LMFDB - Embedded newform 1280.2.n.q.767.4

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:	$\Q(\zeta_{20})$
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			767.4
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	1280.767
Dual form			1280.2.n.q.1023.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 + 1.61803i) q^{3} +(1.17557 - 1.90211i) q^{5} +(1.17557 - 1.17557i) q^{7} +2.23607i q^{9} +O(q^{10})$	\(q+(1.61803 + 1.61803i) q^{3} +(1.17557 - 1.90211i) q^{5} +(1.17557 - 1.17557i) q^{7} +2.23607i q^{9} +1.23607i q^{11} +(3.07768 - 3.07768i) q^{13} +(4.97980 - 1.17557i) q^{15} +(-1.00000 - 1.00000i) q^{17} -2.00000 q^{19} +3.80423 q^{21} +(2.62866 + 2.62866i) q^{23} +(-2.23607 - 4.47214i) q^{25} +(1.23607 - 1.23607i) q^{27} -1.45309i q^{29} +5.25731i q^{31} +(-2.00000 + 2.00000i) q^{33} +(-0.854102 - 3.61803i) q^{35} +(-3.07768 - 3.07768i) q^{37} +9.95959 q^{39} +7.70820 q^{41} +(2.38197 + 2.38197i) q^{43} +(4.25325 + 2.62866i) q^{45} +(7.33094 - 7.33094i) q^{47} +4.23607i q^{49} -3.23607i q^{51} +(-0.726543 + 0.726543i) q^{53} +(2.35114 + 1.45309i) q^{55} +(-3.23607 - 3.23607i) q^{57} -8.47214 q^{59} -9.95959 q^{61} +(2.62866 + 2.62866i) q^{63} +(-2.23607 - 9.47214i) q^{65} +(-2.38197 + 2.38197i) q^{67} +8.50651i q^{69} -7.05342i q^{71} +(-8.70820 + 8.70820i) q^{73} +(3.61803 - 10.8541i) q^{75} +(1.45309 + 1.45309i) q^{77} +12.3107 q^{79} +10.7082 q^{81} +(4.38197 + 4.38197i) q^{83} +(-3.07768 + 0.726543i) q^{85} +(2.35114 - 2.35114i) q^{87} +6.47214i q^{89} -7.23607i q^{91} +(-8.50651 + 8.50651i) q^{93} +(-2.35114 + 3.80423i) q^{95} +(-0.236068 - 0.236068i) q^{97} -2.76393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3}+O(q^{10}) $ 8 * q + 4 * q^3	$ 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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.61803	+	1.61803i	0.934172	+	0.934172i	0.997963	−	0.0637909i	$-0.0203191\pi$
$3$	1.61803	+	1.61803i	0.934172	+	0.934172i	−0.0637909	+	0.997963i	$0.520319\pi$
$4$		0			0
$5$	1.17557	−	1.90211i	0.525731	−	0.850651i
$5$	1.17557	−	1.90211i	0.525731	−	0.850651i
$6$		0			0
$7$	1.17557	−	1.17557i	0.444324	−	0.444324i	−0.449138	−	0.893462i	$-0.648269\pi$
$7$	1.17557	−	1.17557i	0.444324	−	0.444324i	0.893462	+	0.449138i	$0.148269\pi$
$8$		0			0
$9$			2.23607i			0.745356i
$10$		0			0
$11$			1.23607i			0.372689i	0.982485	+	0.186344i	$0.0596640\pi$
$11$			1.23607i			0.372689i	−0.982485	+	0.186344i	$0.940336\pi$
$12$		0			0
$13$	3.07768	−	3.07768i	0.853596	−	0.853596i	−0.136978	−	0.990574i	$-0.543739\pi$
$13$	3.07768	−	3.07768i	0.853596	−	0.853596i	0.990574	+	0.136978i	$0.0437390\pi$
$14$		0			0
$15$	4.97980	−	1.17557i	1.28578	−	0.303531i
$16$		0			0
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	0.575363	−	0.817898i	$-0.304861\pi$
$17$	−1.00000	−	1.00000i	−0.242536	−	0.242536i	−0.817898	+	0.575363i	$0.804861\pi$
$18$		0			0
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$		0			0
$21$	3.80423			0.830150
$22$		0			0
$23$	2.62866	+	2.62866i	0.548113	+	0.548113i	0.925895	−	0.377782i	$-0.123313\pi$
$23$	2.62866	+	2.62866i	0.548113	+	0.548113i	−0.377782	+	0.925895i	$0.623313\pi$
$24$		0			0
$25$	−2.23607	−	4.47214i	−0.447214	−	0.894427i
$26$		0			0
$27$	1.23607	−	1.23607i	0.237881	−	0.237881i
$28$		0			0
$29$		−	1.45309i		−	0.269831i	−0.990857	−	0.134916i	$-0.956924\pi$
$29$		−	1.45309i		−	0.269831i	0.990857	−	0.134916i	$-0.0430763\pi$
$30$		0			0
$31$			5.25731i			0.944241i	0.881534	+	0.472120i	$0.156511\pi$
$31$			5.25731i			0.944241i	−0.881534	+	0.472120i	$0.843489\pi$
$32$		0			0
$33$	−2.00000	+	2.00000i	−0.348155	+	0.348155i
$34$		0			0
$35$	−0.854102	−	3.61803i	−0.144370	−	0.611559i
$36$		0			0
$37$	−3.07768	−	3.07768i	−0.505968	−	0.505968i	0.407318	−	0.913286i	$-0.366464\pi$
$37$	−3.07768	−	3.07768i	−0.505968	−	0.505968i	−0.913286	+	0.407318i	$0.866464\pi$
$38$		0			0
$39$	9.95959			1.59481
$40$		0			0
$41$	7.70820			1.20382			0.601910	−	0.798564i	$-0.294407\pi$
$41$	7.70820			1.20382			0.601910	+	0.798564i	$0.294407\pi$
$42$		0			0
$43$	2.38197	+	2.38197i	0.363246	+	0.363246i	0.865007	−	0.501760i	$-0.167314\pi$
$43$	2.38197	+	2.38197i	0.363246	+	0.363246i	−0.501760	+	0.865007i	$0.667314\pi$
$44$		0			0
$45$	4.25325	+	2.62866i	0.634038	+	0.391857i
$46$		0			0
$47$	7.33094	−	7.33094i	1.06933	−	1.06933i	0.0719165	−	0.997411i	$-0.477088\pi$
$47$	7.33094	−	7.33094i	1.06933	−	1.06933i	0.997411	−	0.0719165i	$-0.0229115\pi$
$48$		0			0
$49$			4.23607i			0.605153i
$50$		0			0
$51$		−	3.23607i		−	0.453140i
$52$		0			0
$53$	−0.726543	+	0.726543i	−0.0997983	+	0.0997983i	−0.755243	−	0.655445i	$-0.772481\pi$
$53$	−0.726543	+	0.726543i	−0.0997983	+	0.0997983i	0.655445	+	0.755243i	$0.272481\pi$
$54$		0			0
$55$	2.35114	+	1.45309i	0.317028	+	0.195934i
$56$		0			0
$57$	−3.23607	−	3.23607i	−0.428628	−	0.428628i
$58$		0			0
$59$	−8.47214			−1.10298			−0.551489	−	0.834182i	$-0.685940\pi$
$59$	−8.47214			−1.10298			−0.551489	+	0.834182i	$0.685940\pi$
$60$		0			0
$61$	−9.95959			−1.27520			−0.637598	−	0.770370i	$-0.720072\pi$
$61$	−9.95959			−1.27520			−0.637598	+	0.770370i	$0.720072\pi$
$62$		0			0
$63$	2.62866	+	2.62866i	0.331179	+	0.331179i
$64$		0			0
$65$	−2.23607	−	9.47214i	−0.277350	−	1.17487i
$66$		0			0
$67$	−2.38197	+	2.38197i	−0.291003	+	0.291003i	−0.837477	−	0.546473i	$-0.815970\pi$
$67$	−2.38197	+	2.38197i	−0.291003	+	0.291003i	0.546473	+	0.837477i	$0.315970\pi$
$68$		0			0
$69$			8.50651i			1.02406i
$70$		0			0
$71$		−	7.05342i		−	0.837087i	−0.908197	−	0.418544i	$-0.862541\pi$
$71$		−	7.05342i		−	0.837087i	0.908197	−	0.418544i	$-0.137459\pi$
$72$		0			0
$73$	−8.70820	+	8.70820i	−1.01922	+	1.01922i	−0.0194065	+	0.999812i	$0.506178\pi$
$73$	−8.70820	+	8.70820i	−1.01922	+	1.01922i	−0.999812	+	0.0194065i	$0.993822\pi$
$74$		0			0
$75$	3.61803	−	10.8541i	0.417775	−	1.25332i
$76$		0			0
$77$	1.45309	+	1.45309i	0.165594	+	0.165594i
$78$		0			0
$79$	12.3107			1.38507			0.692533	−	0.721386i	$-0.256495\pi$
$79$	12.3107			1.38507			0.692533	+	0.721386i	$0.256495\pi$
$80$		0			0
$81$	10.7082			1.18980
$82$		0			0
$83$	4.38197	+	4.38197i	0.480983	+	0.480983i	0.905446	−	0.424462i	$-0.139537\pi$
$83$	4.38197	+	4.38197i	0.480983	+	0.480983i	−0.424462	+	0.905446i	$0.639537\pi$
$84$		0			0
$85$	−3.07768	+	0.726543i	−0.333822	+	0.0788046i
$86$		0			0
$87$	2.35114	−	2.35114i	0.252069	−	0.252069i
$88$		0			0
$89$			6.47214i			0.686045i	0.939327	+	0.343023i	$0.111451\pi$
$89$			6.47214i			0.686045i	−0.939327	+	0.343023i	$0.888549\pi$
$90$		0			0
$91$		−	7.23607i		−	0.758546i
$92$		0			0
$93$	−8.50651	+	8.50651i	−0.882084	+	0.882084i
$94$		0			0
$95$	−2.35114	+	3.80423i	−0.241222	+	0.390305i
$96$		0			0
$97$	−0.236068	−	0.236068i	−0.0239691	−	0.0239691i	0.695021	−	0.718990i	$-0.255395\pi$
$97$	−0.236068	−	0.236068i	−0.0239691	−	0.0239691i	−0.718990	+	0.695021i	$0.755395\pi$
$98$		0			0
$99$	−2.76393			−0.277786
$100$		0			0
$101$	−12.3107			−1.22496			−0.612482	−	0.790485i	$-0.709829\pi$
$101$	−12.3107			−1.22496			−0.612482	+	0.790485i	$0.709829\pi$
$102$		0			0
$103$	7.33094	+	7.33094i	0.722339	+	0.722339i	0.969081	−	0.246742i	$-0.0793601\pi$
$103$	7.33094	+	7.33094i	0.722339	+	0.722339i	−0.246742	+	0.969081i	$0.579360\pi$
$104$		0			0
$105$	4.47214	−	7.23607i	0.436436	−	0.706168i
$106$		0			0
$107$	−12.0902	+	12.0902i	−1.16880	+	1.16880i	−0.186310	+	0.982491i	$0.559653\pi$
$107$	−12.0902	+	12.0902i	−1.16880	+	1.16880i	−0.982491	+	0.186310i	$0.940347\pi$
$108$		0			0
$109$			6.71040i			0.642739i	0.946954	+	0.321370i	$0.104143\pi$
$109$			6.71040i			0.642739i	−0.946954	+	0.321370i	$0.895857\pi$
$110$		0			0
$111$		−	9.95959i		−	0.945323i
$112$		0			0
$113$	−4.70820	+	4.70820i	−0.442911	+	0.442911i	−0.892989	−	0.450078i	$-0.851396\pi$
$113$	−4.70820	+	4.70820i	−0.442911	+	0.442911i	0.450078	+	0.892989i	$0.351396\pi$
$114$		0			0
$115$	8.09017	−	1.90983i	0.754412	−	0.178093i
$116$		0			0
$117$	6.88191	+	6.88191i	0.636233	+	0.636233i
$118$		0			0
$119$	−2.35114			−0.215529
$120$		0			0
$121$	9.47214			0.861103
$122$		0			0
$123$	12.4721	+	12.4721i	1.12457	+	1.12457i
$124$		0			0
$125$	−11.1352	−	1.00406i	−0.995959	−	0.0898056i
$126$		0			0
$127$	−8.78402	+	8.78402i	−0.779456	+	0.779456i	−0.979738	−	0.200282i	$-0.935814\pi$
$127$	−8.78402	+	8.78402i	−0.779456	+	0.779456i	0.200282	+	0.979738i	$0.435814\pi$
$128$		0			0
$129$			7.70820i			0.678670i
$130$		0			0
$131$		−	0.291796i		−	0.0254943i	−0.999919	−	0.0127472i	$-0.995942\pi$
$131$		−	0.291796i		−	0.0254943i	0.999919	−	0.0127472i	$-0.00405766\pi$
$132$		0			0
$133$	−2.35114	+	2.35114i	−0.203870	+	0.203870i
$134$		0			0
$135$	−0.898056	−	3.80423i	−0.0772924	−	0.327416i
$136$		0			0
$137$	−3.47214	−	3.47214i	−0.296645	−	0.296645i	0.543054	−	0.839698i	$-0.317268\pi$
$137$	−3.47214	−	3.47214i	−0.296645	−	0.296645i	−0.839698	+	0.543054i	$0.817268\pi$
$138$		0			0
$139$	5.41641			0.459414			0.229707	−	0.973260i	$-0.426223\pi$
$139$	5.41641			0.459414			0.229707	+	0.973260i	$0.426223\pi$
$140$		0			0
$141$	23.7234			1.99787
$142$		0			0
$143$	3.80423	+	3.80423i	0.318125	+	0.318125i
$144$		0			0
$145$	−2.76393	−	1.70820i	−0.229532	−	0.141859i
$146$		0			0
$147$	−6.85410	+	6.85410i	−0.565317	+	0.565317i
$148$		0			0
$149$		−	13.2088i		−	1.08211i	−0.840988	−	0.541053i	$-0.818026\pi$
$149$		−	13.2088i		−	1.08211i	0.840988	−	0.541053i	$-0.181974\pi$
$150$		0			0
$151$			14.6619i			1.19317i	0.802551	+	0.596583i	$0.203475\pi$
$151$			14.6619i			1.19317i	−0.802551	+	0.596583i	$0.796525\pi$
$152$		0			0
$153$	2.23607	−	2.23607i	0.180775	−	0.180775i
$154$		0			0
$155$	10.0000	+	6.18034i	0.803219	+	0.496417i
$156$		0			0
$157$	−9.78808	−	9.78808i	−0.781174	−	0.781174i	0.198855	−	0.980029i	$-0.436278\pi$
$157$	−9.78808	−	9.78808i	−0.781174	−	0.781174i	−0.980029	+	0.198855i	$0.936278\pi$
$158$		0			0
$159$	−2.35114			−0.186458
$160$		0			0
$161$	6.18034			0.487079
$162$		0			0
$163$	7.14590	+	7.14590i	0.559710	+	0.559710i	0.929225	−	0.369515i	$-0.120476\pi$
$163$	7.14590	+	7.14590i	0.559710	+	0.559710i	−0.369515	+	0.929225i	$0.620476\pi$
$164$		0			0
$165$	1.45309	+	6.15537i	0.113123	+	0.479195i
$166$		0			0
$167$	0.277515	−	0.277515i	0.0214747	−	0.0214747i	−0.696288	−	0.717763i	$-0.745166\pi$
$167$	0.277515	−	0.277515i	0.0214747	−	0.0214747i	0.717763	+	0.696288i	$0.245166\pi$
$168$		0			0
$169$		−	5.94427i		−	0.457252i
$170$		0			0
$171$		−	4.47214i		−	0.341993i
$172$		0			0
$173$	6.32688	−	6.32688i	0.481024	−	0.481024i	−0.424435	−	0.905459i	$-0.639527\pi$
$173$	6.32688	−	6.32688i	0.481024	−	0.481024i	0.905459	+	0.424435i	$0.139527\pi$
$174$		0			0
$175$	−7.88597	−	2.62866i	−0.596123	−	0.198708i
$176$		0			0
$177$	−13.7082	−	13.7082i	−1.03037	−	1.03037i
$178$		0			0
$179$	−16.4721			−1.23119			−0.615593	−	0.788065i	$-0.711083\pi$
$179$	−16.4721			−1.23119			−0.615593	+	0.788065i	$0.711083\pi$
$180$		0			0
$181$	9.40456			0.699036			0.349518	−	0.936930i	$-0.386345\pi$
$181$	9.40456			0.699036			0.349518	+	0.936930i	$0.386345\pi$
$182$		0			0
$183$	−16.1150	−	16.1150i	−1.19125	−	1.19125i
$184$		0			0
$185$	−9.47214	+	2.23607i	−0.696405	+	0.164399i
$186$		0			0
$187$	1.23607	−	1.23607i	0.0903902	−	0.0903902i
$188$		0			0
$189$		−	2.90617i		−	0.211393i
$190$		0			0
$191$		−	12.8658i		−	0.930934i	−0.885065	−	0.465467i	$-0.845886\pi$
$191$		−	12.8658i		−	0.930934i	0.885065	−	0.465467i	$-0.154114\pi$
$192$		0			0
$193$	−7.47214	+	7.47214i	−0.537856	+	0.537856i	−0.922899	−	0.385043i	$-0.874187\pi$
$193$	−7.47214	+	7.47214i	−0.537856	+	0.537856i	0.385043	+	0.922899i	$0.374187\pi$
$194$		0			0
$195$	11.7082	−	18.9443i	0.838442	−	1.35663i
$196$		0			0
$197$	−2.17963	−	2.17963i	−0.155292	−	0.155292i	0.625185	−	0.780477i	$-0.285024\pi$
$197$	−2.17963	−	2.17963i	−0.155292	−	0.155292i	−0.780477	+	0.625185i	$0.785024\pi$
$198$		0			0
$199$	−18.1231			−1.28471			−0.642355	−	0.766407i	$-0.722043\pi$
$199$	−18.1231			−1.28471			−0.642355	+	0.766407i	$0.722043\pi$
$200$		0			0
$201$	−7.70820			−0.543695
$202$		0			0
$203$	−1.70820	−	1.70820i	−0.119892	−	0.119892i
$204$		0			0
$205$	9.06154	−	14.6619i	0.632885	−	1.02403i
$206$		0			0
$207$	−5.87785	+	5.87785i	−0.408539	+	0.408539i
$208$		0			0
$209$		−	2.47214i		−	0.171001i
$210$		0			0
$211$		−	15.7082i		−	1.08140i	−0.841216	−	0.540699i	$-0.818160\pi$
$211$		−	15.7082i		−	1.08140i	0.841216	−	0.540699i	$-0.181840\pi$
$212$		0			0
$213$	11.4127	−	11.4127i	0.781984	−	0.781984i
$214$		0			0
$215$	7.33094	−	1.73060i	0.499966	−	0.118026i
$216$		0			0
$217$	6.18034	+	6.18034i	0.419549	+	0.419549i
$218$		0			0
$219$	−28.1803			−1.90425
$220$		0			0
$221$	−6.15537			−0.414055
$222$		0			0
$223$	−1.73060	−	1.73060i	−0.115890	−	0.115890i	0.646784	−	0.762673i	$-0.276114\pi$
$223$	−1.73060	−	1.73060i	−0.115890	−	0.115890i	−0.762673	+	0.646784i	$0.776114\pi$
$224$		0			0
$225$	10.0000	−	5.00000i	0.666667	−	0.333333i
$226$		0			0
$227$	−11.6180	+	11.6180i	−0.771116	+	0.771116i	−0.978302	−	0.207186i	$-0.933570\pi$
$227$	−11.6180	+	11.6180i	−0.771116	+	0.771116i	0.207186	+	0.978302i	$0.433570\pi$
$228$		0			0
$229$		−	21.3723i		−	1.41232i	−0.708053	−	0.706160i	$-0.750426\pi$
$229$		−	21.3723i		−	1.41232i	0.708053	−	0.706160i	$-0.249574\pi$
$230$		0			0
$231$			4.70228i			0.309387i
$232$		0			0
$233$	3.47214	−	3.47214i	0.227467	−	0.227467i	−0.584167	−	0.811634i	$-0.698579\pi$
$233$	3.47214	−	3.47214i	0.227467	−	0.227467i	0.811634	+	0.584167i	$0.198579\pi$
$234$		0			0
$235$	−5.32624	−	22.5623i	−0.347445	−	1.47180i
$236$		0			0
$237$	19.9192	+	19.9192i	1.29389	+	1.29389i
$238$		0			0
$239$	−29.3238			−1.89680			−0.948398	−	0.317083i	$-0.897297\pi$
$239$	−29.3238			−1.89680			−0.948398	+	0.317083i	$0.897297\pi$
$240$		0			0
$241$	6.76393			0.435703			0.217852	−	0.975982i	$-0.430095\pi$
$241$	6.76393			0.435703			0.217852	+	0.975982i	$0.430095\pi$
$242$		0			0
$243$	13.6180	+	13.6180i	0.873597	+	0.873597i
$244$		0			0
$245$	8.05748	+	4.97980i	0.514774	+	0.318148i
$246$		0			0
$247$	−6.15537	+	6.15537i	−0.391657	+	0.391657i
$248$		0			0
$249$			14.1803i			0.898643i
$250$		0			0
$251$		−	22.1803i		−	1.40001i	−0.714138	−	0.700005i	$-0.753181\pi$
$251$		−	22.1803i		−	1.40001i	0.714138	−	0.700005i	$-0.246819\pi$
$252$		0			0
$253$	−3.24920	+	3.24920i	−0.204275	+	0.204275i
$254$		0			0
$255$	−6.15537	−	3.80423i	−0.385464	−	0.238230i
$256$		0			0
$257$	18.7082	+	18.7082i	1.16699	+	1.16699i	0.982913	+	0.184073i	$0.0589283\pi$
$257$	18.7082	+	18.7082i	1.16699	+	1.16699i	0.184073	+	0.982913i	$0.441072\pi$
$258$		0			0
$259$	−7.23607			−0.449627
$260$		0			0
$261$	3.24920			0.201120
$262$		0			0
$263$	−16.3925	−	16.3925i	−1.01080	−	1.01080i	−0.999941	−	0.0108623i	$-0.996542\pi$
$263$	−16.3925	−	16.3925i	−1.01080	−	1.01080i	−0.0108623	−	0.999941i	$-0.503458\pi$
$264$		0			0
$265$	0.527864	+	2.23607i	0.0324264	+	0.137361i
$266$		0			0
$267$	−10.4721	+	10.4721i	−0.640884	+	0.640884i
$268$		0			0
$269$		−	17.9111i		−	1.09206i	−0.837766	−	0.546029i	$-0.816139\pi$
$269$		−	17.9111i		−	1.09206i	0.837766	−	0.546029i	$-0.183861\pi$
$270$		0			0
$271$			31.6749i			1.92411i	0.272851	+	0.962056i	$0.412033\pi$
$271$			31.6749i			1.92411i	−0.272851	+	0.962056i	$0.587967\pi$
$272$		0			0
$273$	11.7082	−	11.7082i	0.708613	−	0.708613i
$274$		0			0
$275$	5.52786	−	2.76393i	0.333343	−	0.166671i
$276$		0			0
$277$	2.17963	+	2.17963i	0.130961	+	0.130961i	0.769549	−	0.638588i	$-0.220481\pi$
$277$	2.17963	+	2.17963i	0.130961	+	0.130961i	−0.638588	+	0.769549i	$0.720481\pi$
$278$		0			0
$279$	−11.7557			−0.703796
$280$		0			0
$281$	−3.70820			−0.221213			−0.110606	−	0.993864i	$-0.535279\pi$
$281$	−3.70820			−0.221213			−0.110606	+	0.993864i	$0.535279\pi$
$282$		0			0
$283$	15.6180	+	15.6180i	0.928396	+	0.928396i	0.997602	−	0.0692066i	$-0.0220468\pi$
$283$	15.6180	+	15.6180i	0.928396	+	0.928396i	−0.0692066	+	0.997602i	$0.522047\pi$
$284$		0			0
$285$	−9.95959	+	2.35114i	−0.589955	+	0.139270i
$286$		0			0
$287$	9.06154	−	9.06154i	0.534886	−	0.534886i
$288$		0			0
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$		−	0.763932i		−	0.0447825i
$292$		0			0
$293$	0.726543	−	0.726543i	0.0424451	−	0.0424451i	−0.685566	−	0.728011i	$-0.740445\pi$
$293$	0.726543	−	0.726543i	0.0424451	−	0.0424451i	0.728011	+	0.685566i	$0.240445\pi$
$294$		0			0
$295$	−9.95959	+	16.1150i	−0.579870	+	0.938249i
$296$		0			0
$297$	1.52786	+	1.52786i	0.0886557	+	0.0886557i
$298$		0			0
$299$	16.1803			0.935733
$300$		0			0
$301$	5.60034			0.322798
$302$		0			0
$303$	−19.9192	−	19.9192i	−1.14433	−	1.14433i
$304$		0			0
$305$	−11.7082	+	18.9443i	−0.670410	+	1.08475i
$306$		0			0
$307$	6.56231	−	6.56231i	0.374531	−	0.374531i	−0.494594	−	0.869124i	$-0.664683\pi$
$307$	6.56231	−	6.56231i	0.374531	−	0.374531i	0.869124	+	0.494594i	$0.164683\pi$
$308$		0			0
$309$			23.7234i			1.34958i
$310$		0			0
$311$		−	8.16348i		−	0.462909i	−0.972846	−	0.231454i	$-0.925652\pi$
$311$		−	8.16348i		−	0.462909i	0.972846	−	0.231454i	$-0.0743484\pi$
$312$		0			0
$313$	6.23607	−	6.23607i	0.352483	−	0.352483i	−0.508549	−	0.861033i	$-0.669818\pi$
$313$	6.23607	−	6.23607i	0.352483	−	0.352483i	0.861033	+	0.508549i	$0.169818\pi$
$314$		0			0
$315$	8.09017	−	1.90983i	0.455829	−	0.107607i
$316$		0			0
$317$	−10.6861	−	10.6861i	−0.600193	−	0.600193i	0.340171	−	0.940364i	$-0.389515\pi$
$317$	−10.6861	−	10.6861i	−0.600193	−	0.600193i	−0.940364	+	0.340171i	$0.889515\pi$
$318$		0			0
$319$	1.79611			0.100563
$320$		0			0
$321$	−39.1246			−2.18372
$322$		0			0
$323$	2.00000	+	2.00000i	0.111283	+	0.111283i
$324$		0			0
$325$	−20.6457	−	6.88191i	−1.14522	−	0.381740i
$326$		0			0
$327$	−10.8576	+	10.8576i	−0.600429	+	0.600429i
$328$		0			0
$329$		−	17.2361i		−	0.950255i
$330$		0			0
$331$			28.0689i			1.54281i	0.636347	+	0.771403i	$0.280445\pi$
$331$			28.0689i			1.54281i	−0.636347	+	0.771403i	$0.719555\pi$
$332$		0			0
$333$	6.88191	−	6.88191i	0.377126	−	0.377126i
$334$		0			0
$335$	1.73060	+	7.33094i	0.0945528	+	0.400532i
$336$		0			0
$337$	−2.05573	−	2.05573i	−0.111983	−	0.111983i	0.648895	−	0.760878i	$-0.275231\pi$
$337$	−2.05573	−	2.05573i	−0.111983	−	0.111983i	−0.760878	+	0.648895i	$0.775231\pi$
$338$		0			0
$339$	−15.2361			−0.827510
$340$		0			0
$341$	−6.49839			−0.351908
$342$		0			0
$343$	13.2088	+	13.2088i	0.713208	+	0.713208i
$344$		0			0
$345$	16.1803	+	10.0000i	0.871120	+	0.538382i
$346$		0			0
$347$	3.03444	−	3.03444i	0.162897	−	0.162897i	−0.620952	−	0.783849i	$-0.713254\pi$
$347$	3.03444	−	3.03444i	0.162897	−	0.162897i	0.783849	+	0.620952i	$0.213254\pi$
$348$		0			0
$349$			15.5599i			0.832904i	0.909158	+	0.416452i	$0.136727\pi$
$349$			15.5599i			0.832904i	−0.909158	+	0.416452i	$0.863273\pi$
$350$		0			0
$351$		−	7.60845i		−	0.406109i
$352$		0			0
$353$	4.41641	−	4.41641i	0.235062	−	0.235062i	−0.579740	−	0.814802i	$-0.696846\pi$
$353$	4.41641	−	4.41641i	0.235062	−	0.235062i	0.814802	+	0.579740i	$0.196846\pi$
$354$		0			0
$355$	−13.4164	−	8.29180i	−0.712069	−	0.440083i
$356$		0			0
$357$	−3.80423	−	3.80423i	−0.201341	−	0.201341i
$358$		0			0
$359$	−1.79611			−0.0947952			−0.0473976	−	0.998876i	$-0.515093\pi$
$359$	−1.79611			−0.0947952			−0.0473976	+	0.998876i	$0.515093\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$	15.3262	+	15.3262i	0.804419	+	0.804419i
$364$		0			0
$365$	6.32688	+	26.8011i	0.331164	+	1.40283i
$366$		0			0
$367$	−24.0009	+	24.0009i	−1.25284	+	1.25284i	−0.298396	+	0.954442i	$0.596452\pi$
$367$	−24.0009	+	24.0009i	−1.25284	+	1.25284i	−0.954442	+	0.298396i	$0.903548\pi$
$368$		0			0
$369$			17.2361i			0.897274i
$370$		0			0
$371$			1.70820i			0.0886855i
$372$		0			0
$373$	−15.0454	+	15.0454i	−0.779021	+	0.779021i	−0.979664	−	0.200644i	$-0.935697\pi$
$373$	−15.0454	+	15.0454i	−0.779021	+	0.779021i	0.200644	+	0.979664i	$0.435697\pi$
$374$		0			0
$375$	−16.3925	−	19.6417i	−0.846504	−	1.01429i
$376$		0			0
$377$	−4.47214	−	4.47214i	−0.230327	−	0.230327i
$378$		0			0
$379$	−35.8885			−1.84347			−0.921735	−	0.387820i	$-0.873228\pi$
$379$	−35.8885			−1.84347			−0.921735	+	0.387820i	$0.873228\pi$
$380$		0			0
$381$	−28.4257			−1.45629
$382$		0			0
$383$	−11.1352	−	11.1352i	−0.568980	−	0.568980i	0.362862	−	0.931843i	$-0.381799\pi$
$383$	−11.1352	−	11.1352i	−0.568980	−	0.568980i	−0.931843	+	0.362862i	$0.881799\pi$
$384$		0			0
$385$	4.47214	−	1.05573i	0.227921	−	0.0538049i
$386$		0			0
$387$	−5.32624	+	5.32624i	−0.270748	+	0.270748i
$388$		0			0
$389$			23.7234i			1.20282i	0.798939	+	0.601412i	$0.205395\pi$
$389$			23.7234i			1.20282i	−0.798939	+	0.601412i	$0.794605\pi$
$390$		0			0
$391$		−	5.25731i		−	0.265874i
$392$		0			0
$393$	0.472136	−	0.472136i	0.0238161	−	0.0238161i
$394$		0			0
$395$	14.4721	−	23.4164i	0.728172	−	1.17821i
$396$		0			0
$397$	−7.22494	−	7.22494i	−0.362609	−	0.362609i	0.502164	−	0.864773i	$-0.332538\pi$
$397$	−7.22494	−	7.22494i	−0.362609	−	0.362609i	−0.864773	+	0.502164i	$0.832538\pi$
$398$		0			0
$399$	−7.60845			−0.380899
$400$		0			0
$401$	−3.88854			−0.194185			−0.0970923	−	0.995275i	$-0.530954\pi$
$401$	−3.88854			−0.194185			−0.0970923	+	0.995275i	$0.530954\pi$
$402$		0			0
$403$	16.1803	+	16.1803i	0.806000	+	0.806000i
$404$		0			0
$405$	12.5882	−	20.3682i	0.625515	−	1.01210i
$406$		0			0
$407$	3.80423	−	3.80423i	0.188568	−	0.188568i
$408$		0			0
$409$		−	27.5967i		−	1.36457i	−0.731086	−	0.682286i	$-0.760986\pi$
$409$		−	27.5967i		−	1.36457i	0.731086	−	0.682286i	$-0.239014\pi$
$410$		0			0
$411$		−	11.2361i		−	0.554234i
$412$		0			0
$413$	−9.95959	+	9.95959i	−0.490080	+	0.490080i
$414$		0			0
$415$	13.4863	−	3.18368i	0.662017	−	0.156281i
$416$		0			0
$417$	8.76393	+	8.76393i	0.429172	+	0.429172i
$418$		0			0
$419$	24.8328			1.21316			0.606581	−	0.795022i	$-0.292540\pi$
$419$	24.8328			1.21316			0.606581	+	0.795022i	$0.292540\pi$
$420$		0			0
$421$	3.46120			0.168689			0.0843443	−	0.996437i	$-0.473120\pi$
$421$	3.46120			0.168689			0.0843443	+	0.996437i	$0.473120\pi$
$422$		0			0
$423$	16.3925	+	16.3925i	0.797029	+	0.797029i
$424$		0			0
$425$	−2.23607	+	6.70820i	−0.108465	+	0.325396i
$426$		0			0
$427$	−11.7082	+	11.7082i	−0.566600	+	0.566600i
$428$		0			0
$429$			12.3107i			0.594368i
$430$		0			0
$431$		−	11.7557i		−	0.566252i	−0.959083	−	0.283126i	$-0.908628\pi$
$431$		−	11.7557i		−	0.566252i	0.959083	−	0.283126i	$-0.0913715\pi$
$432$		0			0
$433$	23.1803	−	23.1803i	1.11398	−	1.11398i	0.121369	−	0.992608i	$-0.461272\pi$
$433$	23.1803	−	23.1803i	1.11398	−	1.11398i	0.992608	−	0.121369i	$-0.0387283\pi$
$434$		0			0
$435$	−1.70820	−	7.23607i	−0.0819021	−	0.346943i
$436$		0			0
$437$	−5.25731	−	5.25731i	−0.251491	−	0.251491i
$438$		0			0
$439$	11.2007			0.534579			0.267290	−	0.963616i	$-0.413872\pi$
$439$	11.2007			0.534579			0.267290	+	0.963616i	$0.413872\pi$
$440$		0			0
$441$	−9.47214			−0.451054
$442$		0			0
$443$	10.0902	+	10.0902i	0.479398	+	0.479398i	0.904939	−	0.425541i	$-0.139916\pi$
$443$	10.0902	+	10.0902i	0.479398	+	0.479398i	−0.425541	+	0.904939i	$0.639916\pi$
$444$		0			0
$445$	12.3107	+	7.60845i	0.583585	+	0.360675i
$446$		0			0
$447$	21.3723	−	21.3723i	1.01087	−	1.01087i
$448$		0			0
$449$		−	31.5967i		−	1.49114i	−0.666426	−	0.745571i	$-0.732177\pi$
$449$		−	31.5967i		−	1.49114i	0.666426	−	0.745571i	$-0.267823\pi$
$450$		0			0
$451$			9.52786i			0.448650i
$452$		0			0
$453$	−23.7234	+	23.7234i	−1.11462	+	1.11462i
$454$		0			0
$455$	−13.7638	−	8.50651i	−0.645258	−	0.398791i
$456$		0			0
$457$	21.6525	+	21.6525i	1.01286	+	1.01286i	0.999916	+	0.0129439i	$0.00412028\pi$
$457$	21.6525	+	21.6525i	1.01286	+	1.01286i	0.0129439	+	0.999916i	$0.495880\pi$
$458$		0			0
$459$	−2.47214			−0.115389
$460$		0			0
$461$	−6.49839			−0.302660			−0.151330	−	0.988483i	$-0.548356\pi$
$461$	−6.49839			−0.302660			−0.151330	+	0.988483i	$0.548356\pi$
$462$		0			0
$463$	17.2905	+	17.2905i	0.803559	+	0.803559i	0.983650	−	0.180091i	$-0.0576392\pi$
$463$	17.2905	+	17.2905i	0.803559	+	0.803559i	−0.180091	+	0.983650i	$0.557639\pi$
$464$		0			0
$465$	6.18034	+	26.1803i	0.286606	+	1.21408i
$466$		0			0
$467$	−2.67376	+	2.67376i	−0.123727	+	0.123727i	−0.766259	−	0.642532i	$-0.777884\pi$
$467$	−2.67376	+	2.67376i	−0.123727	+	0.123727i	0.642532	+	0.766259i	$0.277884\pi$
$468$		0			0
$469$			5.60034i			0.258600i
$470$		0			0
$471$		−	31.6749i		−	1.45950i
$472$		0			0
$473$	−2.94427	+	2.94427i	−0.135378	+	0.135378i
$474$		0			0
$475$	4.47214	+	8.94427i	0.205196	+	0.410391i
$476$		0			0
$477$	−1.62460	−	1.62460i	−0.0743853	−	0.0743853i
$478$		0			0
$479$	7.60845			0.347639			0.173820	−	0.984778i	$-0.444389\pi$
$479$	7.60845			0.347639			0.173820	+	0.984778i	$0.444389\pi$
$480$		0			0
$481$	−18.9443			−0.863784
$482$		0			0
$483$	10.0000	+	10.0000i	0.455016	+	0.455016i
$484$		0			0
$485$	−0.726543	+	0.171513i	−0.0329906	+	0.00778802i
$486$		0			0
$487$	−9.33905	+	9.33905i	−0.423193	+	0.423193i	−0.886302	−	0.463109i	$-0.846734\pi$
$487$	−9.33905	+	9.33905i	−0.423193	+	0.423193i	0.463109	+	0.886302i	$0.346734\pi$
$488$		0			0
$489$			23.1246i			1.04573i
$490$		0			0
$491$		−	10.7639i		−	0.485769i	−0.970055	−	0.242885i	$-0.921906\pi$
$491$		−	10.7639i		−	0.485769i	0.970055	−	0.242885i	$-0.0780937\pi$
$492$		0			0
$493$	−1.45309	+	1.45309i	−0.0654437	+	0.0654437i
$494$		0			0
$495$	−3.24920	+	5.25731i	−0.146041	+	0.236299i
$496$		0			0
$497$	−8.29180	−	8.29180i	−0.371938	−	0.371938i
$498$		0			0
$499$	−23.8885			−1.06940			−0.534699	−	0.845043i	$-0.679575\pi$
$499$	−23.8885			−1.06940			−0.534699	+	0.845043i	$0.679575\pi$
$500$		0			0
$501$	0.898056			0.0401222
$502$		0			0
$503$	5.53483	+	5.53483i	0.246786	+	0.246786i	0.819650	−	0.572864i	$-0.194168\pi$
$503$	5.53483	+	5.53483i	0.246786	+	0.246786i	−0.572864	+	0.819650i	$0.694168\pi$
$504$		0			0
$505$	−14.4721	+	23.4164i	−0.644002	+	1.04202i
$506$		0			0
$507$	9.61803	−	9.61803i	0.427152	−	0.427152i
$508$		0			0
$509$		−	9.06154i		−	0.401646i	−0.979628	−	0.200823i	$-0.935638\pi$
$509$		−	9.06154i		−	0.401646i	0.979628	−	0.200823i	$-0.0643615\pi$
$510$		0			0
$511$			20.4742i			0.905726i
$512$		0			0
$513$	−2.47214	+	2.47214i	−0.109147	+	0.109147i
$514$		0			0
$515$	22.5623	−	5.32624i	0.994214	−	0.234702i
$516$		0			0
$517$	9.06154	+	9.06154i	0.398526	+	0.398526i
$518$		0			0
$519$	20.4742			0.898718
$520$		0			0
$521$	−8.47214			−0.371171			−0.185586	−	0.982628i	$-0.559418\pi$
$521$	−8.47214			−0.371171			−0.185586	+	0.982628i	$0.559418\pi$
$522$		0			0
$523$	−16.7426	−	16.7426i	−0.732105	−	0.732105i	0.238932	−	0.971036i	$-0.423203\pi$
$523$	−16.7426	−	16.7426i	−0.732105	−	0.732105i	−0.971036	+	0.238932i	$0.923203\pi$
$524$		0			0
$525$	−8.50651	−	17.0130i	−0.371254	−	0.742509i
$526$		0			0
$527$	5.25731	−	5.25731i	0.229012	−	0.229012i
$528$		0			0
$529$		−	9.18034i		−	0.399145i
$530$		0			0
$531$		−	18.9443i		−	0.822111i
$532$		0			0
$533$	23.7234	−	23.7234i	1.02758	−	1.02758i
$534$		0			0
$535$	8.78402	+	37.2097i	0.379766	+	1.60872i
$536$		0			0
$537$	−26.6525	−	26.6525i	−1.15014	−	1.15014i
$538$		0			0
$539$	−5.23607			−0.225533
$540$		0			0
$541$	−2.90617			−0.124946			−0.0624730	−	0.998047i	$-0.519899\pi$
$541$	−2.90617			−0.124946			−0.0624730	+	0.998047i	$0.519899\pi$
$542$		0			0
$543$	15.2169	+	15.2169i	0.653020	+	0.653020i
$544$		0			0
$545$	12.7639	+	7.88854i	0.546747	+	0.337908i
$546$		0			0
$547$	−8.56231	+	8.56231i	−0.366098	+	0.366098i	−0.866052	−	0.499954i	$-0.833350\pi$
$547$	−8.56231	+	8.56231i	−0.366098	+	0.366098i	0.499954	+	0.866052i	$0.333350\pi$
$548$		0			0
$549$		−	22.2703i		−	0.950474i
$550$		0			0
$551$			2.90617i			0.123807i
$552$		0			0
$553$	14.4721	−	14.4721i	0.615418	−	0.615418i
$554$		0			0
$555$	−18.9443	−	11.7082i	−0.804140	−	0.496986i
$556$		0			0
$557$	17.1845	+	17.1845i	0.728132	+	0.728132i	0.970247	−	0.242116i	$-0.0778413\pi$
$557$	17.1845	+	17.1845i	0.728132	+	0.728132i	−0.242116	+	0.970247i	$0.577841\pi$
$558$		0			0
$559$	14.6619			0.620131
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−11.3262	−	11.3262i	−0.477344	−	0.477344i	0.426937	−	0.904281i	$-0.359593\pi$
$563$	−11.3262	−	11.3262i	−0.477344	−	0.477344i	−0.904281	+	0.426937i	$0.859593\pi$
$564$		0			0
$565$	3.42071	+	14.4904i	0.143910	+	0.609614i
$566$		0			0
$567$	12.5882	−	12.5882i	0.528657	−	0.528657i
$568$		0			0
$569$		−	13.1246i		−	0.550212i	−0.961414	−	0.275106i	$-0.911287\pi$
$569$		−	13.1246i		−	0.550212i	0.961414	−	0.275106i	$-0.0887130\pi$
$570$		0			0
$571$		−	8.65248i		−	0.362095i	−0.983474	−	0.181047i	$-0.942051\pi$
$571$		−	8.65248i		−	0.362095i	0.983474	−	0.181047i	$-0.0579488\pi$
$572$		0			0
$573$	20.8172	−	20.8172i	0.869653	−	0.869653i
$574$		0			0
$575$	5.87785	−	17.6336i	0.245123	−	0.735370i
$576$		0			0
$577$	21.7639	+	21.7639i	0.906044	+	0.906044i	0.995950	−	0.0899059i	$-0.0286566\pi$
$577$	21.7639	+	21.7639i	0.906044	+	0.906044i	−0.0899059	+	0.995950i	$0.528657\pi$
$578$		0			0
$579$	−24.1803			−1.00490
$580$		0			0
$581$	10.3026			0.427425
$582$		0			0
$583$	−0.898056	−	0.898056i	−0.0371937	−	0.0371937i
$584$		0			0
$585$	21.1803	−	5.00000i	0.875699	−	0.206725i
$586$		0			0
$587$	−5.90983	+	5.90983i	−0.243925	+	0.243925i	−0.818472	−	0.574547i	$-0.805178\pi$
$587$	−5.90983	+	5.90983i	−0.243925	+	0.243925i	0.574547	+	0.818472i	$0.305178\pi$
$588$		0			0
$589$		−	10.5146i		−	0.433247i
$590$		0			0
$591$		−	7.05342i		−	0.290139i
$592$		0			0
$593$	−6.41641	+	6.41641i	−0.263490	+	0.263490i	−0.826470	−	0.562980i	$-0.809655\pi$
$593$	−6.41641	+	6.41641i	−0.263490	+	0.263490i	0.562980	+	0.826470i	$0.309655\pi$
$594$		0			0
$595$	−2.76393	+	4.47214i	−0.113310	+	0.183340i
$596$		0			0
$597$	−29.3238	−	29.3238i	−1.20014	−	1.20014i
$598$		0			0
$599$	27.5276			1.12475			0.562374	−	0.826883i	$-0.309888\pi$
$599$	27.5276			1.12475			0.562374	+	0.826883i	$0.309888\pi$
$600$		0			0
$601$	4.29180			0.175066			0.0875330	−	0.996162i	$-0.472102\pi$
$601$	4.29180			0.175066			0.0875330	+	0.996162i	$0.472102\pi$
$602$		0			0
$603$	−5.32624	−	5.32624i	−0.216901	−	0.216901i
$604$		0			0
$605$	11.1352	−	18.0171i	0.452709	−	0.732498i
$606$		0			0
$607$	−6.08985	+	6.08985i	−0.247180	+	0.247180i	−0.819812	−	0.572633i	$-0.805922\pi$
$607$	−6.08985	+	6.08985i	−0.247180	+	0.247180i	0.572633	+	0.819812i	$0.305922\pi$
$608$		0			0
$609$		−	5.52786i		−	0.224000i
$610$		0			0
$611$		−	45.1246i		−	1.82555i
$612$		0			0
$613$	27.3561	−	27.3561i	1.10490	−	1.10490i	0.111094	−	0.993810i	$-0.464565\pi$
$613$	27.3561	−	27.3561i	1.10490	−	1.10490i	0.993810	−	0.111094i	$-0.0354353\pi$
$614$		0			0
$615$	38.3853	−	9.06154i	1.54784	−	0.365396i
$616$		0			0
$617$	30.8885	+	30.8885i	1.24353	+	1.24353i	0.958528	+	0.284998i	$0.0919929\pi$
$617$	30.8885	+	30.8885i	1.24353	+	1.24353i	0.284998	+	0.958528i	$0.408007\pi$
$618$		0			0
$619$	27.3050			1.09748			0.548739	−	0.835994i	$-0.315108\pi$
$619$	27.3050			1.09748			0.548739	+	0.835994i	$0.315108\pi$
$620$		0			0
$621$	6.49839			0.260772
$622$		0			0
$623$	7.60845	+	7.60845i	0.304826	+	0.304826i
$624$		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
$629$			6.15537i			0.245431i
$630$		0			0
$631$			28.0827i			1.11795i	0.829183	+	0.558977i	$0.188806\pi$
$631$			28.0827i			1.11795i	−0.829183	+	0.558977i	$0.811194\pi$
$632$		0			0
$633$	25.4164	−	25.4164i	1.01021	−	1.01021i
$634$		0			0
$635$	6.38197	+	27.0344i	0.253261	+	1.07283i
$636$		0			0
$637$	13.0373	+	13.0373i	0.516556	+	0.516556i
$638$		0			0
$639$	15.7719			0.623928
$640$		0			0
$641$	−7.34752			−0.290210			−0.145105	−	0.989416i	$-0.546352\pi$
$641$	−7.34752			−0.290210			−0.145105	+	0.989416i	$0.546352\pi$
$642$		0			0
$643$	−8.56231	−	8.56231i	−0.337664	−	0.337664i	0.517823	−	0.855488i	$-0.326742\pi$
$643$	−8.56231	−	8.56231i	−0.337664	−	0.337664i	−0.855488	+	0.517823i	$0.826742\pi$
$644$		0			0
$645$	14.6619	+	9.06154i	0.577311	+	0.356798i
$646$		0			0
$647$	22.8909	−	22.8909i	0.899933	−	0.899933i	−0.0954968	−	0.995430i	$-0.530444\pi$
$647$	22.8909	−	22.8909i	0.899933	−	0.899933i	0.995430	+	0.0954968i	$0.0304440\pi$
$648$		0			0
$649$		−	10.4721i		−	0.411067i
$650$		0			0
$651$			20.0000i			0.783862i
$652$		0			0
$653$	11.2412	−	11.2412i	0.439901	−	0.439901i	−0.452078	−	0.891979i	$-0.649317\pi$
$653$	11.2412	−	11.2412i	0.439901	−	0.439901i	0.891979	+	0.452078i	$0.149317\pi$
$654$		0			0
$655$	−0.555029	−	0.343027i	−0.0216868	−	0.0134032i
$656$		0			0
$657$	−19.4721	−	19.4721i	−0.759680	−	0.759680i
$658$		0			0
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$		0			0
$661$	2.35114			0.0914488			0.0457244	−	0.998954i	$-0.485440\pi$
$661$	2.35114			0.0914488			0.0457244	+	0.998954i	$0.485440\pi$
$662$		0			0
$663$	−9.95959	−	9.95959i	−0.386799	−	0.386799i
$664$		0			0
$665$	1.70820	+	7.23607i	0.0662413	+	0.280603i
$666$		0			0
$667$	3.81966	−	3.81966i	0.147898	−	0.147898i
$668$		0			0
$669$		−	5.60034i		−	0.216522i
$670$		0			0
$671$		−	12.3107i		−	0.475251i
$672$		0			0
$673$	−30.7082	+	30.7082i	−1.18371	+	1.18371i	−0.204940	+	0.978775i	$0.565700\pi$
$673$	−30.7082	+	30.7082i	−1.18371	+	1.18371i	−0.978775	+	0.204940i	$0.934300\pi$
$674$		0			0
$675$	−8.29180	−	2.76393i	−0.319151	−	0.106384i
$676$		0			0
$677$	8.33499	+	8.33499i	0.320340	+	0.320340i	0.848897	−	0.528558i	$-0.177267\pi$
$677$	8.33499	+	8.33499i	0.320340	+	0.320340i	−0.528558	+	0.848897i	$0.677267\pi$
$678$		0			0
$679$	−0.555029			−0.0213001
$680$		0			0
$681$	−37.5967			−1.44071
$682$		0			0
$683$	1.79837	+	1.79837i	0.0688129	+	0.0688129i	0.740676	−	0.671863i	$-0.234506\pi$
$683$	1.79837	+	1.79837i	0.0688129	+	0.0688129i	−0.671863	+	0.740676i	$0.734506\pi$
$684$		0			0
$685$	−10.6861	+	2.52265i	−0.408296	+	0.0963857i
$686$		0			0
$687$	34.5811	−	34.5811i	1.31935	−	1.31935i
$688$		0			0
$689$			4.47214i			0.170375i
$690$		0			0
$691$			31.1246i			1.18404i	0.805925	+	0.592018i	$0.201669\pi$
$691$			31.1246i			1.18404i	−0.805925	+	0.592018i	$0.798331\pi$
$692$		0			0
$693$	−3.24920	+	3.24920i	−0.123427	+	0.123427i
$694$		0			0
$695$	6.36737	−	10.3026i	0.241528	−	0.390801i
$696$		0			0
$697$	−7.70820	−	7.70820i	−0.291969	−	0.291969i
$698$		0			0
$699$	11.2361			0.424987
$700$		0			0
$701$	40.3934			1.52564			0.762819	−	0.646612i	$-0.223815\pi$
$701$	40.3934			1.52564			0.762819	+	0.646612i	$0.223815\pi$
$702$		0			0
$703$	6.15537	+	6.15537i	0.232154	+	0.232154i
$704$		0			0
$705$	27.8885	−	45.1246i	1.05034	−	1.69949i
$706$		0			0
$707$	−14.4721	+	14.4721i	−0.544281	+	0.544281i
$708$		0			0
$709$		−	13.7638i		−	0.516911i	−0.966023	−	0.258456i	$-0.916786\pi$
$709$		−	13.7638i		−	0.516911i	0.966023	−	0.258456i	$-0.0832136\pi$
$710$		0			0
$711$			27.5276i			1.03237i
$712$		0			0
$713$	−13.8197	+	13.8197i	−0.517550	+	0.517550i
$714$		0			0
$715$	11.7082	−	2.76393i	0.437862	−	0.103365i
$716$		0			0
$717$	−47.4468	−	47.4468i	−1.77193	−	1.77193i
$718$		0			0
$719$	44.5407			1.66109			0.830543	−	0.556954i	$-0.188030\pi$
$719$	44.5407			1.66109			0.830543	+	0.556954i	$0.188030\pi$
$720$		0			0
$721$	17.2361			0.641905
$722$		0			0
$723$	10.9443	+	10.9443i	0.407022	+	0.407022i
$724$		0			0
$725$	−6.49839	+	3.24920i	−0.241344	+	0.120672i
$726$		0			0
$727$	5.87785	−	5.87785i	0.217997	−	0.217997i	−0.589657	−	0.807654i	$-0.700737\pi$
$727$	5.87785	−	5.87785i	0.217997	−	0.217997i	0.807654	+	0.589657i	$0.200737\pi$
$728$		0			0
$729$			11.9443i			0.442380i
$730$		0			0
$731$		−	4.76393i		−	0.176200i
$732$		0			0
$733$	−1.28157	+	1.28157i	−0.0473359	+	0.0473359i	−0.730379	−	0.683043i	$-0.760656\pi$
$733$	−1.28157	+	1.28157i	−0.0473359	+	0.0473359i	0.683043	+	0.730379i	$0.260656\pi$
$734$		0			0
$735$	4.97980	+	21.0948i	0.183683	+	0.778092i
$736$		0			0
$737$	−2.94427	−	2.94427i	−0.108454	−	0.108454i
$738$		0			0
$739$	17.4164			0.640673			0.320336	−	0.947304i	$-0.396204\pi$
$739$	17.4164			0.640673			0.320336	+	0.947304i	$0.396204\pi$
$740$		0			0
$741$	−19.9192			−0.731750
$742$		0			0
$743$	−13.4863	−	13.4863i	−0.494765	−	0.494765i	0.415039	−	0.909804i	$-0.363768\pi$
$743$	−13.4863	−	13.4863i	−0.494765	−	0.494765i	−0.909804	+	0.415039i	$0.863768\pi$
$744$		0			0
$745$	−25.1246	−	15.5279i	−0.920495	−	0.568897i
$746$		0			0
$747$	−9.79837	+	9.79837i	−0.358504	+	0.358504i
$748$		0			0
$749$			28.4257i			1.03865i
$750$		0			0
$751$		−	7.05342i		−	0.257383i	−0.991685	−	0.128692i	$-0.958922\pi$
$751$		−	7.05342i		−	0.257383i	0.991685	−	0.128692i	$-0.0410777\pi$
$752$		0			0
$753$	35.8885	−	35.8885i	1.30785	−	1.30785i
$754$		0			0
$755$	27.8885	+	17.2361i	1.01497	+	0.627285i
$756$		0			0
$757$	38.0018	+	38.0018i	1.38120	+	1.38120i	0.842497	+	0.538701i	$0.181085\pi$
$757$	38.0018	+	38.0018i	1.38120	+	1.38120i	0.538701	+	0.842497i	$0.318915\pi$
$758$		0			0
$759$	−10.5146			−0.381657
$760$		0			0
$761$	14.9443			0.541729			0.270865	−	0.962617i	$-0.412690\pi$
$761$	14.9443			0.541729			0.270865	+	0.962617i	$0.412690\pi$
$762$		0			0
$763$	7.88854	+	7.88854i	0.285584	+	0.285584i
$764$		0			0
$765$	−1.62460	−	6.88191i	−0.0587375	−	0.248816i
$766$		0			0
$767$	−26.0746	+	26.0746i	−0.941498	+	0.941498i
$768$		0			0
$769$			2.47214i			0.0891475i	0.999006	+	0.0445738i	$0.0141930\pi$
$769$			2.47214i			0.0891475i	−0.999006	+	0.0445738i	$0.985807\pi$
$770$		0			0
$771$			60.5410i			2.18033i
$772$		0			0
$773$	−4.18774	+	4.18774i	−0.150623	+	0.150623i	−0.778396	−	0.627773i	$-0.783966\pi$
$773$	−4.18774	+	4.18774i	−0.150623	+	0.150623i	0.627773	+	0.778396i	$0.283966\pi$
$774$		0			0
$775$	23.5114	−	11.7557i	0.844555	−	0.422277i
$776$		0			0
$777$	−11.7082	−	11.7082i	−0.420029	−	0.420029i
$778$		0			0
$779$	−15.4164			−0.552350
$780$		0			0
$781$	8.71851			0.311973
$782$		0			0
$783$	−1.79611	−	1.79611i	−0.0641878	−	0.0641878i
$784$		0			0
$785$	−30.1246	+	7.11146i	−1.07519	+	0.253819i
$786$		0			0
$787$	11.1459	−	11.1459i	0.397308	−	0.397308i	−0.479974	−	0.877283i	$-0.659354\pi$
$787$	11.1459	−	11.1459i	0.397308	−	0.397308i	0.877283	+	0.479974i	$0.159354\pi$
$788$		0			0
$789$		−	53.0472i		−	1.88853i
$790$		0			0
$791$			11.0697i			0.393591i
$792$		0			0
$793$	−30.6525	+	30.6525i	−1.08850	+	1.08850i
$794$		0			0
$795$	−2.76393	+	4.47214i	−0.0980266	+	0.158610i
$796$		0			0
$797$	19.7477	+	19.7477i	0.699498	+	0.699498i	0.964302	−	0.264804i	$-0.0853072\pi$
$797$	19.7477	+	19.7477i	0.699498	+	0.699498i	−0.264804	+	0.964302i	$0.585307\pi$
$798$		0			0
$799$	−14.6619			−0.518700
$800$		0			0
$801$	−14.4721			−0.511348
$802$		0			0
$803$	−10.7639	−	10.7639i	−0.379851	−	0.379851i
$804$		0			0
$805$	7.26543	−	11.7557i	0.256073	−	0.414334i
$806$		0			0
$807$	28.9807	−	28.9807i	1.02017	−	1.02017i
$808$		0			0
$809$		−	12.9443i		−	0.455096i	−0.973767	−	0.227548i	$-0.926929\pi$
$809$		−	12.9443i		−	0.455096i	0.973767	−	0.227548i	$-0.0730709\pi$
$810$		0			0
$811$		−	32.0689i		−	1.12609i	−0.826426	−	0.563045i	$-0.809630\pi$
$811$		−	32.0689i		−	1.12609i	0.826426	−	0.563045i	$-0.190370\pi$
$812$		0			0
$813$	−51.2511	+	51.2511i	−1.79745	+	1.79745i
$814$		0			0
$815$	21.9928	−	5.19180i	0.770375	−	0.181861i
$816$		0			0
$817$	−4.76393	−	4.76393i	−0.166669	−	0.166669i
$818$		0			0
$819$	16.1803			0.565387
$820$		0			0
$821$	−20.4742			−0.714555			−0.357278	−	0.933998i	$-0.616295\pi$
$821$	−20.4742			−0.714555			−0.357278	+	0.933998i	$0.616295\pi$
$822$		0			0
$823$	24.3440	+	24.3440i	0.848577	+	0.848577i	0.989956	−	0.141379i	$-0.0451535\pi$
$823$	24.3440	+	24.3440i	0.848577	+	0.848577i	−0.141379	+	0.989956i	$0.545154\pi$
$824$		0			0
$825$	13.4164	+	4.47214i	0.467099	+	0.155700i
$826$		0			0
$827$	−14.8541	+	14.8541i	−0.516528	+	0.516528i	−0.916519	−	0.399991i	$-0.869013\pi$
$827$	−14.8541	+	14.8541i	−0.516528	+	0.516528i	0.399991	+	0.916519i	$0.369013\pi$
$828$		0			0
$829$			3.11817i			0.108299i	0.998533	+	0.0541493i	$0.0172447\pi$
$829$			3.11817i			0.108299i	−0.998533	+	0.0541493i	$0.982755\pi$
$830$		0			0
$831$			7.05342i			0.244681i
$832$		0			0
$833$	4.23607	−	4.23607i	0.146771	−	0.146771i
$834$		0			0
$835$	−0.201626	−	0.854102i	−0.00697756	−	0.0295574i
$836$		0			0
$837$	6.49839	+	6.49839i	0.224617	+	0.224617i
$838$		0			0
$839$	−9.40456			−0.324682			−0.162341	−	0.986735i	$-0.551904\pi$
$839$	−9.40456			−0.324682			−0.162341	+	0.986735i	$0.551904\pi$
$840$		0			0
$841$	26.8885			0.927191
$842$		0			0
$843$	−6.00000	−	6.00000i	−0.206651	−	0.206651i
$844$		0			0
$845$	−11.3067	−	6.98791i	−0.388962	−	0.240391i
$846$		0			0
$847$	11.1352	−	11.1352i	0.382609	−	0.382609i
$848$		0			0
$849$			50.5410i			1.73456i
$850$		0			0
$851$		−	16.1803i		−	0.554655i
$852$		0			0
$853$	−24.7930	+	24.7930i	−0.848896	+	0.848896i	−0.989995	−	0.141100i	$-0.954936\pi$
$853$	−24.7930	+	24.7930i	−0.848896	+	0.848896i	0.141100	+	0.989995i	$0.454936\pi$
$854$		0			0
$855$	−8.50651	−	5.25731i	−0.290916	−	0.179796i
$856$		0			0
$857$	17.8328	+	17.8328i	0.609157	+	0.609157i	0.942726	−	0.333568i	$-0.108253\pi$
$857$	17.8328	+	17.8328i	0.609157	+	0.609157i	−0.333568	+	0.942726i	$0.608253\pi$
$858$		0			0
$859$	7.52786			0.256847			0.128424	−	0.991719i	$-0.459008\pi$
$859$	7.52786			0.256847			0.128424	+	0.991719i	$0.459008\pi$
$860$		0			0
$861$	29.3238			0.999351
$862$		0			0
$863$	−6.22088	−	6.22088i	−0.211761	−	0.211761i	0.593254	−	0.805015i	$-0.297843\pi$
$863$	−6.22088	−	6.22088i	−0.211761	−	0.211761i	−0.805015	+	0.593254i	$0.797843\pi$
$864$		0			0
$865$	−4.59675	−	19.4721i	−0.156294	−	0.662072i
$866$		0			0
$867$	24.2705	−	24.2705i	0.824270	−	0.824270i
$868$		0			0
$869$			15.2169i			0.516198i
$870$		0			0
$871$			14.6619i			0.496799i
$872$		0			0
$873$	0.527864	−	0.527864i	0.0178655	−	0.0178655i
$874$		0			0
$875$	−14.2705	+	11.9098i	−0.482431	+	0.402626i
$876$		0			0
$877$	−5.08580	−	5.08580i	−0.171735	−	0.171735i	0.616006	−	0.787741i	$-0.288750\pi$
$877$	−5.08580	−	5.08580i	−0.171735	−	0.171735i	−0.787741	+	0.616006i	$0.788750\pi$
$878$		0			0
$879$	2.35114			0.0793020
$880$		0			0
$881$	47.1246			1.58767			0.793834	−	0.608134i	$-0.208082\pi$
$881$	47.1246			1.58767			0.793834	+	0.608134i	$0.208082\pi$
$882$		0			0
$883$	−21.7984	−	21.7984i	−0.733574	−	0.733574i	0.237752	−	0.971326i	$-0.423589\pi$
$883$	−21.7984	−	21.7984i	−0.733574	−	0.733574i	−0.971326	+	0.237752i	$0.923589\pi$
$884$		0			0
$885$	−42.1895	+	9.95959i	−1.41818	+	0.334788i
$886$		0			0
$887$	−28.1482	+	28.1482i	−0.945123	+	0.945123i	−0.998571	−	0.0534473i	$-0.982979\pi$
$887$	−28.1482	+	28.1482i	−0.945123	+	0.945123i	0.0534473	+	0.998571i	$0.482979\pi$
$888$		0			0
$889$			20.6525i			0.692662i
$890$		0			0
$891$			13.2361i			0.443425i
$892$		0			0
$893$	−14.6619	+	14.6619i	−0.490641	+	0.490641i
$894$		0			0
$895$	−19.3642	+	31.3319i	−0.647272	+	1.04731i
$896$		0			0
$897$	26.1803	+	26.1803i	0.874136	+	0.874136i
$898$		0			0
$899$	7.63932			0.254786
$900$		0			0
$901$	1.45309			0.0484093
$902$		0			0
$903$	9.06154	+	9.06154i	0.301549	+	0.301549i
$904$		0			0
$905$	11.0557	−	17.8885i	0.367505	−	0.594635i
$906$		0			0
$907$	23.3262	−	23.3262i	0.774535	−	0.774535i	−0.204361	−	0.978896i	$-0.565512\pi$
$907$	23.3262	−	23.3262i	0.774535	−	0.774535i	0.978896	+	0.204361i	$0.0655115\pi$
$908$		0			0
$909$		−	27.5276i		−	0.913034i
$910$		0			0
$911$		−	25.1765i		−	0.834135i	−0.908876	−	0.417067i	$-0.863058\pi$
$911$		−	25.1765i		−	0.834135i	0.908876	−	0.417067i	$-0.136942\pi$
$912$		0			0
$913$	−5.41641	+	5.41641i	−0.179257	+	0.179257i
$914$		0			0
$915$	−49.5967	+	11.7082i	−1.63962	+	0.387061i
$916$		0			0
$917$	−0.343027	−	0.343027i	−0.0113277	−	0.0113277i
$918$		0			0
$919$	−21.7153			−0.716322			−0.358161	−	0.933660i	$-0.616596\pi$
$919$	−21.7153			−0.716322			−0.358161	+	0.933660i	$0.616596\pi$
$920$		0			0
$921$	21.2361			0.699752
$922$		0			0
$923$	−21.7082	−	21.7082i	−0.714534	−	0.714534i
$924$		0			0
$925$	−6.88191	+	20.6457i	−0.226276	+	0.678827i
$926$		0			0
$927$	−16.3925	+	16.3925i	−0.538400	+	0.538400i
$928$		0			0
$929$		−	5.34752i		−	0.175447i	−0.996145	−	0.0877233i	$-0.972041\pi$
$929$		−	5.34752i		−	0.175447i	0.996145	−	0.0877233i	$-0.0279591\pi$
$930$		0			0
$931$		−	8.47214i		−	0.277663i
$932$		0			0
$933$	13.2088	−	13.2088i	0.432436	−	0.432436i
$934$		0			0
$935$	−0.898056	−	3.80423i	−0.0293696	−	0.124411i
$936$		0			0
$937$	−20.3050	−	20.3050i	−0.663334	−	0.663334i	0.292831	−	0.956164i	$-0.405403\pi$
$937$	−20.3050	−	20.3050i	−0.663334	−	0.663334i	−0.956164	+	0.292831i	$0.905403\pi$
$938$		0			0
$939$	20.1803			0.658561
$940$		0			0
$941$	−60.8676			−1.98423			−0.992114	−	0.125340i	$-0.959998\pi$
$941$	−60.8676			−1.98423			−0.992114	+	0.125340i	$0.959998\pi$
$942$		0			0
$943$	20.2622	+	20.2622i	0.659828	+	0.659828i
$944$		0			0
$945$	−5.52786	−	3.41641i	−0.179821	−	0.111136i
$946$		0			0
$947$	−8.85410	+	8.85410i	−0.287720	+	0.287720i	−0.836178	−	0.548458i	$-0.815215\pi$
$947$	−8.85410	+	8.85410i	−0.287720	+	0.287720i	0.548458	+	0.836178i	$0.315215\pi$
$948$		0			0
$949$			53.6022i			1.74000i
$950$		0			0
$951$		−	34.5811i		−	1.12137i
$952$		0			0
$953$	6.81966	−	6.81966i	0.220910	−	0.220910i	−0.587971	−	0.808882i	$-0.700073\pi$
$953$	6.81966	−	6.81966i	0.220910	−	0.220910i	0.808882	+	0.587971i	$0.200073\pi$
$954$		0			0
$955$	−24.4721	−	15.1246i	−0.791900	−	0.489421i
$956$		0			0
$957$	2.90617	+	2.90617i	0.0939431	+	0.0939431i
$958$		0			0
$959$	−8.16348			−0.263613
$960$		0			0
$961$	3.36068			0.108409
$962$		0			0
$963$	−27.0344	−	27.0344i	−0.871173	−	0.871173i
$964$		0			0
$965$	5.42882	+	22.9969i	0.174760	+	0.740295i
$966$		0			0
$967$	−12.0332	+	12.0332i	−0.386962	+	0.386962i	−0.873602	−	0.486640i	$-0.838222\pi$
$967$	−12.0332	+	12.0332i	−0.386962	+	0.386962i	0.486640	+	0.873602i	$0.338222\pi$
$968$		0			0
$969$			6.47214i			0.207915i
$970$		0			0
$971$			33.5967i			1.07817i	0.842251	+	0.539085i	$0.181230\pi$
$971$			33.5967i			1.07817i	−0.842251	+	0.539085i	$0.818770\pi$
$972$		0			0
$973$	6.36737	−	6.36737i	0.204128	−	0.204128i
$974$		0			0
$975$	−22.2703	−	44.5407i	−0.713221	−	1.42644i
$976$		0			0
$977$	−28.2361	−	28.2361i	−0.903352	−	0.903352i	0.0923727	−	0.995725i	$-0.470555\pi$
$977$	−28.2361	−	28.2361i	−0.903352	−	0.903352i	−0.995725	+	0.0923727i	$0.970555\pi$
$978$		0			0
$979$	−8.00000			−0.255681
$980$		0			0
$981$	−15.0049			−0.479070
$982$		0			0
$983$	0.620541	+	0.620541i	0.0197922	+	0.0197922i	0.716934	−	0.697141i	$-0.245545\pi$
$983$	0.620541	+	0.620541i	0.0197922	+	0.0197922i	−0.697141	+	0.716934i	$0.745545\pi$
$984$		0			0
$985$	−6.70820	+	1.58359i	−0.213741	+	0.0504574i
$986$		0			0
$987$	27.8885	−	27.8885i	0.887702	−	0.887702i
$988$		0			0
$989$			12.5227i			0.398200i
$990$		0			0
$991$			19.3642i			0.615123i	0.951528	+	0.307561i	$0.0995129\pi$
$991$			19.3642i			0.615123i	−0.951528	+	0.307561i	$0.900487\pi$
$992$		0			0
$993$	−45.4164	+	45.4164i	−1.44125	+	1.44125i
$994$		0			0
$995$	−21.3050	+	34.4721i	−0.675412	+	1.09284i
$996$		0			0
$997$	−35.6506	−	35.6506i	−1.12907	−	1.12907i	−0.990329	−	0.138738i	$-0.955696\pi$
$997$	−35.6506	−	35.6506i	−1.12907	−	1.12907i	−0.138738	−	0.990329i	$-0.544304\pi$
$998$		0			0
$999$	−7.60845			−0.240721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1280.2.n.q.767.4		8
4.3	odd	2		1280.2.n.m.767.2		8
5.3	odd	4		1280.2.n.m.1023.2		8
8.3	odd	2	inner	1280.2.n.q.767.3		8
8.5	even	2		1280.2.n.m.767.1		8
16.3	odd	4		160.2.o.a.47.3		8
16.5	even	4		160.2.o.a.47.4		8
16.11	odd	4		40.2.k.a.27.2	yes	8
16.13	even	4		40.2.k.a.27.4	yes	8
20.3	even	4	inner	1280.2.n.q.1023.4		8
40.3	even	4		1280.2.n.m.1023.1		8
40.13	odd	4	inner	1280.2.n.q.1023.3		8
48.5	odd	4		1440.2.bi.c.847.1		8
48.11	even	4		360.2.w.c.307.3		8
48.29	odd	4		360.2.w.c.307.1		8
48.35	even	4		1440.2.bi.c.847.4		8
80.3	even	4		160.2.o.a.143.4		8
80.13	odd	4		40.2.k.a.3.2	✓	8
80.19	odd	4		800.2.o.g.207.1		8
80.27	even	4		200.2.k.h.43.1		8
80.29	even	4		200.2.k.h.107.1		8
80.37	odd	4		800.2.o.g.143.1		8
80.43	even	4		40.2.k.a.3.4	yes	8
80.53	odd	4		160.2.o.a.143.3		8
80.59	odd	4		200.2.k.h.107.3		8
80.67	even	4		800.2.o.g.143.2		8
80.69	even	4		800.2.o.g.207.2		8
80.77	odd	4		200.2.k.h.43.3		8
240.53	even	4		1440.2.bi.c.1423.4		8
240.83	odd	4		1440.2.bi.c.1423.1		8
240.173	even	4		360.2.w.c.163.3		8
240.203	odd	4		360.2.w.c.163.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.2.k.a.3.2	✓	8	80.13	odd	4
40.2.k.a.3.4	yes	8	80.43	even	4
40.2.k.a.27.2	yes	8	16.11	odd	4
40.2.k.a.27.4	yes	8	16.13	even	4
160.2.o.a.47.3		8	16.3	odd	4
160.2.o.a.47.4		8	16.5	even	4
160.2.o.a.143.3		8	80.53	odd	4
160.2.o.a.143.4		8	80.3	even	4
200.2.k.h.43.1		8	80.27	even	4
200.2.k.h.43.3		8	80.77	odd	4
200.2.k.h.107.1		8	80.29	even	4
200.2.k.h.107.3		8	80.59	odd	4
360.2.w.c.163.1		8	240.203	odd	4
360.2.w.c.163.3		8	240.173	even	4
360.2.w.c.307.1		8	48.29	odd	4
360.2.w.c.307.3		8	48.11	even	4
800.2.o.g.143.1		8	80.37	odd	4
800.2.o.g.143.2		8	80.67	even	4
800.2.o.g.207.1		8	80.19	odd	4
800.2.o.g.207.2		8	80.69	even	4
1280.2.n.m.767.1		8	8.5	even	2
1280.2.n.m.767.2		8	4.3	odd	2
1280.2.n.m.1023.1		8	40.3	even	4
1280.2.n.m.1023.2		8	5.3	odd	4
1280.2.n.q.767.3		8	8.3	odd	2	inner
1280.2.n.q.767.4		8	1.1	even	1	trivial
1280.2.n.q.1023.3		8	40.13	odd	4	inner
1280.2.n.q.1023.4		8	20.3	even	4	inner
1440.2.bi.c.847.1		8	48.5	odd	4
1440.2.bi.c.847.4		8	48.35	even	4
1440.2.bi.c.1423.1		8	240.83	odd	4
1440.2.bi.c.1423.4		8	240.53	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.61803 + 1.61803i) q^{3} +(1.17557 - 1.90211i) q^{5} +(1.17557 - 1.17557i) q^{7} +2.23607i q^{9} +O(q^{10})\)	\(q+(1.61803 + 1.61803i) q^{3} +(1.17557 - 1.90211i) q^{5} +(1.17557 - 1.17557i) q^{7} +2.23607i q^{9} +1.23607i q^{11} +(3.07768 - 3.07768i) q^{13} +(4.97980 - 1.17557i) q^{15} +(-1.00000 - 1.00000i) q^{17} -2.00000 q^{19} +3.80423 q^{21} +(2.62866 + 2.62866i) q^{23} +(-2.23607 - 4.47214i) q^{25} +(1.23607 - 1.23607i) q^{27} -1.45309i q^{29} +5.25731i q^{31} +(-2.00000 + 2.00000i) q^{33} +(-0.854102 - 3.61803i) q^{35} +(-3.07768 - 3.07768i) q^{37} +9.95959 q^{39} +7.70820 q^{41} +(2.38197 + 2.38197i) q^{43} +(4.25325 + 2.62866i) q^{45} +(7.33094 - 7.33094i) q^{47} +4.23607i q^{49} -3.23607i q^{51} +(-0.726543 + 0.726543i) q^{53} +(2.35114 + 1.45309i) q^{55} +(-3.23607 - 3.23607i) q^{57} -8.47214 q^{59} -9.95959 q^{61} +(2.62866 + 2.62866i) q^{63} +(-2.23607 - 9.47214i) q^{65} +(-2.38197 + 2.38197i) q^{67} +8.50651i q^{69} -7.05342i q^{71} +(-8.70820 + 8.70820i) q^{73} +(3.61803 - 10.8541i) q^{75} +(1.45309 + 1.45309i) q^{77} +12.3107 q^{79} +10.7082 q^{81} +(4.38197 + 4.38197i) q^{83} +(-3.07768 + 0.726543i) q^{85} +(2.35114 - 2.35114i) q^{87} +6.47214i q^{89} -7.23607i q^{91} +(-8.50651 + 8.50651i) q^{93} +(-2.35114 + 3.80423i) q^{95} +(-0.236068 - 0.236068i) q^{97} -2.76393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3}+O(q^{10}) \) 8 * q + 4 * q^3	\( 8 q + 4 q^{3} - 8 q^{17} - 16 q^{19} - 8 q^{27} - 16 q^{33} + 20 q^{35} + 8 q^{41} + 28 q^{43} - 8 q^{57} - 32 q^{59} - 28 q^{67} - 16 q^{73} + 20 q^{75} + 32 q^{81} + 44 q^{83} + 16 q^{97} - 40 q^{99}+O(q^{100}) \) 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

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Representations

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Database

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