LMFDB - Embedded newform 1280.2.n.n.1023.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1280,2,Mod(767,1280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1280, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1280.767");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.2208514587$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 320)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1023.3
Root			$-0.228425 - 1.39564i$ of defining polynomial
Character	$\chi$	$=$	1280.1023
Dual form			1280.2.n.n.767.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456850 - 0.456850i) q^{3} +(-0.456850 + 2.18890i) q^{5} +(-2.79129 - 2.79129i) q^{7} +2.58258i q^{9} +O(q^{10})$	\(q+(0.456850 - 0.456850i) q^{3} +(-0.456850 + 2.18890i) q^{5} +(-2.79129 - 2.79129i) q^{7} +2.58258i q^{9} -4.37780i q^{11} +(1.73205 + 1.73205i) q^{13} +(0.791288 + 1.20871i) q^{15} +(3.00000 - 3.00000i) q^{17} +3.46410 q^{19} -2.55040 q^{21} +(-0.791288 + 0.791288i) q^{23} +(-4.58258 - 2.00000i) q^{25} +(2.55040 + 2.55040i) q^{27} -5.29150i q^{29} +1.58258i q^{31} +(-2.00000 - 2.00000i) q^{33} +(7.38505 - 4.83465i) q^{35} +(5.19615 - 5.19615i) q^{37} +1.58258 q^{39} +7.58258 q^{41} +(8.29875 - 8.29875i) q^{43} +(-5.65300 - 1.17985i) q^{45} +(-0.791288 - 0.791288i) q^{47} +8.58258i q^{49} -2.74110i q^{51} +(-2.64575 - 2.64575i) q^{53} +(9.58258 + 2.00000i) q^{55} +(1.58258 - 1.58258i) q^{57} +5.29150 q^{59} +9.66930 q^{61} +(7.20871 - 7.20871i) q^{63} +(-4.58258 + 3.00000i) q^{65} +(-8.29875 - 8.29875i) q^{67} +0.723000i q^{69} +13.5826i q^{71} +(-0.582576 - 0.582576i) q^{73} +(-3.00725 + 1.17985i) q^{75} +(-12.2197 + 12.2197i) q^{77} -12.0000 q^{79} -5.41742 q^{81} +(4.83465 - 4.83465i) q^{83} +(5.19615 + 7.93725i) q^{85} +(-2.41742 - 2.41742i) q^{87} -3.16515i q^{89} -9.66930i q^{91} +(0.723000 + 0.723000i) q^{93} +(-1.58258 + 7.58258i) q^{95} +(0.582576 - 0.582576i) q^{97} +11.3060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^7	$ 8 q - 4 q^{7} - 12 q^{15} + 24 q^{17} + 12 q^{23} - 16 q^{33} - 24 q^{39} + 24 q^{41} + 12 q^{47} + 40 q^{55} - 24 q^{57} + 76 q^{63} + 32 q^{73} - 96 q^{79} - 80 q^{81} - 56 q^{87} + 24 q^{95} - 32 q^{97}+O(q^{100}) $ 8 * q - 4 * q^7 - 12 * q^15 + 24 * q^17 + 12 * q^23 - 16 * q^33 - 24 * q^39 + 24 * q^41 + 12 * q^47 + 40 * q^55 - 24 * q^57 + 76 * q^63 + 32 * q^73 - 96 * q^79 - 80 * q^81 - 56 * q^87 + 24 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.456850	−	0.456850i	0.263763	−	0.263763i	−0.562818	−	0.826581i	$-0.690283\pi$
$3$	0.456850	−	0.456850i	0.263763	−	0.263763i	0.826581	+	0.562818i	$0.190283\pi$
$4$		0			0
$5$	−0.456850	+	2.18890i	−0.204310	+	0.978906i
$5$	−0.456850	+	2.18890i	−0.204310	+	0.978906i
$6$		0			0
$7$	−2.79129	−	2.79129i	−1.05501	−	1.05501i	−0.998396	−	0.0566113i	$-0.981970\pi$
$7$	−2.79129	−	2.79129i	−1.05501	−	1.05501i	−0.0566113	−	0.998396i	$-0.518030\pi$
$8$		0			0
$9$			2.58258i			0.860859i
$10$		0			0
$11$		−	4.37780i		−	1.31996i	−0.751284	−	0.659979i	$-0.770565\pi$
$11$		−	4.37780i		−	1.31996i	0.751284	−	0.659979i	$-0.229435\pi$
$12$		0			0
$13$	1.73205	+	1.73205i	0.480384	+	0.480384i	0.905254	−	0.424870i	$-0.139680\pi$
$13$	1.73205	+	1.73205i	0.480384	+	0.480384i	−0.424870	+	0.905254i	$0.639680\pi$
$14$		0			0
$15$	0.791288	+	1.20871i	0.204310	+	0.312088i
$16$		0			0
$17$	3.00000	−	3.00000i	0.727607	−	0.727607i	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	3.00000	−	3.00000i	0.727607	−	0.727607i	0.970143	+	0.242536i	$0.0779791\pi$
$18$		0			0
$19$	3.46410			0.794719			0.397360	−	0.917663i	$-0.369927\pi$
$19$	3.46410			0.794719			0.397360	+	0.917663i	$0.369927\pi$
$20$		0			0
$21$	−2.55040			−0.556543
$22$		0			0
$23$	−0.791288	+	0.791288i	−0.164995	+	0.164995i	−0.784775	−	0.619780i	$-0.787222\pi$
$23$	−0.791288	+	0.791288i	−0.164995	+	0.164995i	0.619780	+	0.784775i	$0.287222\pi$
$24$		0			0
$25$	−4.58258	−	2.00000i	−0.916515	−	0.400000i
$26$		0			0
$27$	2.55040	+	2.55040i	0.490825	+	0.490825i
$28$		0			0
$29$		−	5.29150i		−	0.982607i	−0.870988	−	0.491304i	$-0.836521\pi$
$29$		−	5.29150i		−	0.982607i	0.870988	−	0.491304i	$-0.163479\pi$
$30$		0			0
$31$			1.58258i			0.284239i	0.989850	+	0.142119i	$0.0453917\pi$
$31$			1.58258i			0.284239i	−0.989850	+	0.142119i	$0.954608\pi$
$32$		0			0
$33$	−2.00000	−	2.00000i	−0.348155	−	0.348155i
$34$		0			0
$35$	7.38505	−	4.83465i	1.24830	−	0.817205i
$36$		0			0
$37$	5.19615	−	5.19615i	0.854242	−	0.854242i	−0.136410	−	0.990652i	$-0.543557\pi$
$37$	5.19615	−	5.19615i	0.854242	−	0.854242i	0.990652	+	0.136410i	$0.0435565\pi$
$38$		0			0
$39$	1.58258			0.253415
$40$		0			0
$41$	7.58258			1.18420			0.592100	−	0.805865i	$-0.298299\pi$
$41$	7.58258			1.18420			0.592100	+	0.805865i	$0.298299\pi$
$42$		0			0
$43$	8.29875	−	8.29875i	1.26555	−	1.26555i	0.317184	−	0.948364i	$-0.397263\pi$
$43$	8.29875	−	8.29875i	1.26555	−	1.26555i	0.948364	−	0.317184i	$-0.102737\pi$
$44$		0			0
$45$	−5.65300	−	1.17985i	−0.842700	−	0.175882i
$46$		0			0
$47$	−0.791288	−	0.791288i	−0.115421	−	0.115421i	0.647037	−	0.762458i	$-0.276008\pi$
$47$	−0.791288	−	0.791288i	−0.115421	−	0.115421i	−0.762458	+	0.647037i	$0.776008\pi$
$48$		0			0
$49$			8.58258i			1.22608i
$50$		0			0
$51$		−	2.74110i		−	0.383831i
$52$		0			0
$53$	−2.64575	−	2.64575i	−0.363422	−	0.363422i	0.501649	−	0.865071i	$-0.332727\pi$
$53$	−2.64575	−	2.64575i	−0.363422	−	0.363422i	−0.865071	+	0.501649i	$0.832727\pi$
$54$		0			0
$55$	9.58258	+	2.00000i	1.29211	+	0.269680i
$56$		0			0
$57$	1.58258	−	1.58258i	0.209617	−	0.209617i
$58$		0			0
$59$	5.29150			0.688895			0.344447	−	0.938806i	$-0.388066\pi$
$59$	5.29150			0.688895			0.344447	+	0.938806i	$0.388066\pi$
$60$		0			0
$61$	9.66930			1.23803			0.619014	−	0.785380i	$-0.287532\pi$
$61$	9.66930			1.23803			0.619014	+	0.785380i	$0.287532\pi$
$62$		0			0
$63$	7.20871	−	7.20871i	0.908212	−	0.908212i
$64$		0			0
$65$	−4.58258	+	3.00000i	−0.568399	+	0.372104i
$66$		0			0
$67$	−8.29875	−	8.29875i	−1.01385	−	1.01385i	−0.999903	−	0.0139515i	$-0.995559\pi$
$67$	−8.29875	−	8.29875i	−1.01385	−	1.01385i	−0.0139515	−	0.999903i	$-0.504441\pi$
$68$		0			0
$69$			0.723000i			0.0870390i
$70$		0			0
$71$			13.5826i			1.61196i	0.591946	+	0.805978i	$0.298360\pi$
$71$			13.5826i			1.61196i	−0.591946	+	0.805978i	$0.701640\pi$
$72$		0			0
$73$	−0.582576	−	0.582576i	−0.0681853	−	0.0681853i	0.672192	−	0.740377i	$-0.265353\pi$
$73$	−0.582576	−	0.582576i	−0.0681853	−	0.0681853i	−0.740377	+	0.672192i	$0.765353\pi$
$74$		0			0
$75$	−3.00725	+	1.17985i	−0.347247	+	0.136237i
$76$		0			0
$77$	−12.2197	+	12.2197i	−1.39256	+	1.39256i
$78$		0			0
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$		0			0
$81$	−5.41742			−0.601936
$82$		0			0
$83$	4.83465	−	4.83465i	0.530672	−	0.530672i	−0.390100	−	0.920772i	$-0.627560\pi$
$83$	4.83465	−	4.83465i	0.530672	−	0.530672i	0.920772	+	0.390100i	$0.127560\pi$
$84$		0			0
$85$	5.19615	+	7.93725i	0.563602	+	0.860916i
$86$		0			0
$87$	−2.41742	−	2.41742i	−0.259175	−	0.259175i
$88$		0			0
$89$		−	3.16515i		−	0.335505i	−0.985829	−	0.167753i	$-0.946349\pi$
$89$		−	3.16515i		−	0.335505i	0.985829	−	0.167753i	$-0.0536510\pi$
$90$		0			0
$91$		−	9.66930i		−	1.01362i
$92$		0			0
$93$	0.723000	+	0.723000i	0.0749716	+	0.0749716i
$94$		0			0
$95$	−1.58258	+	7.58258i	−0.162369	+	0.777956i
$96$		0			0
$97$	0.582576	−	0.582576i	0.0591516	−	0.0591516i	−0.676912	−	0.736064i	$-0.736682\pi$
$97$	0.582576	−	0.582576i	0.0591516	−	0.0591516i	0.736064	+	0.676912i	$0.236682\pi$
$98$		0			0
$99$	11.3060			1.13630
$100$		0			0
$101$	3.65480			0.363666			0.181833	−	0.983329i	$-0.441797\pi$
$101$	3.65480			0.363666			0.181833	+	0.983329i	$0.441797\pi$
$102$		0			0
$103$	10.3739	−	10.3739i	1.02217	−	1.02217i	0.0224185	−	0.999749i	$-0.492863\pi$
$103$	10.3739	−	10.3739i	1.02217	−	1.02217i	0.999749	−	0.0224185i	$-0.00713662\pi$
$104$		0			0
$105$	1.16515	−	5.58258i	0.113707	−	0.544804i
$106$		0			0
$107$	8.29875	+	8.29875i	0.802271	+	0.802271i	0.983450	−	0.181179i	$-0.0579914\pi$
$107$	8.29875	+	8.29875i	0.802271	+	0.802271i	−0.181179	+	0.983450i	$0.557991\pi$
$108$		0			0
$109$			6.20520i			0.594351i	0.954823	+	0.297175i	$0.0960446\pi$
$109$			6.20520i			0.594351i	−0.954823	+	0.297175i	$0.903955\pi$
$110$		0			0
$111$		−	4.74773i		−	0.450634i
$112$		0			0
$113$	−4.58258	−	4.58258i	−0.431092	−	0.431092i	0.457907	−	0.889000i	$-0.348599\pi$
$113$	−4.58258	−	4.58258i	−0.431092	−	0.431092i	−0.889000	+	0.457907i	$0.848599\pi$
$114$		0			0
$115$	−1.37055	−	2.09355i	−0.127805	−	0.195225i
$116$		0			0
$117$	−4.47315	+	4.47315i	−0.413543	+	0.413543i
$118$		0			0
$119$	−16.7477			−1.53526
$120$		0			0
$121$	−8.16515			−0.742286
$122$		0			0
$123$	3.46410	−	3.46410i	0.312348	−	0.312348i
$124$		0			0
$125$	6.47135	−	9.11710i	0.578815	−	0.815459i
$126$		0			0
$127$	−1.20871	−	1.20871i	−0.107256	−	0.107256i	0.651442	−	0.758698i	$-0.274164\pi$
$127$	−1.20871	−	1.20871i	−0.107256	−	0.107256i	−0.758698	+	0.651442i	$0.774164\pi$
$128$		0			0
$129$		−	7.58258i		−	0.667609i
$130$		0			0
$131$			11.3060i			0.987810i	0.869516	+	0.493905i	$0.164431\pi$
$131$			11.3060i			0.987810i	−0.869516	+	0.493905i	$0.835569\pi$
$132$		0			0
$133$	−9.66930	−	9.66930i	−0.838435	−	0.838435i
$134$		0			0
$135$	−6.74773	+	4.41742i	−0.580752	+	0.380191i
$136$		0			0
$137$	−12.1652	+	12.1652i	−1.03934	+	1.03934i	−0.0401452	+	0.999194i	$0.512782\pi$
$137$	−12.1652	+	12.1652i	−1.03934	+	1.03934i	−0.999194	+	0.0401452i	$0.987218\pi$
$138$		0			0
$139$	−8.94630			−0.758816			−0.379408	−	0.925230i	$-0.623872\pi$
$139$	−8.94630			−0.758816			−0.379408	+	0.925230i	$0.623872\pi$
$140$		0			0
$141$	−0.723000			−0.0608876
$142$		0			0
$143$	7.58258	−	7.58258i	0.634087	−	0.634087i
$144$		0			0
$145$	11.5826	+	2.41742i	0.961881	+	0.200756i
$146$		0			0
$147$	3.92095	+	3.92095i	0.323395	+	0.323395i
$148$		0			0
$149$			4.37780i			0.358644i	0.983790	+	0.179322i	$0.0573903\pi$
$149$			4.37780i			0.358644i	−0.983790	+	0.179322i	$0.942610\pi$
$150$		0			0
$151$		−	12.7477i		−	1.03740i	−0.854958	−	0.518698i	$-0.826417\pi$
$151$		−	12.7477i		−	1.03740i	0.854958	−	0.518698i	$-0.173583\pi$
$152$		0			0
$153$	7.74773	+	7.74773i	0.626367	+	0.626367i
$154$		0			0
$155$	−3.46410	−	0.723000i	−0.278243	−	0.0580728i
$156$		0			0
$157$	11.4014	−	11.4014i	0.909927	−	0.909927i	−0.0863386	−	0.996266i	$-0.527517\pi$
$157$	11.4014	−	11.4014i	0.909927	−	0.909927i	0.996266	+	0.0863386i	$0.0275167\pi$
$158$		0			0
$159$	−2.41742			−0.191714
$160$		0			0
$161$	4.41742			0.348142
$162$		0			0
$163$	−8.29875	+	8.29875i	−0.650009	+	0.650009i	−0.952995	−	0.302986i	$-0.902016\pi$
$163$	−8.29875	+	8.29875i	−0.650009	+	0.650009i	0.302986	+	0.952995i	$0.402016\pi$
$164$		0			0
$165$	5.29150	−	3.46410i	0.411943	−	0.269680i
$166$		0			0
$167$	−11.2087	−	11.2087i	−0.867356	−	0.867356i	0.124823	−	0.992179i	$-0.460164\pi$
$167$	−11.2087	−	11.2087i	−0.867356	−	0.867356i	−0.992179	+	0.124823i	$0.960164\pi$
$168$		0			0
$169$		−	7.00000i		−	0.538462i
$170$		0			0
$171$			8.94630i			0.684141i
$172$		0			0
$173$	−8.66025	−	8.66025i	−0.658427	−	0.658427i	0.296581	−	0.955008i	$-0.404154\pi$
$173$	−8.66025	−	8.66025i	−0.658427	−	0.658427i	−0.955008	+	0.296581i	$0.904154\pi$
$174$		0			0
$175$	7.20871	+	18.3739i	0.544927	+	1.38893i
$176$		0			0
$177$	2.41742	−	2.41742i	0.181705	−	0.181705i
$178$		0			0
$179$	−8.56490			−0.640171			−0.320085	−	0.947389i	$-0.603712\pi$
$179$	−8.56490			−0.640171			−0.320085	+	0.947389i	$0.603712\pi$
$180$		0			0
$181$	−6.92820			−0.514969			−0.257485	−	0.966282i	$-0.582894\pi$
$181$	−6.92820			−0.514969			−0.257485	+	0.966282i	$0.582894\pi$
$182$		0			0
$183$	4.41742	−	4.41742i	0.326545	−	0.326545i
$184$		0			0
$185$	9.00000	+	13.7477i	0.661693	+	1.01075i
$186$		0			0
$187$	−13.1334	−	13.1334i	−0.960410	−	0.960410i
$188$		0			0
$189$		−	14.2378i		−	1.03565i
$190$		0			0
$191$			13.5826i			0.982801i	0.870934	+	0.491400i	$0.163515\pi$
$191$			13.5826i			0.982801i	−0.870934	+	0.491400i	$0.836485\pi$
$192$		0			0
$193$	14.1652	+	14.1652i	1.01963	+	1.01963i	0.999803	+	0.0198265i	$0.00631138\pi$
$193$	14.1652	+	14.1652i	1.01963	+	1.01963i	0.0198265	+	0.999803i	$0.493689\pi$
$194$		0			0
$195$	−0.723000	+	3.46410i	−0.0517751	+	0.248069i
$196$		0			0
$197$	2.64575	−	2.64575i	0.188502	−	0.188502i	−0.606546	−	0.795048i	$-0.707446\pi$
$197$	2.64575	−	2.64575i	0.188502	−	0.188502i	0.795048	+	0.606546i	$0.207446\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$	−7.58258			−0.534834
$202$		0			0
$203$	−14.7701	+	14.7701i	−1.03666	+	1.03666i
$204$		0			0
$205$	−3.46410	+	16.5975i	−0.241943	+	1.15922i
$206$		0			0
$207$	−2.04356	−	2.04356i	−0.142037	−	0.142037i
$208$		0			0
$209$		−	15.1652i		−	1.04900i
$210$		0			0
$211$		−	7.65120i		−	0.526731i	−0.964696	−	0.263365i	$-0.915168\pi$
$211$		−	7.65120i		−	0.526731i	0.964696	−	0.263365i	$-0.0848324\pi$
$212$		0			0
$213$	6.20520	+	6.20520i	0.425174	+	0.425174i
$214$		0			0
$215$	14.3739	+	21.9564i	0.980289	+	1.49742i
$216$		0			0
$217$	4.41742	−	4.41742i	0.299874	−	0.299874i
$218$		0			0
$219$	−0.532300			−0.0359695
$220$		0			0
$221$	10.3923			0.699062
$222$		0			0
$223$	12.3739	−	12.3739i	0.828615	−	0.828615i	−0.158710	−	0.987325i	$-0.550734\pi$
$223$	12.3739	−	12.3739i	0.828615	−	0.828615i	0.987325	+	0.158710i	$0.0507335\pi$
$224$		0			0
$225$	5.16515	−	11.8348i	0.344343	−	0.788990i
$226$		0			0
$227$	6.66205	+	6.66205i	0.442176	+	0.442176i	0.892743	−	0.450567i	$-0.148778\pi$
$227$	6.66205	+	6.66205i	0.442176	+	0.442176i	−0.450567	+	0.892743i	$0.648778\pi$
$228$		0			0
$229$		−	3.46410i		−	0.228914i	−0.993428	−	0.114457i	$-0.963487\pi$
$229$		−	3.46410i		−	0.228914i	0.993428	−	0.114457i	$-0.0365129\pi$
$230$		0			0
$231$			11.1652i			0.734613i
$232$		0			0
$233$	−6.16515	−	6.16515i	−0.403892	−	0.403892i	0.475710	−	0.879602i	$-0.342191\pi$
$233$	−6.16515	−	6.16515i	−0.403892	−	0.403892i	−0.879602	+	0.475710i	$0.842191\pi$
$234$		0			0
$235$	2.09355	−	1.37055i	0.136568	−	0.0894049i
$236$		0			0
$237$	−5.48220	+	5.48220i	−0.356107	+	0.356107i
$238$		0			0
$239$	−3.16515			−0.204737			−0.102368	−	0.994747i	$-0.532642\pi$
$239$	−3.16515			−0.204737			−0.102368	+	0.994747i	$0.532642\pi$
$240$		0			0
$241$	−10.7477			−0.692322			−0.346161	−	0.938175i	$-0.612515\pi$
$241$	−10.7477			−0.692322			−0.346161	+	0.938175i	$0.612515\pi$
$242$		0			0
$243$	−10.1262	+	10.1262i	−0.649593	+	0.649593i
$244$		0			0
$245$	−18.7864	−	3.92095i	−1.20022	−	0.250500i
$246$		0			0
$247$	6.00000	+	6.00000i	0.381771	+	0.381771i
$248$		0			0
$249$		−	4.41742i		−	0.279943i
$250$		0			0
$251$			18.2342i			1.15093i	0.817825	+	0.575467i	$0.195179\pi$
$251$			18.2342i			1.15093i	−0.817825	+	0.575467i	$0.804821\pi$
$252$		0			0
$253$	3.46410	+	3.46410i	0.217786	+	0.217786i
$254$		0			0
$255$	6.00000	+	1.25227i	0.375735	+	0.0784204i
$256$		0			0
$257$	−19.7477	+	19.7477i	−1.23183	+	1.23183i	−0.268569	+	0.963260i	$0.586551\pi$
$257$	−19.7477	+	19.7477i	−1.23183	+	1.23183i	−0.963260	+	0.268569i	$0.913449\pi$
$258$		0			0
$259$	−29.0079			−1.80246
$260$		0			0
$261$	13.6657			0.845886
$262$		0			0
$263$	18.7913	−	18.7913i	1.15872	−	1.15872i	0.173969	−	0.984751i	$-0.444341\pi$
$263$	18.7913	−	18.7913i	1.15872	−	1.15872i	0.984751	−	0.173969i	$-0.0556594\pi$
$264$		0			0
$265$	7.00000	−	4.58258i	0.430007	−	0.281505i
$266$		0			0
$267$	−1.44600	−	1.44600i	−0.0884938	−	0.0884938i
$268$		0			0
$269$			23.7164i			1.44602i	0.690840	+	0.723008i	$0.257241\pi$
$269$			23.7164i			1.44602i	−0.690840	+	0.723008i	$0.742759\pi$
$270$		0			0
$271$			8.74773i			0.531387i	0.964058	+	0.265693i	$0.0856008\pi$
$271$			8.74773i			0.531387i	−0.964058	+	0.265693i	$0.914399\pi$
$272$		0			0
$273$	−4.41742	−	4.41742i	−0.267355	−	0.267355i
$274$		0			0
$275$	−8.75560	+	20.0616i	−0.527983	+	1.20976i
$276$		0			0
$277$	−5.91915	+	5.91915i	−0.355647	+	0.355647i	−0.862206	−	0.506558i	$-0.830917\pi$
$277$	−5.91915	+	5.91915i	−0.355647	+	0.355647i	0.506558	+	0.862206i	$0.330917\pi$
$278$		0			0
$279$	−4.08712			−0.244690
$280$		0			0
$281$	10.7477			0.641156			0.320578	−	0.947222i	$-0.396123\pi$
$281$	10.7477			0.641156			0.320578	+	0.947222i	$0.396123\pi$
$282$		0			0
$283$	−17.2451	+	17.2451i	−1.02511	+	1.02511i	−0.0254359	+	0.999676i	$0.508097\pi$
$283$	−17.2451	+	17.2451i	−1.02511	+	1.02511i	−0.999676	+	0.0254359i	$0.991903\pi$
$284$		0			0
$285$	2.74110	+	4.18710i	0.162369	+	0.248023i
$286$		0			0
$287$	−21.1652	−	21.1652i	−1.24934	−	1.24934i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$		−	0.532300i		−	0.0312040i
$292$		0			0
$293$	23.4304	+	23.4304i	1.36882	+	1.36882i	0.862131	+	0.506685i	$0.169129\pi$
$293$	23.4304	+	23.4304i	1.36882	+	1.36882i	0.506685	+	0.862131i	$0.330871\pi$
$294$		0			0
$295$	−2.41742	+	11.5826i	−0.140748	+	0.674364i
$296$		0			0
$297$	11.1652	−	11.1652i	0.647868	−	0.647868i
$298$		0			0
$299$	−2.74110			−0.158522
$300$		0			0
$301$	−46.3284			−2.67033
$302$		0			0
$303$	1.66970	−	1.66970i	0.0959216	−	0.0959216i
$304$		0			0
$305$	−4.41742	+	21.1652i	−0.252941	+	1.21191i
$306$		0			0
$307$	−1.37055	−	1.37055i	−0.0782215	−	0.0782215i	0.666914	−	0.745135i	$-0.267615\pi$
$307$	−1.37055	−	1.37055i	−0.0782215	−	0.0782215i	−0.745135	+	0.666914i	$0.767615\pi$
$308$		0			0
$309$		−	9.47860i		−	0.539219i
$310$		0			0
$311$			10.4174i			0.590718i	0.955386	+	0.295359i	$0.0954392\pi$
$311$			10.4174i			0.590718i	−0.955386	+	0.295359i	$0.904561\pi$
$312$		0			0
$313$	−2.58258	−	2.58258i	−0.145976	−	0.145976i	0.630342	−	0.776318i	$-0.282915\pi$
$313$	−2.58258	−	2.58258i	−0.145976	−	0.145976i	−0.776318	+	0.630342i	$0.782915\pi$
$314$		0			0
$315$	12.4859	+	19.0725i	0.703498	+	1.07461i
$316$		0			0
$317$	17.6066	−	17.6066i	0.988883	−	0.988883i	−0.0110560	−	0.999939i	$-0.503519\pi$
$317$	17.6066	−	17.6066i	0.988883	−	0.988883i	0.999939	+	0.0110560i	$0.00351931\pi$
$318$		0			0
$319$	−23.1652			−1.29700
$320$		0			0
$321$	7.58258			0.423218
$322$		0			0
$323$	10.3923	−	10.3923i	0.578243	−	0.578243i
$324$		0			0
$325$	−4.47315	−	11.4014i	−0.248126	−	0.632433i
$326$		0			0
$327$	2.83485	+	2.83485i	0.156767	+	0.156767i
$328$		0			0
$329$			4.41742i			0.243540i
$330$		0			0
$331$			6.20520i			0.341069i	0.985352	+	0.170534i	$0.0545494\pi$
$331$			6.20520i			0.341069i	−0.985352	+	0.170534i	$0.945451\pi$
$332$		0			0
$333$	13.4195	+	13.4195i	0.735382	+	0.735382i
$334$		0			0
$335$	21.9564	−	14.3739i	1.19961	−	0.785328i
$336$		0			0
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	−0.679345	−	0.733819i	$-0.737736\pi$
$337$	1.00000	−	1.00000i	0.0544735	−	0.0544735i	0.733819	+	0.679345i	$0.237736\pi$
$338$		0			0
$339$	−4.18710			−0.227412
$340$		0			0
$341$	6.92820			0.375183
$342$		0			0
$343$	4.41742	−	4.41742i	0.238518	−	0.238518i
$344$		0			0
$345$	−1.58258	−	0.330303i	−0.0852030	−	0.0177829i
$346$		0			0
$347$	3.92095	+	3.92095i	0.210488	+	0.210488i	0.804475	−	0.593987i	$-0.202447\pi$
$347$	3.92095	+	3.92095i	0.210488	+	0.210488i	−0.593987	+	0.804475i	$0.702447\pi$
$348$		0			0
$349$		−	10.3923i		−	0.556287i	−0.960539	−	0.278144i	$-0.910281\pi$
$349$		−	10.3923i		−	0.556287i	0.960539	−	0.278144i	$-0.0897191\pi$
$350$		0			0
$351$			8.83485i			0.471569i
$352$		0			0
$353$	5.83485	+	5.83485i	0.310558	+	0.310558i	0.845126	−	0.534568i	$-0.179526\pi$
$353$	5.83485	+	5.83485i	0.310558	+	0.310558i	−0.534568	+	0.845126i	$0.679526\pi$
$354$		0			0
$355$	−29.7309	−	6.20520i	−1.57795	−	0.329338i
$356$		0			0
$357$	−7.65120	+	7.65120i	−0.404945	+	0.404945i
$358$		0			0
$359$	−8.83485			−0.466285			−0.233143	−	0.972443i	$-0.574901\pi$
$359$	−8.83485			−0.466285			−0.233143	+	0.972443i	$0.574901\pi$
$360$		0			0
$361$	−7.00000			−0.368421
$362$		0			0
$363$	−3.73025	+	3.73025i	−0.195787	+	0.195787i
$364$		0			0
$365$	1.54135	−	1.00905i	0.0806780	−	0.0528161i
$366$		0			0
$367$	−15.5390	−	15.5390i	−0.811130	−	0.811130i	0.173673	−	0.984803i	$-0.444436\pi$
$367$	−15.5390	−	15.5390i	−0.811130	−	0.811130i	−0.984803	+	0.173673i	$0.944436\pi$
$368$		0			0
$369$			19.5826i			1.01943i
$370$		0			0
$371$			14.7701i			0.766826i
$372$		0			0
$373$	−5.19615	−	5.19615i	−0.269047	−	0.269047i	0.559669	−	0.828716i	$-0.310928\pi$
$373$	−5.19615	−	5.19615i	−0.269047	−	0.269047i	−0.828716	+	0.559669i	$0.810928\pi$
$374$		0			0
$375$	−1.20871	−	7.12159i	−0.0624176	−	0.367757i
$376$		0			0
$377$	9.16515	−	9.16515i	0.472029	−	0.472029i
$378$		0			0
$379$	−10.3923			−0.533817			−0.266908	−	0.963722i	$-0.586002\pi$
$379$	−10.3923			−0.533817			−0.266908	+	0.963722i	$0.586002\pi$
$380$		0			0
$381$	−1.10440			−0.0565802
$382$		0			0
$383$	−3.62614	+	3.62614i	−0.185287	+	0.185287i	−0.793655	−	0.608368i	$-0.791824\pi$
$383$	−3.62614	+	3.62614i	−0.185287	+	0.185287i	0.608368	+	0.793655i	$0.291824\pi$
$384$		0			0
$385$	−21.1652	−	32.3303i	−1.07868	−	1.64770i
$386$		0			0
$387$	21.4322	+	21.4322i	1.08946	+	1.08946i
$388$		0			0
$389$		−	30.2632i		−	1.53441i	−0.641404	−	0.767203i	$-0.721648\pi$
$389$		−	30.2632i		−	1.53441i	0.641404	−	0.767203i	$-0.278352\pi$
$390$		0			0
$391$			4.74773i			0.240103i
$392$		0			0
$393$	5.16515	+	5.16515i	0.260547	+	0.260547i
$394$		0			0
$395$	5.48220	−	26.2668i	0.275840	−	1.32163i
$396$		0			0
$397$	7.93725	−	7.93725i	0.398359	−	0.398359i	−0.479295	−	0.877654i	$-0.659107\pi$
$397$	7.93725	−	7.93725i	0.398359	−	0.398359i	0.877654	+	0.479295i	$0.159107\pi$
$398$		0			0
$399$	−8.83485			−0.442296
$400$		0			0
$401$	12.3303			0.615746			0.307873	−	0.951427i	$-0.400383\pi$
$401$	12.3303			0.615746			0.307873	+	0.951427i	$0.400383\pi$
$402$		0			0
$403$	−2.74110	+	2.74110i	−0.136544	+	0.136544i
$404$		0			0
$405$	2.47495	−	11.8582i	0.122981	−	0.589239i
$406$		0			0
$407$	−22.7477	−	22.7477i	−1.12756	−	1.12756i
$408$		0			0
$409$			25.5826i			1.26498i	0.774570	+	0.632488i	$0.217966\pi$
$409$			25.5826i			1.26498i	−0.774570	+	0.632488i	$0.782034\pi$
$410$		0			0
$411$			11.1153i			0.548278i
$412$		0			0
$413$	−14.7701	−	14.7701i	−0.726789	−	0.726789i
$414$		0			0
$415$	8.37386	+	12.7913i	0.411057	+	0.627900i
$416$		0			0
$417$	−4.08712	+	4.08712i	−0.200147	+	0.200147i
$418$		0			0
$419$	0.190700			0.00931632			0.00465816	−	0.999989i	$-0.498517\pi$
$419$	0.190700			0.00931632			0.00465816	+	0.999989i	$0.498517\pi$
$420$		0			0
$421$	−2.74110			−0.133593			−0.0667966	−	0.997767i	$-0.521278\pi$
$421$	−2.74110			−0.133593			−0.0667966	+	0.997767i	$0.521278\pi$
$422$		0			0
$423$	2.04356	−	2.04356i	0.0993613	−	0.0993613i
$424$		0			0
$425$	−19.7477	+	7.74773i	−0.957905	+	0.375820i
$426$		0			0
$427$	−26.9898	−	26.9898i	−1.30613	−	1.30613i
$428$		0			0
$429$		−	6.92820i		−	0.334497i
$430$		0			0
$431$			16.7477i			0.806710i	0.915044	+	0.403355i	$0.132156\pi$
$431$			16.7477i			0.806710i	−0.915044	+	0.403355i	$0.867844\pi$
$432$		0			0
$433$	−14.5826	−	14.5826i	−0.700794	−	0.700794i	0.263787	−	0.964581i	$-0.415028\pi$
$433$	−14.5826	−	14.5826i	−0.700794	−	0.700794i	−0.964581	+	0.263787i	$0.915028\pi$
$434$		0			0
$435$	6.39590	−	4.18710i	0.306660	−	0.200756i
$436$		0			0
$437$	−2.74110	+	2.74110i	−0.131125	+	0.131125i
$438$		0			0
$439$	−29.4955			−1.40774			−0.703871	−	0.710328i	$-0.748547\pi$
$439$	−29.4955			−1.40774			−0.703871	+	0.710328i	$0.748547\pi$
$440$		0			0
$441$	−22.1652			−1.05548
$442$		0			0
$443$	−1.17985	+	1.17985i	−0.0560564	+	0.0560564i	−0.734579	−	0.678523i	$-0.762620\pi$
$443$	−1.17985	+	1.17985i	−0.0560564	+	0.0560564i	0.678523	+	0.734579i	$0.262620\pi$
$444$		0			0
$445$	6.92820	+	1.44600i	0.328428	+	0.0685470i
$446$		0			0
$447$	2.00000	+	2.00000i	0.0945968	+	0.0945968i
$448$		0			0
$449$		−	10.4174i		−	0.491629i	−0.969317	−	0.245814i	$-0.920945\pi$
$449$		−	10.4174i		−	0.491629i	0.969317	−	0.245814i	$-0.0790553\pi$
$450$		0			0
$451$		−	33.1950i		−	1.56309i
$452$		0			0
$453$	−5.82380	−	5.82380i	−0.273626	−	0.273626i
$454$		0			0
$455$	21.1652	+	4.41742i	0.992238	+	0.207092i
$456$		0			0
$457$	−3.41742	+	3.41742i	−0.159860	+	0.159860i	−0.782505	−	0.622644i	$-0.786058\pi$
$457$	−3.41742	+	3.41742i	−0.159860	+	0.159860i	0.622644	+	0.782505i	$0.286058\pi$
$458$		0			0
$459$	15.3024			0.714255
$460$		0			0
$461$	17.5112			0.815578			0.407789	−	0.913076i	$-0.366300\pi$
$461$	17.5112			0.815578			0.407789	+	0.913076i	$0.366300\pi$
$462$		0			0
$463$	16.7913	−	16.7913i	0.780357	−	0.780357i	−0.199534	−	0.979891i	$-0.563943\pi$
$463$	16.7913	−	16.7913i	0.780357	−	0.780357i	0.979891	+	0.199534i	$0.0639427\pi$
$464$		0			0
$465$	−1.91288	+	1.25227i	−0.0887076	+	0.0580728i
$466$		0			0
$467$	−7.57575	−	7.57575i	−0.350564	−	0.350564i	0.509755	−	0.860319i	$-0.329736\pi$
$467$	−7.57575	−	7.57575i	−0.350564	−	0.350564i	−0.860319	+	0.509755i	$0.829736\pi$
$468$		0			0
$469$			46.3284i			2.13925i
$470$		0			0
$471$		−	10.4174i		−	0.480010i
$472$		0			0
$473$	−36.3303	−	36.3303i	−1.67047	−	1.67047i
$474$		0			0
$475$	−15.8745	−	6.92820i	−0.728372	−	0.317888i
$476$		0			0
$477$	6.83285	−	6.83285i	0.312855	−	0.312855i
$478$		0			0
$479$	21.4955			0.982152			0.491076	−	0.871117i	$-0.336604\pi$
$479$	21.4955			0.982152			0.491076	+	0.871117i	$0.336604\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$	2.01810	−	2.01810i	0.0918268	−	0.0918268i
$484$		0			0
$485$	1.00905	+	1.54135i	0.0458186	+	0.0699891i
$486$		0			0
$487$	0.373864	+	0.373864i	0.0169414	+	0.0169414i	0.715527	−	0.698585i	$-0.246187\pi$
$487$	0.373864	+	0.373864i	0.0169414	+	0.0169414i	−0.698585	+	0.715527i	$0.746187\pi$
$488$		0			0
$489$			7.58258i			0.342896i
$490$		0			0
$491$			9.86001i			0.444976i	0.974935	+	0.222488i	$0.0714178\pi$
$491$			9.86001i			0.444976i	−0.974935	+	0.222488i	$0.928582\pi$
$492$		0			0
$493$	−15.8745	−	15.8745i	−0.714952	−	0.714952i
$494$		0			0
$495$	−5.16515	+	24.7477i	−0.232156	+	1.11233i
$496$		0			0
$497$	37.9129	−	37.9129i	1.70063	−	1.70063i
$498$		0			0
$499$	24.2487			1.08552			0.542761	−	0.839887i	$-0.317379\pi$
$499$	24.2487			1.08552			0.542761	+	0.839887i	$0.317379\pi$
$500$		0			0
$501$	−10.2414			−0.457552
$502$		0			0
$503$	17.5390	−	17.5390i	0.782026	−	0.782026i	−0.198146	−	0.980172i	$-0.563492\pi$
$503$	17.5390	−	17.5390i	0.782026	−	0.782026i	0.980172	+	0.198146i	$0.0634922\pi$
$504$		0			0
$505$	−1.66970	+	8.00000i	−0.0743006	+	0.355995i
$506$		0			0
$507$	−3.19795	−	3.19795i	−0.142026	−	0.142026i
$508$		0			0
$509$			38.4865i			1.70588i	0.522005	+	0.852942i	$0.325184\pi$
$509$			38.4865i			1.70588i	−0.522005	+	0.852942i	$0.674816\pi$
$510$		0			0
$511$			3.25227i			0.143872i
$512$		0			0
$513$	8.83485	+	8.83485i	0.390068	+	0.390068i
$514$		0			0
$515$	17.9681	+	27.4467i	0.791767	+	1.20944i
$516$		0			0
$517$	−3.46410	+	3.46410i	−0.152351	+	0.152351i
$518$		0			0
$519$	−7.91288			−0.347337
$520$		0			0
$521$	33.1652			1.45299			0.726496	−	0.687171i	$-0.241148\pi$
$521$	33.1652			1.45299			0.726496	+	0.687171i	$0.241148\pi$
$522$		0			0
$523$	15.9500	−	15.9500i	0.697443	−	0.697443i	−0.266415	−	0.963858i	$-0.585839\pi$
$523$	15.9500	−	15.9500i	0.697443	−	0.697443i	0.963858	+	0.266415i	$0.0858393\pi$
$524$		0			0
$525$	11.6874	+	5.10080i	0.510080	+	0.222617i
$526$		0			0
$527$	4.74773	+	4.74773i	0.206814	+	0.206814i
$528$		0			0
$529$			21.7477i			0.945553i
$530$		0			0
$531$			13.6657i			0.593041i
$532$		0			0
$533$	13.1334	+	13.1334i	0.568871	+	0.568871i
$534$		0			0
$535$	−21.9564	+	14.3739i	−0.949260	+	0.621436i
$536$		0			0
$537$	−3.91288	+	3.91288i	−0.168853	+	0.168853i
$538$		0			0
$539$	37.5728			1.61838
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$		0			0
$543$	−3.16515	+	3.16515i	−0.135830	+	0.135830i
$544$		0			0
$545$	−13.5826	−	2.83485i	−0.581814	−	0.121432i
$546$		0			0
$547$	−0.647551	−	0.647551i	−0.0276873	−	0.0276873i	0.693128	−	0.720815i	$-0.256232\pi$
$547$	−0.647551	−	0.647551i	−0.0276873	−	0.0276873i	−0.720815	+	0.693128i	$0.756232\pi$
$548$		0			0
$549$			24.9717i			1.06577i
$550$		0			0
$551$		−	18.3303i		−	0.780897i
$552$		0			0
$553$	33.4955	+	33.4955i	1.42437	+	1.42437i
$554$		0			0
$555$	10.3923	+	2.16900i	0.441129	+	0.0920689i
$556$		0			0
$557$	−10.2970	+	10.2970i	−0.436296	+	0.436296i	−0.890763	−	0.454467i	$-0.849830\pi$
$557$	−10.2970	+	10.2970i	−0.436296	+	0.436296i	0.454467	+	0.890763i	$0.349830\pi$
$558$		0			0
$559$	28.7477			1.21590
$560$		0			0
$561$	−12.0000			−0.506640
$562$		0			0
$563$	14.3133	−	14.3133i	0.603232	−	0.603232i	−0.337937	−	0.941169i	$-0.609729\pi$
$563$	14.3133	−	14.3133i	0.603232	−	0.603232i	0.941169	+	0.337937i	$0.109729\pi$
$564$		0			0
$565$	12.1244	−	7.93725i	0.510075	−	0.333923i
$566$		0			0
$567$	15.1216	+	15.1216i	0.635047	+	0.635047i
$568$		0			0
$569$			4.74773i			0.199035i	0.995036	+	0.0995175i	$0.0317299\pi$
$569$			4.74773i			0.199035i	−0.995036	+	0.0995175i	$0.968270\pi$
$570$		0			0
$571$		−	39.4002i		−	1.64885i	−0.565973	−	0.824424i	$-0.691499\pi$
$571$		−	39.4002i		−	1.64885i	0.565973	−	0.824424i	$-0.308501\pi$
$572$		0			0
$573$	6.20520	+	6.20520i	0.259226	+	0.259226i
$574$		0			0
$575$	5.20871	−	2.04356i	0.217218	−	0.0852224i
$576$		0			0
$577$	−11.7477	+	11.7477i	−0.489064	+	0.489064i	−0.908011	−	0.418947i	$-0.862399\pi$
$577$	−11.7477	+	11.7477i	−0.489064	+	0.489064i	0.418947	+	0.908011i	$0.362399\pi$
$578$		0			0
$579$	12.9427			0.537881
$580$		0			0
$581$	−26.9898			−1.11973
$582$		0			0
$583$	−11.5826	+	11.5826i	−0.479701	+	0.479701i
$584$		0			0
$585$	−7.74773	−	11.8348i	−0.320329	−	0.489311i
$586$		0			0
$587$	28.3604	+	28.3604i	1.17056	+	1.17056i	0.982077	+	0.188481i	$0.0603562\pi$
$587$	28.3604	+	28.3604i	1.17056	+	1.17056i	0.188481	+	0.982077i	$0.439644\pi$
$588$		0			0
$589$			5.48220i			0.225890i
$590$		0			0
$591$		−	2.41742i		−	0.0994395i
$592$		0			0
$593$	0.165151	+	0.165151i	0.00678195	+	0.00678195i	0.710490	−	0.703708i	$-0.248474\pi$
$593$	0.165151	+	0.165151i	0.00678195	+	0.00678195i	−0.703708	+	0.710490i	$0.748474\pi$
$594$		0			0
$595$	7.65120	−	36.6591i	0.313669	−	1.50288i
$596$		0			0
$597$	−1.82740	+	1.82740i	−0.0747905	+	0.0747905i
$598$		0			0
$599$	42.3303			1.72957			0.864785	−	0.502143i	$-0.167455\pi$
$599$	42.3303			1.72957			0.864785	+	0.502143i	$0.167455\pi$
$600$		0			0
$601$	2.74773			0.112082			0.0560411	−	0.998428i	$-0.482152\pi$
$601$	2.74773			0.112082			0.0560411	+	0.998428i	$0.482152\pi$
$602$		0			0
$603$	21.4322	−	21.4322i	0.872785	−	0.872785i
$604$		0			0
$605$	3.73025	−	17.8727i	0.151656	−	0.726629i
$606$		0			0
$607$	6.37386	+	6.37386i	0.258707	+	0.258707i	0.824528	−	0.565821i	$-0.191441\pi$
$607$	6.37386	+	6.37386i	0.258707	+	0.258707i	−0.565821	+	0.824528i	$0.691441\pi$
$608$		0			0
$609$			13.4955i			0.546863i
$610$		0			0
$611$		−	2.74110i		−	0.110893i
$612$		0			0
$613$	−8.66025	−	8.66025i	−0.349784	−	0.349784i	0.510245	−	0.860029i	$-0.329555\pi$
$613$	−8.66025	−	8.66025i	−0.349784	−	0.349784i	−0.860029	+	0.510245i	$0.829555\pi$
$614$		0			0
$615$	6.00000	+	9.16515i	0.241943	+	0.369575i
$616$		0			0
$617$	−3.00000	+	3.00000i	−0.120775	+	0.120775i	−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−3.00000	+	3.00000i	−0.120775	+	0.120775i	0.644136	+	0.764911i	$0.277217\pi$
$618$		0			0
$619$	−29.7309			−1.19499			−0.597493	−	0.801874i	$-0.703836\pi$
$619$	−29.7309			−1.19499			−0.597493	+	0.801874i	$0.703836\pi$
$620$		0			0
$621$	−4.03620			−0.161967
$622$		0			0
$623$	−8.83485	+	8.83485i	−0.353961	+	0.353961i
$624$		0			0
$625$	17.0000	+	18.3303i	0.680000	+	0.733212i
$626$		0			0
$627$	−6.92820	−	6.92820i	−0.276686	−	0.276686i
$628$		0			0
$629$		−	31.1769i		−	1.24310i
$630$		0			0
$631$			47.0780i			1.87415i	0.349132	+	0.937073i	$0.386476\pi$
$631$			47.0780i			1.87415i	−0.349132	+	0.937073i	$0.613524\pi$
$632$		0			0
$633$	−3.49545	−	3.49545i	−0.138932	−	0.138932i
$634$		0			0
$635$	3.19795	−	2.09355i	0.126907	−	0.0830800i
$636$		0			0
$637$	−14.8655	+	14.8655i	−0.588991	+	0.588991i
$638$		0			0
$639$	−35.0780			−1.38767
$640$		0			0
$641$	25.9129			1.02350			0.511749	−	0.859135i	$-0.328998\pi$
$641$	25.9129			1.02350			0.511749	+	0.859135i	$0.328998\pi$
$642$		0			0
$643$	18.6911	−	18.6911i	0.737103	−	0.737103i	−0.234913	−	0.972016i	$-0.575481\pi$
$643$	18.6911	−	18.6911i	0.737103	−	0.737103i	0.972016	+	0.234913i	$0.0754805\pi$
$644$		0			0
$645$	16.5975	+	3.46410i	0.653526	+	0.136399i
$646$		0			0
$647$	−0.460985	−	0.460985i	−0.0181232	−	0.0181232i	0.697987	−	0.716110i	$-0.254079\pi$
$647$	−0.460985	−	0.460985i	−0.0181232	−	0.0181232i	−0.716110	+	0.697987i	$0.754079\pi$
$648$		0			0
$649$		−	23.1652i		−	0.909312i
$650$		0			0
$651$		−	4.03620i		−	0.158191i
$652$		0			0
$653$	11.4014	+	11.4014i	0.446170	+	0.446170i	0.894079	−	0.447909i	$-0.147831\pi$
$653$	11.4014	+	11.4014i	0.446170	+	0.446170i	−0.447909	+	0.894079i	$0.647831\pi$
$654$		0			0
$655$	−24.7477	−	5.16515i	−0.966974	−	0.201819i
$656$		0			0
$657$	1.50455	−	1.50455i	0.0586979	−	0.0586979i
$658$		0			0
$659$	3.84550			0.149800			0.0748998	−	0.997191i	$-0.476136\pi$
$659$	3.84550			0.149800			0.0748998	+	0.997191i	$0.476136\pi$
$660$		0			0
$661$	41.4183			1.61099			0.805493	−	0.592605i	$-0.201901\pi$
$661$	41.4183			1.61099			0.805493	+	0.592605i	$0.201901\pi$
$662$		0			0
$663$	4.74773	−	4.74773i	0.184386	−	0.184386i
$664$		0			0
$665$	25.5826	−	16.7477i	0.992050	−	0.649449i
$666$		0			0
$667$	4.18710	+	4.18710i	0.162125	+	0.162125i
$668$		0			0
$669$		−	11.3060i		−	0.437115i
$670$		0			0
$671$		−	42.3303i		−	1.63414i
$672$		0			0
$673$	−18.5826	−	18.5826i	−0.716306	−	0.716306i	0.251541	−	0.967847i	$-0.419063\pi$
$673$	−18.5826	−	18.5826i	−0.716306	−	0.716306i	−0.967847	+	0.251541i	$0.919063\pi$
$674$		0			0
$675$	−6.58660	−	16.7882i	−0.253519	−	0.646178i
$676$		0			0
$677$	18.3296	−	18.3296i	0.704462	−	0.704462i	−0.260903	−	0.965365i	$-0.584020\pi$
$677$	18.3296	−	18.3296i	0.704462	−	0.704462i	0.965365	+	0.260903i	$0.0840202\pi$
$678$		0			0
$679$	−3.25227			−0.124811
$680$		0			0
$681$	6.08712			0.233259
$682$		0			0
$683$	6.85275	−	6.85275i	0.262213	−	0.262213i	−0.563739	−	0.825953i	$-0.690638\pi$
$683$	6.85275	−	6.85275i	0.262213	−	0.262213i	0.825953	+	0.563739i	$0.190638\pi$
$684$		0			0
$685$	−21.0707	−	32.1860i	−0.805069	−	1.22976i
$686$		0			0
$687$	−1.58258	−	1.58258i	−0.0603790	−	0.0603790i
$688$		0			0
$689$		−	9.16515i		−	0.349164i
$690$		0			0
$691$		−	32.4720i		−	1.23529i	−0.786456	−	0.617647i	$-0.788086\pi$
$691$		−	32.4720i		−	1.23529i	0.786456	−	0.617647i	$-0.211914\pi$
$692$		0			0
$693$	−31.5583	−	31.5583i	−1.19880	−	1.19880i
$694$		0			0
$695$	4.08712	−	19.5826i	0.155033	−	0.742809i
$696$		0			0
$697$	22.7477	−	22.7477i	0.861632	−	0.861632i
$698$		0			0
$699$	−5.63310			−0.213063
$700$		0			0
$701$	−19.8709			−0.750514			−0.375257	−	0.926921i	$-0.622446\pi$
$701$	−19.8709			−0.750514			−0.375257	+	0.926921i	$0.622446\pi$
$702$		0			0
$703$	18.0000	−	18.0000i	0.678883	−	0.678883i
$704$		0			0
$705$	0.330303	−	1.58258i	0.0124399	−	0.0596032i
$706$		0			0
$707$	−10.2016	−	10.2016i	−0.383671	−	0.383671i
$708$		0			0
$709$		−	4.91010i		−	0.184403i	−0.995740	−	0.0922014i	$-0.970610\pi$
$709$		−	4.91010i		−	0.184403i	0.995740	−	0.0922014i	$-0.0293904\pi$
$710$		0			0
$711$		−	30.9909i		−	1.16225i
$712$		0			0
$713$	−1.25227	−	1.25227i	−0.0468980	−	0.0468980i
$714$		0			0
$715$	13.1334	+	20.0616i	0.491162	+	0.750262i
$716$		0			0
$717$	−1.44600	+	1.44600i	−0.0540019	+	0.0540019i
$718$		0			0
$719$	−39.8258			−1.48525			−0.742625	−	0.669707i	$-0.766420\pi$
$719$	−39.8258			−1.48525			−0.742625	+	0.669707i	$0.766420\pi$
$720$		0			0
$721$	−57.9129			−2.15679
$722$		0			0
$723$	−4.91010	+	4.91010i	−0.182609	+	0.182609i
$724$		0			0
$725$	−10.5830	+	24.2487i	−0.393043	+	0.900575i
$726$		0			0
$727$	−5.95644	−	5.95644i	−0.220912	−	0.220912i	0.587970	−	0.808882i	$-0.299927\pi$
$727$	−5.95644	−	5.95644i	−0.220912	−	0.220912i	−0.808882	+	0.587970i	$0.799927\pi$
$728$		0			0
$729$		−	7.00000i		−	0.259259i
$730$		0			0
$731$		−	49.7925i		−	1.84164i
$732$		0			0
$733$	17.6066	+	17.6066i	0.650313	+	0.650313i	0.953068	−	0.302755i	$-0.0979065\pi$
$733$	17.6066	+	17.6066i	0.650313	+	0.650313i	−0.302755	+	0.953068i	$0.597906\pi$
$734$		0			0
$735$	−10.3739	+	6.79129i	−0.382646	+	0.250500i
$736$		0			0
$737$	−36.3303	+	36.3303i	−1.33824	+	1.33824i
$738$		0			0
$739$	−2.01810			−0.0742371			−0.0371185	−	0.999311i	$-0.511818\pi$
$739$	−2.01810			−0.0742371			−0.0371185	+	0.999311i	$0.511818\pi$
$740$		0			0
$741$	5.48220			0.201394
$742$		0			0
$743$	−17.2087	+	17.2087i	−0.631326	+	0.631326i	−0.948401	−	0.317074i	$-0.897300\pi$
$743$	−17.2087	+	17.2087i	−0.631326	+	0.631326i	0.317074	+	0.948401i	$0.397300\pi$
$744$		0			0
$745$	−9.58258	−	2.00000i	−0.351078	−	0.0732743i
$746$		0			0
$747$	12.4859	+	12.4859i	0.456834	+	0.456834i
$748$		0			0
$749$		−	46.3284i		−	1.69280i
$750$		0			0
$751$		−	23.0780i		−	0.842129i	−0.907031	−	0.421065i	$-0.861657\pi$
$751$		−	23.0780i		−	0.842129i	0.907031	−	0.421065i	$-0.138343\pi$
$752$		0			0
$753$	8.33030	+	8.33030i	0.303573	+	0.303573i
$754$		0			0
$755$	27.9035	+	5.82380i	1.01551	+	0.211950i
$756$		0			0
$757$	20.3477	−	20.3477i	0.739548	−	0.739548i	−0.232942	−	0.972491i	$-0.574835\pi$
$757$	20.3477	−	20.3477i	0.739548	−	0.739548i	0.972491	+	0.232942i	$0.0748353\pi$
$758$		0			0
$759$	3.16515			0.114888
$760$		0			0
$761$	−6.00000			−0.217500			−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000			−0.217500			−0.108750	+	0.994069i	$0.534685\pi$
$762$		0			0
$763$	17.3205	−	17.3205i	0.627044	−	0.627044i
$764$		0			0
$765$	−20.4986	+	13.4195i	−0.741127	+	0.485181i
$766$		0			0
$767$	9.16515	+	9.16515i	0.330934	+	0.330934i
$768$		0			0
$769$		−	37.4955i		−	1.35212i	−0.736846	−	0.676060i	$-0.763686\pi$
$769$		−	37.4955i		−	1.35212i	0.736846	−	0.676060i	$-0.236314\pi$
$770$		0			0
$771$			18.0435i			0.649821i
$772$		0			0
$773$	−0.286051	−	0.286051i	−0.0102885	−	0.0102885i	0.701944	−	0.712232i	$-0.252316\pi$
$773$	−0.286051	−	0.286051i	−0.0102885	−	0.0102885i	−0.712232	+	0.701944i	$0.752316\pi$
$774$		0			0
$775$	3.16515	−	7.25227i	0.113696	−	0.260509i
$776$		0			0
$777$	−13.2523	+	13.2523i	−0.475423	+	0.475423i
$778$		0			0
$779$	26.2668			0.941106
$780$		0			0
$781$	59.4618			2.12771
$782$		0			0
$783$	13.4955	−	13.4955i	0.482288	−	0.482288i
$784$		0			0
$785$	19.7477	+	30.1652i	0.704827	+	1.07664i
$786$		0			0
$787$	−20.7092	−	20.7092i	−0.738202	−	0.738202i	0.234028	−	0.972230i	$-0.424809\pi$
$787$	−20.7092	−	20.7092i	−0.738202	−	0.738202i	−0.972230	+	0.234028i	$0.924809\pi$
$788$		0			0
$789$		−	17.1696i		−	0.611254i
$790$		0			0
$791$			25.5826i			0.909612i
$792$		0			0
$793$	16.7477	+	16.7477i	0.594729	+	0.594729i
$794$		0			0
$795$	1.10440	−	5.29150i	0.0391691	−	0.187670i
$796$		0			0
$797$	−34.9271	+	34.9271i	−1.23718	+	1.23718i	−0.276032	+	0.961149i	$0.589019\pi$
$797$	−34.9271	+	34.9271i	−1.23718	+	1.23718i	−0.961149	+	0.276032i	$0.910981\pi$
$798$		0			0
$799$	−4.74773			−0.167963
$800$		0			0
$801$	8.17424			0.288823
$802$		0			0
$803$	−2.55040	+	2.55040i	−0.0900017	+	0.0900017i
$804$		0			0
$805$	−2.01810	+	9.66930i	−0.0711287	+	0.340798i
$806$		0			0
$807$	10.8348	+	10.8348i	0.381405	+	0.381405i
$808$		0			0
$809$		−	30.3303i		−	1.06636i	−0.846003	−	0.533178i	$-0.820997\pi$
$809$		−	30.3303i		−	1.06636i	0.846003	−	0.533178i	$-0.179003\pi$
$810$		0			0
$811$		−	2.16900i		−	0.0761639i	−0.999275	−	0.0380820i	$-0.987875\pi$
$811$		−	2.16900i		−	0.0761639i	0.999275	−	0.0380820i	$-0.0121248\pi$
$812$		0			0
$813$	3.99640	+	3.99640i	0.140160	+	0.140160i
$814$		0			0
$815$	−14.3739	−	21.9564i	−0.503494	−	0.769101i
$816$		0			0
$817$	28.7477	−	28.7477i	1.00576	−	1.00576i
$818$		0			0
$819$	24.9717			0.872582
$820$		0			0
$821$	−54.8933			−1.91579			−0.957895	−	0.287118i	$-0.907303\pi$
$821$	−54.8933			−1.91579			−0.957895	+	0.287118i	$0.907303\pi$
$822$		0			0
$823$	3.20871	−	3.20871i	0.111849	−	0.111849i	−0.648967	−	0.760816i	$-0.724799\pi$
$823$	3.20871	−	3.20871i	0.111849	−	0.111849i	0.760816	+	0.648967i	$0.224799\pi$
$824$		0			0
$825$	5.16515	+	13.1652i	0.179827	+	0.458352i
$826$		0			0
$827$	14.1226	+	14.1226i	0.491089	+	0.491089i	0.908649	−	0.417560i	$-0.137115\pi$
$827$	14.1226	+	14.1226i	0.491089	+	0.491089i	−0.417560	+	0.908649i	$0.637115\pi$
$828$		0			0
$829$		−	7.65120i		−	0.265737i	−0.991134	−	0.132869i	$-0.957581\pi$
$829$		−	7.65120i		−	0.265737i	0.991134	−	0.132869i	$-0.0424188\pi$
$830$		0			0
$831$			5.40833i			0.187613i
$832$		0			0
$833$	25.7477	+	25.7477i	0.892106	+	0.892106i
$834$		0			0
$835$	29.6555	−	19.4141i	1.02627	−	0.671851i
$836$		0			0
$837$	−4.03620	+	4.03620i	−0.139512	+	0.139512i
$838$		0			0
$839$	−30.3303			−1.04712			−0.523559	−	0.851989i	$-0.675396\pi$
$839$	−30.3303			−1.04712			−0.523559	+	0.851989i	$0.675396\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		0			0
$843$	4.91010	−	4.91010i	0.169113	−	0.169113i
$844$		0			0
$845$	15.3223	+	3.19795i	0.527103	+	0.110013i
$846$		0			0
$847$	22.7913	+	22.7913i	0.783118	+	0.783118i
$848$		0			0
$849$			15.7568i			0.540773i
$850$		0			0
$851$			8.22330i			0.281891i
$852$		0			0
$853$	36.9452	+	36.9452i	1.26498	+	1.26498i	0.948650	+	0.316329i	$0.102450\pi$
$853$	36.9452	+	36.9452i	1.26498	+	1.26498i	0.316329	+	0.948650i	$0.397550\pi$
$854$		0			0
$855$	−19.5826	−	4.08712i	−0.669710	−	0.139777i
$856$		0			0
$857$	−39.3303	+	39.3303i	−1.34350	+	1.34350i	−0.450947	+	0.892551i	$0.648914\pi$
$857$	−39.3303	+	39.3303i	−1.34350	+	1.34350i	−0.892551	+	0.450947i	$0.851086\pi$
$858$		0			0
$859$	−2.01810			−0.0688567			−0.0344284	−	0.999407i	$-0.510961\pi$
$859$	−2.01810			−0.0688567			−0.0344284	+	0.999407i	$0.510961\pi$
$860$		0			0
$861$	−19.3386			−0.659058
$862$		0			0
$863$	−32.7042	+	32.7042i	−1.11326	+	1.11326i	−0.120556	+	0.992706i	$0.538468\pi$
$863$	−32.7042	+	32.7042i	−1.11326	+	1.11326i	−0.992706	+	0.120556i	$0.961532\pi$
$864$		0			0
$865$	22.9129	−	15.0000i	0.779061	−	0.510015i
$866$		0			0
$867$	−0.456850	−	0.456850i	−0.0155154	−	0.0155154i
$868$		0			0
$869$			52.5336i			1.78208i
$870$		0			0
$871$		−	28.7477i		−	0.974080i
$872$		0			0
$873$	1.50455	+	1.50455i	0.0509212	+	0.0509212i
$874$		0			0
$875$	−43.5119	+	7.38505i	−1.47097	+	0.249660i
$876$		0			0
$877$	19.7756	−	19.7756i	0.667773	−	0.667773i	−0.289427	−	0.957200i	$-0.593465\pi$
$877$	19.7756	−	19.7756i	0.667773	−	0.667773i	0.957200	+	0.289427i	$0.0934647\pi$
$878$		0			0
$879$	21.4083			0.722085
$880$		0			0
$881$	−55.5826			−1.87262			−0.936312	−	0.351169i	$-0.885784\pi$
$881$	−55.5826			−1.87262			−0.936312	+	0.351169i	$0.885784\pi$
$882$		0			0
$883$	−22.1552	+	22.1552i	−0.745581	+	0.745581i	−0.973646	−	0.228065i	$-0.926760\pi$
$883$	−22.1552	+	22.1552i	−0.745581	+	0.745581i	0.228065	+	0.973646i	$0.426760\pi$
$884$		0			0
$885$	4.18710	+	6.39590i	0.140748	+	0.214996i
$886$		0			0
$887$	−21.9564	−	21.9564i	−0.737225	−	0.737225i	0.234815	−	0.972040i	$-0.424552\pi$
$887$	−21.9564	−	21.9564i	−0.737225	−	0.737225i	−0.972040	+	0.234815i	$0.924552\pi$
$888$		0			0
$889$			6.74773i			0.226312i
$890$		0			0
$891$			23.7164i			0.794530i
$892$		0			0
$893$	−2.74110	−	2.74110i	−0.0917275	−	0.0917275i
$894$		0			0
$895$	3.91288	−	18.7477i	0.130793	−	0.626667i
$896$		0			0
$897$	−1.25227	+	1.25227i	−0.0418122	+	0.0418122i
$898$		0			0
$899$	8.37420			0.279295
$900$		0			0
$901$	−15.8745			−0.528857
$902$		0			0
$903$	−21.1652	+	21.1652i	−0.704332	+	0.704332i
$904$		0			0
$905$	3.16515	−	15.1652i	0.105213	−	0.504107i
$906$		0			0
$907$	−11.0399	−	11.0399i	−0.366572	−	0.366572i	0.499653	−	0.866226i	$-0.333461\pi$
$907$	−11.0399	−	11.0399i	−0.366572	−	0.366572i	−0.866226	+	0.499653i	$0.833461\pi$
$908$		0			0
$909$			9.43880i			0.313065i
$910$		0			0
$911$			49.5826i			1.64274i	0.570393	+	0.821372i	$0.306791\pi$
$911$			49.5826i			1.64274i	−0.570393	+	0.821372i	$0.693209\pi$
$912$		0			0
$913$	−21.1652	−	21.1652i	−0.700464	−	0.700464i
$914$		0			0
$915$	7.65120	+	11.6874i	0.252941	+	0.386374i
$916$		0			0
$917$	31.5583	−	31.5583i	1.04215	−	1.04215i
$918$		0			0
$919$	42.3303			1.39635			0.698174	−	0.715928i	$-0.253996\pi$
$919$	42.3303			1.39635			0.698174	+	0.715928i	$0.253996\pi$
$920$		0			0
$921$	−1.25227			−0.0412638
$922$		0			0
$923$	−23.5257	+	23.5257i	−0.774358	+	0.774358i
$924$		0			0
$925$	−34.2041	+	13.4195i	−1.12462	+	0.441229i
$926$		0			0
$927$	26.7913	+	26.7913i	0.879941	+	0.879941i
$928$		0			0
$929$		−	19.9129i		−	0.653320i	−0.945142	−	0.326660i	$-0.894077\pi$
$929$		−	19.9129i		−	0.653320i	0.945142	−	0.326660i	$-0.105923\pi$
$930$		0			0
$931$			29.7309i			0.974391i
$932$		0			0
$933$	4.75920	+	4.75920i	0.155809	+	0.155809i
$934$		0			0
$935$	34.7477	−	22.7477i	1.13637	−	0.743930i
$936$		0			0
$937$	−34.1652	+	34.1652i	−1.11613	+	1.11613i	−0.123822	+	0.992304i	$0.539515\pi$
$937$	−34.1652	+	34.1652i	−1.11613	+	1.11613i	−0.992304	+	0.123822i	$0.960485\pi$
$938$		0			0
$939$	−2.35970			−0.0770059
$940$		0			0
$941$	24.4394			0.796702			0.398351	−	0.917233i	$-0.369583\pi$
$941$	24.4394			0.796702			0.398351	+	0.917233i	$0.369583\pi$
$942$		0			0
$943$	−6.00000	+	6.00000i	−0.195387	+	0.195387i
$944$		0			0
$945$	31.1652	+	6.50455i	1.01380	+	0.211593i
$946$		0			0
$947$	14.6947	+	14.6947i	0.477512	+	0.477512i	0.904335	−	0.426823i	$-0.140367\pi$
$947$	14.6947	+	14.6947i	0.477512	+	0.477512i	−0.426823	+	0.904335i	$0.640367\pi$
$948$		0			0
$949$		−	2.01810i		−	0.0655103i
$950$		0			0
$951$		−	16.0871i		−	0.521661i
$952$		0			0
$953$	10.9129	+	10.9129i	0.353503	+	0.353503i	0.861411	−	0.507908i	$-0.169581\pi$
$953$	10.9129	+	10.9129i	0.353503	+	0.353503i	−0.507908	+	0.861411i	$0.669581\pi$
$954$		0			0
$955$	−29.7309	−	6.20520i	−0.962070	−	0.200796i
$956$		0			0
$957$	−10.5830	+	10.5830i	−0.342100	+	0.342100i
$958$		0			0
$959$	67.9129			2.19302
$960$		0			0
$961$	28.4955			0.919208
$962$		0			0
$963$	−21.4322	+	21.4322i	−0.690642	+	0.690642i
$964$		0			0
$965$	−37.4775	+	24.5348i	−1.20644	+	0.789802i
$966$		0			0
$967$	8.79129	+	8.79129i	0.282709	+	0.282709i	0.834188	−	0.551480i	$-0.185937\pi$
$967$	8.79129	+	8.79129i	0.282709	+	0.282709i	−0.551480	+	0.834188i	$0.685937\pi$
$968$		0			0
$969$		−	9.49545i		−	0.305038i
$970$		0			0
$971$		−	37.5728i		−	1.20577i	−0.797828	−	0.602885i	$-0.794018\pi$
$971$		−	37.5728i		−	1.20577i	0.797828	−	0.602885i	$-0.205982\pi$
$972$		0			0
$973$	24.9717	+	24.9717i	0.800556	+	0.800556i
$974$		0			0
$975$	−7.25227	−	3.16515i	−0.232259	−	0.101366i
$976$		0			0
$977$	28.5826	−	28.5826i	0.914438	−	0.914438i	−0.0821799	−	0.996618i	$-0.526188\pi$
$977$	28.5826	−	28.5826i	0.914438	−	0.914438i	0.996618	+	0.0821799i	$0.0261882\pi$
$978$		0			0
$979$	−13.8564			−0.442853
$980$		0			0
$981$	−16.0254			−0.511652
$982$		0			0
$983$	−26.7042	+	26.7042i	−0.851731	+	0.851731i	−0.990346	−	0.138616i	$-0.955735\pi$
$983$	−26.7042	+	26.7042i	−0.851731	+	0.851731i	0.138616	+	0.990346i	$0.455735\pi$
$984$		0			0
$985$	4.58258	+	7.00000i	0.146013	+	0.223039i
$986$		0			0
$987$	2.01810	+	2.01810i	0.0642369	+	0.0642369i
$988$		0			0
$989$			13.1334i			0.417618i
$990$		0			0
$991$		−	3.25227i		−	0.103312i	−0.998665	−	0.0516559i	$-0.983550\pi$
$991$		−	3.25227i		−	0.103312i	0.998665	−	0.0516559i	$-0.0164499\pi$
$992$		0			0
$993$	2.83485	+	2.83485i	0.0899612	+	0.0899612i
$994$		0			0
$995$	1.82740	−	8.75560i	0.0579325	−	0.277571i
$996$		0			0
$997$	−17.6066	+	17.6066i	−0.557605	+	0.557605i	−0.928625	−	0.371020i	$-0.879008\pi$
$997$	−17.6066	+	17.6066i	−0.557605	+	0.557605i	0.371020	+	0.928625i	$0.379008\pi$
$998$		0			0
$999$	26.5045			0.838567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.n.1023.3		8
4.3	odd	2		1280.2.n.p.1023.2		8
5.2	odd	4		1280.2.n.p.767.2		8
8.3	odd	2		1280.2.n.p.1023.3		8
8.5	even	2	inner	1280.2.n.n.1023.2		8
16.3	odd	4		320.2.o.e.223.2	✓	8
16.5	even	4		320.2.o.f.223.2	yes	8
16.11	odd	4		320.2.o.e.223.3	yes	8
16.13	even	4		320.2.o.f.223.3	yes	8
20.7	even	4	inner	1280.2.n.n.767.3		8
40.27	even	4	inner	1280.2.n.n.767.2		8
40.37	odd	4		1280.2.n.p.767.3		8
80.3	even	4		1600.2.o.e.607.3		8
80.13	odd	4		1600.2.o.l.607.2		8
80.19	odd	4		1600.2.o.l.543.3		8
80.27	even	4		320.2.o.f.287.3	yes	8
80.29	even	4		1600.2.o.e.543.2		8
80.37	odd	4		320.2.o.e.287.2	yes	8
80.43	even	4		1600.2.o.e.607.2		8
80.53	odd	4		1600.2.o.l.607.3		8
80.59	odd	4		1600.2.o.l.543.2		8
80.67	even	4		320.2.o.f.287.2	yes	8
80.69	even	4		1600.2.o.e.543.3		8
80.77	odd	4		320.2.o.e.287.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
320.2.o.e.223.2	✓	8	16.3	odd	4
320.2.o.e.223.3	yes	8	16.11	odd	4
320.2.o.e.287.2	yes	8	80.37	odd	4
320.2.o.e.287.3	yes	8	80.77	odd	4
320.2.o.f.223.2	yes	8	16.5	even	4
320.2.o.f.223.3	yes	8	16.13	even	4
320.2.o.f.287.2	yes	8	80.67	even	4
320.2.o.f.287.3	yes	8	80.27	even	4
1280.2.n.n.767.2		8	40.27	even	4	inner
1280.2.n.n.767.3		8	20.7	even	4	inner
1280.2.n.n.1023.2		8	8.5	even	2	inner
1280.2.n.n.1023.3		8	1.1	even	1	trivial
1280.2.n.p.767.2		8	5.2	odd	4
1280.2.n.p.767.3		8	40.37	odd	4
1280.2.n.p.1023.2		8	4.3	odd	2
1280.2.n.p.1023.3		8	8.3	odd	2
1600.2.o.e.543.2		8	80.29	even	4
1600.2.o.e.543.3		8	80.69	even	4
1600.2.o.e.607.2		8	80.43	even	4
1600.2.o.e.607.3		8	80.3	even	4
1600.2.o.l.543.2		8	80.59	odd	4
1600.2.o.l.543.3		8	80.19	odd	4
1600.2.o.l.607.2		8	80.13	odd	4
1600.2.o.l.607.3		8	80.53	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.456850 - 0.456850i) q^{3} +(-0.456850 + 2.18890i) q^{5} +(-2.79129 - 2.79129i) q^{7} +2.58258i q^{9} +O(q^{10})\)	\(q+(0.456850 - 0.456850i) q^{3} +(-0.456850 + 2.18890i) q^{5} +(-2.79129 - 2.79129i) q^{7} +2.58258i q^{9} -4.37780i q^{11} +(1.73205 + 1.73205i) q^{13} +(0.791288 + 1.20871i) q^{15} +(3.00000 - 3.00000i) q^{17} +3.46410 q^{19} -2.55040 q^{21} +(-0.791288 + 0.791288i) q^{23} +(-4.58258 - 2.00000i) q^{25} +(2.55040 + 2.55040i) q^{27} -5.29150i q^{29} +1.58258i q^{31} +(-2.00000 - 2.00000i) q^{33} +(7.38505 - 4.83465i) q^{35} +(5.19615 - 5.19615i) q^{37} +1.58258 q^{39} +7.58258 q^{41} +(8.29875 - 8.29875i) q^{43} +(-5.65300 - 1.17985i) q^{45} +(-0.791288 - 0.791288i) q^{47} +8.58258i q^{49} -2.74110i q^{51} +(-2.64575 - 2.64575i) q^{53} +(9.58258 + 2.00000i) q^{55} +(1.58258 - 1.58258i) q^{57} +5.29150 q^{59} +9.66930 q^{61} +(7.20871 - 7.20871i) q^{63} +(-4.58258 + 3.00000i) q^{65} +(-8.29875 - 8.29875i) q^{67} +0.723000i q^{69} +13.5826i q^{71} +(-0.582576 - 0.582576i) q^{73} +(-3.00725 + 1.17985i) q^{75} +(-12.2197 + 12.2197i) q^{77} -12.0000 q^{79} -5.41742 q^{81} +(4.83465 - 4.83465i) q^{83} +(5.19615 + 7.93725i) q^{85} +(-2.41742 - 2.41742i) q^{87} -3.16515i q^{89} -9.66930i q^{91} +(0.723000 + 0.723000i) q^{93} +(-1.58258 + 7.58258i) q^{95} +(0.582576 - 0.582576i) q^{97} +11.3060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^7	\( 8 q - 4 q^{7} - 12 q^{15} + 24 q^{17} + 12 q^{23} - 16 q^{33} - 24 q^{39} + 24 q^{41} + 12 q^{47} + 40 q^{55} - 24 q^{57} + 76 q^{63} + 32 q^{73} - 96 q^{79} - 80 q^{81} - 56 q^{87} + 24 q^{95} - 32 q^{97}+O(q^{100}) \) 8 * q - 4 * q^7 - 12 * q^15 + 24 * q^17 + 12 * q^23 - 16 * q^33 - 24 * q^39 + 24 * q^41 + 12 * q^47 + 40 * q^55 - 24 * q^57 + 76 * q^63 + 32 * q^73 - 96 * q^79 - 80 * q^81 - 56 * q^87 + 24 * q^95 - 32 * q^97

Introduction

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