LMFDB - Embedded newform 1024.2.g.d.641.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, degree $4$, 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:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			641.3
Root			$0.130526 + 0.991445i$ of defining polynomial
Character	$\chi$	$=$	1024.641
Dual form			1024.2.g.d.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.445644 + 0.184592i) q^{3} +(0.565826 + 1.36603i) q^{5} +(0.135131 - 0.135131i) q^{7} +(-1.95680 - 1.95680i) q^{9} +O(q^{10})$	\(q+(0.445644 + 0.184592i) q^{3} +(0.565826 + 1.36603i) q^{5} +(0.135131 - 0.135131i) q^{7} +(-1.95680 - 1.95680i) q^{9} +(3.12395 - 1.29398i) q^{11} +(0.951812 - 2.29788i) q^{13} +0.713208i q^{15} +3.11099i q^{17} +(2.48451 - 5.99813i) q^{19} +(0.0851642 - 0.0352762i) q^{21} +(5.18330 + 5.18330i) q^{23} +(1.98967 - 1.98967i) q^{25} +(-1.06460 - 2.57018i) q^{27} +(-4.33315 - 1.79485i) q^{29} +7.44503 q^{31} +1.63103 q^{33} +(0.261052 + 0.108131i) q^{35} +(3.49768 + 8.44414i) q^{37} +(0.848339 - 0.848339i) q^{39} +(-4.27792 - 4.27792i) q^{41} +(4.33227 - 1.79448i) q^{43} +(1.56583 - 3.78024i) q^{45} +12.0952i q^{47} +6.96348i q^{49} +(-0.574263 + 1.38639i) q^{51} +(3.42713 - 1.41956i) q^{53} +(3.53523 + 3.53523i) q^{55} +(2.21441 - 2.21441i) q^{57} +(-1.16425 - 2.81074i) q^{59} +(-8.72911 - 3.61571i) q^{61} -0.528846 q^{63} +3.67752 q^{65} +(7.15047 + 2.96182i) q^{67} +(1.35311 + 3.26670i) q^{69} +(-2.86020 + 2.86020i) q^{71} +(-2.49697 - 2.49697i) q^{73} +(1.25396 - 0.519408i) q^{75} +(0.247285 - 0.596999i) q^{77} -8.39967i q^{79} +6.96008i q^{81} +(5.42005 - 13.0852i) q^{83} +(-4.24969 + 1.76028i) q^{85} +(-1.59973 - 1.59973i) q^{87} +(-4.96713 + 4.96713i) q^{89} +(-0.181895 - 0.439133i) q^{91} +(3.31784 + 1.37429i) q^{93} +9.59940 q^{95} -2.87492 q^{97} +(-8.64500 - 3.58087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^5 + 16 * q^9	$ 16 q - 8 q^{5} + 16 q^{9} + 24 q^{13} - 48 q^{21} + 32 q^{25} - 8 q^{29} - 80 q^{33} + 8 q^{37} + 16 q^{41} + 8 q^{45} + 40 q^{53} + 16 q^{57} + 8 q^{61} - 32 q^{65} - 32 q^{73} + 32 q^{77} - 32 q^{85} - 32 q^{89} + 48 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 16 * q^9 + 24 * q^13 - 48 * q^21 + 32 * q^25 - 8 * q^29 - 80 * q^33 + 8 * q^37 + 16 * q^41 + 8 * q^45 + 40 * q^53 + 16 * q^57 + 8 * q^61 - 32 * q^65 - 32 * q^73 + 32 * q^77 - 32 * q^85 - 32 * q^89 + 48 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.445644	+	0.184592i	0.257293	+	0.106574i	0.507602	−	0.861592i	$-0.330532\pi$
$3$	0.445644	+	0.184592i	0.257293	+	0.106574i	−0.250309	+	0.968166i	$0.580532\pi$
$4$		0			0
$5$	0.565826	+	1.36603i	0.253045	+	0.610905i	0.998447	−	0.0557103i	$-0.0177423\pi$
$5$	0.565826	+	1.36603i	0.253045	+	0.610905i	−0.745402	+	0.666615i	$0.767742\pi$
$6$		0			0
$7$	0.135131	−	0.135131i	0.0510746	−	0.0510746i	−0.681108	−	0.732183i	$-0.738502\pi$
$7$	0.135131	−	0.135131i	0.0510746	−	0.0510746i	0.732183	+	0.681108i	$0.238502\pi$
$8$		0			0
$9$	−1.95680	−	1.95680i	−0.652265	−	0.652265i
$10$		0			0
$11$	3.12395	−	1.29398i	0.941907	−	0.390151i	0.141724	−	0.989906i	$-0.454736\pi$
$11$	3.12395	−	1.29398i	0.941907	−	0.390151i	0.800183	+	0.599756i	$0.204736\pi$
$12$		0			0
$13$	0.951812	−	2.29788i	0.263985	−	0.637316i	−0.735193	−	0.677858i	$-0.762908\pi$
$13$	0.951812	−	2.29788i	0.263985	−	0.637316i	0.999178	+	0.0405417i	$0.0129084\pi$
$14$		0			0
$15$			0.713208i			0.184150i
$16$		0			0
$17$			3.11099i			0.754525i	0.926106	+	0.377263i	$0.123135\pi$
$17$			3.11099i			0.754525i	−0.926106	+	0.377263i	$0.876865\pi$
$18$		0			0
$19$	2.48451	−	5.99813i	0.569985	−	1.37607i	−0.331582	−	0.943426i	$-0.607582\pi$
$19$	2.48451	−	5.99813i	0.569985	−	1.37607i	0.901567	−	0.432639i	$-0.142418\pi$
$20$		0			0
$21$	0.0851642	−	0.0352762i	0.0185844	−	0.00769789i
$22$		0			0
$23$	5.18330	+	5.18330i	1.08079	+	1.08079i	0.996436	+	0.0843577i	$0.0268838\pi$
$23$	5.18330	+	5.18330i	1.08079	+	1.08079i	0.0843577	+	0.996436i	$0.473116\pi$
$24$		0			0
$25$	1.98967	−	1.98967i	0.397934	−	0.397934i
$26$		0			0
$27$	−1.06460	−	2.57018i	−0.204883	−	0.494631i
$28$		0			0
$29$	−4.33315	−	1.79485i	−0.804646	−	0.333295i	−0.0578306	−	0.998326i	$-0.518418\pi$
$29$	−4.33315	−	1.79485i	−0.804646	−	0.333295i	−0.746816	+	0.665031i	$0.768418\pi$
$30$		0			0
$31$	7.44503			1.33717			0.668584	−	0.743637i	$-0.266901\pi$
$31$	7.44503			1.33717			0.668584	+	0.743637i	$0.266901\pi$
$32$		0			0
$33$	1.63103			0.283926
$34$		0			0
$35$	0.261052	+	0.108131i	0.0441259	+	0.0182775i
$36$		0			0
$37$	3.49768	+	8.44414i	0.575015	+	1.38821i	0.897239	+	0.441545i	$0.145569\pi$
$37$	3.49768	+	8.44414i	0.575015	+	1.38821i	−0.322224	+	0.946663i	$0.604431\pi$
$38$		0			0
$39$	0.848339	−	0.848339i	0.135843	−	0.135843i
$40$		0			0
$41$	−4.27792	−	4.27792i	−0.668098	−	0.668098i	0.289177	−	0.957276i	$-0.406618\pi$
$41$	−4.27792	−	4.27792i	−0.668098	−	0.668098i	−0.957276	+	0.289177i	$0.906618\pi$
$42$		0			0
$43$	4.33227	−	1.79448i	0.660664	−	0.273656i	−0.0270537	−	0.999634i	$-0.508613\pi$
$43$	4.33227	−	1.79448i	0.660664	−	0.273656i	0.687718	+	0.725978i	$0.258613\pi$
$44$		0			0
$45$	1.56583	−	3.78024i	0.233420	−	0.563525i
$46$		0			0
$47$			12.0952i			1.76426i	0.471002	+	0.882132i	$0.343892\pi$
$47$			12.0952i			1.76426i	−0.471002	+	0.882132i	$0.656108\pi$
$48$		0			0
$49$			6.96348i			0.994783i
$50$		0			0
$51$	−0.574263	+	1.38639i	−0.0804129	+	0.194134i
$52$		0			0
$53$	3.42713	−	1.41956i	0.470752	−	0.194992i	−0.134680	−	0.990889i	$-0.543001\pi$
$53$	3.42713	−	1.41956i	0.470752	−	0.194992i	0.605432	+	0.795897i	$0.293001\pi$
$54$		0			0
$55$	3.53523	+	3.53523i	0.476690	+	0.476690i
$56$		0			0
$57$	2.21441	−	2.21441i	0.293306	−	0.293306i
$58$		0			0
$59$	−1.16425	−	2.81074i	−0.151572	−	0.365927i	0.829795	−	0.558068i	$-0.188457\pi$
$59$	−1.16425	−	2.81074i	−0.151572	−	0.365927i	−0.981367	+	0.192140i	$0.938457\pi$
$60$		0			0
$61$	−8.72911	−	3.61571i	−1.11765	−	0.462945i	−0.254083	−	0.967183i	$-0.581774\pi$
$61$	−8.72911	−	3.61571i	−1.11765	−	0.462945i	−0.863565	+	0.504238i	$0.831774\pi$
$62$		0			0
$63$	−0.528846			−0.0666284
$64$		0			0
$65$	3.67752			0.456140
$66$		0			0
$67$	7.15047	+	2.96182i	0.873569	+	0.361844i	0.773999	−	0.633186i	$-0.218253\pi$
$67$	7.15047	+	2.96182i	0.873569	+	0.361844i	0.0995698	+	0.995031i	$0.468253\pi$
$68$		0			0
$69$	1.35311	+	3.26670i	0.162896	+	0.393265i
$70$		0			0
$71$	−2.86020	+	2.86020i	−0.339444	+	0.339444i	−0.856158	−	0.516714i	$-0.827155\pi$
$71$	−2.86020	+	2.86020i	−0.339444	+	0.339444i	0.516714	+	0.856158i	$0.327155\pi$
$72$		0			0
$73$	−2.49697	−	2.49697i	−0.292249	−	0.292249i	0.545719	−	0.837968i	$-0.316256\pi$
$73$	−2.49697	−	2.49697i	−0.292249	−	0.292249i	−0.837968	+	0.545719i	$0.816256\pi$
$74$		0			0
$75$	1.25396	−	0.519408i	0.144795	−	0.0599760i
$76$		0			0
$77$	0.247285	−	0.596999i	0.0281807	−	0.0680343i
$78$		0			0
$79$		−	8.39967i		−	0.945036i	−0.881321	−	0.472518i	$-0.843345\pi$
$79$		−	8.39967i		−	0.945036i	0.881321	−	0.472518i	$-0.156655\pi$
$80$		0			0
$81$			6.96008i			0.773342i
$82$		0			0
$83$	5.42005	−	13.0852i	0.594928	−	1.43628i	−0.283764	−	0.958894i	$-0.591583\pi$
$83$	5.42005	−	13.0852i	0.594928	−	1.43628i	0.878692	−	0.477389i	$-0.158417\pi$
$84$		0			0
$85$	−4.24969	+	1.76028i	−0.460943	+	0.190929i
$86$		0			0
$87$	−1.59973	−	1.59973i	−0.171509	−	0.171509i
$88$		0			0
$89$	−4.96713	+	4.96713i	−0.526514	+	0.526514i	−0.919531	−	0.393017i	$-0.871431\pi$
$89$	−4.96713	+	4.96713i	−0.526514	+	0.526514i	0.393017	+	0.919531i	$0.371431\pi$
$90$		0			0
$91$	−0.181895	−	0.439133i	−0.0190677	−	0.0460336i
$92$		0			0
$93$	3.31784	+	1.37429i	0.344044	+	0.142508i
$94$		0			0
$95$	9.59940			0.984877
$96$		0			0
$97$	−2.87492			−0.291903			−0.145952	−	0.989292i	$-0.546624\pi$
$97$	−2.87492			−0.291903			−0.145952	+	0.989292i	$0.546624\pi$
$98$		0			0
$99$	−8.64500	−	3.58087i	−0.868855	−	0.359891i
$100$		0			0
$101$	−3.00170	−	7.24674i	−0.298680	−	0.721078i	−0.999966	−	0.00819809i	$-0.997390\pi$
$101$	−3.00170	−	7.24674i	−0.298680	−	0.721078i	0.701286	−	0.712880i	$-0.252610\pi$
$102$		0			0
$103$	4.12067	−	4.12067i	0.406022	−	0.406022i	−0.474327	−	0.880349i	$-0.657308\pi$
$103$	4.12067	−	4.12067i	0.406022	−	0.406022i	0.880349	+	0.474327i	$0.157308\pi$
$104$		0			0
$105$	0.0963763	+	0.0963763i	0.00940537	+	0.00940537i
$106$		0			0
$107$	5.55900	−	2.30261i	0.537409	−	0.222602i	−0.0974360	−	0.995242i	$-0.531064\pi$
$107$	5.55900	−	2.30261i	0.537409	−	0.222602i	0.634845	+	0.772640i	$0.281064\pi$
$108$		0			0
$109$	1.73740	−	4.19445i	0.166413	−	0.401756i	−0.818571	−	0.574406i	$-0.805233\pi$
$109$	1.73740	−	4.19445i	0.166413	−	0.401756i	0.984983	+	0.172650i	$0.0552331\pi$
$110$		0			0
$111$			4.40873i			0.418458i
$112$		0			0
$113$		−	9.86370i		−	0.927899i	−0.885862	−	0.463950i	$-0.846432\pi$
$113$		−	9.86370i		−	0.927899i	0.885862	−	0.463950i	$-0.153568\pi$
$114$		0			0
$115$	−4.14767	+	10.0134i	−0.386773	+	0.933752i
$116$		0			0
$117$	−6.35898	+	2.63397i	−0.587888	+	0.243511i
$118$		0			0
$119$	0.420390	+	0.420390i	0.0385371	+	0.0385371i
$120$		0			0
$121$	0.306509	−	0.306509i	0.0278645	−	0.0278645i
$122$		0			0
$123$	−1.11676	−	2.69610i	−0.100695	−	0.243099i
$124$		0			0
$125$	10.6739	+	4.42126i	0.954700	+	0.395450i
$126$		0			0
$127$	−15.4530			−1.37123			−0.685614	−	0.727965i	$-0.740466\pi$
$127$	−15.4530			−1.37123			−0.685614	+	0.727965i	$0.740466\pi$
$128$		0			0
$129$	2.26190			0.199149
$130$		0			0
$131$	14.5797	+	6.03911i	1.27383	+	0.527639i	0.914128	−	0.405427i	$-0.132877\pi$
$131$	14.5797	+	6.03911i	1.27383	+	0.527639i	0.359706	+	0.933066i	$0.382877\pi$
$132$		0			0
$133$	−0.474798	−	1.14626i	−0.0411702	−	0.0993937i
$134$		0			0
$135$	2.90855	−	2.90855i	0.250328	−	0.250328i
$136$		0			0
$137$	5.83183	+	5.83183i	0.498247	+	0.498247i	0.910892	−	0.412645i	$-0.135395\pi$
$137$	5.83183	+	5.83183i	0.498247	+	0.498247i	−0.412645	+	0.910892i	$0.635395\pi$
$138$		0			0
$139$	−7.31458	+	3.02980i	−0.620414	+	0.256984i	−0.670674	−	0.741752i	$-0.733995\pi$
$139$	−7.31458	+	3.02980i	−0.620414	+	0.256984i	0.0502598	+	0.998736i	$0.483995\pi$
$140$		0			0
$141$	−2.23267	+	5.39015i	−0.188025	+	0.453932i
$142$		0			0
$143$		−	8.41009i		−	0.703287i
$144$		0			0
$145$		−	6.93477i		−	0.575901i
$146$		0			0
$147$	−1.28540	+	3.10323i	−0.106018	+	0.255950i
$148$		0			0
$149$	6.56583	−	2.71965i	0.537893	−	0.222803i	−0.0971630	−	0.995268i	$-0.530977\pi$
$149$	6.56583	−	2.71965i	0.537893	−	0.222803i	0.635056	+	0.772466i	$0.280977\pi$
$150$		0			0
$151$	−10.7733	−	10.7733i	−0.876722	−	0.876722i	0.116472	−	0.993194i	$-0.462842\pi$
$151$	−10.7733	−	10.7733i	−0.876722	−	0.876722i	−0.993194	+	0.116472i	$0.962842\pi$
$152$		0			0
$153$	6.08757	−	6.08757i	0.492151	−	0.492151i
$154$		0			0
$155$	4.21260	+	10.1701i	0.338364	+	0.816883i
$156$		0			0
$157$	0.532954	+	0.220757i	0.0425344	+	0.0176183i	0.403849	−	0.914826i	$-0.367672\pi$
$157$	0.532954	+	0.220757i	0.0425344	+	0.0176183i	−0.361315	+	0.932444i	$0.617672\pi$
$158$		0			0
$159$	1.78932			0.141902
$160$		0			0
$161$	1.40085			0.110402
$162$		0			0
$163$	−22.3602	−	9.26188i	−1.75138	−	0.725447i	−0.997669	−	0.0682454i	$-0.978260\pi$
$163$	−22.3602	−	9.26188i	−1.75138	−	0.725447i	−0.753715	−	0.657201i	$-0.771740\pi$
$164$		0			0
$165$	0.922880	+	2.22803i	0.0718461	+	0.173452i
$166$		0			0
$167$	−11.2141	+	11.2141i	−0.867770	+	0.867770i	−0.992225	−	0.124455i	$-0.960282\pi$
$167$	−11.2141	+	11.2141i	−0.867770	+	0.867770i	0.124455	+	0.992225i	$0.460282\pi$
$168$		0			0
$169$	4.81809	+	4.81809i	0.370623	+	0.370623i
$170$		0			0
$171$	−16.5988	+	6.87544i	−1.26934	+	0.525778i
$172$		0			0
$173$	−8.36603	+	20.1974i	−0.636057	+	1.53558i	0.195833	+	0.980637i	$0.437259\pi$
$173$	−8.36603	+	20.1974i	−0.636057	+	1.53558i	−0.831890	+	0.554940i	$0.812741\pi$
$174$		0			0
$175$		−	0.537730i		−	0.0406486i
$176$		0			0
$177$		−	1.46750i		−	0.110304i
$178$		0			0
$179$	−5.86300	+	14.1545i	−0.438221	+	1.05796i	0.538342	+	0.842727i	$0.319051\pi$
$179$	−5.86300	+	14.1545i	−0.438221	+	1.05796i	−0.976563	+	0.215233i	$0.930949\pi$
$180$		0			0
$181$	9.74737	−	4.03749i	0.724516	−	0.300104i	0.0102198	−	0.999948i	$-0.496747\pi$
$181$	9.74737	−	4.03749i	0.724516	−	0.300104i	0.714296	+	0.699843i	$0.246747\pi$
$182$		0			0
$183$	−3.22264	−	3.22264i	−0.238225	−	0.238225i
$184$		0			0
$185$	−9.55583	+	9.55583i	−0.702559	+	0.702559i
$186$		0			0
$187$	4.02557	+	9.71858i	0.294379	+	0.710693i
$188$		0			0
$189$	−0.491170	−	0.203449i	−0.0357274	−	0.0147988i
$190$		0			0
$191$	−22.9763			−1.66250			−0.831252	−	0.555896i	$-0.812375\pi$
$191$	−22.9763			−1.66250			−0.831252	+	0.555896i	$0.812375\pi$
$192$		0			0
$193$	−18.2368			−1.31271			−0.656355	−	0.754452i	$-0.727903\pi$
$193$	−18.2368			−1.31271			−0.656355	+	0.754452i	$0.727903\pi$
$194$		0			0
$195$	1.63887	+	0.678840i	0.117362	+	0.0486128i
$196$		0			0
$197$	−8.56510	−	20.6780i	−0.610238	−	1.47324i	−0.862740	−	0.505648i	$-0.831253\pi$
$197$	−8.56510	−	20.6780i	−0.610238	−	1.47324i	0.252502	−	0.967596i	$-0.418747\pi$
$198$		0			0
$199$	4.62301	−	4.62301i	0.327717	−	0.327717i	−0.524001	−	0.851718i	$-0.675561\pi$
$199$	4.62301	−	4.62301i	0.327717	−	0.327717i	0.851718	+	0.524001i	$0.175561\pi$
$200$		0			0
$201$	2.63984	+	2.63984i	0.186200	+	0.186200i
$202$		0			0
$203$	−0.828081	+	0.343002i	−0.0581199	+	0.0240741i
$204$		0			0
$205$	3.42319	−	8.26430i	0.239086	−	0.577204i
$206$		0			0
$207$		−	20.2853i		−	1.40993i
$208$		0			0
$209$		−	21.9528i		−	1.51851i
$210$		0			0
$211$	−3.21429	+	7.75999i	−0.221281	+	0.534220i	−0.995064	−	0.0992305i	$-0.968362\pi$
$211$	−3.21429	+	7.75999i	−0.221281	+	0.534220i	0.773783	+	0.633450i	$0.218362\pi$
$212$		0			0
$213$	−1.80260	+	0.746663i	−0.123512	+	0.0511605i
$214$		0			0
$215$	4.90262	+	4.90262i	0.334356	+	0.334356i
$216$		0			0
$217$	1.00605	−	1.00605i	0.0682953	−	0.0682953i
$218$		0			0
$219$	−0.651841	−	1.57368i	−0.0440473	−	0.106340i
$220$		0			0
$221$	7.14867	+	2.96108i	0.480871	+	0.199183i
$222$		0			0
$223$	6.64899			0.445249			0.222625	−	0.974904i	$-0.428538\pi$
$223$	6.64899			0.445249			0.222625	+	0.974904i	$0.428538\pi$
$224$		0			0
$225$	−7.78675			−0.519116
$226$		0			0
$227$	−5.82482	−	2.41272i	−0.386607	−	0.160138i	0.180910	−	0.983500i	$-0.442096\pi$
$227$	−5.82482	−	2.41272i	−0.386607	−	0.160138i	−0.567517	+	0.823362i	$0.692096\pi$
$228$		0			0
$229$	−6.23338	−	15.0487i	−0.411913	−	0.994446i	−0.984624	−	0.174689i	$-0.944108\pi$
$229$	−6.23338	−	15.0487i	−0.411913	−	0.994446i	0.572711	−	0.819758i	$-0.305892\pi$
$230$		0			0
$231$	0.220402	−	0.220402i	0.0145014	−	0.0145014i
$232$		0			0
$233$	17.8296	+	17.8296i	1.16806	+	1.16806i	0.982665	+	0.185390i	$0.0593549\pi$
$233$	17.8296	+	17.8296i	1.16806	+	1.16806i	0.185390	+	0.982665i	$0.440645\pi$
$234$		0			0
$235$	−16.5223	+	6.84377i	−1.07780	+	0.446438i
$236$		0			0
$237$	1.55051	−	3.74326i	0.100716	−	0.243151i
$238$		0			0
$239$			14.7833i			0.956254i	0.878291	+	0.478127i	$0.158684\pi$
$239$			14.7833i			0.956254i	−0.878291	+	0.478127i	$0.841316\pi$
$240$		0			0
$241$		−	2.03919i		−	0.131356i	−0.997841	−	0.0656779i	$-0.979079\pi$
$241$		−	2.03919i		−	0.131356i	0.997841	−	0.0656779i	$-0.0209210\pi$
$242$		0			0
$243$	−4.47858	+	10.8122i	−0.287301	+	0.693606i
$244$		0			0
$245$	−9.51229	+	3.94012i	−0.607718	+	0.251725i
$246$		0			0
$247$	−11.4182	−	11.4182i	−0.726522	−	0.726522i
$248$		0			0
$249$	4.83083	−	4.83083i	0.306141	−	0.306141i
$250$		0			0
$251$	3.32624	+	8.03025i	0.209950	+	0.506865i	0.993415	−	0.114571i	$-0.0365495\pi$
$251$	3.32624	+	8.03025i	0.209950	+	0.506865i	−0.783465	+	0.621436i	$0.786549\pi$
$252$		0			0
$253$	22.8995	+	9.48528i	1.43968	+	0.596335i
$254$		0			0
$255$	−2.21878			−0.138946
$256$		0			0
$257$	2.91308			0.181713			0.0908563	−	0.995864i	$-0.471040\pi$
$257$	2.91308			0.181713			0.0908563	+	0.995864i	$0.471040\pi$
$258$		0			0
$259$	1.61371	+	0.668419i	0.100271	+	0.0415335i
$260$		0			0
$261$	4.96694	+	11.9913i	0.307446	+	0.742240i
$262$		0			0
$263$	0.119315	−	0.119315i	0.00735727	−	0.00735727i	−0.703419	−	0.710776i	$-0.748344\pi$
$263$	0.119315	−	0.119315i	0.00735727	−	0.00735727i	0.710776	+	0.703419i	$0.248344\pi$
$264$		0			0
$265$	3.87832	+	3.87832i	0.238243	+	0.238243i
$266$		0			0
$267$	−3.13046	+	1.29668i	−0.191581	+	0.0793556i
$268$		0			0
$269$	−12.0000	+	28.9705i	−0.731651	+	1.76636i	−0.0946356	+	0.995512i	$0.530169\pi$
$269$	−12.0000	+	28.9705i	−0.731651	+	1.76636i	−0.637016	+	0.770851i	$0.719831\pi$
$270$		0			0
$271$		−	18.1938i		−	1.10520i	−0.833447	−	0.552599i	$-0.813636\pi$
$271$		−	18.1938i		−	1.10520i	0.833447	−	0.552599i	$-0.186364\pi$
$272$		0			0
$273$		−	0.229273i		−	0.0138762i
$274$		0			0
$275$	3.64103	−	8.79022i	0.219562	−	0.530070i
$276$		0			0
$277$	−9.37475	+	3.88315i	−0.563274	+	0.233316i	−0.646106	−	0.763248i	$-0.723604\pi$
$277$	−9.37475	+	3.88315i	−0.563274	+	0.233316i	0.0828318	+	0.996564i	$0.473604\pi$
$278$		0			0
$279$	−14.5684	−	14.5684i	−0.872188	−	0.872188i
$280$		0			0
$281$	−12.5916	+	12.5916i	−0.751151	+	0.751151i	−0.974694	−	0.223543i	$-0.928238\pi$
$281$	−12.5916	+	12.5916i	−0.751151	+	0.751151i	0.223543	+	0.974694i	$0.428238\pi$
$282$		0			0
$283$	−6.21821	−	15.0121i	−0.369634	−	0.892376i	−0.993810	−	0.111092i	$-0.964565\pi$
$283$	−6.21821	−	15.0121i	−0.369634	−	0.892376i	0.624176	−	0.781284i	$-0.285435\pi$
$284$		0			0
$285$	4.27792	+	1.77197i	0.253402	+	0.104963i
$286$		0			0
$287$	−1.15616			−0.0682457
$288$		0			0
$289$	7.32175			0.430691
$290$		0			0
$291$	−1.28119	−	0.530686i	−0.0751047	−	0.0311094i
$292$		0			0
$293$	−5.60966	−	13.5429i	−0.327720	−	0.791186i	−0.998761	−	0.0497657i	$-0.984153\pi$
$293$	−5.60966	−	13.5429i	−0.327720	−	0.791186i	0.671041	−	0.741420i	$-0.265847\pi$
$294$		0			0
$295$	3.18078	−	3.18078i	0.185192	−	0.185192i
$296$		0			0
$297$	−6.65153	−	6.65153i	−0.385961	−	0.385961i
$298$		0			0
$299$	16.8441	−	6.97706i	0.974121	−	0.403494i
$300$		0			0
$301$	0.342932	−	0.827912i	0.0197663	−	0.0477200i
$302$		0			0
$303$		−	3.78356i		−	0.217360i
$304$		0			0
$305$		−	13.9700i		−	0.799923i
$306$		0			0
$307$	−4.62413	+	11.1636i	−0.263913	+	0.637143i	−0.999174	−	0.0406418i	$-0.987060\pi$
$307$	−4.62413	+	11.1636i	−0.263913	+	0.637143i	0.735261	+	0.677784i	$0.237060\pi$
$308$		0			0
$309$	2.59700	−	1.07571i	0.147738	−	0.0611951i
$310$		0			0
$311$	−5.03317	−	5.03317i	−0.285405	−	0.285405i	0.549855	−	0.835260i	$-0.314683\pi$
$311$	−5.03317	−	5.03317i	−0.285405	−	0.285405i	−0.835260	+	0.549855i	$0.814683\pi$
$312$		0			0
$313$	2.58454	−	2.58454i	0.146087	−	0.146087i	−0.630281	−	0.776367i	$-0.717060\pi$
$313$	2.58454	−	2.58454i	0.146087	−	0.146087i	0.776367	+	0.630281i	$0.217060\pi$
$314$		0			0
$315$	−0.299235	−	0.722417i	−0.0168600	−	0.0407036i
$316$		0			0
$317$	−19.8296	−	8.21371i	−1.11374	−	0.461328i	−0.251518	−	0.967853i	$-0.580930\pi$
$317$	−19.8296	−	8.21371i	−1.11374	−	0.461328i	−0.862225	+	0.506525i	$0.830930\pi$
$318$		0			0
$319$	−15.8591			−0.887937
$320$		0			0
$321$	2.90238			0.161995
$322$		0			0
$323$	18.6601	+	7.72927i	1.03828	+	0.430068i
$324$		0			0
$325$	−2.67822	−	6.46580i	−0.148561	−	0.358658i
$326$		0			0
$327$	1.54852	−	1.54852i	0.0856336	−	0.0856336i
$328$		0			0
$329$	1.63443	+	1.63443i	0.0901090	+	0.0901090i
$330$		0			0
$331$	−11.6828	+	4.83918i	−0.642146	+	0.265986i	−0.679904	−	0.733301i	$-0.737978\pi$
$331$	−11.6828	+	4.83918i	−0.642146	+	0.265986i	0.0377578	+	0.999287i	$0.487978\pi$
$332$		0			0
$333$	9.67922	−	23.3677i	0.530418	−	1.28054i
$334$		0			0
$335$			11.4436i			0.625231i
$336$		0			0
$337$			17.3525i			0.945254i	0.881263	+	0.472627i	$0.156694\pi$
$337$			17.3525i			0.945254i	−0.881263	+	0.472627i	$0.843306\pi$
$338$		0			0
$339$	1.82076	−	4.39570i	0.0988901	−	0.238742i
$340$		0			0
$341$	23.2579	−	9.63375i	1.25949	−	0.521697i
$342$		0			0
$343$	1.88689	+	1.88689i	0.101883	+	0.101883i
$344$		0			0
$345$	−3.69677	+	3.69677i	−0.199028	+	0.199028i
$346$		0			0
$347$	6.67513	+	16.1152i	0.358340	+	0.865109i	0.995534	+	0.0944054i	$0.0300950\pi$
$347$	6.67513	+	16.1152i	0.358340	+	0.865109i	−0.637194	+	0.770703i	$0.719905\pi$
$348$		0			0
$349$	−0.479418	−	0.198581i	−0.0256626	−	0.0106298i	0.369815	−	0.929105i	$-0.379421\pi$
$349$	−0.479418	−	0.198581i	−0.0256626	−	0.0106298i	−0.395478	+	0.918476i	$0.629421\pi$
$350$		0			0
$351$	−6.91925			−0.369322
$352$		0			0
$353$	−2.30663			−0.122769			−0.0613846	−	0.998114i	$-0.519552\pi$
$353$	−2.30663			−0.122769			−0.0613846	+	0.998114i	$0.519552\pi$
$354$		0			0
$355$	−5.52549	−	2.28873i	−0.293262	−	0.121473i
$356$		0			0
$357$	0.109744	+	0.264945i	0.00580826	+	0.0140224i
$358$		0			0
$359$	−6.02599	+	6.02599i	−0.318039	+	0.318039i	−0.848014	−	0.529974i	$-0.822202\pi$
$359$	−6.02599	+	6.02599i	−0.318039	+	0.318039i	0.529974	+	0.848014i	$0.322202\pi$
$360$		0			0
$361$	−16.3698	−	16.3698i	−0.861567	−	0.861567i
$362$		0			0
$363$	0.193173	−	0.0800150i	0.0101390	−	0.00419970i
$364$		0			0
$365$	1.99808	−	4.82378i	0.104584	−	0.252488i
$366$		0			0
$367$		−	5.67199i		−	0.296076i	−0.988982	−	0.148038i	$-0.952704\pi$
$367$		−	5.67199i		−	0.296076i	0.988982	−	0.148038i	$-0.0472957\pi$
$368$		0			0
$369$			16.7420i			0.871555i
$370$		0			0
$371$	0.271283	−	0.654936i	0.0140843	−	0.0340026i
$372$		0			0
$373$	−32.1599	+	13.3210i	−1.66517	+	0.689738i	−0.998455	−	0.0555710i	$-0.982302\pi$
$373$	−32.1599	+	13.3210i	−1.66517	+	0.689738i	−0.666719	+	0.745309i	$0.732302\pi$
$374$		0			0
$375$	3.94062	+	3.94062i	0.203493	+	0.203493i
$376$		0			0
$377$	−8.24869	+	8.24869i	−0.424829	+	0.424829i
$378$		0			0
$379$	−1.20243	−	2.90292i	−0.0617647	−	0.149113i	0.889984	−	0.455992i	$-0.150715\pi$
$379$	−1.20243	−	2.90292i	−0.0617647	−	0.149113i	−0.951749	+	0.306879i	$0.900715\pi$
$380$		0			0
$381$	−6.88652	−	2.85249i	−0.352807	−	0.146138i
$382$		0			0
$383$	26.6159			1.36001			0.680004	−	0.733208i	$-0.261978\pi$
$383$	26.6159			1.36001			0.680004	+	0.733208i	$0.261978\pi$
$384$		0			0
$385$	0.955435			0.0486935
$386$		0			0
$387$	−11.9888	−	4.96592i	−0.609425	−	0.252432i
$388$		0			0
$389$	4.69648	+	11.3383i	0.238121	+	0.574875i	0.997088	−	0.0762534i	$-0.0242958\pi$
$389$	4.69648	+	11.3383i	0.238121	+	0.574875i	−0.758967	+	0.651129i	$0.774296\pi$
$390$		0			0
$391$	−16.1252	+	16.1252i	−0.815486	+	0.815486i
$392$		0			0
$393$	5.38259	+	5.38259i	0.271516	+	0.271516i
$394$		0			0
$395$	11.4742	−	4.75275i	0.577327	−	0.239137i
$396$		0			0
$397$	−5.47337	+	13.2139i	−0.274700	+	0.663185i	−0.999672	−	0.0255930i	$-0.991853\pi$
$397$	−5.47337	+	13.2139i	−0.274700	+	0.663185i	0.724972	+	0.688778i	$0.241853\pi$
$398$		0			0
$399$		−	0.598470i		−	0.0299610i
$400$		0			0
$401$		−	12.8160i		−	0.639999i	−0.947418	−	0.320000i	$-0.896317\pi$
$401$		−	12.8160i		−	0.639999i	0.947418	−	0.320000i	$-0.103683\pi$
$402$		0			0
$403$	7.08627	−	17.1078i	0.352992	−	0.852199i
$404$		0			0
$405$	−9.50765	+	3.93820i	−0.472439	+	0.195691i
$406$		0			0
$407$	21.8532	+	21.8532i	1.08322	+	1.08322i
$408$		0			0
$409$	10.5505	−	10.5505i	0.521689	−	0.521689i	−0.396392	−	0.918081i	$-0.629738\pi$
$409$	10.5505	−	10.5505i	0.521689	−	0.521689i	0.918081	+	0.396392i	$0.129738\pi$
$410$		0			0
$411$	1.52241	+	3.67543i	0.0750951	+	0.181296i
$412$		0			0
$413$	−0.537143	−	0.222492i	−0.0264311	−	0.0109481i
$414$		0			0
$415$	20.9415			1.02798
$416$		0			0
$417$	−3.81897			−0.187016
$418$		0			0
$419$	21.6069	+	8.94989i	1.05557	+	0.437231i	0.841876	−	0.539671i	$-0.181451\pi$
$419$	21.6069	+	8.94989i	1.05557	+	0.437231i	0.213692	+	0.976901i	$0.431451\pi$
$420$		0			0
$421$	14.2268	+	34.3466i	0.693372	+	1.67395i	0.737873	+	0.674939i	$0.235830\pi$
$421$	14.2268	+	34.3466i	0.693372	+	1.67395i	−0.0445009	+	0.999009i	$0.514170\pi$
$422$		0			0
$423$	23.6678	−	23.6678i	1.15077	−	1.15077i
$424$		0			0
$425$	6.18983	+	6.18983i	0.300251	+	0.300251i
$426$		0			0
$427$	−1.66816	+	0.690976i	−0.0807281	+	0.0334387i
$428$		0			0
$429$	1.55243	−	3.74791i	0.0749522	−	0.180951i
$430$		0			0
$431$			27.4006i			1.31984i	0.751335	+	0.659921i	$0.229410\pi$
$431$			27.4006i			1.31984i	−0.751335	+	0.659921i	$0.770590\pi$
$432$		0			0
$433$			17.6255i			0.847027i	0.905890	+	0.423514i	$0.139203\pi$
$433$			17.6255i			0.847027i	−0.905890	+	0.423514i	$0.860797\pi$
$434$		0			0
$435$	1.28010	−	3.09044i	0.0613762	−	0.148175i
$436$		0			0
$437$	43.9681	−	18.2122i	2.10328	−	0.871206i
$438$		0			0
$439$	12.9463	+	12.9463i	0.617894	+	0.617894i	0.944991	−	0.327097i	$-0.106070\pi$
$439$	12.9463	+	12.9463i	0.617894	+	0.617894i	−0.327097	+	0.944991i	$0.606070\pi$
$440$		0			0
$441$	13.6261	−	13.6261i	0.648862	−	0.648862i
$442$		0			0
$443$	−12.7824	−	30.8594i	−0.607309	−	1.46617i	−0.865915	−	0.500191i	$-0.833263\pi$
$443$	−12.7824	−	30.8594i	−0.607309	−	1.46617i	0.258606	−	0.965983i	$-0.416737\pi$
$444$		0			0
$445$	−9.59575	−	3.97469i	−0.454882	−	0.188418i
$446$		0			0
$447$	3.42805			0.162141
$448$		0			0
$449$	0.0878169			0.00414433			0.00207217	−	0.999998i	$-0.499340\pi$
$449$	0.0878169			0.00414433			0.00207217	+	0.999998i	$0.499340\pi$
$450$		0			0
$451$	−18.8996	−	7.82845i	−0.889946	−	0.368628i
$452$		0			0
$453$	−2.81241	−	6.78975i	−0.132138	−	0.319010i
$454$		0			0
$455$	0.496946	−	0.496946i	0.0232972	−	0.0232972i
$456$		0			0
$457$	−11.3331	−	11.3331i	−0.530141	−	0.530141i	0.390473	−	0.920614i	$-0.372311\pi$
$457$	−11.3331	−	11.3331i	−0.530141	−	0.530141i	−0.920614	+	0.390473i	$0.872311\pi$
$458$		0			0
$459$	7.99579	−	3.31196i	0.373211	−	0.154589i
$460$		0			0
$461$	6.04506	−	14.5941i	0.281546	−	0.679713i	−0.718326	−	0.695707i	$-0.755091\pi$
$461$	6.04506	−	14.5941i	0.281546	−	0.679713i	0.999872	+	0.0159940i	$0.00509127\pi$
$462$		0			0
$463$			21.2329i			0.986779i	0.869809	+	0.493389i	$0.164242\pi$
$463$			21.2329i			0.986779i	−0.869809	+	0.493389i	$0.835758\pi$
$464$		0			0
$465$			5.30986i			0.246239i
$466$		0			0
$467$	3.82134	−	9.22554i	0.176831	−	0.426907i	−0.810468	−	0.585783i	$-0.800787\pi$
$467$	3.82134	−	9.22554i	0.176831	−	0.426907i	0.987299	+	0.158876i	$0.0507870\pi$
$468$		0			0
$469$	1.36648	−	0.566015i	0.0630982	−	0.0261361i
$470$		0			0
$471$	0.196758	+	0.196758i	0.00906613	+	0.00906613i
$472$		0			0
$473$	11.2118	−	11.2118i	0.515517	−	0.515517i
$474$		0			0
$475$	−6.99094	−	16.8776i	−0.320766	−	0.774399i
$476$		0			0
$477$	−9.48398	−	3.92839i	−0.434241	−	0.179869i
$478$		0			0
$479$	4.02741			0.184017			0.0920085	−	0.995758i	$-0.470671\pi$
$479$	4.02741			0.184017			0.0920085	+	0.995758i	$0.470671\pi$
$480$		0			0
$481$	22.7327			1.03652
$482$		0			0
$483$	0.624279	+	0.258585i	0.0284057	+	0.0117660i
$484$		0			0
$485$	−1.62670	−	3.92721i	−0.0738648	−	0.178325i
$486$		0			0
$487$	6.69427	−	6.69427i	0.303346	−	0.303346i	−0.538975	−	0.842322i	$-0.681188\pi$
$487$	6.69427	−	6.69427i	0.303346	−	0.303346i	0.842322	+	0.538975i	$0.181188\pi$
$488$		0			0
$489$	−8.25501	−	8.25501i	−0.373305	−	0.373305i
$490$		0			0
$491$	31.6286	−	13.1010i	1.42738	−	0.591239i	0.470675	−	0.882307i	$-0.344011\pi$
$491$	31.6286	−	13.1010i	1.42738	−	0.591239i	0.956702	+	0.291068i	$0.0940105\pi$
$492$		0			0
$493$	5.58376	−	13.4804i	0.251480	−	0.607126i
$494$		0			0
$495$		−	13.8354i		−	0.621857i
$496$		0			0
$497$			0.773002i			0.0346739i
$498$		0			0
$499$	6.07387	−	14.6636i	0.271904	−	0.656434i	−0.727661	−	0.685937i	$-0.759393\pi$
$499$	6.07387	−	14.6636i	0.271904	−	0.656434i	0.999565	+	0.0295034i	$0.00939258\pi$
$500$		0			0
$501$	−7.06750	+	2.92746i	−0.315753	+	0.130789i
$502$		0			0
$503$	16.7932	+	16.7932i	0.748773	+	0.748773i	0.974249	−	0.225476i	$-0.0723938\pi$
$503$	16.7932	+	16.7932i	0.748773	+	0.748773i	−0.225476	+	0.974249i	$0.572394\pi$
$504$		0			0
$505$	8.20080	−	8.20080i	0.364931	−	0.364931i
$506$		0			0
$507$	1.25778	+	3.03654i	0.0558598	+	0.134857i
$508$		0			0
$509$	8.90119	+	3.68700i	0.394539	+	0.163423i	0.571127	−	0.820862i	$-0.306506\pi$
$509$	8.90119	+	3.68700i	0.394539	+	0.163423i	−0.176589	+	0.984285i	$0.556506\pi$
$510$		0			0
$511$	−0.674835			−0.0298530
$512$		0			0
$513$	−18.0613			−0.797424
$514$		0			0
$515$	7.96053	+	3.29736i	0.350783	+	0.145299i
$516$		0			0
$517$	15.6510	+	37.7848i	0.688329	+	1.66177i
$518$		0			0
$519$	−7.45654	+	7.45654i	−0.327306	+	0.327306i
$520$		0			0
$521$	−25.4229	−	25.4229i	−1.11380	−	1.11380i	−0.992632	−	0.121167i	$-0.961336\pi$
$521$	−25.4229	−	25.4229i	−1.11380	−	1.11380i	−0.121167	−	0.992632i	$-0.538664\pi$
$522$		0			0
$523$	8.68795	−	3.59867i	0.379897	−	0.157359i	−0.184559	−	0.982821i	$-0.559086\pi$
$523$	8.68795	−	3.59867i	0.379897	−	0.157359i	0.564457	+	0.825463i	$0.309086\pi$
$524$		0			0
$525$	0.0992607	−	0.239636i	0.00433209	−	0.0104586i
$526$		0			0
$527$			23.1614i			1.00893i
$528$		0			0
$529$			30.7332i			1.33623i
$530$		0			0
$531$	−3.22185	+	7.77824i	−0.139816	+	0.337547i
$532$		0			0
$533$	−13.9019	+	5.75836i	−0.602158	+	0.249422i
$534$		0			0
$535$	6.29085	+	6.29085i	0.271977	+	0.271977i
$536$		0			0
$537$	−5.22562	+	5.22562i	−0.225502	+	0.225502i
$538$		0			0
$539$	9.01063	+	21.7536i	0.388115	+	0.936993i
$540$		0			0
$541$	−29.6140	−	12.2665i	−1.27320	−	0.527379i	−0.359268	−	0.933235i	$-0.616974\pi$
$541$	−29.6140	−	12.2665i	−1.27320	−	0.527379i	−0.913937	+	0.405856i	$0.866974\pi$
$542$		0			0
$543$	5.08915			0.218396
$544$		0			0
$545$	6.71279			0.287545
$546$		0			0
$547$	11.4126	+	4.72724i	0.487966	+	0.202122i	0.613081	−	0.790020i	$-0.289930\pi$
$547$	11.4126	+	4.72724i	0.487966	+	0.202122i	−0.125115	+	0.992142i	$0.539930\pi$
$548$		0			0
$549$	10.0059	+	24.1563i	0.427040	+	1.03097i
$550$		0			0
$551$	−21.5315	+	21.5315i	−0.917273	+	0.917273i
$552$		0			0
$553$	−1.13505	−	1.13505i	−0.0482673	−	0.0482673i
$554$		0			0
$555$	−6.02243	+	2.49457i	−0.255638	+	0.105889i
$556$		0			0
$557$	−5.82814	+	14.0704i	−0.246946	+	0.596180i	−0.997942	−	0.0641266i	$-0.979574\pi$
$557$	−5.82814	+	14.0704i	−0.246946	+	0.596180i	0.750996	+	0.660307i	$0.229574\pi$
$558$		0			0
$559$		−	11.6630i		−	0.493293i
$560$		0			0
$561$			5.07412i			0.214229i
$562$		0			0
$563$	18.0589	−	43.5982i	0.761094	−	1.83744i	0.283057	−	0.959103i	$-0.408651\pi$
$563$	18.0589	−	43.5982i	0.761094	−	1.83744i	0.478036	−	0.878340i	$-0.341349\pi$
$564$		0			0
$565$	13.4741	−	5.58114i	0.566858	−	0.234800i
$566$		0			0
$567$	0.940520	+	0.940520i	0.0394981	+	0.0394981i
$568$		0			0
$569$	−16.6968	+	16.6968i	−0.699965	+	0.699965i	−0.964403	−	0.264438i	$-0.914814\pi$
$569$	−16.6968	+	16.6968i	−0.699965	+	0.699965i	0.264438	+	0.964403i	$0.414814\pi$
$570$		0			0
$571$	10.6509	+	25.7136i	0.445728	+	1.07608i	0.973907	+	0.226949i	$0.0728751\pi$
$571$	10.6509	+	25.7136i	0.445728	+	1.07608i	−0.528179	+	0.849133i	$0.677125\pi$
$572$		0			0
$573$	−10.2392	−	4.24123i	−0.427750	−	0.177180i
$574$		0			0
$575$	20.6261			0.860168
$576$		0			0
$577$	42.1981			1.75673			0.878365	−	0.477991i	$-0.158635\pi$
$577$	42.1981			1.75673			0.878365	+	0.477991i	$0.158635\pi$
$578$		0			0
$579$	−8.12710	−	3.36636i	−0.337751	−	0.139901i
$580$		0			0
$581$	−1.03579	−	2.50062i	−0.0429719	−	0.103743i
$582$		0			0
$583$	8.86929	−	8.86929i	0.367328	−	0.367328i
$584$		0			0
$585$	−7.19615	−	7.19615i	−0.297524	−	0.297524i
$586$		0			0
$587$	17.3546	−	7.18852i	0.716302	−	0.296702i	0.00539239	−	0.999985i	$-0.498284\pi$
$587$	17.3546	−	7.18852i	0.716302	−	0.296702i	0.710909	+	0.703284i	$0.248284\pi$
$588$		0			0
$589$	18.4972	−	44.6563i	0.762166	−	1.84003i
$590$		0			0
$591$		−	10.7961i		−	0.444091i
$592$		0			0
$593$		−	0.516291i		−	0.0212015i	−0.999944	−	0.0106008i	$-0.996626\pi$
$593$		−	0.516291i		−	0.0212015i	0.999944	−	0.0106008i	$-0.00337439\pi$
$594$		0			0
$595$	−0.336396	+	0.812131i	−0.0137909	+	0.0332941i
$596$		0			0
$597$	2.91359	−	1.20685i	0.119245	−	0.0493930i
$598$		0			0
$599$	13.6567	+	13.6567i	0.557999	+	0.557999i	0.928737	−	0.370738i	$-0.120895\pi$
$599$	13.6567	+	13.6567i	0.557999	+	0.557999i	−0.370738	+	0.928737i	$0.620895\pi$
$600$		0			0
$601$	3.24556	−	3.24556i	0.132389	−	0.132389i	−0.637807	−	0.770196i	$-0.720158\pi$
$601$	3.24556	−	3.24556i	0.132389	−	0.132389i	0.770196	+	0.637807i	$0.220158\pi$
$602$		0			0
$603$	−8.19633	−	19.7877i	−0.333780	−	0.805817i
$604$		0			0
$605$	0.592131	+	0.245268i	0.0240735	+	0.00997158i
$606$		0			0
$607$	−13.8854			−0.563591			−0.281795	−	0.959475i	$-0.590930\pi$
$607$	−13.8854			−0.563591			−0.281795	+	0.959475i	$0.590930\pi$
$608$		0			0
$609$	−0.432345			−0.0175195
$610$		0			0
$611$	27.7932	+	11.5123i	1.12439	+	0.465739i
$612$		0			0
$613$	−8.69556	−	20.9929i	−0.351210	−	0.847896i	−0.996471	−	0.0839342i	$-0.973251\pi$
$613$	−8.69556	−	20.9929i	−0.351210	−	0.847896i	0.645261	−	0.763962i	$-0.276749\pi$
$614$		0			0
$615$	3.05105	−	3.05105i	0.123030	−	0.123030i
$616$		0			0
$617$	−11.1547	−	11.1547i	−0.449072	−	0.449072i	0.445974	−	0.895046i	$-0.352857\pi$
$617$	−11.1547	−	11.1547i	−0.449072	−	0.449072i	−0.895046	+	0.445974i	$0.852857\pi$
$618$		0			0
$619$	−0.399768	+	0.165589i	−0.0160680	+	0.00665559i	−0.390703	−	0.920517i	$-0.627768\pi$
$619$	−0.399768	+	0.165589i	−0.0160680	+	0.00665559i	0.374635	+	0.927172i	$0.377768\pi$
$620$		0			0
$621$	7.80385	−	18.8402i	0.313158	−	0.756029i
$622$		0			0
$623$			1.34242i			0.0537830i
$624$		0			0
$625$			3.01337i			0.120535i
$626$		0			0
$627$	4.05231	−	9.78313i	0.161834	−	0.390701i
$628$		0			0
$629$	−26.2696	+	10.8812i	−1.04744	+	0.433863i
$630$		0			0
$631$	−8.48708	−	8.48708i	−0.337865	−	0.337865i	0.517698	−	0.855563i	$-0.326789\pi$
$631$	−8.48708	−	8.48708i	−0.337865	−	0.337865i	−0.855563	+	0.517698i	$0.826789\pi$
$632$		0			0
$633$	−2.86486	+	2.86486i	−0.113868	+	0.113868i
$634$		0			0
$635$	−8.74369	−	21.1091i	−0.346983	−	0.837690i
$636$		0			0
$637$	16.0012	+	6.62792i	0.633991	+	0.262608i
$638$		0			0
$639$	11.1937			0.442814
$640$		0			0
$641$	22.4227			0.885644			0.442822	−	0.896610i	$-0.353977\pi$
$641$	22.4227			0.885644			0.442822	+	0.896610i	$0.353977\pi$
$642$		0			0
$643$	−9.79639	−	4.05780i	−0.386332	−	0.160024i	0.181060	−	0.983472i	$-0.442047\pi$
$643$	−9.79639	−	4.05780i	−0.386332	−	0.160024i	−0.567391	+	0.823448i	$0.692047\pi$
$644$		0			0
$645$	1.27984	+	3.08981i	0.0503937	+	0.121661i
$646$		0			0
$647$	26.4018	−	26.4018i	1.03796	−	1.03796i	0.0387106	−	0.999250i	$-0.487675\pi$
$647$	26.4018	−	26.4018i	1.03796	−	1.03796i	0.999250	−	0.0387106i	$-0.0123251\pi$
$648$		0			0
$649$	−7.27410	−	7.27410i	−0.285534	−	0.285534i
$650$		0			0
$651$	0.634051	−	0.262632i	0.0248504	−	0.0102934i
$652$		0			0
$653$	−10.8284	+	26.1421i	−0.423748	+	1.02302i	0.557484	+	0.830188i	$0.311767\pi$
$653$	−10.8284	+	26.1421i	−0.423748	+	1.02302i	−0.981232	+	0.192831i	$0.938233\pi$
$654$		0			0
$655$			23.3333i			0.911708i
$656$		0			0
$657$			9.77214i			0.381247i
$658$		0			0
$659$	−6.27260	+	15.1434i	−0.244346	+	0.589903i	−0.997705	−	0.0677059i	$-0.978432\pi$
$659$	−6.27260	+	15.1434i	−0.244346	+	0.589903i	0.753359	+	0.657609i	$0.228432\pi$
$660$		0			0
$661$	16.3513	−	6.77294i	0.635993	−	0.263437i	−0.0413040	−	0.999147i	$-0.513151\pi$
$661$	16.3513	−	6.77294i	0.635993	−	0.263437i	0.677297	+	0.735710i	$0.263151\pi$
$662$		0			0
$663$	2.63917	+	2.63917i	0.102497	+	0.102497i
$664$		0			0
$665$	1.29717	−	1.29717i	0.0503022	−	0.0503022i
$666$		0			0
$667$	−13.1568	−	31.7633i	−0.509433	−	1.22988i
$668$		0			0
$669$	2.96308	+	1.22735i	0.114559	+	0.0474521i
$670$		0			0
$671$	−31.9480			−1.23334
$672$		0			0
$673$	−49.6916			−1.91547			−0.957735	−	0.287654i	$-0.907125\pi$
$673$	−49.6916			−1.91547			−0.957735	+	0.287654i	$0.907125\pi$
$674$		0			0
$675$	−7.23200	−	2.99559i	−0.278360	−	0.115300i
$676$		0			0
$677$	9.44122	+	22.7931i	0.362856	+	0.876011i	0.994880	+	0.101063i	$0.0322242\pi$
$677$	9.44122	+	22.7931i	0.362856	+	0.876011i	−0.632024	+	0.774948i	$0.717776\pi$
$678$		0			0
$679$	−0.388489	+	0.388489i	−0.0149088	+	0.0149088i
$680$		0			0
$681$	−2.15043	−	2.15043i	−0.0824046	−	0.0824046i
$682$		0			0
$683$	25.9915	−	10.7660i	0.994535	−	0.411950i	0.174745	−	0.984614i	$-0.444090\pi$
$683$	25.9915	−	10.7660i	0.994535	−	0.411950i	0.819790	+	0.572664i	$0.194090\pi$
$684$		0			0
$685$	−4.66662	+	11.2662i	−0.178302	+	0.430460i
$686$		0			0
$687$		−	7.85700i		−	0.299763i
$688$		0			0
$689$		−	9.22627i		−	0.351493i
$690$		0			0
$691$	−0.634146	+	1.53096i	−0.0241240	+	0.0582406i	−0.935483	−	0.353373i	$-0.885035\pi$
$691$	−0.634146	+	1.53096i	−0.0241240	+	0.0582406i	0.911358	+	0.411614i	$0.135035\pi$
$692$		0			0
$693$	−1.65209	+	0.684318i	−0.0627577	+	0.0259951i
$694$		0			0
$695$	−8.27756	−	8.27756i	−0.313986	−	0.313986i
$696$		0			0
$697$	13.3085	−	13.3085i	0.504097	−	0.504097i
$698$		0			0
$699$	4.65446	+	11.2369i	0.176048	+	0.425017i
$700$		0			0
$701$	−22.3030	−	9.23819i	−0.842371	−	0.348921i	−0.0805829	−	0.996748i	$-0.525678\pi$
$701$	−22.3030	−	9.23819i	−0.842371	−	0.348921i	−0.761788	+	0.647826i	$0.775678\pi$
$702$		0			0
$703$	59.3391			2.23802
$704$		0			0
$705$	−8.62639			−0.324888
$706$		0			0
$707$	−1.38488	−	0.573636i	−0.0520837	−	0.0215738i
$708$		0			0
$709$	−4.69095	−	11.3249i	−0.176172	−	0.425317i	0.810985	−	0.585066i	$-0.198932\pi$
$709$	−4.69095	−	11.3249i	−0.176172	−	0.425317i	−0.987158	+	0.159749i	$0.948932\pi$
$710$		0			0
$711$	−16.4364	+	16.4364i	−0.616414	+	0.616414i
$712$		0			0
$713$	38.5899	+	38.5899i	1.44520	+	1.44520i
$714$		0			0
$715$	11.4884	−	4.75865i	0.429641	−	0.177963i
$716$		0			0
$717$	−2.72888	+	6.58811i	−0.101912	+	0.246037i
$718$		0			0
$719$			18.8205i			0.701888i	0.936397	+	0.350944i	$0.114139\pi$
$719$			18.8205i			0.701888i	−0.936397	+	0.350944i	$0.885861\pi$
$720$		0			0
$721$		−	1.11366i		−	0.0414748i
$722$		0			0
$723$	0.376418	−	0.908754i	0.0139991	−	0.0337969i
$724$		0			0
$725$	−12.1927	+	5.05038i	−0.452825	+	0.187566i
$726$		0			0
$727$	−16.7869	−	16.7869i	−0.622593	−	0.622593i	0.323601	−	0.946194i	$-0.395107\pi$
$727$	−16.7869	−	16.7869i	−0.622593	−	0.622593i	−0.946194	+	0.323601i	$0.895107\pi$
$728$		0			0
$729$	10.7729	−	10.7729i	0.398994	−	0.398994i
$730$		0			0
$731$	5.58262	+	13.4776i	0.206481	+	0.498488i
$732$		0			0
$733$	30.8799	+	12.7909i	1.14058	+	0.472442i	0.871363	−	0.490639i	$-0.163236\pi$
$733$	30.8799	+	12.7909i	1.14058	+	0.472442i	0.269213	+	0.963081i	$0.413236\pi$
$734$		0			0
$735$	−4.96641			−0.183189
$736$		0			0
$737$	26.1703			0.963995
$738$		0			0
$739$	12.1968	+	5.05208i	0.448667	+	0.185844i	0.595564	−	0.803308i	$-0.296929\pi$
$739$	12.1968	+	5.05208i	0.448667	+	0.185844i	−0.146897	+	0.989152i	$0.546929\pi$
$740$		0			0
$741$	−2.98074	−	7.19615i	−0.109500	−	0.264357i
$742$		0			0
$743$	−14.2144	+	14.2144i	−0.521476	+	0.521476i	−0.918017	−	0.396541i	$-0.870211\pi$
$743$	−14.2144	+	14.2144i	−0.521476	+	0.521476i	0.396541	+	0.918017i	$0.370211\pi$
$744$		0			0
$745$	7.43023	+	7.43023i	0.272223	+	0.272223i
$746$		0			0
$747$	−36.2109	+	14.9991i	−1.32489	+	0.548787i
$748$		0			0
$749$	0.440038	−	1.06234i	0.0160786	−	0.0388172i
$750$		0			0
$751$		−	17.6604i		−	0.644438i	−0.946665	−	0.322219i	$-0.895571\pi$
$751$		−	17.6604i		−	0.644438i	0.946665	−	0.322219i	$-0.104429\pi$
$752$		0			0
$753$			4.19263i			0.152788i
$754$		0			0
$755$	8.62082	−	20.8125i	0.313744	−	0.757444i
$756$		0			0
$757$	−5.46821	+	2.26500i	−0.198745	+	0.0823230i	−0.479836	−	0.877358i	$-0.659304\pi$
$757$	−5.46821	+	2.26500i	−0.198745	+	0.0823230i	0.281091	+	0.959681i	$0.409304\pi$
$758$		0			0
$759$	8.45412	+	8.45412i	0.306865	+	0.306865i
$760$		0			0
$761$	−8.84304	+	8.84304i	−0.320560	+	0.320560i	−0.848982	−	0.528422i	$-0.822784\pi$
$761$	−8.84304	+	8.84304i	−0.320560	+	0.320560i	0.528422	+	0.848982i	$0.322784\pi$
$762$		0			0
$763$	−0.332023	−	0.801575i	−0.0120200	−	0.0290190i
$764$		0			0
$765$	11.7603	+	4.87127i	0.425194	+	0.176121i
$766$		0			0
$767$	−7.56688			−0.273224
$768$		0			0
$769$	−32.3761			−1.16751			−0.583755	−	0.811930i	$-0.698417\pi$
$769$	−32.3761			−1.16751			−0.583755	+	0.811930i	$0.698417\pi$
$770$		0			0
$771$	1.29820	+	0.537730i	0.0467534	+	0.0193659i
$772$		0			0
$773$	−8.99455	−	21.7148i	−0.323511	−	0.781026i	−0.999045	−	0.0436963i	$-0.986087\pi$
$773$	−8.99455	−	21.7148i	−0.323511	−	0.781026i	0.675533	−	0.737329i	$-0.263913\pi$
$774$		0			0
$775$	14.8131	−	14.8131i	0.532104	−	0.532104i
$776$		0			0
$777$	0.595754	+	0.595754i	0.0213726	+	0.0213726i
$778$		0			0
$779$	−36.2880	+	15.0310i	−1.30015	+	0.538541i
$780$		0			0
$781$	−5.23408	+	12.6362i	−0.187290	+	0.452158i
$782$		0			0
$783$			13.0478i			0.466289i
$784$		0			0
$785$			0.852939i			0.0304427i
$786$		0			0
$787$	−21.0157	+	50.7364i	−0.749129	+	1.80856i	−0.185266	+	0.982688i	$0.559315\pi$
$787$	−21.0157	+	50.7364i	−0.749129	+	1.80856i	−0.563862	+	0.825869i	$0.690685\pi$
$788$		0			0
$789$	0.0751966	−	0.0311474i	0.00267707	−	0.00110888i
$790$		0			0
$791$	−1.33289	−	1.33289i	−0.0473921	−	0.0473921i
$792$		0			0
$793$	−16.6169	+	16.6169i	−0.590085	+	0.590085i
$794$		0			0
$795$	1.01244	+	2.44425i	0.0359077	+	0.0866888i
$796$		0			0
$797$	−16.3420	−	6.76906i	−0.578862	−	0.239772i	0.0739887	−	0.997259i	$-0.476427\pi$
$797$	−16.3420	−	6.76906i	−0.578862	−	0.239772i	−0.652851	+	0.757487i	$0.726427\pi$
$798$		0			0
$799$	−37.6280			−1.33118
$800$		0			0
$801$	19.4393			0.686854
$802$		0			0
$803$	−11.0315	−	4.56938i	−0.389292	−	0.161250i
$804$		0			0
$805$	0.792635	+	1.91359i	0.0279367	+	0.0674452i
$806$		0			0
$807$	−10.6954	+	10.6954i	−0.376497	+	0.376497i
$808$		0			0
$809$	4.39282	+	4.39282i	0.154443	+	0.154443i	0.780099	−	0.625656i	$-0.215169\pi$
$809$	4.39282	+	4.39282i	0.154443	+	0.154443i	−0.625656	+	0.780099i	$0.715169\pi$
$810$		0			0
$811$	−27.1174	+	11.2324i	−0.952219	+	0.394422i	−0.804065	−	0.594542i	$-0.797333\pi$
$811$	−27.1174	+	11.2324i	−0.952219	+	0.394422i	−0.148155	+	0.988964i	$0.547333\pi$
$812$		0			0
$813$	3.35844	−	8.10798i	0.117786	−	0.284359i
$814$		0			0
$815$		−	35.7852i		−	1.25350i
$816$		0			0
$817$		−	30.4439i		−	1.06510i
$818$		0			0
$819$	−0.503362	+	1.21522i	−0.0175889	+	0.0424633i
$820$		0			0
$821$	45.4570	−	18.8289i	1.58646	−	0.657134i	0.597041	−	0.802211i	$-0.296343\pi$
$821$	45.4570	−	18.8289i	1.58646	−	0.657134i	0.989420	+	0.145077i	$0.0463430\pi$
$822$		0			0
$823$	14.4059	+	14.4059i	0.502158	+	0.502158i	0.912108	−	0.409950i	$-0.134454\pi$
$823$	14.4059	+	14.4059i	0.502158	+	0.502158i	−0.409950	+	0.912108i	$0.634454\pi$
$824$		0			0
$825$	3.24521	−	3.24521i	0.112984	−	0.112984i
$826$		0			0
$827$	5.27851	+	12.7434i	0.183552	+	0.443133i	0.988694	−	0.149949i	$-0.0479110\pi$
$827$	5.27851	+	12.7434i	0.183552	+	0.443133i	−0.805142	+	0.593082i	$0.797911\pi$
$828$		0			0
$829$	−48.0679	−	19.9104i	−1.66947	−	0.691516i	−0.670728	−	0.741704i	$-0.734018\pi$
$829$	−48.0679	−	19.9104i	−1.66947	−	0.691516i	−0.998740	+	0.0501876i	$0.984018\pi$
$830$		0			0
$831$	−4.89460			−0.169792
$832$		0			0
$833$	−21.6633			−0.750589
$834$		0			0
$835$	−21.6639	−	8.97348i	−0.749710	−	0.310540i
$836$		0			0
$837$	−7.92600	−	19.1351i	−0.273963	−	0.661404i
$838$		0			0
$839$	−5.48780	+	5.48780i	−0.189460	+	0.189460i	−0.795463	−	0.606003i	$-0.792772\pi$
$839$	−5.48780	+	5.48780i	−0.189460	+	0.189460i	0.606003	+	0.795463i	$0.292772\pi$
$840$		0			0
$841$	−4.95137	−	4.95137i	−0.170737	−	0.170737i
$842$		0			0
$843$	−7.93568	+	3.28706i	−0.273319	+	0.113213i
$844$		0			0
$845$	−3.85544	+	9.30784i	−0.132631	+	0.320200i
$846$		0			0
$847$		−	0.0828376i		−	0.00284633i
$848$		0			0
$849$		−	7.83788i		−	0.268995i
$850$		0			0
$851$	−25.6390	+	61.8981i	−0.878894	+	2.12184i
$852$		0			0
$853$	−19.7936	+	8.19878i	−0.677720	+	0.280721i	−0.694874	−	0.719132i	$-0.744540\pi$
$853$	−19.7936	+	8.19878i	−0.677720	+	0.280721i	0.0171533	+	0.999853i	$0.494540\pi$
$854$		0			0
$855$	−18.7841	−	18.7841i	−0.642401	−	0.642401i
$856$		0			0
$857$	−25.5086	+	25.5086i	−0.871358	+	0.871358i	−0.992620	−	0.121263i	$-0.961306\pi$
$857$	−25.5086	+	25.5086i	−0.871358	+	0.871358i	0.121263	+	0.992620i	$0.461306\pi$
$858$		0			0
$859$	8.64207	+	20.8638i	0.294864	+	0.711864i	0.999996	+	0.00278818i	$0.000887508\pi$
$859$	8.64207	+	20.8638i	0.294864	+	0.711864i	−0.705132	+	0.709076i	$0.749112\pi$
$860$		0			0
$861$	−0.515234	−	0.213417i	−0.0175591	−	0.00727323i
$862$		0			0
$863$	0.587161			0.0199872			0.00999360	−	0.999950i	$-0.496819\pi$
$863$	0.587161			0.0199872			0.00999360	+	0.999950i	$0.496819\pi$
$864$		0			0
$865$	−32.3238			−1.09904
$866$		0			0
$867$	3.26290	+	1.35154i	0.110814	+	0.0459006i
$868$		0			0
$869$	−10.8690	−	26.2402i	−0.368706	−	0.890136i
$870$		0			0
$871$	13.6118	−	13.6118i	0.461218	−	0.461218i
$872$		0			0
$873$	5.62562	+	5.62562i	0.190398	+	0.190398i
$874$		0			0
$875$	2.03982	−	0.844919i	0.0689583	−	0.0285635i
$876$		0			0
$877$	0.801899	−	1.93596i	0.0270782	−	0.0653726i	−0.909762	−	0.415130i	$-0.863736\pi$
$877$	0.801899	−	1.93596i	0.0270782	−	0.0653726i	0.936840	+	0.349758i	$0.113736\pi$
$878$		0			0
$879$		−	7.07082i		−	0.238493i
$880$		0			0
$881$			6.47745i			0.218231i	0.994029	+	0.109115i	$0.0348018\pi$
$881$			6.47745i			0.218231i	−0.994029	+	0.109115i	$0.965198\pi$
$882$		0			0
$883$	5.84419	−	14.1091i	0.196673	−	0.474810i	−0.794520	−	0.607238i	$-0.792277\pi$
$883$	5.84419	−	14.1091i	0.196673	−	0.474810i	0.991193	+	0.132428i	$0.0422775\pi$
$884$		0			0
$885$	2.00464	−	0.830351i	0.0673854	−	0.0279119i
$886$		0			0
$887$	−26.9437	−	26.9437i	−0.904679	−	0.904679i	0.0911573	−	0.995837i	$-0.470943\pi$
$887$	−26.9437	−	26.9437i	−0.904679	−	0.904679i	−0.995837	+	0.0911573i	$0.970943\pi$
$888$		0			0
$889$	−2.08817	+	2.08817i	−0.0700349	+	0.0700349i
$890$		0			0
$891$	9.00623	+	21.7430i	0.301720	+	0.728416i
$892$		0			0
$893$	72.5485	+	30.0506i	2.42774	+	1.00560i
$894$		0			0
$895$	−22.6529			−0.757203
$896$		0			0
$897$	8.79440			0.293636
$898$		0			0
$899$	−32.2605	−	13.3627i	−1.07595	−	0.445672i
$900$		0			0
$901$	4.41624	+	10.6617i	0.147126	+	0.355194i
$902$		0			0
$903$	0.305652	−	0.305652i	0.0101714	−	0.0101714i
$904$		0			0
$905$	11.0306	+	11.0306i	0.366671	+	0.366671i
$906$		0			0
$907$	9.29454	−	3.84992i	0.308620	−	0.127835i	−0.222998	−	0.974819i	$-0.571584\pi$
$907$	9.29454	−	3.84992i	0.308620	−	0.127835i	0.531618	+	0.846984i	$0.321584\pi$
$908$		0			0
$909$	−8.30669	+	20.0541i	−0.275515	+	0.665153i
$910$		0			0
$911$			17.1254i			0.567389i	0.958915	+	0.283694i	$0.0915601\pi$
$911$			17.1254i			0.567389i	−0.958915	+	0.283694i	$0.908440\pi$
$912$		0			0
$913$		−	47.8909i		−	1.58496i
$914$		0			0
$915$	2.57876	−	6.22567i	0.0852511	−	0.205814i
$916$		0			0
$917$	2.78623	−	1.15409i	0.0920095	−	0.0381116i
$918$		0			0
$919$	−29.1179	−	29.1179i	−0.960510	−	0.960510i	0.0387392	−	0.999249i	$-0.487666\pi$
$919$	−29.1179	−	29.1179i	−0.960510	−	0.960510i	−0.999249	+	0.0387392i	$0.987666\pi$
$920$		0			0
$921$	−4.12144	+	4.12144i	−0.135806	+	0.135806i
$922$		0			0
$923$	3.85002	+	9.29477i	0.126725	+	0.305941i
$924$		0			0
$925$	23.7603	+	9.84182i	0.781232	+	0.323597i
$926$		0			0
$927$	−16.1266			−0.529668
$928$		0			0
$929$	2.16235			0.0709445			0.0354722	−	0.999371i	$-0.488706\pi$
$929$	2.16235			0.0709445			0.0354722	+	0.999371i	$0.488706\pi$
$930$		0			0
$931$	41.7679	+	17.3008i	1.36889	+	0.567011i
$932$		0			0
$933$	−1.31392	−	3.17209i	−0.0430159	−	0.103850i
$934$		0			0
$935$	−10.9981	+	10.9981i	−0.359675	+	0.359675i
$936$		0			0
$937$	26.7802	+	26.7802i	0.874871	+	0.874871i	0.992998	−	0.118127i	$-0.0376890\pi$
$937$	26.7802	+	26.7802i	0.874871	+	0.874871i	−0.118127	+	0.992998i	$0.537689\pi$
$938$		0			0
$939$	1.62887	−	0.674701i	0.0531562	−	0.0220180i
$940$		0			0
$941$	−16.3059	+	39.3660i	−0.531558	+	1.28329i	0.398933	+	0.916980i	$0.369380\pi$
$941$	−16.3059	+	39.3660i	−0.531558	+	1.28329i	−0.930491	+	0.366314i	$0.880620\pi$
$942$		0			0
$943$		−	44.3475i		−	1.44415i
$944$		0			0
$945$		−	0.786068i		−	0.0255708i
$946$		0			0
$947$	0.466171	−	1.12544i	0.0151485	−	0.0365718i	−0.916124	−	0.400894i	$-0.868699\pi$
$947$	0.466171	−	1.12544i	0.0151485	−	0.0365718i	0.931273	+	0.364323i	$0.118699\pi$
$948$		0			0
$949$	−8.11439	+	3.36109i	−0.263404	+	0.109106i
$950$		0			0
$951$	−7.32078	−	7.32078i	−0.237393	−	0.237393i
$952$		0			0
$953$	31.4229	−	31.4229i	1.01789	−	1.01789i	0.0180517	−	0.999837i	$-0.494254\pi$
$953$	31.4229	−	31.4229i	1.01789	−	1.01789i	0.999837	−	0.0180517i	$-0.00574635\pi$
$954$		0			0
$955$	−13.0006	−	31.3862i	−0.420689	−	1.01563i
$956$		0			0
$957$	−7.06750	−	2.92746i	−0.228460	−	0.0946312i
$958$		0			0
$959$	1.57612			0.0508955
$960$		0			0
$961$	24.4285			0.788017
$962$		0			0
$963$	−15.3836	−	6.37208i	−0.495728	−	0.205337i
$964$		0			0
$965$	−10.3188	−	24.9119i	−0.332175	−	0.801941i
$966$		0			0
$967$	−17.7661	+	17.7661i	−0.571319	+	0.571319i	−0.932497	−	0.361178i	$-0.882375\pi$
$967$	−17.7661	+	17.7661i	−0.571319	+	0.571319i	0.361178	+	0.932497i	$0.382375\pi$
$968$		0			0
$969$	6.88901	+	6.88901i	0.221307	+	0.221307i
$970$		0			0
$971$	−53.6939	+	22.2407i	−1.72312	+	0.713739i	−0.723390	+	0.690440i	$0.757417\pi$
$971$	−53.6939	+	22.2407i	−1.72312	+	0.713739i	−0.999729	+	0.0232989i	$0.992583\pi$
$972$		0			0
$973$	−0.579005	+	1.39784i	−0.0185620	+	0.0448128i
$974$		0			0
$975$		−	3.37583i		−	0.108113i
$976$		0			0
$977$		−	16.3541i		−	0.523215i	−0.965174	−	0.261608i	$-0.915747\pi$
$977$		−	16.3541i		−	0.523215i	0.965174	−	0.261608i	$-0.0842527\pi$
$978$		0			0
$979$	−9.08969	+	21.9445i	−0.290508	+	0.701348i
$980$		0			0
$981$	−11.6074	+	4.80795i	−0.370596	+	0.153506i
$982$		0			0
$983$	5.23497	+	5.23497i	0.166970	+	0.166970i	0.785646	−	0.618676i	$-0.212331\pi$
$983$	5.23497	+	5.23497i	0.166970	+	0.166970i	−0.618676	+	0.785646i	$0.712331\pi$
$984$		0			0
$985$	23.4003	−	23.4003i	0.745595	−	0.745595i
$986$		0			0
$987$	0.426672	+	1.03008i	0.0135811	+	0.0327877i
$988$		0			0
$989$	31.7568	+	13.1541i	1.00981	+	0.418276i
$990$		0			0
$991$	−41.6039			−1.32159			−0.660796	−	0.750566i	$-0.729781\pi$
$991$	−41.6039			−1.32159			−0.660796	+	0.750566i	$0.729781\pi$
$992$		0			0
$993$	−6.09966			−0.193567
$994$		0			0
$995$	8.93098	+	3.69933i	0.283131	+	0.117277i
$996$		0			0
$997$	−12.1681	−	29.3764i	−0.385368	−	0.930361i	−0.990907	−	0.134545i	$-0.957043\pi$
$997$	−12.1681	−	29.3764i	−0.385368	−	0.930361i	0.605539	−	0.795815i	$-0.292957\pi$
$998$		0			0
$999$	17.9793	−	17.9793i	0.568840	−	0.568840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.d.641.3	yes	16
4.3	odd	2	inner	1024.2.g.d.641.2	yes	16
8.3	odd	2		1024.2.g.g.641.3	yes	16
8.5	even	2		1024.2.g.g.641.2	yes	16
16.3	odd	4		1024.2.g.f.129.3	yes	16
16.5	even	4		1024.2.g.a.129.3	yes	16
16.11	odd	4		1024.2.g.a.129.2	✓	16
16.13	even	4		1024.2.g.f.129.2	yes	16
32.3	odd	8		1024.2.g.a.897.2	yes	16
32.5	even	8		1024.2.g.g.385.2	yes	16
32.11	odd	8	inner	1024.2.g.d.385.2	yes	16
32.13	even	8		1024.2.g.f.897.2	yes	16
32.19	odd	8		1024.2.g.f.897.3	yes	16
32.21	even	8	inner	1024.2.g.d.385.3	yes	16
32.27	odd	8		1024.2.g.g.385.3	yes	16
32.29	even	8		1024.2.g.a.897.3	yes	16
64.11	odd	16		4096.2.a.i.1.5		8
64.21	even	16		4096.2.a.i.1.6		8
64.43	odd	16		4096.2.a.s.1.4		8
64.53	even	16		4096.2.a.s.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.129.2	✓	16	16.11	odd	4
1024.2.g.a.129.3	yes	16	16.5	even	4
1024.2.g.a.897.2	yes	16	32.3	odd	8
1024.2.g.a.897.3	yes	16	32.29	even	8
1024.2.g.d.385.2	yes	16	32.11	odd	8	inner
1024.2.g.d.385.3	yes	16	32.21	even	8	inner
1024.2.g.d.641.2	yes	16	4.3	odd	2	inner
1024.2.g.d.641.3	yes	16	1.1	even	1	trivial
1024.2.g.f.129.2	yes	16	16.13	even	4
1024.2.g.f.129.3	yes	16	16.3	odd	4
1024.2.g.f.897.2	yes	16	32.13	even	8
1024.2.g.f.897.3	yes	16	32.19	odd	8
1024.2.g.g.385.2	yes	16	32.5	even	8
1024.2.g.g.385.3	yes	16	32.27	odd	8
1024.2.g.g.641.2	yes	16	8.5	even	2
1024.2.g.g.641.3	yes	16	8.3	odd	2
4096.2.a.i.1.5		8	64.11	odd	16
4096.2.a.i.1.6		8	64.21	even	16
4096.2.a.s.1.3		8	64.53	even	16
4096.2.a.s.1.4		8	64.43	odd	16

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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.445644 + 0.184592i) q^{3} +(0.565826 + 1.36603i) q^{5} +(0.135131 - 0.135131i) q^{7} +(-1.95680 - 1.95680i) q^{9} +O(q^{10})\)	\(q+(0.445644 + 0.184592i) q^{3} +(0.565826 + 1.36603i) q^{5} +(0.135131 - 0.135131i) q^{7} +(-1.95680 - 1.95680i) q^{9} +(3.12395 - 1.29398i) q^{11} +(0.951812 - 2.29788i) q^{13} +0.713208i q^{15} +3.11099i q^{17} +(2.48451 - 5.99813i) q^{19} +(0.0851642 - 0.0352762i) q^{21} +(5.18330 + 5.18330i) q^{23} +(1.98967 - 1.98967i) q^{25} +(-1.06460 - 2.57018i) q^{27} +(-4.33315 - 1.79485i) q^{29} +7.44503 q^{31} +1.63103 q^{33} +(0.261052 + 0.108131i) q^{35} +(3.49768 + 8.44414i) q^{37} +(0.848339 - 0.848339i) q^{39} +(-4.27792 - 4.27792i) q^{41} +(4.33227 - 1.79448i) q^{43} +(1.56583 - 3.78024i) q^{45} +12.0952i q^{47} +6.96348i q^{49} +(-0.574263 + 1.38639i) q^{51} +(3.42713 - 1.41956i) q^{53} +(3.53523 + 3.53523i) q^{55} +(2.21441 - 2.21441i) q^{57} +(-1.16425 - 2.81074i) q^{59} +(-8.72911 - 3.61571i) q^{61} -0.528846 q^{63} +3.67752 q^{65} +(7.15047 + 2.96182i) q^{67} +(1.35311 + 3.26670i) q^{69} +(-2.86020 + 2.86020i) q^{71} +(-2.49697 - 2.49697i) q^{73} +(1.25396 - 0.519408i) q^{75} +(0.247285 - 0.596999i) q^{77} -8.39967i q^{79} +6.96008i q^{81} +(5.42005 - 13.0852i) q^{83} +(-4.24969 + 1.76028i) q^{85} +(-1.59973 - 1.59973i) q^{87} +(-4.96713 + 4.96713i) q^{89} +(-0.181895 - 0.439133i) q^{91} +(3.31784 + 1.37429i) q^{93} +9.59940 q^{95} -2.87492 q^{97} +(-8.64500 - 3.58087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 + 16 * q^9	\( 16 q - 8 q^{5} + 16 q^{9} + 24 q^{13} - 48 q^{21} + 32 q^{25} - 8 q^{29} - 80 q^{33} + 8 q^{37} + 16 q^{41} + 8 q^{45} + 40 q^{53} + 16 q^{57} + 8 q^{61} - 32 q^{65} - 32 q^{73} + 32 q^{77} - 32 q^{85} - 32 q^{89} + 48 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 16 * q^9 + 24 * q^13 - 48 * q^21 + 32 * q^25 - 8 * q^29 - 80 * q^33 + 8 * q^37 + 16 * q^41 + 8 * q^45 + 40 * q^53 + 16 * q^57 + 8 * q^61 - 32 * q^65 - 32 * q^73 + 32 * q^77 - 32 * q^85 - 32 * q^89 + 48 * q^93 - 16 * q^97

Introduction

L-functions

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Database

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