LMFDB - Embedded newform 1024.2.g.a.129.3

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			129.3
Root			$-0.130526 - 0.991445i$ of defining polynomial
Character	$\chi$	$=$	1024.129
Dual form			1024.2.g.a.897.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.184592 - 0.445644i) q^{3} +(-1.36603 + 0.565826i) q^{5} +(-0.135131 + 0.135131i) q^{7} +(1.95680 + 1.95680i) q^{9} +O(q^{10})$	\(q+(0.184592 - 0.445644i) q^{3} +(-1.36603 + 0.565826i) q^{5} +(-0.135131 + 0.135131i) q^{7} +(1.95680 + 1.95680i) q^{9} +(1.29398 + 3.12395i) q^{11} +(-2.29788 - 0.951812i) q^{13} +0.713208i q^{15} +3.11099i q^{17} +(-5.99813 - 2.48451i) q^{19} +(0.0352762 + 0.0851642i) q^{21} +(-5.18330 - 5.18330i) q^{23} +(-1.98967 + 1.98967i) q^{25} +(2.57018 - 1.06460i) q^{27} +(-1.79485 + 4.33315i) q^{29} +7.44503 q^{31} +1.63103 q^{33} +(0.108131 - 0.261052i) q^{35} +(-8.44414 + 3.49768i) q^{37} +(-0.848339 + 0.848339i) q^{39} +(4.27792 + 4.27792i) q^{41} +(1.79448 + 4.33227i) q^{43} +(-3.78024 - 1.56583i) q^{45} +12.0952i q^{47} +6.96348i q^{49} +(1.38639 + 0.574263i) q^{51} +(1.41956 + 3.42713i) q^{53} +(-3.53523 - 3.53523i) q^{55} +(-2.21441 + 2.21441i) q^{57} +(2.81074 - 1.16425i) q^{59} +(-3.61571 + 8.72911i) q^{61} -0.528846 q^{63} +3.67752 q^{65} +(2.96182 - 7.15047i) q^{67} +(-3.26670 + 1.35311i) q^{69} +(2.86020 - 2.86020i) q^{71} +(2.49697 + 2.49697i) q^{73} +(0.519408 + 1.25396i) q^{75} +(-0.596999 - 0.247285i) q^{77} -8.39967i q^{79} +6.96008i q^{81} +(-13.0852 - 5.42005i) q^{83} +(-1.76028 - 4.24969i) q^{85} +(1.59973 + 1.59973i) q^{87} +(4.96713 - 4.96713i) q^{89} +(0.439133 - 0.181895i) q^{91} +(1.37429 - 3.31784i) q^{93} +9.59940 q^{95} -2.87492 q^{97} +(-3.58087 + 8.64500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

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	$-0.830532\pi$
$3$	0.184592	−	0.445644i	0.106574	−	0.257293i	0.968166	+	0.250309i	$0.0805322\pi$
$4$		0			0
$5$	−1.36603	+	0.565826i	−0.610905	+	0.253045i	−0.666615	−	0.745402i	$-0.732258\pi$
$5$	−1.36603	+	0.565826i	−0.610905	+	0.253045i	0.0557103	+	0.998447i	$0.482258\pi$
$6$		0			0
$7$	−0.135131	+	0.135131i	−0.0510746	+	0.0510746i	−0.732183	−	0.681108i	$-0.761498\pi$
$7$	−0.135131	+	0.135131i	−0.0510746	+	0.0510746i	0.681108	+	0.732183i	$0.261498\pi$
$8$		0			0
$9$	1.95680	+	1.95680i	0.652265	+	0.652265i
$10$		0			0
$11$	1.29398	+	3.12395i	0.390151	+	0.941907i	0.989906	+	0.141724i	$0.0452645\pi$
$11$	1.29398	+	3.12395i	0.390151	+	0.941907i	−0.599756	+	0.800183i	$0.704736\pi$
$12$		0			0
$13$	−2.29788	−	0.951812i	−0.637316	−	0.263985i	0.0405417	−	0.999178i	$-0.487092\pi$
$13$	−2.29788	−	0.951812i	−0.637316	−	0.263985i	−0.677858	+	0.735193i	$0.737092\pi$
$14$		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
$19$	−5.99813	−	2.48451i	−1.37607	−	0.569985i	−0.432639	−	0.901567i	$-0.642418\pi$
$19$	−5.99813	−	2.48451i	−1.37607	−	0.569985i	−0.943426	+	0.331582i	$0.892418\pi$
$20$		0			0
$21$	0.0352762	+	0.0851642i	0.00769789	+	0.0185844i
$22$		0			0
$23$	−5.18330	−	5.18330i	−1.08079	−	1.08079i	−0.996436	−	0.0843577i	$-0.973116\pi$
$23$	−5.18330	−	5.18330i	−1.08079	−	1.08079i	−0.0843577	−	0.996436i	$-0.526884\pi$
$24$		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	0.665031	+	0.746816i	$0.268418\pi$
$29$	−1.79485	+	4.33315i	−0.333295	+	0.804646i	−0.998326	+	0.0578306i	$0.981582\pi$
$30$		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	$-0.895569\pi$
$37$	−8.44414	+	3.49768i	−1.38821	+	0.575015i	−0.441545	+	0.897239i	$0.645569\pi$
$38$		0			0
$39$	−0.848339	+	0.848339i	−0.135843	+	0.135843i
$40$		0			0
$41$	4.27792	+	4.27792i	0.668098	+	0.668098i	0.957276	−	0.289177i	$-0.0933817\pi$
$41$	4.27792	+	4.27792i	0.668098	+	0.668098i	−0.289177	+	0.957276i	$0.593382\pi$
$42$		0			0
$43$	1.79448	+	4.33227i	0.273656	+	0.660664i	0.999634	−	0.0270537i	$-0.00861252\pi$
$43$	1.79448	+	4.33227i	0.273656	+	0.660664i	−0.725978	+	0.687718i	$0.758613\pi$
$44$		0			0
$45$	−3.78024	−	1.56583i	−0.563525	−	0.233420i
$46$		0			0
$47$			12.0952i			1.76426i	0.471002	+	0.882132i	$0.343892\pi$
$47$			12.0952i			1.76426i	−0.471002	+	0.882132i	$0.656108\pi$
$48$		0			0
$49$			6.96348i			0.994783i
$50$		0			0
$51$	1.38639	+	0.574263i	0.194134	+	0.0804129i
$52$		0			0
$53$	1.41956	+	3.42713i	0.194992	+	0.470752i	0.990889	−	0.134680i	$-0.0430005\pi$
$53$	1.41956	+	3.42713i	0.194992	+	0.470752i	−0.795897	+	0.605432i	$0.793001\pi$
$54$		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	$-0.561543\pi$
$59$	2.81074	−	1.16425i	0.365927	−	0.151572i	0.558068	+	0.829795i	$0.311543\pi$
$60$		0			0
$61$	−3.61571	+	8.72911i	−0.462945	+	1.11765i	0.504238	+	0.863565i	$0.331774\pi$
$61$	−3.61571	+	8.72911i	−0.462945	+	1.11765i	−0.967183	+	0.254083i	$0.918226\pi$
$62$		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	−0.633186	−	0.773999i	$-0.718253\pi$
$67$	2.96182	−	7.15047i	0.361844	−	0.873569i	0.995031	−	0.0995698i	$-0.0317467\pi$
$68$		0			0
$69$	−3.26670	+	1.35311i	−0.393265	+	0.162896i
$70$		0			0
$71$	2.86020	−	2.86020i	0.339444	−	0.339444i	−0.516714	−	0.856158i	$-0.672845\pi$
$71$	2.86020	−	2.86020i	0.339444	−	0.339444i	0.856158	+	0.516714i	$0.172845\pi$
$72$		0			0
$73$	2.49697	+	2.49697i	0.292249	+	0.292249i	0.837968	−	0.545719i	$-0.183744\pi$
$73$	2.49697	+	2.49697i	0.292249	+	0.292249i	−0.545719	+	0.837968i	$0.683744\pi$
$74$		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	$-0.843345\pi$
$79$		−	8.39967i		−	0.945036i	0.881321	−	0.472518i	$-0.156655\pi$
$80$		0			0
$81$			6.96008i			0.773342i
$82$		0			0
$83$	−13.0852	−	5.42005i	−1.43628	−	0.594928i	−0.477389	−	0.878692i	$-0.658417\pi$
$83$	−13.0852	−	5.42005i	−1.43628	−	0.594928i	−0.958894	+	0.283764i	$0.908417\pi$
$84$		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	−0.393017	−	0.919531i	$-0.628569\pi$
$89$	4.96713	−	4.96713i	0.526514	−	0.526514i	0.919531	+	0.393017i	$0.128569\pi$
$90$		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	$-0.497390\pi$
$101$	7.24674	−	3.00170i	0.721078	−	0.298680i	0.712880	+	0.701286i	$0.247390\pi$
$102$		0			0
$103$	−4.12067	+	4.12067i	−0.406022	+	0.406022i	−0.880349	−	0.474327i	$-0.842692\pi$
$103$	−4.12067	+	4.12067i	−0.406022	+	0.406022i	0.474327	+	0.880349i	$0.342692\pi$
$104$		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	$-0.0310641\pi$
$107$	2.30261	+	5.55900i	0.222602	+	0.537409i	−0.772640	+	0.634845i	$0.781064\pi$
$108$		0			0
$109$	−4.19445	−	1.73740i	−0.401756	−	0.166413i	0.172650	−	0.984983i	$-0.444767\pi$
$109$	−4.19445	−	1.73740i	−0.401756	−	0.166413i	−0.574406	+	0.818571i	$0.694767\pi$
$110$		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
$115$	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	−0.405427	−	0.914128i	$-0.632877\pi$
$131$	6.03911	−	14.5797i	0.527639	−	1.27383i	0.933066	−	0.359706i	$-0.117123\pi$
$132$		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	0.412645	−	0.910892i	$-0.364605\pi$
$137$	−5.83183	−	5.83183i	−0.498247	−	0.498247i	−0.910892	+	0.412645i	$0.864605\pi$
$138$		0			0
$139$	−3.02980	−	7.31458i	−0.256984	−	0.620414i	0.741752	−	0.670674i	$-0.233995\pi$
$139$	−3.02980	−	7.31458i	−0.256984	−	0.620414i	−0.998736	+	0.0502598i	$0.983995\pi$
$140$		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	$-0.0309768\pi$
$149$	2.71965	+	6.56583i	0.222803	+	0.537893i	−0.772466	+	0.635056i	$0.780977\pi$
$150$		0			0
$151$	10.7733	+	10.7733i	0.876722	+	0.876722i	0.993194	−	0.116472i	$-0.0371584\pi$
$151$	10.7733	+	10.7733i	0.876722	+	0.876722i	−0.116472	+	0.993194i	$0.537158\pi$
$152$		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	$-0.867672\pi$
$157$	0.220757	−	0.532954i	0.0176183	−	0.0425344i	0.932444	+	0.361315i	$0.117672\pi$
$158$		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	−0.0682454	+	0.997669i	$0.521740\pi$
$163$	−9.26188	+	22.3602i	−0.725447	+	1.75138i	−0.657201	+	0.753715i	$0.728260\pi$
$164$		0			0
$165$	−2.22803	+	0.922880i	−0.173452	+	0.0718461i
$166$		0			0
$167$	11.2141	−	11.2141i	0.867770	−	0.867770i	−0.124455	−	0.992225i	$-0.539718\pi$
$167$	11.2141	−	11.2141i	0.867770	−	0.867770i	0.992225	+	0.124455i	$0.0397184\pi$
$168$		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	$-0.0627410\pi$
$173$	20.1974	+	8.36603i	1.53558	+	0.636057i	0.554940	+	0.831890i	$0.312741\pi$
$174$		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	$-0.180949\pi$
$179$	14.1545	+	5.86300i	1.05796	+	0.438221i	0.215233	+	0.976563i	$0.430949\pi$
$180$		0			0
$181$	4.03749	+	9.74737i	0.300104	+	0.724516i	0.999948	+	0.0102198i	$0.00325311\pi$
$181$	4.03749	+	9.74737i	0.300104	+	0.724516i	−0.699843	+	0.714296i	$0.746747\pi$
$182$		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	$-0.331253\pi$
$197$	20.6780	−	8.56510i	1.47324	−	0.610238i	0.967596	+	0.252502i	$0.0812534\pi$
$198$		0			0
$199$	−4.62301	+	4.62301i	−0.327717	+	0.327717i	−0.851718	−	0.524001i	$-0.824439\pi$
$199$	−4.62301	+	4.62301i	−0.327717	+	0.327717i	0.524001	+	0.851718i	$0.324439\pi$
$200$		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	$-0.281638\pi$
$211$	7.75999	+	3.21429i	0.534220	+	0.221281i	−0.0992305	+	0.995064i	$0.531638\pi$
$212$		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	$-0.942096\pi$
$227$	−2.41272	+	5.82482i	−0.160138	+	0.386607i	0.823362	+	0.567517i	$0.192096\pi$
$228$		0			0
$229$	15.0487	−	6.23338i	0.994446	−	0.411913i	0.174689	−	0.984624i	$-0.444108\pi$
$229$	15.0487	−	6.23338i	0.994446	−	0.411913i	0.819758	+	0.572711i	$0.194108\pi$
$230$		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	$-0.940645\pi$
$233$	−17.8296	−	17.8296i	−1.16806	−	1.16806i	−0.185390	−	0.982665i	$-0.559355\pi$
$234$		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	$0.158684\pi$
$239$			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
$243$	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	$-0.713451\pi$
$251$	−8.03025	+	3.32624i	−0.506865	+	0.209950i	0.114571	+	0.993415i	$0.463451\pi$
$252$		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	−0.710776	−	0.703419i	$-0.751656\pi$
$263$	−0.119315	+	0.119315i	−0.00735727	+	0.00735727i	0.703419	+	0.710776i	$0.251656\pi$
$264$		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	0.995512	+	0.0946356i	$0.0301686\pi$
$269$	28.9705	+	12.0000i	1.76636	+	0.731651i	0.770851	+	0.637016i	$0.219831\pi$
$270$		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
$275$	−8.79022	−	3.64103i	−0.530070	−	0.219562i
$276$		0			0
$277$	−3.88315	−	9.37475i	−0.233316	−	0.563274i	0.763248	−	0.646106i	$-0.223604\pi$
$277$	−3.88315	−	9.37475i	−0.233316	−	0.563274i	−0.996564	+	0.0828318i	$0.973604\pi$
$278$		0			0
$279$	14.5684	+	14.5684i	0.872188	+	0.872188i
$280$		0			0
$281$	12.5916	−	12.5916i	0.751151	−	0.751151i	−0.223543	−	0.974694i	$-0.571762\pi$
$281$	12.5916	−	12.5916i	0.751151	−	0.751151i	0.974694	+	0.223543i	$0.0717623\pi$
$282$		0			0
$283$	15.0121	−	6.21821i	0.892376	−	0.369634i	0.111092	−	0.993810i	$-0.464565\pi$
$283$	15.0121	−	6.21821i	0.892376	−	0.369634i	0.781284	+	0.624176i	$0.214565\pi$
$284$		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	$-0.484153\pi$
$293$	13.5429	−	5.60966i	0.791186	−	0.327720i	0.741420	+	0.671041i	$0.234153\pi$
$294$		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	$-0.262940\pi$
$307$	11.1636	+	4.62413i	0.637143	+	0.263913i	−0.0406418	+	0.999174i	$0.512940\pi$
$308$		0			0
$309$	1.07571	+	2.59700i	0.0611951	+	0.147738i
$310$		0			0
$311$	5.03317	+	5.03317i	0.285405	+	0.285405i	0.835260	−	0.549855i	$-0.185317\pi$
$311$	5.03317	+	5.03317i	0.285405	+	0.285405i	−0.549855	+	0.835260i	$0.685317\pi$
$312$		0			0
$313$	−2.58454	+	2.58454i	−0.146087	+	0.146087i	−0.776367	−	0.630281i	$-0.782940\pi$
$313$	−2.58454	+	2.58454i	−0.146087	+	0.146087i	0.630281	+	0.776367i	$0.282940\pi$
$314$		0			0
$315$	0.722417	−	0.299235i	0.0407036	−	0.0168600i
$316$		0			0
$317$	−8.21371	+	19.8296i	−0.461328	+	1.11374i	0.506525	+	0.862225i	$0.330930\pi$
$317$	−8.21371	+	19.8296i	−0.461328	+	1.11374i	−0.967853	+	0.251518i	$0.919070\pi$
$318$		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	$-0.237978\pi$
$331$	−4.83918	−	11.6828i	−0.265986	−	0.642146i	−0.999287	+	0.0377578i	$0.987978\pi$
$332$		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	$0.156694\pi$
$337$			17.3525i			0.945254i	−0.881263	+	0.472627i	$0.843306\pi$
$338$		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	$-0.780095\pi$
$347$	−16.1152	+	6.67513i	−0.865109	+	0.358340i	−0.0944054	+	0.995534i	$0.530095\pi$
$348$		0			0
$349$	−0.198581	+	0.479418i	−0.0106298	+	0.0256626i	−0.929105	−	0.369815i	$-0.879421\pi$
$349$	−0.198581	+	0.479418i	−0.0106298	+	0.0256626i	0.918476	+	0.395478i	$0.129421\pi$
$350$		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	−0.529974	−	0.848014i	$-0.677798\pi$
$359$	6.02599	−	6.02599i	0.318039	−	0.318039i	0.848014	+	0.529974i	$0.177798\pi$
$360$		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	$-0.952704\pi$
$367$		−	5.67199i		−	0.296076i	0.988982	−	0.148038i	$-0.0472957\pi$
$368$		0			0
$369$			16.7420i			0.871555i
$370$		0			0
$371$	−0.654936	−	0.271283i	−0.0340026	−	0.0140843i
$372$		0			0
$373$	−13.3210	−	32.1599i	−0.689738	−	1.66517i	−0.745309	−	0.666719i	$-0.767698\pi$
$373$	−13.3210	−	32.1599i	−0.689738	−	1.66517i	0.0555710	−	0.998455i	$-0.482302\pi$
$374$		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	$-0.599285\pi$
$379$	2.90292	−	1.20243i	0.149113	−	0.0617647i	0.455992	+	0.889984i	$0.349285\pi$
$380$		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	$-0.725704\pi$
$389$	−11.3383	+	4.69648i	−0.574875	+	0.238121i	0.0762534	+	0.997088i	$0.475704\pi$
$390$		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	$-0.258147\pi$
$397$	13.2139	+	5.47337i	0.663185	+	0.274700i	−0.0255930	+	0.999672i	$0.508147\pi$
$398$		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
$403$	−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	−0.918081	−	0.396392i	$-0.870262\pi$
$409$	−10.5505	+	10.5505i	−0.521689	+	0.521689i	0.396392	+	0.918081i	$0.370262\pi$
$410$		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	−0.539671	−	0.841876i	$-0.681451\pi$
$419$	8.94989	−	21.6069i	0.437231	−	1.05557i	0.976901	−	0.213692i	$-0.0685488\pi$
$420$		0			0
$421$	−34.3466	+	14.2268i	−1.67395	+	0.693372i	−0.999009	−	0.0445009i	$-0.985830\pi$
$421$	−34.3466	+	14.2268i	−1.67395	+	0.693372i	−0.674939	+	0.737873i	$0.735830\pi$
$422$		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	$0.229410\pi$
$431$			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
$435$	−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	0.327097	−	0.944991i	$-0.393930\pi$
$439$	−12.9463	−	12.9463i	−0.617894	−	0.617894i	−0.944991	+	0.327097i	$0.893930\pi$
$440$		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	$-0.333263\pi$
$443$	30.8594	−	12.7824i	1.46617	−	0.607309i	0.965983	+	0.258606i	$0.0832632\pi$
$444$		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	0.920614	−	0.390473i	$-0.127689\pi$
$457$	11.3331	+	11.3331i	0.530141	+	0.530141i	−0.390473	+	0.920614i	$0.627689\pi$
$458$		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	$-0.494909\pi$
$461$	−14.5941	−	6.04506i	−0.679713	−	0.281546i	−0.695707	+	0.718326i	$0.744909\pi$
$462$		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
$467$	−9.22554	−	3.82134i	−0.426907	−	0.176831i	0.158876	−	0.987299i	$-0.449213\pi$
$467$	−9.22554	−	3.82134i	−0.426907	−	0.176831i	−0.585783	+	0.810468i	$0.699213\pi$
$468$		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	−0.842322	−	0.538975i	$-0.818812\pi$
$487$	−6.69427	+	6.69427i	−0.303346	+	0.303346i	0.538975	+	0.842322i	$0.318812\pi$
$488$		0			0
$489$	8.25501	+	8.25501i	0.373305	+	0.373305i
$490$		0			0
$491$	13.1010	+	31.6286i	0.591239	+	1.42738i	0.882307	+	0.470675i	$0.155989\pi$
$491$	13.1010	+	31.6286i	0.591239	+	1.42738i	−0.291068	+	0.956702i	$0.594011\pi$
$492$		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	$-0.490607\pi$
$499$	−14.6636	−	6.07387i	−0.656434	−	0.271904i	−0.685937	+	0.727661i	$0.740607\pi$
$500$		0			0
$501$	−2.92746	−	7.06750i	−0.130789	−	0.315753i
$502$		0			0
$503$	−16.7932	−	16.7932i	−0.748773	−	0.748773i	0.225476	−	0.974249i	$-0.427606\pi$
$503$	−16.7932	−	16.7932i	−0.748773	−	0.748773i	−0.974249	+	0.225476i	$0.927606\pi$
$504$		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	$-0.806506\pi$
$509$	3.68700	−	8.90119i	0.163423	−	0.394539i	0.984285	+	0.176589i	$0.0565063\pi$
$510$		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	0.992632	+	0.121167i	$0.0386636\pi$
$521$	25.4229	+	25.4229i	1.11380	+	1.11380i	0.121167	+	0.992632i	$0.461336\pi$
$522$		0			0
$523$	3.59867	+	8.68795i	0.157359	+	0.379897i	0.982821	−	0.184559i	$-0.0590858\pi$
$523$	3.59867	+	8.68795i	0.157359	+	0.379897i	−0.825463	+	0.564457i	$0.809086\pi$
$524$		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	0.405856	+	0.913937i	$0.366974\pi$
$541$	−12.2665	+	29.6140i	−0.527379	+	1.27320i	−0.933235	+	0.359268i	$0.883026\pi$
$542$		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	$-0.789930\pi$
$547$	4.72724	−	11.4126i	0.202122	−	0.487966i	0.992142	+	0.125115i	$0.0399300\pi$
$548$		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	$-0.270426\pi$
$557$	14.0704	+	5.82814i	0.596180	+	0.246946i	−0.0641266	+	0.997942i	$0.520426\pi$
$558$		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	−0.959103	−	0.283057i	$-0.908651\pi$
$563$	−43.5982	−	18.0589i	−1.83744	−	0.761094i	−0.878340	−	0.478036i	$-0.841349\pi$
$564$		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	−0.264438	−	0.964403i	$-0.585186\pi$
$569$	16.6968	−	16.6968i	0.699965	−	0.699965i	0.964403	+	0.264438i	$0.0851863\pi$
$570$		0			0
$571$	−25.7136	+	10.6509i	−1.07608	+	0.445728i	−0.849133	−	0.528179i	$-0.822875\pi$
$571$	−25.7136	+	10.6509i	−1.07608	+	0.445728i	−0.226949	+	0.973907i	$0.572875\pi$
$572$		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	0.999985	+	0.00539239i	$0.00171646\pi$
$587$	7.18852	+	17.3546i	0.296702	+	0.716302i	−0.703284	+	0.710909i	$0.748284\pi$
$588$		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	$-0.996626\pi$
$593$		−	0.516291i		−	0.0212015i	0.999944	−	0.0106008i	$-0.00337439\pi$
$594$		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	0.370738	−	0.928737i	$-0.379105\pi$
$599$	−13.6567	−	13.6567i	−0.557999	−	0.557999i	−0.928737	+	0.370738i	$0.879105\pi$
$600$		0			0
$601$	−3.24556	+	3.24556i	−0.132389	+	0.132389i	−0.770196	−	0.637807i	$-0.779842\pi$
$601$	−3.24556	+	3.24556i	−0.132389	+	0.132389i	0.637807	+	0.770196i	$0.279842\pi$
$602$		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	$-0.473251\pi$
$613$	20.9929	−	8.69556i	0.847896	−	0.351210i	0.763962	+	0.645261i	$0.223251\pi$
$614$		0			0
$615$	−3.05105	+	3.05105i	−0.123030	+	0.123030i
$616$		0			0
$617$	11.1547	+	11.1547i	0.449072	+	0.449072i	0.895046	−	0.445974i	$-0.147143\pi$
$617$	11.1547	+	11.1547i	0.449072	+	0.449072i	−0.445974	+	0.895046i	$0.647143\pi$
$618$		0			0
$619$	−0.165589	−	0.399768i	−0.00665559	−	0.0160680i	0.920517	−	0.390703i	$-0.127768\pi$
$619$	−0.165589	−	0.399768i	−0.00665559	−	0.0160680i	−0.927172	+	0.374635i	$0.877768\pi$
$620$		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	0.855563	−	0.517698i	$-0.173211\pi$
$631$	8.48708	+	8.48708i	0.337865	+	0.337865i	−0.517698	+	0.855563i	$0.673211\pi$
$632$		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	$-0.942047\pi$
$643$	−4.05780	+	9.79639i	−0.160024	+	0.386332i	0.823448	+	0.567391i	$0.192047\pi$
$644$		0			0
$645$	−3.08981	+	1.27984i	−0.121661	+	0.0503937i
$646$		0			0
$647$	−26.4018	+	26.4018i	−1.03796	+	1.03796i	−0.0387106	+	0.999250i	$0.512325\pi$
$647$	−26.4018	+	26.4018i	−1.03796	+	1.03796i	−0.999250	+	0.0387106i	$0.987675\pi$
$648$		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	$-0.188233\pi$
$653$	26.1421	+	10.8284i	1.02302	+	0.423748i	0.192831	+	0.981232i	$0.438233\pi$
$654$		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	$-0.271568\pi$
$659$	15.1434	+	6.27260i	0.589903	+	0.244346i	−0.0677059	+	0.997705i	$0.521568\pi$
$660$		0			0
$661$	6.77294	+	16.3513i	0.263437	+	0.635993i	0.999147	−	0.0413040i	$-0.0131512\pi$
$661$	6.77294	+	16.3513i	0.263437	+	0.635993i	−0.735710	+	0.677297i	$0.763151\pi$
$662$		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	$-0.782224\pi$
$677$	−22.7931	+	9.44122i	−0.876011	+	0.362856i	−0.101063	+	0.994880i	$0.532224\pi$
$678$		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	0.984614	+	0.174745i	$0.0559101\pi$
$683$	10.7660	+	25.9915i	0.411950	+	0.994535i	−0.572664	+	0.819790i	$0.694090\pi$
$684$		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	$-0.364965\pi$
$691$	1.53096	+	0.634146i	0.0582406	+	0.0241240i	−0.353373	+	0.935483i	$0.614965\pi$
$692$		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	0.647826	+	0.761788i	$0.275678\pi$
$701$	−9.23819	+	22.3030i	−0.348921	+	0.842371i	−0.996748	+	0.0805829i	$0.974322\pi$
$702$		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	$-0.551068\pi$
$709$	11.3249	−	4.69095i	0.425317	−	0.176172i	0.585066	+	0.810985i	$0.301068\pi$
$710$		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	$0.114139\pi$
$719$			18.8205i			0.701888i	−0.936397	+	0.350944i	$0.885861\pi$
$720$		0			0
$721$		−	1.11366i		−	0.0414748i
$722$		0			0
$723$	−0.908754	−	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	0.946194	−	0.323601i	$-0.104893\pi$
$727$	16.7869	+	16.7869i	0.622593	+	0.622593i	−0.323601	+	0.946194i	$0.604893\pi$
$728$		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	−0.490639	−	0.871363i	$-0.663236\pi$
$733$	12.7909	−	30.8799i	0.472442	−	1.14058i	0.963081	−	0.269213i	$-0.0867636\pi$
$734$		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	$-0.796929\pi$
$739$	5.05208	−	12.1968i	0.185844	−	0.448667i	0.989152	+	0.146897i	$0.0469287\pi$
$740$		0			0
$741$	7.19615	−	2.98074i	0.264357	−	0.109500i
$742$		0			0
$743$	14.2144	−	14.2144i	0.521476	−	0.521476i	−0.396541	−	0.918017i	$-0.629789\pi$
$743$	14.2144	−	14.2144i	0.521476	−	0.521476i	0.918017	+	0.396541i	$0.129789\pi$
$744$		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	$-0.895571\pi$
$751$		−	17.6604i		−	0.644438i	0.946665	−	0.322219i	$-0.104429\pi$
$752$		0			0
$753$			4.19263i			0.152788i
$754$		0			0
$755$	−20.8125	−	8.62082i	−0.757444	−	0.313744i
$756$		0			0
$757$	−2.26500	−	5.46821i	−0.0823230	−	0.198745i	0.877358	−	0.479836i	$-0.159304\pi$
$757$	−2.26500	−	5.46821i	−0.0823230	−	0.198745i	−0.959681	+	0.281091i	$0.909304\pi$
$758$		0			0
$759$	−8.45412	−	8.45412i	−0.306865	−	0.306865i
$760$		0			0
$761$	8.84304	−	8.84304i	0.320560	−	0.320560i	−0.528422	−	0.848982i	$-0.677216\pi$
$761$	8.84304	−	8.84304i	0.320560	−	0.320560i	0.848982	+	0.528422i	$0.177216\pi$
$762$		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	$-0.486087\pi$
$773$	21.7148	−	8.99455i	0.781026	−	0.323511i	0.737329	+	0.675533i	$0.236087\pi$
$774$		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	0.982688	+	0.185266i	$0.0593148\pi$
$787$	50.7364	+	21.0157i	1.80856	+	0.749129i	0.825869	+	0.563862i	$0.190685\pi$
$788$		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	$-0.976427\pi$
$797$	−6.76906	+	16.3420i	−0.239772	+	0.578862i	0.757487	+	0.652851i	$0.226427\pi$
$798$		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	0.625656	−	0.780099i	$-0.284831\pi$
$809$	−4.39282	−	4.39282i	−0.154443	−	0.154443i	−0.780099	+	0.625656i	$0.784831\pi$
$810$		0			0
$811$	−11.2324	−	27.1174i	−0.394422	−	0.952219i	−0.988964	−	0.148155i	$-0.952667\pi$
$811$	−11.2324	−	27.1174i	−0.394422	−	0.952219i	0.594542	−	0.804065i	$-0.297333\pi$
$812$		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	0.802211	+	0.597041i	$0.203657\pi$
$821$	18.8289	+	45.4570i	0.657134	+	1.58646i	−0.145077	+	0.989420i	$0.546343\pi$
$822$		0			0
$823$	−14.4059	−	14.4059i	−0.502158	−	0.502158i	0.409950	−	0.912108i	$-0.365546\pi$
$823$	−14.4059	−	14.4059i	−0.502158	−	0.502158i	−0.912108	+	0.409950i	$0.865546\pi$
$824$		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	$-0.702089\pi$
$827$	−12.7434	+	5.27851i	−0.443133	+	0.183552i	0.149949	+	0.988694i	$0.452089\pi$
$828$		0			0
$829$	−19.9104	+	48.0679i	−0.691516	+	1.66947i	0.0501876	+	0.998740i	$0.484018\pi$
$829$	−19.9104	+	48.0679i	−0.691516	+	1.66947i	−0.741704	+	0.670728i	$0.765982\pi$
$830$		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	−0.606003	−	0.795463i	$-0.707228\pi$
$839$	5.48780	−	5.48780i	0.189460	−	0.189460i	0.795463	+	0.606003i	$0.207228\pi$
$840$		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	$-0.244540\pi$
$853$	−8.19878	−	19.7936i	−0.280721	−	0.677720i	−0.999853	+	0.0171533i	$0.994540\pi$
$854$		0			0
$855$	18.7841	+	18.7841i	0.642401	+	0.642401i
$856$		0			0
$857$	25.5086	−	25.5086i	0.871358	−	0.871358i	−0.121263	−	0.992620i	$-0.538694\pi$
$857$	25.5086	−	25.5086i	0.871358	−	0.871358i	0.992620	+	0.121263i	$0.0386943\pi$
$858$		0			0
$859$	−20.8638	+	8.64207i	−0.711864	+	0.294864i	−0.709076	−	0.705132i	$-0.750888\pi$
$859$	−20.8638	+	8.64207i	−0.711864	+	0.294864i	−0.00278818	+	0.999996i	$0.500888\pi$
$860$		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	$-0.386264\pi$
$877$	−1.93596	−	0.801899i	−0.0653726	−	0.0270782i	−0.415130	+	0.909762i	$0.636264\pi$
$878$		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
$883$	−14.1091	−	5.84419i	−0.474810	−	0.196673i	0.132428	−	0.991193i	$-0.457723\pi$
$883$	−14.1091	−	5.84419i	−0.474810	−	0.196673i	−0.607238	+	0.794520i	$0.707723\pi$
$884$		0			0
$885$	0.830351	+	2.00464i	0.0279119	+	0.0673854i
$886$		0			0
$887$	26.9437	+	26.9437i	0.904679	+	0.904679i	0.995837	−	0.0911573i	$-0.0290566\pi$
$887$	26.9437	+	26.9437i	0.904679	+	0.904679i	−0.0911573	+	0.995837i	$0.529057\pi$
$888$		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	$-0.0715843\pi$
$907$	3.84992	+	9.29454i	0.127835	+	0.308620i	−0.846984	+	0.531618i	$0.821584\pi$
$908$		0			0
$909$	20.0541	+	8.30669i	0.665153	+	0.275515i
$910$		0			0
$911$			17.1254i			0.567389i	0.958915	+	0.283694i	$0.0915601\pi$
$911$			17.1254i			0.567389i	−0.958915	+	0.283694i	$0.908440\pi$
$912$		0			0
$913$		−	47.8909i		−	1.58496i
$914$		0			0
$915$	−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	0.999249	−	0.0387392i	$-0.0123342\pi$
$919$	29.1179	+	29.1179i	0.960510	+	0.960510i	−0.0387392	+	0.999249i	$0.512334\pi$
$920$		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	0.118127	−	0.992998i	$-0.462311\pi$
$937$	−26.7802	−	26.7802i	−0.874871	−	0.874871i	−0.992998	+	0.118127i	$0.962311\pi$
$938$		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	$-0.130620\pi$
$941$	39.3660	+	16.3059i	1.28329	+	0.531558i	0.366314	+	0.930491i	$0.380620\pi$
$942$		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	$-0.381301\pi$
$947$	−1.12544	−	0.466171i	−0.0365718	−	0.0151485i	−0.400894	+	0.916124i	$0.631301\pi$
$948$		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	−0.0180517	+	0.999837i	$0.505746\pi$
$953$	−31.4229	+	31.4229i	−1.01789	+	1.01789i	−0.999837	+	0.0180517i	$0.994254\pi$
$954$		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	−0.361178	−	0.932497i	$-0.617625\pi$
$967$	17.7661	−	17.7661i	0.571319	−	0.571319i	0.932497	+	0.361178i	$0.117625\pi$
$968$		0			0
$969$	−6.88901	−	6.88901i	−0.221307	−	0.221307i
$970$		0			0
$971$	−22.2407	−	53.6939i	−0.713739	−	1.72312i	−0.690440	−	0.723390i	$-0.742583\pi$
$971$	−22.2407	−	53.6939i	−0.713739	−	1.72312i	−0.0232989	−	0.999729i	$-0.507417\pi$
$972$		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	$-0.915747\pi$
$977$		−	16.3541i		−	0.523215i	0.965174	−	0.261608i	$-0.0842527\pi$
$978$		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	0.618676	−	0.785646i	$-0.287669\pi$
$983$	−5.23497	−	5.23497i	−0.166970	−	0.166970i	−0.785646	+	0.618676i	$0.787669\pi$
$984$		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	$-0.457043\pi$
$997$	29.3764	−	12.1681i	0.930361	−	0.385368i	0.795815	+	0.605539i	$0.207043\pi$
$998$		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.a.129.3	yes	16
4.3	odd	2	inner	1024.2.g.a.129.2	✓	16
8.3	odd	2		1024.2.g.f.129.3	yes	16
8.5	even	2		1024.2.g.f.129.2	yes	16
16.3	odd	4		1024.2.g.d.641.2	yes	16
16.5	even	4		1024.2.g.g.641.2	yes	16
16.11	odd	4		1024.2.g.g.641.3	yes	16
16.13	even	4		1024.2.g.d.641.3	yes	16
32.3	odd	8		1024.2.g.d.385.2	yes	16
32.5	even	8	inner	1024.2.g.a.897.3	yes	16
32.11	odd	8		1024.2.g.f.897.3	yes	16
32.13	even	8		1024.2.g.g.385.2	yes	16
32.19	odd	8		1024.2.g.g.385.3	yes	16
32.21	even	8		1024.2.g.f.897.2	yes	16
32.27	odd	8	inner	1024.2.g.a.897.2	yes	16
32.29	even	8		1024.2.g.d.385.3	yes	16
64.5	even	16		4096.2.a.s.1.3		8
64.27	odd	16		4096.2.a.s.1.4		8
64.37	even	16		4096.2.a.i.1.6		8
64.59	odd	16		4096.2.a.i.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.a.129.2	✓	16	4.3	odd	2	inner
1024.2.g.a.129.3	yes	16	1.1	even	1	trivial
1024.2.g.a.897.2	yes	16	32.27	odd	8	inner
1024.2.g.a.897.3	yes	16	32.5	even	8	inner
1024.2.g.d.385.2	yes	16	32.3	odd	8
1024.2.g.d.385.3	yes	16	32.29	even	8
1024.2.g.d.641.2	yes	16	16.3	odd	4
1024.2.g.d.641.3	yes	16	16.13	even	4
1024.2.g.f.129.2	yes	16	8.5	even	2
1024.2.g.f.129.3	yes	16	8.3	odd	2
1024.2.g.f.897.2	yes	16	32.21	even	8
1024.2.g.f.897.3	yes	16	32.11	odd	8
1024.2.g.g.385.2	yes	16	32.13	even	8
1024.2.g.g.385.3	yes	16	32.19	odd	8
1024.2.g.g.641.2	yes	16	16.5	even	4
1024.2.g.g.641.3	yes	16	16.11	odd	4
4096.2.a.i.1.5		8	64.59	odd	16
4096.2.a.i.1.6		8	64.37	even	16
4096.2.a.s.1.3		8	64.5	even	16
4096.2.a.s.1.4		8	64.27	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

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Database

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