LMFDB - Embedded newform 1280.2.n.m.1023.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1280,2,Mod(767,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.767"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [8,0,-4,0,0,0,0,0,0,0,0,0,0] 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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1023.4
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1280.1023
Dual form			1280.2.n.m.767.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.618034 - 0.618034i) q^{3} +(1.90211 - 1.17557i) q^{5} +(-1.90211 - 1.90211i) q^{7} +2.23607i q^{9} -3.23607i q^{11} +(0.726543 + 0.726543i) q^{13} +(0.449028 - 1.90211i) q^{15} +(-1.00000 + 1.00000i) q^{17} +2.00000 q^{19} -2.35114 q^{21} +(4.25325 - 4.25325i) q^{23} +(2.23607 - 4.47214i) q^{25} +(3.23607 + 3.23607i) q^{27} -6.15537i q^{29} -8.50651i q^{31} +(-2.00000 - 2.00000i) q^{33} +(-5.85410 - 1.38197i) q^{35} +(-0.726543 + 0.726543i) q^{37} +0.898056 q^{39} -5.70820 q^{41} +(-4.61803 + 4.61803i) q^{43} +(2.62866 + 4.25325i) q^{45} +(-3.35520 - 3.35520i) q^{47} +0.236068i q^{49} +1.23607i q^{51} +(3.07768 + 3.07768i) q^{53} +(-3.80423 - 6.15537i) q^{55} +(1.23607 - 1.23607i) q^{57} -0.472136 q^{59} +0.898056 q^{61} +(4.25325 - 4.25325i) q^{63} +(2.23607 + 0.527864i) q^{65} +(4.61803 + 4.61803i) q^{67} -5.25731i q^{69} -11.4127i q^{71} +(4.70820 + 4.70820i) q^{73} +(-1.38197 - 4.14590i) q^{75} +(-6.15537 + 6.15537i) q^{77} -2.90617 q^{79} -2.70820 q^{81} +(-6.61803 + 6.61803i) q^{83} +(-0.726543 + 3.07768i) q^{85} +(-3.80423 - 3.80423i) q^{87} +2.47214i q^{89} -2.76393i q^{91} +(-5.25731 - 5.25731i) q^{93} +(3.80423 - 2.35114i) q^{95} +(4.23607 - 4.23607i) q^{97} +7.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{17} + 16 q^{19} + 8 q^{27} - 16 q^{33} - 20 q^{35} + 8 q^{41} - 28 q^{43} - 8 q^{57} + 32 q^{59} + 28 q^{67} - 16 q^{73} - 20 q^{75} + 32 q^{81} - 44 q^{83} + 16 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^17 + 16 * q^19 + 8 * q^27 - 16 * q^33 - 20 * q^35 + 8 * q^41 - 28 * q^43 - 8 * q^57 + 32 * q^59 + 28 * q^67 - 16 * q^73 - 20 * q^75 + 32 * q^81 - 44 * q^83 + 16 * q^97 + 40 * q^99

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
$3$	0.618034	−	0.618034i	0.356822	−	0.356822i	−0.505818	−	0.862640i	$-0.668809\pi$
$3$	0.618034	−	0.618034i	0.356822	−	0.356822i	0.862640	+	0.505818i	$0.168809\pi$
$4$		0			0
$5$	1.90211	−	1.17557i	0.850651	−	0.525731i
$5$	1.90211	−	1.17557i	0.850651	−	0.525731i
$6$		0			0
$7$	−1.90211	−	1.90211i	−0.718931	−	0.718931i	0.249455	−	0.968386i	$-0.419748\pi$
$7$	−1.90211	−	1.90211i	−0.718931	−	0.718931i	−0.968386	+	0.249455i	$0.919748\pi$
$8$		0			0
$9$			2.23607i			0.745356i
$10$		0			0
$11$		−	3.23607i		−	0.975711i	−0.872924	−	0.487856i	$-0.837779\pi$
$11$		−	3.23607i		−	0.975711i	0.872924	−	0.487856i	$-0.162221\pi$
$12$		0			0
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	0.800645	−	0.599139i	$-0.204490\pi$
$13$	0.726543	+	0.726543i	0.201507	+	0.201507i	−0.599139	+	0.800645i	$0.704490\pi$
$14$		0			0
$15$	0.449028	−	1.90211i	0.115939	−	0.491123i
$16$		0			0
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$		0			0
$21$	−2.35114			−0.513061
$22$		0			0
$23$	4.25325	−	4.25325i	0.886865	−	0.886865i	−0.107356	−	0.994221i	$-0.534238\pi$
$23$	4.25325	−	4.25325i	0.886865	−	0.886865i	0.994221	+	0.107356i	$0.0342384\pi$
$24$		0			0
$25$	2.23607	−	4.47214i	0.447214	−	0.894427i
$26$		0			0
$27$	3.23607	+	3.23607i	0.622782	+	0.622782i
$28$		0			0
$29$		−	6.15537i		−	1.14302i	−0.820594	−	0.571511i	$-0.806357\pi$
$29$		−	6.15537i		−	1.14302i	0.820594	−	0.571511i	$-0.193643\pi$
$30$		0			0
$31$		−	8.50651i		−	1.52781i	−0.645326	−	0.763907i	$-0.723279\pi$
$31$		−	8.50651i		−	1.52781i	0.645326	−	0.763907i	$-0.276721\pi$
$32$		0			0
$33$	−2.00000	−	2.00000i	−0.348155	−	0.348155i
$34$		0			0
$35$	−5.85410	−	1.38197i	−0.989524	−	0.233595i
$36$		0			0
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	−0.764302	−	0.644859i	$-0.776916\pi$
$37$	−0.726543	+	0.726543i	−0.119443	+	0.119443i	0.644859	+	0.764302i	$0.276916\pi$
$38$		0			0
$39$	0.898056			0.143804
$40$		0			0
$41$	−5.70820			−0.891472			−0.445736	−	0.895165i	$-0.647058\pi$
$41$	−5.70820			−0.891472			−0.445736	+	0.895165i	$0.647058\pi$
$42$		0			0
$43$	−4.61803	+	4.61803i	−0.704244	+	0.704244i	−0.965319	−	0.261075i	$-0.915923\pi$
$43$	−4.61803	+	4.61803i	−0.704244	+	0.704244i	0.261075	+	0.965319i	$0.415923\pi$
$44$		0			0
$45$	2.62866	+	4.25325i	0.391857	+	0.634038i
$46$		0			0
$47$	−3.35520	−	3.35520i	−0.489406	−	0.489406i	0.418713	−	0.908119i	$-0.362481\pi$
$47$	−3.35520	−	3.35520i	−0.489406	−	0.489406i	−0.908119	+	0.418713i	$0.862481\pi$
$48$		0			0
$49$			0.236068i			0.0337240i
$50$		0			0
$51$			1.23607i			0.173084i
$52$		0			0
$53$	3.07768	+	3.07768i	0.422752	+	0.422752i	0.886150	−	0.463398i	$-0.153370\pi$
$53$	3.07768	+	3.07768i	0.422752	+	0.422752i	−0.463398	+	0.886150i	$0.653370\pi$
$54$		0			0
$55$	−3.80423	−	6.15537i	−0.512962	−	0.829990i
$56$		0			0
$57$	1.23607	−	1.23607i	0.163721	−	0.163721i
$58$		0			0
$59$	−0.472136			−0.0614669			−0.0307334	−	0.999528i	$-0.509784\pi$
$59$	−0.472136			−0.0614669			−0.0307334	+	0.999528i	$0.509784\pi$
$60$		0			0
$61$	0.898056			0.114984			0.0574921	−	0.998346i	$-0.481690\pi$
$61$	0.898056			0.114984			0.0574921	+	0.998346i	$0.481690\pi$
$62$		0			0
$63$	4.25325	−	4.25325i	0.535860	−	0.535860i
$64$		0			0
$65$	2.23607	+	0.527864i	0.277350	+	0.0654735i
$66$		0			0
$67$	4.61803	+	4.61803i	0.564183	+	0.564183i	0.930493	−	0.366310i	$-0.119379\pi$
$67$	4.61803	+	4.61803i	0.564183	+	0.564183i	−0.366310	+	0.930493i	$0.619379\pi$
$68$		0			0
$69$		−	5.25731i		−	0.632906i
$70$		0			0
$71$		−	11.4127i		−	1.35444i	−0.735783	−	0.677218i	$-0.763185\pi$
$71$		−	11.4127i		−	1.35444i	0.735783	−	0.677218i	$-0.236815\pi$
$72$		0			0
$73$	4.70820	+	4.70820i	0.551054	+	0.551054i	0.926745	−	0.375691i	$-0.122595\pi$
$73$	4.70820	+	4.70820i	0.551054	+	0.551054i	−0.375691	+	0.926745i	$0.622595\pi$
$74$		0			0
$75$	−1.38197	−	4.14590i	−0.159576	−	0.478727i
$76$		0			0
$77$	−6.15537	+	6.15537i	−0.701469	+	0.701469i
$78$		0			0
$79$	−2.90617			−0.326970			−0.163485	−	0.986546i	$-0.552273\pi$
$79$	−2.90617			−0.326970			−0.163485	+	0.986546i	$0.552273\pi$
$80$		0			0
$81$	−2.70820			−0.300912
$82$		0			0
$83$	−6.61803	+	6.61803i	−0.726424	+	0.726424i	−0.969905	−	0.243482i	$-0.921710\pi$
$83$	−6.61803	+	6.61803i	−0.726424	+	0.726424i	0.243482	+	0.969905i	$0.421710\pi$
$84$		0			0
$85$	−0.726543	+	3.07768i	−0.0788046	+	0.333822i
$86$		0			0
$87$	−3.80423	−	3.80423i	−0.407856	−	0.407856i
$88$		0			0
$89$			2.47214i			0.262046i	0.991379	+	0.131023i	$0.0418262\pi$
$89$			2.47214i			0.262046i	−0.991379	+	0.131023i	$0.958174\pi$
$90$		0			0
$91$		−	2.76393i		−	0.289739i
$92$		0			0
$93$	−5.25731	−	5.25731i	−0.545158	−	0.545158i
$94$		0			0
$95$	3.80423	−	2.35114i	0.390305	−	0.241222i
$96$		0			0
$97$	4.23607	−	4.23607i	0.430108	−	0.430108i	−0.458557	−	0.888665i	$-0.651634\pi$
$97$	4.23607	−	4.23607i	0.430108	−	0.430108i	0.888665	+	0.458557i	$0.151634\pi$
$98$		0			0
$99$	7.23607			0.727252
$100$		0			0
$101$	−2.90617			−0.289175			−0.144587	−	0.989492i	$-0.546185\pi$
$101$	−2.90617			−0.289175			−0.144587	+	0.989492i	$0.546185\pi$
$102$		0			0
$103$	−3.35520	+	3.35520i	−0.330597	+	0.330597i	−0.852813	−	0.522216i	$-0.825106\pi$
$103$	−3.35520	+	3.35520i	−0.330597	+	0.330597i	0.522216	+	0.852813i	$0.325106\pi$
$104$		0			0
$105$	−4.47214	+	2.76393i	−0.436436	+	0.269732i
$106$		0			0
$107$	0.909830	+	0.909830i	0.0879566	+	0.0879566i	0.749716	−	0.661760i	$-0.230190\pi$
$107$	0.909830	+	0.909830i	0.0879566	+	0.0879566i	−0.661760	+	0.749716i	$0.730190\pi$
$108$		0			0
$109$			14.6619i			1.40435i	0.712003	+	0.702176i	$0.247788\pi$
$109$			14.6619i			1.40435i	−0.712003	+	0.702176i	$0.752212\pi$
$110$		0			0
$111$			0.898056i			0.0852397i
$112$		0			0
$113$	8.70820	+	8.70820i	0.819199	+	0.819199i	0.985992	−	0.166793i	$-0.0533412\pi$
$113$	8.70820	+	8.70820i	0.819199	+	0.819199i	−0.166793	+	0.985992i	$0.553341\pi$
$114$		0			0
$115$	3.09017	−	13.0902i	0.288160	−	1.22066i
$116$		0			0
$117$	−1.62460	+	1.62460i	−0.150194	+	0.150194i
$118$		0			0
$119$	3.80423			0.348733
$120$		0			0
$121$	0.527864			0.0479876
$122$		0			0
$123$	−3.52786	+	3.52786i	−0.318097	+	0.318097i
$124$		0			0
$125$	−1.00406	−	11.1352i	−0.0898056	−	0.995959i
$126$		0			0
$127$	−2.80017	−	2.80017i	−0.248475	−	0.248475i	0.571870	−	0.820344i	$-0.306218\pi$
$127$	−2.80017	−	2.80017i	−0.248475	−	0.248475i	−0.820344	+	0.571870i	$0.806218\pi$
$128$		0			0
$129$			5.70820i			0.502579i
$130$		0			0
$131$		−	13.7082i		−	1.19769i	−0.800864	−	0.598846i	$-0.795626\pi$
$131$		−	13.7082i		−	1.19769i	0.800864	−	0.598846i	$-0.204374\pi$
$132$		0			0
$133$	−3.80423	−	3.80423i	−0.329868	−	0.329868i
$134$		0			0
$135$	9.95959	+	2.35114i	0.857185	+	0.202354i
$136$		0			0
$137$	5.47214	−	5.47214i	0.467516	−	0.467516i	−0.433593	−	0.901109i	$-0.642754\pi$
$137$	5.47214	−	5.47214i	0.467516	−	0.467516i	0.901109	+	0.433593i	$0.142754\pi$
$138$		0			0
$139$	21.4164			1.81652			0.908258	−	0.418411i	$-0.137413\pi$
$139$	21.4164			1.81652			0.908258	+	0.418411i	$0.137413\pi$
$140$		0			0
$141$	−4.14725			−0.349262
$142$		0			0
$143$	2.35114	−	2.35114i	0.196612	−	0.196612i
$144$		0			0
$145$	−7.23607	−	11.7082i	−0.600923	−	0.972313i
$146$		0			0
$147$	0.145898	+	0.145898i	0.0120335	+	0.0120335i
$148$		0			0
$149$			12.8658i			1.05400i	0.849864	+	0.527002i	$0.176684\pi$
$149$			12.8658i			1.05400i	−0.849864	+	0.527002i	$0.823316\pi$
$150$		0			0
$151$			6.71040i			0.546084i	0.962002	+	0.273042i	$0.0880298\pi$
$151$			6.71040i			0.546084i	−0.962002	+	0.273042i	$0.911970\pi$
$152$		0			0
$153$	−2.23607	−	2.23607i	−0.180775	−	0.180775i
$154$		0			0
$155$	−10.0000	−	16.1803i	−0.803219	−	1.29964i
$156$		0			0
$157$	13.9353	−	13.9353i	1.11216	−	1.11216i	0.119303	−	0.992858i	$-0.461934\pi$
$157$	13.9353	−	13.9353i	1.11216	−	1.11216i	0.992858	−	0.119303i	$-0.0380659\pi$
$158$		0			0
$159$	3.80423			0.301695
$160$		0			0
$161$	−16.1803			−1.27519
$162$		0			0
$163$	−13.8541	+	13.8541i	−1.08514	+	1.08514i	−0.0891157	+	0.996021i	$0.528404\pi$
$163$	−13.8541	+	13.8541i	−1.08514	+	1.08514i	−0.996021	+	0.0891157i	$0.971596\pi$
$164$		0			0
$165$	−6.15537	−	1.45309i	−0.479195	−	0.113123i
$166$		0			0
$167$	8.05748	+	8.05748i	0.623507	+	0.623507i	0.946426	−	0.322920i	$-0.104664\pi$
$167$	8.05748	+	8.05748i	0.623507	+	0.623507i	−0.322920	+	0.946426i	$0.604664\pi$
$168$		0			0
$169$		−	11.9443i		−	0.918790i
$170$		0			0
$171$			4.47214i			0.341993i
$172$		0			0
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.994208	+	0.107474i	$0.0342762\pi$
$173$	14.4904	+	14.4904i	1.10168	+	1.10168i	0.107474	+	0.994208i	$0.465724\pi$
$174$		0			0
$175$	−12.7598	+	4.25325i	−0.964547	+	0.321516i
$176$		0			0
$177$	−0.291796	+	0.291796i	−0.0219327	+	0.0219327i
$178$		0			0
$179$	7.52786			0.562659			0.281329	−	0.959611i	$-0.409225\pi$
$179$	7.52786			0.562659			0.281329	+	0.959611i	$0.409225\pi$
$180$		0			0
$181$	15.2169			1.13106			0.565532	−	0.824726i	$-0.308671\pi$
$181$	15.2169			1.13106			0.565532	+	0.824726i	$0.308671\pi$
$182$		0			0
$183$	0.555029	−	0.555029i	0.0410289	−	0.0410289i
$184$		0			0
$185$	−0.527864	+	2.23607i	−0.0388093	+	0.164399i
$186$		0			0
$187$	3.23607	+	3.23607i	0.236645	+	0.236645i
$188$		0			0
$189$		−	12.3107i		−	0.895474i
$190$		0			0
$191$			13.2088i			0.955755i	0.878427	+	0.477877i	$0.158594\pi$
$191$			13.2088i			0.955755i	−0.878427	+	0.477877i	$0.841406\pi$
$192$		0			0
$193$	1.47214	+	1.47214i	0.105967	+	0.105967i	0.758102	−	0.652136i	$-0.226127\pi$
$193$	1.47214	+	1.47214i	0.105967	+	0.105967i	−0.652136	+	0.758102i	$0.726127\pi$
$194$		0			0
$195$	1.70820	−	1.05573i	0.122327	−	0.0756023i
$196$		0			0
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	−0.297038	−	0.954866i	$-0.595999\pi$
$197$	9.23305	−	9.23305i	0.657828	−	0.657828i	0.954866	+	0.297038i	$0.0959988\pi$
$198$		0			0
$199$	−21.7153			−1.53936			−0.769678	−	0.638432i	$-0.779583\pi$
$199$	−21.7153			−1.53936			−0.769678	+	0.638432i	$0.779583\pi$
$200$		0			0
$201$	5.70820			0.402626
$202$		0			0
$203$	−11.7082	+	11.7082i	−0.821755	+	0.821755i
$204$		0			0
$205$	−10.8576	+	6.71040i	−0.758331	+	0.468674i
$206$		0			0
$207$	9.51057	+	9.51057i	0.661030	+	0.661030i
$208$		0			0
$209$		−	6.47214i		−	0.447687i
$210$		0			0
$211$		−	2.29180i		−	0.157774i	−0.996884	−	0.0788869i	$-0.974863\pi$
$211$		−	2.29180i		−	0.157774i	0.996884	−	0.0788869i	$-0.0251366\pi$
$212$		0			0
$213$	−7.05342	−	7.05342i	−0.483293	−	0.483293i
$214$		0			0
$215$	−3.35520	+	14.2128i	−0.228823	+	0.969308i
$216$		0			0
$217$	−16.1803	+	16.1803i	−1.09839	+	1.09839i
$218$		0			0
$219$	5.81966			0.393256
$220$		0			0
$221$	−1.45309			−0.0977451
$222$		0			0
$223$	−14.2128	+	14.2128i	−0.951763	+	0.951763i	−0.998889	−	0.0471263i	$-0.984994\pi$
$223$	−14.2128	+	14.2128i	−0.951763	+	0.951763i	0.0471263	+	0.998889i	$0.484994\pi$
$224$		0			0
$225$	10.0000	+	5.00000i	0.666667	+	0.333333i
$226$		0			0
$227$	9.38197	+	9.38197i	0.622703	+	0.622703i	0.946222	−	0.323519i	$-0.104866\pi$
$227$	9.38197	+	9.38197i	0.622703	+	0.622703i	−0.323519	+	0.946222i	$0.604866\pi$
$228$		0			0
$229$		−	7.95148i		−	0.525449i	−0.964871	−	0.262724i	$-0.915379\pi$
$229$		−	7.95148i		−	0.525449i	0.964871	−	0.262724i	$-0.0846210\pi$
$230$		0			0
$231$			7.60845i			0.500599i
$232$		0			0
$233$	−5.47214	−	5.47214i	−0.358492	−	0.358492i	0.504765	−	0.863257i	$-0.331579\pi$
$233$	−5.47214	−	5.47214i	−0.358492	−	0.358492i	−0.863257	+	0.504765i	$0.831579\pi$
$234$		0			0
$235$	−10.3262	−	2.43769i	−0.673609	−	0.159018i
$236$		0			0
$237$	−1.79611	+	1.79611i	−0.116670	+	0.116670i
$238$		0			0
$239$	13.4208			0.868119			0.434059	−	0.900884i	$-0.357081\pi$
$239$	13.4208			0.868119			0.434059	+	0.900884i	$0.357081\pi$
$240$		0			0
$241$	11.2361			0.723779			0.361889	−	0.932221i	$-0.382132\pi$
$241$	11.2361			0.723779			0.361889	+	0.932221i	$0.382132\pi$
$242$		0			0
$243$	−11.3820	+	11.3820i	−0.730153	+	0.730153i
$244$		0			0
$245$	0.277515	+	0.449028i	0.0177298	+	0.0286873i
$246$		0			0
$247$	1.45309	+	1.45309i	0.0924576	+	0.0924576i
$248$		0			0
$249$			8.18034i			0.518408i
$250$		0			0
$251$			0.180340i			0.0113830i	0.999984	+	0.00569148i	$0.00181166\pi$
$251$			0.180340i			0.0113830i	−0.999984	+	0.00569148i	$0.998188\pi$
$252$		0			0
$253$	−13.7638	−	13.7638i	−0.865324	−	0.865324i
$254$		0			0
$255$	1.45309	+	2.35114i	0.0909957	+	0.147234i
$256$		0			0
$257$	5.29180	−	5.29180i	0.330093	−	0.330093i	−0.522529	−	0.852622i	$-0.675011\pi$
$257$	5.29180	−	5.29180i	0.330093	−	0.330093i	0.852622	+	0.522529i	$0.175011\pi$
$258$		0			0
$259$	2.76393			0.171742
$260$		0			0
$261$	13.7638			0.851959
$262$		0			0
$263$	−7.50245	+	7.50245i	−0.462621	+	0.462621i	−0.899514	−	0.436893i	$-0.856079\pi$
$263$	−7.50245	+	7.50245i	−0.462621	+	0.462621i	0.436893	+	0.899514i	$0.356079\pi$
$264$		0			0
$265$	9.47214	+	2.23607i	0.581869	+	0.137361i
$266$		0			0
$267$	1.52786	+	1.52786i	0.0935038	+	0.0935038i
$268$		0			0
$269$			20.4742i			1.24833i	0.781291	+	0.624167i	$0.214562\pi$
$269$			20.4742i			1.24833i	−0.781291	+	0.624167i	$0.785438\pi$
$270$		0			0
$271$			17.2250i			1.04635i	0.852227	+	0.523173i	$0.175252\pi$
$271$			17.2250i			1.04635i	−0.852227	+	0.523173i	$0.824748\pi$
$272$		0			0
$273$	−1.70820	−	1.70820i	−0.103385	−	0.103385i
$274$		0			0
$275$	−14.4721	−	7.23607i	−0.872703	−	0.436351i
$276$		0			0
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	−0.927811	−	0.373051i	$-0.878312\pi$
$277$	−9.23305	+	9.23305i	−0.554760	+	0.554760i	0.373051	+	0.927811i	$0.378312\pi$
$278$		0			0
$279$	19.0211			1.13877
$280$		0			0
$281$	9.70820			0.579143			0.289571	−	0.957156i	$-0.406487\pi$
$281$	9.70820			0.579143			0.289571	+	0.957156i	$0.406487\pi$
$282$		0			0
$283$	−13.3820	+	13.3820i	−0.795475	+	0.795475i	−0.982378	−	0.186903i	$-0.940155\pi$
$283$	−13.3820	+	13.3820i	−0.795475	+	0.795475i	0.186903	+	0.982378i	$0.440155\pi$
$284$		0			0
$285$	0.898056	−	3.80423i	0.0531962	−	0.225343i
$286$		0			0
$287$	10.8576	+	10.8576i	0.640907	+	0.640907i
$288$		0			0
$289$			15.0000i			0.882353i
$290$		0			0
$291$		−	5.23607i		−	0.306944i
$292$		0			0
$293$	−3.07768	−	3.07768i	−0.179800	−	0.179800i	0.611469	−	0.791269i	$-0.290579\pi$
$293$	−3.07768	−	3.07768i	−0.179800	−	0.179800i	−0.791269	+	0.611469i	$0.790579\pi$
$294$		0			0
$295$	−0.898056	+	0.555029i	−0.0522868	+	0.0323150i
$296$		0			0
$297$	10.4721	−	10.4721i	0.607655	−	0.607655i
$298$		0			0
$299$	6.18034			0.357418
$300$		0			0
$301$	17.5680			1.01261
$302$		0			0
$303$	−1.79611	+	1.79611i	−0.103184	+	0.103184i
$304$		0			0
$305$	1.70820	−	1.05573i	0.0978115	−	0.0604508i
$306$		0			0
$307$	13.5623	+	13.5623i	0.774042	+	0.774042i	0.978810	−	0.204769i	$-0.0656442\pi$
$307$	13.5623	+	13.5623i	0.774042	+	0.774042i	−0.204769	+	0.978810i	$0.565644\pi$
$308$		0			0
$309$			4.14725i			0.235929i
$310$		0			0
$311$			20.8172i			1.18044i	0.807243	+	0.590219i	$0.200959\pi$
$311$			20.8172i			1.18044i	−0.807243	+	0.590219i	$0.799041\pi$
$312$		0			0
$313$	1.76393	+	1.76393i	0.0997033	+	0.0997033i	0.755199	−	0.655496i	$-0.227540\pi$
$313$	1.76393	+	1.76393i	0.0997033	+	0.0997033i	−0.655496	+	0.755199i	$0.727540\pi$
$314$		0			0
$315$	3.09017	−	13.0902i	0.174111	−	0.737548i
$316$		0			0
$317$	3.97574	−	3.97574i	0.223300	−	0.223300i	−0.586587	−	0.809886i	$-0.699529\pi$
$317$	3.97574	−	3.97574i	0.223300	−	0.223300i	0.809886	+	0.586587i	$0.199529\pi$
$318$		0			0
$319$	−19.9192			−1.11526
$320$		0			0
$321$	1.12461			0.0627697
$322$		0			0
$323$	−2.00000	+	2.00000i	−0.111283	+	0.111283i
$324$		0			0
$325$	4.87380	−	1.62460i	0.270350	−	0.0901165i
$326$		0			0
$327$	9.06154	+	9.06154i	0.501104	+	0.501104i
$328$		0			0
$329$			12.7639i			0.703698i
$330$		0			0
$331$		−	30.0689i		−	1.65274i	−0.563131	−	0.826368i	$-0.690403\pi$
$331$		−	30.0689i		−	1.65274i	0.563131	−	0.826368i	$-0.309597\pi$
$332$		0			0
$333$	−1.62460	−	1.62460i	−0.0890274	−	0.0890274i
$334$		0			0
$335$	14.2128	+	3.35520i	0.776531	+	0.183314i
$336$		0			0
$337$	−19.9443	+	19.9443i	−1.08643	+	1.08643i	−0.0905410	+	0.995893i	$0.528860\pi$
$337$	−19.9443	+	19.9443i	−1.08643	+	1.08643i	−0.995893	+	0.0905410i	$0.971140\pi$
$338$		0			0
$339$	10.7639			0.584617
$340$		0			0
$341$	−27.5276			−1.49071
$342$		0			0
$343$	−12.8658	+	12.8658i	−0.694686	+	0.694686i
$344$		0			0
$345$	−6.18034	−	10.0000i	−0.332738	−	0.538382i
$346$		0			0
$347$	26.0344	+	26.0344i	1.39760	+	1.39760i	0.806862	+	0.590740i	$0.201164\pi$
$347$	26.0344	+	26.0344i	1.39760	+	1.39760i	0.590740	+	0.806862i	$0.298836\pi$
$348$		0			0
$349$		−	16.6700i		−	0.892324i	−0.894952	−	0.446162i	$-0.852791\pi$
$349$		−	16.6700i		−	0.892324i	0.894952	−	0.446162i	$-0.147209\pi$
$350$		0			0
$351$			4.70228i			0.250989i
$352$		0			0
$353$	−22.4164	−	22.4164i	−1.19311	−	1.19311i	−0.976191	−	0.216914i	$-0.930401\pi$
$353$	−22.4164	−	22.4164i	−1.19311	−	1.19311i	−0.216914	−	0.976191i	$-0.569599\pi$
$354$		0			0
$355$	−13.4164	−	21.7082i	−0.712069	−	1.15215i
$356$		0			0
$357$	2.35114	−	2.35114i	0.124436	−	0.124436i
$358$		0			0
$359$	19.9192			1.05129			0.525647	−	0.850703i	$-0.323823\pi$
$359$	19.9192			1.05129			0.525647	+	0.850703i	$0.323823\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$	0.326238	−	0.326238i	0.0171231	−	0.0171231i
$364$		0			0
$365$	14.4904	+	3.42071i	0.758460	+	0.179048i
$366$		0			0
$367$	−12.2047	−	12.2047i	−0.637082	−	0.637082i	0.312753	−	0.949835i	$-0.398749\pi$
$367$	−12.2047	−	12.2047i	−0.637082	−	0.637082i	−0.949835	+	0.312753i	$0.898749\pi$
$368$		0			0
$369$		−	12.7639i		−	0.664464i
$370$		0			0
$371$		−	11.7082i		−	0.607860i
$372$		0			0
$373$	22.4418	+	22.4418i	1.16199	+	1.16199i	0.984038	+	0.177956i	$0.0569485\pi$
$373$	22.4418	+	22.4418i	1.16199	+	1.16199i	0.177956	+	0.984038i	$0.443052\pi$
$374$		0			0
$375$	−7.50245	−	6.26137i	−0.387425	−	0.323336i
$376$		0			0
$377$	4.47214	−	4.47214i	0.230327	−	0.230327i
$378$		0			0
$379$	0.111456			0.00572512			0.00286256	−	0.999996i	$-0.499089\pi$
$379$	0.111456			0.00572512			0.00286256	+	0.999996i	$0.499089\pi$
$380$		0			0
$381$	−3.46120			−0.177323
$382$		0			0
$383$	1.00406	−	1.00406i	0.0513049	−	0.0513049i	−0.680989	−	0.732294i	$-0.738450\pi$
$383$	1.00406	−	1.00406i	0.0513049	−	0.0513049i	0.732294	+	0.680989i	$0.238450\pi$
$384$		0			0
$385$	−4.47214	+	18.9443i	−0.227921	+	0.965489i
$386$		0			0
$387$	−10.3262	−	10.3262i	−0.524912	−	0.524912i
$388$		0			0
$389$			4.14725i			0.210274i	0.994458	+	0.105137i	$0.0335281\pi$
$389$			4.14725i			0.210274i	−0.994458	+	0.105137i	$0.966472\pi$
$390$		0			0
$391$			8.50651i			0.430193i
$392$		0			0
$393$	−8.47214	−	8.47214i	−0.427363	−	0.427363i
$394$		0			0
$395$	−5.52786	+	3.41641i	−0.278137	+	0.171898i
$396$		0			0
$397$	−24.4500	+	24.4500i	−1.22711	+	1.22711i	−0.262055	+	0.965053i	$0.584400\pi$
$397$	−24.4500	+	24.4500i	−1.22711	+	1.22711i	−0.965053	+	0.262055i	$0.915600\pi$
$398$		0			0
$399$	−4.70228			−0.235409
$400$		0			0
$401$	31.8885			1.59244			0.796219	−	0.605009i	$-0.206830\pi$
$401$	31.8885			1.59244			0.796219	+	0.605009i	$0.206830\pi$
$402$		0			0
$403$	6.18034	−	6.18034i	0.307865	−	0.307865i
$404$		0			0
$405$	−5.15131	+	3.18368i	−0.255971	+	0.158199i
$406$		0			0
$407$	2.35114	+	2.35114i	0.116542	+	0.116542i
$408$		0			0
$409$		−	21.5967i		−	1.06789i	−0.845519	−	0.533945i	$-0.820709\pi$
$409$		−	21.5967i		−	1.06789i	0.845519	−	0.533945i	$-0.179291\pi$
$410$		0			0
$411$		−	6.76393i		−	0.333640i
$412$		0			0
$413$	0.898056	+	0.898056i	0.0441904	+	0.0441904i
$414$		0			0
$415$	−4.80828	+	20.3682i	−0.236029	+	0.999836i
$416$		0			0
$417$	13.2361	−	13.2361i	0.648173	−	0.648173i
$418$		0			0
$419$	28.8328			1.40858			0.704288	−	0.709915i	$-0.251267\pi$
$419$	28.8328			1.40858			0.704288	+	0.709915i	$0.251267\pi$
$420$		0			0
$421$	−28.4257			−1.38538			−0.692692	−	0.721234i	$-0.743575\pi$
$421$	−28.4257			−1.38538			−0.692692	+	0.721234i	$0.743575\pi$
$422$		0			0
$423$	7.50245	−	7.50245i	0.364782	−	0.364782i
$424$		0			0
$425$	2.23607	+	6.70820i	0.108465	+	0.325396i
$426$		0			0
$427$	−1.70820	−	1.70820i	−0.0826658	−	0.0826658i
$428$		0			0
$429$		−	2.90617i		−	0.140311i
$430$		0			0
$431$		−	19.0211i		−	0.916216i	−0.888897	−	0.458108i	$-0.848527\pi$
$431$		−	19.0211i		−	0.916216i	0.888897	−	0.458108i	$-0.151473\pi$
$432$		0			0
$433$	0.819660	+	0.819660i	0.0393904	+	0.0393904i	0.726528	−	0.687137i	$-0.241133\pi$
$433$	0.819660	+	0.819660i	0.0393904	+	0.0393904i	−0.687137	+	0.726528i	$0.741133\pi$
$434$		0			0
$435$	−11.7082	−	2.76393i	−0.561365	−	0.132520i
$436$		0			0
$437$	8.50651	−	8.50651i	0.406921	−	0.406921i
$438$		0			0
$439$	−35.1361			−1.67695			−0.838477	−	0.544937i	$-0.816554\pi$
$439$	−35.1361			−1.67695			−0.838477	+	0.544937i	$0.816554\pi$
$440$		0			0
$441$	−0.527864			−0.0251364
$442$		0			0
$443$	1.09017	−	1.09017i	0.0517955	−	0.0517955i	−0.680735	−	0.732530i	$-0.738339\pi$
$443$	1.09017	−	1.09017i	0.0517955	−	0.0517955i	0.732530	+	0.680735i	$0.238339\pi$
$444$		0			0
$445$	2.90617	+	4.70228i	0.137766	+	0.222910i
$446$		0			0
$447$	7.95148	+	7.95148i	0.376092	+	0.376092i
$448$		0			0
$449$		−	17.5967i		−	0.830442i	−0.909721	−	0.415221i	$-0.863704\pi$
$449$		−	17.5967i		−	0.830442i	0.909721	−	0.415221i	$-0.136296\pi$
$450$		0			0
$451$			18.4721i			0.869819i
$452$		0			0
$453$	4.14725	+	4.14725i	0.194855	+	0.194855i
$454$		0			0
$455$	−3.24920	−	5.25731i	−0.152325	−	0.246467i
$456$		0			0
$457$	−9.65248	+	9.65248i	−0.451524	+	0.451524i	−0.895860	−	0.444336i	$-0.853440\pi$
$457$	−9.65248	+	9.65248i	−0.451524	+	0.451524i	0.444336	+	0.895860i	$0.353440\pi$
$458$		0			0
$459$	−6.47214			−0.302093
$460$		0			0
$461$	−27.5276			−1.28209			−0.641045	−	0.767503i	$-0.721499\pi$
$461$	−27.5276			−1.28209			−0.641045	+	0.767503i	$0.721499\pi$
$462$		0			0
$463$	−2.45714	+	2.45714i	−0.114193	+	0.114193i	−0.761894	−	0.647701i	$-0.775730\pi$
$463$	−2.45714	+	2.45714i	−0.114193	+	0.114193i	0.647701	+	0.761894i	$0.275730\pi$
$464$		0			0
$465$	−16.1803	−	3.81966i	−0.750345	−	0.177132i
$466$		0			0
$467$	18.3262	+	18.3262i	0.848037	+	0.848037i	0.989888	−	0.141851i	$-0.0453054\pi$
$467$	18.3262	+	18.3262i	0.848037	+	0.848037i	−0.141851	+	0.989888i	$0.545305\pi$
$468$		0			0
$469$		−	17.5680i		−	0.811217i
$470$		0			0
$471$		−	17.2250i		−	0.793687i
$472$		0			0
$473$	14.9443	+	14.9443i	0.687138	+	0.687138i
$474$		0			0
$475$	4.47214	−	8.94427i	0.205196	−	0.410391i
$476$		0			0
$477$	−6.88191	+	6.88191i	−0.315101	+	0.315101i
$478$		0			0
$479$	4.70228			0.214853			0.107426	−	0.994213i	$-0.465739\pi$
$479$	4.70228			0.214853			0.107426	+	0.994213i	$0.465739\pi$
$480$		0			0
$481$	−1.05573			−0.0481371
$482$		0			0
$483$	−10.0000	+	10.0000i	−0.455016	+	0.455016i
$484$		0			0
$485$	3.07768	−	13.0373i	0.139750	−	0.591992i
$486$		0			0
$487$	−18.9151	−	18.9151i	−0.857126	−	0.857126i	0.133872	−	0.990999i	$-0.457259\pi$
$487$	−18.9151	−	18.9151i	−0.857126	−	0.857126i	−0.990999	+	0.133872i	$0.957259\pi$
$488$		0			0
$489$			17.1246i			0.774402i
$490$		0			0
$491$		−	15.2361i		−	0.687594i	−0.939044	−	0.343797i	$-0.888287\pi$
$491$		−	15.2361i		−	0.687594i	0.939044	−	0.343797i	$-0.111713\pi$
$492$		0			0
$493$	6.15537	+	6.15537i	0.277224	+	0.277224i
$494$		0			0
$495$	13.7638	−	8.50651i	0.618638	−	0.382339i
$496$		0			0
$497$	−21.7082	+	21.7082i	−0.973746	+	0.973746i
$498$		0			0
$499$	−11.8885			−0.532204			−0.266102	−	0.963945i	$-0.585736\pi$
$499$	−11.8885			−0.532204			−0.266102	+	0.963945i	$0.585736\pi$
$500$		0			0
$501$	9.95959			0.444962
$502$		0			0
$503$	16.5640	−	16.5640i	0.738552	−	0.738552i	−0.233746	−	0.972298i	$-0.575098\pi$
$503$	16.5640	−	16.5640i	0.738552	−	0.738552i	0.972298	+	0.233746i	$0.0750984\pi$
$504$		0			0
$505$	−5.52786	+	3.41641i	−0.245987	+	0.152028i
$506$		0			0
$507$	−7.38197	−	7.38197i	−0.327845	−	0.327845i
$508$		0			0
$509$		−	10.8576i		−	0.481257i	−0.970617	−	0.240628i	$-0.922646\pi$
$509$		−	10.8576i		−	0.481257i	0.970617	−	0.240628i	$-0.0773535\pi$
$510$		0			0
$511$		−	17.9111i		−	0.792339i
$512$		0			0
$513$	6.47214	+	6.47214i	0.285752	+	0.285752i
$514$		0			0
$515$	−2.43769	+	10.3262i	−0.107418	+	0.455028i
$516$		0			0
$517$	−10.8576	+	10.8576i	−0.477519	+	0.477519i
$518$		0			0
$519$	17.9111			0.786209
$520$		0			0
$521$	0.472136			0.0206847			0.0103423	−	0.999947i	$-0.496708\pi$
$521$	0.472136			0.0206847			0.0103423	+	0.999947i	$0.496708\pi$
$522$		0			0
$523$	−25.7426	+	25.7426i	−1.12565	+	1.12565i	−0.134770	+	0.990877i	$0.543030\pi$
$523$	−25.7426	+	25.7426i	−1.12565	+	1.12565i	−0.990877	+	0.134770i	$0.956970\pi$
$524$		0			0
$525$	−5.25731	+	10.5146i	−0.229448	+	0.458896i
$526$		0			0
$527$	8.50651	+	8.50651i	0.370549	+	0.370549i
$528$		0			0
$529$		−	13.1803i		−	0.573058i
$530$		0			0
$531$		−	1.05573i		−	0.0458147i
$532$		0			0
$533$	−4.14725	−	4.14725i	−0.179637	−	0.179637i
$534$		0			0
$535$	2.80017	+	0.661030i	0.121062	+	0.0285788i
$536$		0			0
$537$	4.65248	−	4.65248i	0.200769	−	0.200769i
$538$		0			0
$539$	0.763932			0.0329049
$540$		0			0
$541$	12.3107			0.529280			0.264640	−	0.964347i	$-0.414747\pi$
$541$	12.3107			0.529280			0.264640	+	0.964347i	$0.414747\pi$
$542$		0			0
$543$	9.40456	−	9.40456i	0.403588	−	0.403588i
$544$		0			0
$545$	17.2361	+	27.8885i	0.738312	+	1.19461i
$546$		0			0
$547$	−11.5623	−	11.5623i	−0.494369	−	0.494369i	0.415311	−	0.909679i	$-0.363673\pi$
$547$	−11.5623	−	11.5623i	−0.494369	−	0.494369i	−0.909679	+	0.415311i	$0.863673\pi$
$548$		0			0
$549$			2.00811i			0.0857042i
$550$		0			0
$551$		−	12.3107i		−	0.524455i
$552$		0			0
$553$	5.52786	+	5.52786i	0.235069	+	0.235069i
$554$		0			0
$555$	1.05573	+	1.70820i	0.0448132	+	0.0725092i
$556$		0			0
$557$	23.5519	−	23.5519i	0.997926	−	0.997926i	−0.00207187	−	0.999998i	$-0.500659\pi$
$557$	23.5519	−	23.5519i	0.997926	−	0.997926i	0.999998	+	0.00207187i	$0.000659497\pi$
$558$		0			0
$559$	−6.71040			−0.283820
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−4.32624	+	4.32624i	−0.182329	+	0.182329i	−0.792370	−	0.610041i	$-0.791153\pi$
$563$	−4.32624	+	4.32624i	−0.182329	+	0.182329i	0.610041	+	0.792370i	$0.291153\pi$
$564$		0			0
$565$	26.8011	+	6.32688i	1.12753	+	0.266174i
$566$		0			0
$567$	5.15131	+	5.15131i	0.216335	+	0.216335i
$568$		0			0
$569$		−	27.1246i		−	1.13712i	−0.822641	−	0.568561i	$-0.807500\pi$
$569$		−	27.1246i		−	1.13712i	0.822641	−	0.568561i	$-0.192500\pi$
$570$		0			0
$571$			22.6525i			0.947977i	0.880531	+	0.473988i	$0.157186\pi$
$571$			22.6525i			0.947977i	−0.880531	+	0.473988i	$0.842814\pi$
$572$		0			0
$573$	8.16348	+	8.16348i	0.341034	+	0.341034i
$574$		0			0
$575$	−9.51057	−	28.5317i	−0.396618	−	1.18985i
$576$		0			0
$577$	26.2361	−	26.2361i	1.09222	−	1.09222i	0.0969307	−	0.995291i	$-0.469097\pi$
$577$	26.2361	−	26.2361i	1.09222	−	1.09222i	0.995291	−	0.0969307i	$-0.0309025\pi$
$578$		0			0
$579$	1.81966			0.0756225
$580$		0			0
$581$	25.1765			1.04450
$582$		0			0
$583$	9.95959	−	9.95959i	0.412484	−	0.412484i
$584$		0			0
$585$	−1.18034	+	5.00000i	−0.0488010	+	0.206725i
$586$		0			0
$587$	17.0902	+	17.0902i	0.705387	+	0.705387i	0.965562	−	0.260175i	$-0.0837802\pi$
$587$	17.0902	+	17.0902i	0.705387	+	0.705387i	−0.260175	+	0.965562i	$0.583780\pi$
$588$		0			0
$589$		−	17.0130i		−	0.701009i
$590$		0			0
$591$		−	11.4127i		−	0.469455i
$592$		0			0
$593$	20.4164	+	20.4164i	0.838401	+	0.838401i	0.988648	−	0.150247i	$-0.0480069\pi$
$593$	20.4164	+	20.4164i	0.838401	+	0.838401i	−0.150247	+	0.988648i	$0.548007\pi$
$594$		0			0
$595$	7.23607	−	4.47214i	0.296650	−	0.183340i
$596$		0			0
$597$	−13.4208	+	13.4208i	−0.549276	+	0.549276i
$598$		0			0
$599$	6.49839			0.265517			0.132759	−	0.991148i	$-0.457617\pi$
$599$	6.49839			0.265517			0.132759	+	0.991148i	$0.457617\pi$
$600$		0			0
$601$	17.7082			0.722333			0.361166	−	0.932501i	$-0.382379\pi$
$601$	17.7082			0.722333			0.361166	+	0.932501i	$0.382379\pi$
$602$		0			0
$603$	−10.3262	+	10.3262i	−0.420517	+	0.420517i
$604$		0			0
$605$	1.00406	−	0.620541i	0.0408207	−	0.0252286i
$606$		0			0
$607$	−32.6789	−	32.6789i	−1.32640	−	1.32640i	−0.908489	−	0.417908i	$-0.862763\pi$
$607$	−32.6789	−	32.6789i	−1.32640	−	1.32640i	−0.417908	−	0.908489i	$-0.637237\pi$
$608$		0			0
$609$			14.4721i			0.586441i
$610$		0			0
$611$		−	4.87539i		−	0.197237i
$612$		0			0
$613$	−19.5357	−	19.5357i	−0.789038	−	0.789038i	0.192298	−	0.981337i	$-0.438406\pi$
$613$	−19.5357	−	19.5357i	−0.789038	−	0.789038i	−0.981337	+	0.192298i	$0.938406\pi$
$614$		0			0
$615$	−2.56314	+	10.8576i	−0.103356	+	0.437823i
$616$		0			0
$617$	−4.88854	+	4.88854i	−0.196805	+	0.196805i	−0.798629	−	0.601824i	$-0.794441\pi$
$617$	−4.88854	+	4.88854i	−0.196805	+	0.196805i	0.601824	+	0.798629i	$0.294441\pi$
$618$		0			0
$619$	35.3050			1.41903			0.709513	−	0.704692i	$-0.248915\pi$
$619$	35.3050			1.41903			0.709513	+	0.704692i	$0.248915\pi$
$620$		0			0
$621$	27.5276			1.10465
$622$		0			0
$623$	4.70228	−	4.70228i	0.188393	−	0.188393i
$624$		0			0
$625$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$626$		0			0
$627$	−4.00000	−	4.00000i	−0.159745	−	0.159745i
$628$		0			0
$629$		−	1.45309i		−	0.0579383i
$630$		0			0
$631$		−	22.6134i		−	0.900223i	−0.892972	−	0.450112i	$-0.851384\pi$
$631$		−	22.6134i		−	0.900223i	0.892972	−	0.450112i	$-0.148616\pi$
$632$		0			0
$633$	−1.41641	−	1.41641i	−0.0562972	−	0.0562972i
$634$		0			0
$635$	−8.61803	−	2.03444i	−0.341996	−	0.0807344i
$636$		0			0
$637$	−0.171513	+	0.171513i	−0.00679561	+	0.00679561i
$638$		0			0
$639$	25.5195			1.00954
$640$		0			0
$641$	−38.6525			−1.52668			−0.763341	−	0.645996i	$-0.776442\pi$
$641$	−38.6525			−1.52668			−0.763341	+	0.645996i	$0.776442\pi$
$642$		0			0
$643$	−11.5623	+	11.5623i	−0.455973	+	0.455973i	−0.897331	−	0.441358i	$-0.854497\pi$
$643$	−11.5623	+	11.5623i	−0.455973	+	0.455973i	0.441358	+	0.897331i	$0.354497\pi$
$644$		0			0
$645$	6.71040	+	10.8576i	0.264222	+	0.427520i
$646$		0			0
$647$	−20.0252	−	20.0252i	−0.787271	−	0.787271i	0.193775	−	0.981046i	$-0.437927\pi$
$647$	−20.0252	−	20.0252i	−0.787271	−	0.787271i	−0.981046	+	0.193775i	$0.937927\pi$
$648$		0			0
$649$			1.52786i			0.0599739i
$650$		0			0
$651$			20.0000i			0.783862i
$652$		0			0
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	0.194661	−	0.980871i	$-0.437639\pi$
$653$	−20.0907	−	20.0907i	−0.786210	−	0.786210i	−0.980871	+	0.194661i	$0.937639\pi$
$654$		0			0
$655$	−16.1150	−	26.0746i	−0.629664	−	1.01882i
$656$		0			0
$657$	−10.5279	+	10.5279i	−0.410731	+	0.410731i
$658$		0			0
$659$	−18.0000			−0.701180			−0.350590	−	0.936529i	$-0.614019\pi$
$659$	−18.0000			−0.701180			−0.350590	+	0.936529i	$0.614019\pi$
$660$		0			0
$661$	3.80423			0.147967			0.0739836	−	0.997259i	$-0.476429\pi$
$661$	3.80423			0.147967			0.0739836	+	0.997259i	$0.476429\pi$
$662$		0			0
$663$	−0.898056	+	0.898056i	−0.0348776	+	0.0348776i
$664$		0			0
$665$	−11.7082	−	2.76393i	−0.454025	−	0.107181i
$666$		0			0
$667$	−26.1803	−	26.1803i	−1.01371	−	1.01371i
$668$		0			0
$669$			17.5680i			0.679220i
$670$		0			0
$671$		−	2.90617i		−	0.112191i
$672$		0			0
$673$	−17.2918	−	17.2918i	−0.666550	−	0.666550i	0.290366	−	0.956916i	$-0.406223\pi$
$673$	−17.2918	−	17.2918i	−0.666550	−	0.666550i	−0.956916	+	0.290366i	$0.906223\pi$
$674$		0			0
$675$	21.7082	−	7.23607i	0.835549	−	0.278516i
$676$		0			0
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	−0.840625	−	0.541617i	$-0.817812\pi$
$677$	−7.77997	+	7.77997i	−0.299008	+	0.299008i	0.541617	+	0.840625i	$0.317812\pi$
$678$		0			0
$679$	−16.1150			−0.618435
$680$		0			0
$681$	11.5967			0.444388
$682$		0			0
$683$	22.7984	−	22.7984i	0.872356	−	0.872356i	−0.120373	−	0.992729i	$-0.538409\pi$
$683$	22.7984	−	22.7984i	0.872356	−	0.872356i	0.992729	+	0.120373i	$0.0384091\pi$
$684$		0			0
$685$	3.97574	−	16.8415i	0.151905	−	0.643481i
$686$		0			0
$687$	−4.91428	−	4.91428i	−0.187492	−	0.187492i
$688$		0			0
$689$			4.47214i			0.170375i
$690$		0			0
$691$		−	9.12461i		−	0.347117i	−0.984824	−	0.173558i	$-0.944473\pi$
$691$		−	9.12461i		−	0.347117i	0.984824	−	0.173558i	$-0.0555265\pi$
$692$		0			0
$693$	−13.7638	−	13.7638i	−0.522844	−	0.522844i
$694$		0			0
$695$	40.7364	−	25.1765i	1.54522	−	0.954999i
$696$		0			0
$697$	5.70820	−	5.70820i	0.216214	−	0.216214i
$698$		0			0
$699$	−6.76393			−0.255835
$700$		0			0
$701$	−19.7072			−0.744330			−0.372165	−	0.928167i	$-0.621384\pi$
$701$	−19.7072			−0.744330			−0.372165	+	0.928167i	$0.621384\pi$
$702$		0			0
$703$	−1.45309	+	1.45309i	−0.0548041	+	0.0548041i
$704$		0			0
$705$	−7.88854	+	4.87539i	−0.297100	+	0.183618i
$706$		0			0
$707$	5.52786	+	5.52786i	0.207897	+	0.207897i
$708$		0			0
$709$		−	3.24920i		−	0.122026i	−0.998137	−	0.0610131i	$-0.980567\pi$
$709$		−	3.24920i		−	0.122026i	0.998137	−	0.0610131i	$-0.0194331\pi$
$710$		0			0
$711$		−	6.49839i		−	0.243709i
$712$		0			0
$713$	−36.1803	−	36.1803i	−1.35496	−	1.35496i
$714$		0			0
$715$	1.70820	−	7.23607i	0.0638832	−	0.270614i
$716$		0			0
$717$	8.29451	−	8.29451i	0.309764	−	0.309764i
$718$		0			0
$719$	−4.01623			−0.149780			−0.0748900	−	0.997192i	$-0.523861\pi$
$719$	−4.01623			−0.149780			−0.0748900	+	0.997192i	$0.523861\pi$
$720$		0			0
$721$	12.7639			0.475354
$722$		0			0
$723$	6.94427	−	6.94427i	0.258260	−	0.258260i
$724$		0			0
$725$	−27.5276	−	13.7638i	−1.02235	−	0.511175i
$726$		0			0
$727$	−9.51057	−	9.51057i	−0.352727	−	0.352727i	0.508396	−	0.861123i	$-0.330239\pi$
$727$	−9.51057	−	9.51057i	−0.352727	−	0.352727i	−0.861123	+	0.508396i	$0.830239\pi$
$728$		0			0
$729$			5.94427i			0.220158i
$730$		0			0
$731$		−	9.23607i		−	0.341608i
$732$		0			0
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	0.966303	−	0.257407i	$-0.0828680\pi$
$733$	19.1926	+	19.1926i	0.708896	+	0.708896i	−0.257407	+	0.966303i	$0.582868\pi$
$734$		0			0
$735$	0.449028	+	0.106001i	0.0165626	+	0.00390991i
$736$		0			0
$737$	14.9443	−	14.9443i	0.550479	−	0.550479i
$738$		0			0
$739$	9.41641			0.346388			0.173194	−	0.984888i	$-0.444591\pi$
$739$	9.41641			0.346388			0.173194	+	0.984888i	$0.444591\pi$
$740$		0			0
$741$	1.79611			0.0659818
$742$		0			0
$743$	4.80828	−	4.80828i	0.176399	−	0.176399i	−0.613385	−	0.789784i	$-0.710193\pi$
$743$	4.80828	−	4.80828i	0.176399	−	0.176399i	0.789784	+	0.613385i	$0.210193\pi$
$744$		0			0
$745$	15.1246	+	24.4721i	0.554123	+	0.896590i
$746$		0			0
$747$	−14.7984	−	14.7984i	−0.541444	−	0.541444i
$748$		0			0
$749$		−	3.46120i		−	0.126469i
$750$		0			0
$751$		−	11.4127i		−	0.416455i	−0.978080	−	0.208227i	$-0.933231\pi$
$751$		−	11.4127i		−	0.416455i	0.978080	−	0.208227i	$-0.0667694\pi$
$752$		0			0
$753$	0.111456	+	0.111456i	0.00406169	+	0.00406169i
$754$		0			0
$755$	7.88854	+	12.7639i	0.287094	+	0.464527i
$756$		0			0
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.166709	−	0.986006i	$-0.446686\pi$
$757$	31.7154	−	31.7154i	1.15272	−	1.15272i	0.986006	−	0.166709i	$-0.0533140\pi$
$758$		0			0
$759$	−17.0130			−0.617533
$760$		0			0
$761$	−2.94427			−0.106730			−0.0533649	−	0.998575i	$-0.516995\pi$
$761$	−2.94427			−0.106730			−0.0533649	+	0.998575i	$0.516995\pi$
$762$		0			0
$763$	27.8885	−	27.8885i	1.00963	−	1.00963i
$764$		0			0
$765$	−6.88191	−	1.62460i	−0.248816	−	0.0587375i
$766$		0			0
$767$	−0.343027	−	0.343027i	−0.0123860	−	0.0123860i
$768$		0			0
$769$			6.47214i			0.233391i	0.993168	+	0.116696i	$0.0372302\pi$
$769$			6.47214i			0.233391i	−0.993168	+	0.116696i	$0.962770\pi$
$770$		0			0
$771$		−	6.54102i		−	0.235569i
$772$		0			0
$773$	31.5034	+	31.5034i	1.13310	+	1.13310i	0.989659	+	0.143439i	$0.0458159\pi$
$773$	31.5034	+	31.5034i	1.13310	+	1.13310i	0.143439	+	0.989659i	$0.454184\pi$
$774$		0			0
$775$	−38.0423	−	19.0211i	−1.36652	−	0.683259i
$776$		0			0
$777$	1.70820	−	1.70820i	0.0612815	−	0.0612815i
$778$		0			0
$779$	−11.4164			−0.409035
$780$		0			0
$781$	−36.9322			−1.32154
$782$		0			0
$783$	19.9192	−	19.9192i	0.711854	−	0.711854i
$784$		0			0
$785$	10.1246	−	42.8885i	0.361363	−	1.53076i
$786$		0			0
$787$	−17.8541	−	17.8541i	−0.636430	−	0.636430i	0.313243	−	0.949673i	$-0.398585\pi$
$787$	−17.8541	−	17.8541i	−0.636430	−	0.636430i	−0.949673	+	0.313243i	$0.898585\pi$
$788$		0			0
$789$			9.27354i			0.330147i
$790$		0			0
$791$		−	33.1280i		−	1.17790i
$792$		0			0
$793$	0.652476	+	0.652476i	0.0231701	+	0.0231701i
$794$		0			0
$795$	7.23607	−	4.47214i	0.256637	−	0.158610i
$796$		0			0
$797$	−14.8334	+	14.8334i	−0.525426	+	0.525426i	−0.919205	−	0.393779i	$-0.871167\pi$
$797$	−14.8334	+	14.8334i	−0.525426	+	0.525426i	0.393779	+	0.919205i	$0.371167\pi$
$798$		0			0
$799$	6.71040			0.237397
$800$		0			0
$801$	−5.52786			−0.195317
$802$		0			0
$803$	15.2361	−	15.2361i	0.537669	−	0.537669i
$804$		0			0
$805$	−30.7768	+	19.0211i	−1.08474	+	0.670407i
$806$		0			0
$807$	12.6538	+	12.6538i	0.445433	+	0.445433i
$808$		0			0
$809$		−	4.94427i		−	0.173831i	−0.996216	−	0.0869157i	$-0.972299\pi$
$809$		−	4.94427i		−	0.173831i	0.996216	−	0.0869157i	$-0.0277011\pi$
$810$		0			0
$811$			26.0689i			0.915402i	0.889106	+	0.457701i	$0.151327\pi$
$811$			26.0689i			0.915402i	−0.889106	+	0.457701i	$0.848673\pi$
$812$		0			0
$813$	10.6456	+	10.6456i	0.373359	+	0.373359i
$814$		0			0
$815$	−10.0656	+	42.6385i	−0.352582	+	1.49356i
$816$		0			0
$817$	−9.23607	+	9.23607i	−0.323129	+	0.323129i
$818$		0			0
$819$	6.18034			0.215959
$820$		0			0
$821$	17.9111			0.625101			0.312550	−	0.949901i	$-0.398817\pi$
$821$	17.9111			0.625101			0.312550	+	0.949901i	$0.398817\pi$
$822$		0			0
$823$	−13.8698	+	13.8698i	−0.483472	+	0.483472i	−0.906238	−	0.422767i	$-0.861059\pi$
$823$	−13.8698	+	13.8698i	−0.483472	+	0.483472i	0.422767	+	0.906238i	$0.361059\pi$
$824$		0			0
$825$	−13.4164	+	4.47214i	−0.467099	+	0.155700i
$826$		0			0
$827$	8.14590	+	8.14590i	0.283261	+	0.283261i	0.834408	−	0.551147i	$-0.185810\pi$
$827$	8.14590	+	8.14590i	0.283261	+	0.283261i	−0.551147	+	0.834408i	$0.685810\pi$
$828$		0			0
$829$			54.5002i			1.89287i	0.322892	+	0.946436i	$0.395345\pi$
$829$			54.5002i			1.89287i	−0.322892	+	0.946436i	$0.604655\pi$
$830$		0			0
$831$			11.4127i			0.395901i
$832$		0			0
$833$	−0.236068	−	0.236068i	−0.00817927	−	0.00817927i
$834$		0			0
$835$	24.7984	+	5.85410i	0.858183	+	0.202590i
$836$		0			0
$837$	27.5276	−	27.5276i	0.951494	−	0.951494i
$838$		0			0
$839$	15.2169			0.525346			0.262673	−	0.964885i	$-0.415396\pi$
$839$	15.2169			0.525346			0.262673	+	0.964885i	$0.415396\pi$
$840$		0			0
$841$	−8.88854			−0.306502
$842$		0			0
$843$	6.00000	−	6.00000i	0.206651	−	0.206651i
$844$		0			0
$845$	−14.0413	−	22.7194i	−0.483037	−	0.781570i
$846$		0			0
$847$	−1.00406	−	1.00406i	−0.0344998	−	0.0344998i
$848$		0			0
$849$			16.5410i			0.567686i
$850$		0			0
$851$			6.18034i			0.211859i
$852$		0			0
$853$	−18.8496	−	18.8496i	−0.645399	−	0.645399i	0.306479	−	0.951877i	$-0.400849\pi$
$853$	−18.8496	−	18.8496i	−0.645399	−	0.645399i	−0.951877	+	0.306479i	$0.900849\pi$
$854$		0			0
$855$	5.25731	+	8.50651i	0.179796	+	0.290916i
$856$		0			0
$857$	−35.8328	+	35.8328i	−1.22403	+	1.22403i	−0.257837	+	0.966188i	$0.583010\pi$
$857$	−35.8328	+	35.8328i	−1.22403	+	1.22403i	−0.966188	+	0.257837i	$0.916990\pi$
$858$		0			0
$859$	−16.4721			−0.562022			−0.281011	−	0.959705i	$-0.590670\pi$
$859$	−16.4721			−0.562022			−0.281011	+	0.959705i	$0.590670\pi$
$860$		0			0
$861$	13.4208			0.457379
$862$		0			0
$863$	35.5851	−	35.5851i	1.21133	−	1.21133i	0.240743	−	0.970589i	$-0.422609\pi$
$863$	35.5851	−	35.5851i	1.21133	−	1.21133i	0.970589	−	0.240743i	$-0.0773909\pi$
$864$		0			0
$865$	44.5967	+	10.5279i	1.51633	+	0.357958i
$866$		0			0
$867$	9.27051	+	9.27051i	0.314843	+	0.314843i
$868$		0			0
$869$			9.40456i			0.319028i
$870$		0			0
$871$			6.71040i			0.227373i
$872$		0			0
$873$	9.47214	+	9.47214i	0.320583	+	0.320583i
$874$		0			0
$875$	−19.2705	+	23.0902i	−0.651462	+	0.780590i
$876$		0			0
$877$	21.5438	−	21.5438i	0.727482	−	0.727482i	−0.242636	−	0.970118i	$-0.578012\pi$
$877$	21.5438	−	21.5438i	0.727482	−	0.727482i	0.970118	+	0.242636i	$0.0780119\pi$
$878$		0			0
$879$	−3.80423			−0.128313
$880$		0			0
$881$	6.87539			0.231638			0.115819	−	0.993270i	$-0.463051\pi$
$881$	6.87539			0.231638			0.115819	+	0.993270i	$0.463051\pi$
$882$		0			0
$883$	−2.79837	+	2.79837i	−0.0941728	+	0.0941728i	−0.752624	−	0.658451i	$-0.771212\pi$
$883$	−2.79837	+	2.79837i	−0.0941728	+	0.0941728i	0.658451	+	0.752624i	$0.271212\pi$
$884$		0			0
$885$	−0.212002	+	0.898056i	−0.00712638	+	0.0301878i
$886$		0			0
$887$	11.5187	+	11.5187i	0.386759	+	0.386759i	0.873530	−	0.486770i	$-0.161825\pi$
$887$	11.5187	+	11.5187i	0.386759	+	0.386759i	−0.486770	+	0.873530i	$0.661825\pi$
$888$		0			0
$889$			10.6525i			0.357273i
$890$		0			0
$891$			8.76393i			0.293603i
$892$		0			0
$893$	−6.71040	−	6.71040i	−0.224555	−	0.224555i
$894$		0			0
$895$	14.3188	−	8.84953i	0.478626	−	0.295807i
$896$		0			0
$897$	3.81966	−	3.81966i	0.127535	−	0.127535i
$898$		0			0
$899$	−52.3607			−1.74633
$900$		0			0
$901$	−6.15537			−0.205065
$902$		0			0
$903$	10.8576	−	10.8576i	0.361320	−	0.361320i
$904$		0			0
$905$	28.9443	−	17.8885i	0.962140	−	0.594635i
$906$		0			0
$907$	−7.67376	−	7.67376i	−0.254803	−	0.254803i	0.568133	−	0.822936i	$-0.307666\pi$
$907$	−7.67376	−	7.67376i	−0.254803	−	0.254803i	−0.822936	+	0.568133i	$0.807666\pi$
$908$		0			0
$909$		−	6.49839i		−	0.215538i
$910$		0			0
$911$			10.3026i			0.341341i	0.985328	+	0.170671i	$0.0545934\pi$
$911$			10.3026i			0.341341i	−0.985328	+	0.170671i	$0.945407\pi$
$912$		0			0
$913$	21.4164	+	21.4164i	0.708780	+	0.708780i
$914$		0			0
$915$	0.403252	−	1.70820i	0.0133311	−	0.0564715i
$916$		0			0
$917$	−26.0746	+	26.0746i	−0.861058	+	0.861058i
$918$		0			0
$919$	18.1231			0.597825			0.298913	−	0.954281i	$-0.403376\pi$
$919$	18.1231			0.597825			0.298913	+	0.954281i	$0.403376\pi$
$920$		0			0
$921$	16.7639			0.552390
$922$		0			0
$923$	8.29180	−	8.29180i	0.272928	−	0.272928i
$924$		0			0
$925$	1.62460	+	4.87380i	0.0534165	+	0.160249i
$926$		0			0
$927$	−7.50245	−	7.50245i	−0.246413	−	0.246413i
$928$		0			0
$929$			36.6525i			1.20253i	0.799050	+	0.601264i	$0.205336\pi$
$929$			36.6525i			1.20253i	−0.799050	+	0.601264i	$0.794664\pi$
$930$		0			0
$931$			0.472136i			0.0154736i
$932$		0			0
$933$	12.8658	+	12.8658i	0.421206	+	0.421206i
$934$		0			0
$935$	9.95959	+	2.35114i	0.325714	+	0.0768905i
$936$		0			0
$937$	42.3050	−	42.3050i	1.38204	−	1.38204i	0.541056	−	0.840987i	$-0.318025\pi$
$937$	42.3050	−	42.3050i	1.38204	−	1.38204i	0.840987	−	0.541056i	$-0.181975\pi$
$938$		0			0
$939$	2.18034			0.0711527
$940$		0			0
$941$	37.6183			1.22632			0.613160	−	0.789959i	$-0.289898\pi$
$941$	37.6183			1.22632			0.613160	+	0.789959i	$0.289898\pi$
$942$		0			0
$943$	−24.2784	+	24.2784i	−0.790615	+	0.790615i
$944$		0			0
$945$	−14.4721	−	23.4164i	−0.470779	−	0.761736i
$946$		0			0
$947$	2.14590	+	2.14590i	0.0697323	+	0.0697323i	0.741113	−	0.671381i	$-0.234298\pi$
$947$	2.14590	+	2.14590i	0.0697323	+	0.0697323i	−0.671381	+	0.741113i	$0.734298\pi$
$948$		0			0
$949$			6.84142i			0.222082i
$950$		0			0
$951$		−	4.91428i		−	0.159357i
$952$		0			0
$953$	29.1803	+	29.1803i	0.945244	+	0.945244i	0.998577	−	0.0533329i	$-0.0169844\pi$
$953$	29.1803	+	29.1803i	0.945244	+	0.945244i	−0.0533329	+	0.998577i	$0.516984\pi$
$954$		0			0
$955$	15.5279	+	25.1246i	0.502470	+	0.813013i
$956$		0			0
$957$	−12.3107	+	12.3107i	−0.397950	+	0.397950i
$958$		0			0
$959$	−20.8172			−0.672224
$960$		0			0
$961$	−41.3607			−1.33422
$962$		0			0
$963$	−2.03444	+	2.03444i	−0.0655590	+	0.0655590i
$964$		0			0
$965$	4.53077	+	1.06957i	0.145851	+	0.0344307i
$966$		0			0
$967$	10.9637	+	10.9637i	0.352567	+	0.352567i	0.861064	−	0.508497i	$-0.169799\pi$
$967$	10.9637	+	10.9637i	0.352567	+	0.352567i	−0.508497	+	0.861064i	$0.669799\pi$
$968$		0			0
$969$			2.47214i			0.0794164i
$970$		0			0
$971$		−	15.5967i		−	0.500523i	−0.968178	−	0.250262i	$-0.919483\pi$
$971$		−	15.5967i		−	0.500523i	0.968178	−	0.250262i	$-0.0805167\pi$
$972$		0			0
$973$	−40.7364	−	40.7364i	−1.30595	−	1.30595i
$974$		0			0
$975$	2.00811	−	4.01623i	0.0643111	−	0.128622i
$976$		0			0
$977$	−23.7639	+	23.7639i	−0.760276	+	0.760276i	−0.976372	−	0.216096i	$-0.930667\pi$
$977$	−23.7639	+	23.7639i	−0.760276	+	0.760276i	0.216096	+	0.976372i	$0.430667\pi$
$978$		0			0
$979$	8.00000			0.255681
$980$		0			0
$981$	−32.7849			−1.04674
$982$		0			0
$983$	−18.0171	+	18.0171i	−0.574655	+	0.574655i	−0.933426	−	0.358770i	$-0.883196\pi$
$983$	−18.0171	+	18.0171i	−0.574655	+	0.574655i	0.358770	+	0.933426i	$0.383196\pi$
$984$		0			0
$985$	6.70820	−	28.4164i	0.213741	−	0.905422i
$986$		0			0
$987$	7.88854	+	7.88854i	0.251095	+	0.251095i
$988$		0			0
$989$			39.2833i			1.24914i
$990$		0			0
$991$			14.3188i			0.454853i	0.973795	+	0.227427i	$0.0730312\pi$
$991$			14.3188i			0.454853i	−0.973795	+	0.227427i	$0.926969\pi$
$992$		0			0
$993$	−18.5836	−	18.5836i	−0.589732	−	0.589732i
$994$		0			0
$995$	−41.3050	+	25.5279i	−1.30945	+	0.809288i
$996$		0			0
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	−0.993934	−	0.109979i	$-0.964922\pi$
$997$	−27.9112	+	27.9112i	−0.883955	+	0.883955i	0.109979	+	0.993934i	$0.464922\pi$
$998$		0			0
$999$	−4.70228			−0.148774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.m.1023.4		8
4.3	odd	2		1280.2.n.q.1023.2		8
5.2	odd	4		1280.2.n.q.767.2		8
8.3	odd	2	inner	1280.2.n.m.1023.3		8
8.5	even	2		1280.2.n.q.1023.1		8
16.3	odd	4		160.2.o.a.143.1		8
16.5	even	4		160.2.o.a.143.2		8
16.11	odd	4		40.2.k.a.3.1	✓	8
16.13	even	4		40.2.k.a.3.3	yes	8
20.7	even	4	inner	1280.2.n.m.767.4		8
40.27	even	4		1280.2.n.q.767.1		8
40.37	odd	4	inner	1280.2.n.m.767.3		8
48.5	odd	4		1440.2.bi.c.1423.2		8
48.11	even	4		360.2.w.c.163.4		8
48.29	odd	4		360.2.w.c.163.2		8
48.35	even	4		1440.2.bi.c.1423.3		8
80.3	even	4		800.2.o.g.207.3		8
80.13	odd	4		200.2.k.h.107.4		8
80.19	odd	4		800.2.o.g.143.4		8
80.27	even	4		40.2.k.a.27.3	yes	8
80.29	even	4		200.2.k.h.43.2		8
80.37	odd	4		160.2.o.a.47.1		8
80.43	even	4		200.2.k.h.107.2		8
80.53	odd	4		800.2.o.g.207.4		8
80.59	odd	4		200.2.k.h.43.4		8
80.67	even	4		160.2.o.a.47.2		8
80.69	even	4		800.2.o.g.143.3		8
80.77	odd	4		40.2.k.a.27.1	yes	8
240.77	even	4		360.2.w.c.307.4		8
240.107	odd	4		360.2.w.c.307.2		8
240.197	even	4		1440.2.bi.c.847.3		8
240.227	odd	4		1440.2.bi.c.847.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.1	✓	8	16.11	odd	4
40.2.k.a.3.3	yes	8	16.13	even	4
40.2.k.a.27.1	yes	8	80.77	odd	4
40.2.k.a.27.3	yes	8	80.27	even	4
160.2.o.a.47.1		8	80.37	odd	4
160.2.o.a.47.2		8	80.67	even	4
160.2.o.a.143.1		8	16.3	odd	4
160.2.o.a.143.2		8	16.5	even	4
200.2.k.h.43.2		8	80.29	even	4
200.2.k.h.43.4		8	80.59	odd	4
200.2.k.h.107.2		8	80.43	even	4
200.2.k.h.107.4		8	80.13	odd	4
360.2.w.c.163.2		8	48.29	odd	4
360.2.w.c.163.4		8	48.11	even	4
360.2.w.c.307.2		8	240.107	odd	4
360.2.w.c.307.4		8	240.77	even	4
800.2.o.g.143.3		8	80.69	even	4
800.2.o.g.143.4		8	80.19	odd	4
800.2.o.g.207.3		8	80.3	even	4
800.2.o.g.207.4		8	80.53	odd	4
1280.2.n.m.767.3		8	40.37	odd	4	inner
1280.2.n.m.767.4		8	20.7	even	4	inner
1280.2.n.m.1023.3		8	8.3	odd	2	inner
1280.2.n.m.1023.4		8	1.1	even	1	trivial
1280.2.n.q.767.1		8	40.27	even	4
1280.2.n.q.767.2		8	5.2	odd	4
1280.2.n.q.1023.1		8	8.5	even	2
1280.2.n.q.1023.2		8	4.3	odd	2
1440.2.bi.c.847.2		8	240.227	odd	4
1440.2.bi.c.847.3		8	240.197	even	4
1440.2.bi.c.1423.2		8	48.5	odd	4
1440.2.bi.c.1423.3		8	48.35	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.618034 - 0.618034i) q^{3} +(1.90211 - 1.17557i) q^{5} +(-1.90211 - 1.90211i) q^{7} +2.23607i q^{9} -3.23607i q^{11} +(0.726543 + 0.726543i) q^{13} +(0.449028 - 1.90211i) q^{15} +(-1.00000 + 1.00000i) q^{17} +2.00000 q^{19} -2.35114 q^{21} +(4.25325 - 4.25325i) q^{23} +(2.23607 - 4.47214i) q^{25} +(3.23607 + 3.23607i) q^{27} -6.15537i q^{29} -8.50651i q^{31} +(-2.00000 - 2.00000i) q^{33} +(-5.85410 - 1.38197i) q^{35} +(-0.726543 + 0.726543i) q^{37} +0.898056 q^{39} -5.70820 q^{41} +(-4.61803 + 4.61803i) q^{43} +(2.62866 + 4.25325i) q^{45} +(-3.35520 - 3.35520i) q^{47} +0.236068i q^{49} +1.23607i q^{51} +(3.07768 + 3.07768i) q^{53} +(-3.80423 - 6.15537i) q^{55} +(1.23607 - 1.23607i) q^{57} -0.472136 q^{59} +0.898056 q^{61} +(4.25325 - 4.25325i) q^{63} +(2.23607 + 0.527864i) q^{65} +(4.61803 + 4.61803i) q^{67} -5.25731i q^{69} -11.4127i q^{71} +(4.70820 + 4.70820i) q^{73} +(-1.38197 - 4.14590i) q^{75} +(-6.15537 + 6.15537i) q^{77} -2.90617 q^{79} -2.70820 q^{81} +(-6.61803 + 6.61803i) q^{83} +(-0.726543 + 3.07768i) q^{85} +(-3.80423 - 3.80423i) q^{87} +2.47214i q^{89} -2.76393i q^{91} +(-5.25731 - 5.25731i) q^{93} +(3.80423 - 2.35114i) q^{95} +(4.23607 - 4.23607i) q^{97} +7.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{17} + 16 q^{19} + 8 q^{27} - 16 q^{33} - 20 q^{35} + 8 q^{41} - 28 q^{43} - 8 q^{57} + 32 q^{59} + 28 q^{67} - 16 q^{73} - 20 q^{75} + 32 q^{81} - 44 q^{83} + 16 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^17 + 16 * q^19 + 8 * q^27 - 16 * q^33 - 20 * q^35 + 8 * q^41 - 28 * q^43 - 8 * q^57 + 32 * q^59 + 28 * q^67 - 16 * q^73 - 20 * q^75 + 32 * q^81 - 44 * q^83 + 16 * q^97 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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