LMFDB - Embedded newform 1024.2.g.f.897.2

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			897.2
Root			$0.130526 - 0.991445i$ of defining polynomial
Character	$\chi$	$=$	1024.897
Dual form			1024.2.g.f.129.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.184592 - 0.445644i) q^{3} +(1.36603 + 0.565826i) q^{5} +(-0.135131 - 0.135131i) q^{7} +(1.95680 - 1.95680i) q^{9} +O(q^{10})$	\(q+(-0.184592 - 0.445644i) q^{3} +(1.36603 + 0.565826i) q^{5} +(-0.135131 - 0.135131i) q^{7} +(1.95680 - 1.95680i) q^{9} +(-1.29398 + 3.12395i) q^{11} +(2.29788 - 0.951812i) q^{13} -0.713208i q^{15} -3.11099i q^{17} +(5.99813 - 2.48451i) q^{19} +(-0.0352762 + 0.0851642i) q^{21} +(-5.18330 + 5.18330i) q^{23} +(-1.98967 - 1.98967i) q^{25} +(-2.57018 - 1.06460i) q^{27} +(1.79485 + 4.33315i) q^{29} +7.44503 q^{31} +1.63103 q^{33} +(-0.108131 - 0.261052i) q^{35} +(8.44414 + 3.49768i) q^{37} +(-0.848339 - 0.848339i) q^{39} +(4.27792 - 4.27792i) q^{41} +(-1.79448 + 4.33227i) q^{43} +(3.78024 - 1.56583i) q^{45} -12.0952i q^{47} -6.96348i q^{49} +(-1.38639 + 0.574263i) q^{51} +(-1.41956 + 3.42713i) q^{53} +(-3.53523 + 3.53523i) q^{55} +(-2.21441 - 2.21441i) q^{57} +(-2.81074 - 1.16425i) q^{59} +(3.61571 + 8.72911i) q^{61} -0.528846 q^{63} +3.67752 q^{65} +(-2.96182 - 7.15047i) q^{67} +(3.26670 + 1.35311i) q^{69} +(2.86020 + 2.86020i) q^{71} +(2.49697 - 2.49697i) q^{73} +(-0.519408 + 1.25396i) q^{75} +(0.596999 - 0.247285i) q^{77} +8.39967i q^{79} -6.96008i q^{81} +(13.0852 - 5.42005i) q^{83} +(1.76028 - 4.24969i) q^{85} +(1.59973 - 1.59973i) q^{87} +(4.96713 + 4.96713i) q^{89} +(-0.439133 - 0.181895i) q^{91} +(-1.37429 - 3.31784i) q^{93} +9.59940 q^{95} -2.87492 q^{97} +(3.58087 + 8.64500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 8 q^{13} + 16 q^{21} - 32 q^{25} - 24 q^{29} - 80 q^{33} + 40 q^{37} - 16 q^{41} + 24 q^{45} - 56 q^{53} - 16 q^{57} + 8 q^{61} - 32 q^{65} - 64 q^{69} + 32 q^{73} + 64 q^{77} - 48 q^{85} + 32 q^{89} + 80 q^{93} - 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 - 16 * q^9 - 8 * q^13 + 16 * q^21 - 32 * q^25 - 24 * q^29 - 80 * q^33 + 40 * q^37 - 16 * q^41 + 24 * q^45 - 56 * q^53 - 16 * q^57 + 8 * q^61 - 32 * q^65 - 64 * q^69 + 32 * q^73 + 64 * q^77 - 48 * q^85 + 32 * q^89 + 80 * q^93 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.184592	−	0.445644i	−0.106574	−	0.257293i	0.861592	−	0.507602i	$-0.169468\pi$
$3$	−0.184592	−	0.445644i	−0.106574	−	0.257293i	−0.968166	+	0.250309i	$0.919468\pi$
$4$		0			0
$5$	1.36603	+	0.565826i	0.610905	+	0.253045i	0.666615	−	0.745402i	$-0.267742\pi$
$5$	1.36603	+	0.565826i	0.610905	+	0.253045i	−0.0557103	+	0.998447i	$0.517742\pi$
$6$		0			0
$7$	−0.135131	−	0.135131i	−0.0510746	−	0.0510746i	0.681108	−	0.732183i	$-0.261498\pi$
$7$	−0.135131	−	0.135131i	−0.0510746	−	0.0510746i	−0.732183	+	0.681108i	$0.761498\pi$
$8$		0			0
$9$	1.95680	−	1.95680i	0.652265	−	0.652265i
$10$		0			0
$11$	−1.29398	+	3.12395i	−0.390151	+	0.941907i	0.599756	+	0.800183i	$0.295264\pi$
$11$	−1.29398	+	3.12395i	−0.390151	+	0.941907i	−0.989906	+	0.141724i	$0.954736\pi$
$12$		0			0
$13$	2.29788	−	0.951812i	0.637316	−	0.263985i	−0.0405417	−	0.999178i	$-0.512908\pi$
$13$	2.29788	−	0.951812i	0.637316	−	0.263985i	0.677858	+	0.735193i	$0.262908\pi$
$14$		0			0
$15$		−	0.713208i		−	0.184150i
$16$		0			0
$17$		−	3.11099i		−	0.754525i	−0.926106	−	0.377263i	$-0.876865\pi$
$17$		−	3.11099i		−	0.754525i	0.926106	−	0.377263i	$-0.123135\pi$
$18$		0			0
$19$	5.99813	−	2.48451i	1.37607	−	0.569985i	0.432639	−	0.901567i	$-0.357582\pi$
$19$	5.99813	−	2.48451i	1.37607	−	0.569985i	0.943426	+	0.331582i	$0.107582\pi$
$20$		0			0
$21$	−0.0352762	+	0.0851642i	−0.00769789	+	0.0185844i
$22$		0			0
$23$	−5.18330	+	5.18330i	−1.08079	+	1.08079i	−0.0843577	+	0.996436i	$0.526884\pi$
$23$	−5.18330	+	5.18330i	−1.08079	+	1.08079i	−0.996436	+	0.0843577i	$0.973116\pi$
$24$		0			0
$25$	−1.98967	−	1.98967i	−0.397934	−	0.397934i
$26$		0			0
$27$	−2.57018	−	1.06460i	−0.494631	−	0.204883i
$28$		0			0
$29$	1.79485	+	4.33315i	0.333295	+	0.804646i	0.998326	+	0.0578306i	$0.0184183\pi$
$29$	1.79485	+	4.33315i	0.333295	+	0.804646i	−0.665031	+	0.746816i	$0.731582\pi$
$30$		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
$35$	−0.108131	−	0.261052i	−0.0182775	−	0.0441259i
$36$		0			0
$37$	8.44414	+	3.49768i	1.38821	+	0.575015i	0.946663	−	0.322224i	$-0.104431\pi$
$37$	8.44414	+	3.49768i	1.38821	+	0.575015i	0.441545	+	0.897239i	$0.354431\pi$
$38$		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	$-0.593382\pi$
$41$	4.27792	−	4.27792i	0.668098	−	0.668098i	0.957276	+	0.289177i	$0.0933817\pi$
$42$		0			0
$43$	−1.79448	+	4.33227i	−0.273656	+	0.660664i	−0.999634	−	0.0270537i	$-0.991387\pi$
$43$	−1.79448	+	4.33227i	−0.273656	+	0.660664i	0.725978	+	0.687718i	$0.241387\pi$
$44$		0			0
$45$	3.78024	−	1.56583i	0.563525	−	0.233420i
$46$		0			0
$47$		−	12.0952i		−	1.76426i	−0.471002	−	0.882132i	$-0.656108\pi$
$47$		−	12.0952i		−	1.76426i	0.471002	−	0.882132i	$-0.343892\pi$
$48$		0			0
$49$		−	6.96348i		−	0.994783i
$50$		0			0
$51$	−1.38639	+	0.574263i	−0.194134	+	0.0804129i
$52$		0			0
$53$	−1.41956	+	3.42713i	−0.194992	+	0.470752i	−0.990889	−	0.134680i	$-0.956999\pi$
$53$	−1.41956	+	3.42713i	−0.194992	+	0.470752i	0.795897	+	0.605432i	$0.206999\pi$
$54$		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
$59$	−2.81074	−	1.16425i	−0.365927	−	0.151572i	0.192140	−	0.981367i	$-0.438457\pi$
$59$	−2.81074	−	1.16425i	−0.365927	−	0.151572i	−0.558068	+	0.829795i	$0.688457\pi$
$60$		0			0
$61$	3.61571	+	8.72911i	0.462945	+	1.11765i	0.967183	+	0.254083i	$0.0817735\pi$
$61$	3.61571	+	8.72911i	0.462945	+	1.11765i	−0.504238	+	0.863565i	$0.668226\pi$
$62$		0			0
$63$	−0.528846			−0.0666284
$64$		0			0
$65$	3.67752			0.456140
$66$		0			0
$67$	−2.96182	−	7.15047i	−0.361844	−	0.873569i	−0.995031	−	0.0995698i	$-0.968253\pi$
$67$	−2.96182	−	7.15047i	−0.361844	−	0.873569i	0.633186	−	0.773999i	$-0.281747\pi$
$68$		0			0
$69$	3.26670	+	1.35311i	0.393265	+	0.162896i
$70$		0			0
$71$	2.86020	+	2.86020i	0.339444	+	0.339444i	0.856158	−	0.516714i	$-0.172845\pi$
$71$	2.86020	+	2.86020i	0.339444	+	0.339444i	−0.516714	+	0.856158i	$0.672845\pi$
$72$		0			0
$73$	2.49697	−	2.49697i	0.292249	−	0.292249i	−0.545719	−	0.837968i	$-0.683744\pi$
$73$	2.49697	−	2.49697i	0.292249	−	0.292249i	0.837968	+	0.545719i	$0.183744\pi$
$74$		0			0
$75$	−0.519408	+	1.25396i	−0.0599760	+	0.144795i
$76$		0			0
$77$	0.596999	−	0.247285i	0.0680343	−	0.0281807i
$78$		0			0
$79$			8.39967i			0.945036i	0.881321	+	0.472518i	$0.156655\pi$
$79$			8.39967i			0.945036i	−0.881321	+	0.472518i	$0.843345\pi$
$80$		0			0
$81$		−	6.96008i		−	0.773342i
$82$		0			0
$83$	13.0852	−	5.42005i	1.43628	−	0.594928i	0.477389	−	0.878692i	$-0.341583\pi$
$83$	13.0852	−	5.42005i	1.43628	−	0.594928i	0.958894	+	0.283764i	$0.0915832\pi$
$84$		0			0
$85$	1.76028	−	4.24969i	0.190929	−	0.460943i
$86$		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	$-0.128569\pi$
$89$	4.96713	+	4.96713i	0.526514	+	0.526514i	−0.393017	+	0.919531i	$0.628569\pi$
$90$		0			0
$91$	−0.439133	−	0.181895i	−0.0460336	−	0.0190677i
$92$		0			0
$93$	−1.37429	−	3.31784i	−0.142508	−	0.344044i
$94$		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
$99$	3.58087	+	8.64500i	0.359891	+	0.868855i
$100$		0			0
$101$	−7.24674	−	3.00170i	−0.721078	−	0.298680i	−0.00819809	−	0.999966i	$-0.502610\pi$
$101$	−7.24674	−	3.00170i	−0.721078	−	0.298680i	−0.712880	+	0.701286i	$0.752610\pi$
$102$		0			0
$103$	−4.12067	−	4.12067i	−0.406022	−	0.406022i	0.474327	−	0.880349i	$-0.342692\pi$
$103$	−4.12067	−	4.12067i	−0.406022	−	0.406022i	−0.880349	+	0.474327i	$0.842692\pi$
$104$		0			0
$105$	−0.0963763	+	0.0963763i	−0.00940537	+	0.00940537i
$106$		0			0
$107$	−2.30261	+	5.55900i	−0.222602	+	0.537409i	−0.995242	−	0.0974360i	$-0.968936\pi$
$107$	−2.30261	+	5.55900i	−0.222602	+	0.537409i	0.772640	+	0.634845i	$0.218936\pi$
$108$		0			0
$109$	4.19445	−	1.73740i	0.401756	−	0.166413i	−0.172650	−	0.984983i	$-0.555233\pi$
$109$	4.19445	−	1.73740i	0.401756	−	0.166413i	0.574406	+	0.818571i	$0.305233\pi$
$110$		0			0
$111$		−	4.40873i		−	0.418458i
$112$		0			0
$113$			9.86370i			0.927899i	0.885862	+	0.463950i	$0.153568\pi$
$113$			9.86370i			0.927899i	−0.885862	+	0.463950i	$0.846432\pi$
$114$		0			0
$115$	−10.0134	+	4.14767i	−0.933752	+	0.386773i
$116$		0			0
$117$	2.63397	−	6.35898i	0.243511	−	0.587888i
$118$		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
$123$	−2.69610	−	1.11676i	−0.243099	−	0.100695i
$124$		0			0
$125$	−4.42126	−	10.6739i	−0.395450	−	0.954700i
$126$		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
$131$	−6.03911	−	14.5797i	−0.527639	−	1.27383i	−0.933066	−	0.359706i	$-0.882877\pi$
$131$	−6.03911	−	14.5797i	−0.527639	−	1.27383i	0.405427	−	0.914128i	$-0.367123\pi$
$132$		0			0
$133$	−1.14626	−	0.474798i	−0.0993937	−	0.0411702i
$134$		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	$-0.864605\pi$
$137$	−5.83183	+	5.83183i	−0.498247	+	0.498247i	0.412645	+	0.910892i	$0.364605\pi$
$138$		0			0
$139$	3.02980	−	7.31458i	0.256984	−	0.620414i	−0.741752	−	0.670674i	$-0.766005\pi$
$139$	3.02980	−	7.31458i	0.256984	−	0.620414i	0.998736	+	0.0502598i	$0.0160049\pi$
$140$		0			0
$141$	−5.39015	+	2.23267i	−0.453932	+	0.188025i
$142$		0			0
$143$			8.41009i			0.703287i
$144$		0			0
$145$			6.93477i			0.575901i
$146$		0			0
$147$	−3.10323	+	1.28540i	−0.255950	+	0.106018i
$148$		0			0
$149$	−2.71965	+	6.56583i	−0.222803	+	0.537893i	−0.995268	−	0.0971630i	$-0.969023\pi$
$149$	−2.71965	+	6.56583i	−0.222803	+	0.537893i	0.772466	+	0.635056i	$0.219023\pi$
$150$		0			0
$151$	10.7733	−	10.7733i	0.876722	−	0.876722i	−0.116472	−	0.993194i	$-0.537158\pi$
$151$	10.7733	−	10.7733i	0.876722	−	0.876722i	0.993194	+	0.116472i	$0.0371584\pi$
$152$		0			0
$153$	−6.08757	−	6.08757i	−0.492151	−	0.492151i
$154$		0			0
$155$	10.1701	+	4.21260i	0.816883	+	0.338364i
$156$		0			0
$157$	−0.220757	−	0.532954i	−0.0176183	−	0.0425344i	0.914826	−	0.403849i	$-0.132328\pi$
$157$	−0.220757	−	0.532954i	−0.0176183	−	0.0425344i	−0.932444	+	0.361315i	$0.882328\pi$
$158$		0			0
$159$	1.78932			0.141902
$160$		0			0
$161$	1.40085			0.110402
$162$		0			0
$163$	9.26188	+	22.3602i	0.725447	+	1.75138i	0.657201	+	0.753715i	$0.271740\pi$
$163$	9.26188	+	22.3602i	0.725447	+	1.75138i	0.0682454	+	0.997669i	$0.478260\pi$
$164$		0			0
$165$	2.22803	+	0.922880i	0.173452	+	0.0718461i
$166$		0			0
$167$	11.2141	+	11.2141i	0.867770	+	0.867770i	0.992225	−	0.124455i	$-0.0397184\pi$
$167$	11.2141	+	11.2141i	0.867770	+	0.867770i	−0.124455	+	0.992225i	$0.539718\pi$
$168$		0			0
$169$	−4.81809	+	4.81809i	−0.370623	+	0.370623i
$170$		0			0
$171$	6.87544	−	16.5988i	0.525778	−	1.26934i
$172$		0			0
$173$	−20.1974	+	8.36603i	−1.53558	+	0.636057i	−0.980637	−	0.195833i	$-0.937259\pi$
$173$	−20.1974	+	8.36603i	−1.53558	+	0.636057i	−0.554940	+	0.831890i	$0.687259\pi$
$174$		0			0
$175$			0.537730i			0.0406486i
$176$		0			0
$177$			1.46750i			0.110304i
$178$		0			0
$179$	−14.1545	+	5.86300i	−1.05796	+	0.438221i	−0.842727	−	0.538342i	$-0.819051\pi$
$179$	−14.1545	+	5.86300i	−1.05796	+	0.438221i	−0.215233	+	0.976563i	$0.569051\pi$
$180$		0			0
$181$	−4.03749	+	9.74737i	−0.300104	+	0.724516i	0.699843	+	0.714296i	$0.253253\pi$
$181$	−4.03749	+	9.74737i	−0.300104	+	0.724516i	−0.999948	+	0.0102198i	$0.996747\pi$
$182$		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
$187$	9.71858	+	4.02557i	0.710693	+	0.294379i
$188$		0			0
$189$	0.203449	+	0.491170i	0.0147988	+	0.0357274i
$190$		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
$195$	−0.678840	−	1.63887i	−0.0486128	−	0.117362i
$196$		0			0
$197$	−20.6780	−	8.56510i	−1.47324	−	0.610238i	−0.505648	−	0.862740i	$-0.668747\pi$
$197$	−20.6780	−	8.56510i	−1.47324	−	0.610238i	−0.967596	+	0.252502i	$0.918747\pi$
$198$		0			0
$199$	−4.62301	−	4.62301i	−0.327717	−	0.327717i	0.524001	−	0.851718i	$-0.324439\pi$
$199$	−4.62301	−	4.62301i	−0.327717	−	0.327717i	−0.851718	+	0.524001i	$0.824439\pi$
$200$		0			0
$201$	−2.63984	+	2.63984i	−0.186200	+	0.186200i
$202$		0			0
$203$	0.343002	−	0.828081i	0.0240741	−	0.0581199i
$204$		0			0
$205$	8.26430	−	3.42319i	0.577204	−	0.239086i
$206$		0			0
$207$			20.2853i			1.40993i
$208$		0			0
$209$			21.9528i			1.51851i
$210$		0			0
$211$	−7.75999	+	3.21429i	−0.534220	+	0.221281i	−0.633450	−	0.773783i	$-0.718362\pi$
$211$	−7.75999	+	3.21429i	−0.534220	+	0.221281i	0.0992305	+	0.995064i	$0.468362\pi$
$212$		0			0
$213$	0.746663	−	1.80260i	0.0511605	−	0.123512i
$214$		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
$219$	−1.57368	−	0.651841i	−0.106340	−	0.0440473i
$220$		0			0
$221$	−2.96108	−	7.14867i	−0.199183	−	0.480871i
$222$		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
$227$	2.41272	+	5.82482i	0.160138	+	0.386607i	0.983500	−	0.180910i	$-0.0579043\pi$
$227$	2.41272	+	5.82482i	0.160138	+	0.386607i	−0.823362	+	0.567517i	$0.807904\pi$
$228$		0			0
$229$	−15.0487	−	6.23338i	−0.994446	−	0.411913i	−0.174689	−	0.984624i	$-0.555892\pi$
$229$	−15.0487	−	6.23338i	−0.994446	−	0.411913i	−0.819758	+	0.572711i	$0.805892\pi$
$230$		0			0
$231$	−0.220402	−	0.220402i	−0.0145014	−	0.0145014i
$232$		0			0
$233$	−17.8296	+	17.8296i	−1.16806	+	1.16806i	−0.185390	+	0.982665i	$0.559355\pi$
$233$	−17.8296	+	17.8296i	−1.16806	+	1.16806i	−0.982665	+	0.185390i	$0.940645\pi$
$234$		0			0
$235$	6.84377	−	16.5223i	0.446438	−	1.07780i
$236$		0			0
$237$	3.74326	−	1.55051i	0.243151	−	0.100716i
$238$		0			0
$239$		−	14.7833i		−	0.956254i	−0.878291	−	0.478127i	$-0.841316\pi$
$239$		−	14.7833i		−	0.956254i	0.878291	−	0.478127i	$-0.158684\pi$
$240$		0			0
$241$			2.03919i			0.131356i	0.997841	+	0.0656779i	$0.0209210\pi$
$241$			2.03919i			0.131356i	−0.997841	+	0.0656779i	$0.979079\pi$
$242$		0			0
$243$	−10.8122	+	4.47858i	−0.693606	+	0.287301i
$244$		0			0
$245$	3.94012	−	9.51229i	0.251725	−	0.607718i
$246$		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
$251$	8.03025	+	3.32624i	0.506865	+	0.209950i	0.621436	−	0.783465i	$-0.286549\pi$
$251$	8.03025	+	3.32624i	0.506865	+	0.209950i	−0.114571	+	0.993415i	$0.536549\pi$
$252$		0			0
$253$	−9.48528	−	22.8995i	−0.596335	−	1.43968i
$254$		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
$259$	−0.668419	−	1.61371i	−0.0415335	−	0.100271i
$260$		0			0
$261$	11.9913	+	4.96694i	0.742240	+	0.307446i
$262$		0			0
$263$	−0.119315	−	0.119315i	−0.00735727	−	0.00735727i	0.703419	−	0.710776i	$-0.251656\pi$
$263$	−0.119315	−	0.119315i	−0.00735727	−	0.00735727i	−0.710776	+	0.703419i	$0.751656\pi$
$264$		0			0
$265$	−3.87832	+	3.87832i	−0.238243	+	0.238243i
$266$		0			0
$267$	1.29668	−	3.13046i	0.0793556	−	0.191581i
$268$		0			0
$269$	−28.9705	+	12.0000i	−1.76636	+	0.731651i	−0.770851	+	0.637016i	$0.780169\pi$
$269$	−28.9705	+	12.0000i	−1.76636	+	0.731651i	−0.995512	+	0.0946356i	$0.969831\pi$
$270$		0			0
$271$			18.1938i			1.10520i	0.833447	+	0.552599i	$0.186364\pi$
$271$			18.1938i			1.10520i	−0.833447	+	0.552599i	$0.813636\pi$
$272$		0			0
$273$			0.229273i			0.0138762i
$274$		0			0
$275$	8.79022	−	3.64103i	0.530070	−	0.219562i
$276$		0			0
$277$	3.88315	−	9.37475i	0.233316	−	0.563274i	−0.763248	−	0.646106i	$-0.776396\pi$
$277$	3.88315	−	9.37475i	0.233316	−	0.563274i	0.996564	+	0.0828318i	$0.0263964\pi$
$278$		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	$-0.0717623\pi$
$281$	12.5916	+	12.5916i	0.751151	+	0.751151i	−0.223543	+	0.974694i	$0.571762\pi$
$282$		0			0
$283$	−15.0121	−	6.21821i	−0.892376	−	0.369634i	−0.111092	−	0.993810i	$-0.535435\pi$
$283$	−15.0121	−	6.21821i	−0.892376	−	0.369634i	−0.781284	+	0.624176i	$0.785435\pi$
$284$		0			0
$285$	−1.77197	−	4.27792i	−0.104963	−	0.253402i
$286$		0			0
$287$	−1.15616			−0.0682457
$288$		0			0
$289$	7.32175			0.430691
$290$		0			0
$291$	0.530686	+	1.28119i	0.0311094	+	0.0751047i
$292$		0			0
$293$	−13.5429	−	5.60966i	−0.791186	−	0.327720i	−0.0497657	−	0.998761i	$-0.515847\pi$
$293$	−13.5429	−	5.60966i	−0.791186	−	0.327720i	−0.741420	+	0.671041i	$0.765847\pi$
$294$		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
$299$	−6.97706	+	16.8441i	−0.403494	+	0.974121i
$300$		0			0
$301$	0.827912	−	0.342932i	0.0477200	−	0.0197663i
$302$		0			0
$303$			3.78356i			0.217360i
$304$		0			0
$305$			13.9700i			0.799923i
$306$		0			0
$307$	−11.1636	+	4.62413i	−0.637143	+	0.263913i	−0.677784	−	0.735261i	$-0.737060\pi$
$307$	−11.1636	+	4.62413i	−0.637143	+	0.263913i	0.0406418	+	0.999174i	$0.487060\pi$
$308$		0			0
$309$	−1.07571	+	2.59700i	−0.0611951	+	0.147738i
$310$		0			0
$311$	5.03317	−	5.03317i	0.285405	−	0.285405i	−0.549855	−	0.835260i	$-0.685317\pi$
$311$	5.03317	−	5.03317i	0.285405	−	0.285405i	0.835260	+	0.549855i	$0.185317\pi$
$312$		0			0
$313$	−2.58454	−	2.58454i	−0.146087	−	0.146087i	0.630281	−	0.776367i	$-0.282940\pi$
$313$	−2.58454	−	2.58454i	−0.146087	−	0.146087i	−0.776367	+	0.630281i	$0.782940\pi$
$314$		0			0
$315$	−0.722417	−	0.299235i	−0.0407036	−	0.0168600i
$316$		0			0
$317$	8.21371	+	19.8296i	0.461328	+	1.11374i	0.967853	+	0.251518i	$0.0809299\pi$
$317$	8.21371	+	19.8296i	0.461328	+	1.11374i	−0.506525	+	0.862225i	$0.669070\pi$
$318$		0			0
$319$	−15.8591			−0.887937
$320$		0			0
$321$	2.90238			0.161995
$322$		0			0
$323$	−7.72927	−	18.6601i	−0.430068	−	1.03828i
$324$		0			0
$325$	−6.46580	−	2.67822i	−0.358658	−	0.148561i
$326$		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
$331$	4.83918	−	11.6828i	0.265986	−	0.642146i	−0.733301	−	0.679904i	$-0.762022\pi$
$331$	4.83918	−	11.6828i	0.265986	−	0.642146i	0.999287	+	0.0377578i	$0.0120216\pi$
$332$		0			0
$333$	23.3677	−	9.67922i	1.28054	−	0.530418i
$334$		0			0
$335$		−	11.4436i		−	0.625231i
$336$		0			0
$337$		−	17.3525i		−	0.945254i	−0.881263	−	0.472627i	$-0.843306\pi$
$337$		−	17.3525i		−	0.945254i	0.881263	−	0.472627i	$-0.156694\pi$
$338$		0			0
$339$	4.39570	−	1.82076i	0.238742	−	0.0988901i
$340$		0			0
$341$	−9.63375	+	23.2579i	−0.521697	+	1.25949i
$342$		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
$347$	16.1152	+	6.67513i	0.865109	+	0.358340i	0.770703	−	0.637194i	$-0.219905\pi$
$347$	16.1152	+	6.67513i	0.865109	+	0.358340i	0.0944054	+	0.995534i	$0.469905\pi$
$348$		0			0
$349$	0.198581	+	0.479418i	0.0106298	+	0.0256626i	0.929105	−	0.369815i	$-0.120579\pi$
$349$	0.198581	+	0.479418i	0.0106298	+	0.0256626i	−0.918476	+	0.395478i	$0.870579\pi$
$350$		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
$355$	2.28873	+	5.52549i	0.121473	+	0.293262i
$356$		0			0
$357$	0.264945	+	0.109744i	0.0140224	+	0.00580826i
$358$		0			0
$359$	6.02599	+	6.02599i	0.318039	+	0.318039i	0.848014	−	0.529974i	$-0.177798\pi$
$359$	6.02599	+	6.02599i	0.318039	+	0.318039i	−0.529974	+	0.848014i	$0.677798\pi$
$360$		0			0
$361$	16.3698	−	16.3698i	0.861567	−	0.861567i
$362$		0			0
$363$	−0.0800150	+	0.193173i	−0.00419970	+	0.0101390i
$364$		0			0
$365$	4.82378	−	1.99808i	0.252488	−	0.104584i
$366$		0			0
$367$			5.67199i			0.296076i	0.988982	+	0.148038i	$0.0472957\pi$
$367$			5.67199i			0.296076i	−0.988982	+	0.148038i	$0.952704\pi$
$368$		0			0
$369$		−	16.7420i		−	0.871555i
$370$		0			0
$371$	0.654936	−	0.271283i	0.0340026	−	0.0140843i
$372$		0			0
$373$	13.3210	−	32.1599i	0.689738	−	1.66517i	−0.0555710	−	0.998455i	$-0.517698\pi$
$373$	13.3210	−	32.1599i	0.689738	−	1.66517i	0.745309	−	0.666719i	$-0.232302\pi$
$374$		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
$379$	−2.90292	−	1.20243i	−0.149113	−	0.0617647i	0.306879	−	0.951749i	$-0.400715\pi$
$379$	−2.90292	−	1.20243i	−0.149113	−	0.0617647i	−0.455992	+	0.889984i	$0.650715\pi$
$380$		0			0
$381$	2.85249	+	6.88652i	0.146138	+	0.352807i
$382$		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
$387$	4.96592	+	11.9888i	0.252432	+	0.609425i
$388$		0			0
$389$	11.3383	+	4.69648i	0.574875	+	0.238121i	0.651129	−	0.758967i	$-0.274296\pi$
$389$	11.3383	+	4.69648i	0.574875	+	0.238121i	−0.0762534	+	0.997088i	$0.524296\pi$
$390$		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
$395$	−4.75275	+	11.4742i	−0.239137	+	0.577327i
$396$		0			0
$397$	−13.2139	+	5.47337i	−0.663185	+	0.274700i	−0.688778	−	0.724972i	$-0.741853\pi$
$397$	−13.2139	+	5.47337i	−0.663185	+	0.274700i	0.0255930	+	0.999672i	$0.491853\pi$
$398$		0			0
$399$			0.598470i			0.0299610i
$400$		0			0
$401$			12.8160i			0.639999i	0.947418	+	0.320000i	$0.103683\pi$
$401$			12.8160i			0.639999i	−0.947418	+	0.320000i	$0.896317\pi$
$402$		0			0
$403$	17.1078	−	7.08627i	0.852199	−	0.352992i
$404$		0			0
$405$	3.93820	−	9.50765i	0.195691	−	0.472439i
$406$		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	$-0.370262\pi$
$409$	−10.5505	−	10.5505i	−0.521689	−	0.521689i	−0.918081	+	0.396392i	$0.870262\pi$
$410$		0			0
$411$	3.67543	+	1.52241i	0.181296	+	0.0750951i
$412$		0			0
$413$	0.222492	+	0.537143i	0.0109481	+	0.0264311i
$414$		0			0
$415$	20.9415			1.02798
$416$		0			0
$417$	−3.81897			−0.187016
$418$		0			0
$419$	−8.94989	−	21.6069i	−0.437231	−	1.05557i	−0.976901	−	0.213692i	$-0.931451\pi$
$419$	−8.94989	−	21.6069i	−0.437231	−	1.05557i	0.539671	−	0.841876i	$-0.318549\pi$
$420$		0			0
$421$	34.3466	+	14.2268i	1.67395	+	0.693372i	0.999009	−	0.0445009i	$-0.0141698\pi$
$421$	34.3466	+	14.2268i	1.67395	+	0.693372i	0.674939	+	0.737873i	$0.264170\pi$
$422$		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
$427$	0.690976	−	1.66816i	0.0334387	−	0.0807281i
$428$		0			0
$429$	3.74791	−	1.55243i	0.180951	−	0.0749522i
$430$		0			0
$431$		−	27.4006i		−	1.31984i	−0.751335	−	0.659921i	$-0.770590\pi$
$431$		−	27.4006i		−	1.31984i	0.751335	−	0.659921i	$-0.229410\pi$
$432$		0			0
$433$		−	17.6255i		−	0.847027i	−0.905890	−	0.423514i	$-0.860797\pi$
$433$		−	17.6255i		−	0.847027i	0.905890	−	0.423514i	$-0.139203\pi$
$434$		0			0
$435$	3.09044	−	1.28010i	0.148175	−	0.0613762i
$436$		0			0
$437$	−18.2122	+	43.9681i	−0.871206	+	2.10328i
$438$		0			0
$439$	−12.9463	+	12.9463i	−0.617894	+	0.617894i	−0.944991	−	0.327097i	$-0.893930\pi$
$439$	−12.9463	+	12.9463i	−0.617894	+	0.617894i	0.327097	+	0.944991i	$0.393930\pi$
$440$		0			0
$441$	−13.6261	−	13.6261i	−0.648862	−	0.648862i
$442$		0			0
$443$	−30.8594	−	12.7824i	−1.46617	−	0.607309i	−0.500191	−	0.865915i	$-0.666737\pi$
$443$	−30.8594	−	12.7824i	−1.46617	−	0.607309i	−0.965983	+	0.258606i	$0.916737\pi$
$444$		0			0
$445$	3.97469	+	9.59575i	0.188418	+	0.454882i
$446$		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
$451$	7.82845	+	18.8996i	0.368628	+	0.889946i
$452$		0			0
$453$	−6.78975	−	2.81241i	−0.319010	−	0.132138i
$454$		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	$-0.627689\pi$
$457$	11.3331	−	11.3331i	0.530141	−	0.530141i	0.920614	+	0.390473i	$0.127689\pi$
$458$		0			0
$459$	−3.31196	+	7.99579i	−0.154589	+	0.373211i
$460$		0			0
$461$	14.5941	−	6.04506i	0.679713	−	0.281546i	−0.0159940	−	0.999872i	$-0.505091\pi$
$461$	14.5941	−	6.04506i	0.679713	−	0.281546i	0.695707	+	0.718326i	$0.255091\pi$
$462$		0			0
$463$		−	21.2329i		−	0.986779i	−0.869809	−	0.493389i	$-0.835758\pi$
$463$		−	21.2329i		−	0.986779i	0.869809	−	0.493389i	$-0.164242\pi$
$464$		0			0
$465$		−	5.30986i		−	0.246239i
$466$		0			0
$467$	9.22554	−	3.82134i	0.426907	−	0.176831i	−0.158876	−	0.987299i	$-0.550787\pi$
$467$	9.22554	−	3.82134i	0.426907	−	0.176831i	0.585783	+	0.810468i	$0.300787\pi$
$468$		0			0
$469$	−0.566015	+	1.36648i	−0.0261361	+	0.0630982i
$470$		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
$475$	−16.8776	−	6.99094i	−0.774399	−	0.320766i
$476$		0			0
$477$	3.92839	+	9.48398i	0.179869	+	0.434241i
$478$		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
$483$	−0.258585	−	0.624279i	−0.0117660	−	0.0284057i
$484$		0			0
$485$	−3.92721	−	1.62670i	−0.178325	−	0.0738648i
$486$		0			0
$487$	−6.69427	−	6.69427i	−0.303346	−	0.303346i	0.538975	−	0.842322i	$-0.318812\pi$
$487$	−6.69427	−	6.69427i	−0.303346	−	0.303346i	−0.842322	+	0.538975i	$0.818812\pi$
$488$		0			0
$489$	8.25501	−	8.25501i	0.373305	−	0.373305i
$490$		0			0
$491$	−13.1010	+	31.6286i	−0.591239	+	1.42738i	0.291068	+	0.956702i	$0.405989\pi$
$491$	−13.1010	+	31.6286i	−0.591239	+	1.42738i	−0.882307	+	0.470675i	$0.844011\pi$
$492$		0			0
$493$	13.4804	−	5.58376i	0.607126	−	0.251480i
$494$		0			0
$495$			13.8354i			0.621857i
$496$		0			0
$497$		−	0.773002i		−	0.0346739i
$498$		0			0
$499$	14.6636	−	6.07387i	0.656434	−	0.271904i	−0.0295034	−	0.999565i	$-0.509393\pi$
$499$	14.6636	−	6.07387i	0.656434	−	0.271904i	0.685937	+	0.727661i	$0.259393\pi$
$500$		0			0
$501$	2.92746	−	7.06750i	0.130789	−	0.315753i
$502$		0			0
$503$	−16.7932	+	16.7932i	−0.748773	+	0.748773i	−0.974249	−	0.225476i	$-0.927606\pi$
$503$	−16.7932	+	16.7932i	−0.748773	+	0.748773i	0.225476	+	0.974249i	$0.427606\pi$
$504$		0			0
$505$	−8.20080	−	8.20080i	−0.364931	−	0.364931i
$506$		0			0
$507$	3.03654	+	1.25778i	0.134857	+	0.0558598i
$508$		0			0
$509$	−3.68700	−	8.90119i	−0.163423	−	0.394539i	0.820862	−	0.571127i	$-0.193494\pi$
$509$	−3.68700	−	8.90119i	−0.163423	−	0.394539i	−0.984285	+	0.176589i	$0.943494\pi$
$510$		0			0
$511$	−0.674835			−0.0298530
$512$		0			0
$513$	−18.0613			−0.797424
$514$		0			0
$515$	−3.29736	−	7.96053i	−0.145299	−	0.350783i
$516$		0			0
$517$	37.7848	+	15.6510i	1.66177	+	0.688329i
$518$		0			0
$519$	7.45654	+	7.45654i	0.327306	+	0.327306i
$520$		0			0
$521$	25.4229	−	25.4229i	1.11380	−	1.11380i	0.121167	−	0.992632i	$-0.461336\pi$
$521$	25.4229	−	25.4229i	1.11380	−	1.11380i	0.992632	−	0.121167i	$-0.0386636\pi$
$522$		0			0
$523$	−3.59867	+	8.68795i	−0.157359	+	0.379897i	−0.982821	−	0.184559i	$-0.940914\pi$
$523$	−3.59867	+	8.68795i	−0.157359	+	0.379897i	0.825463	+	0.564457i	$0.190914\pi$
$524$		0			0
$525$	0.239636	−	0.0992607i	0.0104586	−	0.00433209i
$526$		0			0
$527$		−	23.1614i		−	1.00893i
$528$		0			0
$529$		−	30.7332i		−	1.33623i
$530$		0			0
$531$	−7.77824	+	3.22185i	−0.337547	+	0.139816i
$532$		0			0
$533$	5.75836	−	13.9019i	0.249422	−	0.602158i
$534$		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
$539$	21.7536	+	9.01063i	0.936993	+	0.388115i
$540$		0			0
$541$	12.2665	+	29.6140i	0.527379	+	1.27320i	0.933235	+	0.359268i	$0.116974\pi$
$541$	12.2665	+	29.6140i	0.527379	+	1.27320i	−0.405856	+	0.913937i	$0.633026\pi$
$542$		0			0
$543$	5.08915			0.218396
$544$		0			0
$545$	6.71279			0.287545
$546$		0			0
$547$	−4.72724	−	11.4126i	−0.202122	−	0.487966i	0.790020	−	0.613081i	$-0.210070\pi$
$547$	−4.72724	−	11.4126i	−0.202122	−	0.487966i	−0.992142	+	0.125115i	$0.960070\pi$
$548$		0			0
$549$	24.1563	+	10.0059i	1.03097	+	0.427040i
$550$		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
$555$	2.49457	−	6.02243i	0.105889	−	0.255638i
$556$		0			0
$557$	−14.0704	+	5.82814i	−0.596180	+	0.246946i	−0.660307	−	0.750996i	$-0.729574\pi$
$557$	−14.0704	+	5.82814i	−0.596180	+	0.246946i	0.0641266	+	0.997942i	$0.479574\pi$
$558$		0			0
$559$			11.6630i			0.493293i
$560$		0			0
$561$		−	5.07412i		−	0.214229i
$562$		0			0
$563$	43.5982	−	18.0589i	1.83744	−	0.761094i	0.878340	−	0.478036i	$-0.158651\pi$
$563$	43.5982	−	18.0589i	1.83744	−	0.761094i	0.959103	−	0.283057i	$-0.0913487\pi$
$564$		0			0
$565$	−5.58114	+	13.4741i	−0.234800	+	0.566858i
$566$		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	$-0.0851863\pi$
$569$	16.6968	+	16.6968i	0.699965	+	0.699965i	−0.264438	+	0.964403i	$0.585186\pi$
$570$		0			0
$571$	25.7136	+	10.6509i	1.07608	+	0.445728i	0.849133	−	0.528179i	$-0.177125\pi$
$571$	25.7136	+	10.6509i	1.07608	+	0.445728i	0.226949	+	0.973907i	$0.427125\pi$
$572$		0			0
$573$	4.24123	+	10.2392i	0.177180	+	0.427750i
$574$		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
$579$	3.36636	+	8.12710i	0.139901	+	0.337751i
$580$		0			0
$581$	−2.50062	−	1.03579i	−0.103743	−	0.0429719i
$582$		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
$587$	−7.18852	+	17.3546i	−0.296702	+	0.716302i	0.703284	+	0.710909i	$0.251716\pi$
$587$	−7.18852	+	17.3546i	−0.296702	+	0.716302i	−0.999985	+	0.00539239i	$0.998284\pi$
$588$		0			0
$589$	44.6563	−	18.4972i	1.84003	−	0.762166i
$590$		0			0
$591$			10.7961i			0.444091i
$592$		0			0
$593$			0.516291i			0.0212015i	0.999944	+	0.0106008i	$0.00337439\pi$
$593$			0.516291i			0.0212015i	−0.999944	+	0.0106008i	$0.996626\pi$
$594$		0			0
$595$	−0.812131	+	0.336396i	−0.0332941	+	0.0137909i
$596$		0			0
$597$	−1.20685	+	2.91359i	−0.0493930	+	0.119245i
$598$		0			0
$599$	−13.6567	+	13.6567i	−0.557999	+	0.557999i	−0.928737	−	0.370738i	$-0.879105\pi$
$599$	−13.6567	+	13.6567i	−0.557999	+	0.557999i	0.370738	+	0.928737i	$0.379105\pi$
$600$		0			0
$601$	−3.24556	−	3.24556i	−0.132389	−	0.132389i	0.637807	−	0.770196i	$-0.279842\pi$
$601$	−3.24556	−	3.24556i	−0.132389	−	0.132389i	−0.770196	+	0.637807i	$0.779842\pi$
$602$		0			0
$603$	−19.7877	−	8.19633i	−0.805817	−	0.333780i
$604$		0			0
$605$	−0.245268	−	0.592131i	−0.00997158	−	0.0240735i
$606$		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
$611$	−11.5123	−	27.7932i	−0.465739	−	1.12439i
$612$		0			0
$613$	−20.9929	−	8.69556i	−0.847896	−	0.351210i	−0.0839342	−	0.996471i	$-0.526749\pi$
$613$	−20.9929	−	8.69556i	−0.847896	−	0.351210i	−0.763962	+	0.645261i	$0.776749\pi$
$614$		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	$-0.647143\pi$
$617$	11.1547	−	11.1547i	0.449072	−	0.449072i	0.895046	+	0.445974i	$0.147143\pi$
$618$		0			0
$619$	0.165589	−	0.399768i	0.00665559	−	0.0160680i	−0.920517	−	0.390703i	$-0.872232\pi$
$619$	0.165589	−	0.399768i	0.00665559	−	0.0160680i	0.927172	+	0.374635i	$0.122232\pi$
$620$		0			0
$621$	18.8402	−	7.80385i	0.756029	−	0.313158i
$622$		0			0
$623$		−	1.34242i		−	0.0537830i
$624$		0			0
$625$		−	3.01337i		−	0.120535i
$626$		0			0
$627$	9.78313	−	4.05231i	0.390701	−	0.161834i
$628$		0			0
$629$	10.8812	−	26.2696i	0.433863	−	1.04744i
$630$		0			0
$631$	8.48708	−	8.48708i	0.337865	−	0.337865i	−0.517698	−	0.855563i	$-0.673211\pi$
$631$	8.48708	−	8.48708i	0.337865	−	0.337865i	0.855563	+	0.517698i	$0.173211\pi$
$632$		0			0
$633$	2.86486	+	2.86486i	0.113868	+	0.113868i
$634$		0			0
$635$	−21.1091	−	8.74369i	−0.837690	−	0.346983i
$636$		0			0
$637$	−6.62792	−	16.0012i	−0.262608	−	0.633991i
$638$		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
$643$	4.05780	+	9.79639i	0.160024	+	0.386332i	0.983472	−	0.181060i	$-0.0579527\pi$
$643$	4.05780	+	9.79639i	0.160024	+	0.386332i	−0.823448	+	0.567391i	$0.807953\pi$
$644$		0			0
$645$	3.08981	+	1.27984i	0.121661	+	0.0503937i
$646$		0			0
$647$	−26.4018	−	26.4018i	−1.03796	−	1.03796i	−0.999250	−	0.0387106i	$-0.987675\pi$
$647$	−26.4018	−	26.4018i	−1.03796	−	1.03796i	−0.0387106	−	0.999250i	$-0.512325\pi$
$648$		0			0
$649$	7.27410	−	7.27410i	0.285534	−	0.285534i
$650$		0			0
$651$	−0.262632	+	0.634051i	−0.0102934	+	0.0248504i
$652$		0			0
$653$	−26.1421	+	10.8284i	−1.02302	+	0.423748i	−0.830188	−	0.557484i	$-0.811767\pi$
$653$	−26.1421	+	10.8284i	−1.02302	+	0.423748i	−0.192831	+	0.981232i	$0.561767\pi$
$654$		0			0
$655$		−	23.3333i		−	0.911708i
$656$		0			0
$657$		−	9.77214i		−	0.381247i
$658$		0			0
$659$	−15.1434	+	6.27260i	−0.589903	+	0.244346i	−0.657609	−	0.753359i	$-0.728432\pi$
$659$	−15.1434	+	6.27260i	−0.589903	+	0.244346i	0.0677059	+	0.997705i	$0.478432\pi$
$660$		0			0
$661$	−6.77294	+	16.3513i	−0.263437	+	0.635993i	−0.999147	−	0.0413040i	$-0.986849\pi$
$661$	−6.77294	+	16.3513i	−0.263437	+	0.635993i	0.735710	+	0.677297i	$0.236849\pi$
$662$		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
$667$	−31.7633	−	13.1568i	−1.22988	−	0.509433i
$668$		0			0
$669$	−1.22735	−	2.96308i	−0.0474521	−	0.114559i
$670$		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
$675$	2.99559	+	7.23200i	0.115300	+	0.278360i
$676$		0			0
$677$	22.7931	+	9.44122i	0.876011	+	0.362856i	0.774948	−	0.632024i	$-0.217776\pi$
$677$	22.7931	+	9.44122i	0.876011	+	0.362856i	0.101063	+	0.994880i	$0.467776\pi$
$678$		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
$683$	−10.7660	+	25.9915i	−0.411950	+	0.994535i	0.572664	+	0.819790i	$0.305910\pi$
$683$	−10.7660	+	25.9915i	−0.411950	+	0.994535i	−0.984614	+	0.174745i	$0.944090\pi$
$684$		0			0
$685$	−11.2662	+	4.66662i	−0.430460	+	0.178302i
$686$		0			0
$687$			7.85700i			0.299763i
$688$		0			0
$689$			9.22627i			0.351493i
$690$		0			0
$691$	−1.53096	+	0.634146i	−0.0582406	+	0.0241240i	−0.411614	−	0.911358i	$-0.635035\pi$
$691$	−1.53096	+	0.634146i	−0.0582406	+	0.0241240i	0.353373	+	0.935483i	$0.385035\pi$
$692$		0			0
$693$	0.684318	−	1.65209i	0.0259951	−	0.0627577i
$694$		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
$699$	11.2369	+	4.65446i	0.425017	+	0.176048i
$700$		0			0
$701$	9.23819	+	22.3030i	0.348921	+	0.842371i	0.996748	+	0.0805829i	$0.0256782\pi$
$701$	9.23819	+	22.3030i	0.348921	+	0.842371i	−0.647826	+	0.761788i	$0.724322\pi$
$702$		0			0
$703$	59.3391			2.23802
$704$		0			0
$705$	−8.62639			−0.324888
$706$		0			0
$707$	0.573636	+	1.38488i	0.0215738	+	0.0520837i
$708$		0			0
$709$	−11.3249	−	4.69095i	−0.425317	−	0.176172i	0.159749	−	0.987158i	$-0.448932\pi$
$709$	−11.3249	−	4.69095i	−0.425317	−	0.176172i	−0.585066	+	0.810985i	$0.698932\pi$
$710$		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
$715$	−4.75865	+	11.4884i	−0.177963	+	0.429641i
$716$		0			0
$717$	−6.58811	+	2.72888i	−0.246037	+	0.101912i
$718$		0			0
$719$		−	18.8205i		−	0.701888i	−0.936397	−	0.350944i	$-0.885861\pi$
$719$		−	18.8205i		−	0.701888i	0.936397	−	0.350944i	$-0.114139\pi$
$720$		0			0
$721$			1.11366i			0.0414748i
$722$		0			0
$723$	0.908754	−	0.376418i	0.0337969	−	0.0139991i
$724$		0			0
$725$	5.05038	−	12.1927i	0.187566	−	0.452825i
$726$		0			0
$727$	16.7869	−	16.7869i	0.622593	−	0.622593i	−0.323601	−	0.946194i	$-0.604893\pi$
$727$	16.7869	−	16.7869i	0.622593	−	0.622593i	0.946194	+	0.323601i	$0.104893\pi$
$728$		0			0
$729$	−10.7729	−	10.7729i	−0.398994	−	0.398994i
$730$		0			0
$731$	13.4776	+	5.58262i	0.498488	+	0.206481i
$732$		0			0
$733$	−12.7909	−	30.8799i	−0.472442	−	1.14058i	−0.963081	−	0.269213i	$-0.913236\pi$
$733$	−12.7909	−	30.8799i	−0.472442	−	1.14058i	0.490639	−	0.871363i	$-0.336764\pi$
$734$		0			0
$735$	−4.96641			−0.183189
$736$		0			0
$737$	26.1703			0.963995
$738$		0			0
$739$	−5.05208	−	12.1968i	−0.185844	−	0.448667i	0.803308	−	0.595564i	$-0.203071\pi$
$739$	−5.05208	−	12.1968i	−0.185844	−	0.448667i	−0.989152	+	0.146897i	$0.953071\pi$
$740$		0			0
$741$	−7.19615	−	2.98074i	−0.264357	−	0.109500i
$742$		0			0
$743$	14.2144	+	14.2144i	0.521476	+	0.521476i	0.918017	−	0.396541i	$-0.129789\pi$
$743$	14.2144	+	14.2144i	0.521476	+	0.521476i	−0.396541	+	0.918017i	$0.629789\pi$
$744$		0			0
$745$	−7.43023	+	7.43023i	−0.272223	+	0.272223i
$746$		0			0
$747$	14.9991	−	36.2109i	0.548787	−	1.32489i
$748$		0			0
$749$	1.06234	−	0.440038i	0.0388172	−	0.0160786i
$750$		0			0
$751$			17.6604i			0.644438i	0.946665	+	0.322219i	$0.104429\pi$
$751$			17.6604i			0.644438i	−0.946665	+	0.322219i	$0.895571\pi$
$752$		0			0
$753$		−	4.19263i		−	0.152788i
$754$		0			0
$755$	20.8125	−	8.62082i	0.757444	−	0.313744i
$756$		0			0
$757$	2.26500	−	5.46821i	0.0823230	−	0.198745i	−0.877358	−	0.479836i	$-0.840696\pi$
$757$	2.26500	−	5.46821i	0.0823230	−	0.198745i	0.959681	+	0.281091i	$0.0906962\pi$
$758$		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	$-0.177216\pi$
$761$	8.84304	+	8.84304i	0.320560	+	0.320560i	−0.528422	+	0.848982i	$0.677216\pi$
$762$		0			0
$763$	−0.801575	−	0.332023i	−0.0290190	−	0.0120200i
$764$		0			0
$765$	−4.87127	−	11.7603i	−0.176121	−	0.425194i
$766$		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
$771$	−0.537730	−	1.29820i	−0.0193659	−	0.0467534i
$772$		0			0
$773$	−21.7148	−	8.99455i	−0.781026	−	0.323511i	−0.0436963	−	0.999045i	$-0.513913\pi$
$773$	−21.7148	−	8.99455i	−0.781026	−	0.323511i	−0.737329	+	0.675533i	$0.763913\pi$
$774$		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
$779$	15.0310	−	36.2880i	0.538541	−	1.30015i
$780$		0			0
$781$	−12.6362	+	5.23408i	−0.452158	+	0.187290i
$782$		0			0
$783$		−	13.0478i		−	0.466289i
$784$		0			0
$785$		−	0.852939i		−	0.0304427i
$786$		0			0
$787$	−50.7364	+	21.0157i	−1.80856	+	0.749129i	−0.825869	+	0.563862i	$0.809315\pi$
$787$	−50.7364	+	21.0157i	−1.80856	+	0.749129i	−0.982688	+	0.185266i	$0.940685\pi$
$788$		0			0
$789$	−0.0311474	+	0.0751966i	−0.00110888	+	0.00267707i
$790$		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
$795$	2.44425	+	1.01244i	0.0866888	+	0.0359077i
$796$		0			0
$797$	6.76906	+	16.3420i	0.239772	+	0.578862i	0.997259	−	0.0739887i	$-0.0235729\pi$
$797$	6.76906	+	16.3420i	0.239772	+	0.578862i	−0.757487	+	0.652851i	$0.773573\pi$
$798$		0			0
$799$	−37.6280			−1.33118
$800$		0			0
$801$	19.4393			0.686854
$802$		0			0
$803$	4.56938	+	11.0315i	0.161250	+	0.389292i
$804$		0			0
$805$	1.91359	+	0.792635i	0.0674452	+	0.0279367i
$806$		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	$-0.784831\pi$
$809$	−4.39282	+	4.39282i	−0.154443	+	0.154443i	0.625656	+	0.780099i	$0.284831\pi$
$810$		0			0
$811$	11.2324	−	27.1174i	0.394422	−	0.952219i	−0.594542	−	0.804065i	$-0.702667\pi$
$811$	11.2324	−	27.1174i	0.394422	−	0.952219i	0.988964	−	0.148155i	$-0.0473334\pi$
$812$		0			0
$813$	8.10798	−	3.35844i	0.284359	−	0.117786i
$814$		0			0
$815$			35.7852i			1.25350i
$816$		0			0
$817$			30.4439i			1.06510i
$818$		0			0
$819$	−1.21522	+	0.503362i	−0.0424633	+	0.0175889i
$820$		0			0
$821$	−18.8289	+	45.4570i	−0.657134	+	1.58646i	0.145077	+	0.989420i	$0.453657\pi$
$821$	−18.8289	+	45.4570i	−0.657134	+	1.58646i	−0.802211	+	0.597041i	$0.796343\pi$
$822$		0			0
$823$	−14.4059	+	14.4059i	−0.502158	+	0.502158i	−0.912108	−	0.409950i	$-0.865546\pi$
$823$	−14.4059	+	14.4059i	−0.502158	+	0.502158i	0.409950	+	0.912108i	$0.365546\pi$
$824$		0			0
$825$	−3.24521	−	3.24521i	−0.112984	−	0.112984i
$826$		0			0
$827$	12.7434	+	5.27851i	0.443133	+	0.183552i	0.593082	−	0.805142i	$-0.297911\pi$
$827$	12.7434	+	5.27851i	0.443133	+	0.183552i	−0.149949	+	0.988694i	$0.547911\pi$
$828$		0			0
$829$	19.9104	+	48.0679i	0.691516	+	1.66947i	0.741704	+	0.670728i	$0.234018\pi$
$829$	19.9104	+	48.0679i	0.691516	+	1.66947i	−0.0501876	+	0.998740i	$0.515982\pi$
$830$		0			0
$831$	−4.89460			−0.169792
$832$		0			0
$833$	−21.6633			−0.750589
$834$		0			0
$835$	8.97348	+	21.6639i	0.310540	+	0.749710i
$836$		0			0
$837$	−19.1351	−	7.92600i	−0.661404	−	0.273963i
$838$		0			0
$839$	5.48780	+	5.48780i	0.189460	+	0.189460i	0.795463	−	0.606003i	$-0.207228\pi$
$839$	5.48780	+	5.48780i	0.189460	+	0.189460i	−0.606003	+	0.795463i	$0.707228\pi$
$840$		0			0
$841$	4.95137	−	4.95137i	0.170737	−	0.170737i
$842$		0			0
$843$	3.28706	−	7.93568i	0.113213	−	0.273319i
$844$		0			0
$845$	−9.30784	+	3.85544i	−0.320200	+	0.132631i
$846$		0			0
$847$			0.0828376i			0.00284633i
$848$		0			0
$849$			7.83788i			0.268995i
$850$		0			0
$851$	−61.8981	+	25.6390i	−2.12184	+	0.878894i
$852$		0			0
$853$	8.19878	−	19.7936i	0.280721	−	0.677720i	−0.719132	−	0.694874i	$-0.755460\pi$
$853$	8.19878	−	19.7936i	0.280721	−	0.677720i	0.999853	+	0.0171533i	$0.00546034\pi$
$854$		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	$-0.0386943\pi$
$857$	25.5086	+	25.5086i	0.871358	+	0.871358i	−0.121263	+	0.992620i	$0.538694\pi$
$858$		0			0
$859$	20.8638	+	8.64207i	0.711864	+	0.294864i	0.709076	−	0.705132i	$-0.249112\pi$
$859$	20.8638	+	8.64207i	0.711864	+	0.294864i	0.00278818	+	0.999996i	$0.499112\pi$
$860$		0			0
$861$	0.213417	+	0.515234i	0.00727323	+	0.0175591i
$862$		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
$867$	−1.35154	−	3.26290i	−0.0459006	−	0.110814i
$868$		0			0
$869$	−26.2402	−	10.8690i	−0.890136	−	0.368706i
$870$		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
$875$	−0.844919	+	2.03982i	−0.0285635	+	0.0689583i
$876$		0			0
$877$	1.93596	−	0.801899i	0.0653726	−	0.0270782i	−0.349758	−	0.936840i	$-0.613736\pi$
$877$	1.93596	−	0.801899i	0.0653726	−	0.0270782i	0.415130	+	0.909762i	$0.363736\pi$
$878$		0			0
$879$			7.07082i			0.238493i
$880$		0			0
$881$		−	6.47745i		−	0.218231i	−0.994029	−	0.109115i	$-0.965198\pi$
$881$		−	6.47745i		−	0.218231i	0.994029	−	0.109115i	$-0.0348018\pi$
$882$		0			0
$883$	14.1091	−	5.84419i	0.474810	−	0.196673i	−0.132428	−	0.991193i	$-0.542277\pi$
$883$	14.1091	−	5.84419i	0.474810	−	0.196673i	0.607238	+	0.794520i	$0.292277\pi$
$884$		0			0
$885$	−0.830351	+	2.00464i	−0.0279119	+	0.0673854i
$886$		0			0
$887$	26.9437	−	26.9437i	0.904679	−	0.904679i	−0.0911573	−	0.995837i	$-0.529057\pi$
$887$	26.9437	−	26.9437i	0.904679	−	0.904679i	0.995837	+	0.0911573i	$0.0290566\pi$
$888$		0			0
$889$	2.08817	+	2.08817i	0.0700349	+	0.0700349i
$890$		0			0
$891$	21.7430	+	9.00623i	0.728416	+	0.301720i
$892$		0			0
$893$	−30.0506	−	72.5485i	−1.00560	−	2.42774i
$894$		0			0
$895$	−22.6529			−0.757203
$896$		0			0
$897$	8.79440			0.293636
$898$		0			0
$899$	13.3627	+	32.2605i	0.445672	+	1.07595i
$900$		0			0
$901$	10.6617	+	4.41624i	0.355194	+	0.147126i
$902$		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
$907$	−3.84992	+	9.29454i	−0.127835	+	0.308620i	−0.974819	−	0.222998i	$-0.928416\pi$
$907$	−3.84992	+	9.29454i	−0.127835	+	0.308620i	0.846984	+	0.531618i	$0.178416\pi$
$908$		0			0
$909$	−20.0541	+	8.30669i	−0.665153	+	0.275515i
$910$		0			0
$911$		−	17.1254i		−	0.567389i	−0.958915	−	0.283694i	$-0.908440\pi$
$911$		−	17.1254i		−	0.567389i	0.958915	−	0.283694i	$-0.0915601\pi$
$912$		0			0
$913$			47.8909i			1.58496i
$914$		0			0
$915$	6.22567	−	2.57876i	0.205814	−	0.0852511i
$916$		0			0
$917$	−1.15409	+	2.78623i	−0.0381116	+	0.0920095i
$918$		0			0
$919$	29.1179	−	29.1179i	0.960510	−	0.960510i	−0.0387392	−	0.999249i	$-0.512334\pi$
$919$	29.1179	−	29.1179i	0.960510	−	0.960510i	0.999249	+	0.0387392i	$0.0123342\pi$
$920$		0			0
$921$	4.12144	+	4.12144i	0.135806	+	0.135806i
$922$		0			0
$923$	9.29477	+	3.85002i	0.305941	+	0.126725i
$924$		0			0
$925$	−9.84182	−	23.7603i	−0.323597	−	0.781232i
$926$		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
$931$	−17.3008	−	41.7679i	−0.567011	−	1.36889i
$932$		0			0
$933$	−3.17209	−	1.31392i	−0.103850	−	0.0430159i
$934$		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	$-0.962311\pi$
$937$	−26.7802	+	26.7802i	−0.874871	+	0.874871i	0.118127	+	0.992998i	$0.462311\pi$
$938$		0			0
$939$	−0.674701	+	1.62887i	−0.0220180	+	0.0531562i
$940$		0			0
$941$	−39.3660	+	16.3059i	−1.28329	+	0.531558i	−0.916980	−	0.398933i	$-0.869380\pi$
$941$	−39.3660	+	16.3059i	−1.28329	+	0.531558i	−0.366314	+	0.930491i	$0.619380\pi$
$942$		0			0
$943$			44.3475i			1.44415i
$944$		0			0
$945$			0.786068i			0.0255708i
$946$		0			0
$947$	1.12544	−	0.466171i	0.0365718	−	0.0151485i	−0.364323	−	0.931273i	$-0.618699\pi$
$947$	1.12544	−	0.466171i	0.0365718	−	0.0151485i	0.400894	+	0.916124i	$0.368699\pi$
$948$		0			0
$949$	3.36109	−	8.11439i	0.109106	−	0.263404i
$950$		0			0
$951$	7.32078	−	7.32078i	0.237393	−	0.237393i
$952$		0			0
$953$	−31.4229	−	31.4229i	−1.01789	−	1.01789i	−0.999837	−	0.0180517i	$-0.994254\pi$
$953$	−31.4229	−	31.4229i	−1.01789	−	1.01789i	−0.0180517	−	0.999837i	$-0.505746\pi$
$954$		0			0
$955$	−31.3862	−	13.0006i	−1.01563	−	0.420689i
$956$		0			0
$957$	2.92746	+	7.06750i	0.0946312	+	0.228460i
$958$		0			0
$959$	1.57612			0.0508955
$960$		0			0
$961$	24.4285			0.788017
$962$		0			0
$963$	6.37208	+	15.3836i	0.205337	+	0.495728i
$964$		0			0
$965$	−24.9119	−	10.3188i	−0.801941	−	0.332175i
$966$		0			0
$967$	17.7661	+	17.7661i	0.571319	+	0.571319i	0.932497	−	0.361178i	$-0.117625\pi$
$967$	17.7661	+	17.7661i	0.571319	+	0.571319i	−0.361178	+	0.932497i	$0.617625\pi$
$968$		0			0
$969$	−6.88901	+	6.88901i	−0.221307	+	0.221307i
$970$		0			0
$971$	22.2407	−	53.6939i	0.713739	−	1.72312i	0.0232989	−	0.999729i	$-0.492583\pi$
$971$	22.2407	−	53.6939i	0.713739	−	1.72312i	0.690440	−	0.723390i	$-0.257417\pi$
$972$		0			0
$973$	−1.39784	+	0.579005i	−0.0448128	+	0.0185620i
$974$		0			0
$975$			3.37583i			0.108113i
$976$		0			0
$977$			16.3541i			0.523215i	0.965174	+	0.261608i	$0.0842527\pi$
$977$			16.3541i			0.523215i	−0.965174	+	0.261608i	$0.915747\pi$
$978$		0			0
$979$	−21.9445	+	9.08969i	−0.701348	+	0.290508i
$980$		0			0
$981$	4.80795	−	11.6074i	0.153506	−	0.370596i
$982$		0			0
$983$	−5.23497	+	5.23497i	−0.166970	+	0.166970i	−0.785646	−	0.618676i	$-0.787669\pi$
$983$	−5.23497	+	5.23497i	−0.166970	+	0.166970i	0.618676	+	0.785646i	$0.287669\pi$
$984$		0			0
$985$	−23.4003	−	23.4003i	−0.745595	−	0.745595i
$986$		0			0
$987$	1.03008	+	0.426672i	0.0327877	+	0.0135811i
$988$		0			0
$989$	−13.1541	−	31.7568i	−0.418276	−	1.00981i
$990$		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
$995$	−3.69933	−	8.93098i	−0.117277	−	0.283131i
$996$		0			0
$997$	−29.3764	−	12.1681i	−0.930361	−	0.385368i	−0.134545	−	0.990907i	$-0.542957\pi$
$997$	−29.3764	−	12.1681i	−0.930361	−	0.385368i	−0.795815	+	0.605539i	$0.792957\pi$
$998$		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.f.897.2	yes	16
4.3	odd	2	inner	1024.2.g.f.897.3	yes	16
8.3	odd	2		1024.2.g.a.897.2	yes	16
8.5	even	2		1024.2.g.a.897.3	yes	16
16.3	odd	4		1024.2.g.d.385.2	yes	16
16.5	even	4		1024.2.g.g.385.2	yes	16
16.11	odd	4		1024.2.g.g.385.3	yes	16
16.13	even	4		1024.2.g.d.385.3	yes	16
32.3	odd	8		1024.2.g.a.129.2	✓	16
32.5	even	8		1024.2.g.d.641.3	yes	16
32.11	odd	8		1024.2.g.g.641.3	yes	16
32.13	even	8	inner	1024.2.g.f.129.2	yes	16
32.19	odd	8	inner	1024.2.g.f.129.3	yes	16
32.21	even	8		1024.2.g.g.641.2	yes	16
32.27	odd	8		1024.2.g.d.641.2	yes	16
32.29	even	8		1024.2.g.a.129.3	yes	16
64.13	even	16		4096.2.a.i.1.6		8
64.19	odd	16		4096.2.a.i.1.5		8
64.45	even	16		4096.2.a.s.1.3		8
64.51	odd	16		4096.2.a.s.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.129.2	✓	16	32.3	odd	8
1024.2.g.a.129.3	yes	16	32.29	even	8
1024.2.g.a.897.2	yes	16	8.3	odd	2
1024.2.g.a.897.3	yes	16	8.5	even	2
1024.2.g.d.385.2	yes	16	16.3	odd	4
1024.2.g.d.385.3	yes	16	16.13	even	4
1024.2.g.d.641.2	yes	16	32.27	odd	8
1024.2.g.d.641.3	yes	16	32.5	even	8
1024.2.g.f.129.2	yes	16	32.13	even	8	inner
1024.2.g.f.129.3	yes	16	32.19	odd	8	inner
1024.2.g.f.897.2	yes	16	1.1	even	1	trivial
1024.2.g.f.897.3	yes	16	4.3	odd	2	inner
1024.2.g.g.385.2	yes	16	16.5	even	4
1024.2.g.g.385.3	yes	16	16.11	odd	4
1024.2.g.g.641.2	yes	16	32.21	even	8
1024.2.g.g.641.3	yes	16	32.11	odd	8
4096.2.a.i.1.5		8	64.19	odd	16
4096.2.a.i.1.6		8	64.13	even	16
4096.2.a.s.1.3		8	64.45	even	16
4096.2.a.s.1.4		8	64.51	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)

\(f(q)\)	\(=\)	\(q+(-0.184592 - 0.445644i) q^{3} +(1.36603 + 0.565826i) q^{5} +(-0.135131 - 0.135131i) q^{7} +(1.95680 - 1.95680i) q^{9} +O(q^{10})\)	\(q+(-0.184592 - 0.445644i) q^{3} +(1.36603 + 0.565826i) q^{5} +(-0.135131 - 0.135131i) q^{7} +(1.95680 - 1.95680i) q^{9} +(-1.29398 + 3.12395i) q^{11} +(2.29788 - 0.951812i) q^{13} -0.713208i q^{15} -3.11099i q^{17} +(5.99813 - 2.48451i) q^{19} +(-0.0352762 + 0.0851642i) q^{21} +(-5.18330 + 5.18330i) q^{23} +(-1.98967 - 1.98967i) q^{25} +(-2.57018 - 1.06460i) q^{27} +(1.79485 + 4.33315i) q^{29} +7.44503 q^{31} +1.63103 q^{33} +(-0.108131 - 0.261052i) q^{35} +(8.44414 + 3.49768i) q^{37} +(-0.848339 - 0.848339i) q^{39} +(4.27792 - 4.27792i) q^{41} +(-1.79448 + 4.33227i) q^{43} +(3.78024 - 1.56583i) q^{45} -12.0952i q^{47} -6.96348i q^{49} +(-1.38639 + 0.574263i) q^{51} +(-1.41956 + 3.42713i) q^{53} +(-3.53523 + 3.53523i) q^{55} +(-2.21441 - 2.21441i) q^{57} +(-2.81074 - 1.16425i) q^{59} +(3.61571 + 8.72911i) q^{61} -0.528846 q^{63} +3.67752 q^{65} +(-2.96182 - 7.15047i) q^{67} +(3.26670 + 1.35311i) q^{69} +(2.86020 + 2.86020i) q^{71} +(2.49697 - 2.49697i) q^{73} +(-0.519408 + 1.25396i) q^{75} +(0.596999 - 0.247285i) q^{77} +8.39967i q^{79} -6.96008i q^{81} +(13.0852 - 5.42005i) q^{83} +(1.76028 - 4.24969i) q^{85} +(1.59973 - 1.59973i) q^{87} +(4.96713 + 4.96713i) q^{89} +(-0.439133 - 0.181895i) q^{91} +(-1.37429 - 3.31784i) q^{93} +9.59940 q^{95} -2.87492 q^{97} +(3.58087 + 8.64500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^5 - 16 * q^9	\( 16 q + 8 q^{5} - 16 q^{9} - 8 q^{13} + 16 q^{21} - 32 q^{25} - 24 q^{29} - 80 q^{33} + 40 q^{37} - 16 q^{41} + 24 q^{45} - 56 q^{53} - 16 q^{57} + 8 q^{61} - 32 q^{65} - 64 q^{69} + 32 q^{73} + 64 q^{77} - 48 q^{85} + 32 q^{89} + 80 q^{93} - 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 16 * q^9 - 8 * q^13 + 16 * q^21 - 32 * q^25 - 24 * q^29 - 80 * q^33 + 40 * q^37 - 16 * q^41 + 24 * q^45 - 56 * q^53 - 16 * q^57 + 8 * q^61 - 32 * q^65 - 64 * q^69 + 32 * q^73 + 64 * q^77 - 48 * q^85 + 32 * q^89 + 80 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more