978 - 1.49978i) q^{97} +(-1.54289 + 1.54289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{9} + 16 q^{13} + 8 q^{17} + 8 q^{21} + 16 q^{25} - 16 q^{29} + 56 q^{33} - 40 q^{45} - 8 q^{57} - 8 q^{61} - 72 q^{65} + 40 q^{69} + 8 q^{73} - 64 q^{81} - 24 q^{85} - 16 q^{89} + 224 q^{93}+ \cdots + 72 q^{97}+O(q^{100}) \) 32 * q - 32 * q^9 + 16 * q^13 + 8 * q^17 + 8 * q^21 + 16 * q^25 - 16 * q^29 + 56 * q^33 - 40 * q^45 - 8 * q^57 - 8 * q^61 - 72 * q^65 + 40 * q^69 + 8 * q^73 - 64 * q^81 - 24 * q^85 - 16 * q^89 + 224 * q^93 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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