LMFDB - Embedded newform 882.2.f.j.589.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (of order $3$, degree $2$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			589.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.589
Dual form			882.2.f.j.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 2.98735i) q^{5} +(-0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 2.98735i) q^{5} +(-0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -3.44949 q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.72474 - 0.158919i) q^{12} +(-2.44949 + 4.24264i) q^{13} +(-5.94949 + 0.548188i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +(2.94949 - 0.548188i) q^{18} -7.44949 q^{19} +(1.72474 + 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(-3.44949 - 5.97469i) q^{25} +4.89898 q^{26} +(5.00000 - 1.41421i) q^{27} +(-1.44949 - 2.51059i) q^{29} +(3.44949 + 4.87832i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.44949 + 3.14626i) q^{33} +(1.00000 + 1.73205i) q^{34} +(-1.94949 - 2.28024i) q^{36} -7.79796 q^{37} +(3.72474 + 6.45145i) q^{38} +(8.44949 - 0.778539i) q^{39} +(1.72474 - 2.98735i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +2.00000 q^{44} +(6.72474 + 7.86566i) q^{45} -1.00000 q^{46} +(-4.89898 - 8.48528i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(-3.44949 + 5.97469i) q^{50} +(2.00000 + 2.82843i) q^{51} +(-2.44949 - 4.24264i) q^{52} -1.10102 q^{53} +(-3.72474 - 3.62302i) q^{54} -6.89898 q^{55} +(7.44949 + 10.5352i) q^{57} +(-1.44949 + 2.51059i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(2.50000 - 5.42650i) q^{60} +(5.72474 + 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(8.44949 + 14.6349i) q^{65} +(3.44949 - 0.317837i) q^{66} +(1.55051 - 2.68556i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.72474 + 0.158919i) q^{69} +9.89898 q^{71} +(-1.00000 + 2.82843i) q^{72} -2.89898 q^{73} +(3.89898 + 6.75323i) q^{74} +(-5.00000 + 10.8530i) q^{75} +(3.72474 - 6.45145i) q^{76} +(-4.89898 - 6.92820i) q^{78} +(-3.94949 - 6.84072i) q^{79} -3.44949 q^{80} +(-7.00000 - 5.65685i) q^{81} +9.79796 q^{82} +(1.00000 + 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +(1.44949 - 2.51059i) q^{86} +(-2.10102 + 4.56048i) q^{87} +(-1.00000 - 1.73205i) q^{88} +7.10102 q^{89} +(3.44949 - 9.75663i) q^{90} +(0.500000 + 0.866025i) q^{92} +(-10.3485 + 0.953512i) q^{93} +(-4.89898 + 8.48528i) q^{94} +(-12.8485 + 22.2542i) q^{95} +(1.72474 - 0.158919i) q^{96} +(-3.44949 - 5.97469i) q^{97} +(5.89898 - 1.09638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 20 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} - 4 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} + 4 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 24 q^{39} + 2 q^{40} - 4 q^{43} + 8 q^{44} + 22 q^{45} - 4 q^{46} + 2 q^{48} - 4 q^{50} + 8 q^{51} - 24 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} - 4 q^{59} + 10 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} - 4 q^{72} + 8 q^{73} - 4 q^{74} - 20 q^{75} + 10 q^{76} - 6 q^{79} - 4 q^{80} - 28 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} - 28 q^{87} - 4 q^{88} + 48 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 + 2 * q^12 - 14 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 - 20 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 - 4 * q^24 - 4 * q^25 + 20 * q^27 + 4 * q^29 + 4 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 + 8 * q^37 + 10 * q^38 + 24 * q^39 + 2 * q^40 - 4 * q^43 + 8 * q^44 + 22 * q^45 - 4 * q^46 + 2 * q^48 - 4 * q^50 + 8 * q^51 - 24 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 + 4 * q^58 - 4 * q^59 + 10 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 + 4 * q^68 - 2 * q^69 + 20 * q^71 - 4 * q^72 + 8 * q^73 - 4 * q^74 - 20 * q^75 + 10 * q^76 - 6 * q^79 - 4 * q^80 - 28 * q^81 + 4 * q^83 - 4 * q^85 - 4 * q^86 - 28 * q^87 - 4 * q^88 + 48 * q^89 + 4 * q^90 + 2 * q^92 - 12 * q^93 - 22 * q^95 + 2 * q^96 - 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.72474	−	2.98735i	0.771329	−	1.33598i	−0.165505	−	0.986209i	$-0.552925\pi$
$5$	1.72474	−	2.98735i	0.771329	−	1.33598i	0.936835	−	0.349773i	$-0.113741\pi$
$6$	−0.724745	+	1.57313i	−0.295876	+	0.642229i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$	−3.44949			−1.09082
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	1.72474	−	0.158919i	0.497891	−	0.0458759i
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	0.295806	+	0.955248i	$0.404412\pi$
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	−0.975172	+	0.221449i	$0.928921\pi$
$14$		0			0
$15$	−5.94949	+	0.548188i	−1.53615	+	0.141542i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	2.94949	−	0.548188i	0.695201	−	0.129209i
$19$	−7.44949			−1.70903			−0.854515	−	0.519427i	$-0.826146\pi$
$19$	−7.44949			−1.70903			−0.854515	+	0.519427i	$0.826146\pi$
$20$	1.72474	+	2.98735i	0.385665	+	0.667991i
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	−1.00000	−	1.41421i	−0.204124	−	0.288675i
$25$	−3.44949	−	5.97469i	−0.689898	−	1.19494i
$26$	4.89898			0.960769
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$		0			0
$29$	−1.44949	−	2.51059i	−0.269163	−	0.466205i	0.699483	−	0.714650i	$-0.253414\pi$
$29$	−1.44949	−	2.51059i	−0.269163	−	0.466205i	−0.968646	+	0.248445i	$0.920081\pi$
$30$	3.44949	+	4.87832i	0.629788	+	0.890654i
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.44949	+	3.14626i	−0.252324	+	0.547694i
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$	−1.94949	−	2.28024i	−0.324915	−	0.380040i
$37$	−7.79796			−1.28198			−0.640988	−	0.767551i	$-0.721475\pi$
$37$	−7.79796			−1.28198			−0.640988	+	0.767551i	$0.721475\pi$
$38$	3.72474	+	6.45145i	0.604233	+	1.04656i
$39$	8.44949	−	0.778539i	1.35300	−	0.124666i
$40$	1.72474	−	2.98735i	0.272706	−	0.472341i
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	0.175106	+	0.984550i	$0.443973\pi$
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	−0.940198	+	0.340629i	$0.889360\pi$
$42$		0			0
$43$	1.44949	+	2.51059i	0.221045	+	0.382861i	0.955126	−	0.296201i	$-0.0957199\pi$
$43$	1.44949	+	2.51059i	0.221045	+	0.382861i	−0.734080	+	0.679062i	$0.762387\pi$
$44$	2.00000			0.301511
$45$	6.72474	+	7.86566i	1.00247	+	1.17254i
$46$	−1.00000			−0.147442
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	−0.963118	−	0.269081i	$-0.913280\pi$
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	0.248528	−	0.968625i	$-0.420053\pi$
$48$	−0.724745	+	1.57313i	−0.104608	+	0.227062i
$49$		0			0
$50$	−3.44949	+	5.97469i	−0.487832	+	0.844949i
$51$	2.00000	+	2.82843i	0.280056	+	0.396059i
$52$	−2.44949	−	4.24264i	−0.339683	−	0.588348i
$53$	−1.10102			−0.151237			−0.0756184	−	0.997137i	$-0.524093\pi$
$53$	−1.10102			−0.151237			−0.0756184	+	0.997137i	$0.524093\pi$
$54$	−3.72474	−	3.62302i	−0.506874	−	0.493031i
$55$	−6.89898			−0.930258
$56$		0			0
$57$	7.44949	+	10.5352i	0.986709	+	1.39542i
$58$	−1.44949	+	2.51059i	−0.190327	+	0.329657i
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	−0.923749	−	0.382998i	$-0.874892\pi$
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	0.793560	+	0.608492i	$0.208225\pi$
$60$	2.50000	−	5.42650i	0.322749	−	0.700559i
$61$	5.72474	+	9.91555i	0.732978	+	1.26956i	0.955605	+	0.294652i	$0.0952037\pi$
$61$	5.72474	+	9.91555i	0.732978	+	1.26956i	−0.222626	+	0.974904i	$0.571463\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	8.44949	+	14.6349i	1.04803	+	1.81524i
$66$	3.44949	−	0.317837i	0.424603	−	0.0391231i
$67$	1.55051	−	2.68556i	0.189425	−	0.328094i	−0.755634	−	0.654994i	$-0.772671\pi$
$67$	1.55051	−	2.68556i	0.189425	−	0.328094i	0.945059	+	0.326901i	$0.106004\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−1.72474	+	0.158919i	−0.207635	+	0.0191316i
$70$		0			0
$71$	9.89898			1.17479			0.587396	−	0.809299i	$-0.300153\pi$
$71$	9.89898			1.17479			0.587396	+	0.809299i	$0.300153\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	−2.89898			−0.339300			−0.169650	−	0.985504i	$-0.554264\pi$
$73$	−2.89898			−0.339300			−0.169650	+	0.985504i	$0.554264\pi$
$74$	3.89898	+	6.75323i	0.453247	+	0.785047i
$75$	−5.00000	+	10.8530i	−0.577350	+	1.25320i
$76$	3.72474	−	6.45145i	0.427258	−	0.740032i
$77$		0			0
$78$	−4.89898	−	6.92820i	−0.554700	−	0.784465i
$79$	−3.94949	−	6.84072i	−0.444352	−	0.769641i	0.553655	−	0.832746i	$-0.313233\pi$
$79$	−3.94949	−	6.84072i	−0.444352	−	0.769641i	−0.998007	+	0.0631057i	$0.979899\pi$
$80$	−3.44949			−0.385665
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	9.79796			1.08200
$83$	1.00000	+	1.73205i	0.109764	+	0.190117i	0.915675	−	0.401920i	$-0.131657\pi$
$83$	1.00000	+	1.73205i	0.109764	+	0.190117i	−0.805910	+	0.592037i	$0.798324\pi$
$84$		0			0
$85$	−3.44949	+	5.97469i	−0.374150	+	0.648046i
$86$	1.44949	−	2.51059i	0.156302	−	0.270724i
$87$	−2.10102	+	4.56048i	−0.225253	+	0.488935i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	7.10102			0.752707			0.376353	−	0.926476i	$-0.377178\pi$
$89$	7.10102			0.752707			0.376353	+	0.926476i	$0.377178\pi$
$90$	3.44949	−	9.75663i	0.363608	−	1.02844i
$91$		0			0
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	−10.3485	+	0.953512i	−1.07309	+	0.0988746i
$94$	−4.89898	+	8.48528i	−0.505291	+	0.875190i
$95$	−12.8485	+	22.2542i	−1.31823	+	2.28323i
$96$	1.72474	−	0.158919i	0.176031	−	0.0162196i
$97$	−3.44949	−	5.97469i	−0.350243	−	0.606638i	0.636049	−	0.771649i	$-0.280568\pi$
$97$	−3.44949	−	5.97469i	−0.350243	−	0.606638i	−0.986292	+	0.165011i	$0.947234\pi$
$98$		0			0
$99$	5.89898	−	1.09638i	0.592870	−	0.110190i
$100$	6.89898			0.689898
$101$	3.62372	+	6.27647i	0.360574	+	0.624533i	0.988055	−	0.154099i	$-0.0492475\pi$
$101$	3.62372	+	6.27647i	0.360574	+	0.624533i	−0.627481	+	0.778632i	$0.715914\pi$
$102$	1.44949	−	3.14626i	0.143521	−	0.311527i
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$	−2.44949	+	4.24264i	−0.240192	+	0.416025i
$105$		0			0
$106$	0.550510	+	0.953512i	0.0534703	+	0.0926132i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−1.27526	+	5.03723i	−0.122711	+	0.484708i
$109$	−16.6969			−1.59928			−0.799638	−	0.600482i	$-0.794975\pi$
$109$	−16.6969			−1.59928			−0.799638	+	0.600482i	$0.794975\pi$
$110$	3.44949	+	5.97469i	0.328896	+	0.569664i
$111$	7.79796	+	11.0280i	0.740150	+	1.04673i
$112$		0			0
$113$	7.94949	−	13.7689i	0.747825	−	1.29527i	−0.201038	−	0.979583i	$-0.564431\pi$
$113$	7.94949	−	13.7689i	0.747825	−	1.29527i	0.948863	−	0.315688i	$-0.102235\pi$
$114$	5.39898	−	11.7190i	0.505661	−	1.09759i
$115$	−1.72474	−	2.98735i	−0.160833	−	0.278571i
$116$	2.89898			0.269163
$117$	−9.55051	−	11.1708i	−0.882945	−	1.03274i
$118$	2.00000			0.184115
$119$		0			0
$120$	−5.94949	+	0.548188i	−0.543112	+	0.0500425i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	5.72474	−	9.91555i	0.518294	−	0.897712i
$123$	16.8990	−	1.55708i	1.52373	−	0.140397i
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	−6.55051			−0.585895
$126$		0			0
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.10102	−	4.56048i	0.184985	−	0.401528i
$130$	8.44949	−	14.6349i	0.741069	−	1.28357i
$131$	−6.72474	+	11.6476i	−0.587544	+	1.01766i	0.407009	+	0.913424i	$0.366572\pi$
$131$	−6.72474	+	11.6476i	−0.587544	+	1.01766i	−0.994553	+	0.104232i	$0.966762\pi$
$132$	−2.00000	−	2.82843i	−0.174078	−	0.246183i
$133$		0			0
$134$	−3.10102			−0.267887
$135$	4.39898	−	17.3759i	0.378604	−	1.49548i
$136$	−2.00000			−0.171499
$137$	5.89898	+	10.2173i	0.503984	+	0.872926i	0.999989	+	0.00460626i	$0.00146622\pi$
$137$	5.89898	+	10.2173i	0.503984	+	0.872926i	−0.496006	+	0.868319i	$0.665200\pi$
$138$	1.00000	+	1.41421i	0.0851257	+	0.120386i
$139$	4.72474	−	8.18350i	0.400748	−	0.694115i	−0.593069	−	0.805152i	$-0.702084\pi$
$139$	4.72474	−	8.18350i	0.400748	−	0.694115i	0.993816	+	0.111037i	$0.0354171\pi$
$140$		0			0
$141$	−7.10102	+	15.4135i	−0.598014	+	1.29805i
$142$	−4.94949	−	8.57277i	−0.415352	−	0.719411i
$143$	9.79796			0.819346
$144$	2.94949	−	0.548188i	0.245791	−	0.0456823i
$145$	−10.0000			−0.830455
$146$	1.44949	+	2.51059i	0.119961	+	0.207778i
$147$		0			0
$148$	3.89898	−	6.75323i	0.320494	−	0.555112i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	11.8990	−	1.09638i	0.971548	−	0.0895188i
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	0.949637	−	0.313353i	$-0.101452\pi$
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	−0.746190	+	0.665733i	$0.768119\pi$
$152$	−7.44949			−0.604233
$153$	2.00000	−	5.65685i	0.161690	−	0.457330i
$154$		0			0
$155$	−10.3485	−	17.9241i	−0.831209	−	1.43970i
$156$	−3.55051	+	7.70674i	−0.284268	+	0.617033i
$157$	3.17423	−	5.49794i	0.253332	−	0.438783i	−0.711109	−	0.703081i	$-0.751807\pi$
$157$	3.17423	−	5.49794i	0.253332	−	0.438783i	0.964441	+	0.264298i	$0.0851403\pi$
$158$	−3.94949	+	6.84072i	−0.314205	+	0.544218i
$159$	1.10102	+	1.55708i	0.0873166	+	0.123484i
$160$	1.72474	+	2.98735i	0.136353	+	0.236170i
$161$		0			0
$162$	−1.39898	+	8.89060i	−0.109914	+	0.698512i
$163$	−0.202041			−0.0158251			−0.00791254	−	0.999969i	$-0.502519\pi$
$163$	−0.202041			−0.0158251			−0.00791254	+	0.999969i	$0.502519\pi$
$164$	−4.89898	−	8.48528i	−0.382546	−	0.662589i
$165$	6.89898	+	9.75663i	0.537085	+	0.759553i
$166$	1.00000	−	1.73205i	0.0776151	−	0.134433i
$167$	9.34847	−	16.1920i	0.723406	−	1.25298i	−0.236220	−	0.971700i	$-0.575909\pi$
$167$	9.34847	−	16.1920i	0.723406	−	1.25298i	0.959627	−	0.281277i	$-0.0907579\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	6.89898			0.529128
$171$	7.44949	−	21.0703i	0.569677	−	1.61129i
$172$	−2.89898			−0.221045
$173$	−6.44949	−	11.1708i	−0.490346	−	0.849304i	0.509593	−	0.860416i	$-0.329796\pi$
$173$	−6.44949	−	11.1708i	−0.490346	−	0.849304i	−0.999938	+	0.0111123i	$0.996463\pi$
$174$	5.00000	−	0.460702i	0.379049	−	0.0349257i
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	3.44949	−	0.317837i	0.259280	−	0.0238901i
$178$	−3.55051	−	6.14966i	−0.266122	−	0.460937i
$179$	−8.69694			−0.650040			−0.325020	−	0.945707i	$-0.605371\pi$
$179$	−8.69694			−0.650040			−0.325020	+	0.945707i	$0.605371\pi$
$180$	−10.1742	+	1.89097i	−0.758343	+	0.140945i
$181$	−4.34847			−0.323219			−0.161610	−	0.986855i	$-0.551669\pi$
$181$	−4.34847			−0.323219			−0.161610	+	0.986855i	$0.551669\pi$
$182$		0			0
$183$	8.29796	−	18.0116i	0.613403	−	1.33145i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−13.4495	+	23.2952i	−0.988826	+	1.71270i
$186$	6.00000	+	8.48528i	0.439941	+	0.622171i
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$	9.79796			0.714590
$189$		0			0
$190$	25.6969			1.86425
$191$	−6.94949	−	12.0369i	−0.502847	−	0.870957i	−0.999995	−	0.00329106i	$-0.998952\pi$
$191$	−6.94949	−	12.0369i	−0.502847	−	0.870957i	0.497147	−	0.867666i	$-0.334381\pi$
$192$	−1.00000	−	1.41421i	−0.0721688	−	0.102062i
$193$	4.05051	−	7.01569i	0.291562	−	0.505000i	−0.682617	−	0.730776i	$-0.739158\pi$
$193$	4.05051	−	7.01569i	0.291562	−	0.505000i	0.974179	+	0.225776i	$0.0724917\pi$
$194$	−3.44949	+	5.97469i	−0.247659	+	0.428958i
$195$	12.2474	−	26.5843i	0.877058	−	1.90374i
$196$		0			0
$197$	−12.6969			−0.904619			−0.452310	−	0.891861i	$-0.649400\pi$
$197$	−12.6969			−0.904619			−0.452310	+	0.891861i	$0.649400\pi$
$198$	−3.89898	−	4.56048i	−0.277088	−	0.324099i
$199$	−6.89898			−0.489056			−0.244528	−	0.969642i	$-0.578633\pi$
$199$	−6.89898			−0.489056			−0.244528	+	0.969642i	$0.578633\pi$
$200$	−3.44949	−	5.97469i	−0.243916	−	0.422474i
$201$	−5.34847	+	0.492810i	−0.377252	+	0.0347601i
$202$	3.62372	−	6.27647i	0.254964	−	0.441611i
$203$		0			0
$204$	−3.44949	+	0.317837i	−0.241513	+	0.0222531i
$205$	16.8990	+	29.2699i	1.18028	+	2.04430i
$206$	−14.0000			−0.975426
$207$	1.94949	+	2.28024i	0.135499	+	0.158488i
$208$	4.89898			0.339683
$209$	7.44949	+	12.9029i	0.515292	+	0.892512i
$210$		0			0
$211$	−1.55051	+	2.68556i	−0.106742	+	0.184882i	−0.914448	−	0.404703i	$-0.867375\pi$
$211$	−1.55051	+	2.68556i	−0.106742	+	0.184882i	0.807707	+	0.589584i	$0.200708\pi$
$212$	0.550510	−	0.953512i	0.0378092	−	0.0654875i
$213$	−9.89898	−	13.9993i	−0.678267	−	0.959214i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	10.0000			0.681994
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$		0			0
$218$	8.34847	+	14.4600i	0.565430	+	0.979353i
$219$	2.89898	+	4.09978i	0.195895	+	0.277037i
$220$	3.44949	−	5.97469i	0.232565	−	0.402814i
$221$	4.89898	−	8.48528i	0.329541	−	0.570782i
$222$	5.65153	−	12.2672i	0.379306	−	0.823322i
$223$	−10.4495	−	18.0990i	−0.699750	−	1.21200i	−0.968553	−	0.248807i	$-0.919962\pi$
$223$	−10.4495	−	18.0990i	−0.699750	−	1.21200i	0.268804	−	0.963195i	$-0.413372\pi$
$224$		0			0
$225$	20.3485	−	3.78194i	1.35656	−	0.252129i
$226$	−15.8990			−1.05758
$227$	−0.275255	−	0.476756i	−0.0182693	−	0.0316434i	0.856746	−	0.515738i	$-0.172482\pi$
$227$	−0.275255	−	0.476756i	−0.0182693	−	0.0316434i	−0.875016	+	0.484095i	$0.839149\pi$
$228$	−12.8485	+	1.18386i	−0.850911	+	0.0784032i
$229$	−11.6237	+	20.1329i	−0.768117	+	1.33042i	0.170465	+	0.985364i	$0.445473\pi$
$229$	−11.6237	+	20.1329i	−0.768117	+	1.33042i	−0.938583	+	0.345055i	$0.887860\pi$
$230$	−1.72474	+	2.98735i	−0.113726	+	0.196980i
$231$		0			0
$232$	−1.44949	−	2.51059i	−0.0951637	−	0.164828i
$233$	−7.00000			−0.458585			−0.229293	−	0.973358i	$-0.573641\pi$
$233$	−7.00000			−0.458585			−0.229293	+	0.973358i	$0.573641\pi$
$234$	−4.89898	+	13.8564i	−0.320256	+	0.905822i
$235$	−33.7980			−2.20474
$236$	−1.00000	−	1.73205i	−0.0650945	−	0.112747i
$237$	−5.72474	+	12.4261i	−0.371862	+	0.807164i
$238$		0			0
$239$	6.39898	−	11.0834i	0.413916	−	0.716923i	−0.581398	−	0.813619i	$-0.697494\pi$
$239$	6.39898	−	11.0834i	0.413916	−	0.716923i	0.995314	+	0.0966962i	$0.0308275\pi$
$240$	3.44949	+	4.87832i	0.222664	+	0.314894i
$241$	−4.44949	−	7.70674i	−0.286617	−	0.496435i	0.686383	−	0.727240i	$-0.259197\pi$
$241$	−4.44949	−	7.70674i	−0.286617	−	0.496435i	−0.973000	+	0.230805i	$0.925864\pi$
$242$	−7.00000			−0.449977
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$	−11.4495			−0.732978
$245$		0			0
$246$	−9.79796	−	13.8564i	−0.624695	−	0.883452i
$247$	18.2474	−	31.6055i	1.16106	−	2.01101i
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$	1.44949	−	3.14626i	0.0918577	−	0.199386i
$250$	3.27526	+	5.67291i	0.207145	+	0.358786i
$251$	−12.5505			−0.792181			−0.396091	−	0.918211i	$-0.629633\pi$
$251$	−12.5505			−0.792181			−0.396091	+	0.918211i	$0.629633\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	1.50000	+	2.59808i	0.0941184	+	0.163018i
$255$	11.8990	−	1.09638i	0.745143	−	0.0686577i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.8990	−	24.0737i	0.866995	−	1.50168i	0.00194150	−	0.999998i	$-0.499382\pi$
$257$	13.8990	−	24.0737i	0.866995	−	1.50168i	0.865053	−	0.501680i	$-0.167285\pi$
$258$	−5.00000	+	0.460702i	−0.311286	+	0.0286820i
$259$		0			0
$260$	−16.8990			−1.04803
$261$	8.55051	−	1.58919i	0.529263	−	0.0983682i
$262$	13.4495			0.830912
$263$	−8.05051	−	13.9439i	−0.496416	−	0.859817i	0.503576	−	0.863951i	$-0.332017\pi$
$263$	−8.05051	−	13.9439i	−0.496416	−	0.859817i	−0.999991	+	0.00413383i	$0.998684\pi$
$264$	−1.44949	+	3.14626i	−0.0892099	+	0.193639i
$265$	−1.89898	+	3.28913i	−0.116653	+	0.202050i
$266$		0			0
$267$	−7.10102	−	10.0424i	−0.434575	−	0.614582i
$268$	1.55051	+	2.68556i	0.0947125	+	0.164047i
$269$	3.65153			0.222638			0.111319	−	0.993785i	$-0.464493\pi$
$269$	3.65153			0.222638			0.111319	+	0.993785i	$0.464493\pi$
$270$	−17.2474	+	4.87832i	−1.04965	+	0.296885i
$271$	−16.8990			−1.02654			−0.513270	−	0.858227i	$-0.671566\pi$
$271$	−16.8990			−1.02654			−0.513270	+	0.858227i	$0.671566\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$		0			0
$274$	5.89898	−	10.2173i	0.356370	−	0.617252i
$275$	−6.89898	+	11.9494i	−0.416024	+	0.720575i
$276$	0.724745	−	1.57313i	0.0436245	−	0.0946914i
$277$	−5.34847	−	9.26382i	−0.321358	−	0.556609i	0.659410	−	0.751783i	$-0.270806\pi$
$277$	−5.34847	−	9.26382i	−0.321358	−	0.556609i	−0.980769	+	0.195174i	$0.937473\pi$
$278$	−9.44949			−0.566743
$279$	11.6969	+	13.6814i	0.700277	+	0.819086i
$280$		0			0
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	0.996887	+	0.0788417i	$0.0251222\pi$
$281$	9.50000	+	16.4545i	0.566722	+	0.981592i	−0.430165	+	0.902750i	$0.641545\pi$
$282$	16.8990	−	1.55708i	1.00632	−	0.0927227i
$283$	−10.2753	+	17.7973i	−0.610801	+	1.05794i	0.380305	+	0.924861i	$0.375819\pi$
$283$	−10.2753	+	17.7973i	−0.610801	+	1.05794i	−0.991106	+	0.133077i	$0.957514\pi$
$284$	−4.94949	+	8.57277i	−0.293698	+	0.508700i
$285$	44.3207	−	4.08372i	2.62533	−	0.241899i
$286$	−4.89898	−	8.48528i	−0.289683	−	0.501745i
$287$		0			0
$288$	−1.94949	−	2.28024i	−0.114875	−	0.134364i
$289$	−13.0000			−0.764706
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$	−5.00000	+	10.8530i	−0.293105	+	0.636215i
$292$	1.44949	−	2.51059i	0.0848250	−	0.146921i
$293$	13.6237	−	23.5970i	0.795906	−	1.37855i	−0.126356	−	0.991985i	$-0.540328\pi$
$293$	13.6237	−	23.5970i	0.795906	−	1.37855i	0.922262	−	0.386565i	$-0.126339\pi$
$294$		0			0
$295$	3.44949	+	5.97469i	0.200837	+	0.347860i
$296$	−7.79796			−0.453247
$297$	−7.44949	−	7.24604i	−0.432263	−	0.420458i
$298$	−6.00000			−0.347571
$299$	2.44949	+	4.24264i	0.141658	+	0.245358i
$300$	−6.89898	−	9.75663i	−0.398313	−	0.563299i
$301$		0			0
$302$	2.50000	−	4.33013i	0.143859	−	0.249171i
$303$	5.25255	−	11.4012i	0.301751	−	0.654982i
$304$	3.72474	+	6.45145i	0.213629	+	0.370016i
$305$	39.4949			2.26147
$306$	−5.89898	+	1.09638i	−0.337222	+	0.0626757i
$307$	−0.752551			−0.0429504			−0.0214752	−	0.999769i	$-0.506836\pi$
$307$	−0.752551			−0.0429504			−0.0214752	+	0.999769i	$0.506836\pi$
$308$		0			0
$309$	−24.1464	+	2.22486i	−1.37364	+	0.126568i
$310$	−10.3485	+	17.9241i	−0.587754	+	1.01802i
$311$	0.651531	−	1.12848i	0.0369449	−	0.0639905i	−0.846962	−	0.531654i	$-0.821571\pi$
$311$	0.651531	−	1.12848i	0.0369449	−	0.0639905i	0.883907	+	0.467663i	$0.154904\pi$
$312$	8.44949	−	0.778539i	0.478358	−	0.0440761i
$313$	12.3485	+	21.3882i	0.697977	+	1.20893i	0.969167	+	0.246405i	$0.0792495\pi$
$313$	12.3485	+	21.3882i	0.697977	+	1.20893i	−0.271190	+	0.962526i	$0.587417\pi$
$314$	−6.34847			−0.358265
$315$		0			0
$316$	7.89898			0.444352
$317$	4.34847	+	7.53177i	0.244234	+	0.423026i	0.961916	−	0.273345i	$-0.0881300\pi$
$317$	4.34847	+	7.53177i	0.244234	+	0.423026i	−0.717682	+	0.696371i	$0.754797\pi$
$318$	0.797959	−	1.73205i	0.0447473	−	0.0971286i
$319$	−2.89898	+	5.02118i	−0.162312	+	0.281132i
$320$	1.72474	−	2.98735i	0.0964162	−	0.166998i
$321$	12.0000	+	16.9706i	0.669775	+	0.947204i
$322$		0			0
$323$	14.8990			0.829001
$324$	8.39898	−	3.23375i	0.466610	−	0.179653i
$325$	33.7980			1.87477
$326$	0.101021	+	0.174973i	0.00559501	+	0.00969084i
$327$	16.6969	+	23.6130i	0.923343	+	1.30580i
$328$	−4.89898	+	8.48528i	−0.270501	+	0.468521i
$329$		0			0
$330$	5.00000	−	10.8530i	0.275241	−	0.597438i
$331$	12.3485	+	21.3882i	0.678733	+	1.17560i	0.975363	+	0.220608i	$0.0708041\pi$
$331$	12.3485	+	21.3882i	0.678733	+	1.17560i	−0.296629	+	0.954993i	$0.595863\pi$
$332$	−2.00000			−0.109764
$333$	7.79796	−	22.0560i	0.427326	−	1.20866i
$334$	−18.6969			−1.02305
$335$	−5.34847	−	9.26382i	−0.292218	−	0.506137i
$336$		0			0
$337$	−17.6969	+	30.6520i	−0.964014	+	1.66972i	−0.251772	+	0.967787i	$0.581013\pi$
$337$	−17.6969	+	30.6520i	−0.964014	+	1.66972i	−0.712242	+	0.701934i	$0.752320\pi$
$338$	−5.50000	+	9.52628i	−0.299161	+	0.518161i
$339$	−27.4217	+	2.52664i	−1.48934	+	0.137228i
$340$	−3.44949	−	5.97469i	−0.187075	−	0.324023i
$341$	−12.0000			−0.649836
$342$	−21.9722	+	4.08372i	−1.18812	+	0.220822i
$343$		0			0
$344$	1.44949	+	2.51059i	0.0781512	+	0.135362i
$345$	−2.50000	+	5.42650i	−0.134595	+	0.292153i
$346$	−6.44949	+	11.1708i	−0.346727	+	0.600548i
$347$	9.79796	−	16.9706i	0.525982	−	0.911028i	−0.473560	−	0.880762i	$-0.657031\pi$
$347$	9.79796	−	16.9706i	0.525982	−	0.911028i	0.999542	−	0.0302659i	$-0.00963541\pi$
$348$	−2.89898	−	4.09978i	−0.155402	−	0.219771i
$349$	10.4495	+	18.0990i	0.559348	+	0.968820i	0.997551	+	0.0699435i	$0.0222819\pi$
$349$	10.4495	+	18.0990i	0.559348	+	0.968820i	−0.438203	+	0.898876i	$0.644385\pi$
$350$		0			0
$351$	−6.24745	+	24.6773i	−0.333464	+	1.31718i
$352$	2.00000			0.106600
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	−2.00000	−	2.82843i	−0.106299	−	0.150329i
$355$	17.0732	−	29.5717i	0.906152	−	1.56950i
$356$	−3.55051	+	6.14966i	−0.188177	+	0.325932i
$357$		0			0
$358$	4.34847	+	7.53177i	0.229824	+	0.398066i
$359$	10.7980			0.569894			0.284947	−	0.958543i	$-0.408024\pi$
$359$	10.7980			0.569894			0.284947	+	0.958543i	$0.408024\pi$
$360$	6.72474	+	7.86566i	0.354425	+	0.414557i
$361$	36.4949			1.92078
$362$	2.17423	+	3.76588i	0.114275	+	0.197931i
$363$	−12.0732	+	1.11243i	−0.633679	+	0.0583875i
$364$		0			0
$365$	−5.00000	+	8.66025i	−0.261712	+	0.453298i
$366$	−19.7474	+	1.81954i	−1.03222	+	0.0951087i
$367$	2.89898	+	5.02118i	0.151325	+	0.262103i	0.931715	−	0.363190i	$-0.118313\pi$
$367$	2.89898	+	5.02118i	0.151325	+	0.262103i	−0.780389	+	0.625294i	$0.784979\pi$
$368$	−1.00000			−0.0521286
$369$	−19.1010	−	22.3417i	−0.994359	−	1.16306i
$370$	26.8990			1.39841
$371$		0			0
$372$	4.34847	−	9.43879i	0.225458	−	0.489379i
$373$	−1.44949	+	2.51059i	−0.0750517	+	0.129993i	−0.901109	−	0.433593i	$-0.857246\pi$
$373$	−1.44949	+	2.51059i	−0.0750517	+	0.129993i	0.826057	+	0.563587i	$0.190579\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$	6.55051	+	9.26382i	0.338267	+	0.478382i
$376$	−4.89898	−	8.48528i	−0.252646	−	0.437595i
$377$	14.2020			0.731442
$378$		0			0
$379$	−26.4949			−1.36095			−0.680476	−	0.732771i	$-0.738227\pi$
$379$	−26.4949			−1.36095			−0.680476	+	0.732771i	$0.738227\pi$
$380$	−12.8485	−	22.2542i	−0.659113	−	1.14162i
$381$	3.00000	+	4.24264i	0.153695	+	0.217357i
$382$	−6.94949	+	12.0369i	−0.355567	+	0.615860i
$383$	3.44949	−	5.97469i	0.176261	−	0.305292i	−0.764336	−	0.644818i	$-0.776933\pi$
$383$	3.44949	−	5.97469i	0.176261	−	0.305292i	0.940597	+	0.339526i	$0.110266\pi$
$384$	−0.724745	+	1.57313i	−0.0369845	+	0.0802786i
$385$		0			0
$386$	−8.10102			−0.412331
$387$	−8.55051	+	1.58919i	−0.434647	+	0.0807829i
$388$	6.89898			0.350243
$389$	7.55051	+	13.0779i	0.382826	+	0.663074i	0.991465	−	0.130373i	$-0.0416175\pi$
$389$	7.55051	+	13.0779i	0.382826	+	0.663074i	−0.608639	+	0.793447i	$0.708284\pi$
$390$	−29.1464	+	2.68556i	−1.47589	+	0.135989i
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$	23.1969	−	2.13737i	1.17013	−	0.107816i
$394$	6.34847	+	10.9959i	0.319831	+	0.553964i
$395$	−27.2474			−1.37097
$396$	−2.00000	+	5.65685i	−0.100504	+	0.284268i
$397$	−9.30306			−0.466907			−0.233454	−	0.972368i	$-0.575003\pi$
$397$	−9.30306			−0.466907			−0.233454	+	0.972368i	$0.575003\pi$
$398$	3.44949	+	5.97469i	0.172907	+	0.299484i
$399$		0			0
$400$	−3.44949	+	5.97469i	−0.172474	+	0.298735i
$401$	5.05051	−	8.74774i	0.252210	−	0.436841i	−0.711924	−	0.702257i	$-0.752176\pi$
$401$	5.05051	−	8.74774i	0.252210	−	0.436841i	0.964134	+	0.265416i	$0.0855091\pi$
$402$	3.10102	+	4.38551i	0.154665	+	0.218729i
$403$	14.6969	+	25.4558i	0.732107	+	1.26805i
$404$	−7.24745			−0.360574
$405$	−28.9722	+	11.1548i	−1.43964	+	0.554286i
$406$		0			0
$407$	7.79796	+	13.5065i	0.386530	+	0.669490i
$408$	2.00000	+	2.82843i	0.0990148	+	0.140028i
$409$	2.89898	−	5.02118i	0.143345	−	0.248281i	−0.785409	−	0.618977i	$-0.787547\pi$
$409$	2.89898	−	5.02118i	0.143345	−	0.248281i	0.928754	+	0.370696i	$0.120881\pi$
$410$	16.8990	−	29.2699i	0.834581	−	1.44554i
$411$	8.55051	−	18.5597i	0.421766	−	0.915485i
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$	1.00000	−	2.82843i	0.0491473	−	0.139010i
$415$	6.89898			0.338658
$416$	−2.44949	−	4.24264i	−0.120096	−	0.208013i
$417$	−16.2980	+	1.50170i	−0.798114	+	0.0735386i
$418$	7.44949	−	12.9029i	0.364366	−	0.631101i
$419$	12.2753	−	21.2614i	0.599685	−	1.03869i	−0.393182	−	0.919461i	$-0.628626\pi$
$419$	12.2753	−	21.2614i	0.599685	−	1.03869i	0.992867	−	0.119225i	$-0.0380410\pi$
$420$		0			0
$421$	−6.55051	−	11.3458i	−0.319252	−	0.552961i	0.661080	−	0.750316i	$-0.270098\pi$
$421$	−6.55051	−	11.3458i	−0.319252	−	0.552961i	−0.980332	+	0.197354i	$0.936765\pi$
$422$	3.10102			0.150955
$423$	28.8990	−	5.37113i	1.40512	−	0.261153i
$424$	−1.10102			−0.0534703
$425$	6.89898	+	11.9494i	0.334650	+	0.579630i
$426$	−7.17423	+	15.5724i	−0.347593	+	0.754485i
$427$		0			0
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$	−9.79796	−	13.8564i	−0.473050	−	0.668994i
$430$	−5.00000	−	8.66025i	−0.241121	−	0.417635i
$431$	−7.59592			−0.365882			−0.182941	−	0.983124i	$-0.558562\pi$
$431$	−7.59592			−0.365882			−0.182941	+	0.983124i	$0.558562\pi$
$432$	−3.72474	−	3.62302i	−0.179207	−	0.174313i
$433$	−11.7980			−0.566974			−0.283487	−	0.958976i	$-0.591491\pi$
$433$	−11.7980			−0.566974			−0.283487	+	0.958976i	$0.591491\pi$
$434$		0			0
$435$	10.0000	+	14.1421i	0.479463	+	0.678064i
$436$	8.34847	−	14.4600i	0.399819	−	0.692507i
$437$	−3.72474	+	6.45145i	−0.178179	+	0.308615i
$438$	2.10102	−	4.56048i	0.100391	−	0.217908i
$439$	10.8990	+	18.8776i	0.520180	+	0.900978i	0.999725	+	0.0234607i	$0.00746845\pi$
$439$	10.8990	+	18.8776i	0.520180	+	0.900978i	−0.479545	+	0.877517i	$0.659198\pi$
$440$	−6.89898			−0.328896
$441$		0			0
$442$	−9.79796			−0.466041
$443$	2.55051	+	4.41761i	0.121178	+	0.209887i	0.920233	−	0.391372i	$-0.127999\pi$
$443$	2.55051	+	4.41761i	0.121178	+	0.209887i	−0.799054	+	0.601259i	$0.794666\pi$
$444$	−13.4495	+	1.23924i	−0.638285	+	0.0588118i
$445$	12.2474	−	21.2132i	0.580585	−	1.00560i
$446$	−10.4495	+	18.0990i	−0.494798	+	0.857015i
$447$	−10.3485	+	0.953512i	−0.489466	+	0.0450996i
$448$		0			0
$449$	−18.5959			−0.877596			−0.438798	−	0.898586i	$-0.644596\pi$
$449$	−18.5959			−0.877596			−0.438798	+	0.898586i	$0.644596\pi$
$450$	−13.4495	−	15.7313i	−0.634015	−	0.741582i
$451$	19.5959			0.922736
$452$	7.94949	+	13.7689i	0.373913	+	0.647636i
$453$	3.62372	−	7.86566i	0.170257	−	0.369561i
$454$	−0.275255	+	0.476756i	−0.0129184	+	0.0223753i
$455$		0			0
$456$	7.44949	+	10.5352i	0.348854	+	0.493355i
$457$	−15.7474	−	27.2754i	−0.736635	−	1.27589i	−0.954002	−	0.299799i	$-0.903080\pi$
$457$	−15.7474	−	27.2754i	−0.736635	−	1.27589i	0.217368	−	0.976090i	$-0.430253\pi$
$458$	23.2474			1.08628
$459$	−10.0000	+	2.82843i	−0.466760	+	0.132020i
$460$	3.44949			0.160833
$461$	10.1742	+	17.6223i	0.473861	+	0.820752i	0.999552	−	0.0299238i	$-0.00952645\pi$
$461$	10.1742	+	17.6223i	0.473861	+	0.820752i	−0.525691	+	0.850676i	$0.676193\pi$
$462$		0			0
$463$	12.8485	−	22.2542i	0.597119	−	1.03424i	−0.396125	−	0.918197i	$-0.629645\pi$
$463$	12.8485	−	22.2542i	0.597119	−	1.03424i	0.993244	−	0.116044i	$-0.0370213\pi$
$464$	−1.44949	+	2.51059i	−0.0672909	+	0.116551i
$465$	−15.0000	+	32.5590i	−0.695608	+	1.50989i
$466$	3.50000	+	6.06218i	0.162134	+	0.280825i
$467$	−10.0000			−0.462745			−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000			−0.462745			−0.231372	+	0.972865i	$0.574322\pi$
$468$	14.4495	−	2.68556i	0.667928	−	0.124140i
$469$		0			0
$470$	16.8990	+	29.2699i	0.779492	+	1.35012i
$471$	−10.9495	+	1.00889i	−0.504526	+	0.0464872i
$472$	−1.00000	+	1.73205i	−0.0460287	+	0.0797241i
$473$	2.89898	−	5.02118i	0.133295	−	0.230874i
$474$	13.6237	−	1.25529i	0.625758	−	0.0576576i
$475$	25.6969	+	44.5084i	1.17906	+	2.04219i
$476$		0			0
$477$	1.10102	−	3.11416i	0.0504123	−	0.142587i
$478$	−12.7980			−0.585365
$479$	−14.7980	−	25.6308i	−0.676136	−	1.17110i	−0.976135	−	0.217163i	$-0.930320\pi$
$479$	−14.7980	−	25.6308i	−0.676136	−	1.17110i	0.299999	−	0.953939i	$-0.403013\pi$
$480$	2.50000	−	5.42650i	0.114109	−	0.247685i
$481$	19.1010	−	33.0839i	0.870932	−	1.50850i
$482$	−4.44949	+	7.70674i	−0.202669	+	0.351032i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−23.7980			−1.08061
$486$	13.9722	−	6.91215i	0.633792	−	0.313541i
$487$	22.3939			1.01476			0.507382	−	0.861721i	$-0.330613\pi$
$487$	22.3939			1.01476			0.507382	+	0.861721i	$0.330613\pi$
$488$	5.72474	+	9.91555i	0.259147	+	0.448856i
$489$	0.202041	+	0.285729i	0.00913661	+	0.0129211i
$490$		0			0
$491$	1.89898	−	3.28913i	0.0856997	−	0.148436i	−0.819989	−	0.572379i	$-0.806021\pi$
$491$	1.89898	−	3.28913i	0.0856997	−	0.148436i	0.905689	+	0.423942i	$0.139354\pi$
$492$	−7.10102	+	15.4135i	−0.320139	+	0.694894i
$493$	2.89898	+	5.02118i	0.130563	+	0.226143i
$494$	−36.4949			−1.64198
$495$	6.89898	−	19.5133i	0.310086	−	0.877056i
$496$	−6.00000			−0.269408
$497$		0			0
$498$	−3.44949	+	0.317837i	−0.154575	+	0.0142426i
$499$	−16.6969	+	28.9199i	−0.747458	+	1.29463i	0.201580	+	0.979472i	$0.435392\pi$
$499$	−16.6969	+	28.9199i	−0.747458	+	1.29463i	−0.949038	+	0.315163i	$0.897941\pi$
$500$	3.27526	−	5.67291i	0.146474	−	0.253700i
$501$	−32.2474	+	2.97129i	−1.44071	+	0.132748i
$502$	6.27526	+	10.8691i	0.280078	+	0.485110i
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$	−7.97219	+	17.3045i	−0.354058	+	0.768518i
$508$	1.50000	−	2.59808i	0.0665517	−	0.115271i
$509$	−8.44949	+	14.6349i	−0.374517	+	0.648683i	−0.990255	−	0.139269i	$-0.955525\pi$
$509$	−8.44949	+	14.6349i	−0.374517	+	0.648683i	0.615738	+	0.787951i	$0.288858\pi$
$510$	−6.89898	−	9.75663i	−0.305492	−	0.432031i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−37.2474	+	10.5352i	−1.64452	+	0.465139i
$514$	−27.7980			−1.22612
$515$	−24.1464	−	41.8228i	−1.06402	−	1.84293i
$516$	2.89898	+	4.09978i	0.127620	+	0.180483i
$517$	−9.79796	+	16.9706i	−0.430914	+	0.746364i
$518$		0			0
$519$	−9.34847	+	20.2918i	−0.410352	+	0.890711i
$520$	8.44949	+	14.6349i	0.370535	+	0.641785i
$521$	38.6969			1.69534			0.847672	−	0.530521i	$-0.178004\pi$
$521$	38.6969			1.69534			0.847672	+	0.530521i	$0.178004\pi$
$522$	−5.65153	−	6.61037i	−0.247361	−	0.289328i
$523$	−0.348469			−0.0152375			−0.00761875	−	0.999971i	$-0.502425\pi$
$523$	−0.348469			−0.0152375			−0.00761875	+	0.999971i	$0.502425\pi$
$524$	−6.72474	−	11.6476i	−0.293772	−	0.508828i
$525$		0			0
$526$	−8.05051	+	13.9439i	−0.351019	+	0.607983i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	3.44949	−	0.317837i	0.150120	−	0.0138321i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	3.79796			0.164973
$531$	−3.89898	−	4.56048i	−0.169201	−	0.197908i
$532$		0			0
$533$	−24.0000	−	41.5692i	−1.03956	−	1.80056i
$534$	−5.14643	+	11.1708i	−0.222708	+	0.483410i
$535$	−20.6969	+	35.8481i	−0.894807	+	1.54985i
$536$	1.55051	−	2.68556i	0.0669718	−	0.115999i
$537$	8.69694	+	12.2993i	0.375301	+	0.530755i
$538$	−1.82577	−	3.16232i	−0.0787143	−	0.136337i
$539$		0			0
$540$	12.8485	+	12.4976i	0.552910	+	0.537810i
$541$	30.4949			1.31108			0.655539	−	0.755161i	$-0.272441\pi$
$541$	30.4949			1.31108			0.655539	+	0.755161i	$0.272441\pi$
$542$	8.44949	+	14.6349i	0.362937	+	0.628625i
$543$	4.34847	+	6.14966i	0.186611	+	0.263907i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	−28.7980	+	49.8795i	−1.23357	+	2.13660i
$546$		0			0
$547$	−15.7980	−	27.3629i	−0.675472	−	1.16995i	−0.976331	−	0.216283i	$-0.930607\pi$
$547$	−15.7980	−	27.3629i	−0.675472	−	1.16995i	0.300859	−	0.953669i	$-0.402727\pi$
$548$	−11.7980			−0.503984
$549$	−33.7702	+	6.27647i	−1.44127	+	0.267873i
$550$	13.7980			0.588347
$551$	10.7980	+	18.7026i	0.460009	+	0.796758i
$552$	−1.72474	+	0.158919i	−0.0734100	+	0.00676403i
$553$		0			0
$554$	−5.34847	+	9.26382i	−0.227235	+	0.393582i
$555$	46.3939	−	4.27475i	1.96931	−	0.181453i
$556$	4.72474	+	8.18350i	0.200374	+	0.347058i
$557$	−3.10102			−0.131394			−0.0656972	−	0.997840i	$-0.520927\pi$
$557$	−3.10102			−0.131394			−0.0656972	+	0.997840i	$0.520927\pi$
$558$	6.00000	−	16.9706i	0.254000	−	0.718421i
$559$	−14.2020			−0.600682
$560$		0			0
$561$	2.89898	−	6.29253i	0.122395	−	0.265671i
$562$	9.50000	−	16.4545i	0.400733	−	0.694090i
$563$	6.97219	−	12.0762i	0.293843	−	0.508951i	−0.680872	−	0.732402i	$-0.738399\pi$
$563$	6.97219	−	12.0762i	0.293843	−	0.508951i	0.974715	+	0.223451i	$0.0717324\pi$
$564$	−9.79796	−	13.8564i	−0.412568	−	0.583460i
$565$	−27.4217	−	47.4957i	−1.15364	−	1.99816i
$566$	20.5505			0.863802
$567$		0			0
$568$	9.89898			0.415352
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$	−25.6969	−	36.3410i	−1.07633	−	1.52216i
$571$	−7.10102	+	12.2993i	−0.297168	+	0.514711i	−0.975487	−	0.220057i	$-0.929376\pi$
$571$	−7.10102	+	12.2993i	−0.297168	+	0.514711i	0.678319	+	0.734768i	$0.262709\pi$
$572$	−4.89898	+	8.48528i	−0.204837	+	0.354787i
$573$	−10.0732	+	21.8649i	−0.420815	+	0.913421i
$574$		0			0
$575$	−6.89898			−0.287707
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	−23.5959			−0.982311			−0.491155	−	0.871072i	$-0.663425\pi$
$577$	−23.5959			−0.982311			−0.491155	+	0.871072i	$0.663425\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−13.9722	+	1.28740i	−0.580665	+	0.0535026i
$580$	5.00000	−	8.66025i	0.207614	−	0.359597i
$581$		0			0
$582$	11.8990	−	1.09638i	0.493229	−	0.0454463i
$583$	1.10102	+	1.90702i	0.0455996	+	0.0789808i
$584$	−2.89898			−0.119961
$585$	−49.8434	+	9.26382i	−2.06077	+	0.383012i
$586$	−27.2474			−1.12558
$587$	−9.07321	−	15.7153i	−0.374492	−	0.648639i	0.615759	−	0.787934i	$-0.288849\pi$
$587$	−9.07321	−	15.7153i	−0.374492	−	0.648639i	−0.990251	+	0.139296i	$0.955516\pi$
$588$		0			0
$589$	−22.3485	+	38.7087i	−0.920853	+	1.59496i
$590$	3.44949	−	5.97469i	0.142013	−	0.245974i
$591$	12.6969	+	17.9562i	0.522282	+	0.738619i
$592$	3.89898	+	6.75323i	0.160247	+	0.277556i
$593$	14.6969			0.603531			0.301765	−	0.953382i	$-0.402424\pi$
$593$	14.6969			0.603531			0.301765	+	0.953382i	$0.402424\pi$
$594$	−2.55051	+	10.0745i	−0.104649	+	0.413360i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	6.89898	+	9.75663i	0.282356	+	0.399312i
$598$	2.44949	−	4.24264i	0.100167	−	0.173494i
$599$	7.10102	−	12.2993i	0.290140	−	0.502537i	−0.683703	−	0.729761i	$-0.739632\pi$
$599$	7.10102	−	12.2993i	0.290140	−	0.502537i	0.973843	+	0.227224i	$0.0729648\pi$
$600$	−5.00000	+	10.8530i	−0.204124	+	0.443072i
$601$	−6.34847	−	10.9959i	−0.258959	−	0.448531i	0.707004	−	0.707210i	$-0.250046\pi$
$601$	−6.34847	−	10.9959i	−0.258959	−	0.448531i	−0.965963	+	0.258679i	$0.916713\pi$
$602$		0			0
$603$	6.04541	+	7.07107i	0.246188	+	0.287956i
$604$	−5.00000			−0.203447
$605$	−12.0732	−	20.9114i	−0.490846	−	0.850170i
$606$	−12.5000	+	1.15175i	−0.507778	+	0.0467868i
$607$	−4.34847	+	7.53177i	−0.176499	+	0.305705i	−0.940679	−	0.339298i	$-0.889811\pi$
$607$	−4.34847	+	7.53177i	−0.176499	+	0.305705i	0.764180	+	0.645003i	$0.223144\pi$
$608$	3.72474	−	6.45145i	0.151058	−	0.261641i
$609$		0			0
$610$	−19.7474	−	34.2036i	−0.799551	−	1.38486i
$611$	48.0000			1.94187
$612$	3.89898	+	4.56048i	0.157607	+	0.184346i
$613$	14.6969			0.593604			0.296802	−	0.954939i	$-0.404080\pi$
$613$	14.6969			0.593604			0.296802	+	0.954939i	$0.404080\pi$
$614$	0.376276	+	0.651729i	0.0151852	+	0.0263016i
$615$	24.4949	−	53.1687i	0.987730	−	2.14397i
$616$		0			0
$617$	−21.6969	+	37.5802i	−0.873486	+	1.51292i	−0.0151189	+	0.999886i	$0.504813\pi$
$617$	−21.6969	+	37.5802i	−0.873486	+	1.51292i	−0.858367	+	0.513036i	$0.828521\pi$
$618$	14.0000	+	19.7990i	0.563163	+	0.796432i
$619$	−2.07321	−	3.59091i	−0.0833295	−	0.144331i	0.821349	−	0.570426i	$-0.193222\pi$
$619$	−2.07321	−	3.59091i	−0.0833295	−	0.144331i	−0.904678	+	0.426096i	$0.859889\pi$
$620$	20.6969			0.831209
$621$	1.27526	−	5.03723i	0.0511742	−	0.202137i
$622$	−1.30306			−0.0522480
$623$		0			0
$624$	−4.89898	−	6.92820i	−0.196116	−	0.277350i
$625$	5.94949	−	10.3048i	0.237980	−	0.412193i
$626$	12.3485	−	21.3882i	0.493544	−	0.854843i
$627$	10.7980	−	23.4381i	0.431229	−	0.936026i
$628$	3.17423	+	5.49794i	0.126666	+	0.219392i
$629$	15.5959			0.621850
$630$		0			0
$631$	18.1010			0.720590			0.360295	−	0.932838i	$-0.382676\pi$
$631$	18.1010			0.720590			0.360295	+	0.932838i	$0.382676\pi$
$632$	−3.94949	−	6.84072i	−0.157102	−	0.272109i
$633$	5.34847	−	0.492810i	0.212583	−	0.0195874i
$634$	4.34847	−	7.53177i	0.172700	−	0.299125i
$635$	−5.17423	+	8.96204i	−0.205333	+	0.355648i
$636$	−1.89898	+	0.174973i	−0.0752994	+	0.00693812i
$637$		0			0
$638$	5.79796			0.229543
$639$	−9.89898	+	27.9985i	−0.391598	+	1.10761i
$640$	−3.44949			−0.136353
$641$	−20.7474	−	35.9356i	−0.819475	−	1.41937i	−0.906070	−	0.423129i	$-0.860932\pi$
$641$	−20.7474	−	35.9356i	−0.819475	−	1.41937i	0.0865947	−	0.996244i	$-0.472401\pi$
$642$	8.69694	−	18.8776i	0.343241	−	0.745039i
$643$	9.69694	−	16.7956i	0.382410	−	0.662353i	−0.608996	−	0.793173i	$-0.708428\pi$
$643$	9.69694	−	16.7956i	0.382410	−	0.662353i	0.991406	+	0.130820i	$0.0417609\pi$
$644$		0			0
$645$	−10.0000	−	14.1421i	−0.393750	−	0.556846i
$646$	−7.44949	−	12.9029i	−0.293096	−	0.507658i
$647$	21.3031			0.837510			0.418755	−	0.908099i	$-0.362467\pi$
$647$	21.3031			0.837510			0.418755	+	0.908099i	$0.362467\pi$
$648$	−7.00000	−	5.65685i	−0.274986	−	0.222222i
$649$	4.00000			0.157014
$650$	−16.8990	−	29.2699i	−0.662833	−	1.14806i
$651$		0			0
$652$	0.101021	−	0.174973i	0.00395627	−	0.00685246i
$653$	4.89898	−	8.48528i	0.191712	−	0.332055i	−0.754106	−	0.656753i	$-0.771929\pi$
$653$	4.89898	−	8.48528i	0.191712	−	0.332055i	0.945818	+	0.324698i	$0.105263\pi$
$654$	12.1010	−	26.2665i	0.473187	−	1.02710i
$655$	23.1969	+	40.1783i	0.906379	+	1.56990i
$656$	9.79796			0.382546
$657$	2.89898	−	8.19955i	0.113100	−	0.319895i
$658$		0			0
$659$	−2.34847	−	4.06767i	−0.0914834	−	0.158454i	0.816652	−	0.577130i	$-0.195828\pi$
$659$	−2.34847	−	4.06767i	−0.0914834	−	0.158454i	−0.908136	+	0.418676i	$0.862494\pi$
$660$	−11.8990	+	1.09638i	−0.463167	+	0.0426764i
$661$	4.72474	−	8.18350i	0.183771	−	0.318301i	−0.759391	−	0.650635i	$-0.774503\pi$
$661$	4.72474	−	8.18350i	0.183771	−	0.318301i	0.943162	+	0.332334i	$0.107836\pi$
$662$	12.3485	−	21.3882i	0.479937	−	0.831275i
$663$	−16.8990	+	1.55708i	−0.656302	+	0.0604719i
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$	−23.0000	+	4.27475i	−0.891232	+	0.165643i
$667$	−2.89898			−0.112249
$668$	9.34847	+	16.1920i	0.361703	+	0.626488i
$669$	−15.1464	+	32.8769i	−0.585595	+	1.27109i
$670$	−5.34847	+	9.26382i	−0.206629	+	0.357893i
$671$	11.4495	−	19.8311i	0.442003	−	0.765571i
$672$		0			0
$673$	−15.2980	−	26.4968i	−0.589693	−	1.02138i	−0.994272	−	0.106875i	$-0.965915\pi$
$673$	−15.2980	−	26.4968i	−0.589693	−	1.02138i	0.404579	−	0.914503i	$-0.367418\pi$
$674$	35.3939			1.36332
$675$	−25.6969	−	24.9951i	−0.989076	−	0.962063i
$676$	11.0000			0.423077
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	0.689557	−	0.724232i	$-0.257805\pi$
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	−0.971981	+	0.235058i	$0.924472\pi$
$678$	15.8990	+	22.4846i	0.610597	+	0.863514i
$679$		0			0
$680$	−3.44949	+	5.97469i	−0.132282	+	0.229119i
$681$	−0.398979	+	0.866025i	−0.0152889	+	0.0331862i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	32.2020			1.23218			0.616088	−	0.787677i	$-0.288716\pi$
$683$	32.2020			1.23218			0.616088	+	0.787677i	$0.288716\pi$
$684$	14.5227	+	16.9866i	0.555289	+	0.649500i
$685$	40.6969			1.55495
$686$		0			0
$687$	40.0959	−	3.69445i	1.52975	−	0.140952i
$688$	1.44949	−	2.51059i	0.0552613	−	0.0957153i
$689$	2.69694	−	4.67123i	0.102745	−	0.177960i
$690$	5.94949	−	0.548188i	0.226493	−	0.0208692i
$691$	3.47730	+	6.02285i	0.132283	+	0.229120i	0.924556	−	0.381046i	$-0.124436\pi$
$691$	3.47730	+	6.02285i	0.132283	+	0.229120i	−0.792274	+	0.610166i	$0.791103\pi$
$692$	12.8990			0.490346
$693$		0			0
$694$	−19.5959			−0.743851
$695$	−16.2980	−	28.2289i	−0.618217	−	1.07078i
$696$	−2.10102	+	4.56048i	−0.0796390	+	0.172864i
$697$	9.79796	−	16.9706i	0.371124	−	0.642806i
$698$	10.4495	−	18.0990i	0.395519	−	0.685059i
$699$	7.00000	+	9.89949i	0.264764	+	0.374433i
$700$		0			0
$701$	51.3939			1.94112			0.970560	−	0.240860i	$-0.0774293\pi$
$701$	51.3939			1.94112			0.970560	+	0.240860i	$0.0774293\pi$
$702$	24.4949	−	6.92820i	0.924500	−	0.261488i
$703$	58.0908			2.19094
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	33.7980	+	47.7975i	1.27290	+	1.80016i
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$		0			0
$708$	−1.44949	+	3.14626i	−0.0544752	+	0.118244i
$709$	5.79796	+	10.0424i	0.217747	+	0.377149i	0.954119	−	0.299428i	$-0.0967959\pi$
$709$	5.79796	+	10.0424i	0.217747	+	0.377149i	−0.736372	+	0.676577i	$0.763463\pi$
$710$	−34.1464			−1.28149
$711$	23.2980	−	4.33013i	0.873742	−	0.162392i
$712$	7.10102			0.266122
$713$	−3.00000	−	5.19615i	−0.112351	−	0.194597i
$714$		0			0
$715$	16.8990	−	29.2699i	0.631986	−	1.09463i
$716$	4.34847	−	7.53177i	0.162510	−	0.281475i
$717$	−22.0732	+	2.03383i	−0.824339	+	0.0759549i
$718$	−5.39898	−	9.35131i	−0.201488	−	0.348988i
$719$	9.79796			0.365402			0.182701	−	0.983169i	$-0.441516\pi$
$719$	9.79796			0.365402			0.182701	+	0.983169i	$0.441516\pi$
$720$	3.44949	−	9.75663i	0.128555	−	0.363608i
$721$		0			0
$722$	−18.2474	−	31.6055i	−0.679100	−	1.17624i
$723$	−6.44949	+	13.9993i	−0.239859	+	0.520638i
$724$	2.17423	−	3.76588i	0.0808048	−	0.139958i
$725$	−10.0000	+	17.3205i	−0.371391	+	0.643268i
$726$	7.00000	+	9.89949i	0.259794	+	0.367405i
$727$	20.2474	+	35.0696i	0.750936	+	1.30066i	0.947369	+	0.320143i	$0.103731\pi$
$727$	20.2474	+	35.0696i	0.750936	+	1.30066i	−0.196433	+	0.980517i	$0.562936\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	10.0000			0.370117
$731$	−2.89898	−	5.02118i	−0.107223	−	0.185715i
$732$	11.4495	+	16.1920i	0.423185	+	0.598474i
$733$	−6.27526	+	10.8691i	−0.231782	+	0.401458i	−0.958333	−	0.285655i	$-0.907789\pi$
$733$	−6.27526	+	10.8691i	−0.231782	+	0.401458i	0.726551	+	0.687113i	$0.241122\pi$
$734$	2.89898	−	5.02118i	0.107003	−	0.185335i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−6.20204			−0.228455
$738$	−9.79796	+	27.7128i	−0.360668	+	1.02012i
$739$	−25.5959			−0.941561			−0.470781	−	0.882250i	$-0.656028\pi$
$739$	−25.5959			−0.941561			−0.470781	+	0.882250i	$0.656028\pi$
$740$	−13.4495	−	23.2952i	−0.494413	−	0.856349i
$741$	−62.9444	+	5.79972i	−2.31232	+	0.213058i
$742$		0			0
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$	−10.3485	+	0.953512i	−0.379393	+	0.0349574i
$745$	−10.3485	−	17.9241i	−0.379139	−	0.656687i
$746$	2.89898			0.106139
$747$	−5.89898	+	1.09638i	−0.215832	+	0.0401143i
$748$	−4.00000			−0.146254
$749$		0			0
$750$	4.74745	−	10.3048i	0.173352	−	0.376279i
$751$	−20.2980	+	35.1571i	−0.740683	+	1.28290i	0.211502	+	0.977378i	$0.432165\pi$
$751$	−20.2980	+	35.1571i	−0.740683	+	1.28290i	−0.952185	+	0.305523i	$0.901169\pi$
$752$	−4.89898	+	8.48528i	−0.178647	+	0.309426i
$753$	12.5505	+	17.7491i	0.457366	+	0.646813i
$754$	−7.10102	−	12.2993i	−0.258604	−	0.447915i
$755$	17.2474			0.627699
$756$		0			0
$757$	23.3939			0.850265			0.425132	−	0.905131i	$-0.360228\pi$
$757$	23.3939			0.850265			0.425132	+	0.905131i	$0.360228\pi$
$758$	13.2474	+	22.9453i	0.481169	+	0.833409i
$759$	2.00000	+	2.82843i	0.0725954	+	0.102665i
$760$	−12.8485	+	22.2542i	−0.466063	+	0.807245i
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	−0.847331	−	0.531065i	$-0.821792\pi$
$761$	1.00000	−	1.73205i	0.0362500	−	0.0627868i	0.883581	+	0.468278i	$0.155125\pi$
$762$	2.17423	−	4.71940i	0.0787642	−	0.170966i
$763$		0			0
$764$	13.8990			0.502847
$765$	−13.4495	−	15.7313i	−0.486267	−	0.568767i
$766$	−6.89898			−0.249270
$767$	−4.89898	−	8.48528i	−0.176892	−	0.306386i
$768$	1.72474	−	0.158919i	0.0622364	−	0.00573448i
$769$	27.0454	−	46.8440i	0.975282	−	1.68924i	0.296282	−	0.955100i	$-0.404253\pi$
$769$	27.0454	−	46.8440i	0.975282	−	1.68924i	0.679000	−	0.734138i	$-0.262414\pi$
$770$		0			0
$771$	−47.9444	+	4.41761i	−1.72667	+	0.159096i
$772$	4.05051	+	7.01569i	0.145781	+	0.252500i
$773$	19.9444			0.717350			0.358675	−	0.933463i	$-0.383229\pi$
$773$	19.9444			0.717350			0.358675	+	0.933463i	$0.383229\pi$
$774$	5.65153	+	6.61037i	0.203140	+	0.237605i
$775$	−41.3939			−1.48691
$776$	−3.44949	−	5.97469i	−0.123829	−	0.214479i
$777$		0			0
$778$	7.55051	−	13.0779i	0.270699	−	0.468864i
$779$	36.4949	−	63.2110i	1.30757	−	2.26477i
$780$	16.8990	+	23.8988i	0.605081	+	0.855713i
$781$	−9.89898	−	17.1455i	−0.354213	−	0.613515i
$782$	2.00000			0.0715199
$783$	−10.7980	−	10.5031i	−0.385888	−	0.375349i
$784$		0			0
$785$	−10.9495	−	18.9651i	−0.390804	−	0.676892i
$786$	−13.4495	−	19.0205i	−0.479727	−	0.678437i
$787$	23.6969	−	41.0443i	0.844705	−	1.46307i	−0.0411728	−	0.999152i	$-0.513109\pi$
$787$	23.6969	−	41.0443i	0.844705	−	1.46307i	0.885877	−	0.463919i	$-0.153557\pi$
$788$	6.34847	−	10.9959i	0.226155	−	0.391712i
$789$	−11.6691	+	25.3290i	−0.415432	+	0.901737i
$790$	13.6237	+	23.5970i	0.484710	+	0.839543i
$791$		0			0
$792$	5.89898	−	1.09638i	0.209611	−	0.0389580i
$793$	−56.0908			−1.99184
$794$	4.65153	+	8.05669i	0.165077	+	0.285921i
$795$	6.55051	−	0.603566i	0.232323	−	0.0214063i
$796$	3.44949	−	5.97469i	0.122264	−	0.211767i
$797$	17.9722	−	31.1288i	0.636608	−	1.10264i	−0.349564	−	0.936912i	$-0.613670\pi$
$797$	17.9722	−	31.1288i	0.636608	−	1.10264i	0.986172	−	0.165725i	$-0.0529963\pi$
$798$		0			0
$799$	9.79796	+	16.9706i	0.346627	+	0.600375i
$800$	6.89898			0.243916
$801$	−7.10102	+	20.0847i	−0.250902	+	0.709659i
$802$	−10.1010			−0.356679
$803$	2.89898	+	5.02118i	0.102303	+	0.177194i
$804$	2.24745	−	4.87832i	0.0792614	−	0.172045i
$805$		0			0
$806$	14.6969	−	25.4558i	0.517678	−	0.896644i
$807$	−3.65153	−	5.16404i	−0.128540	−	0.181783i
$808$	3.62372	+	6.27647i	0.127482	+	0.220806i
$809$	−35.7980			−1.25859			−0.629295	−	0.777167i	$-0.716656\pi$
$809$	−35.7980			−1.25859			−0.629295	+	0.777167i	$0.716656\pi$
$810$	24.1464	+	19.5133i	0.848419	+	0.685626i
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$	16.8990	+	23.8988i	0.592673	+	0.838166i
$814$	7.79796	−	13.5065i	0.273318	−	0.473401i
$815$	−0.348469	+	0.603566i	−0.0122063	+	0.0211420i
$816$	1.44949	−	3.14626i	0.0507423	−	0.110141i
$817$	−10.7980	−	18.7026i	−0.377773	−	0.654322i
$818$	−5.79796			−0.202721
$819$		0			0
$820$	−33.7980			−1.18028
$821$	−19.7980	−	34.2911i	−0.690954	−	1.19677i	−0.971526	−	0.236934i	$-0.923858\pi$
$821$	−19.7980	−	34.2911i	−0.690954	−	1.19677i	0.280572	−	0.959833i	$-0.409476\pi$
$822$	−20.3485	+	1.87492i	−0.709734	+	0.0653952i
$823$	−22.6969	+	39.3123i	−0.791166	+	1.37034i	0.134080	+	0.990970i	$0.457192\pi$
$823$	−22.6969	+	39.3123i	−0.791166	+	1.37034i	−0.925246	+	0.379368i	$0.876141\pi$
$824$	7.00000	−	12.1244i	0.243857	−	0.422372i
$825$	23.7980	−	2.19275i	0.828539	−	0.0763418i
$826$		0			0
$827$	12.4949			0.434490			0.217245	−	0.976117i	$-0.430293\pi$
$827$	12.4949			0.434490			0.217245	+	0.976117i	$0.430293\pi$
$828$	−2.94949	+	0.548188i	−0.102502	+	0.0190509i
$829$	−30.6969			−1.06615			−0.533074	−	0.846068i	$-0.678963\pi$
$829$	−30.6969			−1.06615			−0.533074	+	0.846068i	$0.678963\pi$
$830$	−3.44949	−	5.97469i	−0.119734	−	0.207385i
$831$	−7.75255	+	16.8277i	−0.268933	+	0.583746i
$832$	−2.44949	+	4.24264i	−0.0849208	+	0.147087i
$833$		0			0
$834$	9.44949	+	13.3636i	0.327209	+	0.462744i
$835$	−32.2474	−	55.8542i	−1.11597	−	1.93291i
$836$	−14.8990			−0.515292
$837$	7.65153	−	30.2234i	0.264476	−	1.04467i
$838$	−24.5505			−0.848083
$839$	−22.4495	−	38.8837i	−0.775042	−	1.34241i	−0.934771	−	0.355252i	$-0.884395\pi$
$839$	−22.4495	−	38.8837i	−0.775042	−	1.34241i	0.159728	−	0.987161i	$-0.448938\pi$
$840$		0			0
$841$	10.2980	−	17.8366i	0.355102	−	0.615055i
$842$	−6.55051	+	11.3458i	−0.225745	+	0.391003i
$843$	13.7702	−	29.8895i	0.474269	−	1.02945i
$844$	−1.55051	−	2.68556i	−0.0533708	−	0.0924409i
$845$	−37.9444			−1.30533
$846$	−19.1010	−	22.3417i	−0.656707	−	0.768123i
$847$		0			0
$848$	0.550510	+	0.953512i	0.0189046	+	0.0327437i
$849$	35.4444	−	3.26586i	1.21645	−	0.112084i
$850$	6.89898	−	11.9494i	0.236633	−	0.409860i
$851$	−3.89898	+	6.75323i	−0.133655	+	0.231498i
$852$	17.0732	−	1.57313i	0.584919	−	0.0538946i
$853$	−19.4217	−	33.6393i	−0.664986	−	1.15179i	−0.979289	−	0.202467i	$-0.935104\pi$
$853$	−19.4217	−	33.6393i	−0.664986	−	1.15179i	0.314303	−	0.949323i	$-0.398229\pi$
$854$		0			0
$855$	−50.0959	−	58.5952i	−1.71324	−	2.00391i
$856$	−12.0000			−0.410152
$857$	−12.5505	−	21.7381i	−0.428717	−	0.742560i	0.568042	−	0.822999i	$-0.307701\pi$
$857$	−12.5505	−	21.7381i	−0.428717	−	0.742560i	−0.996760	+	0.0804393i	$0.974368\pi$
$858$	−7.10102	+	15.4135i	−0.242425	+	0.526208i
$859$	−5.00000	+	8.66025i	−0.170598	+	0.295484i	−0.938629	−	0.344928i	$-0.887903\pi$
$859$	−5.00000	+	8.66025i	−0.170598	+	0.295484i	0.768031	+	0.640412i	$0.221237\pi$
$860$	−5.00000	+	8.66025i	−0.170499	+	0.295312i
$861$		0			0
$862$	3.79796	+	6.57826i	0.129359	+	0.224056i
$863$	2.10102			0.0715196			0.0357598	−	0.999360i	$-0.488615\pi$
$863$	2.10102			0.0715196			0.0357598	+	0.999360i	$0.488615\pi$
$864$	−1.27526	+	5.03723i	−0.0433851	+	0.171370i
$865$	−44.4949			−1.51287
$866$	5.89898	+	10.2173i	0.200455	+	0.347199i
$867$	13.0000	+	18.3848i	0.441503	+	0.624380i
$868$		0			0
$869$	−7.89898	+	13.6814i	−0.267955	+	0.464111i
$870$	7.24745	−	15.7313i	0.245712	−	0.533342i
$871$	7.59592	+	13.1565i	0.257378	+	0.445792i
$872$	−16.6969			−0.565430
$873$	20.3485	−	3.78194i	0.688691	−	0.127999i
$874$	7.44949			0.251983
$875$		0			0
$876$	−5.00000	+	0.460702i	−0.168934	+	0.0155657i
$877$	13.2474	−	22.9453i	0.447335	−	0.774806i	−0.550877	−	0.834586i	$-0.685707\pi$
$877$	13.2474	−	22.9453i	0.447335	−	0.774806i	0.998212	+	0.0597803i	$0.0190400\pi$
$878$	10.8990	−	18.8776i	0.367823	−	0.637088i
$879$	−46.9949	+	4.33013i	−1.58510	+	0.146052i
$880$	3.44949	+	5.97469i	0.116282	+	0.201407i
$881$	19.5959			0.660203			0.330102	−	0.943945i	$-0.392917\pi$
$881$	19.5959			0.660203			0.330102	+	0.943945i	$0.392917\pi$
$882$		0			0
$883$	−0.202041			−0.00679922			−0.00339961	−	0.999994i	$-0.501082\pi$
$883$	−0.202041			−0.00679922			−0.00339961	+	0.999994i	$0.501082\pi$
$884$	4.89898	+	8.48528i	0.164771	+	0.285391i
$885$	5.00000	−	10.8530i	0.168073	−	0.364820i
$886$	2.55051	−	4.41761i	0.0856861	−	0.148413i
$887$	−16.8990	+	29.2699i	−0.567412	+	0.982787i	0.429409	+	0.903110i	$0.358722\pi$
$887$	−16.8990	+	29.2699i	−0.567412	+	0.982787i	−0.996821	+	0.0796764i	$0.974611\pi$
$888$	7.79796	+	11.0280i	0.261682	+	0.370075i
$889$		0			0
$890$	−24.4949			−0.821071
$891$	−2.79796	+	17.7812i	−0.0937352	+	0.595693i
$892$	20.8990			0.699750
$893$	36.4949	+	63.2110i	1.22126	+	2.11528i
$894$	6.00000	+	8.48528i	0.200670	+	0.283790i
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$	3.55051	−	7.70674i	0.118548	−	0.257321i
$898$	9.29796	+	16.1045i	0.310277	+	0.537415i
$899$	−17.3939			−0.580118
$900$	−6.89898	+	19.5133i	−0.229966	+	0.650442i
$901$	2.20204			0.0733606
$902$	−9.79796	−	16.9706i	−0.326236	−	0.565058i
$903$		0			0
$904$	7.94949	−	13.7689i	0.264396	−	0.457947i
$905$	−7.50000	+	12.9904i	−0.249308	+	0.431815i
$906$	−8.62372	+	0.794593i	−0.286504	+	0.0263986i
$907$	13.3485	+	23.1202i	0.443229	+	0.767695i	0.997927	−	0.0643570i	$-0.0204996\pi$
$907$	13.3485	+	23.1202i	0.443229	+	0.767695i	−0.554698	+	0.832052i	$0.687166\pi$
$908$	0.550510			0.0182693
$909$	−21.3763	+	3.97297i	−0.709006	+	0.131775i
$910$		0			0
$911$	22.9949	+	39.8283i	0.761855	+	1.31957i	0.941893	+	0.335912i	$0.109044\pi$
$911$	22.9949	+	39.8283i	0.761855	+	1.31957i	−0.180038	+	0.983660i	$0.557622\pi$
$912$	5.39898	−	11.7190i	0.178778	−	0.388056i
$913$	2.00000	−	3.46410i	0.0661903	−	0.114645i
$914$	−15.7474	+	27.2754i	−0.520879	+	0.902189i
$915$	−39.4949	−	55.8542i	−1.30566	−	1.84648i
$916$	−11.6237	−	20.1329i	−0.384059	−	0.665209i
$917$		0			0
$918$	7.44949	+	7.24604i	0.245870	+	0.239155i
$919$	3.69694			0.121951			0.0609754	−	0.998139i	$-0.480579\pi$
$919$	3.69694			0.121951			0.0609754	+	0.998139i	$0.480579\pi$
$920$	−1.72474	−	2.98735i	−0.0568632	−	0.0984899i
$921$	0.752551	+	1.06427i	0.0247974	+	0.0350688i
$922$	10.1742	−	17.6223i	0.335071	−	0.580359i
$923$	−24.2474	+	41.9978i	−0.798114	+	1.38237i
$924$		0			0
$925$	26.8990	+	46.5904i	0.884433	+	1.53188i
$926$	−25.6969			−0.844454
$927$	27.2929	+	31.9233i	0.896415	+	1.04850i
$928$	2.89898			0.0951637
$929$	−17.1464	−	29.6985i	−0.562556	−	0.974376i	−0.997272	−	0.0738083i	$-0.976485\pi$
$929$	−17.1464	−	29.6985i	−0.562556	−	0.974376i	0.434716	−	0.900567i	$-0.356849\pi$
$930$	35.6969	−	3.28913i	1.17055	−	0.107855i
$931$		0			0
$932$	3.50000	−	6.06218i	0.114646	−	0.198573i
$933$	−2.24745	+	0.207081i	−0.0735782	+	0.00677952i
$934$	5.00000	+	8.66025i	0.163605	+	0.283372i
$935$	13.7980			0.451242
$936$	−9.55051	−	11.1708i	−0.312168	−	0.365130i
$937$	−6.40408			−0.209212			−0.104606	−	0.994514i	$-0.533358\pi$
$937$	−6.40408			−0.209212			−0.104606	+	0.994514i	$0.533358\pi$
$938$		0			0
$939$	17.8990	−	38.8515i	0.584111	−	1.26787i
$940$	16.8990	−	29.2699i	0.551184	−	0.954679i
$941$	1.72474	−	2.98735i	0.0562251	−	0.0973847i	−0.836543	−	0.547901i	$-0.815427\pi$
$941$	1.72474	−	2.98735i	0.0562251	−	0.0973847i	0.892768	+	0.450517i	$0.148760\pi$
$942$	6.34847	+	8.97809i	0.206844	+	0.292522i
$943$	4.89898	+	8.48528i	0.159533	+	0.276319i
$944$	2.00000			0.0650945
$945$		0			0
$946$	−5.79796			−0.188508
$947$	−1.75255	−	3.03551i	−0.0569503	−	0.0986408i	0.836145	−	0.548509i	$-0.184804\pi$
$947$	−1.75255	−	3.03551i	−0.0569503	−	0.0986408i	−0.893095	+	0.449868i	$0.851471\pi$
$948$	−7.89898	−	11.1708i	−0.256547	−	0.362812i
$949$	7.10102	−	12.2993i	0.230509	−	0.399253i
$950$	25.6969	−	44.5084i	0.833719	−	1.44404i
$951$	6.30306	−	13.6814i	0.204391	−	0.443651i
$952$		0			0
$953$	55.3939			1.79438			0.897192	−	0.441641i	$-0.145604\pi$
$953$	55.3939			1.79438			0.897192	+	0.441641i	$0.145604\pi$
$954$	−3.24745	+	0.603566i	−0.105140	+	0.0195412i
$955$	−47.9444			−1.55144
$956$	6.39898	+	11.0834i	0.206958	+	0.358461i
$957$	10.0000	−	0.921404i	0.323254	−	0.0297848i
$958$	−14.7980	+	25.6308i	−0.478100	+	0.828094i
$959$		0			0
$960$	−5.94949	+	0.548188i	−0.192019	+	0.0176927i
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	−38.2020			−1.23168
$963$	12.0000	−	33.9411i	0.386695	−	1.09374i
$964$	8.89898			0.286617
$965$	−13.9722	−	24.2005i	−0.449781	−	0.779043i
$966$		0			0
$967$	7.29796	−	12.6404i	0.234687	−	0.406489i	−0.724495	−	0.689280i	$-0.757927\pi$
$967$	7.29796	−	12.6404i	0.234687	−	0.406489i	0.959182	+	0.282791i	$0.0912603\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	−14.8990	−	21.0703i	−0.478624	−	0.676877i
$970$	11.8990	+	20.6096i	0.382053	+	0.661736i
$971$	53.9444			1.73116			0.865579	−	0.500773i	$-0.166951\pi$
$971$	53.9444			1.73116			0.865579	+	0.500773i	$0.166951\pi$
$972$	−12.9722	−	8.64420i	−0.416083	−	0.277263i
$973$		0			0
$974$	−11.1969	−	19.3937i	−0.358773	−	0.621413i
$975$	−33.7980	−	47.7975i	−1.08240	−	1.53075i
$976$	5.72474	−	9.91555i	0.183245	−	0.317389i
$977$	−0.797959	+	1.38211i	−0.0255290	+	0.0442175i	−0.878508	−	0.477728i	$-0.841460\pi$
$977$	−0.797959	+	1.38211i	−0.0255290	+	0.0442175i	0.852979	+	0.521946i	$0.174794\pi$
$978$	0.146428	−	0.317837i	0.00468226	−	0.0101633i
$979$	−7.10102	−	12.2993i	−0.226950	−	0.393088i
$980$		0			0
$981$	16.6969	−	47.2261i	0.533092	−	1.50781i
$982$	−3.79796			−0.121198
$983$	22.5959	+	39.1373i	0.720698	+	1.24829i	0.960720	+	0.277518i	$0.0895118\pi$
$983$	22.5959	+	39.1373i	0.720698	+	1.24829i	−0.240023	+	0.970767i	$0.577155\pi$
$984$	16.8990	−	1.55708i	0.538720	−	0.0496378i
$985$	−21.8990	+	37.9301i	−0.697760	+	1.20855i
$986$	2.89898	−	5.02118i	0.0923223	−	0.159907i
$987$		0			0
$988$	18.2474	+	31.6055i	0.580529	+	1.00551i
$989$	2.89898			0.0921822
$990$	−20.3485	+	3.78194i	−0.646717	+	0.120198i
$991$	17.7980			0.565371			0.282685	−	0.959213i	$-0.408775\pi$
$991$	17.7980			0.565371			0.282685	+	0.959213i	$0.408775\pi$
$992$	3.00000	+	5.19615i	0.0952501	+	0.164978i
$993$	17.8990	−	38.8515i	0.568007	−	1.23292i
$994$		0			0
$995$	−11.8990	+	20.6096i	−0.377223	+	0.653369i
$996$	2.00000	+	2.82843i	0.0633724	+	0.0896221i
$997$	8.92679	+	15.4616i	0.282714	+	0.489675i	0.972052	−	0.234764i	$-0.0754319\pi$
$997$	8.92679	+	15.4616i	0.282714	+	0.489675i	−0.689338	+	0.724440i	$0.742099\pi$
$998$	33.3939			1.05706
$999$	−38.9898	+	11.0280i	−1.23358	+	0.348910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.j.589.1		4
3.2	odd	2		2646.2.f.k.1765.1		4
7.2	even	3		882.2.h.l.67.2		4
7.3	odd	6		882.2.e.m.373.2		4
7.4	even	3		882.2.e.n.373.1		4
7.5	odd	6		882.2.h.k.67.1		4
7.6	odd	2		126.2.f.c.85.2	yes	4
9.2	odd	6		2646.2.f.k.883.1		4
9.4	even	3		7938.2.a.bn.1.1		2
9.5	odd	6		7938.2.a.bm.1.2		2
9.7	even	3	inner	882.2.f.j.295.2		4
21.2	odd	6		2646.2.h.n.361.2		4
21.5	even	6		2646.2.h.m.361.1		4
21.11	odd	6		2646.2.e.k.1549.1		4
21.17	even	6		2646.2.e.l.1549.2		4
21.20	even	2		378.2.f.d.253.2		4
28.27	even	2		1008.2.r.e.337.1		4
63.2	odd	6		2646.2.e.k.2125.1		4
63.11	odd	6		2646.2.h.n.667.2		4
63.13	odd	6		1134.2.a.p.1.2		2
63.16	even	3		882.2.e.n.655.1		4
63.20	even	6		378.2.f.d.127.2		4
63.25	even	3		882.2.h.l.79.2		4
63.34	odd	6		126.2.f.c.43.1	✓	4
63.38	even	6		2646.2.h.m.667.1		4
63.41	even	6		1134.2.a.i.1.1		2
63.47	even	6		2646.2.e.l.2125.2		4
63.52	odd	6		882.2.h.k.79.1		4
63.61	odd	6		882.2.e.m.655.2		4
84.83	odd	2		3024.2.r.e.1009.2		4
252.83	odd	6		3024.2.r.e.2017.2		4
252.139	even	6		9072.2.a.bk.1.2		2
252.167	odd	6		9072.2.a.bd.1.1		2
252.223	even	6		1008.2.r.e.673.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.1	✓	4	63.34	odd	6
126.2.f.c.85.2	yes	4	7.6	odd	2
378.2.f.d.127.2		4	63.20	even	6
378.2.f.d.253.2		4	21.20	even	2
882.2.e.m.373.2		4	7.3	odd	6
882.2.e.m.655.2		4	63.61	odd	6
882.2.e.n.373.1		4	7.4	even	3
882.2.e.n.655.1		4	63.16	even	3
882.2.f.j.295.2		4	9.7	even	3	inner
882.2.f.j.589.1		4	1.1	even	1	trivial
882.2.h.k.67.1		4	7.5	odd	6
882.2.h.k.79.1		4	63.52	odd	6
882.2.h.l.67.2		4	7.2	even	3
882.2.h.l.79.2		4	63.25	even	3
1008.2.r.e.337.1		4	28.27	even	2
1008.2.r.e.673.2		4	252.223	even	6
1134.2.a.i.1.1		2	63.41	even	6
1134.2.a.p.1.2		2	63.13	odd	6
2646.2.e.k.1549.1		4	21.11	odd	6
2646.2.e.k.2125.1		4	63.2	odd	6
2646.2.e.l.1549.2		4	21.17	even	6
2646.2.e.l.2125.2		4	63.47	even	6
2646.2.f.k.883.1		4	9.2	odd	6
2646.2.f.k.1765.1		4	3.2	odd	2
2646.2.h.m.361.1		4	21.5	even	6
2646.2.h.m.667.1		4	63.38	even	6
2646.2.h.n.361.2		4	21.2	odd	6
2646.2.h.n.667.2		4	63.11	odd	6
3024.2.r.e.1009.2		4	84.83	odd	2
3024.2.r.e.2017.2		4	252.83	odd	6
7938.2.a.bm.1.2		2	9.5	odd	6
7938.2.a.bn.1.1		2	9.4	even	3
9072.2.a.bd.1.1		2	252.167	odd	6
9072.2.a.bk.1.2		2	252.139	even	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 2.98735i) q^{5} +(-0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72474 - 2.98735i) q^{5} +(-0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} -3.44949 q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.72474 - 0.158919i) q^{12} +(-2.44949 + 4.24264i) q^{13} +(-5.94949 + 0.548188i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +(2.94949 - 0.548188i) q^{18} -7.44949 q^{19} +(1.72474 + 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(-3.44949 - 5.97469i) q^{25} +4.89898 q^{26} +(5.00000 - 1.41421i) q^{27} +(-1.44949 - 2.51059i) q^{29} +(3.44949 + 4.87832i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.44949 + 3.14626i) q^{33} +(1.00000 + 1.73205i) q^{34} +(-1.94949 - 2.28024i) q^{36} -7.79796 q^{37} +(3.72474 + 6.45145i) q^{38} +(8.44949 - 0.778539i) q^{39} +(1.72474 - 2.98735i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +2.00000 q^{44} +(6.72474 + 7.86566i) q^{45} -1.00000 q^{46} +(-4.89898 - 8.48528i) q^{47} +(-0.724745 + 1.57313i) q^{48} +(-3.44949 + 5.97469i) q^{50} +(2.00000 + 2.82843i) q^{51} +(-2.44949 - 4.24264i) q^{52} -1.10102 q^{53} +(-3.72474 - 3.62302i) q^{54} -6.89898 q^{55} +(7.44949 + 10.5352i) q^{57} +(-1.44949 + 2.51059i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(2.50000 - 5.42650i) q^{60} +(5.72474 + 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(8.44949 + 14.6349i) q^{65} +(3.44949 - 0.317837i) q^{66} +(1.55051 - 2.68556i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-1.72474 + 0.158919i) q^{69} +9.89898 q^{71} +(-1.00000 + 2.82843i) q^{72} -2.89898 q^{73} +(3.89898 + 6.75323i) q^{74} +(-5.00000 + 10.8530i) q^{75} +(3.72474 - 6.45145i) q^{76} +(-4.89898 - 6.92820i) q^{78} +(-3.94949 - 6.84072i) q^{79} -3.44949 q^{80} +(-7.00000 - 5.65685i) q^{81} +9.79796 q^{82} +(1.00000 + 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +(1.44949 - 2.51059i) q^{86} +(-2.10102 + 4.56048i) q^{87} +(-1.00000 - 1.73205i) q^{88} +7.10102 q^{89} +(3.44949 - 9.75663i) q^{90} +(0.500000 + 0.866025i) q^{92} +(-10.3485 + 0.953512i) q^{93} +(-4.89898 + 8.48528i) q^{94} +(-12.8485 + 22.2542i) q^{95} +(1.72474 - 0.158919i) q^{96} +(-3.44949 - 5.97469i) q^{97} +(5.89898 - 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 20 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} - 4 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} + 4 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 24 q^{39} + 2 q^{40} - 4 q^{43} + 8 q^{44} + 22 q^{45} - 4 q^{46} + 2 q^{48} - 4 q^{50} + 8 q^{51} - 24 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} - 4 q^{59} + 10 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} - 4 q^{72} + 8 q^{73} - 4 q^{74} - 20 q^{75} + 10 q^{76} - 6 q^{79} - 4 q^{80} - 28 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} - 28 q^{87} - 4 q^{88} + 48 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 + 2 * q^12 - 14 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 - 20 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 - 4 * q^24 - 4 * q^25 + 20 * q^27 + 4 * q^29 + 4 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 + 8 * q^37 + 10 * q^38 + 24 * q^39 + 2 * q^40 - 4 * q^43 + 8 * q^44 + 22 * q^45 - 4 * q^46 + 2 * q^48 - 4 * q^50 + 8 * q^51 - 24 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 + 4 * q^58 - 4 * q^59 + 10 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 + 4 * q^68 - 2 * q^69 + 20 * q^71 - 4 * q^72 + 8 * q^73 - 4 * q^74 - 20 * q^75 + 10 * q^76 - 6 * q^79 - 4 * q^80 - 28 * q^81 + 4 * q^83 - 4 * q^85 - 4 * q^86 - 28 * q^87 - 4 * q^88 + 48 * q^89 + 4 * q^90 + 2 * q^92 - 12 * q^93 - 22 * q^95 + 2 * q^96 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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