LMFDB - Embedded newform 882.2.h.l.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not 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			67.1
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.l.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.44949 q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.44949 q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +(-0.724745 + 1.25529i) q^{10} +2.00000 q^{11} +(-1.00000 + 1.41421i) q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(1.27526 + 2.20881i) q^{19} +(-0.724745 - 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} -1.00000 q^{23} +(-0.724745 - 1.57313i) q^{24} -2.89898 q^{25} +(2.44949 + 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(3.44949 + 5.97469i) q^{29} +(2.50000 + 0.230351i) 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} +(2.94949 + 0.548188i) q^{36} +(-5.89898 - 10.2173i) q^{37} -2.55051 q^{38} +(-8.44949 - 0.778539i) q^{39} +1.44949 q^{40} +(4.89898 - 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-2.82577 + 3.30518i) q^{45} +(0.500000 - 0.866025i) q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 + 0.158919i) q^{48} +(1.44949 - 2.51059i) q^{50} +(-3.44949 - 0.317837i) q^{51} -4.89898 q^{52} +(5.44949 - 9.43879i) q^{53} +(-3.72474 + 3.62302i) q^{54} +2.89898 q^{55} +(2.55051 - 3.60697i) q^{57} -6.89898 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-1.44949 + 2.04989i) q^{60} +(3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.55051 - 6.14966i) q^{65} +(3.44949 + 0.317837i) q^{66} +(6.44949 + 11.1708i) q^{67} -2.00000 q^{68} +(0.724745 + 1.57313i) q^{69} +0.101021 q^{71} +(-1.94949 + 2.28024i) q^{72} +(-3.44949 + 5.97469i) q^{73} +11.7980 q^{74} +(2.10102 + 4.56048i) q^{75} +(1.27526 - 2.20881i) q^{76} +(4.89898 - 6.92820i) q^{78} +(0.949490 - 1.64456i) q^{79} +(-0.724745 + 1.25529i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(4.89898 + 8.48528i) q^{82} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +6.89898 q^{86} +(6.89898 - 9.75663i) q^{87} +2.00000 q^{88} +(-8.44949 - 14.6349i) q^{89} +(-1.44949 - 4.09978i) q^{90} +(0.500000 + 0.866025i) q^{92} +(6.00000 - 8.48528i) q^{93} +(4.89898 + 8.48528i) q^{94} +(1.84847 + 3.20164i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(1.44949 + 2.51059i) q^{97} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{11} - 4 q^{12} - 14 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} + 2 q^{24} + 8 q^{25} + 20 q^{27} + 4 q^{29} + 10 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 20 q^{38} - 24 q^{39} - 4 q^{40} - 4 q^{43} - 4 q^{44} - 26 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} - 8 q^{58} - 4 q^{59} + 4 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} - 8 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} + 8 q^{74} + 28 q^{75} + 10 q^{76} - 6 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} + 8 q^{86} + 8 q^{87} + 8 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} + 24 q^{93} - 22 q^{95} - 4 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 8 * q^11 - 4 * q^12 - 14 * q^15 - 2 * q^16 + 4 * q^17 - 4 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^22 - 4 * q^23 + 2 * q^24 + 8 * q^25 + 20 * q^27 + 4 * q^29 + 10 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 20 * q^38 - 24 * q^39 - 4 * q^40 - 4 * q^43 - 4 * q^44 - 26 * q^45 + 2 * q^46 + 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 - 8 * q^58 - 4 * q^59 + 4 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 - 8 * q^68 - 2 * q^69 + 20 * q^71 + 2 * q^72 - 4 * q^73 + 8 * q^74 + 28 * q^75 + 10 * q^76 - 6 * q^79 + 2 * q^80 + 14 * q^81 + 4 * q^83 - 4 * q^85 + 8 * q^86 + 8 * q^87 + 8 * q^88 - 24 * q^89 + 4 * q^90 + 2 * q^92 + 24 * q^93 - 22 * q^95 - 4 * q^96 - 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.724745	−	1.57313i	−0.418432	−	0.908248i
$3$	−0.724745	−	1.57313i	−0.418432	−	0.908248i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.44949			0.648232			0.324116	−	0.946017i	$-0.394933\pi$
$5$	1.44949			0.648232			0.324116	+	0.946017i	$0.394933\pi$
$6$	1.72474	+	0.158919i	0.704124	+	0.0648783i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.94949	+	2.28024i	−0.649830	+	0.760080i
$10$	−0.724745	+	1.25529i	−0.229184	+	0.396959i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	−0.295806	−	0.955248i	$-0.595588\pi$
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710785\pi$
$14$		0			0
$15$	−1.05051	−	2.28024i	−0.271241	−	0.588755i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−1.00000	−	2.82843i	−0.235702	−	0.666667i
$19$	1.27526	+	2.20881i	0.292564	+	0.506735i	0.974415	−	0.224756i	$-0.0721584\pi$
$19$	1.27526	+	2.20881i	0.292564	+	0.506735i	−0.681852	+	0.731491i	$0.738825\pi$
$20$	−0.724745	−	1.25529i	−0.162058	−	0.280692i
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$	−0.724745	−	1.57313i	−0.147938	−	0.321114i
$25$	−2.89898			−0.579796
$26$	2.44949	+	4.24264i	0.480384	+	0.832050i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$		0			0
$29$	3.44949	+	5.97469i	0.640554	+	1.10947i	0.985309	+	0.170780i	$0.0546286\pi$
$29$	3.44949	+	5.97469i	0.640554	+	1.10947i	−0.344755	+	0.938693i	$0.612038\pi$
$30$	2.50000	+	0.230351i	0.456435	+	0.0420561i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−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
$36$	2.94949	+	0.548188i	0.491582	+	0.0913647i
$37$	−5.89898	−	10.2173i	−0.969786	−	1.67972i	−0.696165	−	0.717881i	$-0.745112\pi$
$37$	−5.89898	−	10.2173i	−0.969786	−	1.67972i	−0.273621	−	0.961838i	$-0.588221\pi$
$38$	−2.55051			−0.413747
$39$	−8.44949	−	0.778539i	−1.35300	−	0.124666i
$40$	1.44949			0.229184
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	−0.175106	−	0.984550i	$-0.556027\pi$
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	0.940198	−	0.340629i	$-0.110640\pi$
$42$		0			0
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	−0.999540	−	0.0303367i	$-0.990342\pi$
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	0.473497	−	0.880795i	$-0.342991\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−2.82577	+	3.30518i	−0.421240	+	0.492708i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	−0.248528	−	0.968625i	$-0.579947\pi$
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	0.963118	−	0.269081i	$-0.0867199\pi$
$48$	1.72474	+	0.158919i	0.248945	+	0.0229379i
$49$		0			0
$50$	1.44949	−	2.51059i	0.204989	−	0.355051i
$51$	−3.44949	−	0.317837i	−0.483025	−	0.0445061i
$52$	−4.89898			−0.679366
$53$	5.44949	−	9.43879i	0.748545	−	1.29652i	−0.199975	−	0.979801i	$-0.564086\pi$
$53$	5.44949	−	9.43879i	0.748545	−	1.29652i	0.948520	−	0.316717i	$-0.102581\pi$
$54$	−3.72474	+	3.62302i	−0.506874	+	0.493031i
$55$	2.89898			0.390898
$56$		0			0
$57$	2.55051	−	3.60697i	0.337823	−	0.477754i
$58$	−6.89898			−0.905880
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$	−1.44949	+	2.04989i	−0.187128	+	0.264639i
$61$	3.27526	−	5.67291i	0.419353	−	0.726341i	−0.576521	−	0.817082i	$-0.695590\pi$
$61$	3.27526	−	5.67291i	0.419353	−	0.726341i	0.995875	+	0.0907408i	$0.0289235\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	3.55051	−	6.14966i	0.440387	−	0.762772i
$66$	3.44949	+	0.317837i	0.424603	+	0.0391231i
$67$	6.44949	+	11.1708i	0.787931	+	1.36474i	0.927233	+	0.374486i	$0.122181\pi$
$67$	6.44949	+	11.1708i	0.787931	+	1.36474i	−0.139302	+	0.990250i	$0.544486\pi$
$68$	−2.00000			−0.242536
$69$	0.724745	+	1.57313i	0.0872490	+	0.189383i
$70$		0			0
$71$	0.101021			0.0119889			0.00599446	−	0.999982i	$-0.498092\pi$
$71$	0.101021			0.0119889			0.00599446	+	0.999982i	$0.498092\pi$
$72$	−1.94949	+	2.28024i	−0.229750	+	0.268729i
$73$	−3.44949	+	5.97469i	−0.403732	+	0.699285i	−0.994173	−	0.107796i	$-0.965621\pi$
$73$	−3.44949	+	5.97469i	−0.403732	+	0.699285i	0.590441	+	0.807081i	$0.298954\pi$
$74$	11.7980			1.37148
$75$	2.10102	+	4.56048i	0.242605	+	0.526599i
$76$	1.27526	−	2.20881i	0.146282	−	0.253368i
$77$		0			0
$78$	4.89898	−	6.92820i	0.554700	−	0.784465i
$79$	0.949490	−	1.64456i	0.106826	−	0.185028i	−0.807657	−	0.589653i	$-0.799265\pi$
$79$	0.949490	−	1.64456i	0.106826	−	0.185028i	0.914483	+	0.404625i	$0.132598\pi$
$80$	−0.724745	+	1.25529i	−0.0810289	+	0.140346i
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$	4.89898	+	8.48528i	0.541002	+	0.937043i
$83$	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
$85$	1.44949	−	2.51059i	0.157219	−	0.272312i
$86$	6.89898			0.743936
$87$	6.89898	−	9.75663i	0.739648	−	1.04602i
$88$	2.00000			0.213201
$89$	−8.44949	−	14.6349i	−0.895644	−	1.55130i	−0.833005	−	0.553265i	$-0.813382\pi$
$89$	−8.44949	−	14.6349i	−0.895644	−	1.55130i	−0.0626387	−	0.998036i	$-0.519952\pi$
$90$	−1.44949	−	4.09978i	−0.152790	−	0.432154i
$91$		0			0
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$	6.00000	−	8.48528i	0.622171	−	0.879883i
$94$	4.89898	+	8.48528i	0.505291	+	0.875190i
$95$	1.84847	+	3.20164i	0.189649	+	0.328482i
$96$	−1.00000	+	1.41421i	−0.102062	+	0.144338i
$97$	1.44949	+	2.51059i	0.147173	+	0.254912i	0.930182	−	0.367099i	$-0.119649\pi$
$97$	1.44949	+	2.51059i	0.147173	+	0.254912i	−0.783008	+	0.622011i	$0.786316\pi$
$98$		0			0
$99$	−3.89898	+	4.56048i	−0.391862	+	0.458345i
$100$	1.44949	+	2.51059i	0.144949	+	0.251059i
$101$	17.2474			1.71619			0.858093	−	0.513495i	$-0.171649\pi$
$101$	17.2474			1.71619			0.858093	+	0.513495i	$0.171649\pi$
$102$	2.00000	−	2.82843i	0.198030	−	0.280056i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	2.44949	−	4.24264i	0.240192	−	0.416025i
$105$		0			0
$106$	5.44949	+	9.43879i	0.529301	+	0.916777i
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−1.27526	−	5.03723i	−0.122711	−	0.484708i
$109$	−6.34847	+	10.9959i	−0.608073	+	1.05321i	0.383485	+	0.923547i	$0.374724\pi$
$109$	−6.34847	+	10.9959i	−0.608073	+	1.05321i	−0.991558	+	0.129666i	$0.958609\pi$
$110$	−1.44949	+	2.51059i	−0.138203	+	0.239375i
$111$	−11.7980	+	16.6848i	−1.11981	+	1.58365i
$112$		0			0
$113$	3.05051	−	5.28364i	0.286968	−	0.497043i	−0.686117	−	0.727492i	$-0.740686\pi$
$113$	3.05051	−	5.28364i	0.286968	−	0.497043i	0.973084	+	0.230449i	$0.0740194\pi$
$114$	1.84847	+	4.01229i	0.173125	+	0.375785i
$115$	−1.44949			−0.135166
$116$	3.44949	−	5.97469i	0.320277	−	0.554736i
$117$	4.89898	+	13.8564i	0.452911	+	1.28103i
$118$	2.00000			0.184115
$119$		0			0
$120$	−1.05051	−	2.28024i	−0.0958980	−	0.208156i
$121$	−7.00000			−0.636364
$122$	3.27526	+	5.67291i	0.296528	+	0.513601i
$123$	−16.8990	−	1.55708i	−1.52373	−	0.140397i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	−11.4495			−1.02407
$126$		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
$129$	−6.89898	+	9.75663i	−0.607421	+	0.859023i
$130$	3.55051	+	6.14966i	0.311400	+	0.539361i
$131$	8.55051			0.747062			0.373531	−	0.927618i	$-0.378147\pi$
$131$	8.55051			0.747062			0.373531	+	0.927618i	$0.378147\pi$
$132$	−2.00000	+	2.82843i	−0.174078	+	0.246183i
$133$		0			0
$134$	−12.8990			−1.11430
$135$	7.24745	+	2.04989i	0.623761	+	0.176426i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	7.79796			0.666225			0.333112	−	0.942887i	$-0.391901\pi$
$137$	7.79796			0.666225			0.333112	+	0.942887i	$0.391901\pi$
$138$	−1.72474	−	0.158919i	−0.146820	−	0.0135281i
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	−0.753253	−	0.657730i	$-0.771517\pi$
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	0.946238	+	0.323471i	$0.104850\pi$
$140$		0			0
$141$	−16.8990	−	1.55708i	−1.42315	−	0.131130i
$142$	−0.0505103	+	0.0874863i	−0.00423873	+	0.00734169i
$143$	4.89898	−	8.48528i	0.409673	−	0.709575i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$	−3.44949	−	5.97469i	−0.285482	−	0.494469i
$147$		0			0
$148$	−5.89898	+	10.2173i	−0.484893	+	0.839860i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	−5.00000	−	0.460702i	−0.408248	−	0.0376161i
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$	1.27526	+	2.20881i	0.103437	+	0.179158i
$153$	2.00000	+	5.65685i	0.161690	+	0.457330i
$154$		0			0
$155$	4.34847	+	7.53177i	0.349277	+	0.604966i
$156$	3.55051	+	7.70674i	0.284268	+	0.617033i
$157$	−4.17423	−	7.22999i	−0.333140	−	0.577016i	0.649986	−	0.759947i	$-0.274775\pi$
$157$	−4.17423	−	7.22999i	−0.333140	−	0.577016i	−0.983126	+	0.182931i	$0.941442\pi$
$158$	0.949490	+	1.64456i	0.0755373	+	0.130835i
$159$	−18.7980	−	1.73205i	−1.49078	−	0.137361i
$160$	−0.724745	−	1.25529i	−0.0572961	−	0.0992398i
$161$		0			0
$162$	8.39898	+	3.23375i	0.659886	+	0.254067i
$163$	9.89898	+	17.1455i	0.775348	+	1.34294i	0.934599	+	0.355704i	$0.115759\pi$
$163$	9.89898	+	17.1455i	0.775348	+	1.34294i	−0.159251	+	0.987238i	$0.550908\pi$
$164$	−9.79796			−0.765092
$165$	−2.10102	−	4.56048i	−0.163564	−	0.355033i
$166$	−2.00000			−0.155230
$167$	−5.34847	+	9.26382i	−0.413877	+	0.716856i	−0.995310	−	0.0967384i	$-0.969159\pi$
$167$	−5.34847	+	9.26382i	−0.413877	+	0.716856i	0.581433	+	0.813594i	$0.302492\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	1.44949	+	2.51059i	0.111171	+	0.192553i
$171$	−7.52270	−	1.39816i	−0.575276	−	0.106920i
$172$	−3.44949	+	5.97469i	−0.263021	+	0.455566i
$173$	−1.55051	+	2.68556i	−0.117883	+	0.204180i	−0.918929	−	0.394424i	$-0.870944\pi$
$173$	−1.55051	+	2.68556i	−0.117883	+	0.204180i	0.801045	+	0.598604i	$0.204277\pi$
$174$	5.00000	+	10.8530i	0.379049	+	0.822764i
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	−2.00000	+	2.82843i	−0.150329	+	0.212598i
$178$	16.8990			1.26663
$179$	−10.3485	+	17.9241i	−0.773481	+	1.33971i	0.162163	+	0.986764i	$0.448153\pi$
$179$	−10.3485	+	17.9241i	−0.773481	+	1.33971i	−0.935644	+	0.352944i	$0.885181\pi$
$180$	4.27526	+	0.794593i	0.318659	+	0.0592255i
$181$	10.3485			0.769196			0.384598	−	0.923084i	$-0.374340\pi$
$181$	10.3485			0.769196			0.384598	+	0.923084i	$0.374340\pi$
$182$		0			0
$183$	−11.2980	−	1.04100i	−0.835169	−	0.0769528i
$184$	−1.00000			−0.0737210
$185$	−8.55051	−	14.8099i	−0.628646	−	1.08885i
$186$	4.34847	+	9.43879i	0.318845	+	0.692086i
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	−9.79796			−0.714590
$189$		0			0
$190$	−3.69694			−0.268204
$191$	−2.05051	+	3.55159i	−0.148370	+	0.256984i	−0.930625	−	0.365974i	$-0.880736\pi$
$191$	−2.05051	+	3.55159i	−0.148370	+	0.256984i	0.782255	+	0.622958i	$0.214069\pi$
$192$	−0.724745	−	1.57313i	−0.0523040	−	0.113531i
$193$	8.94949	+	15.5010i	0.644198	+	1.11578i	0.984486	+	0.175463i	$0.0561422\pi$
$193$	8.94949	+	15.5010i	0.644198	+	1.11578i	−0.340288	+	0.940321i	$0.610524\pi$
$194$	−2.89898			−0.208135
$195$	−12.2474	−	1.12848i	−0.877058	−	0.0808124i
$196$		0			0
$197$	16.6969			1.18961			0.594804	−	0.803871i	$-0.297230\pi$
$197$	16.6969			1.18961			0.594804	+	0.803871i	$0.297230\pi$
$198$	−2.00000	−	5.65685i	−0.142134	−	0.402015i
$199$	−1.44949	+	2.51059i	−0.102752	+	0.177971i	−0.912817	−	0.408368i	$-0.866098\pi$
$199$	−1.44949	+	2.51059i	−0.102752	+	0.177971i	0.810066	+	0.586339i	$0.199431\pi$
$200$	−2.89898			−0.204989
$201$	12.8990	−	18.2419i	0.909824	−	1.28669i
$202$	−8.62372	+	14.9367i	−0.606763	+	1.05094i
$203$		0			0
$204$	1.44949	+	3.14626i	0.101485	+	0.220283i
$205$	7.10102	−	12.2993i	0.495957	−	0.859022i
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$	1.94949	−	2.28024i	0.135499	−	0.158488i
$208$	2.44949	+	4.24264i	0.169842	+	0.294174i
$209$	2.55051	+	4.41761i	0.176422	+	0.305573i
$210$		0			0
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	−0.997982	−	0.0634968i	$-0.979775\pi$
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	0.553981	+	0.832529i	$0.313108\pi$
$212$	−10.8990			−0.748545
$213$	−0.0732141	−	0.158919i	−0.00501655	−	0.0108889i
$214$	−12.0000			−0.820303
$215$	−5.00000	−	8.66025i	−0.340997	−	0.590624i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$		0			0
$218$	−6.34847	−	10.9959i	−0.429973	−	0.744734i
$219$	11.8990	+	1.09638i	0.804059	+	0.0740862i
$220$	−1.44949	−	2.51059i	−0.0977246	−	0.169264i
$221$	−4.89898	−	8.48528i	−0.329541	−	0.570782i
$222$	−8.55051	−	18.5597i	−0.573873	−	1.24565i
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	0.618136	−	0.786071i	$-0.287888\pi$
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	−0.989826	+	0.142286i	$0.954555\pi$
$224$		0			0
$225$	5.65153	−	6.61037i	0.376769	−	0.440691i
$226$	3.05051	+	5.28364i	0.202917	+	0.351462i
$227$	5.44949			0.361695			0.180848	−	0.983511i	$-0.442116\pi$
$227$	5.44949			0.361695			0.180848	+	0.983511i	$0.442116\pi$
$228$	−4.39898	−	0.405324i	−0.291330	−	0.0268432i
$229$	−1.24745			−0.0824337			−0.0412169	−	0.999150i	$-0.513123\pi$
$229$	−1.24745			−0.0824337			−0.0412169	+	0.999150i	$0.513123\pi$
$230$	0.724745	−	1.25529i	0.0477883	−	0.0827717i
$231$		0			0
$232$	3.44949	+	5.97469i	0.226470	+	0.392258i
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	0.957599	−	0.288106i	$-0.0930254\pi$
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	−0.728306	+	0.685252i	$0.759692\pi$
$234$	−14.4495	−	2.68556i	−0.944593	−	0.175561i
$235$	7.10102	−	12.2993i	0.463220	−	0.802320i
$236$	−1.00000	+	1.73205i	−0.0650945	+	0.112747i
$237$	−3.27526	−	0.301783i	−0.212751	−	0.0196029i
$238$		0			0
$239$	−3.39898	+	5.88721i	−0.219862	+	0.380812i	−0.954766	−	0.297360i	$-0.903894\pi$
$239$	−3.39898	+	5.88721i	−0.219862	+	0.380812i	0.734904	+	0.678171i	$0.237227\pi$
$240$	2.50000	+	0.230351i	0.161374	+	0.0148691i
$241$	−0.898979			−0.0579084			−0.0289542	−	0.999581i	$-0.509218\pi$
$241$	−0.898979			−0.0579084			−0.0289542	+	0.999581i	$0.509218\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	−12.9722	+	8.64420i	−0.832167	+	0.554526i
$244$	−6.55051			−0.419353
$245$		0			0
$246$	9.79796	−	13.8564i	0.624695	−	0.883452i
$247$	12.4949			0.795031
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$	2.00000	−	2.82843i	0.126745	−	0.179244i
$250$	5.72474	−	9.91555i	0.362065	−	0.627114i
$251$	−17.4495			−1.10140			−0.550701	−	0.834703i	$-0.685640\pi$
$251$	−17.4495			−1.10140			−0.550701	+	0.834703i	$0.685640\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	1.50000	−	2.59808i	0.0941184	−	0.163018i
$255$	−5.00000	−	0.460702i	−0.313112	−	0.0288503i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.20204			−0.511629			−0.255815	−	0.966726i	$-0.582344\pi$
$257$	−8.20204			−0.511629			−0.255815	+	0.966726i	$0.582344\pi$
$258$	−5.00000	−	10.8530i	−0.311286	−	0.675679i
$259$		0			0
$260$	−7.10102			−0.440387
$261$	−20.3485	−	3.78194i	−1.25954	−	0.234096i
$262$	−4.27526	+	7.40496i	−0.264126	+	0.457480i
$263$	25.8990			1.59700			0.798500	−	0.601995i	$-0.205627\pi$
$263$	25.8990			1.59700			0.798500	+	0.601995i	$0.205627\pi$
$264$	−1.44949	−	3.14626i	−0.0892099	−	0.193639i
$265$	7.89898	−	13.6814i	0.485230	−	0.840444i
$266$		0			0
$267$	−16.8990	+	23.8988i	−1.03420	+	1.46258i
$268$	6.44949	−	11.1708i	0.393965	−	0.682368i
$269$	−9.17423	+	15.8902i	−0.559363	+	0.968845i	0.438187	+	0.898884i	$0.355621\pi$
$269$	−9.17423	+	15.8902i	−0.559363	+	0.968845i	−0.997550	+	0.0699611i	$0.977712\pi$
$270$	−5.39898	+	5.25153i	−0.328571	+	0.319598i
$271$	3.55051	+	6.14966i	0.215678	+	0.373565i	0.953482	−	0.301450i	$-0.0974705\pi$
$271$	3.55051	+	6.14966i	0.215678	+	0.373565i	−0.737804	+	0.675015i	$0.764137\pi$
$272$	1.00000	+	1.73205i	0.0606339	+	0.105021i
$273$		0			0
$274$	−3.89898	+	6.75323i	−0.235546	+	0.407978i
$275$	−5.79796			−0.349630
$276$	1.00000	−	1.41421i	0.0601929	−	0.0851257i
$277$	−18.6969			−1.12339			−0.561695	−	0.827344i	$-0.689851\pi$
$277$	−18.6969			−1.12339			−0.561695	+	0.827344i	$0.689851\pi$
$278$	2.27526	+	3.94086i	0.136461	+	0.236357i
$279$	−17.6969	−	3.28913i	−1.05949	−	0.196915i
$280$		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	$0.641545\pi$
$282$	9.79796	−	13.8564i	0.583460	−	0.825137i
$283$	−12.7247	−	22.0399i	−0.756408	−	1.31014i	−0.944672	−	0.328018i	$-0.893619\pi$
$283$	−12.7247	−	22.0399i	−0.756408	−	1.31014i	0.188264	−	0.982118i	$-0.439714\pi$
$284$	−0.0505103	−	0.0874863i	−0.00299723	−	0.00519136i
$285$	3.69694	−	5.22826i	0.218988	−	0.309695i
$286$	4.89898	+	8.48528i	0.289683	+	0.501745i
$287$		0			0
$288$	2.94949	+	0.548188i	0.173800	+	0.0323023i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−10.0000			−0.587220
$291$	2.89898	−	4.09978i	0.169941	−	0.240333i
$292$	6.89898			0.403732
$293$	1.37628	−	2.38378i	0.0804029	−	0.139262i	−0.823020	−	0.568012i	$-0.807713\pi$
$293$	1.37628	−	2.38378i	0.0804029	−	0.139262i	0.903423	+	0.428750i	$0.141046\pi$
$294$		0			0
$295$	−1.44949	−	2.51059i	−0.0843926	−	0.146172i
$296$	−5.89898	−	10.2173i	−0.342871	−	0.593870i
$297$	10.0000	+	2.82843i	0.580259	+	0.164122i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−2.44949	+	4.24264i	−0.141658	+	0.245358i
$300$	2.89898	−	4.09978i	0.167373	−	0.236701i
$301$		0			0
$302$	2.50000	−	4.33013i	0.143859	−	0.249171i
$303$	−12.5000	−	27.1325i	−0.718106	−	1.55872i
$304$	−2.55051			−0.146282
$305$	4.74745	−	8.22282i	0.271838	−	0.470837i
$306$	−5.89898	−	1.09638i	−0.337222	−	0.0626757i
$307$	−25.2474			−1.44095			−0.720474	−	0.693482i	$-0.756076\pi$
$307$	−25.2474			−1.44095			−0.720474	+	0.693482i	$0.756076\pi$
$308$		0			0
$309$	10.1464	+	22.0239i	0.577210	+	1.25289i
$310$	−8.69694			−0.493953
$311$	15.3485	+	26.5843i	0.870332	+	1.50746i	0.861654	+	0.507497i	$0.169429\pi$
$311$	15.3485	+	26.5843i	0.870332	+	1.50746i	0.00867810	+	0.999962i	$0.497238\pi$
$312$	−8.44949	−	0.778539i	−0.478358	−	0.0440761i
$313$	−2.34847	+	4.06767i	−0.132743	+	0.229918i	−0.924733	−	0.380616i	$-0.875712\pi$
$313$	−2.34847	+	4.06767i	−0.132743	+	0.229918i	0.791990	+	0.610534i	$0.209045\pi$
$314$	8.34847			0.471131
$315$		0			0
$316$	−1.89898			−0.106826
$317$	−10.3485	+	17.9241i	−0.581228	+	1.00672i	0.414106	+	0.910229i	$0.364094\pi$
$317$	−10.3485	+	17.9241i	−0.581228	+	1.00672i	−0.995334	+	0.0964878i	$0.969239\pi$
$318$	10.8990	−	15.4135i	0.611184	−	0.864345i
$319$	6.89898	+	11.9494i	0.386269	+	0.669037i
$320$	1.44949			0.0810289
$321$	12.0000	−	16.9706i	0.669775	−	0.947204i
$322$		0			0
$323$	5.10102			0.283828
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$	−7.10102	+	12.2993i	−0.393894	+	0.682244i
$326$	−19.7980			−1.09651
$327$	21.8990	+	2.01778i	1.21102	+	0.111583i
$328$	4.89898	−	8.48528i	0.270501	−	0.468521i
$329$		0			0
$330$	5.00000	+	0.460702i	0.275241	+	0.0253608i
$331$	−2.34847	+	4.06767i	−0.129084	+	0.223579i	−0.923322	−	0.384027i	$-0.874537\pi$
$331$	−2.34847	+	4.06767i	−0.129084	+	0.223579i	0.794238	+	0.607606i	$0.207870\pi$
$332$	1.00000	−	1.73205i	0.0548821	−	0.0950586i
$333$	34.7980	+	6.46750i	1.90692	+	0.354417i
$334$	−5.34847	−	9.26382i	−0.292655	−	0.506894i
$335$	9.34847	+	16.1920i	0.510761	+	0.884665i
$336$		0			0
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	−0.348877	−	0.937168i	$-0.613437\pi$
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	0.986050	−	0.166447i	$-0.0532296\pi$
$338$	11.0000			0.598321
$339$	−10.5227	−	0.969566i	−0.571515	−	0.0526596i
$340$	−2.89898			−0.157219
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	4.97219	−	5.81577i	0.268865	−	0.314481i
$343$		0			0
$344$	−3.44949	−	5.97469i	−0.185984	−	0.322134i
$345$	1.05051	+	2.28024i	0.0565576	+	0.122764i
$346$	−1.55051	−	2.68556i	−0.0833559	−	0.144377i
$347$	−9.79796	−	16.9706i	−0.525982	−	0.911028i	−0.999542	−	0.0302659i	$-0.990365\pi$
$347$	−9.79796	−	16.9706i	−0.525982	−	0.911028i	0.473560	−	0.880762i	$-0.342969\pi$
$348$	−11.8990	−	1.09638i	−0.637852	−	0.0587719i
$349$	5.55051	+	9.61377i	0.297112	+	0.514613i	0.975474	−	0.220115i	$-0.0706432\pi$
$349$	5.55051	+	9.61377i	0.297112	+	0.514613i	−0.678362	+	0.734728i	$0.737310\pi$
$350$		0			0
$351$	18.2474	−	17.7491i	0.973977	−	0.947377i
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	−1.44949	−	3.14626i	−0.0770395	−	0.167222i
$355$	0.146428			0.00777160
$356$	−8.44949	+	14.6349i	−0.447822	+	0.775651i
$357$		0			0
$358$	−10.3485	−	17.9241i	−0.546934	−	0.947317i
$359$	4.39898	+	7.61926i	0.232169	+	0.402129i	0.958446	−	0.285273i	$-0.0920843\pi$
$359$	4.39898	+	7.61926i	0.232169	+	0.402129i	−0.726277	+	0.687402i	$0.758751\pi$
$360$	−2.82577	+	3.30518i	−0.148931	+	0.174198i
$361$	6.24745	−	10.8209i	0.328813	−	0.569521i
$362$	−5.17423	+	8.96204i	−0.271952	+	0.471034i
$363$	5.07321	+	11.0119i	0.266275	+	0.577976i
$364$		0			0
$365$	−5.00000	+	8.66025i	−0.261712	+	0.453298i
$366$	6.55051	−	9.26382i	0.342401	−	0.484228i
$367$	13.7980			0.720248			0.360124	−	0.932905i	$-0.382734\pi$
$367$	13.7980			0.720248			0.360124	+	0.932905i	$0.382734\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	9.79796	+	27.7128i	0.510061	+	1.44267i
$370$	17.1010			0.889040
$371$		0			0
$372$	−10.3485	−	0.953512i	−0.536543	−	0.0494373i
$373$	−6.89898			−0.357216			−0.178608	−	0.983920i	$-0.557159\pi$
$373$	−6.89898			−0.357216			−0.178608	+	0.983920i	$0.557159\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	8.29796	+	18.0116i	0.428505	+	0.930113i
$376$	4.89898	−	8.48528i	0.252646	−	0.437595i
$377$	33.7980			1.74068
$378$		0			0
$379$	22.4949			1.15549			0.577743	−	0.816219i	$-0.303934\pi$
$379$	22.4949			1.15549			0.577743	+	0.816219i	$0.303934\pi$
$380$	1.84847	−	3.20164i	0.0948245	−	0.164241i
$381$	2.17423	+	4.71940i	0.111389	+	0.241782i
$382$	−2.05051	−	3.55159i	−0.104913	−	0.181715i
$383$	2.89898			0.148131			0.0740655	−	0.997253i	$-0.476403\pi$
$383$	2.89898			0.148131			0.0740655	+	0.997253i	$0.476403\pi$
$384$	1.72474	+	0.158919i	0.0880155	+	0.00810978i
$385$		0			0
$386$	−17.8990			−0.911034
$387$	20.3485	+	3.78194i	1.03437	+	0.192247i
$388$	1.44949	−	2.51059i	0.0735867	−	0.127456i
$389$	−24.8990			−1.26243			−0.631214	−	0.775609i	$-0.717443\pi$
$389$	−24.8990			−1.26243			−0.631214	+	0.775609i	$0.717443\pi$
$390$	7.10102	−	10.0424i	0.359574	−	0.508515i
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$	−6.19694	−	13.4511i	−0.312594	−	0.678517i
$394$	−8.34847	+	14.4600i	−0.420590	+	0.728483i
$395$	1.37628	−	2.38378i	0.0692479	−	0.119941i
$396$	5.89898	+	1.09638i	0.296435	+	0.0550950i
$397$	19.3485	+	33.5125i	0.971072	+	1.68195i	0.692332	+	0.721579i	$0.256583\pi$
$397$	19.3485	+	33.5125i	0.971072	+	1.68195i	0.278740	+	0.960367i	$0.410083\pi$
$398$	−1.44949	−	2.51059i	−0.0726564	−	0.125844i
$399$		0			0
$400$	1.44949	−	2.51059i	0.0724745	−	0.125529i
$401$	−19.8990			−0.993708			−0.496854	−	0.867834i	$-0.665511\pi$
$401$	−19.8990			−0.993708			−0.496854	+	0.867834i	$0.665511\pi$
$402$	9.34847	+	20.2918i	0.466259	+	1.01206i
$403$	29.3939			1.46421
$404$	−8.62372	−	14.9367i	−0.429046	−	0.743130i
$405$	−2.02781	−	12.8868i	−0.100763	−	0.640352i
$406$		0			0
$407$	−11.7980	−	20.4347i	−0.584803	−	1.01291i
$408$	−3.44949	−	0.317837i	−0.170775	−	0.0157353i
$409$	−6.89898	−	11.9494i	−0.341133	−	0.590859i	0.643511	−	0.765437i	$-0.277477\pi$
$409$	−6.89898	−	11.9494i	−0.341133	−	0.590859i	−0.984643	+	0.174578i	$0.944144\pi$
$410$	7.10102	+	12.2993i	0.350694	+	0.607421i
$411$	−5.65153	−	12.2672i	−0.278769	−	0.605097i
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$	1.00000	+	2.82843i	0.0491473	+	0.139010i
$415$	1.44949	+	2.51059i	0.0711527	+	0.123240i
$416$	−4.89898			−0.240192
$417$	−7.84847	−	0.723161i	−0.384341	−	0.0354133i
$418$	−5.10102			−0.249499
$419$	14.7247	−	25.5040i	0.719351	−	1.24595i	−0.241906	−	0.970300i	$-0.577773\pi$
$419$	14.7247	−	25.5040i	0.719351	−	1.24595i	0.961257	−	0.275653i	$-0.0888940\pi$
$420$		0			0
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	−0.997662	−	0.0683385i	$-0.978230\pi$
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	0.439648	−	0.898170i	$-0.355103\pi$
$422$	−6.44949	−	11.1708i	−0.313956	−	0.543788i
$423$	9.79796	+	27.7128i	0.476393	+	1.34744i
$424$	5.44949	−	9.43879i	0.264651	−	0.458388i
$425$	−2.89898	+	5.02118i	−0.140621	+	0.243563i
$426$	0.174235	+	0.0160540i	0.00844169	+	0.000777821i
$427$		0			0
$428$	6.00000	−	10.3923i	0.290021	−	0.502331i
$429$	−16.8990	−	1.55708i	−0.815890	−	0.0751764i
$430$	10.0000			0.482243
$431$	−15.7980	+	27.3629i	−0.760961	+	1.31802i	0.181395	+	0.983410i	$0.441939\pi$
$431$	−15.7980	+	27.3629i	−0.760961	+	1.31802i	−0.942356	+	0.334613i	$0.891395\pi$
$432$	−3.72474	+	3.62302i	−0.179207	+	0.174313i
$433$	7.79796			0.374746			0.187373	−	0.982289i	$-0.440003\pi$
$433$	7.79796			0.374746			0.187373	+	0.982289i	$0.440003\pi$
$434$		0			0
$435$	10.0000	−	14.1421i	0.479463	−	0.678064i
$436$	12.6969			0.608073
$437$	−1.27526	−	2.20881i	−0.0610037	−	0.105662i
$438$	−6.89898	+	9.75663i	−0.329646	+	0.466190i
$439$	1.10102	−	1.90702i	0.0525488	−	0.0910173i	−0.838554	−	0.544818i	$-0.816599\pi$
$439$	1.10102	−	1.90702i	0.0525488	−	0.0910173i	0.891103	+	0.453801i	$0.149932\pi$
$440$	2.89898			0.138203
$441$		0			0
$442$	9.79796			0.466041
$443$	7.44949	−	12.9029i	0.353936	−	0.613035i	−0.632999	−	0.774152i	$-0.718176\pi$
$443$	7.44949	−	12.9029i	0.353936	−	0.613035i	0.986935	+	0.161117i	$0.0515098\pi$
$444$	20.3485	+	1.87492i	0.965696	+	0.0889795i
$445$	−12.2474	−	21.2132i	−0.580585	−	1.00560i
$446$	11.1010			0.525649
$447$	4.34847	+	9.43879i	0.205676	+	0.446440i
$448$		0			0
$449$	20.5959			0.971981			0.485991	−	0.873964i	$-0.338459\pi$
$449$	20.5959			0.971981			0.485991	+	0.873964i	$0.338459\pi$
$450$	2.89898	+	8.19955i	0.136659	+	0.386531i
$451$	9.79796	−	16.9706i	0.461368	−	0.799113i
$452$	−6.10102			−0.286968
$453$	3.62372	+	7.86566i	0.170257	+	0.369561i
$454$	−2.72474	+	4.71940i	−0.127879	+	0.221492i
$455$		0			0
$456$	2.55051	−	3.60697i	0.119439	−	0.168912i
$457$	8.74745	−	15.1510i	0.409188	−	0.708735i	−0.585611	−	0.810593i	$-0.699145\pi$
$457$	8.74745	−	15.1510i	0.409188	−	0.708735i	0.994799	+	0.101857i	$0.0324785\pi$
$458$	0.623724	−	1.08032i	0.0291447	−	0.0504801i
$459$	7.44949	−	7.24604i	0.347712	−	0.338216i
$460$	0.724745	+	1.25529i	0.0337914	+	0.0585284i
$461$	2.82577	+	4.89437i	0.131609	+	0.227954i	0.924297	−	0.381674i	$-0.124652\pi$
$461$	2.82577	+	4.89437i	0.131609	+	0.227954i	−0.792688	+	0.609628i	$0.791319\pi$
$462$		0			0
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	−0.905777	−	0.423755i	$-0.860712\pi$
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	0.819871	+	0.572548i	$0.194045\pi$
$464$	−6.89898			−0.320277
$465$	8.69694	−	12.2993i	0.403311	−	0.570368i
$466$	−7.00000			−0.324269
$467$	5.00000	+	8.66025i	0.231372	+	0.400749i	0.958212	−	0.286058i	$-0.0923451\pi$
$467$	5.00000	+	8.66025i	0.231372	+	0.400749i	−0.726840	+	0.686807i	$0.759012\pi$
$468$	9.55051	−	11.1708i	0.441472	−	0.516372i
$469$		0			0
$470$	7.10102	+	12.2993i	0.327546	+	0.567326i
$471$	−8.34847	+	11.8065i	−0.384677	+	0.544016i
$472$	−1.00000	−	1.73205i	−0.0460287	−	0.0797241i
$473$	−6.89898	−	11.9494i	−0.317215	−	0.549433i
$474$	1.89898	−	2.68556i	0.0872230	−	0.123352i
$475$	−3.69694	−	6.40329i	−0.169627	−	0.293803i
$476$		0			0
$477$	10.8990	+	30.8270i	0.499030	+	1.41147i
$478$	−3.39898	−	5.88721i	−0.155466	−	0.269274i
$479$	−9.59592			−0.438449			−0.219224	−	0.975674i	$-0.570353\pi$
$479$	−9.59592			−0.438449			−0.219224	+	0.975674i	$0.570353\pi$
$480$	−1.44949	+	2.04989i	−0.0661599	+	0.0935642i
$481$	−57.7980			−2.63536
$482$	0.449490	−	0.778539i	0.0204737	−	0.0354615i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	2.10102	+	3.63907i	0.0954024	+	0.165242i
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$	18.1969	−	31.5180i	0.824582	−	1.42822i	−0.0776564	−	0.996980i	$-0.524744\pi$
$487$	18.1969	−	31.5180i	0.824582	−	1.42822i	0.902238	−	0.431238i	$-0.141923\pi$
$488$	3.27526	−	5.67291i	0.148264	−	0.256800i
$489$	19.7980	−	27.9985i	0.895295	−	1.26614i
$490$		0			0
$491$	−7.89898	+	13.6814i	−0.356476	+	0.617434i	−0.987369	−	0.158435i	$-0.949355\pi$
$491$	−7.89898	+	13.6814i	−0.356476	+	0.617434i	0.630893	+	0.775869i	$0.282688\pi$
$492$	7.10102	+	15.4135i	0.320139	+	0.694894i
$493$	13.7980			0.621429
$494$	−6.24745	+	10.8209i	−0.281086	+	0.486855i
$495$	−5.65153	+	6.61037i	−0.254017	+	0.297114i
$496$	−6.00000			−0.269408
$497$		0			0
$498$	1.44949	+	3.14626i	0.0649532	+	0.140987i
$499$	−25.3939			−1.13679			−0.568393	−	0.822757i	$-0.692435\pi$
$499$	−25.3939			−1.13679			−0.568393	+	0.822757i	$0.692435\pi$
$500$	5.72474	+	9.91555i	0.256018	+	0.443437i
$501$	18.4495	+	1.69994i	0.824262	+	0.0759478i
$502$	8.72474	−	15.1117i	0.389404	−	0.674468i
$503$	24.4949			1.09217			0.546087	−	0.837729i	$-0.316117\pi$
$503$	24.4949			1.09217			0.546087	+	0.837729i	$0.316117\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	1.00000	−	1.73205i	0.0444554	−	0.0769991i
$507$	−11.0000	+	15.5563i	−0.488527	+	0.690882i
$508$	1.50000	+	2.59808i	0.0665517	+	0.115271i
$509$	7.10102			0.314747			0.157374	−	0.987539i	$-0.449697\pi$
$509$	7.10102			0.314747			0.157374	+	0.987539i	$0.449697\pi$
$510$	2.89898	−	4.09978i	0.128369	−	0.181541i
$511$		0			0
$512$	1.00000			0.0441942
$513$	3.25255	+	12.8475i	0.143604	+	0.567232i
$514$	4.10102	−	7.10318i	0.180888	−	0.313308i
$515$	−20.2929			−0.894210
$516$	11.8990	+	1.09638i	0.523823	+	0.0482653i
$517$	9.79796	−	16.9706i	0.430914	−	0.746364i
$518$		0			0
$519$	5.34847	+	0.492810i	0.234772	+	0.0216320i
$520$	3.55051	−	6.14966i	0.155700	−	0.269681i
$521$	−4.65153	+	8.05669i	−0.203787	+	0.352970i	−0.949746	−	0.313023i	$-0.898658\pi$
$521$	−4.65153	+	8.05669i	−0.203787	+	0.352970i	0.745958	+	0.665993i	$0.231992\pi$
$522$	13.4495	−	15.7313i	0.588668	−	0.688541i
$523$	−7.17423	−	12.4261i	−0.313707	−	0.543357i	0.665455	−	0.746438i	$-0.268238\pi$
$523$	−7.17423	−	12.4261i	−0.313707	−	0.543357i	−0.979162	+	0.203081i	$0.934904\pi$
$524$	−4.27526	−	7.40496i	−0.186765	−	0.323487i
$525$		0			0
$526$	−12.9495	+	22.4292i	−0.564625	+	0.977958i
$527$	12.0000			0.522728
$528$	3.44949	+	0.317837i	0.150120	+	0.0138321i
$529$	−22.0000			−0.956522
$530$	7.89898	+	13.6814i	0.343110	+	0.594284i
$531$	5.89898	+	1.09638i	0.255994	+	0.0475787i
$532$		0			0
$533$	−24.0000	−	41.5692i	−1.03956	−	1.80056i
$534$	−12.2474	−	26.5843i	−0.529999	−	1.15042i
$535$	8.69694	+	15.0635i	0.376001	+	0.651254i
$536$	6.44949	+	11.1708i	0.278576	+	0.482507i
$537$	35.6969	+	3.28913i	1.54044	+	0.141936i
$538$	−9.17423	−	15.8902i	−0.395529	−	0.685077i
$539$		0			0
$540$	−1.84847	−	7.30142i	−0.0795455	−	0.314203i
$541$	9.24745	+	16.0171i	0.397579	+	0.688627i	0.993427	−	0.114471i	$-0.0365172\pi$
$541$	9.24745	+	16.0171i	0.397579	+	0.688627i	−0.595848	+	0.803097i	$0.703184\pi$
$542$	−7.10102			−0.305015
$543$	−7.50000	−	16.2795i	−0.321856	−	0.698621i
$544$	−2.00000			−0.0857493
$545$	−9.20204	+	15.9384i	−0.394172	+	0.682726i
$546$		0			0
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	0.935725	−	0.352730i	$-0.114747\pi$
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	−0.773336	+	0.633996i	$0.781413\pi$
$548$	−3.89898	−	6.75323i	−0.166556	−	0.288484i
$549$	6.55051	+	18.5276i	0.279569	+	0.790740i
$550$	2.89898	−	5.02118i	0.123613	−	0.214104i
$551$	−8.79796	+	15.2385i	−0.374806	+	0.649182i
$552$	0.724745	+	1.57313i	0.0308472	+	0.0669570i
$553$		0			0
$554$	9.34847	−	16.1920i	0.397178	−	0.687933i
$555$	−17.1010	+	24.1845i	−0.725898	+	1.02657i
$556$	−4.55051			−0.192985
$557$	6.44949	−	11.1708i	0.273274	−	0.473324i	−0.696424	−	0.717630i	$-0.745227\pi$
$557$	6.44949	−	11.1708i	0.273274	−	0.473324i	0.969698	+	0.244306i	$0.0785602\pi$
$558$	11.6969	−	13.6814i	0.495171	−	0.579181i
$559$	−33.7980			−1.42950
$560$		0			0
$561$	−6.89898	−	0.635674i	−0.291275	−	0.0268382i
$562$	−19.0000			−0.801467
$563$	−19.9722	−	34.5929i	−0.841728	−	1.45791i	−0.888433	−	0.459006i	$-0.848206\pi$
$563$	−19.9722	−	34.5929i	−0.841728	−	1.45791i	0.0467054	−	0.998909i	$-0.485128\pi$
$564$	7.10102	+	15.4135i	0.299007	+	0.649025i
$565$	4.42168	−	7.65858i	0.186022	−	0.322199i
$566$	25.4495			1.06972
$567$		0			0
$568$	0.101021			0.00423873
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$	2.67934	+	5.81577i	0.112225	+	0.243596i
$571$	−16.8990	−	29.2699i	−0.707200	−	1.22491i	−0.965892	−	0.258947i	$-0.916625\pi$
$571$	−16.8990	−	29.2699i	−0.707200	−	1.22491i	0.258691	−	0.965960i	$-0.416709\pi$
$572$	−9.79796			−0.409673
$573$	7.07321	+	0.651729i	0.295488	+	0.0272263i
$574$		0			0
$575$	2.89898			0.120896
$576$	−1.94949	+	2.28024i	−0.0812287	+	0.0950100i
$577$	−7.79796	+	13.5065i	−0.324633	+	0.562281i	−0.981438	−	0.191779i	$-0.938574\pi$
$577$	−7.79796	+	13.5065i	−0.324633	+	0.562281i	0.656805	+	0.754061i	$0.271908\pi$
$578$	−13.0000			−0.540729
$579$	17.8990	−	25.3130i	0.743856	−	1.05197i
$580$	5.00000	−	8.66025i	0.207614	−	0.359597i
$581$		0			0
$582$	2.10102	+	4.56048i	0.0870901	+	0.189038i
$583$	10.8990	−	18.8776i	0.451390	−	0.781830i
$584$	−3.44949	+	5.97469i	−0.142741	+	0.247234i
$585$	7.10102	+	20.0847i	0.293591	+	0.830401i
$586$	1.37628	+	2.38378i	0.0568534	+	0.0984730i
$587$	8.07321	+	13.9832i	0.333217	+	0.577149i	0.983141	−	0.182850i	$-0.0585324\pi$
$587$	8.07321	+	13.9832i	0.333217	+	0.577149i	−0.649924	+	0.760000i	$0.725199\pi$
$588$		0			0
$589$	−7.65153	+	13.2528i	−0.315276	+	0.546074i
$590$	2.89898			0.119349
$591$	−12.1010	−	26.2665i	−0.497769	−	1.08046i
$592$	11.7980			0.484893
$593$	7.34847	+	12.7279i	0.301765	+	0.522673i	0.976536	−	0.215355i	$-0.0690907\pi$
$593$	7.34847	+	12.7279i	0.301765	+	0.522673i	−0.674770	+	0.738028i	$0.735757\pi$
$594$	−7.44949	+	7.24604i	−0.305656	+	0.297309i
$595$		0			0
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	5.00000	+	0.460702i	0.204636	+	0.0188553i
$598$	−2.44949	−	4.24264i	−0.100167	−	0.173494i
$599$	16.8990	+	29.2699i	0.690474	+	1.19594i	0.971683	+	0.236289i	$0.0759312\pi$
$599$	16.8990	+	29.2699i	0.690474	+	1.19594i	−0.281209	+	0.959646i	$0.590736\pi$
$600$	2.10102	+	4.56048i	0.0857738	+	0.186181i
$601$	8.34847	+	14.4600i	0.340541	+	0.589835i	0.984533	−	0.175198i	$-0.0560564\pi$
$601$	8.34847	+	14.4600i	0.340541	+	0.589835i	−0.643992	+	0.765032i	$0.722723\pi$
$602$		0			0
$603$	−38.0454	−	7.07107i	−1.54933	−	0.287956i
$604$	2.50000	+	4.33013i	0.101724	+	0.176190i
$605$	−10.1464			−0.412511
$606$	29.7474	+	2.74094i	1.20841	+	0.111343i
$607$	−20.6969			−0.840063			−0.420031	−	0.907510i	$-0.637981\pi$
$607$	−20.6969			−0.840063			−0.420031	+	0.907510i	$0.637981\pi$
$608$	1.27526	−	2.20881i	0.0517184	−	0.0895789i
$609$		0			0
$610$	4.74745	+	8.22282i	0.192219	+	0.332932i
$611$	−24.0000	−	41.5692i	−0.970936	−	1.68171i
$612$	3.89898	−	4.56048i	0.157607	−	0.184346i
$613$	7.34847	−	12.7279i	0.296802	−	0.514076i	−0.678601	−	0.734508i	$-0.737413\pi$
$613$	7.34847	−	12.7279i	0.296802	−	0.514076i	0.975402	+	0.220432i	$0.0707466\pi$
$614$	12.6237	−	21.8649i	0.509452	−	0.882397i
$615$	−24.4949	−	2.25697i	−0.987730	−	0.0910098i
$616$		0			0
$617$	7.69694	−	13.3315i	0.309867	−	0.536706i	−0.668466	−	0.743743i	$-0.733049\pi$
$617$	7.69694	−	13.3315i	0.309867	−	0.536706i	0.978333	+	0.207037i	$0.0663821\pi$
$618$	−24.1464	−	2.22486i	−0.971312	−	0.0894970i
$619$	−30.1464			−1.21169			−0.605844	−	0.795584i	$-0.707164\pi$
$619$	−30.1464			−1.21169			−0.605844	+	0.795584i	$0.707164\pi$
$620$	4.34847	−	7.53177i	0.174639	−	0.302483i
$621$	−5.00000	−	1.41421i	−0.200643	−	0.0567504i
$622$	−30.6969			−1.23084
$623$		0			0
$624$	4.89898	−	6.92820i	0.196116	−	0.277350i
$625$	−2.10102			−0.0840408
$626$	−2.34847	−	4.06767i	−0.0938637	−	0.162577i
$627$	5.10102	−	7.21393i	0.203715	−	0.288097i
$628$	−4.17423	+	7.22999i	−0.166570	+	0.288508i
$629$	−23.5959			−0.940831
$630$		0			0
$631$	27.8990			1.11064			0.555320	−	0.831636i	$-0.312596\pi$
$631$	27.8990			1.11064			0.555320	+	0.831636i	$0.312596\pi$
$632$	0.949490	−	1.64456i	0.0377687	−	0.0654173i
$633$	22.2474	+	2.04989i	0.884257	+	0.0814757i
$634$	−10.3485	−	17.9241i	−0.410990	−	0.711856i
$635$	−4.34847			−0.172564
$636$	7.89898	+	17.1455i	0.313215	+	0.679865i
$637$		0			0
$638$	−13.7980			−0.546266
$639$	−0.196938	+	0.230351i	−0.00779076	+	0.00911254i
$640$	−0.724745	+	1.25529i	−0.0286481	+	0.0496199i
$641$	−7.49490			−0.296031			−0.148015	−	0.988985i	$-0.547288\pi$
$641$	−7.49490			−0.296031			−0.148015	+	0.988985i	$0.547288\pi$
$642$	8.69694	+	18.8776i	0.343241	+	0.745039i
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	0.157022	+	0.987595i	$0.449811\pi$
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	−0.933793	+	0.357812i	$0.883523\pi$
$644$		0			0
$645$	−10.0000	+	14.1421i	−0.393750	+	0.556846i
$646$	−2.55051	+	4.41761i	−0.100348	+	0.173809i
$647$	−25.3485	+	43.9048i	−0.996551	+	1.72608i	−0.426412	+	0.904529i	$0.640223\pi$
$647$	−25.3485	+	43.9048i	−0.996551	+	1.72608i	−0.570139	+	0.821548i	$0.693111\pi$
$648$	−1.39898	−	8.89060i	−0.0549571	−	0.349256i
$649$	−2.00000	−	3.46410i	−0.0785069	−	0.135978i
$650$	−7.10102	−	12.2993i	−0.278525	−	0.482419i
$651$		0			0
$652$	9.89898	−	17.1455i	0.387674	−	0.671471i
$653$	9.79796			0.383424			0.191712	−	0.981451i	$-0.438596\pi$
$653$	9.79796			0.383424			0.191712	+	0.981451i	$0.438596\pi$
$654$	−12.6969	+	17.9562i	−0.496490	+	0.702142i
$655$	12.3939			0.484269
$656$	4.89898	+	8.48528i	0.191273	+	0.331295i
$657$	−6.89898	−	19.5133i	−0.269155	−	0.761285i
$658$		0			0
$659$	12.3485	+	21.3882i	0.481028	+	0.833165i	0.999763	−	0.0217701i	$-0.00693018\pi$
$659$	12.3485	+	21.3882i	0.481028	+	0.833165i	−0.518735	+	0.854935i	$0.673597\pi$
$660$	−2.89898	+	4.09978i	−0.112843	+	0.159584i
$661$	2.27526	+	3.94086i	0.0884972	+	0.153282i	0.906876	−	0.421397i	$-0.138460\pi$
$661$	2.27526	+	3.94086i	0.0884972	+	0.153282i	−0.818379	+	0.574679i	$0.805127\pi$
$662$	−2.34847	−	4.06767i	−0.0912758	−	0.158094i
$663$	−9.79796	+	13.8564i	−0.380521	+	0.538138i
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$	−23.0000	+	26.9022i	−0.891232	+	1.04244i
$667$	−3.44949	−	5.97469i	−0.133565	−	0.231341i
$668$	10.6969			0.413877
$669$	−11.1010	+	15.6992i	−0.429190	+	0.606967i
$670$	−18.6969			−0.722326
$671$	6.55051	−	11.3458i	0.252880	−	0.438000i
$672$		0			0
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	0.936894	−	0.349612i	$-0.113687\pi$
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	−0.771220	+	0.636568i	$0.780353\pi$
$674$	11.6969	+	20.2597i	0.450549	+	0.780374i
$675$	−14.4949	−	4.09978i	−0.557909	−	0.157800i
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	−0.689557	−	0.724232i	$-0.742195\pi$
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	0.971981	+	0.235058i	$0.0755280\pi$
$678$	6.10102	−	8.62815i	0.234308	−	0.331362i
$679$		0			0
$680$	1.44949	−	2.51059i	0.0555854	−	0.0962767i
$681$	−3.94949	−	8.57277i	−0.151345	−	0.328509i
$682$	−12.0000			−0.459504
$683$	−25.8990	+	44.8583i	−0.990997	+	1.71646i	−0.379551	+	0.925171i	$0.623921\pi$
$683$	−25.8990	+	44.8583i	−0.990997	+	1.71646i	−0.611446	+	0.791286i	$0.709412\pi$
$684$	2.55051	+	7.21393i	0.0975212	+	0.275832i
$685$	11.3031			0.431868
$686$		0			0
$687$	0.904082	+	1.96240i	0.0344929	+	0.0748703i
$688$	6.89898			0.263021
$689$	−26.6969	−	46.2405i	−1.01707	−	1.76162i
$690$	−2.50000	−	0.230351i	−0.0951734	−	0.00876931i
$691$	25.5227	−	44.2066i	0.970929	−	1.68170i	0.278168	−	0.960533i	$-0.410273\pi$
$691$	25.5227	−	44.2066i	0.970929	−	1.68170i	0.692762	−	0.721167i	$-0.256394\pi$
$692$	3.10102			0.117883
$693$		0			0
$694$	19.5959			0.743851
$695$	3.29796	−	5.71223i	0.125099	−	0.216677i
$696$	6.89898	−	9.75663i	0.261505	−	0.369824i
$697$	−9.79796	−	16.9706i	−0.371124	−	0.642806i
$698$	−11.1010			−0.420180
$699$	7.00000	−	9.89949i	0.264764	−	0.374433i
$700$		0			0
$701$	−7.39388			−0.279263			−0.139631	−	0.990204i	$-0.544592\pi$
$701$	−7.39388			−0.279263			−0.139631	+	0.990204i	$0.544592\pi$
$702$	6.24745	+	24.6773i	0.235795	+	0.931385i
$703$	15.0454	−	26.0594i	0.567448	−	0.982849i
$704$	2.00000			0.0753778
$705$	−24.4949	−	2.25697i	−0.922531	−	0.0850024i
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$		0			0
$708$	3.44949	+	0.317837i	0.129640	+	0.0119451i
$709$	−13.7980	+	23.8988i	−0.518193	+	0.897537i	0.481583	+	0.876400i	$0.340062\pi$
$709$	−13.7980	+	23.8988i	−0.518193	+	0.897537i	−0.999777	+	0.0211367i	$0.993271\pi$
$710$	−0.0732141	+	0.126811i	−0.00274768	+	0.00475911i
$711$	1.89898	+	5.37113i	0.0712173	+	0.201433i
$712$	−8.44949	−	14.6349i	−0.316658	−	0.548468i
$713$	−3.00000	−	5.19615i	−0.112351	−	0.194597i
$714$		0			0
$715$	7.10102	−	12.2993i	0.265563	−	0.459969i
$716$	20.6969			0.773481
$717$	11.7247	+	1.08032i	0.437869	+	0.0403454i
$718$	−8.79796			−0.328337
$719$	4.89898	+	8.48528i	0.182701	+	0.316448i	0.942799	−	0.333360i	$-0.108183\pi$
$719$	4.89898	+	8.48528i	0.182701	+	0.316448i	−0.760098	+	0.649808i	$0.774849\pi$
$720$	−1.44949	−	4.09978i	−0.0540193	−	0.152790i
$721$		0			0
$722$	6.24745	+	10.8209i	0.232506	+	0.402712i
$723$	0.651531	+	1.41421i	0.0242307	+	0.0525952i
$724$	−5.17423	−	8.96204i	−0.192299	−	0.333071i
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$	−12.0732	−	1.11243i	−0.448079	−	0.0412862i
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	0.776448	−	0.630181i	$-0.217019\pi$
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	−0.933977	+	0.357333i	$0.883686\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	−13.7980			−0.510336
$732$	4.74745	+	10.3048i	0.175471	+	0.380877i
$733$	17.4495			0.644512			0.322256	−	0.946653i	$-0.395559\pi$
$733$	17.4495			0.644512			0.322256	+	0.946653i	$0.395559\pi$
$734$	−6.89898	+	11.9494i	−0.254646	+	0.441060i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	12.8990	+	22.3417i	0.475140	+	0.822967i
$738$	−28.8990	−	5.37113i	−1.06379	−	0.197714i
$739$	−6.79796	+	11.7744i	−0.250067	+	0.433129i	−0.963544	−	0.267550i	$-0.913786\pi$
$739$	−6.79796	+	11.7744i	−0.250067	+	0.433129i	0.713477	+	0.700679i	$0.247119\pi$
$740$	−8.55051	+	14.8099i	−0.314323	+	0.544423i
$741$	−9.05561	−	19.6561i	−0.332666	−	0.722086i
$742$		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	$0.937072\pi$
$744$	6.00000	−	8.48528i	0.219971	−	0.311086i
$745$	−8.69694			−0.318631
$746$	3.44949	−	5.97469i	0.126295	−	0.218749i
$747$	−5.89898	−	1.09638i	−0.215832	−	0.0401143i
$748$	−4.00000			−0.146254
$749$		0			0
$750$	−19.7474	−	1.81954i	−0.721075	−	0.0664401i
$751$	1.40408			0.0512357			0.0256178	−	0.999672i	$-0.491845\pi$
$751$	1.40408			0.0512357			0.0256178	+	0.999672i	$0.491845\pi$
$752$	4.89898	+	8.48528i	0.178647	+	0.309426i
$753$	12.6464	+	27.4504i	0.460861	+	1.00035i
$754$	−16.8990	+	29.2699i	−0.615425	+	1.06595i
$755$	−7.24745			−0.263762
$756$		0			0
$757$	−35.3939			−1.28641			−0.643206	−	0.765693i	$-0.722396\pi$
$757$	−35.3939			−1.28641			−0.643206	+	0.765693i	$0.722396\pi$
$758$	−11.2474	+	19.4812i	−0.408526	+	0.707587i
$759$	1.44949	+	3.14626i	0.0526131	+	0.114202i
$760$	1.84847	+	3.20164i	0.0670510	+	0.116136i
$761$	−2.00000			−0.0724999			−0.0362500	−	0.999343i	$-0.511541\pi$
$761$	−2.00000			−0.0724999			−0.0362500	+	0.999343i	$0.511541\pi$
$762$	−5.17423	−	0.476756i	−0.187443	−	0.0172710i
$763$		0			0
$764$	4.10102			0.148370
$765$	2.89898	+	8.19955i	0.104813	+	0.296455i
$766$	−1.44949	+	2.51059i	−0.0523722	+	0.0907113i
$767$	−9.79796			−0.353784
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$	−17.0454	+	29.5235i	−0.614673	+	1.06465i	0.375769	+	0.926714i	$0.377379\pi$
$769$	−17.0454	+	29.5235i	−0.614673	+	1.06465i	−0.990442	+	0.137932i	$0.955955\pi$
$770$		0			0
$771$	5.94439	+	12.9029i	0.214082	+	0.464686i
$772$	8.94949	−	15.5010i	0.322099	−	0.557892i
$773$	16.9722	−	29.3967i	0.610447	−	1.05733i	−0.380718	−	0.924691i	$-0.624323\pi$
$773$	16.9722	−	29.3967i	0.610447	−	1.05733i	0.991165	−	0.132635i	$-0.0423437\pi$
$774$	−13.4495	+	15.7313i	−0.483432	+	0.565451i
$775$	−8.69694	−	15.0635i	−0.312403	−	0.541098i
$776$	1.44949	+	2.51059i	0.0520336	+	0.0901249i
$777$		0			0
$778$	12.4495	−	21.5631i	0.446336	−	0.773076i
$779$	24.9898			0.895352
$780$	5.14643	+	11.1708i	0.184272	+	0.399980i
$781$	0.202041			0.00722960
$782$	−1.00000	−	1.73205i	−0.0357599	−	0.0619380i
$783$	8.79796	+	34.7518i	0.314413	+	1.24193i
$784$		0			0
$785$	−6.05051	−	10.4798i	−0.215952	−	0.374040i
$786$	14.7474	+	1.35884i	0.526024	+	0.0484681i
$787$	−5.69694	−	9.86739i	−0.203074	−	0.351734i	0.746443	−	0.665449i	$-0.231760\pi$
$787$	−5.69694	−	9.86739i	−0.203074	−	0.351734i	−0.949517	+	0.313715i	$0.898427\pi$
$788$	−8.34847	−	14.4600i	−0.297402	−	0.515115i
$789$	−18.7702	−	40.7425i	−0.668235	−	1.45047i
$790$	1.37628	+	2.38378i	0.0489657	+	0.0848111i
$791$		0			0
$792$	−3.89898	+	4.56048i	−0.138544	+	0.162050i
$793$	−16.0454	−	27.7915i	−0.569789	−	0.986904i
$794$	−38.6969			−1.37330
$795$	−27.2474	−	2.51059i	−0.966367	−	0.0890414i
$796$	2.89898			0.102752
$797$	−8.97219	+	15.5403i	−0.317811	+	0.550465i	−0.980031	−	0.198844i	$-0.936281\pi$
$797$	−8.97219	+	15.5403i	−0.317811	+	0.550465i	0.662220	+	0.749310i	$0.269615\pi$
$798$		0			0
$799$	−9.79796	−	16.9706i	−0.346627	−	0.600375i
$800$	1.44949	+	2.51059i	0.0512472	+	0.0887628i
$801$	49.8434	+	9.26382i	1.76113	+	0.327321i
$802$	9.94949	−	17.2330i	0.351329	−	0.608519i
$803$	−6.89898	+	11.9494i	−0.243460	+	0.421685i
$804$	−22.2474	−	2.04989i	−0.784607	−	0.0722940i
$805$		0			0
$806$	−14.6969	+	25.4558i	−0.517678	+	0.896644i
$807$	31.6464	+	2.91591i	1.11401	+	0.102645i
$808$	17.2474			0.606763
$809$	8.10102	−	14.0314i	0.284817	−	0.493317i	−0.687748	−	0.725950i	$-0.741401\pi$
$809$	8.10102	−	14.0314i	0.284817	−	0.493317i	0.972565	+	0.232632i	$0.0747339\pi$
$810$	12.1742	+	4.68729i	0.427759	+	0.164695i
$811$	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
$813$	7.10102	−	10.0424i	0.249044	−	0.352201i
$814$	23.5959			0.827036
$815$	14.3485	+	24.8523i	0.502605	+	0.870537i
$816$	2.00000	−	2.82843i	0.0700140	−	0.0990148i
$817$	8.79796	−	15.2385i	0.307802	−	0.533128i
$818$	13.7980			0.482434
$819$		0			0
$820$	−14.2020			−0.495957
$821$	−0.202041	+	0.349945i	−0.00705128	+	0.0122132i	−0.869530	−	0.493881i	$-0.835578\pi$
$821$	−0.202041	+	0.349945i	−0.00705128	+	0.0122132i	0.862478	+	0.506094i	$0.168911\pi$
$822$	13.4495	+	1.23924i	0.469105	+	0.0432235i
$823$	6.69694	+	11.5994i	0.233441	+	0.404331i	0.958818	−	0.284020i	$-0.0916682\pi$
$823$	6.69694	+	11.5994i	0.233441	+	0.404331i	−0.725378	+	0.688351i	$0.758335\pi$
$824$	−14.0000			−0.487713
$825$	4.20204	+	9.12096i	0.146296	+	0.317551i
$826$		0			0
$827$	−36.4949			−1.26905			−0.634526	−	0.772902i	$-0.718805\pi$
$827$	−36.4949			−1.26905			−0.634526	+	0.772902i	$0.718805\pi$
$828$	−2.94949	−	0.548188i	−0.102502	−	0.0190509i
$829$	0.651531	−	1.12848i	0.0226286	−	0.0391939i	−0.854489	−	0.519469i	$-0.826130\pi$
$829$	0.651531	−	1.12848i	0.0226286	−	0.0391939i	0.877118	+	0.480275i	$0.159463\pi$
$830$	−2.89898			−0.100625
$831$	13.5505	+	29.4128i	0.470062	+	1.02032i
$832$	2.44949	−	4.24264i	0.0849208	−	0.147087i
$833$		0			0
$834$	4.55051	−	6.43539i	0.157571	−	0.222839i
$835$	−7.75255	+	13.4278i	−0.268288	+	0.464689i
$836$	2.55051	−	4.41761i	0.0882112	−	0.152786i
$837$	7.65153	+	30.2234i	0.264476	+	1.04467i
$838$	14.7247	+	25.5040i	0.508658	+	0.881021i
$839$	−17.5505	−	30.3984i	−0.605911	−	1.04947i	−0.991907	−	0.126968i	$-0.959475\pi$
$839$	−17.5505	−	30.3984i	−0.605911	−	1.04947i	0.385996	−	0.922500i	$-0.373858\pi$
$840$		0			0
$841$	−9.29796	+	16.1045i	−0.320619	+	0.555329i
$842$	22.8990			0.789151
$843$	19.0000	−	26.8701i	0.654395	−	0.925454i
$844$	12.8990			0.444001
$845$	−7.97219	−	13.8082i	−0.274252	−	0.475018i
$846$	−28.8990	−	5.37113i	−0.993567	−	0.184663i
$847$		0			0
$848$	5.44949	+	9.43879i	0.187136	+	0.324129i
$849$	−25.4495	+	35.9910i	−0.873424	+	1.23521i
$850$	−2.89898	−	5.02118i	−0.0994342	−	0.172225i
$851$	5.89898	+	10.2173i	0.202214	+	0.350246i
$852$	−0.101021	+	0.142865i	−0.00346091	+	0.00489446i
$853$	12.4217	+	21.5150i	0.425310	+	0.736659i	0.996449	−	0.0841942i	$-0.0268316\pi$
$853$	12.4217	+	21.5150i	0.425310	+	0.736659i	−0.571139	+	0.820853i	$0.693498\pi$
$854$		0			0
$855$	−10.9041	−	2.02662i	−0.372912	−	0.0693089i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	34.8990			1.19213			0.596063	−	0.802938i	$-0.296731\pi$
$857$	34.8990			1.19213			0.596063	+	0.802938i	$0.296731\pi$
$858$	9.79796	−	13.8564i	0.334497	−	0.473050i
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	−5.00000	+	8.66025i	−0.170499	+	0.295312i
$861$		0			0
$862$	−15.7980	−	27.3629i	−0.538081	−	0.931983i
$863$	−5.94949	−	10.3048i	−0.202523	−	0.350780i	0.746818	−	0.665029i	$-0.231581\pi$
$863$	−5.94949	−	10.3048i	−0.202523	−	0.350780i	−0.949341	+	0.314249i	$0.898247\pi$
$864$	−1.27526	−	5.03723i	−0.0433851	−	0.171370i
$865$	−2.24745	+	3.89270i	−0.0764155	+	0.132356i
$866$	−3.89898	+	6.75323i	−0.132493	+	0.229484i
$867$	13.0000	−	18.3848i	0.441503	−	0.624380i
$868$		0			0
$869$	1.89898	−	3.28913i	0.0644185	−	0.111576i
$870$	7.24745	+	15.7313i	0.245712	+	0.533342i
$871$	63.1918			2.14117
$872$	−6.34847	+	10.9959i	−0.214986	+	0.372367i
$873$	−8.55051	−	1.58919i	−0.289391	−	0.0537858i
$874$	2.55051			0.0862723
$875$		0			0
$876$	−5.00000	−	10.8530i	−0.168934	−	0.366689i
$877$	22.4949			0.759599			0.379799	−	0.925069i	$-0.375993\pi$
$877$	22.4949			0.759599			0.379799	+	0.925069i	$0.375993\pi$
$878$	1.10102	+	1.90702i	0.0371576	+	0.0643589i
$879$	−4.74745	−	0.437432i	−0.160127	−	0.0147542i
$880$	−1.44949	+	2.51059i	−0.0488623	+	0.0846320i
$881$	−19.5959			−0.660203			−0.330102	−	0.943945i	$-0.607083\pi$
$881$	−19.5959			−0.660203			−0.330102	+	0.943945i	$0.607083\pi$
$882$		0			0
$883$	−19.7980			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$883$	−19.7980			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$884$	−4.89898	+	8.48528i	−0.164771	+	0.285391i
$885$	−2.89898	+	4.09978i	−0.0974481	+	0.137812i
$886$	7.44949	+	12.9029i	0.250271	+	0.433481i
$887$	14.2020			0.476858			0.238429	−	0.971160i	$-0.423368\pi$
$887$	14.2020			0.476858			0.238429	+	0.971160i	$0.423368\pi$
$888$	−11.7980	+	16.6848i	−0.395914	+	0.559906i
$889$		0			0
$890$	24.4949			0.821071
$891$	−2.79796	−	17.7812i	−0.0937352	−	0.595693i
$892$	−5.55051	+	9.61377i	−0.185845	+	0.321893i
$893$	24.9898			0.836252
$894$	−10.3485	−	0.953512i	−0.346105	−	0.0318902i
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$	8.44949	+	0.778539i	0.282120	+	0.0259947i
$898$	−10.2980	+	17.8366i	−0.343647	+	0.595215i
$899$	−20.6969	+	35.8481i	−0.690282	+	1.19560i
$900$	−8.55051	−	1.58919i	−0.285017	−	0.0529729i
$901$	−10.8990	−	18.8776i	−0.363098	−	0.628904i
$902$	9.79796	+	16.9706i	0.326236	+	0.565058i
$903$		0			0
$904$	3.05051	−	5.28364i	0.101458	−	0.175731i
$905$	15.0000			0.498617
$906$	−8.62372	−	0.794593i	−0.286504	−	0.0263986i
$907$	2.69694			0.0895504			0.0447752	−	0.998997i	$-0.485743\pi$
$907$	2.69694			0.0895504			0.0447752	+	0.998997i	$0.485743\pi$
$908$	−2.72474	−	4.71940i	−0.0904238	−	0.156619i
$909$	−33.6237	+	39.3283i	−1.11523	+	1.30444i
$910$		0			0
$911$	−25.9949	−	45.0245i	−0.861249	−	1.49173i	−0.870724	−	0.491773i	$-0.836349\pi$
$911$	−25.9949	−	45.0245i	−0.861249	−	1.49173i	0.00947432	−	0.999955i	$-0.496984\pi$
$912$	1.84847	+	4.01229i	0.0612089	+	0.132860i
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$	8.74745	+	15.1510i	0.289340	+	0.501151i
$915$	−16.3763	−	1.50892i	−0.541383	−	0.0498832i
$916$	0.623724	+	1.08032i	0.0206084	+	0.0356949i
$917$		0			0
$918$	2.55051	+	10.0745i	0.0841794	+	0.332507i
$919$	12.8485	+	22.2542i	0.423832	+	0.734098i	0.996311	−	0.0858213i	$-0.0273514\pi$
$919$	12.8485	+	22.2542i	0.423832	+	0.734098i	−0.572479	+	0.819920i	$0.694018\pi$
$920$	−1.44949			−0.0477883
$921$	18.2980	+	39.7176i	0.602938	+	1.30874i
$922$	−5.65153			−0.186123
$923$	0.247449	−	0.428594i	0.00814487	−	0.0141073i
$924$		0			0
$925$	17.1010	+	29.6198i	0.562278	+	0.973894i
$926$	−1.84847	−	3.20164i	−0.0607445	−	0.105213i
$927$	27.2929	−	31.9233i	0.896415	−	1.04850i
$928$	3.44949	−	5.97469i	0.113235	−	0.196129i
$929$	17.1464	−	29.6985i	0.562556	−	0.974376i	−0.434716	−	0.900567i	$-0.643151\pi$
$929$	17.1464	−	29.6985i	0.562556	−	0.974376i	0.997272	−	0.0738083i	$-0.0235153\pi$
$930$	6.30306	+	13.6814i	0.206686	+	0.448632i
$931$		0			0
$932$	3.50000	−	6.06218i	0.114646	−	0.198573i
$933$	30.6969	−	43.4120i	1.00497	−	1.42125i
$934$	−10.0000			−0.327210
$935$	2.89898	−	5.02118i	0.0948068	−	0.164210i
$936$	4.89898	+	13.8564i	0.160128	+	0.452911i
$937$	−45.5959			−1.48955			−0.744777	−	0.667314i	$-0.767444\pi$
$937$	−45.5959			−1.48955			−0.744777	+	0.667314i	$0.767444\pi$
$938$		0			0
$939$	8.10102	+	0.746431i	0.264367	+	0.0243589i
$940$	−14.2020			−0.463220
$941$	−0.724745	−	1.25529i	−0.0236260	−	0.0409214i	0.853971	−	0.520321i	$-0.174188\pi$
$941$	−0.724745	−	1.25529i	−0.0236260	−	0.0409214i	−0.877597	+	0.479400i	$0.840854\pi$
$942$	−6.05051	−	13.1332i	−0.197136	−	0.427904i
$943$	−4.89898	+	8.48528i	−0.159533	+	0.276319i
$944$	2.00000			0.0650945
$945$		0			0
$946$	13.7980			0.448610
$947$	−26.2474	+	45.4619i	−0.852927	+	1.47731i	0.0256270	+	0.999672i	$0.491842\pi$
$947$	−26.2474	+	45.4619i	−0.852927	+	1.47731i	−0.878554	+	0.477642i	$0.841492\pi$
$948$	1.37628	+	2.98735i	0.0446994	+	0.0970245i
$949$	16.8990	+	29.2699i	0.548564	+	0.950141i
$950$	7.39388			0.239889
$951$	35.6969	+	3.28913i	1.15755	+	0.106657i
$952$		0			0
$953$	−3.39388			−0.109938			−0.0549692	−	0.998488i	$-0.517506\pi$
$953$	−3.39388			−0.109938			−0.0549692	+	0.998488i	$0.517506\pi$
$954$	−32.1464	−	5.97469i	−1.04078	−	0.193438i
$955$	−2.97219	+	5.14799i	−0.0961779	+	0.166585i
$956$	6.79796			0.219862
$957$	13.7980	−	19.5133i	0.446025	−	0.630774i
$958$	4.79796	−	8.31031i	0.155015	−	0.268494i
$959$		0			0
$960$	−1.05051	−	2.28024i	−0.0339051	−	0.0735944i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	28.8990	−	50.0545i	0.931740	−	1.61382i
$963$	−35.3939	−	6.57826i	−1.14055	−	0.211981i
$964$	0.449490	+	0.778539i	0.0144771	+	0.0250751i
$965$	12.9722	+	22.4685i	0.417590	+	0.723287i
$966$		0			0
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	−0.993162	−	0.116746i	$-0.962754\pi$
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	0.597686	+	0.801730i	$0.296087\pi$
$968$	−7.00000			−0.224989
$969$	−3.69694	−	8.02458i	−0.118763	−	0.257787i
$970$	−4.20204			−0.134919
$971$	−0.0278064	−	0.0481621i	−0.000892350	−	0.00154560i	0.865579	−	0.500773i	$-0.166951\pi$
$971$	−0.0278064	−	0.0481621i	−0.000892350	−	0.00154560i	−0.866471	+	0.499227i	$0.833617\pi$
$972$	13.9722	+	6.91215i	0.448158	+	0.221707i
$973$		0			0
$974$	18.1969	+	31.5180i	0.583068	+	1.00990i
$975$	24.4949	+	2.25697i	0.784465	+	0.0722808i
$976$	3.27526	+	5.67291i	0.104838	+	0.181585i
$977$	18.7980	+	32.5590i	0.601400	+	1.04166i	0.992609	+	0.121354i	$0.0387235\pi$
$977$	18.7980	+	32.5590i	0.601400	+	1.04166i	−0.391209	+	0.920302i	$0.627943\pi$
$978$	14.3485	+	31.1448i	0.458813	+	0.995901i
$979$	−16.8990	−	29.2699i	−0.540094	−	0.935470i
$980$		0			0
$981$	−12.6969	−	35.9124i	−0.405382	−	1.14659i
$982$	−7.89898	−	13.6814i	−0.252067	−	0.436592i
$983$	33.1918			1.05866			0.529328	−	0.848418i	$-0.322444\pi$
$983$	33.1918			1.05866			0.529328	+	0.848418i	$0.322444\pi$
$984$	−16.8990	−	1.55708i	−0.538720	−	0.0496378i
$985$	24.2020			0.771141
$986$	−6.89898	+	11.9494i	−0.219708	+	0.380546i
$987$		0			0
$988$	−6.24745	−	10.8209i	−0.198758	−	0.344259i
$989$	3.44949	+	5.97469i	0.109687	+	0.189984i
$990$	−2.89898	−	8.19955i	−0.0921356	−	0.260599i
$991$	0.898979	−	1.55708i	0.0285570	−	0.0494622i	−0.851394	−	0.524527i	$-0.824242\pi$
$991$	0.898979	−	1.55708i	0.0285570	−	0.0494622i	0.879951	+	0.475065i	$0.157575\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$	8.10102	+	0.746431i	0.257078	+	0.0236873i
$994$		0			0
$995$	−2.10102	+	3.63907i	−0.0666068	+	0.115366i
$996$	−3.44949	−	0.317837i	−0.109301	−	0.0100711i
$997$	−52.1464			−1.65149			−0.825747	−	0.564041i	$-0.809246\pi$
$997$	−52.1464			−1.65149			−0.825747	+	0.564041i	$0.809246\pi$
$998$	12.6969	−	21.9917i	0.401915	−	0.696136i
$999$	−15.0454	−	59.4291i	−0.476016	−	1.88025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.l.67.1		4
3.2	odd	2		2646.2.h.n.361.1		4
7.2	even	3		882.2.e.n.373.2		4
7.3	odd	6		126.2.f.c.85.1	yes	4
7.4	even	3		882.2.f.j.589.2		4
7.5	odd	6		882.2.e.m.373.1		4
7.6	odd	2		882.2.h.k.67.2		4
9.2	odd	6		2646.2.e.k.2125.2		4
9.7	even	3		882.2.e.n.655.2		4
21.2	odd	6		2646.2.e.k.1549.2		4
21.5	even	6		2646.2.e.l.1549.1		4
21.11	odd	6		2646.2.f.k.1765.2		4
21.17	even	6		378.2.f.d.253.1		4
21.20	even	2		2646.2.h.m.361.2		4
28.3	even	6		1008.2.r.e.337.2		4
63.2	odd	6		2646.2.h.n.667.1		4
63.4	even	3		7938.2.a.bn.1.2		2
63.11	odd	6		2646.2.f.k.883.2		4
63.16	even	3	inner	882.2.h.l.79.1		4
63.20	even	6		2646.2.e.l.2125.1		4
63.25	even	3		882.2.f.j.295.1		4
63.31	odd	6		1134.2.a.p.1.1		2
63.32	odd	6		7938.2.a.bm.1.1		2
63.34	odd	6		882.2.e.m.655.1		4
63.38	even	6		378.2.f.d.127.1		4
63.47	even	6		2646.2.h.m.667.2		4
63.52	odd	6		126.2.f.c.43.2	✓	4
63.59	even	6		1134.2.a.i.1.2		2
63.61	odd	6		882.2.h.k.79.2		4
84.59	odd	6		3024.2.r.e.1009.1		4
252.31	even	6		9072.2.a.bk.1.1		2
252.59	odd	6		9072.2.a.bd.1.2		2
252.115	even	6		1008.2.r.e.673.1		4
252.227	odd	6		3024.2.r.e.2017.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	63.52	odd	6
126.2.f.c.85.1	yes	4	7.3	odd	6
378.2.f.d.127.1		4	63.38	even	6
378.2.f.d.253.1		4	21.17	even	6
882.2.e.m.373.1		4	7.5	odd	6
882.2.e.m.655.1		4	63.34	odd	6
882.2.e.n.373.2		4	7.2	even	3
882.2.e.n.655.2		4	9.7	even	3
882.2.f.j.295.1		4	63.25	even	3
882.2.f.j.589.2		4	7.4	even	3
882.2.h.k.67.2		4	7.6	odd	2
882.2.h.k.79.2		4	63.61	odd	6
882.2.h.l.67.1		4	1.1	even	1	trivial
882.2.h.l.79.1		4	63.16	even	3	inner
1008.2.r.e.337.2		4	28.3	even	6
1008.2.r.e.673.1		4	252.115	even	6
1134.2.a.i.1.2		2	63.59	even	6
1134.2.a.p.1.1		2	63.31	odd	6
2646.2.e.k.1549.2		4	21.2	odd	6
2646.2.e.k.2125.2		4	9.2	odd	6
2646.2.e.l.1549.1		4	21.5	even	6
2646.2.e.l.2125.1		4	63.20	even	6
2646.2.f.k.883.2		4	63.11	odd	6
2646.2.f.k.1765.2		4	21.11	odd	6
2646.2.h.m.361.2		4	21.20	even	2
2646.2.h.m.667.2		4	63.47	even	6
2646.2.h.n.361.1		4	3.2	odd	2
2646.2.h.n.667.1		4	63.2	odd	6
3024.2.r.e.1009.1		4	84.59	odd	6
3024.2.r.e.2017.1		4	252.227	odd	6
7938.2.a.bm.1.1		2	63.32	odd	6
7938.2.a.bn.1.2		2	63.4	even	3
9072.2.a.bd.1.2		2	252.59	odd	6
9072.2.a.bk.1.1		2	252.31	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.44949 q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.44949 q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +(-0.724745 + 1.25529i) q^{10} +2.00000 q^{11} +(-1.00000 + 1.41421i) q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(1.27526 + 2.20881i) q^{19} +(-0.724745 - 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} -1.00000 q^{23} +(-0.724745 - 1.57313i) q^{24} -2.89898 q^{25} +(2.44949 + 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(3.44949 + 5.97469i) q^{29} +(2.50000 + 0.230351i) 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} +(2.94949 + 0.548188i) q^{36} +(-5.89898 - 10.2173i) q^{37} -2.55051 q^{38} +(-8.44949 - 0.778539i) q^{39} +1.44949 q^{40} +(4.89898 - 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-2.82577 + 3.30518i) q^{45} +(0.500000 - 0.866025i) q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 + 0.158919i) q^{48} +(1.44949 - 2.51059i) q^{50} +(-3.44949 - 0.317837i) q^{51} -4.89898 q^{52} +(5.44949 - 9.43879i) q^{53} +(-3.72474 + 3.62302i) q^{54} +2.89898 q^{55} +(2.55051 - 3.60697i) q^{57} -6.89898 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-1.44949 + 2.04989i) q^{60} +(3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.55051 - 6.14966i) q^{65} +(3.44949 + 0.317837i) q^{66} +(6.44949 + 11.1708i) q^{67} -2.00000 q^{68} +(0.724745 + 1.57313i) q^{69} +0.101021 q^{71} +(-1.94949 + 2.28024i) q^{72} +(-3.44949 + 5.97469i) q^{73} +11.7980 q^{74} +(2.10102 + 4.56048i) q^{75} +(1.27526 - 2.20881i) q^{76} +(4.89898 - 6.92820i) q^{78} +(0.949490 - 1.64456i) q^{79} +(-0.724745 + 1.25529i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(4.89898 + 8.48528i) q^{82} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +6.89898 q^{86} +(6.89898 - 9.75663i) q^{87} +2.00000 q^{88} +(-8.44949 - 14.6349i) q^{89} +(-1.44949 - 4.09978i) q^{90} +(0.500000 + 0.866025i) q^{92} +(6.00000 - 8.48528i) q^{93} +(4.89898 + 8.48528i) q^{94} +(1.84847 + 3.20164i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(1.44949 + 2.51059i) q^{97} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{11} - 4 q^{12} - 14 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} + 2 q^{24} + 8 q^{25} + 20 q^{27} + 4 q^{29} + 10 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 20 q^{38} - 24 q^{39} - 4 q^{40} - 4 q^{43} - 4 q^{44} - 26 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} - 8 q^{58} - 4 q^{59} + 4 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} - 8 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} + 8 q^{74} + 28 q^{75} + 10 q^{76} - 6 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} + 8 q^{86} + 8 q^{87} + 8 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} + 24 q^{93} - 22 q^{95} - 4 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 8 * q^11 - 4 * q^12 - 14 * q^15 - 2 * q^16 + 4 * q^17 - 4 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^22 - 4 * q^23 + 2 * q^24 + 8 * q^25 + 20 * q^27 + 4 * q^29 + 10 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 20 * q^38 - 24 * q^39 - 4 * q^40 - 4 * q^43 - 4 * q^44 - 26 * q^45 + 2 * q^46 + 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 - 8 * q^58 - 4 * q^59 + 4 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 - 8 * q^68 - 2 * q^69 + 20 * q^71 + 2 * q^72 - 4 * q^73 + 8 * q^74 + 28 * q^75 + 10 * q^76 - 6 * q^79 + 2 * q^80 + 14 * q^81 + 4 * q^83 - 4 * q^85 + 8 * q^86 + 8 * q^87 + 8 * q^88 - 24 * q^89 + 4 * q^90 + 2 * q^92 + 24 * q^93 - 22 * q^95 - 4 * q^96 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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