LMFDB - Embedded newform 510.2.u.c.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(121,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 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("510.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.u (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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 220x^{12} + 1016x^{10} + 2568x^{8} + 3552x^{6} + 2472x^{4} + 656x^{2} + 4 $ x^16 + 24x^14 + 220x^12 + 1016x^10 + 2568x^8 + 3552x^6 + 2472x^4 + 656*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			151.4
Root			$-1.55788i$ of defining polynomial
Character	$\chi$	$=$	510.151
Dual form			510.2.u.c.331.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.923880 - 0.382683i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(4.44110 + 1.83956i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.923880 - 0.382683i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(4.44110 + 1.83956i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(0.923880 + 0.382683i) q^{10} +(1.01668 - 2.45448i) q^{11} +(-0.923880 + 0.382683i) q^{12} -4.55356i q^{13} +(1.83956 + 4.44110i) q^{14} +(0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-0.850770 + 4.03438i) q^{17} -1.00000 q^{18} +(-4.27410 - 4.27410i) q^{19} +(0.382683 + 0.923880i) q^{20} +4.80701i q^{21} +(2.45448 - 1.01668i) q^{22} +(-1.65323 + 3.99125i) q^{23} +(-0.923880 - 0.382683i) q^{24} +(0.707107 - 0.707107i) q^{25} +(3.21985 - 3.21985i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.83956 + 4.44110i) q^{28} +(-3.75548 + 1.55557i) q^{29} +1.00000i q^{30} +(1.50736 + 3.63909i) q^{31} +(-0.707107 - 0.707107i) q^{32} +2.65672 q^{33} +(-3.45432 + 2.25115i) q^{34} +4.80701 q^{35} +(-0.707107 - 0.707107i) q^{36} +(2.11652 + 5.10973i) q^{37} -6.04449i q^{38} +(4.20694 - 1.74257i) q^{39} +(-0.382683 + 0.923880i) q^{40} +(-10.4762 - 4.33938i) q^{41} +(-3.39907 + 3.39907i) q^{42} +(5.51985 - 5.51985i) q^{43} +(2.45448 + 1.01668i) q^{44} +(-0.382683 + 0.923880i) q^{45} +(-3.99125 + 1.65323i) q^{46} -1.83866i q^{47} +(-0.382683 - 0.923880i) q^{48} +(11.3896 + 11.3896i) q^{49} +1.00000 q^{50} +(-4.05285 + 0.757880i) q^{51} +4.55356 q^{52} +(-4.15958 - 4.15958i) q^{53} +(-0.382683 - 0.923880i) q^{54} -2.65672i q^{55} +(-4.44110 + 1.83956i) q^{56} +(2.31313 - 5.58438i) q^{57} +(-3.75548 - 1.55557i) q^{58} +(2.47756 - 2.47756i) q^{59} +(-0.707107 + 0.707107i) q^{60} +(-7.08104 - 2.93306i) q^{61} +(-1.50736 + 3.63909i) q^{62} +(-4.44110 + 1.83956i) q^{63} -1.00000i q^{64} +(-1.74257 - 4.20694i) q^{65} +(1.87858 + 1.87858i) q^{66} -13.8487 q^{67} +(-4.03438 - 0.850770i) q^{68} -4.32010 q^{69} +(3.39907 + 3.39907i) q^{70} +(1.86238 + 4.49618i) q^{71} -1.00000i q^{72} +(7.79280 - 3.22788i) q^{73} +(-2.11652 + 5.10973i) q^{74} +(0.923880 + 0.382683i) q^{75} +(4.27410 - 4.27410i) q^{76} +(9.03036 - 9.03036i) q^{77} +(4.20694 + 1.74257i) q^{78} +(5.02704 - 12.1364i) q^{79} +(-0.923880 + 0.382683i) q^{80} -1.00000i q^{81} +(-4.33938 - 10.4762i) q^{82} +(-12.5025 - 12.5025i) q^{83} -4.80701 q^{84} +(0.757880 + 4.05285i) q^{85} +7.80625 q^{86} +(-2.87432 - 2.87432i) q^{87} +(1.01668 + 2.45448i) q^{88} +15.5491i q^{89} +(-0.923880 + 0.382683i) q^{90} +(8.37656 - 20.2228i) q^{91} +(-3.99125 - 1.65323i) q^{92} +(-2.78524 + 2.78524i) q^{93} +(1.30013 - 1.30013i) q^{94} +(-5.58438 - 2.31313i) q^{95} +(0.382683 - 0.923880i) q^{96} +(15.8549 - 6.56732i) q^{97} +16.1074i q^{98} +(1.01668 + 2.45448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 8 q^{14} - 16 q^{16} - 16 q^{18} + 16 q^{19} + 16 q^{23} - 8 q^{28} - 32 q^{29} + 16 q^{33} + 16 q^{35} + 32 q^{37} + 8 q^{39} - 56 q^{41} - 16 q^{42} + 16 q^{43} - 16 q^{49} + 16 q^{50} - 24 q^{51} - 16 q^{53} + 8 q^{56} + 16 q^{57} - 32 q^{58} - 16 q^{59} + 16 q^{61} + 8 q^{63} + 8 q^{65} - 16 q^{66} + 16 q^{67} - 16 q^{68} + 16 q^{70} + 72 q^{71} + 8 q^{73} - 32 q^{74} - 16 q^{76} + 48 q^{77} + 8 q^{78} + 8 q^{82} - 80 q^{83} - 16 q^{84} + 8 q^{85} + 16 q^{86} - 16 q^{87} - 16 q^{93} - 16 q^{94} + 72 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 8 * q^14 - 16 * q^16 - 16 * q^18 + 16 * q^19 + 16 * q^23 - 8 * q^28 - 32 * q^29 + 16 * q^33 + 16 * q^35 + 32 * q^37 + 8 * q^39 - 56 * q^41 - 16 * q^42 + 16 * q^43 - 16 * q^49 + 16 * q^50 - 24 * q^51 - 16 * q^53 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 16 * q^59 + 16 * q^61 + 8 * q^63 + 8 * q^65 - 16 * q^66 + 16 * q^67 - 16 * q^68 + 16 * q^70 + 72 * q^71 + 8 * q^73 - 32 * q^74 - 16 * q^76 + 48 * q^77 + 8 * q^78 + 8 * q^82 - 80 * q^83 - 16 * q^84 + 8 * q^85 + 16 * q^86 - 16 * q^87 - 16 * q^93 - 16 * q^94 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$3$	0.382683	+	0.923880i	0.220942	+	0.533402i
$4$			1.00000i			0.500000i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$6$	−0.382683	+	0.923880i	−0.156230	+	0.377172i
$7$	4.44110	+	1.83956i	1.67858	+	0.695290i	0.999257	−	0.0385510i	$-0.0122742\pi$
$7$	4.44110	+	1.83956i	1.67858	+	0.695290i	0.679321	+	0.733841i	$0.262274\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	0.923880	+	0.382683i	0.292156	+	0.121015i
$11$	1.01668	−	2.45448i	0.306541	−	0.740055i	−0.693271	−	0.720677i	$-0.743831\pi$
$11$	1.01668	−	2.45448i	0.306541	−	0.740055i	0.999812	−	0.0193784i	$-0.00616872\pi$
$12$	−0.923880	+	0.382683i	−0.266701	+	0.110471i
$13$		−	4.55356i		−	1.26293i	−0.775405	−	0.631465i	$-0.782454\pi$
$13$		−	4.55356i		−	1.26293i	0.775405	−	0.631465i	$-0.217546\pi$
$14$	1.83956	+	4.44110i	0.491644	+	1.18693i
$15$	0.707107	+	0.707107i	0.182574	+	0.182574i
$16$	−1.00000			−0.250000
$17$	−0.850770	+	4.03438i	−0.206342	+	0.978480i
$17$	−0.850770	+	4.03438i	−0.206342	+	0.978480i
$18$	−1.00000			−0.235702
$19$	−4.27410	−	4.27410i	−0.980546	−	0.980546i	0.0192687	−	0.999814i	$-0.493866\pi$
$19$	−4.27410	−	4.27410i	−0.980546	−	0.980546i	−0.999814	+	0.0192687i	$0.993866\pi$
$20$	0.382683	+	0.923880i	0.0855706	+	0.206586i
$21$			4.80701i			1.04898i
$22$	2.45448	−	1.01668i	0.523298	−	0.216757i
$23$	−1.65323	+	3.99125i	−0.344723	+	0.832234i	0.652502	+	0.757787i	$0.273719\pi$
$23$	−1.65323	+	3.99125i	−0.344723	+	0.832234i	−0.997225	+	0.0744472i	$0.976281\pi$
$24$	−0.923880	−	0.382683i	−0.188586	−	0.0781149i
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	3.21985	−	3.21985i	0.631465	−	0.631465i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	−1.83956	+	4.44110i	−0.347645	+	0.839289i
$29$	−3.75548	+	1.55557i	−0.697376	+	0.288863i	−0.703069	−	0.711121i	$-0.748188\pi$
$29$	−3.75548	+	1.55557i	−0.697376	+	0.288863i	0.00569354	+	0.999984i	$0.498188\pi$
$30$			1.00000i			0.182574i
$31$	1.50736	+	3.63909i	0.270730	+	0.653599i	0.999515	−	0.0311430i	$-0.00991474\pi$
$31$	1.50736	+	3.63909i	0.270730	+	0.653599i	−0.728785	+	0.684742i	$0.759915\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.65672			0.462475
$34$	−3.45432	+	2.25115i	−0.592411	+	0.386069i
$35$	4.80701			0.812533
$36$	−0.707107	−	0.707107i	−0.117851	−	0.117851i
$37$	2.11652	+	5.10973i	0.347954	+	0.840035i	0.996861	+	0.0791675i	$0.0252262\pi$
$37$	2.11652	+	5.10973i	0.347954	+	0.840035i	−0.648908	+	0.760867i	$0.724774\pi$
$38$		−	6.04449i		−	0.980546i
$39$	4.20694	−	1.74257i	0.673649	−	0.279035i
$40$	−0.382683	+	0.923880i	−0.0605076	+	0.146078i
$41$	−10.4762	−	4.33938i	−1.63610	−	0.677697i	−0.640209	−	0.768201i	$-0.721152\pi$
$41$	−10.4762	−	4.33938i	−1.63610	−	0.677697i	−0.995896	+	0.0905045i	$0.971152\pi$
$42$	−3.39907	+	3.39907i	−0.524488	+	0.524488i
$43$	5.51985	−	5.51985i	0.841769	−	0.841769i	−0.147319	−	0.989089i	$-0.547065\pi$
$43$	5.51985	−	5.51985i	0.841769	−	0.841769i	0.989089	+	0.147319i	$0.0470645\pi$
$44$	2.45448	+	1.01668i	0.370027	+	0.153270i
$45$	−0.382683	+	0.923880i	−0.0570471	+	0.137724i
$46$	−3.99125	+	1.65323i	−0.588478	+	0.243756i
$47$		−	1.83866i		−	0.268196i	−0.990968	−	0.134098i	$-0.957186\pi$
$47$		−	1.83866i		−	0.268196i	0.990968	−	0.134098i	$-0.0428136\pi$
$48$	−0.382683	−	0.923880i	−0.0552356	−	0.133351i
$49$	11.3896	+	11.3896i	1.62709	+	1.62709i
$50$	1.00000			0.141421
$51$	−4.05285	+	0.757880i	−0.567513	+	0.106124i
$52$	4.55356			0.631465
$53$	−4.15958	−	4.15958i	−0.571362	−	0.571362i	0.361147	−	0.932509i	$-0.382385\pi$
$53$	−4.15958	−	4.15958i	−0.571362	−	0.571362i	−0.932509	+	0.361147i	$0.882385\pi$
$54$	−0.382683	−	0.923880i	−0.0520766	−	0.125724i
$55$		−	2.65672i		−	0.358231i
$56$	−4.44110	+	1.83956i	−0.593467	+	0.245822i
$57$	2.31313	−	5.58438i	0.306381	−	0.739669i
$58$	−3.75548	−	1.55557i	−0.493119	−	0.204257i
$59$	2.47756	−	2.47756i	0.322551	−	0.322551i	−0.527194	−	0.849745i	$-0.676756\pi$
$59$	2.47756	−	2.47756i	0.322551	−	0.322551i	0.849745	+	0.527194i	$0.176756\pi$
$60$	−0.707107	+	0.707107i	−0.0912871	+	0.0912871i
$61$	−7.08104	−	2.93306i	−0.906635	−	0.375540i	−0.119867	−	0.992790i	$-0.538247\pi$
$61$	−7.08104	−	2.93306i	−0.906635	−	0.375540i	−0.786767	+	0.617250i	$0.788247\pi$
$62$	−1.50736	+	3.63909i	−0.191435	+	0.462165i
$63$	−4.44110	+	1.83956i	−0.559526	+	0.231763i
$64$		−	1.00000i		−	0.125000i
$65$	−1.74257	−	4.20694i	−0.216139	−	0.521807i
$66$	1.87858	+	1.87858i	0.231237	+	0.231237i
$67$	−13.8487			−1.69189			−0.845946	−	0.533268i	$-0.820964\pi$
$67$	−13.8487			−1.69189			−0.845946	+	0.533268i	$0.820964\pi$
$68$	−4.03438	−	0.850770i	−0.489240	−	0.103171i
$69$	−4.32010			−0.520079
$70$	3.39907	+	3.39907i	0.406267	+	0.406267i
$71$	1.86238	+	4.49618i	0.221024	+	0.533598i	0.995030	−	0.0995801i	$-0.0317499\pi$
$71$	1.86238	+	4.49618i	0.221024	+	0.533598i	−0.774006	+	0.633178i	$0.781750\pi$
$72$		−	1.00000i		−	0.117851i
$73$	7.79280	−	3.22788i	0.912078	−	0.377795i	0.123226	−	0.992379i	$-0.460676\pi$
$73$	7.79280	−	3.22788i	0.912078	−	0.377795i	0.788852	+	0.614584i	$0.210676\pi$
$74$	−2.11652	+	5.10973i	−0.246040	+	0.593994i
$75$	0.923880	+	0.382683i	0.106680	+	0.0441885i
$76$	4.27410	−	4.27410i	0.490273	−	0.490273i
$77$	9.03036	−	9.03036i	1.02911	−	1.02911i
$78$	4.20694	+	1.74257i	0.476342	+	0.197307i
$79$	5.02704	−	12.1364i	0.565587	−	1.36545i	−0.339655	−	0.940550i	$-0.610310\pi$
$79$	5.02704	−	12.1364i	0.565587	−	1.36545i	0.905242	−	0.424897i	$-0.139690\pi$
$80$	−0.923880	+	0.382683i	−0.103293	+	0.0427853i
$81$		−	1.00000i		−	0.111111i
$82$	−4.33938	−	10.4762i	−0.479204	−	1.15690i
$83$	−12.5025	−	12.5025i	−1.37233	−	1.37233i	−0.856978	−	0.515353i	$-0.827661\pi$
$83$	−12.5025	−	12.5025i	−1.37233	−	1.37233i	−0.515353	−	0.856978i	$-0.672339\pi$
$84$	−4.80701			−0.524488
$85$	0.757880	+	4.05285i	0.0822036	+	0.439594i
$86$	7.80625			0.841769
$87$	−2.87432	−	2.87432i	−0.308160	−	0.308160i
$88$	1.01668	+	2.45448i	0.108379	+	0.261649i
$89$			15.5491i			1.64820i	0.566443	+	0.824101i	$0.308319\pi$
$89$			15.5491i			1.64820i	−0.566443	+	0.824101i	$0.691681\pi$
$90$	−0.923880	+	0.382683i	−0.0973855	+	0.0403384i
$91$	8.37656	−	20.2228i	0.878102	−	2.11993i
$92$	−3.99125	−	1.65323i	−0.416117	−	0.172361i
$93$	−2.78524	+	2.78524i	−0.288816	+	0.288816i
$94$	1.30013	−	1.30013i	0.134098	−	0.134098i
$95$	−5.58438	−	2.31313i	−0.572945	−	0.237322i
$96$	0.382683	−	0.923880i	0.0390575	−	0.0942931i
$97$	15.8549	−	6.56732i	1.60982	−	0.666810i	0.617061	−	0.786916i	$-0.288323\pi$
$97$	15.8549	−	6.56732i	1.60982	−	0.666810i	0.992761	+	0.120106i	$0.0383233\pi$
$98$			16.1074i			1.62709i
$99$	1.01668	+	2.45448i	0.102180	+	0.246685i
$100$	0.707107	+	0.707107i	0.0707107	+	0.0707107i
$101$	6.08472			0.605452			0.302726	−	0.953078i	$-0.402103\pi$
$101$	6.08472			0.605452			0.302726	+	0.953078i	$0.402103\pi$
$102$	−3.40170	−	2.32990i	−0.336819	−	0.230694i
$103$	−1.35517			−0.133529			−0.0667645	−	0.997769i	$-0.521268\pi$
$103$	−1.35517			−0.133529			−0.0667645	+	0.997769i	$0.521268\pi$
$104$	3.21985	+	3.21985i	0.315732	+	0.315732i
$105$	1.83956	+	4.44110i	0.179523	+	0.433407i
$106$		−	5.88254i		−	0.571362i
$107$	2.86408	−	1.18634i	0.276881	−	0.114688i	−0.239922	−	0.970792i	$-0.577122\pi$
$107$	2.86408	−	1.18634i	0.276881	−	0.114688i	0.516803	+	0.856104i	$0.327122\pi$
$108$	0.382683	−	0.923880i	0.0368237	−	0.0889003i
$109$	14.2692	+	5.91050i	1.36674	+	0.566123i	0.940903	−	0.338676i	$-0.109979\pi$
$109$	14.2692	+	5.91050i	1.36674	+	0.566123i	0.425839	+	0.904799i	$0.359979\pi$
$110$	1.87858	−	1.87858i	0.179116	−	0.179116i
$111$	−3.91082	+	3.91082i	−0.371199	+	0.371199i
$112$	−4.44110	−	1.83956i	−0.419645	−	0.173822i
$113$	1.58906	−	3.83634i	0.149486	−	0.360892i	−0.831343	−	0.555759i	$-0.812428\pi$
$113$	1.58906	−	3.83634i	0.149486	−	0.360892i	0.980830	+	0.194867i	$0.0624276\pi$
$114$	5.58438	−	2.31313i	0.523025	−	0.216644i
$115$			4.32010i			0.402852i
$116$	−1.55557	−	3.75548i	−0.144431	−	0.348688i
$117$	3.21985	+	3.21985i	0.297675	+	0.297675i
$118$	3.50381			0.322551
$119$	−11.1998	+	16.3520i	−1.02669	+	1.49899i
$120$	−1.00000			−0.0912871
$121$	2.78732	+	2.78732i	0.253393	+	0.253393i
$122$	−2.93306	−	7.08104i	−0.265547	−	0.641087i
$123$		−	11.3393i		−	1.02243i
$124$	−3.63909	+	1.50736i	−0.326800	+	0.135365i
$125$	0.382683	−	0.923880i	0.0342282	−	0.0826343i
$126$	−4.44110	−	1.83956i	−0.395645	−	0.163881i
$127$	−9.25807	+	9.25807i	−0.821521	+	0.821521i	−0.986326	−	0.164805i	$-0.947301\pi$
$127$	−9.25807	+	9.25807i	−0.821521	+	0.821521i	0.164805	+	0.986326i	$0.447301\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	7.21203	+	2.98732i	0.634984	+	0.263019i
$130$	1.74257	−	4.20694i	0.152834	−	0.368973i
$131$	−5.00710	+	2.07401i	−0.437473	+	0.181207i	−0.590539	−	0.807009i	$-0.701085\pi$
$131$	−5.00710	+	2.07401i	−0.437473	+	0.181207i	0.153067	+	0.988216i	$0.451085\pi$
$132$			2.65672i			0.231237i
$133$	−11.1192	−	26.8442i	−0.964159	−	2.32769i
$134$	−9.79253	−	9.79253i	−0.845946	−	0.845946i
$135$	−1.00000			−0.0860663
$136$	−2.25115	−	3.45432i	−0.193034	−	0.296205i
$137$	7.13674			0.609733			0.304866	−	0.952395i	$-0.401388\pi$
$137$	7.13674			0.609733			0.304866	+	0.952395i	$0.401388\pi$
$138$	−3.05477	−	3.05477i	−0.260040	−	0.260040i
$139$	2.78604	+	6.72611i	0.236309	+	0.570501i	0.996896	−	0.0787360i	$-0.0250884\pi$
$139$	2.78604	+	6.72611i	0.236309	+	0.570501i	−0.760586	+	0.649237i	$0.775088\pi$
$140$			4.80701i			0.406267i
$141$	1.69870	−	0.703623i	0.143056	−	0.0592558i
$142$	−1.86238	+	4.49618i	−0.156287	+	0.377311i
$143$	−11.1766	−	4.62951i	−0.934637	−	0.387139i
$144$	0.707107	−	0.707107i	0.0589256	−	0.0589256i
$145$	−2.87432	+	2.87432i	−0.238700	+	0.238700i
$146$	7.79280	+	3.22788i	0.644936	+	0.267141i
$147$	−6.16402	+	14.8813i	−0.508400	+	1.22739i
$148$	−5.10973	+	2.11652i	−0.420017	+	0.173977i
$149$		−	0.266600i		−	0.0218407i	−0.999940	−	0.0109204i	$-0.996524\pi$
$149$		−	0.266600i		−	0.0218407i	0.999940	−	0.0109204i	$-0.00347612\pi$
$150$	0.382683	+	0.923880i	0.0312460	+	0.0754344i
$151$	−9.26764	−	9.26764i	−0.754190	−	0.754190i	0.221068	−	0.975258i	$-0.429046\pi$
$151$	−9.26764	−	9.26764i	−0.754190	−	0.754190i	−0.975258	+	0.221068i	$0.929046\pi$
$152$	6.04449			0.490273
$153$	−2.25115	−	3.45432i	−0.181995	−	0.279265i
$154$	12.7709			1.02911
$155$	2.78524	+	2.78524i	0.223716	+	0.223716i
$156$	1.74257	+	4.20694i	0.139517	+	0.336825i
$157$			2.93377i			0.234140i	0.993124	+	0.117070i	$0.0373502\pi$
$157$			2.93377i			0.234140i	−0.993124	+	0.117070i	$0.962650\pi$
$158$	12.1364	−	5.02704i	0.965517	−	0.399930i
$159$	2.25115	−	5.43476i	0.178528	−	0.431004i
$160$	−0.923880	−	0.382683i	−0.0730391	−	0.0302538i
$161$	−14.6843	+	14.6843i	−1.15729	+	1.15729i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	8.44338	+	3.49736i	0.661336	+	0.273934i	0.688001	−	0.725710i	$-0.258489\pi$
$163$	8.44338	+	3.49736i	0.661336	+	0.273934i	−0.0266644	+	0.999644i	$0.508489\pi$
$164$	4.33938	−	10.4762i	0.338848	−	0.818052i
$165$	2.45448	−	1.01668i	0.191081	−	0.0791485i
$166$		−	17.6812i		−	1.37233i
$167$	−7.29639	−	17.6150i	−0.564611	−	1.36309i	−0.906043	−	0.423186i	$-0.860912\pi$
$167$	−7.29639	−	17.6150i	−0.564611	−	1.36309i	0.341431	−	0.939907i	$-0.389088\pi$
$168$	−3.39907	−	3.39907i	−0.262244	−	0.262244i
$169$	−7.73489			−0.594991
$170$	−2.32990	+	3.40170i	−0.178695	+	0.260899i
$171$	6.04449			0.462234
$172$	5.51985	+	5.51985i	0.420885	+	0.420885i
$173$	1.98870	+	4.80116i	0.151198	+	0.365025i	0.981272	−	0.192629i	$-0.0617015\pi$
$173$	1.98870	+	4.80116i	0.151198	+	0.365025i	−0.830073	+	0.557654i	$0.811701\pi$
$174$		−	4.06491i		−	0.308160i
$175$	4.44110	−	1.83956i	0.335716	−	0.139058i
$176$	−1.01668	+	2.45448i	−0.0766352	+	0.185014i
$177$	3.23709	+	1.34085i	0.243315	+	0.100784i
$178$	−10.9949	+	10.9949i	−0.824101	+	0.824101i
$179$	−0.147827	+	0.147827i	−0.0110491	+	0.0110491i	−0.712610	−	0.701561i	$-0.752487\pi$
$179$	−0.147827	+	0.147827i	−0.0110491	+	0.0110491i	0.701561	+	0.712610i	$0.252487\pi$
$180$	−0.923880	−	0.382683i	−0.0688619	−	0.0285235i
$181$	−5.51860	+	13.3231i	−0.410194	+	0.990297i	0.574891	+	0.818230i	$0.305044\pi$
$181$	−5.51860	+	13.3231i	−0.410194	+	0.990297i	−0.985085	+	0.172067i	$0.944956\pi$
$182$	20.2228	−	8.37656i	1.49901	−	0.620912i
$183$		−	7.66447i		−	0.566574i
$184$	−1.65323	−	3.99125i	−0.121878	−	0.294239i
$185$	3.91082	+	3.91082i	0.287529	+	0.287529i
$186$	−3.93892			−0.288816
$187$	9.03735	+	6.18988i	0.660877	+	0.452648i
$188$	1.83866			0.134098
$189$	−3.39907	−	3.39907i	−0.247246	−	0.247246i
$190$	−2.31313	−	5.58438i	−0.167812	−	0.405133i
$191$			12.3810i			0.895857i	0.894069	+	0.447928i	$0.147838\pi$
$191$			12.3810i			0.895857i	−0.894069	+	0.447928i	$0.852162\pi$
$192$	0.923880	−	0.382683i	0.0666753	−	0.0276178i
$193$	1.37528	−	3.32022i	0.0989949	−	0.238995i	−0.866621	−	0.498966i	$-0.833713\pi$
$193$	1.37528	−	3.32022i	0.0989949	−	0.238995i	0.965616	+	0.259971i	$0.0837131\pi$
$194$	15.8549	+	6.56732i	1.13832	+	0.471506i
$195$	3.21985	−	3.21985i	0.230578	−	0.230578i
$196$	−11.3896	+	11.3896i	−0.813545	+	0.813545i
$197$	4.44333	+	1.84049i	0.316574	+	0.131129i	0.535312	−	0.844654i	$-0.320194\pi$
$197$	4.44333	+	1.84049i	0.316574	+	0.131129i	−0.218738	+	0.975784i	$0.570194\pi$
$198$	−1.01668	+	2.45448i	−0.0722524	+	0.174433i
$199$	−4.10618	+	1.70083i	−0.291079	+	0.120569i	−0.523445	−	0.852060i	$-0.675353\pi$
$199$	−4.10618	+	1.70083i	−0.291079	+	0.120569i	0.232366	+	0.972628i	$0.425353\pi$
$200$			1.00000i			0.0707107i
$201$	−5.29968	−	12.7946i	−0.373811	−	0.902459i
$202$	4.30255	+	4.30255i	0.302726	+	0.302726i
$203$	−19.5401			−1.37144
$204$	−0.757880	−	4.05285i	−0.0530622	−	0.283756i
$205$	−11.3393			−0.791974
$206$	−0.958251	−	0.958251i	−0.0667645	−	0.0667645i
$207$	−1.65323	−	3.99125i	−0.114908	−	0.277411i
$208$			4.55356i			0.315732i
$209$	−14.8361	+	6.14532i	−1.02623	+	0.425080i
$210$	−1.83956	+	4.44110i	−0.126942	+	0.306465i
$211$	−14.4059	−	5.96712i	−0.991744	−	0.410794i	−0.172981	−	0.984925i	$-0.555340\pi$
$211$	−14.4059	−	5.96712i	−0.991744	−	0.410794i	−0.818763	+	0.574131i	$0.805340\pi$
$212$	4.15958	−	4.15958i	0.285681	−	0.285681i
$213$	−3.44123	+	3.44123i	−0.235789	+	0.235789i
$214$	2.86408	+	1.18634i	0.195784	+	0.0810966i
$215$	2.98732	−	7.21203i	0.203734	−	0.491857i
$216$	0.923880	−	0.382683i	0.0628620	−	0.0260383i
$217$			18.9344i			1.28535i
$218$	5.91050	+	14.2692i	0.400310	+	0.966433i
$219$	5.96435	+	5.96435i	0.403033	+	0.403033i
$220$	2.65672			0.179116
$221$	18.3708	+	3.87403i	1.23575	+	0.260596i
$222$	−5.53073			−0.371199
$223$	0.174650	+	0.174650i	0.0116954	+	0.0116954i	0.712930	−	0.701235i	$-0.247368\pi$
$223$	0.174650	+	0.174650i	0.0116954	+	0.0116954i	−0.701235	+	0.712930i	$0.747368\pi$
$224$	−1.83956	−	4.44110i	−0.122911	−	0.296733i
$225$			1.00000i			0.0666667i
$226$	3.83634	−	1.58906i	0.255189	−	0.105703i
$227$	0.0789675	−	0.190644i	0.00524126	−	0.0126535i	−0.921237	−	0.389001i	$-0.872820\pi$
$227$	0.0789675	−	0.190644i	0.00524126	−	0.0126535i	0.926478	+	0.376348i	$0.122820\pi$
$228$	5.58438	+	2.31313i	0.369835	+	0.153191i
$229$	9.08336	−	9.08336i	0.600246	−	0.600246i	−0.340132	−	0.940378i	$-0.610472\pi$
$229$	9.08336	−	9.08336i	0.600246	−	0.600246i	0.940378	+	0.340132i	$0.110472\pi$
$230$	−3.05477	+	3.05477i	−0.201426	+	0.201426i
$231$	11.7987	+	4.88720i	0.776300	+	0.321554i
$232$	1.55557	−	3.75548i	0.102128	−	0.246560i
$233$	0.152513	−	0.0631728i	0.00999143	−	0.00413859i	−0.377682	−	0.925935i	$-0.623279\pi$
$233$	0.152513	−	0.0631728i	0.00999143	−	0.00413859i	0.387674	+	0.921797i	$0.373279\pi$
$234$			4.55356i			0.297675i
$235$	−0.703623	−	1.69870i	−0.0458993	−	0.110811i
$236$	2.47756	+	2.47756i	0.161276	+	0.161276i
$237$	13.1363			0.853294
$238$	−19.4821	+	3.64314i	−1.26284	+	0.236150i
$239$	19.2098			1.24258			0.621288	−	0.783582i	$-0.286610\pi$
$239$	19.2098			1.24258			0.621288	+	0.783582i	$0.286610\pi$
$240$	−0.707107	−	0.707107i	−0.0456435	−	0.0456435i
$241$	1.74161	+	4.20462i	0.112187	+	0.270843i	0.969994	−	0.243128i	$-0.0781736\pi$
$241$	1.74161	+	4.20462i	0.112187	+	0.270843i	−0.857807	+	0.513972i	$0.828174\pi$
$242$			3.94187i			0.253393i
$243$	0.923880	−	0.382683i	0.0592669	−	0.0245492i
$244$	2.93306	−	7.08104i	0.187770	−	0.453317i
$245$	14.8813	+	6.16402i	0.950729	+	0.393805i
$246$	8.01812	−	8.01812i	0.511217	−	0.511217i
$247$	−19.4624	+	19.4624i	−1.23836	+	1.23836i
$248$	−3.63909	−	1.50736i	−0.231082	−	0.0957174i
$249$	6.76632	−	16.3353i	0.428798	−	1.03521i
$250$	0.923880	−	0.382683i	0.0584313	−	0.0242030i
$251$			12.6713i			0.799805i	0.916558	+	0.399903i	$0.130956\pi$
$251$			12.6713i			0.799805i	−0.916558	+	0.399903i	$0.869044\pi$
$252$	−1.83956	−	4.44110i	−0.115882	−	0.279763i
$253$	8.11566	+	8.11566i	0.510227	+	0.510227i
$254$	−13.0929			−0.821521
$255$	−3.45432	+	2.25115i	−0.216318	+	0.140972i
$256$	1.00000			0.0625000
$257$	−7.60700	−	7.60700i	−0.474512	−	0.474512i	0.428859	−	0.903371i	$-0.358916\pi$
$257$	−7.60700	−	7.60700i	−0.474512	−	0.474512i	−0.903371	+	0.428859i	$0.858916\pi$
$258$	2.98732	+	7.21203i	0.185983	+	0.449002i
$259$			26.5863i			1.65199i
$260$	4.20694	−	1.74257i	0.260903	−	0.108070i
$261$	1.55557	−	3.75548i	0.0962875	−	0.232459i
$262$	−5.00710	−	2.07401i	−0.309340	−	0.128133i
$263$	−6.20627	+	6.20627i	−0.382695	+	0.382695i	−0.872072	−	0.489377i	$-0.837224\pi$
$263$	−6.20627	+	6.20627i	−0.382695	+	0.382695i	0.489377	+	0.872072i	$0.337224\pi$
$264$	−1.87858	+	1.87858i	−0.115619	+	0.115619i
$265$	−5.43476	−	2.25115i	−0.333854	−	0.138287i
$266$	11.1192	−	26.8442i	0.681763	−	1.64592i
$267$	−14.3655	+	5.95038i	−0.879154	+	0.364158i
$268$		−	13.8487i		−	0.845946i
$269$	6.65477	+	16.0660i	0.405749	+	0.979564i	0.986243	+	0.165300i	$0.0528591\pi$
$269$	6.65477	+	16.0660i	0.405749	+	0.979564i	−0.580495	+	0.814264i	$0.697141\pi$
$270$	−0.707107	−	0.707107i	−0.0430331	−	0.0430331i
$271$	17.9138			1.08819			0.544093	−	0.839025i	$-0.316874\pi$
$271$	17.9138			1.08819			0.544093	+	0.839025i	$0.316874\pi$
$272$	0.850770	−	4.03438i	0.0515855	−	0.244620i
$273$	21.8890			1.32478
$274$	5.04644	+	5.04644i	0.304866	+	0.304866i
$275$	−1.01668	−	2.45448i	−0.0613082	−	0.148011i
$276$		−	4.32010i		−	0.260040i
$277$	−24.2665	+	10.0515i	−1.45803	+	0.603936i	−0.964094	−	0.265562i	$-0.914442\pi$
$277$	−24.2665	+	10.0515i	−1.45803	+	0.603936i	−0.493936	+	0.869498i	$0.664442\pi$
$278$	−2.78604	+	6.72611i	−0.167096	+	0.403405i
$279$	−3.63909	−	1.50736i	−0.217866	−	0.0902432i
$280$	−3.39907	+	3.39907i	−0.203133	+	0.203133i
$281$	−20.1532	+	20.1532i	−1.20224	+	1.20224i	−0.228755	+	0.973484i	$0.573465\pi$
$281$	−20.1532	+	20.1532i	−1.20224	+	1.20224i	−0.973484	+	0.228755i	$0.926535\pi$
$282$	1.69870	+	0.703623i	0.101156	+	0.0419001i
$283$	1.40101	−	3.38235i	0.0832817	−	0.201060i	−0.876753	−	0.480941i	$-0.840295\pi$
$283$	1.40101	−	3.38235i	0.0832817	−	0.201060i	0.960035	+	0.279881i	$0.0902951\pi$
$284$	−4.49618	+	1.86238i	−0.266799	+	0.110512i
$285$		−	6.04449i		−	0.358045i
$286$	−4.62951	−	11.1766i	−0.273749	−	0.660888i
$287$	−38.5432	−	38.5432i	−2.27513	−	2.27513i
$288$	1.00000			0.0589256
$289$	−15.5524	−	6.86465i	−0.914846	−	0.403803i
$290$	−4.06491			−0.238700
$291$	12.1348	+	12.1348i	0.711356	+	0.711356i
$292$	3.22788	+	7.79280i	0.188898	+	0.456039i
$293$			15.6314i			0.913197i	0.889673	+	0.456598i	$0.150932\pi$
$293$			15.6314i			0.913197i	−0.889673	+	0.456598i	$0.849068\pi$
$294$	−14.8813	+	6.16402i	−0.867893	+	0.359493i
$295$	1.34085	−	3.23709i	0.0780672	−	0.188471i
$296$	−5.10973	−	2.11652i	−0.296997	−	0.123020i
$297$	−1.87858	+	1.87858i	−0.109006	+	0.109006i
$298$	0.188514	−	0.188514i	0.0109204	−	0.0109204i
$299$	18.1744	+	7.52808i	1.05105	+	0.435360i
$300$	−0.382683	+	0.923880i	−0.0220942	+	0.0533402i
$301$	34.6683	−	14.3601i	1.99825	−	0.827702i
$302$		−	13.1064i		−	0.754190i
$303$	2.32852	+	5.62155i	0.133770	+	0.322949i
$304$	4.27410	+	4.27410i	0.245136	+	0.245136i
$305$	−7.66447			−0.438866
$306$	0.850770	−	4.03438i	0.0486353	−	0.230630i
$307$	−1.39589			−0.0796676			−0.0398338	−	0.999206i	$-0.512683\pi$
$307$	−1.39589			−0.0796676			−0.0398338	+	0.999206i	$0.512683\pi$
$308$	9.03036	+	9.03036i	0.514553	+	0.514553i
$309$	−0.518602	−	1.25202i	−0.0295022	−	0.0712247i
$310$			3.93892i			0.223716i
$311$	−3.23049	+	1.33811i	−0.183184	+	0.0758774i	−0.472390	−	0.881389i	$-0.656609\pi$
$311$	−3.23049	+	1.33811i	−0.183184	+	0.0758774i	0.289206	+	0.957267i	$0.406609\pi$
$312$	−1.74257	+	4.20694i	−0.0986537	+	0.238171i
$313$	−21.4957	−	8.90381i	−1.21501	−	0.503273i	−0.319189	−	0.947691i	$-0.603411\pi$
$313$	−21.4957	−	8.90381i	−1.21501	−	0.503273i	−0.895820	+	0.444418i	$0.853411\pi$
$314$	−2.07449	+	2.07449i	−0.117070	+	0.117070i
$315$	−3.39907	+	3.39907i	−0.191516	+	0.191516i
$316$	12.1364	+	5.02704i	0.682724	+	0.282793i
$317$	5.79942	−	14.0010i	0.325728	−	0.786377i	−0.673172	−	0.739486i	$-0.735069\pi$
$317$	5.79942	−	14.0010i	0.325728	−	0.786377i	0.998900	−	0.0468911i	$-0.0149314\pi$
$318$	5.43476	−	2.25115i	0.304766	−	0.126238i
$319$			10.7993i			0.604645i
$320$	−0.382683	−	0.923880i	−0.0213927	−	0.0516464i
$321$	2.19207	+	2.19207i	0.122349	+	0.122349i
$322$	−20.7668			−1.15729
$323$	20.8796	−	13.6070i	1.16177	−	0.757116i
$324$	1.00000			0.0555556
$325$	−3.21985	−	3.21985i	−0.178605	−	0.178605i
$326$	3.49736	+	8.44338i	0.193701	+	0.467635i
$327$			15.4449i			0.854104i
$328$	10.4762	−	4.33938i	0.578450	−	0.239602i
$329$	3.38233	−	8.16566i	0.186474	−	0.450187i
$330$	2.45448	+	1.01668i	0.135115	+	0.0559664i
$331$	−16.9764	+	16.9764i	−0.933108	+	0.933108i	−0.997899	−	0.0647912i	$-0.979362\pi$
$331$	−16.9764	+	16.9764i	−0.933108	+	0.933108i	0.0647912	+	0.997899i	$0.479362\pi$
$332$	12.5025	−	12.5025i	0.686166	−	0.686166i
$333$	−5.10973	−	2.11652i	−0.280012	−	0.115985i
$334$	7.29639	−	17.6150i	0.399241	−	0.963852i
$335$	−12.7946	+	5.29968i	−0.699042	+	0.289553i
$336$		−	4.80701i		−	0.262244i
$337$	10.2837	+	24.8271i	0.560189	+	1.35242i	0.909615	+	0.415452i	$0.136377\pi$
$337$	10.2837	+	24.8271i	0.560189	+	1.35242i	−0.349426	+	0.936964i	$0.613623\pi$
$338$	−5.46939	−	5.46939i	−0.297496	−	0.297496i
$339$	4.15242			0.225529
$340$	−4.05285	+	0.757880i	−0.219797	+	0.0411018i
$341$	10.4646			0.566689
$342$	4.27410	+	4.27410i	0.231117	+	0.231117i
$343$	16.7536	+	40.4467i	0.904609	+	2.18392i
$344$			7.80625i			0.420885i
$345$	−3.99125	+	1.65323i	−0.214882	+	0.0890070i
$346$	−1.98870	+	4.80116i	−0.106913	+	0.258112i
$347$	7.37374	+	3.05430i	0.395843	+	0.163964i	0.571720	−	0.820449i	$-0.306276\pi$
$347$	7.37374	+	3.05430i	0.395843	+	0.163964i	−0.175877	+	0.984412i	$0.556276\pi$
$348$	2.87432	−	2.87432i	0.154080	−	0.154080i
$349$	9.41696	−	9.41696i	0.504078	−	0.504078i	−0.408624	−	0.912703i	$-0.633991\pi$
$349$	9.41696	−	9.41696i	0.504078	−	0.504078i	0.912703	+	0.408624i	$0.133991\pi$
$350$	4.44110	+	1.83956i	0.237387	+	0.0983288i
$351$	−1.74257	+	4.20694i	−0.0930116	+	0.224550i
$352$	−2.45448	+	1.01668i	−0.130824	+	0.0541893i
$353$			16.9293i			0.901054i	0.892763	+	0.450527i	$0.148764\pi$
$353$			16.9293i			0.901054i	−0.892763	+	0.450527i	$0.851236\pi$
$354$	1.34085	+	3.23709i	0.0712653	+	0.172050i
$355$	3.44123	+	3.44123i	0.182641	+	0.182641i
$356$	−15.5491			−0.824101
$357$	−19.3933	−	4.08966i	−1.02640	−	0.216448i
$358$	−0.209059			−0.0110491
$359$	−14.7601	−	14.7601i	−0.779009	−	0.779009i	0.200653	−	0.979662i	$-0.435693\pi$
$359$	−14.7601	−	14.7601i	−0.779009	−	0.779009i	−0.979662	+	0.200653i	$0.935693\pi$
$360$	−0.382683	−	0.923880i	−0.0201692	−	0.0486927i
$361$			17.5358i			0.922939i
$362$	−13.3231	+	5.51860i	−0.700246	+	0.290051i
$363$	−1.50849	+	3.64181i	−0.0791750	+	0.191145i
$364$	20.2228	+	8.37656i	1.05996	+	0.439051i
$365$	5.96435	−	5.96435i	0.312188	−	0.312188i
$366$	5.41960	−	5.41960i	0.283287	−	0.283287i
$367$	8.76611	+	3.63104i	0.457587	+	0.189539i	0.599557	−	0.800332i	$-0.295344\pi$
$367$	8.76611	+	3.63104i	0.457587	+	0.189539i	−0.141970	+	0.989871i	$0.545344\pi$
$368$	1.65323	−	3.99125i	0.0861806	−	0.208058i
$369$	10.4762	−	4.33938i	0.545368	−	0.225899i
$370$			5.53073i			0.287529i
$371$	−10.8213	−	26.1249i	−0.561814	−	1.35634i
$372$	−2.78524	−	2.78524i	−0.144408	−	0.144408i
$373$	8.88776			0.460191			0.230095	−	0.973168i	$-0.426096\pi$
$373$	8.88776			0.460191			0.230095	+	0.973168i	$0.426096\pi$
$374$	2.01347	+	10.7673i	0.104114	+	0.556763i
$375$	1.00000			0.0516398
$376$	1.30013	+	1.30013i	0.0670489	+	0.0670489i
$377$	7.08339	+	17.1008i	0.364813	+	0.880737i
$378$		−	4.80701i		−	0.247246i
$379$	−19.0267	+	7.88113i	−0.977337	+	0.404826i	−0.813439	−	0.581651i	$-0.802407\pi$
$379$	−19.0267	+	7.88113i	−0.977337	+	0.404826i	−0.163899	+	0.986477i	$0.552407\pi$
$380$	2.31313	−	5.58438i	0.118661	−	0.286473i
$381$	−12.0963	−	5.01043i	−0.619710	−	0.256692i
$382$	−8.75468	+	8.75468i	−0.447928	+	0.447928i
$383$	23.0966	−	23.0966i	1.18018	−	1.18018i	0.200482	−	0.979697i	$-0.435749\pi$
$383$	23.0966	−	23.0966i	1.18018	−	1.18018i	0.979697	−	0.200482i	$-0.0642507\pi$
$384$	0.923880	+	0.382683i	0.0471465	+	0.0195287i
$385$	4.88720	−	11.7987i	0.249075	−	0.601319i
$386$	3.32022	−	1.37528i	0.168995	−	0.0700000i
$387$			7.80625i			0.396814i
$388$	6.56732	+	15.8549i	0.333405	+	0.804911i
$389$	19.0603	+	19.0603i	0.966394	+	0.966394i	0.999453	−	0.0330590i	$-0.0105249\pi$
$389$	19.0603	+	19.0603i	0.966394	+	0.966394i	−0.0330590	+	0.999453i	$0.510525\pi$
$390$	4.55356			0.230578
$391$	−14.6957	−	10.0654i	−0.743193	−	0.509029i
$392$	−16.1074			−0.813545
$393$	−3.83227	−	3.83227i	−0.193312	−	0.193312i
$394$	1.84049	+	4.44333i	0.0927225	+	0.223852i
$395$		−	13.1363i		−	0.660959i
$396$	−2.45448	+	1.01668i	−0.123342	+	0.0510901i
$397$	11.7237	−	28.3036i	0.588397	−	1.42051i	−0.296638	−	0.954990i	$-0.595866\pi$
$397$	11.7237	−	28.3036i	0.588397	−	1.42051i	0.885035	−	0.465525i	$-0.154134\pi$
$398$	−4.10618	−	1.70083i	−0.205824	−	0.0852551i
$399$	20.5456	−	20.5456i	1.02857	−	1.02857i
$400$	−0.707107	+	0.707107i	−0.0353553	+	0.0353553i
$401$	26.2727	+	10.8825i	1.31200	+	0.543447i	0.925467	−	0.378829i	$-0.123673\pi$
$401$	26.2727	+	10.8825i	1.31200	+	0.543447i	0.386531	+	0.922276i	$0.373673\pi$
$402$	5.29968	−	12.7946i	0.264324	−	0.638135i
$403$	16.5708	−	6.86385i	0.825450	−	0.341913i
$404$			6.08472i			0.302726i
$405$	−0.382683	−	0.923880i	−0.0190157	−	0.0459079i
$406$	−13.8169	−	13.8169i	−0.685722	−	0.685722i
$407$	14.6936			0.728334
$408$	2.32990	−	3.40170i	0.115347	−	0.168409i
$409$	−30.3744			−1.50192			−0.750960	−	0.660348i	$-0.770409\pi$
$409$	−30.3744			−1.50192			−0.750960	+	0.660348i	$0.770409\pi$
$410$	−8.01812	−	8.01812i	−0.395987	−	0.395987i
$411$	2.73111	+	6.59349i	0.134716	+	0.325233i
$412$		−	1.35517i		−	0.0667645i
$413$	15.5608	−	6.44547i	0.765694	−	0.317161i
$414$	1.65323	−	3.99125i	0.0812519	−	0.196159i
$415$	−16.3353	−	6.76632i	−0.801870	−	0.332146i
$416$	−3.21985	+	3.21985i	−0.157866	+	0.157866i
$417$	−5.14794	+	5.14794i	−0.252096	+	0.252096i
$418$	−14.8361	−	6.14532i	−0.725658	−	0.300577i
$419$	8.44954	−	20.3990i	0.412787	−	0.996556i	−0.571599	−	0.820533i	$-0.693677\pi$
$419$	8.44954	−	20.3990i	0.412787	−	0.996556i	0.984386	−	0.176023i	$-0.0563232\pi$
$420$	−4.44110	+	1.83956i	−0.216704	+	0.0897615i
$421$			2.61967i			0.127675i	0.997960	+	0.0638374i	$0.0203339\pi$
$421$			2.61967i			0.127675i	−0.997960	+	0.0638374i	$0.979666\pi$
$422$	−5.96712	−	14.4059i	−0.290475	−	0.701269i
$423$	1.30013	+	1.30013i	0.0632143	+	0.0632143i
$424$	5.88254			0.285681
$425$	2.25115	+	3.45432i	0.109197	+	0.167559i
$426$	−4.86663			−0.235789
$427$	−26.0521	−	26.0521i	−1.26075	−	1.26075i
$428$	1.18634	+	2.86408i	0.0573439	+	0.138440i
$429$		−	12.0975i		−	0.584073i
$430$	7.21203	−	2.98732i	0.347795	−	0.144061i
$431$	5.10413	−	12.3225i	0.245857	−	0.593552i	−0.751987	−	0.659178i	$-0.770904\pi$
$431$	5.10413	−	12.3225i	0.245857	−	0.593552i	0.997844	+	0.0656261i	$0.0209045\pi$
$432$	0.923880	+	0.382683i	0.0444502	+	0.0184119i
$433$	−7.87874	+	7.87874i	−0.378628	+	0.378628i	−0.870607	−	0.491979i	$-0.836274\pi$
$433$	−7.87874	+	7.87874i	−0.378628	+	0.378628i	0.491979	+	0.870607i	$0.336274\pi$
$434$	−13.3887	+	13.3887i	−0.642677	+	0.642677i
$435$	−3.75548	−	1.55557i	−0.180062	−	0.0745840i
$436$	−5.91050	+	14.2692i	−0.283062	+	0.683371i
$437$	24.1251	−	9.99294i	1.15406	−	0.478027i
$438$			8.43486i			0.403033i
$439$	−11.5229	−	27.8187i	−0.549957	−	1.32771i	−0.917510	−	0.397712i	$-0.869804\pi$
$439$	−11.5229	−	27.8187i	−0.549957	−	1.32771i	0.367553	−	0.930003i	$-0.380196\pi$
$440$	1.87858	+	1.87858i	0.0895578	+	0.0895578i
$441$	−16.1074			−0.767017
$442$	10.2507	+	15.7294i	0.487578	+	0.748173i
$443$	28.4432			1.35138			0.675689	−	0.737187i	$-0.263846\pi$
$443$	28.4432			1.35138			0.675689	+	0.737187i	$0.263846\pi$
$444$	−3.91082	−	3.91082i	−0.185599	−	0.185599i
$445$	5.95038	+	14.3655i	0.282075	+	0.680990i
$446$			0.246992i			0.0116954i
$447$	0.246306	−	0.102023i	0.0116499	−	0.00482554i
$448$	1.83956	−	4.44110i	0.0869112	−	0.209822i
$449$	−30.1469	−	12.4873i	−1.42272	−	0.589310i	−0.467178	−	0.884163i	$-0.654729\pi$
$449$	−30.1469	−	12.4873i	−1.42272	−	0.589310i	−0.955543	+	0.294853i	$0.904729\pi$
$450$	−0.707107	+	0.707107i	−0.0333333	+	0.0333333i
$451$	−21.3019	+	21.3019i	−1.00307	+	1.00307i
$452$	3.83634	+	1.58906i	0.180446	+	0.0747432i
$453$	5.01561	−	12.1088i	0.235654	−	0.568919i
$454$	0.190644	−	0.0789675i	0.00894739	−	0.00370613i
$455$		−	21.8890i		−	1.02617i
$456$	2.31313	+	5.58438i	0.108322	+	0.261513i
$457$	0.544641	+	0.544641i	0.0254772	+	0.0254772i	0.719731	−	0.694253i	$-0.244265\pi$
$457$	0.544641	+	0.544641i	0.0254772	+	0.0254772i	−0.694253	+	0.719731i	$0.744265\pi$
$458$	12.8458			0.600246
$459$	2.32990	−	3.40170i	0.108750	−	0.158778i
$460$	−4.32010			−0.201426
$461$	−15.1089	−	15.1089i	−0.703691	−	0.703691i	0.261510	−	0.965201i	$-0.415780\pi$
$461$	−15.1089	−	15.1089i	−0.703691	−	0.703691i	−0.965201	+	0.261510i	$0.915780\pi$
$462$	4.88720	+	11.7987i	0.227373	+	0.548927i
$463$		−	5.59618i		−	0.260076i	−0.991509	−	0.130038i	$-0.958490\pi$
$463$		−	5.59618i		−	0.260076i	0.991509	−	0.130038i	$-0.0415100\pi$
$464$	3.75548	−	1.55557i	0.174344	−	0.0722156i
$465$	−1.50736	+	3.63909i	−0.0699021	+	0.168759i
$466$	0.152513	+	0.0631728i	0.00706501	+	0.00292642i
$467$	12.3315	−	12.3315i	0.570634	−	0.570634i	−0.361672	−	0.932305i	$-0.617794\pi$
$467$	12.3315	−	12.3315i	0.570634	−	0.570634i	0.932305	+	0.361672i	$0.117794\pi$
$468$	−3.21985	+	3.21985i	−0.148838	+	0.148838i
$469$	−61.5036	−	25.4756i	−2.83997	−	1.17636i
$470$	0.703623	−	1.69870i	0.0324557	−	0.0783550i
$471$	−2.71045	+	1.12270i	−0.124891	+	0.0517314i
$472$			3.50381i			0.161276i
$473$	−7.93646	−	19.1603i	−0.364919	−	0.880992i
$474$	9.28877	+	9.28877i	0.426647	+	0.426647i
$475$	−6.04449			−0.277340
$476$	−16.3520	−	11.1998i	−0.749494	−	0.513344i
$477$	5.88254			0.269343
$478$	13.5834	+	13.5834i	0.621288	+	0.621288i
$479$	−10.1844	−	24.5872i	−0.465335	−	1.12342i	−0.966177	−	0.257880i	$-0.916976\pi$
$479$	−10.1844	−	24.5872i	−0.465335	−	1.12342i	0.500842	−	0.865539i	$-0.333024\pi$
$480$		−	1.00000i		−	0.0456435i
$481$	23.2675	−	9.63770i	1.06090	−	0.439441i
$482$	−1.74161	+	4.20462i	−0.0793282	+	0.191515i
$483$	−19.1860	−	7.94710i	−0.872993	−	0.361606i
$484$	−2.78732	+	2.78732i	−0.126696	+	0.126696i
$485$	12.1348	−	12.1348i	0.551014	−	0.551014i
$486$	0.923880	+	0.382683i	0.0419080	+	0.0173589i
$487$	3.61554	−	8.72869i	0.163836	−	0.395535i	−0.820546	−	0.571580i	$-0.806331\pi$
$487$	3.61554	−	8.72869i	0.163836	−	0.395535i	0.984382	+	0.176045i	$0.0563306\pi$
$488$	7.08104	−	2.93306i	0.320544	−	0.132774i
$489$			9.13905i			0.413282i
$490$	6.16402	+	14.8813i	0.278462	+	0.672267i
$491$	8.09092	+	8.09092i	0.365138	+	0.365138i	0.865700	−	0.500562i	$-0.166873\pi$
$491$	8.09092	+	8.09092i	0.365138	+	0.365138i	−0.500562	+	0.865700i	$0.666873\pi$
$492$	11.3393			0.511217
$493$	−3.08071	−	16.4745i	−0.138748	−	0.741973i
$494$	−27.5239			−1.23836
$495$	1.87858	+	1.87858i	0.0844359	+	0.0844359i
$496$	−1.50736	−	3.63909i	−0.0676824	−	0.163400i
$497$			23.3939i			1.04936i
$498$	16.3353	−	6.76632i	0.732004	−	0.303206i
$499$	−5.28872	+	12.7681i	−0.236756	+	0.571579i	−0.996944	−	0.0781245i	$-0.975107\pi$
$499$	−5.28872	+	12.7681i	−0.236756	+	0.571579i	0.760188	+	0.649703i	$0.225107\pi$
$500$	0.923880	+	0.382683i	0.0413171	+	0.0171141i
$501$	13.4820	−	13.4820i	0.602330	−	0.602330i
$502$	−8.95996	+	8.95996i	−0.399903	+	0.399903i
$503$	−3.51956	−	1.45785i	−0.156929	−	0.0650022i	0.302836	−	0.953043i	$-0.402067\pi$
$503$	−3.51956	−	1.45785i	−0.156929	−	0.0650022i	−0.459765	+	0.888040i	$0.652067\pi$
$504$	1.83956	−	4.44110i	0.0819407	−	0.197822i
$505$	5.62155	−	2.32852i	0.250156	−	0.103618i
$506$			11.4773i			0.510227i
$507$	−2.96001	−	7.14610i	−0.131459	−	0.317370i
$508$	−9.25807	−	9.25807i	−0.410761	−	0.410761i
$509$	−27.4822			−1.21813			−0.609064	−	0.793121i	$-0.708455\pi$
$509$	−27.4822			−1.21813			−0.609064	+	0.793121i	$0.708455\pi$
$510$	−4.03438	−	0.850770i	−0.178645	−	0.0376727i
$511$	40.5465			1.79367
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.31313	+	5.58438i	0.102127	+	0.246556i
$514$		−	10.7579i		−	0.474512i
$515$	−1.25202	+	0.518602i	−0.0551704	+	0.0228523i
$516$	−2.98732	+	7.21203i	−0.131510	+	0.317492i
$517$	−4.51295	−	1.86933i	−0.198479	−	0.0822129i
$518$	−18.7994	+	18.7994i	−0.825996	+	0.825996i
$519$	−3.67465	+	3.67465i	−0.161299	+	0.161299i
$520$	4.20694	+	1.74257i	0.184486	+	0.0764168i
$521$	−3.57183	+	8.62315i	−0.156485	+	0.377787i	−0.982605	−	0.185706i	$-0.940543\pi$
$521$	−3.57183	+	8.62315i	−0.156485	+	0.377787i	0.826121	+	0.563493i	$0.190543\pi$
$522$	3.75548	−	1.55557i	0.164373	−	0.0680856i
$523$			29.1806i			1.27598i	0.770045	+	0.637990i	$0.220234\pi$
$523$			29.1806i			1.27598i	−0.770045	+	0.637990i	$0.779766\pi$
$524$	−2.07401	−	5.00710i	−0.0906035	−	0.218736i
$525$	3.39907	+	3.39907i	0.148348	+	0.148348i
$526$	−8.77699			−0.382695
$527$	−15.9639	+	2.98523i	−0.695397	+	0.130039i
$528$	−2.65672			−0.115619
$529$	3.06652	+	3.06652i	0.133327	+	0.133327i
$530$	−2.25115	−	5.43476i	−0.0977837	−	0.236071i
$531$			3.50381i			0.152052i
$532$	26.8442	−	11.1192i	1.16384	−	0.482080i
$533$	−19.7596	+	47.7039i	−0.855883	+	2.06628i
$534$	−14.3655	−	5.95038i	−0.621656	−	0.257498i
$535$	2.19207	−	2.19207i	0.0947715	−	0.0947715i
$536$	9.79253	−	9.79253i	0.422973	−	0.422973i
$537$	−0.193146	−	0.0800036i	−0.00833485	−	0.00345241i
$538$	−6.65477	+	16.0660i	−0.286908	+	0.692656i
$539$	39.5353	−	16.3761i	1.70291	−	0.705366i
$540$		−	1.00000i		−	0.0430331i
$541$	10.0244	+	24.2011i	0.430983	+	1.04049i	0.978971	+	0.203999i	$0.0653941\pi$
$541$	10.0244	+	24.2011i	0.430983	+	1.04049i	−0.547988	+	0.836486i	$0.684606\pi$
$542$	12.6670	+	12.6670i	0.544093	+	0.544093i
$543$	−14.4208			−0.618856
$544$	3.45432	−	2.25115i	0.148103	−	0.0965172i
$545$	15.4449			0.661586
$546$	15.4779	+	15.4779i	0.662392	+	0.662392i
$547$	10.3519	+	24.9917i	0.442615	+	1.06857i	0.975028	+	0.222082i	$0.0712854\pi$
$547$	10.3519	+	24.9917i	0.442615	+	1.06857i	−0.532413	+	0.846485i	$0.678715\pi$
$548$			7.13674i			0.304866i
$549$	7.08104	−	2.93306i	0.302212	−	0.125180i
$550$	1.01668	−	2.45448i	0.0433514	−	0.104660i
$551$	22.7000	+	9.40264i	0.967052	+	0.400566i
$552$	3.05477	−	3.05477i	0.130020	−	0.130020i
$553$	44.6512	−	44.6512i	1.89876	−	1.89876i
$554$	−24.2665	−	10.0515i	−1.03098	−	0.427047i
$555$	−2.11652	+	5.10973i	−0.0898413	+	0.216896i
$556$	−6.72611	+	2.78604i	−0.285250	+	0.118155i
$557$			6.91753i			0.293105i	0.989203	+	0.146552i	$0.0468177\pi$
$557$			6.91753i			0.293105i	−0.989203	+	0.146552i	$0.953182\pi$
$558$	−1.50736	−	3.63909i	−0.0638116	−	0.154055i
$559$	−25.1350	−	25.1350i	−1.06310	−	1.06310i
$560$	−4.80701			−0.203133
$561$	−2.26025	+	10.7182i	−0.0954280	+	0.452522i
$562$	−28.5009			−1.20224
$563$	−24.1351	−	24.1351i	−1.01718	−	1.01718i	−0.999850	−	0.0173251i	$-0.994485\pi$
$563$	−24.1351	−	24.1351i	−1.01718	−	1.01718i	−0.0173251	−	0.999850i	$-0.505515\pi$
$564$	0.703623	+	1.69870i	0.0296279	+	0.0715280i
$565$		−	4.15242i		−	0.174694i
$566$	3.38235	−	1.40101i	0.142171	−	0.0588890i
$567$	1.83956	−	4.44110i	0.0772544	−	0.186509i
$568$	−4.49618	−	1.86238i	−0.188656	−	0.0781437i
$569$	−19.5941	+	19.5941i	−0.821426	+	0.821426i	−0.986312	−	0.164887i	$-0.947274\pi$
$569$	−19.5941	+	19.5941i	−0.821426	+	0.821426i	0.164887	+	0.986312i	$0.447274\pi$
$570$	4.27410	−	4.27410i	0.179022	−	0.179022i
$571$	−21.5080	−	8.90892i	−0.900083	−	0.372827i	−0.115831	−	0.993269i	$-0.536953\pi$
$571$	−21.5080	−	8.90892i	−0.900083	−	0.372827i	−0.784252	+	0.620442i	$0.786953\pi$
$572$	4.62951	−	11.1766i	0.193570	−	0.467319i
$573$	−11.4385	+	4.73800i	−0.477852	+	0.197933i
$574$		−	54.5083i		−	2.27513i
$575$	1.65323	+	3.99125i	0.0689445	+	0.166447i
$576$	0.707107	+	0.707107i	0.0294628	+	0.0294628i
$577$	5.51048			0.229404			0.114702	−	0.993400i	$-0.463409\pi$
$577$	5.51048			0.229404			0.114702	+	0.993400i	$0.463409\pi$
$578$	−6.14315	−	15.8512i	−0.255521	−	0.659325i
$579$	3.59378			0.149353
$580$	−2.87432	−	2.87432i	−0.119350	−	0.119350i
$581$	−32.5258	−	78.5242i	−1.34940	−	3.25773i
$582$			17.1612i			0.711356i
$583$	−14.4386	+	5.98066i	−0.597986	+	0.247694i
$584$	−3.22788	+	7.79280i	−0.133571	+	0.322468i
$585$	4.20694	+	1.74257i	0.173936	+	0.0720464i
$586$	−11.0531	+	11.0531i	−0.456598	+	0.456598i
$587$	−0.984099	+	0.984099i	−0.0406181	+	0.0406181i	−0.727124	−	0.686506i	$-0.759144\pi$
$587$	−0.984099	+	0.984099i	−0.0406181	+	0.0406181i	0.686506	+	0.727124i	$0.259144\pi$
$588$	−14.8813	−	6.16402i	−0.613693	−	0.254200i
$589$	9.11122	−	21.9964i	0.375421	−	0.906347i
$590$	3.23709	−	1.34085i	0.133269	−	0.0552018i
$591$			4.80943i			0.197834i
$592$	−2.11652	−	5.10973i	−0.0869884	−	0.210009i
$593$	32.7646	+	32.7646i	1.34548	+	1.34548i	0.890503	+	0.454978i	$0.150353\pi$
$593$	32.7646	+	32.7646i	1.34548	+	1.34548i	0.454978	+	0.890503i	$0.349647\pi$
$594$	−2.65672			−0.109006
$595$	−4.08966	+	19.3933i	−0.167660	+	0.795048i
$596$	0.266600			0.0109204
$597$	−3.14273	−	3.14273i	−0.128623	−	0.128623i
$598$	7.52808	+	18.1744i	0.307846	+	0.743207i
$599$		−	41.5318i		−	1.69694i	−0.529240	−	0.848472i	$-0.677523\pi$
$599$		−	41.5318i		−	1.69694i	0.529240	−	0.848472i	$-0.322477\pi$
$600$	−0.923880	+	0.382683i	−0.0377172	+	0.0156230i
$601$	−8.30198	+	20.0427i	−0.338645	+	0.817561i	0.659202	+	0.751966i	$0.270894\pi$
$601$	−8.30198	+	20.0427i	−0.338645	+	0.817561i	−0.997846	+	0.0655945i	$0.979106\pi$
$602$	34.6683	+	14.3601i	1.41298	+	0.585274i
$603$	9.79253	−	9.79253i	0.398783	−	0.398783i
$604$	9.26764	−	9.26764i	0.377095	−	0.377095i
$605$	3.64181	+	1.50849i	0.148061	+	0.0613287i
$606$	−2.32852	+	5.62155i	−0.0945897	+	0.228360i
$607$	−2.71496	+	1.12457i	−0.110197	+	0.0456450i	−0.437101	−	0.899413i	$-0.643995\pi$
$607$	−2.71496	+	1.12457i	−0.110197	+	0.0456450i	0.326904	+	0.945058i	$0.393995\pi$
$608$			6.04449i			0.245136i
$609$	−7.47766	−	18.0527i	−0.303010	−	0.731531i
$610$	−5.41960	−	5.41960i	−0.219433	−	0.219433i
$611$	−8.37243			−0.338712
$612$	3.45432	−	2.25115i	0.139633	−	0.0909973i
$613$	25.6455			1.03581			0.517906	−	0.855438i	$-0.326712\pi$
$613$	25.6455			1.03581			0.517906	+	0.855438i	$0.326712\pi$
$614$	−0.987042	−	0.987042i	−0.0398338	−	0.0398338i
$615$	−4.33938	−	10.4762i	−0.174981	−	0.422440i
$616$			12.7709i			0.514553i
$617$	2.45473	−	1.01678i	0.0988236	−	0.0409341i	−0.332724	−	0.943024i	$-0.607968\pi$
$617$	2.45473	−	1.01678i	0.0988236	−	0.0409341i	0.431548	+	0.902090i	$0.357968\pi$
$618$	0.518602	−	1.25202i	0.0208612	−	0.0503635i
$619$	7.64538	+	3.16682i	0.307294	+	0.127285i	0.531001	−	0.847371i	$-0.321816\pi$
$619$	7.64538	+	3.16682i	0.307294	+	0.127285i	−0.223707	+	0.974656i	$0.571816\pi$
$620$	−2.78524	+	2.78524i	−0.111858	+	0.111858i
$621$	3.05477	−	3.05477i	0.122584	−	0.122584i
$622$	−3.23049	−	1.33811i	−0.129531	−	0.0536534i
$623$	−28.6036	+	69.0551i	−1.14598	+	2.76664i
$624$	−4.20694	+	1.74257i	−0.168412	+	0.0697587i
$625$		−	1.00000i		−	0.0400000i
$626$	−8.90381	−	21.4957i	−0.355868	−	0.859141i
$627$	−11.3551	−	11.3551i	−0.453478	−	0.453478i
$628$	−2.93377			−0.117070
$629$	−22.4153	+	4.19163i	−0.893755	+	0.167131i
$630$	−4.80701			−0.191516
$631$	−11.1118	−	11.1118i	−0.442354	−	0.442354i	0.450449	−	0.892802i	$-0.351264\pi$
$631$	−11.1118	−	11.1118i	−0.442354	−	0.442354i	−0.892802	+	0.450449i	$0.851264\pi$
$632$	5.02704	+	12.1364i	0.199965	+	0.482758i
$633$		−	15.5928i		−	0.619760i
$634$	14.0010	−	5.79942i	0.556053	−	0.230325i
$635$	−5.01043	+	12.0963i	−0.198833	+	0.480025i
$636$	5.43476	+	2.25115i	0.215502	+	0.0892639i
$637$	51.8633	−	51.8633i	2.05490	−	2.05490i
$638$	−7.63626	+	7.63626i	−0.302322	+	0.302322i
$639$	−4.49618	−	1.86238i	−0.177866	−	0.0736746i
$640$	0.382683	−	0.923880i	0.0151269	−	0.0365195i
$641$	19.5495	−	8.09768i	0.772160	−	0.319839i	0.0384130	−	0.999262i	$-0.487770\pi$
$641$	19.5495	−	8.09768i	0.772160	−	0.319839i	0.733747	+	0.679423i	$0.237770\pi$
$642$			3.10006i			0.122349i
$643$	−8.42677	−	20.3440i	−0.332319	−	0.802290i	−0.998407	−	0.0564168i	$-0.982032\pi$
$643$	−8.42677	−	20.3440i	−0.332319	−	0.802290i	0.666088	−	0.745873i	$-0.267968\pi$
$644$	−14.6843	−	14.6843i	−0.578644	−	0.578644i
$645$	7.80625			0.307371
$646$	24.3857	+	5.14247i	0.959444	+	0.202328i
$647$	38.7558			1.52365			0.761824	−	0.647784i	$-0.224304\pi$
$647$	38.7558			1.52365			0.761824	+	0.647784i	$0.224304\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−3.56225	−	8.60004i	−0.139831	−	0.337581i
$650$		−	4.55356i		−	0.178605i
$651$	−17.4931	+	7.24589i	−0.685610	+	0.283989i
$652$	−3.49736	+	8.44338i	−0.136967	+	0.330668i
$653$	−10.8743	−	4.50430i	−0.425546	−	0.176267i	0.159623	−	0.987178i	$-0.448972\pi$
$653$	−10.8743	−	4.50430i	−0.425546	−	0.176267i	−0.585170	+	0.810911i	$0.698972\pi$
$654$	−10.9212	+	10.9212i	−0.427052	+	0.427052i
$655$	−3.83227	+	3.83227i	−0.149739	+	0.149739i
$656$	10.4762	+	4.33938i	0.409026	+	0.169424i
$657$	−3.22788	+	7.79280i	−0.125932	+	0.304026i
$658$	8.16566	−	3.38233i	0.318330	−	0.131857i
$659$			39.9393i			1.55581i	0.628380	+	0.777906i	$0.283718\pi$
$659$			39.9393i			1.55581i	−0.628380	+	0.777906i	$0.716282\pi$
$660$	1.01668	+	2.45448i	0.0395742	+	0.0955407i
$661$	3.47705	+	3.47705i	0.135241	+	0.135241i	0.771487	−	0.636245i	$-0.219513\pi$
$661$	3.47705	+	3.47705i	0.135241	+	0.135241i	−0.636245	+	0.771487i	$0.719513\pi$
$662$	−24.0083			−0.933108
$663$	3.45105	+	18.4549i	0.134028	+	0.716729i
$664$	17.6812			0.686166
$665$	−20.5456	−	20.5456i	−0.796726	−	0.796726i
$666$	−2.11652	−	5.10973i	−0.0820135	−	0.197998i
$667$		−	17.5608i		−	0.679957i
$668$	17.6150	−	7.29639i	0.681546	−	0.282306i
$669$	−0.0945199	+	0.228191i	−0.00365435	+	0.00882238i
$670$	−12.7946	−	5.29968i	−0.494297	−	0.204745i
$671$	−14.3983	+	14.3983i	−0.555841	+	0.555841i
$672$	3.39907	−	3.39907i	0.131122	−	0.131122i
$673$	−34.3184	−	14.2151i	−1.32288	−	0.547953i	−0.394262	−	0.918998i	$-0.629000\pi$
$673$	−34.3184	−	14.2151i	−1.32288	−	0.547953i	−0.928615	+	0.371045i	$0.879000\pi$
$674$	−10.2837	+	24.8271i	−0.396114	+	0.956303i
$675$	−0.923880	+	0.382683i	−0.0355601	+	0.0147295i
$676$		−	7.73489i		−	0.297496i
$677$	−1.58980	−	3.83813i	−0.0611011	−	0.147511i	0.890380	−	0.455218i	$-0.150439\pi$
$677$	−1.58980	−	3.83813i	−0.0611011	−	0.147511i	−0.951481	+	0.307706i	$0.900439\pi$
$678$	2.93621	+	2.93621i	0.112764	+	0.112764i
$679$	82.4942			3.16584
$680$	−3.40170	−	2.32990i	−0.130449	−	0.0893475i
$681$	0.206352			0.00790743
$682$	7.39958	+	7.39958i	0.283345	+	0.283345i
$683$	13.8260	+	33.3790i	0.529039	+	1.27721i	0.932153	+	0.362063i	$0.117928\pi$
$683$	13.8260	+	33.3790i	0.529039	+	1.27721i	−0.403115	+	0.915150i	$0.632072\pi$
$684$			6.04449i			0.231117i
$685$	6.59349	−	2.73111i	0.251924	−	0.104350i
$686$	−16.7536	+	40.4467i	−0.639655	+	1.54426i
$687$	11.8680	+	4.91588i	0.452792	+	0.187553i
$688$	−5.51985	+	5.51985i	−0.210442	+	0.210442i
$689$	−18.9409	+	18.9409i	−0.721591	+	0.721591i
$690$	−3.99125	−	1.65323i	−0.151944	−	0.0629374i
$691$	7.76293	−	18.7414i	0.295316	−	0.712955i	−0.704678	−	0.709527i	$-0.748909\pi$
$691$	7.76293	−	18.7414i	0.295316	−	0.712955i	0.999994	−	0.00342847i	$-0.00109132\pi$
$692$	−4.80116	+	1.98870i	−0.182513	+	0.0755992i
$693$			12.7709i			0.485125i
$694$	3.05430	+	7.37374i	0.115940	+	0.279903i
$695$	5.14794	+	5.14794i	0.195272	+	0.195272i
$696$	4.06491			0.154080
$697$	26.4195	−	38.5730i	1.00071	−	1.46106i
$698$	13.3176			0.504078
$699$	0.116728	+	0.116728i	0.00441506	+	0.00441506i
$700$	1.83956	+	4.44110i	0.0695290	+	0.167858i
$701$			15.9377i			0.601958i	0.953631	+	0.300979i	$0.0973134\pi$
$701$			15.9377i			0.601958i	−0.953631	+	0.300979i	$0.902687\pi$
$702$	−4.20694	+	1.74257i	−0.158781	+	0.0657691i
$703$	12.7933	−	30.8857i	0.482508	−	1.16488i
$704$	−2.45448	−	1.01668i	−0.0925069	−	0.0383176i
$705$	1.30013	−	1.30013i	0.0489656	−	0.0489656i
$706$	−11.9708	+	11.9708i	−0.450527	+	0.450527i
$707$	27.0229	+	11.1932i	1.01630	+	0.420965i
$708$	−1.34085	+	3.23709i	−0.0503922	+	0.121657i
$709$	−40.6473	+	16.8366i	−1.52654	+	0.632314i	−0.978889	−	0.204393i	$-0.934478\pi$
$709$	−40.6473	+	16.8366i	−1.52654	+	0.632314i	−0.547651	+	0.836707i	$0.684478\pi$
$710$			4.86663i			0.182641i
$711$	5.02704	+	12.1364i	0.188529	+	0.455149i
$712$	−10.9949	−	10.9949i	−0.412050	−	0.412050i
$713$	−17.0165			−0.637274
$714$	−10.8213	−	16.6050i	−0.404977	−	0.621425i
$715$	−12.0975			−0.452421
$716$	−0.147827	−	0.147827i	−0.00552457	−	0.00552457i
$717$	7.35126	+	17.7475i	0.274538	+	0.662793i
$718$		−	20.8739i		−	0.779009i
$719$	−19.7235	+	8.16976i	−0.735564	+	0.304681i	−0.718836	−	0.695179i	$-0.755325\pi$
$719$	−19.7235	+	8.16976i	−0.735564	+	0.304681i	−0.0167279	+	0.999860i	$0.505325\pi$
$720$	0.382683	−	0.923880i	0.0142618	−	0.0344310i
$721$	−6.01845	−	2.49293i	−0.224139	−	0.0928414i
$722$	−12.3997	+	12.3997i	−0.461470	+	0.461470i
$723$	−3.21808	+	3.21808i	−0.119682	+	0.119682i
$724$	−13.3231	−	5.51860i	−0.495148	−	0.205097i
$725$	−1.55557	+	3.75548i	−0.0577725	+	0.139475i
$726$	−3.64181	+	1.50849i	−0.135160	+	0.0559852i
$727$			3.91209i			0.145091i	0.997365	+	0.0725457i	$0.0231123\pi$
$727$			3.91209i			0.145091i	−0.997365	+	0.0725457i	$0.976888\pi$
$728$	8.37656	+	20.2228i	0.310456	+	0.749507i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	8.43486			0.312188
$731$	17.5730	+	26.9653i	0.649962	+	0.997347i
$732$	7.66447			0.283287
$733$	−4.89413	−	4.89413i	−0.180769	−	0.180769i	0.610922	−	0.791691i	$-0.290799\pi$
$733$	−4.89413	−	4.89413i	−0.180769	−	0.180769i	−0.791691	+	0.610922i	$0.790799\pi$
$734$	3.63104	+	8.76611i	0.134024	+	0.323563i
$735$			16.1074i			0.594129i
$736$	3.99125	−	1.65323i	0.147120	−	0.0609389i
$737$	−14.0797	+	33.9915i	−0.518634	+	1.25209i
$738$	10.4762	+	4.33938i	0.385634	+	0.159735i
$739$	−2.08224	+	2.08224i	−0.0765964	+	0.0765964i	−0.744367	−	0.667771i	$-0.767249\pi$
$739$	−2.08224	+	2.08224i	−0.0765964	+	0.0765964i	0.667771	+	0.744367i	$0.267249\pi$
$740$	−3.91082	+	3.91082i	−0.143765	+	0.143765i
$741$	−25.4288	−	10.5330i	−0.934150	−	0.386938i
$742$	10.8213	−	26.1249i	0.397263	−	0.959077i
$743$	36.4046	−	15.0793i	1.33556	−	0.553206i	0.403321	−	0.915058i	$-0.367856\pi$
$743$	36.4046	−	15.0793i	1.33556	−	0.553206i	0.932235	+	0.361853i	$0.117856\pi$
$744$		−	3.93892i		−	0.144408i
$745$	−0.102023	−	0.246306i	−0.00373784	−	0.00902395i
$746$	6.28460	+	6.28460i	0.230095	+	0.230095i
$747$	17.6812			0.646923
$748$	−6.18988	+	9.03735i	−0.226324	+	0.330438i
$749$	14.9020			0.544508
$750$	0.707107	+	0.707107i	0.0258199	+	0.0258199i
$751$	12.7402	+	30.7575i	0.464896	+	1.12236i	0.966363	+	0.257181i	$0.0827937\pi$
$751$	12.7402	+	30.7575i	0.464896	+	1.12236i	−0.501467	+	0.865177i	$0.667206\pi$
$752$			1.83866i			0.0670489i
$753$	−11.7068	+	4.84909i	−0.426618	+	0.176711i
$754$	−7.08339	+	17.1008i	−0.257962	+	0.622775i
$755$	−12.1088	−	5.01561i	−0.440683	−	0.182537i
$756$	3.39907	−	3.39907i	0.123623	−	0.123623i
$757$	−33.0038	+	33.0038i	−1.19954	+	1.19954i	−0.225241	+	0.974303i	$0.572317\pi$
$757$	−33.0038	+	33.0038i	−1.19954	+	1.19954i	−0.974303	+	0.225241i	$0.927683\pi$
$758$	−19.0267	−	7.88113i	−0.691082	−	0.286255i
$759$	−4.39216	+	10.6036i	−0.159425	+	0.384887i
$760$	5.58438	−	2.31313i	0.202567	−	0.0839059i
$761$			7.34541i			0.266271i	0.991098	+	0.133135i	$0.0425045\pi$
$761$			7.34541i			0.266271i	−0.991098	+	0.133135i	$0.957495\pi$
$762$	−5.01043	−	12.0963i	−0.181509	−	0.438201i
$763$	52.4982	+	52.4982i	1.90056	+	1.90056i
$764$	−12.3810			−0.447928
$765$	−3.40170	−	2.32990i	−0.122989	−	0.0842376i
$766$	32.6635			1.18018
$767$	−11.2817	−	11.2817i	−0.407360	−	0.407360i
$768$	0.382683	+	0.923880i	0.0138089	+	0.0333376i
$769$			39.8949i			1.43865i	0.694675	+	0.719324i	$0.255548\pi$
$769$			39.8949i			1.43865i	−0.694675	+	0.719324i	$0.744452\pi$
$770$	11.7987	−	4.88720i	0.425197	−	0.176122i
$771$	4.11688	−	9.93903i	0.148266	−	0.357945i
$772$	3.32022	+	1.37528i	0.119497	+	0.0494975i
$773$	26.2026	−	26.2026i	0.942442	−	0.942442i	−0.0559897	−	0.998431i	$-0.517831\pi$
$773$	26.2026	−	26.2026i	0.942442	−	0.942442i	0.998431	+	0.0559897i	$0.0178314\pi$
$774$	−5.51985	+	5.51985i	−0.198407	+	0.198407i
$775$	3.63909	+	1.50736i	0.130720	+	0.0541459i
$776$	−6.56732	+	15.8549i	−0.235753	+	0.569158i
$777$	−24.5625	+	10.1741i	−0.881176	+	0.364995i
$778$			26.9553i			0.966394i
$779$	26.2293	+	63.3232i	0.939763	+	2.26879i
$780$	3.21985	+	3.21985i	0.115289	+	0.115289i
$781$	12.9292			0.462645
$782$	−3.27412	−	17.5087i	−0.117082	−	0.626111i
$783$	4.06491			0.145268
$784$	−11.3896	−	11.3896i	−0.406772	−	0.406772i
$785$	1.12270	+	2.71045i	0.0400710	+	0.0967400i
$786$		−	5.41965i		−	0.193312i
$787$	35.9754	−	14.9015i	1.28238	−	0.531181i	0.365678	−	0.930742i	$-0.380837\pi$
$787$	35.9754	−	14.9015i	1.28238	−	0.531181i	0.916707	+	0.399561i	$0.130837\pi$
$788$	−1.84049	+	4.44333i	−0.0655647	+	0.158287i
$789$	−8.10888	−	3.35881i	−0.288684	−	0.119577i
$790$	9.28877	−	9.28877i	0.330480	−	0.330480i
$791$	14.1144	−	14.1144i	0.501849	−	0.501849i
$792$	−2.45448	−	1.01668i	−0.0872163	−	0.0361262i
$793$	−13.3559	+	32.2439i	−0.474281	+	1.14502i
$794$	28.3036	−	11.7237i	1.00446	−	0.416059i
$795$		−	5.88254i		−	0.208632i
$796$	−1.70083	−	4.10618i	−0.0602844	−	0.145540i
$797$	14.0782	+	14.0782i	0.498676	+	0.498676i	0.911026	−	0.412349i	$-0.135292\pi$
$797$	14.0782	+	14.0782i	0.498676	+	0.498676i	−0.412349	+	0.911026i	$0.635292\pi$
$798$	29.0559			1.02857
$799$	7.41783	+	1.56427i	0.262424	+	0.0553400i
$800$	−1.00000			−0.0353553
$801$	−10.9949	−	10.9949i	−0.388485	−	0.388485i
$802$	10.8825	+	26.2727i	0.384275	+	0.927723i
$803$		−	22.4090i		−	0.790797i
$804$	12.7946	−	5.29968i	0.451229	−	0.186905i
$805$	−7.94710	+	19.1860i	−0.280099	+	0.676218i
$806$	16.5708	+	6.86385i	0.583681	+	0.241769i
$807$	−12.2964	+	12.2964i	−0.432854	+	0.432854i
$808$	−4.30255	+	4.30255i	−0.151363	+	0.151363i
$809$	43.4654	+	18.0040i	1.52816	+	0.632986i	0.979207	−	0.202865i	$-0.0650254\pi$
$809$	43.4654	+	18.0040i	1.52816	+	0.632986i	0.548956	+	0.835851i	$0.315025\pi$
$810$	0.382683	−	0.923880i	0.0134461	−	0.0324618i
$811$	25.9649	−	10.7550i	0.911751	−	0.377660i	0.123025	−	0.992404i	$-0.460741\pi$
$811$	25.9649	−	10.7550i	0.911751	−	0.377660i	0.788727	+	0.614744i	$0.210741\pi$
$812$		−	19.5401i		−	0.685722i
$813$	6.85532	+	16.5502i	0.240427	+	0.580441i
$814$	10.3899	+	10.3899i	0.364167	+	0.364167i
$815$	9.13905			0.320127
$816$	4.05285	−	0.757880i	0.141878	−	0.0265311i
$817$	−47.1848			−1.65079
$818$	−21.4780	−	21.4780i	−0.750960	−	0.750960i
$819$	8.37656	+	20.2228i	0.292701	+	0.706642i
$820$		−	11.3393i		−	0.395987i
$821$	9.51723	−	3.94217i	0.332154	−	0.137583i	−0.210373	−	0.977621i	$-0.567468\pi$
$821$	9.51723	−	3.94217i	0.332154	−	0.137583i	0.542527	+	0.840039i	$0.317468\pi$
$822$	−2.73111	+	6.59349i	−0.0952585	+	0.229974i
$823$	35.9537	+	14.8925i	1.25327	+	0.519120i	0.907836	−	0.419325i	$-0.137733\pi$
$823$	35.9537	+	14.8925i	1.25327	+	0.519120i	0.345430	+	0.938445i	$0.387733\pi$
$824$	0.958251	−	0.958251i	0.0333823	−	0.0333823i
$825$	1.87858	−	1.87858i	0.0654038	−	0.0654038i
$826$	15.5608	+	6.44547i	0.541428	+	0.224267i
$827$	−14.2931	+	34.5066i	−0.497020	+	1.19991i	0.454061	+	0.890971i	$0.349975\pi$
$827$	−14.2931	+	34.5066i	−0.497020	+	1.19991i	−0.951081	+	0.308942i	$0.900025\pi$
$828$	3.99125	−	1.65323i	0.138706	−	0.0574538i
$829$		−	39.3644i		−	1.36718i	−0.729866	−	0.683590i	$-0.760418\pi$
$829$		−	39.3644i		−	1.36718i	0.729866	−	0.683590i	$-0.239582\pi$
$830$	−6.76632	−	16.3353i	−0.234862	−	0.567008i
$831$	−18.5727	−	18.5727i	−0.644281	−	0.644281i
$832$	−4.55356			−0.157866
$833$	−55.6400	+	36.2601i	−1.92781	+	1.25634i
$834$	−7.28029			−0.252096
$835$	−13.4820	−	13.4820i	−0.466563	−	0.466563i
$836$	−6.14532	−	14.8361i	−0.212540	−	0.513117i
$837$		−	3.93892i		−	0.136149i
$838$	20.3990	−	8.44954i	0.704671	−	0.291884i
$839$	16.3894	−	39.5675i	0.565825	−	1.36602i	−0.339221	−	0.940707i	$-0.610163\pi$
$839$	16.3894	−	39.5675i	0.565825	−	1.36602i	0.905046	−	0.425315i	$-0.139837\pi$
$840$	−4.44110	−	1.83956i	−0.153233	−	0.0634710i
$841$	−8.82224	+	8.82224i	−0.304215	+	0.304215i
$842$	−1.85239	+	1.85239i	−0.0638374	+	0.0638374i
$843$	−26.3314	−	10.9068i	−0.906902	−	0.375651i
$844$	5.96712	−	14.4059i	0.205397	−	0.495872i
$845$	−7.14610	+	2.96001i	−0.245833	+	0.101828i
$846$			1.83866i			0.0632143i
$847$	7.25131	+	17.5062i	0.249158	+	0.601521i
$848$	4.15958	+	4.15958i	0.142841	+	0.142841i
$849$	3.66103			0.125646
$850$	−0.850770	+	4.03438i	−0.0291812	+	0.138378i
$851$	−23.8933			−0.819053
$852$	−3.44123	−	3.44123i	−0.117894	−	0.117894i
$853$	−4.35673	−	10.5181i	−0.149172	−	0.360132i	0.831576	−	0.555411i	$-0.187439\pi$
$853$	−4.35673	−	10.5181i	−0.149172	−	0.360132i	−0.980748	+	0.195279i	$0.937439\pi$
$854$		−	36.8432i		−	1.26075i
$855$	5.58438	−	2.31313i	0.190982	−	0.0791072i
$856$	−1.18634	+	2.86408i	−0.0405483	+	0.0978922i
$857$	13.4238	+	5.56030i	0.458547	+	0.189936i	0.599986	−	0.800011i	$-0.295173\pi$
$857$	13.4238	+	5.56030i	0.458547	+	0.189936i	−0.141439	+	0.989947i	$0.545173\pi$
$858$	8.55423	−	8.55423i	0.292037	−	0.292037i
$859$	13.2953	−	13.2953i	0.453630	−	0.453630i	−0.442927	−	0.896558i	$-0.646060\pi$
$859$	13.2953	−	13.2953i	0.453630	−	0.453630i	0.896558	+	0.442927i	$0.146060\pi$
$860$	7.21203	+	2.98732i	0.245928	+	0.101867i
$861$	20.8594	−	50.3591i	0.710888	−	1.71623i
$862$	12.3225	−	5.10413i	0.419704	−	0.173847i
$863$			3.91801i			0.133371i	0.997774	+	0.0666853i	$0.0212423\pi$
$863$			3.91801i			0.133371i	−0.997774	+	0.0666853i	$0.978758\pi$
$864$	0.382683	+	0.923880i	0.0130192	+	0.0314310i
$865$	3.67465	+	3.67465i	0.124942	+	0.124942i
$866$	−11.1422			−0.378628
$867$	0.390474	−	16.9955i	0.0132612	−	0.577198i
$868$	−18.9344			−0.642677
$869$	−24.6776	−	24.6776i	−0.837131	−	0.837131i
$870$	−1.55557	−	3.75548i	−0.0527388	−	0.127323i
$871$			63.0610i			2.13674i
$872$	−14.2692	+	5.91050i	−0.483216	+	0.200155i
$873$	−6.56732	+	15.8549i	−0.222270	+	0.536607i
$874$	24.1251	+	9.99294i	0.816043	+	0.338016i
$875$	3.39907	−	3.39907i	0.114910	−	0.114910i
$876$	−5.96435	+	5.96435i	−0.201517	+	0.201517i
$877$	−9.97129	−	4.13024i	−0.336707	−	0.139468i	0.207923	−	0.978145i	$-0.433330\pi$
$877$	−9.97129	−	4.13024i	−0.336707	−	0.139468i	−0.544629	+	0.838677i	$0.683330\pi$
$878$	11.5229	−	27.8187i	0.388879	−	0.938836i
$879$	−14.4415	+	5.98188i	−0.487101	+	0.201764i
$880$			2.65672i			0.0895578i
$881$	11.6183	+	28.0491i	0.391431	+	0.944999i	0.989629	+	0.143650i	$0.0458839\pi$
$881$	11.6183	+	28.0491i	0.391431	+	0.944999i	−0.598197	+	0.801349i	$0.704116\pi$
$882$	−11.3896	−	11.3896i	−0.383509	−	0.383509i
$883$	−38.7408			−1.30373			−0.651866	−	0.758334i	$-0.726014\pi$
$883$	−38.7408			−1.30373			−0.651866	+	0.758334i	$0.726014\pi$
$884$	−3.87403	+	18.3708i	−0.130298	+	0.617876i
$885$	3.50381			0.117779
$886$	20.1124	+	20.1124i	0.675689	+	0.675689i
$887$	−21.0874	−	50.9095i	−0.708046	−	1.70938i	−0.704826	−	0.709380i	$-0.748975\pi$
$887$	−21.0874	−	50.9095i	−0.708046	−	1.70938i	−0.00322041	−	0.999995i	$-0.501025\pi$
$888$		−	5.53073i		−	0.185599i
$889$	−58.1468	+	24.0852i	−1.95018	+	0.807792i
$890$	−5.95038	+	14.3655i	−0.199457	+	0.481533i
$891$	−2.45448	−	1.01668i	−0.0822283	−	0.0340601i
$892$	−0.174650	+	0.174650i	−0.00584771	+	0.00584771i
$893$	−7.85860	+	7.85860i	−0.262978	+	0.262978i
$894$	0.246306	+	0.102023i	0.00823771	+	0.00341217i
$895$	−0.0800036	+	0.193146i	−0.00267422	+	0.00645615i
$896$	4.44110	−	1.83956i	0.148367	−	0.0614555i
$897$			19.6718i			0.656823i
$898$	−12.4873	−	30.1469i	−0.416705	−	1.00602i
$899$	−11.3217	−	11.3217i	−0.377601	−	0.377601i
$900$	−1.00000			−0.0333333
$901$	20.3202	−	13.2425i	0.676963	−	0.441171i
$902$	−30.1254			−1.00307
$903$	26.5340	+	26.5340i	0.882996	+	0.882996i
$904$	1.58906	+	3.83634i	0.0528514	+	0.127595i
$905$			14.4208i			0.479364i
$906$	12.1088	−	5.01561i	0.402287	−	0.166633i
$907$	−11.3328	+	27.3597i	−0.376298	+	0.908464i	0.616355	+	0.787469i	$0.288609\pi$
$907$	−11.3328	+	27.3597i	−0.376298	+	0.908464i	−0.992653	+	0.120996i	$0.961391\pi$
$908$	0.190644	+	0.0789675i	0.00632676	+	0.00262063i
$909$	−4.30255	+	4.30255i	−0.142706	+	0.142706i
$910$	15.4779	−	15.4779i	0.513086	−	0.513086i
$911$	−2.74299	−	1.13618i	−0.0908792	−	0.0376434i	0.336781	−	0.941583i	$-0.390662\pi$
$911$	−2.74299	−	1.13618i	−0.0908792	−	0.0376434i	−0.427660	+	0.903940i	$0.640662\pi$
$912$	−2.31313	+	5.58438i	−0.0765953	+	0.184917i
$913$	−43.3984	+	17.9762i	−1.43628	+	0.594925i
$914$			0.770239i			0.0254772i
$915$	−2.93306	−	7.08104i	−0.0969641	−	0.234092i
$916$	9.08336	+	9.08336i	0.300123	+	0.300123i
$917$	−26.0523			−0.860323
$918$	4.05285	−	0.757880i	0.133764	−	0.0250138i
$919$	−1.58747			−0.0523659			−0.0261830	−	0.999657i	$-0.508335\pi$
$919$	−1.58747			−0.0523659			−0.0261830	+	0.999657i	$0.508335\pi$
$920$	−3.05477	−	3.05477i	−0.100713	−	0.100713i
$921$	−0.534183	−	1.28963i	−0.0176019	−	0.0424949i
$922$		−	21.3672i		−	0.703691i
$923$	20.4736	−	8.48045i	0.673897	−	0.279137i
$924$	−4.88720	+	11.7987i	−0.160777	+	0.388150i
$925$	5.10973	+	2.11652i	0.168007	+	0.0695908i
$926$	3.95709	−	3.95709i	0.130038	−	0.130038i
$927$	0.958251	−	0.958251i	0.0314731	−	0.0314731i
$928$	3.75548	+	1.55557i	0.123280	+	0.0510642i
$929$	10.5179	−	25.3926i	0.345082	−	0.833103i	−0.652103	−	0.758130i	$-0.726113\pi$
$929$	10.5179	−	25.3926i	0.345082	−	0.833103i	0.997186	−	0.0749724i	$-0.0238869\pi$
$930$	−3.63909	+	1.50736i	−0.119330	+	0.0494283i
$931$		−	97.3608i		−	3.19087i
$932$	0.0631728	+	0.152513i	0.00206929	+	0.00499572i
$933$	−2.47251	−	2.47251i	−0.0809463	−	0.0809463i
$934$	17.4394			0.570634
$935$	10.7182	+	2.26025i	0.350522	+	0.0739182i
$936$	−4.55356			−0.148838
$937$	30.9750	+	30.9750i	1.01191	+	1.01191i	0.999928	+	0.0119821i	$0.00381411\pi$
$937$	30.9750	+	30.9750i	1.01191	+	1.01191i	0.0119821	+	0.999928i	$0.496186\pi$
$938$	−25.4756	−	61.5036i	−0.831809	−	2.00816i
$939$		−	23.2668i		−	0.759283i
$940$	1.69870	−	0.703623i	0.0554054	−	0.0229497i
$941$	11.9128	−	28.7600i	0.388345	−	0.937548i	−0.601946	−	0.798537i	$-0.705608\pi$
$941$	11.9128	−	28.7600i	0.388345	−	0.937548i	0.990291	−	0.139011i	$-0.0443923\pi$
$942$	−2.71045	−	1.12270i	−0.0883111	−	0.0365797i
$943$	34.6391	−	34.6391i	1.12800	−	1.12800i
$944$	−2.47756	+	2.47756i	−0.0806379	+	0.0806379i
$945$	−4.44110	−	1.83956i	−0.144469	−	0.0598410i
$946$	7.93646	−	19.1603i	0.258037	−	0.622956i
$947$	4.98237	−	2.06377i	0.161905	−	0.0670634i	−0.300259	−	0.953858i	$-0.597073\pi$
$947$	4.98237	−	2.06377i	0.161905	−	0.0670634i	0.462164	+	0.886794i	$0.347073\pi$
$948$			13.1363i			0.426647i
$949$	−14.6983	−	35.4849i	−0.477129	−	1.15189i
$950$	−4.27410	−	4.27410i	−0.138670	−	0.138670i
$951$	15.1546			0.491422
$952$	−3.64314	−	19.4821i	−0.118075	−	0.631419i
$953$	−30.3834			−0.984215			−0.492107	−	0.870535i	$-0.663773\pi$
$953$	−30.3834			−0.984215			−0.492107	+	0.870535i	$0.663773\pi$
$954$	4.15958	+	4.15958i	0.134671	+	0.134671i
$955$	4.73800	+	11.4385i	0.153318	+	0.370143i
$956$			19.2098i			0.621288i
$957$	−9.97725	+	4.13271i	−0.322519	+	0.133592i
$958$	10.1844	−	24.5872i	0.329042	−	0.794377i
$959$	31.6950	+	13.1285i	1.02348	+	0.423941i
$960$	0.707107	−	0.707107i	0.0228218	−	0.0228218i
$961$	10.9495	−	10.9495i	0.353209	−	0.353209i
$962$	23.2675	+	9.63770i	0.750173	+	0.310732i
$963$	−1.18634	+	2.86408i	−0.0382293	+	0.0922937i
$964$	−4.20462	+	1.74161i	−0.135422	+	0.0560935i
$965$		−	3.59378i		−	0.115688i
$966$	−7.94710	−	19.1860i	−0.255694	−	0.617300i
$967$	13.3118	+	13.3118i	0.428079	+	0.428079i	0.887974	−	0.459895i	$-0.152113\pi$
$967$	13.3118	+	13.3118i	0.428079	+	0.428079i	−0.459895	+	0.887974i	$0.652113\pi$
$968$	−3.94187			−0.126696
$969$	20.5615	+	14.0830i	0.660532	+	0.452413i
$970$	17.1612			0.551014
$971$	24.4524	+	24.4524i	0.784713	+	0.784713i	0.980622	−	0.195909i	$-0.0627656\pi$
$971$	24.4524	+	24.4524i	0.784713	+	0.784713i	−0.195909	+	0.980622i	$0.562766\pi$
$972$	0.382683	+	0.923880i	0.0122746	+	0.0296334i
$973$			34.9964i			1.12193i
$974$	8.72869	−	3.61554i	0.279685	−	0.115849i
$975$	1.74257	−	4.20694i	0.0558069	−	0.134730i
$976$	7.08104	+	2.93306i	0.226659	+	0.0938851i
$977$	5.96536	−	5.96536i	0.190849	−	0.190849i	−0.605214	−	0.796063i	$-0.706912\pi$
$977$	5.96536	−	5.96536i	0.190849	−	0.190849i	0.796063	+	0.605214i	$0.206912\pi$
$978$	−6.46228	+	6.46228i	−0.206641	+	0.206641i
$979$	38.1650	+	15.8085i	1.21976	+	0.505241i
$980$	−6.16402	+	14.8813i	−0.196902	+	0.475365i
$981$	−14.2692	+	5.91050i	−0.455581	+	0.188708i
$982$			11.4423i			0.365138i
$983$	10.2658	+	24.7839i	0.327429	+	0.790484i	0.998782	+	0.0493458i	$0.0157136\pi$
$983$	10.2658	+	24.7839i	0.327429	+	0.790484i	−0.671353	+	0.741138i	$0.734286\pi$
$984$	8.01812	+	8.01812i	0.255608	+	0.255608i
$985$	4.80943			0.153241
$986$	9.47082	−	13.8276i	0.301612	−	0.440360i
$987$	8.83844			0.281331
$988$	−19.4624	−	19.4624i	−0.619180	−	0.619180i
$989$	12.9055	+	31.1567i	0.410372	+	0.990726i
$990$			2.65672i			0.0844359i
$991$	−8.15979	+	3.37989i	−0.259204	+	0.107366i	−0.508501	−	0.861061i	$-0.669800\pi$
$991$	−8.15979	+	3.37989i	−0.259204	+	0.107366i	0.249297	+	0.968427i	$0.419800\pi$
$992$	1.50736	−	3.63909i	0.0478587	−	0.115541i
$993$	−22.1807	−	9.18756i	−0.703885	−	0.291559i
$994$	−16.5420	+	16.5420i	−0.524681	+	0.524681i
$995$	−3.14273	+	3.14273i	−0.0996313	+	0.0996313i
$996$	16.3353	+	6.76632i	0.517605	+	0.214399i
$997$	16.3634	−	39.5048i	0.518235	−	1.25113i	−0.420751	−	0.907176i	$-0.638233\pi$
$997$	16.3634	−	39.5048i	0.518235	−	1.25113i	0.938986	−	0.343954i	$-0.111767\pi$
$998$	−12.7681	+	5.28872i	−0.404167	+	0.167412i
$999$		−	5.53073i		−	0.174985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.u.c.151.4	✓	16
17.5	odd	16		8670.2.a.cj.1.2		8
17.8	even	8	inner	510.2.u.c.331.4	yes	16
17.12	odd	16		8670.2.a.ck.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.u.c.151.4	✓	16	1.1	even	1	trivial
510.2.u.c.331.4	yes	16	17.8	even	8	inner
8670.2.a.cj.1.2		8	17.5	odd	16
8670.2.a.ck.1.7		8	17.12	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.923880 - 0.382683i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(4.44110 + 1.83956i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} +1.00000i q^{4} +(0.923880 - 0.382683i) q^{5} +(-0.382683 + 0.923880i) q^{6} +(4.44110 + 1.83956i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(0.923880 + 0.382683i) q^{10} +(1.01668 - 2.45448i) q^{11} +(-0.923880 + 0.382683i) q^{12} -4.55356i q^{13} +(1.83956 + 4.44110i) q^{14} +(0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-0.850770 + 4.03438i) q^{17} -1.00000 q^{18} +(-4.27410 - 4.27410i) q^{19} +(0.382683 + 0.923880i) q^{20} +4.80701i q^{21} +(2.45448 - 1.01668i) q^{22} +(-1.65323 + 3.99125i) q^{23} +(-0.923880 - 0.382683i) q^{24} +(0.707107 - 0.707107i) q^{25} +(3.21985 - 3.21985i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(-1.83956 + 4.44110i) q^{28} +(-3.75548 + 1.55557i) q^{29} +1.00000i q^{30} +(1.50736 + 3.63909i) q^{31} +(-0.707107 - 0.707107i) q^{32} +2.65672 q^{33} +(-3.45432 + 2.25115i) q^{34} +4.80701 q^{35} +(-0.707107 - 0.707107i) q^{36} +(2.11652 + 5.10973i) q^{37} -6.04449i q^{38} +(4.20694 - 1.74257i) q^{39} +(-0.382683 + 0.923880i) q^{40} +(-10.4762 - 4.33938i) q^{41} +(-3.39907 + 3.39907i) q^{42} +(5.51985 - 5.51985i) q^{43} +(2.45448 + 1.01668i) q^{44} +(-0.382683 + 0.923880i) q^{45} +(-3.99125 + 1.65323i) q^{46} -1.83866i q^{47} +(-0.382683 - 0.923880i) q^{48} +(11.3896 + 11.3896i) q^{49} +1.00000 q^{50} +(-4.05285 + 0.757880i) q^{51} +4.55356 q^{52} +(-4.15958 - 4.15958i) q^{53} +(-0.382683 - 0.923880i) q^{54} -2.65672i q^{55} +(-4.44110 + 1.83956i) q^{56} +(2.31313 - 5.58438i) q^{57} +(-3.75548 - 1.55557i) q^{58} +(2.47756 - 2.47756i) q^{59} +(-0.707107 + 0.707107i) q^{60} +(-7.08104 - 2.93306i) q^{61} +(-1.50736 + 3.63909i) q^{62} +(-4.44110 + 1.83956i) q^{63} -1.00000i q^{64} +(-1.74257 - 4.20694i) q^{65} +(1.87858 + 1.87858i) q^{66} -13.8487 q^{67} +(-4.03438 - 0.850770i) q^{68} -4.32010 q^{69} +(3.39907 + 3.39907i) q^{70} +(1.86238 + 4.49618i) q^{71} -1.00000i q^{72} +(7.79280 - 3.22788i) q^{73} +(-2.11652 + 5.10973i) q^{74} +(0.923880 + 0.382683i) q^{75} +(4.27410 - 4.27410i) q^{76} +(9.03036 - 9.03036i) q^{77} +(4.20694 + 1.74257i) q^{78} +(5.02704 - 12.1364i) q^{79} +(-0.923880 + 0.382683i) q^{80} -1.00000i q^{81} +(-4.33938 - 10.4762i) q^{82} +(-12.5025 - 12.5025i) q^{83} -4.80701 q^{84} +(0.757880 + 4.05285i) q^{85} +7.80625 q^{86} +(-2.87432 - 2.87432i) q^{87} +(1.01668 + 2.45448i) q^{88} +15.5491i q^{89} +(-0.923880 + 0.382683i) q^{90} +(8.37656 - 20.2228i) q^{91} +(-3.99125 - 1.65323i) q^{92} +(-2.78524 + 2.78524i) q^{93} +(1.30013 - 1.30013i) q^{94} +(-5.58438 - 2.31313i) q^{95} +(0.382683 - 0.923880i) q^{96} +(15.8549 - 6.56732i) q^{97} +16.1074i q^{98} +(1.01668 + 2.45448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 8 q^{14} - 16 q^{16} - 16 q^{18} + 16 q^{19} + 16 q^{23} - 8 q^{28} - 32 q^{29} + 16 q^{33} + 16 q^{35} + 32 q^{37} + 8 q^{39} - 56 q^{41} - 16 q^{42} + 16 q^{43} - 16 q^{49} + 16 q^{50} - 24 q^{51} - 16 q^{53} + 8 q^{56} + 16 q^{57} - 32 q^{58} - 16 q^{59} + 16 q^{61} + 8 q^{63} + 8 q^{65} - 16 q^{66} + 16 q^{67} - 16 q^{68} + 16 q^{70} + 72 q^{71} + 8 q^{73} - 32 q^{74} - 16 q^{76} + 48 q^{77} + 8 q^{78} + 8 q^{82} - 80 q^{83} - 16 q^{84} + 8 q^{85} + 16 q^{86} - 16 q^{87} - 16 q^{93} - 16 q^{94} + 72 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 8 * q^14 - 16 * q^16 - 16 * q^18 + 16 * q^19 + 16 * q^23 - 8 * q^28 - 32 * q^29 + 16 * q^33 + 16 * q^35 + 32 * q^37 + 8 * q^39 - 56 * q^41 - 16 * q^42 + 16 * q^43 - 16 * q^49 + 16 * q^50 - 24 * q^51 - 16 * q^53 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 16 * q^59 + 16 * q^61 + 8 * q^63 + 8 * q^65 - 16 * q^66 + 16 * q^67 - 16 * q^68 + 16 * q^70 + 72 * q^71 + 8 * q^73 - 32 * q^74 - 16 * q^76 + 48 * q^77 + 8 * q^78 + 8 * q^82 - 80 * q^83 - 16 * q^84 + 8 * q^85 + 16 * q^86 - 16 * q^87 - 16 * q^93 - 16 * q^94 + 72 * q^97

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