LMFDB - Embedded newform 882.2.e.n.655.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.n.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.72474 - 0.158919i) q^{3} +1.00000 q^{4} +(-0.724745 + 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.72474 - 0.158919i) q^{3} +1.00000 q^{4} +(-0.724745 + 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +(-0.724745 + 1.25529i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.72474 - 0.158919i) q^{12} +(2.44949 + 4.24264i) q^{13} +(-1.05051 + 2.28024i) q^{15} +1.00000 q^{16} +(1.00000 - 1.73205i) q^{17} +(2.94949 - 0.548188i) q^{18} +(1.27526 + 2.20881i) q^{19} +(-0.724745 + 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.72474 - 0.158919i) q^{24} +(1.44949 + 2.51059i) q^{25} +(2.44949 + 4.24264i) q^{26} +(5.00000 - 1.41421i) q^{27} +(3.44949 - 5.97469i) q^{29} +(-1.05051 + 2.28024i) q^{30} -6.00000 q^{31} +1.00000 q^{32} +(-2.00000 - 2.82843i) q^{33} +(1.00000 - 1.73205i) q^{34} +(2.94949 - 0.548188i) q^{36} +(-5.89898 - 10.2173i) q^{37} +(1.27526 + 2.20881i) q^{38} +(4.89898 + 6.92820i) q^{39} +(-0.724745 + 1.25529i) q^{40} +(4.89898 + 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.44949 + 4.09978i) q^{45} +(0.500000 - 0.866025i) q^{46} -9.79796 q^{47} +(1.72474 - 0.158919i) q^{48} +(1.44949 + 2.51059i) q^{50} +(1.44949 - 3.14626i) q^{51} +(2.44949 + 4.24264i) q^{52} +(5.44949 - 9.43879i) q^{53} +(5.00000 - 1.41421i) q^{54} +2.89898 q^{55} +(2.55051 + 3.60697i) q^{57} +(3.44949 - 5.97469i) q^{58} +2.00000 q^{59} +(-1.05051 + 2.28024i) q^{60} -6.55051 q^{61} -6.00000 q^{62} +1.00000 q^{64} -7.10102 q^{65} +(-2.00000 - 2.82843i) q^{66} -12.8990 q^{67} +(1.00000 - 1.73205i) q^{68} +(0.724745 - 1.57313i) q^{69} +0.101021 q^{71} +(2.94949 - 0.548188i) q^{72} +(-3.44949 + 5.97469i) q^{73} +(-5.89898 - 10.2173i) q^{74} +(2.89898 + 4.09978i) q^{75} +(1.27526 + 2.20881i) q^{76} +(4.89898 + 6.92820i) q^{78} -1.89898 q^{79} +(-0.724745 + 1.25529i) q^{80} +(8.39898 - 3.23375i) q^{81} +(4.89898 + 8.48528i) q^{82} +(1.00000 - 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} +(-3.44949 + 5.97469i) q^{86} +(5.00000 - 10.8530i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(-8.44949 - 14.6349i) q^{89} +(-1.44949 + 4.09978i) q^{90} +(0.500000 - 0.866025i) q^{92} +(-10.3485 + 0.953512i) q^{93} -9.79796 q^{94} -3.69694 q^{95} +(1.72474 - 0.158919i) q^{96} +(1.44949 - 2.51059i) q^{97} +(-3.89898 - 4.56048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} + 2 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 4 q^{32} - 8 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} + 10 q^{38} + 2 q^{40} - 4 q^{43} - 4 q^{44} + 4 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} + 20 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} + 8 q^{59} - 14 q^{60} - 36 q^{61} - 24 q^{62} + 4 q^{64} - 48 q^{65} - 8 q^{66} - 32 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} - 4 q^{74} - 8 q^{75} + 10 q^{76} + 12 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} + 20 q^{87} - 4 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} + 44 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 14 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 + 2 * q^24 - 4 * q^25 + 20 * q^27 + 4 * q^29 - 14 * q^30 - 24 * q^31 + 4 * q^32 - 8 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 + 10 * q^38 + 2 * q^40 - 4 * q^43 - 4 * q^44 + 4 * q^45 + 2 * q^46 + 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 + 20 * q^54 - 8 * q^55 + 20 * q^57 + 4 * q^58 + 8 * q^59 - 14 * q^60 - 36 * q^61 - 24 * q^62 + 4 * q^64 - 48 * q^65 - 8 * q^66 - 32 * q^67 + 4 * q^68 - 2 * q^69 + 20 * q^71 + 2 * q^72 - 4 * q^73 - 4 * q^74 - 8 * q^75 + 10 * q^76 + 12 * q^79 + 2 * q^80 + 14 * q^81 + 4 * q^83 - 4 * q^85 - 4 * q^86 + 20 * q^87 - 4 * q^88 - 24 * q^89 + 4 * q^90 + 2 * q^92 - 12 * q^93 + 44 * 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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$3$	1.72474	−	0.158919i	0.995782	−	0.0917517i
$4$	1.00000			0.500000
$5$	−0.724745	+	1.25529i	−0.324116	+	0.561385i	−0.981333	−	0.192316i	$-0.938400\pi$
$5$	−0.724745	+	1.25529i	−0.324116	+	0.561385i	0.657217	+	0.753701i	$0.271733\pi$
$6$	1.72474	−	0.158919i	0.704124	−	0.0648783i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.94949	−	0.548188i	0.983163	−	0.182729i
$10$	−0.724745	+	1.25529i	−0.229184	+	0.396959i
$11$	−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	0.975172	+	0.221449i	$0.0710785\pi$
$13$	2.44949	+	4.24264i	0.679366	+	1.17670i	−0.295806	+	0.955248i	$0.595588\pi$
$14$		0			0
$15$	−1.05051	+	2.28024i	−0.271241	+	0.588755i
$16$	1.00000			0.250000
$17$	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	$0.0886875\pi$
$18$	2.94949	−	0.548188i	0.695201	−	0.129209i
$19$	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
$23$	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	$0.133420\pi$
$24$	1.72474	−	0.158919i	0.352062	−	0.0324391i
$25$	1.44949	+	2.51059i	0.289898	+	0.502118i
$26$	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	−0.344755	−	0.938693i	$-0.612038\pi$
$29$	3.44949	−	5.97469i	0.640554	−	1.10947i	0.985309	−	0.170780i	$-0.0546286\pi$
$30$	−1.05051	+	2.28024i	−0.191796	+	0.416313i
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	1.00000			0.176777
$33$	−2.00000	−	2.82843i	−0.348155	−	0.492366i
$34$	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	$-0.588221\pi$
$38$	1.27526	+	2.20881i	0.206874	+	0.358316i
$39$	4.89898	+	6.92820i	0.784465	+	1.10940i
$40$	−0.724745	+	1.25529i	−0.114592	+	0.198480i
$41$	4.89898	+	8.48528i	0.765092	+	1.32518i	0.940198	+	0.340629i	$0.110640\pi$
$41$	4.89898	+	8.48528i	0.765092	+	1.32518i	−0.175106	+	0.984550i	$0.556027\pi$
$42$		0			0
$43$	−3.44949	+	5.97469i	−0.526042	+	0.911132i	0.473497	+	0.880795i	$0.342991\pi$
$43$	−3.44949	+	5.97469i	−0.526042	+	0.911132i	−0.999540	+	0.0303367i	$0.990342\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−1.44949	+	4.09978i	−0.216077	+	0.611159i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−9.79796			−1.42918			−0.714590	−	0.699544i	$-0.753387\pi$
$47$	−9.79796			−1.42918			−0.714590	+	0.699544i	$0.753387\pi$
$48$	1.72474	−	0.158919i	0.248945	−	0.0229379i
$49$		0			0
$50$	1.44949	+	2.51059i	0.204989	+	0.355051i
$51$	1.44949	−	3.14626i	0.202969	−	0.440565i
$52$	2.44949	+	4.24264i	0.339683	+	0.588348i
$53$	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	$-0.102581\pi$
$54$	5.00000	−	1.41421i	0.680414	−	0.192450i
$55$	2.89898			0.390898
$56$		0			0
$57$	2.55051	+	3.60697i	0.337823	+	0.477754i
$58$	3.44949	−	5.97469i	0.452940	−	0.784515i
$59$	2.00000			0.260378			0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000			0.260378			0.130189	+	0.991489i	$0.458442\pi$
$60$	−1.05051	+	2.28024i	−0.135620	+	0.294378i
$61$	−6.55051			−0.838707			−0.419353	−	0.907823i	$-0.637743\pi$
$61$	−6.55051			−0.838707			−0.419353	+	0.907823i	$0.637743\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.10102			−0.880773
$66$	−2.00000	−	2.82843i	−0.246183	−	0.348155i
$67$	−12.8990			−1.57586			−0.787931	−	0.615764i	$-0.788847\pi$
$67$	−12.8990			−1.57586			−0.787931	+	0.615764i	$0.788847\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	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	$0.498092\pi$
$72$	2.94949	−	0.548188i	0.347601	−	0.0646046i
$73$	−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	$0.298954\pi$
$74$	−5.89898	−	10.2173i	−0.685742	−	1.18774i
$75$	2.89898	+	4.09978i	0.334745	+	0.473401i
$76$	1.27526	+	2.20881i	0.146282	+	0.253368i
$77$		0			0
$78$	4.89898	+	6.92820i	0.554700	+	0.784465i
$79$	−1.89898			−0.213652			−0.106826	−	0.994278i	$-0.534069\pi$
$79$	−1.89898			−0.213652			−0.106826	+	0.994278i	$0.534069\pi$
$80$	−0.724745	+	1.25529i	−0.0810289	+	0.140346i
$81$	8.39898	−	3.23375i	0.933220	−	0.359306i
$82$	4.89898	+	8.48528i	0.541002	+	0.937043i
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	−0.805910	−	0.592037i	$-0.798324\pi$
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	0.915675	+	0.401920i	$0.131657\pi$
$84$		0			0
$85$	1.44949	+	2.51059i	0.157219	+	0.272312i
$86$	−3.44949	+	5.97469i	−0.371968	+	0.644268i
$87$	5.00000	−	10.8530i	0.536056	−	1.16356i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	−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
$93$	−10.3485	+	0.953512i	−1.07309	+	0.0988746i
$94$	−9.79796			−1.01058
$95$	−3.69694			−0.379298
$96$	1.72474	−	0.158919i	0.176031	−	0.0162196i
$97$	1.44949	−	2.51059i	0.147173	−	0.254912i	−0.783008	−	0.622011i	$-0.786316\pi$
$97$	1.44949	−	2.51059i	0.147173	−	0.254912i	0.930182	+	0.367099i	$0.119649\pi$
$98$		0			0
$99$	−3.89898	−	4.56048i	−0.391862	−	0.458345i
$100$	1.44949	+	2.51059i	0.144949	+	0.251059i
$101$	−8.62372	−	14.9367i	−0.858093	−	1.48626i	−0.873746	−	0.486383i	$-0.838316\pi$
$101$	−8.62372	−	14.9367i	−0.858093	−	1.48626i	0.0156533	−	0.999877i	$-0.495017\pi$
$102$	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
$106$	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	$0.636370\pi$
$108$	5.00000	−	1.41421i	0.481125	−	0.136083i
$109$	−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	$0.958609\pi$
$110$	2.89898			0.276407
$111$	−11.7980	−	16.6848i	−1.11981	−	1.58365i
$112$		0			0
$113$	3.05051	+	5.28364i	0.286968	+	0.497043i	0.973084	−	0.230449i	$-0.0740194\pi$
$113$	3.05051	+	5.28364i	0.286968	+	0.497043i	−0.686117	+	0.727492i	$0.740686\pi$
$114$	2.55051	+	3.60697i	0.238877	+	0.337823i
$115$	0.724745	+	1.25529i	0.0675828	+	0.117057i
$116$	3.44949	−	5.97469i	0.320277	−	0.554736i
$117$	9.55051	+	11.1708i	0.882945	+	1.03274i
$118$	2.00000			0.184115
$119$		0			0
$120$	−1.05051	+	2.28024i	−0.0958980	+	0.208156i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−6.55051			−0.593055
$123$	9.79796	+	13.8564i	0.883452	+	1.24939i
$124$	−6.00000			−0.538816
$125$	−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	$0.542494\pi$
$128$	1.00000			0.0883883
$129$	−5.00000	+	10.8530i	−0.440225	+	0.955554i
$130$	−7.10102			−0.622801
$131$	−4.27526	+	7.40496i	−0.373531	+	0.646974i	−0.990106	−	0.140322i	$-0.955186\pi$
$131$	−4.27526	+	7.40496i	−0.373531	+	0.646974i	0.616575	+	0.787296i	$0.288520\pi$
$132$	−2.00000	−	2.82843i	−0.174078	−	0.246183i
$133$		0			0
$134$	−12.8990			−1.11430
$135$	−1.84847	+	7.30142i	−0.159091	+	0.628406i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−3.89898	−	6.75323i	−0.333112	−	0.576967i	0.650008	−	0.759927i	$-0.274765\pi$
$137$	−3.89898	−	6.75323i	−0.333112	−	0.576967i	−0.983120	+	0.182960i	$0.941432\pi$
$138$	0.724745	−	1.57313i	0.0616944	−	0.133914i
$139$	2.27526	+	3.94086i	0.192985	+	0.334259i	0.946238	−	0.323471i	$-0.104850\pi$
$139$	2.27526	+	3.94086i	0.192985	+	0.334259i	−0.753253	+	0.657730i	$0.771517\pi$
$140$		0			0
$141$	−16.8990	+	1.55708i	−1.42315	+	0.131130i
$142$	0.101021			0.00847745
$143$	4.89898	−	8.48528i	0.409673	−	0.709575i
$144$	2.94949	−	0.548188i	0.245791	−	0.0456823i
$145$	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
$149$	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	$0.0876260\pi$
$150$	2.89898	+	4.09978i	0.236701	+	0.334745i
$151$	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	$0.768119\pi$
$152$	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
$156$	4.89898	+	6.92820i	0.392232	+	0.554700i
$157$	8.34847			0.666280			0.333140	−	0.942877i	$-0.391892\pi$
$157$	8.34847			0.666280			0.333140	+	0.942877i	$0.391892\pi$
$158$	−1.89898			−0.151075
$159$	7.89898	−	17.1455i	0.626430	−	1.35973i
$160$	−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	$0.550908\pi$
$164$	4.89898	+	8.48528i	0.382546	+	0.662589i
$165$	5.00000	−	0.460702i	0.389249	−	0.0358656i
$166$	1.00000	−	1.73205i	0.0776151	−	0.134433i
$167$	−5.34847	−	9.26382i	−0.413877	−	0.716856i	0.581433	−	0.813594i	$-0.302492\pi$
$167$	−5.34847	−	9.26382i	−0.413877	−	0.716856i	−0.995310	+	0.0967384i	$0.969159\pi$
$168$		0			0
$169$	−5.50000	+	9.52628i	−0.423077	+	0.732791i
$170$	1.44949	+	2.51059i	0.111171	+	0.192553i
$171$	4.97219	+	5.81577i	0.380233	+	0.444743i
$172$	−3.44949	+	5.97469i	−0.263021	+	0.455566i
$173$	3.10102			0.235766			0.117883	−	0.993027i	$-0.462389\pi$
$173$	3.10102			0.235766			0.117883	+	0.993027i	$0.462389\pi$
$174$	5.00000	−	10.8530i	0.379049	−	0.822764i
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	3.44949	−	0.317837i	0.259280	−	0.0238901i
$178$	−8.44949	−	14.6349i	−0.633316	−	1.09694i
$179$	−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	$0.885181\pi$
$180$	−1.44949	+	4.09978i	−0.108039	+	0.305579i
$181$	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
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	17.1010			1.25729
$186$	−10.3485	+	0.953512i	−0.758787	+	0.0699149i
$187$	−4.00000			−0.292509
$188$	−9.79796			−0.714590
$189$		0			0
$190$	−3.69694			−0.268204
$191$	4.10102			0.296739			0.148370	−	0.988932i	$-0.452597\pi$
$191$	4.10102			0.296739			0.148370	+	0.988932i	$0.452597\pi$
$192$	1.72474	−	0.158919i	0.124473	−	0.0114690i
$193$	−17.8990			−1.28840			−0.644198	−	0.764858i	$-0.722809\pi$
$193$	−17.8990			−1.28840			−0.644198	+	0.764858i	$0.722809\pi$
$194$	1.44949	−	2.51059i	0.104067	−	0.180250i
$195$	−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	$0.297230\pi$
$198$	−3.89898	−	4.56048i	−0.277088	−	0.324099i
$199$	−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	$0.199431\pi$
$200$	1.44949	+	2.51059i	0.102494	+	0.177526i
$201$	−22.2474	+	2.04989i	−1.56921	+	0.144588i
$202$	−8.62372	−	14.9367i	−0.606763	−	1.05094i
$203$		0			0
$204$	1.44949	−	3.14626i	0.101485	−	0.220283i
$205$	−14.2020			−0.991914
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$	1.00000	−	2.82843i	0.0695048	−	0.196589i
$208$	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	0.553981	−	0.832529i	$-0.313108\pi$
$211$	−6.44949	−	11.1708i	−0.444001	−	0.769033i	−0.997982	+	0.0634968i	$0.979775\pi$
$212$	5.44949	−	9.43879i	0.374272	−	0.648259i
$213$	0.174235	−	0.0160540i	0.0119384	−	0.00110000i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−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
$219$	−5.00000	+	10.8530i	−0.337869	+	0.733378i
$220$	2.89898			0.195449
$221$	9.79796			0.659082
$222$	−11.7980	−	16.6848i	−0.791827	−	1.11981i
$223$	−5.55051	+	9.61377i	−0.371690	+	0.643785i	−0.989826	−	0.142286i	$-0.954555\pi$
$223$	−5.55051	+	9.61377i	−0.371690	+	0.643785i	0.618136	+	0.786071i	$0.287888\pi$
$224$		0			0
$225$	5.65153	+	6.61037i	0.376769	+	0.440691i
$226$	3.05051	+	5.28364i	0.202917	+	0.351462i
$227$	−2.72474	−	4.71940i	−0.180848	−	0.313237i	0.761322	−	0.648374i	$-0.224551\pi$
$227$	−2.72474	−	4.71940i	−0.180848	−	0.313237i	−0.942169	+	0.335137i	$0.891217\pi$
$228$	2.55051	+	3.60697i	0.168912	+	0.238877i
$229$	0.623724	−	1.08032i	0.0412169	−	0.0713897i	−0.844681	−	0.535270i	$-0.820210\pi$
$229$	0.623724	−	1.08032i	0.0412169	−	0.0713897i	0.885898	+	0.463880i	$0.153543\pi$
$230$	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	$0.759692\pi$
$234$	9.55051	+	11.1708i	0.624336	+	0.730261i
$235$	7.10102	−	12.2993i	0.463220	−	0.802320i
$236$	2.00000			0.130189
$237$	−3.27526	+	0.301783i	−0.212751	+	0.0196029i
$238$		0			0
$239$	−3.39898	−	5.88721i	−0.219862	−	0.380812i	0.734904	−	0.678171i	$-0.237227\pi$
$239$	−3.39898	−	5.88721i	−0.219862	−	0.380812i	−0.954766	+	0.297360i	$0.903894\pi$
$240$	−1.05051	+	2.28024i	−0.0678101	+	0.147189i
$241$	0.449490	+	0.778539i	0.0289542	+	0.0501501i	0.880139	−	0.474715i	$-0.157449\pi$
$241$	0.449490	+	0.778539i	0.0289542	+	0.0501501i	−0.851185	+	0.524865i	$0.824116\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	13.9722	−	6.91215i	0.896317	−	0.443415i
$244$	−6.55051			−0.419353
$245$		0			0
$246$	9.79796	+	13.8564i	0.624695	+	0.883452i
$247$	−6.24745	+	10.8209i	−0.397516	+	0.688517i
$248$	−6.00000			−0.381000
$249$	1.44949	−	3.14626i	0.0918577	−	0.199386i
$250$	−11.4495			−0.724129
$251$	−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
$254$	−3.00000			−0.188237
$255$	2.89898	+	4.09978i	0.181541	+	0.256738i
$256$	1.00000			0.0625000
$257$	4.10102	−	7.10318i	0.255815	−	0.443084i	−0.709302	−	0.704905i	$-0.750990\pi$
$257$	4.10102	−	7.10318i	0.255815	−	0.443084i	0.965116	+	0.261821i	$0.0843230\pi$
$258$	−5.00000	+	10.8530i	−0.311286	+	0.675679i
$259$		0			0
$260$	−7.10102			−0.440387
$261$	6.89898	−	19.5133i	0.427036	−	1.20784i
$262$	−4.27526	+	7.40496i	−0.264126	+	0.457480i
$263$	−12.9495	−	22.4292i	−0.798500	−	1.38304i	−0.920593	−	0.390523i	$-0.872294\pi$
$263$	−12.9495	−	22.4292i	−0.798500	−	1.38304i	0.122093	−	0.992519i	$-0.461039\pi$
$264$	−2.00000	−	2.82843i	−0.123091	−	0.174078i
$265$	7.89898	+	13.6814i	0.485230	+	0.840444i
$266$		0			0
$267$	−16.8990	−	23.8988i	−1.03420	−	1.46258i
$268$	−12.8990			−0.787931
$269$	−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	$0.977712\pi$
$270$	−1.84847	+	7.30142i	−0.112494	+	0.444350i
$271$	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
$275$	2.89898	−	5.02118i	0.174815	−	0.302789i
$276$	0.724745	−	1.57313i	0.0436245	−	0.0946914i
$277$	9.34847	+	16.1920i	0.561695	+	0.972884i	0.997349	+	0.0727700i	$0.0231839\pi$
$277$	9.34847	+	16.1920i	0.561695	+	0.972884i	−0.435654	+	0.900114i	$0.643483\pi$
$278$	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	−0.430165	−	0.902750i	$-0.641545\pi$
$281$	9.50000	−	16.4545i	0.566722	−	0.981592i	0.996887	−	0.0788417i	$-0.0251222\pi$
$282$	−16.8990	+	1.55708i	−1.00632	+	0.0927227i
$283$	25.4495			1.51282			0.756408	−	0.654101i	$-0.226953\pi$
$283$	25.4495			1.51282			0.756408	+	0.654101i	$0.226953\pi$
$284$	0.101021			0.00599446
$285$	−6.37628	+	0.587512i	−0.377698	+	0.0348012i
$286$	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
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$	2.10102	−	4.56048i	0.123164	−	0.267340i
$292$	−3.44949	+	5.97469i	−0.201866	+	0.349642i
$293$	1.37628	+	2.38378i	0.0804029	+	0.139262i	0.903423	−	0.428750i	$-0.141046\pi$
$293$	1.37628	+	2.38378i	0.0804029	+	0.139262i	−0.823020	+	0.568012i	$0.807713\pi$
$294$		0			0
$295$	−1.44949	+	2.51059i	−0.0843926	+	0.146172i
$296$	−5.89898	−	10.2173i	−0.342871	−	0.593870i
$297$	−7.44949	−	7.24604i	−0.432263	−	0.420458i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	4.89898			0.283315
$300$	2.89898	+	4.09978i	0.167373	+	0.236701i
$301$		0			0
$302$	2.50000	+	4.33013i	0.143859	+	0.249171i
$303$	−17.2474	−	24.3916i	−0.990840	−	1.40126i
$304$	1.27526	+	2.20881i	0.0731409	+	0.126684i
$305$	4.74745	−	8.22282i	0.271838	−	0.470837i
$306$	2.00000	−	5.65685i	0.114332	−	0.323381i
$307$	−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
$310$	4.34847	−	7.53177i	0.246976	−	0.427776i
$311$	−30.6969			−1.74066			−0.870332	−	0.492466i	$-0.836096\pi$
$311$	−30.6969			−1.74066			−0.870332	+	0.492466i	$0.836096\pi$
$312$	4.89898	+	6.92820i	0.277350	+	0.392232i
$313$	4.69694			0.265487			0.132743	−	0.991150i	$-0.457621\pi$
$313$	4.69694			0.265487			0.132743	+	0.991150i	$0.457621\pi$
$314$	8.34847			0.471131
$315$		0			0
$316$	−1.89898			−0.106826
$317$	20.6969			1.16246			0.581228	−	0.813741i	$-0.302572\pi$
$317$	20.6969			1.16246			0.581228	+	0.813741i	$0.302572\pi$
$318$	7.89898	−	17.1455i	0.442953	−	0.961474i
$319$	−13.7980			−0.772537
$320$	−0.724745	+	1.25529i	−0.0405145	+	0.0701731i
$321$	12.0000	+	16.9706i	0.669775	+	0.947204i
$322$		0			0
$323$	5.10102			0.283828
$324$	8.39898	−	3.23375i	0.466610	−	0.179653i
$325$	−7.10102	+	12.2993i	−0.393894	+	0.682244i
$326$	9.89898	+	17.1455i	0.548254	+	0.949603i
$327$	−9.20204	+	19.9740i	−0.508874	+	1.10456i
$328$	4.89898	+	8.48528i	0.270501	+	0.468521i
$329$		0			0
$330$	5.00000	−	0.460702i	0.275241	−	0.0253608i
$331$	4.69694			0.258167			0.129084	−	0.991634i	$-0.458796\pi$
$331$	4.69694			0.258167			0.129084	+	0.991634i	$0.458796\pi$
$332$	1.00000	−	1.73205i	0.0548821	−	0.0950586i
$333$	−23.0000	−	26.9022i	−1.26039	−	1.47423i
$334$	−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	0.986050	+	0.166447i	$0.0532296\pi$
$337$	11.6969	+	20.2597i	0.637173	+	1.10362i	−0.348877	+	0.937168i	$0.613437\pi$
$338$	−5.50000	+	9.52628i	−0.299161	+	0.518161i
$339$	6.10102	+	8.62815i	0.331362	+	0.468617i
$340$	1.44949	+	2.51059i	0.0786096	+	0.136156i
$341$	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
$345$	1.44949	+	2.04989i	0.0780379	+	0.110362i
$346$	3.10102			0.166712
$347$	19.5959			1.05196			0.525982	−	0.850496i	$-0.323698\pi$
$347$	19.5959			1.05196			0.525982	+	0.850496i	$0.323698\pi$
$348$	5.00000	−	10.8530i	0.268028	−	0.581782i
$349$	5.55051	−	9.61377i	0.297112	−	0.514613i	−0.678362	−	0.734728i	$-0.737310\pi$
$349$	5.55051	−	9.61377i	0.297112	−	0.514613i	0.975474	+	0.220115i	$0.0706432\pi$
$350$		0			0
$351$	18.2474	+	17.7491i	0.973977	+	0.947377i
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−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	$0.884378\pi$
$354$	3.44949	−	0.317837i	0.183338	−	0.0168929i
$355$	−0.0732141	+	0.126811i	−0.00388580	+	0.00673040i
$356$	−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	$0.758751\pi$
$360$	−1.44949	+	4.09978i	−0.0763948	+	0.216077i
$361$	6.24745	−	10.8209i	0.328813	−	0.569521i
$362$	10.3485			0.543903
$363$	5.07321	−	11.0119i	0.266275	−	0.577976i
$364$		0			0
$365$	−5.00000	−	8.66025i	−0.261712	−	0.453298i
$366$	−11.2980	+	1.04100i	−0.590554	+	0.0544138i
$367$	−6.89898	−	11.9494i	−0.360124	−	0.623753i	0.627857	−	0.778329i	$-0.283932\pi$
$367$	−6.89898	−	11.9494i	−0.360124	−	0.623753i	−0.987981	+	0.154576i	$0.950599\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	19.1010	+	22.3417i	0.994359	+	1.16306i
$370$	17.1010			0.889040
$371$		0			0
$372$	−10.3485	+	0.953512i	−0.536543	+	0.0494373i
$373$	3.44949	−	5.97469i	0.178608	−	0.309358i	−0.762796	−	0.646639i	$-0.776174\pi$
$373$	3.44949	−	5.97469i	0.178608	−	0.309358i	0.941404	+	0.337281i	$0.109507\pi$
$374$	−4.00000			−0.206835
$375$	−19.7474	+	1.81954i	−1.01975	+	0.0939605i
$376$	−9.79796			−0.505291
$377$	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	$0.303934\pi$
$380$	−3.69694			−0.189649
$381$	−5.17423	+	0.476756i	−0.265084	+	0.0244249i
$382$	4.10102			0.209826
$383$	−1.44949	+	2.51059i	−0.0740655	+	0.128285i	−0.900679	−	0.434484i	$-0.856931\pi$
$383$	−1.44949	+	2.51059i	−0.0740655	+	0.128285i	0.826614	+	0.562769i	$0.190264\pi$
$384$	1.72474	−	0.158919i	0.0880155	−	0.00810978i
$385$		0			0
$386$	−17.8990			−0.911034
$387$	−6.89898	+	19.5133i	−0.350695	+	0.991915i
$388$	1.44949	−	2.51059i	0.0735867	−	0.127456i
$389$	12.4495	+	21.5631i	0.631214	+	1.09330i	0.987304	+	0.158843i	$0.0507764\pi$
$389$	12.4495	+	21.5631i	0.631214	+	1.09330i	−0.356090	+	0.934452i	$0.615890\pi$
$390$	−12.2474	+	1.12848i	−0.620174	+	0.0571430i
$391$	−1.00000	−	1.73205i	−0.0505722	−	0.0875936i
$392$		0			0
$393$	−6.19694	+	13.4511i	−0.312594	+	0.678517i
$394$	16.6969			0.841180
$395$	1.37628	−	2.38378i	0.0692479	−	0.119941i
$396$	−3.89898	−	4.56048i	−0.195931	−	0.229173i
$397$	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
$401$	9.94949	−	17.2330i	0.496854	−	0.860576i	−0.503140	−	0.864205i	$-0.667822\pi$
$401$	9.94949	−	17.2330i	0.496854	−	0.860576i	0.999993	+	0.00362911i	$0.00115518\pi$
$402$	−22.2474	+	2.04989i	−1.10960	+	0.102239i
$403$	−14.6969	−	25.4558i	−0.732107	−	1.26805i
$404$	−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
$408$	1.44949	−	3.14626i	0.0717604	−	0.155763i
$409$	13.7980			0.682265			0.341133	−	0.940015i	$-0.389189\pi$
$409$	13.7980			0.682265			0.341133	+	0.940015i	$0.389189\pi$
$410$	−14.2020			−0.701389
$411$	−7.79796	−	11.0280i	−0.384645	−	0.543970i
$412$	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
$416$	2.44949	+	4.24264i	0.120096	+	0.208013i
$417$	4.55051	+	6.43539i	0.222839	+	0.315143i
$418$	2.55051	−	4.41761i	0.124750	−	0.216073i
$419$	14.7247	+	25.5040i	0.719351	+	1.24595i	0.961257	+	0.275653i	$0.0888940\pi$
$419$	14.7247	+	25.5040i	0.719351	+	1.24595i	−0.241906	+	0.970300i	$0.577773\pi$
$420$		0			0
$421$	−11.4495	+	19.8311i	−0.558014	+	0.966509i	0.439648	+	0.898170i	$0.355103\pi$
$421$	−11.4495	+	19.8311i	−0.558014	+	0.966509i	−0.997662	+	0.0683385i	$0.978230\pi$
$422$	−6.44949	−	11.1708i	−0.313956	−	0.543788i
$423$	−28.8990	+	5.37113i	−1.40512	+	0.261153i
$424$	5.44949	−	9.43879i	0.264651	−	0.458388i
$425$	5.79796			0.281242
$426$	0.174235	−	0.0160540i	0.00844169	−	0.000777821i
$427$		0			0
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	7.10102	−	15.4135i	0.342841	−	0.744170i
$430$	−5.00000	−	8.66025i	−0.241121	−	0.417635i
$431$	−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	$0.891395\pi$
$432$	5.00000	−	1.41421i	0.240563	−	0.0680414i
$433$	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
$436$	−6.34847	+	10.9959i	−0.304037	+	0.526607i
$437$	2.55051			0.122007
$438$	−5.00000	+	10.8530i	−0.238909	+	0.518577i
$439$	−2.20204			−0.105098			−0.0525488	−	0.998618i	$-0.516735\pi$
$439$	−2.20204			−0.105098			−0.0525488	+	0.998618i	$0.516735\pi$
$440$	2.89898			0.138203
$441$		0			0
$442$	9.79796			0.466041
$443$	−14.8990			−0.707872			−0.353936	−	0.935270i	$-0.615157\pi$
$443$	−14.8990			−0.707872			−0.353936	+	0.935270i	$0.615157\pi$
$444$	−11.7980	−	16.6848i	−0.559906	−	0.791827i
$445$	24.4949			1.16117
$446$	−5.55051	+	9.61377i	−0.262824	+	0.455225i
$447$	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	$0.338459\pi$
$450$	5.65153	+	6.61037i	0.266416	+	0.311616i
$451$	9.79796	−	16.9706i	0.461368	−	0.799113i
$452$	3.05051	+	5.28364i	0.143484	+	0.248521i
$453$	5.00000	+	7.07107i	0.234920	+	0.332228i
$454$	−2.72474	−	4.71940i	−0.127879	−	0.221492i
$455$		0			0
$456$	2.55051	+	3.60697i	0.119439	+	0.168912i
$457$	−17.4949			−0.818377			−0.409188	−	0.912450i	$-0.634188\pi$
$457$	−17.4949			−0.818377			−0.409188	+	0.912450i	$0.634188\pi$
$458$	0.623724	−	1.08032i	0.0291447	−	0.0504801i
$459$	2.55051	−	10.0745i	0.119048	−	0.470236i
$460$	0.724745	+	1.25529i	0.0337914	+	0.0585284i
$461$	2.82577	−	4.89437i	0.131609	−	0.227954i	−0.792688	−	0.609628i	$-0.791319\pi$
$461$	2.82577	−	4.89437i	0.131609	−	0.227954i	0.924297	+	0.381674i	$0.124652\pi$
$462$		0			0
$463$	−1.84847	−	3.20164i	−0.0859057	−	0.148793i	0.819871	−	0.572548i	$-0.194045\pi$
$463$	−1.84847	−	3.20164i	−0.0859057	−	0.148793i	−0.905777	+	0.423755i	$0.860712\pi$
$464$	3.44949	−	5.97469i	0.160139	−	0.277368i
$465$	6.30306	−	13.6814i	0.292297	−	0.634461i
$466$	3.50000	+	6.06218i	0.162134	+	0.280825i
$467$	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
$471$	14.3990	−	1.32673i	0.663470	−	0.0611324i
$472$	2.00000			0.0920575
$473$	13.7980			0.634431
$474$	−3.27526	+	0.301783i	−0.150437	+	0.0138614i
$475$	−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
$479$	4.79796	+	8.31031i	0.219224	+	0.379708i	0.954571	−	0.297983i	$-0.0963140\pi$
$479$	4.79796	+	8.31031i	0.219224	+	0.379708i	−0.735347	+	0.677691i	$0.762981\pi$
$480$	−1.05051	+	2.28024i	−0.0479490	+	0.104078i
$481$	28.8990	−	50.0545i	1.31768	−	2.28229i
$482$	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
$486$	13.9722	−	6.91215i	0.633792	−	0.313541i
$487$	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	$-0.141923\pi$
$488$	−6.55051			−0.296528
$489$	19.7980	+	27.9985i	0.895295	+	1.26614i
$490$		0			0
$491$	−7.89898	−	13.6814i	−0.356476	−	0.617434i	0.630893	−	0.775869i	$-0.282688\pi$
$491$	−7.89898	−	13.6814i	−0.356476	−	0.617434i	−0.987369	+	0.158435i	$0.949355\pi$
$492$	9.79796	+	13.8564i	0.441726	+	0.624695i
$493$	−6.89898	−	11.9494i	−0.310714	−	0.538173i
$494$	−6.24745	+	10.8209i	−0.281086	+	0.486855i
$495$	8.55051	−	1.58919i	0.384317	−	0.0714286i
$496$	−6.00000			−0.269408
$497$		0			0
$498$	1.44949	−	3.14626i	0.0649532	−	0.140987i
$499$	12.6969	−	21.9917i	0.568393	−	0.984486i	−0.428332	−	0.903621i	$-0.640899\pi$
$499$	12.6969	−	21.9917i	0.568393	−	0.984486i	0.996725	−	0.0808642i	$-0.0257680\pi$
$500$	−11.4495			−0.512037
$501$	−10.6969	−	15.1278i	−0.477904	−	0.675858i
$502$	−17.4495			−0.778809
$503$	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
$506$	−2.00000			−0.0889108
$507$	−7.97219	+	17.3045i	−0.354058	+	0.768518i
$508$	−3.00000			−0.133103
$509$	−3.55051	+	6.14966i	−0.157374	+	0.272579i	−0.933921	−	0.357480i	$-0.883636\pi$
$509$	−3.55051	+	6.14966i	−0.157374	+	0.272579i	0.776547	+	0.630059i	$0.216969\pi$
$510$	2.89898	+	4.09978i	0.128369	+	0.181541i
$511$		0			0
$512$	1.00000			0.0441942
$513$	9.50000	+	9.24055i	0.419435	+	0.407980i
$514$	4.10102	−	7.10318i	0.180888	−	0.313308i
$515$	10.1464	+	17.5741i	0.447105	+	0.774409i
$516$	−5.00000	+	10.8530i	−0.220113	+	0.477777i
$517$	9.79796	+	16.9706i	0.430914	+	0.746364i
$518$		0			0
$519$	5.34847	−	0.492810i	0.234772	−	0.0216320i
$520$	−7.10102			−0.311400
$521$	−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	$0.231992\pi$
$522$	6.89898	−	19.5133i	0.301960	−	0.854072i
$523$	−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
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	−2.00000	−	2.82843i	−0.0870388	−	0.123091i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	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
$534$	−16.8990	−	23.8988i	−0.731290	−	1.03420i
$535$	−17.3939			−0.752003
$536$	−12.8990			−0.557151
$537$	−15.0000	+	32.5590i	−0.647298	+	1.40503i
$538$	−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	$0.703184\pi$
$542$	3.55051	+	6.14966i	0.152507	+	0.264151i
$543$	17.8485	−	1.64456i	0.765951	−	0.0705750i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	−9.20204	−	15.9384i	−0.394172	−	0.682726i
$546$		0			0
$547$	3.79796	−	6.57826i	0.162389	−	0.281266i	−0.773336	−	0.633996i	$-0.781413\pi$
$547$	3.79796	−	6.57826i	0.162389	−	0.281266i	0.935725	+	0.352730i	$0.114747\pi$
$548$	−3.89898	−	6.75323i	−0.166556	−	0.288484i
$549$	−19.3207	+	3.59091i	−0.824586	+	0.153256i
$550$	2.89898	−	5.02118i	0.123613	−	0.214104i
$551$	17.5959			0.749611
$552$	0.724745	−	1.57313i	0.0308472	−	0.0669570i
$553$		0			0
$554$	9.34847	+	16.1920i	0.397178	+	0.687933i
$555$	29.4949	−	2.71767i	1.25199	−	0.115359i
$556$	2.27526	+	3.94086i	0.0964923	+	0.167130i
$557$	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	$0.0785602\pi$
$558$	−17.6969	+	3.28913i	−0.749171	+	0.139240i
$559$	−33.7980			−1.42950
$560$		0			0
$561$	−6.89898	+	0.635674i	−0.291275	+	0.0268382i
$562$	9.50000	−	16.4545i	0.400733	−	0.694090i
$563$	39.9444			1.68346			0.841728	−	0.539902i	$-0.181539\pi$
$563$	39.9444			1.68346			0.841728	+	0.539902i	$0.181539\pi$
$564$	−16.8990	+	1.55708i	−0.711575	+	0.0655648i
$565$	−8.84337			−0.372043
$566$	25.4495			1.06972
$567$		0			0
$568$	0.101021			0.00423873
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$	−6.37628	+	0.587512i	−0.267073	+	0.0246082i
$571$	33.7980			1.41440			0.707200	−	0.707013i	$-0.249958\pi$
$571$	33.7980			1.41440			0.707200	+	0.707013i	$0.249958\pi$
$572$	4.89898	−	8.48528i	0.204837	−	0.354787i
$573$	7.07321	−	0.651729i	0.295488	−	0.0272263i
$574$		0			0
$575$	2.89898			0.120896
$576$	2.94949	−	0.548188i	0.122895	−	0.0228412i
$577$	−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	$0.271908\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−30.8712	+	2.84448i	−1.28296	+	0.118213i
$580$	5.00000	+	8.66025i	0.207614	+	0.359597i
$581$		0			0
$582$	2.10102	−	4.56048i	0.0870901	−	0.189038i
$583$	−21.7980			−0.902779
$584$	−3.44949	+	5.97469i	−0.142741	+	0.247234i
$585$	−20.9444	+	3.89270i	−0.865944	+	0.160943i
$586$	1.37628	+	2.38378i	0.0568534	+	0.0984730i
$587$	8.07321	−	13.9832i	0.333217	−	0.577149i	−0.649924	−	0.760000i	$-0.725199\pi$
$587$	8.07321	−	13.9832i	0.333217	−	0.577149i	0.983141	+	0.182850i	$0.0585324\pi$
$588$		0			0
$589$	−7.65153	−	13.2528i	−0.315276	−	0.546074i
$590$	−1.44949	+	2.51059i	−0.0596745	+	0.103359i
$591$	28.7980	−	2.65345i	1.18459	−	0.109149i
$592$	−5.89898	−	10.2173i	−0.242447	−	0.419930i
$593$	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
$597$	−2.10102	+	4.56048i	−0.0859890	+	0.186648i
$598$	4.89898			0.200334
$599$	−33.7980			−1.38095			−0.690474	−	0.723358i	$-0.742598\pi$
$599$	−33.7980			−1.38095			−0.690474	+	0.723358i	$0.742598\pi$
$600$	2.89898	+	4.09978i	0.118350	+	0.167373i
$601$	8.34847	−	14.4600i	0.340541	−	0.589835i	−0.643992	−	0.765032i	$-0.722723\pi$
$601$	8.34847	−	14.4600i	0.340541	−	0.589835i	0.984533	+	0.175198i	$0.0560564\pi$
$602$		0			0
$603$	−38.0454	+	7.07107i	−1.54933	+	0.287956i
$604$	2.50000	+	4.33013i	0.101724	+	0.176190i
$605$	5.07321	+	8.78706i	0.206255	+	0.357245i
$606$	−17.2474	−	24.3916i	−0.700630	−	0.990840i
$607$	10.3485	−	17.9241i	0.420031	−	0.727516i	−0.575911	−	0.817513i	$-0.695352\pi$
$607$	10.3485	−	17.9241i	0.420031	−	0.727516i	0.995942	+	0.0899969i	$0.0286857\pi$
$608$	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
$612$	2.00000	−	5.65685i	0.0808452	−	0.228665i
$613$	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	$0.0707466\pi$
$614$	−25.2474			−1.01890
$615$	−24.4949	+	2.25697i	−0.987730	+	0.0910098i
$616$		0			0
$617$	7.69694	+	13.3315i	0.309867	+	0.536706i	0.978333	−	0.207037i	$-0.0663821\pi$
$617$	7.69694	+	13.3315i	0.309867	+	0.536706i	−0.668466	+	0.743743i	$0.733049\pi$
$618$	10.1464	−	22.0239i	0.408149	−	0.885929i
$619$	15.0732	+	26.1076i	0.605844	+	1.04935i	0.991918	+	0.126884i	$0.0404976\pi$
$619$	15.0732	+	26.1076i	0.605844	+	1.04935i	−0.386074	+	0.922468i	$0.626169\pi$
$620$	4.34847	−	7.53177i	0.174639	−	0.302483i
$621$	1.27526	−	5.03723i	0.0511742	−	0.202137i
$622$	−30.6969			−1.23084
$623$		0			0
$624$	4.89898	+	6.92820i	0.196116	+	0.277350i
$625$	1.05051	−	1.81954i	0.0420204	−	0.0727815i
$626$	4.69694			0.187727
$627$	3.69694	−	8.02458i	0.147642	−	0.320471i
$628$	8.34847			0.333140
$629$	−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	$0.312596\pi$
$632$	−1.89898			−0.0755373
$633$	−12.8990	−	18.2419i	−0.512688	−	0.725051i
$634$	20.6969			0.821980
$635$	2.17423	−	3.76588i	0.0862819	−	0.149445i
$636$	7.89898	−	17.1455i	0.313215	−	0.679865i
$637$		0			0
$638$	−13.7980			−0.546266
$639$	0.297959	−	0.0553782i	0.0117871	−	0.00219073i
$640$	−0.724745	+	1.25529i	−0.0286481	+	0.0496199i
$641$	3.74745	+	6.49077i	0.148015	+	0.256370i	0.930494	−	0.366308i	$-0.119378\pi$
$641$	3.74745	+	6.49077i	0.148015	+	0.256370i	−0.782479	+	0.622678i	$0.786045\pi$
$642$	12.0000	+	16.9706i	0.473602	+	0.669775i
$643$	−19.6969	−	34.1161i	−0.776771	−	1.34541i	−0.933793	−	0.357812i	$-0.883523\pi$
$643$	−19.6969	−	34.1161i	−0.776771	−	1.34541i	0.157022	−	0.987595i	$-0.449811\pi$
$644$		0			0
$645$	−10.0000	−	14.1421i	−0.393750	−	0.556846i
$646$	5.10102			0.200697
$647$	−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	$0.693111\pi$
$648$	8.39898	−	3.23375i	0.329943	−	0.127034i
$649$	−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
$653$	−4.89898	+	8.48528i	−0.191712	+	0.332055i	−0.945818	−	0.324698i	$-0.894737\pi$
$653$	−4.89898	+	8.48528i	−0.191712	+	0.332055i	0.754106	+	0.656753i	$0.228071\pi$
$654$	−9.20204	+	19.9740i	−0.359828	+	0.781044i
$655$	−6.19694	−	10.7334i	−0.242134	−	0.419389i
$656$	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	−0.518735	−	0.854935i	$-0.673597\pi$
$659$	12.3485	−	21.3882i	0.481028	−	0.833165i	0.999763	+	0.0217701i	$0.00693018\pi$
$660$	5.00000	−	0.460702i	0.194625	−	0.0179328i
$661$	−4.55051			−0.176994			−0.0884972	−	0.996076i	$-0.528206\pi$
$661$	−4.55051			−0.176994			−0.0884972	+	0.996076i	$0.528206\pi$
$662$	4.69694			0.182552
$663$	16.8990	−	1.55708i	0.656302	−	0.0604719i
$664$	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
$668$	−5.34847	−	9.26382i	−0.206938	−	0.358428i
$669$	−8.04541	+	17.4634i	−0.311053	+	0.675173i
$670$	9.34847	−	16.1920i	0.361163	−	0.625552i
$671$	6.55051	+	11.3458i	0.252880	+	0.438000i
$672$		0			0
$673$	4.29796	−	7.44428i	0.165674	−	0.286956i	−0.771220	−	0.636568i	$-0.780353\pi$
$673$	4.29796	−	7.44428i	0.165674	−	0.286956i	0.936894	+	0.349612i	$0.113687\pi$
$674$	11.6969	+	20.2597i	0.450549	+	0.780374i
$675$	10.7980	+	10.5031i	0.415614	+	0.404263i
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	−14.6969			−0.564849			−0.282425	−	0.959289i	$-0.591139\pi$
$677$	−14.6969			−0.564849			−0.282425	+	0.959289i	$0.591139\pi$
$678$	6.10102	+	8.62815i	0.234308	+	0.331362i
$679$		0			0
$680$	1.44949	+	2.51059i	0.0555854	+	0.0962767i
$681$	−5.44949	−	7.70674i	−0.208825	−	0.295323i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	−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	$0.709412\pi$
$684$	4.97219	+	5.81577i	0.190117	+	0.222372i
$685$	11.3031			0.431868
$686$		0			0
$687$	0.904082	−	1.96240i	0.0344929	−	0.0748703i
$688$	−3.44949	+	5.97469i	−0.131511	+	0.227783i
$689$	53.3939			2.03414
$690$	1.44949	+	2.04989i	0.0551811	+	0.0780379i
$691$	−51.0454			−1.94186			−0.970929	−	0.239366i	$-0.923060\pi$
$691$	−51.0454			−1.94186			−0.970929	+	0.239366i	$0.923060\pi$
$692$	3.10102			0.117883
$693$		0			0
$694$	19.5959			0.743851
$695$	−6.59592			−0.250197
$696$	5.00000	−	10.8530i	0.189525	−	0.411382i
$697$	19.5959			0.742248
$698$	5.55051	−	9.61377i	0.210090	−	0.363886i
$699$	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	$0.544592\pi$
$702$	18.2474	+	17.7491i	0.688706	+	0.669897i
$703$	15.0454	−	26.0594i	0.567448	−	0.982849i
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	10.2929	−	22.3417i	0.387651	−	0.841437i
$706$	−3.00000	−	5.19615i	−0.112906	−	0.195560i
$707$		0			0
$708$	3.44949	−	0.317837i	0.129640	−	0.0119451i
$709$	27.5959			1.03639			0.518193	−	0.855264i	$-0.326605\pi$
$709$	27.5959			1.03639			0.518193	+	0.855264i	$0.326605\pi$
$710$	−0.0732141	+	0.126811i	−0.00274768	+	0.00475911i
$711$	−5.60102	+	1.04100i	−0.210055	+	0.0390405i
$712$	−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
$716$	−10.3485	+	17.9241i	−0.386740	+	0.669854i
$717$	−6.79796	−	9.61377i	−0.253874	−	0.359033i
$718$	4.39898	+	7.61926i	0.164168	+	0.284348i
$719$	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
$723$	0.898979	+	1.27135i	0.0334334	+	0.0472820i
$724$	10.3485			0.384598
$725$	20.0000			0.742781
$726$	5.07321	−	11.0119i	0.188285	−	0.408691i
$727$	−4.24745	+	7.35680i	−0.157529	+	0.272848i	−0.933977	−	0.357333i	$-0.883686\pi$
$727$	−4.24745	+	7.35680i	−0.157529	+	0.272848i	0.776448	+	0.630181i	$0.217019\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	6.89898	+	11.9494i	0.255168	+	0.441964i
$732$	−11.2980	+	1.04100i	−0.417585	+	0.0384764i
$733$	−8.72474	+	15.1117i	−0.322256	+	0.558163i	−0.980953	−	0.194245i	$-0.937774\pi$
$733$	−8.72474	+	15.1117i	−0.322256	+	0.558163i	0.658697	+	0.752408i	$0.271108\pi$
$734$	−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
$738$	19.1010	+	22.3417i	0.703118	+	0.822409i
$739$	−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	$0.247119\pi$
$740$	17.1010			0.628646
$741$	−9.05561	+	19.6561i	−0.332666	+	0.722086i
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	−10.3485	+	0.953512i	−0.379393	+	0.0349574i
$745$	4.34847	+	7.53177i	0.159316	+	0.275943i
$746$	3.44949	−	5.97469i	0.126295	−	0.218749i
$747$	2.00000	−	5.65685i	0.0731762	−	0.206973i
$748$	−4.00000			−0.146254
$749$		0			0
$750$	−19.7474	+	1.81954i	−0.721075	+	0.0664401i
$751$	−0.702041	+	1.21597i	−0.0256178	+	0.0443714i	−0.878550	−	0.477650i	$-0.841489\pi$
$751$	−0.702041	+	1.21597i	−0.0256178	+	0.0443714i	0.852932	+	0.522022i	$0.174822\pi$
$752$	−9.79796			−0.357295
$753$	−30.0959	+	2.77305i	−1.09676	+	0.101056i
$754$	33.7980			1.23085
$755$	−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	$0.722396\pi$
$758$	22.4949			0.817051
$759$	−3.44949	+	0.317837i	−0.125209	+	0.0115368i
$760$	−3.69694			−0.134102
$761$	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	$0.155125\pi$
$762$	−5.17423	+	0.476756i	−0.187443	+	0.0172710i
$763$		0			0
$764$	4.10102			0.148370
$765$	5.65153	+	6.61037i	0.204332	+	0.238998i
$766$	−1.44949	+	2.51059i	−0.0523722	+	0.0907113i
$767$	4.89898	+	8.48528i	0.176892	+	0.306386i
$768$	1.72474	−	0.158919i	0.0622364	−	0.00573448i
$769$	−17.0454	−	29.5235i	−0.614673	−	1.06465i	−0.990442	−	0.137932i	$-0.955955\pi$
$769$	−17.0454	−	29.5235i	−0.614673	−	1.06465i	0.375769	−	0.926714i	$-0.377379\pi$
$770$		0			0
$771$	5.94439	−	12.9029i	0.214082	−	0.464686i
$772$	−17.8990			−0.644198
$773$	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	$-0.0423437\pi$
$774$	−6.89898	+	19.5133i	−0.247979	+	0.701390i
$775$	−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
$779$	−12.4949	+	21.6418i	−0.447676	+	0.775398i
$780$	−12.2474	+	1.12848i	−0.438529	+	0.0404062i
$781$	−0.101021	−	0.174973i	−0.00361480	−	0.00626101i
$782$	−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
$786$	−6.19694	+	13.4511i	−0.221037	+	0.479784i
$787$	11.3939			0.406148			0.203074	−	0.979163i	$-0.434907\pi$
$787$	11.3939			0.406148			0.203074	+	0.979163i	$0.434907\pi$
$788$	16.6969			0.594804
$789$	−25.8990	−	36.6267i	−0.922028	−	1.30394i
$790$	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
$794$	19.3485	+	33.5125i	0.686651	+	1.18932i
$795$	15.7980	+	22.3417i	0.560296	+	0.792378i
$796$	−1.44949	+	2.51059i	−0.0513758	+	0.0889855i
$797$	−8.97219	−	15.5403i	−0.317811	−	0.550465i	0.662220	−	0.749310i	$-0.269615\pi$
$797$	−8.97219	−	15.5403i	−0.317811	−	0.550465i	−0.980031	+	0.198844i	$0.936281\pi$
$798$		0			0
$799$	−9.79796	+	16.9706i	−0.346627	+	0.600375i
$800$	1.44949	+	2.51059i	0.0512472	+	0.0887628i
$801$	−32.9444	−	38.5337i	−1.16403	−	1.36152i
$802$	9.94949	−	17.2330i	0.351329	−	0.608519i
$803$	13.7980			0.486919
$804$	−22.2474	+	2.04989i	−0.784607	+	0.0722940i
$805$		0			0
$806$	−14.6969	−	25.4558i	−0.517678	−	0.896644i
$807$	−13.2980	+	28.8646i	−0.468110	+	1.01608i
$808$	−8.62372	−	14.9367i	−0.303382	−	0.525472i
$809$	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	$0.0747339\pi$
$810$	−2.02781	+	12.8868i	−0.0712499	+	0.452797i
$811$	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
$814$	−11.7980	+	20.4347i	−0.413518	+	0.716235i
$815$	−28.6969			−1.00521
$816$	1.44949	−	3.14626i	0.0507423	−	0.110141i
$817$	−17.5959			−0.615603
$818$	13.7980			0.482434
$819$		0			0
$820$	−14.2020			−0.495957
$821$	0.404082			0.0141026			0.00705128	−	0.999975i	$-0.497755\pi$
$821$	0.404082			0.0141026			0.00705128	+	0.999975i	$0.497755\pi$
$822$	−7.79796	−	11.0280i	−0.271985	−	0.384645i
$823$	−13.3939			−0.466881			−0.233441	−	0.972371i	$-0.574998\pi$
$823$	−13.3939			−0.466881			−0.233441	+	0.972371i	$0.574998\pi$
$824$	7.00000	−	12.1244i	0.243857	−	0.422372i
$825$	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	$0.718805\pi$
$828$	1.00000	−	2.82843i	0.0347524	−	0.0982946i
$829$	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	$0.159463\pi$
$830$	1.44949	+	2.51059i	0.0503125	+	0.0871438i
$831$	18.6969	+	26.4415i	0.648590	+	0.917244i
$832$	2.44949	+	4.24264i	0.0849208	+	0.147087i
$833$		0			0
$834$	4.55051	+	6.43539i	0.157571	+	0.222839i
$835$	15.5051			0.536576
$836$	2.55051	−	4.41761i	0.0882112	−	0.152786i
$837$	−30.0000	+	8.48528i	−1.03695	+	0.293294i
$838$	14.7247	+	25.5040i	0.508658	+	0.881021i
$839$	−17.5505	+	30.3984i	−0.605911	+	1.04947i	0.385996	+	0.922500i	$0.373858\pi$
$839$	−17.5505	+	30.3984i	−0.605911	+	1.04947i	−0.991907	+	0.126968i	$0.959475\pi$
$840$		0			0
$841$	−9.29796	−	16.1045i	−0.320619	−	0.555329i
$842$	−11.4495	+	19.8311i	−0.394575	+	0.683425i
$843$	13.7702	−	29.8895i	0.474269	−	1.02945i
$844$	−6.44949	−	11.1708i	−0.222001	−	0.384516i
$845$	−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
$849$	43.8939	−	4.04440i	1.50643	−	0.138803i
$850$	5.79796			0.198868
$851$	−11.7980			−0.404429
$852$	0.174235	−	0.0160540i	0.00596918	−	0.000550002i
$853$	12.4217	−	21.5150i	0.425310	−	0.736659i	−0.571139	−	0.820853i	$-0.693498\pi$
$853$	12.4217	−	21.5150i	0.425310	−	0.736659i	0.996449	+	0.0841942i	$0.0268316\pi$
$854$		0			0
$855$	−10.9041	+	2.02662i	−0.372912	+	0.0693089i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−17.4495	−	30.2234i	−0.596063	−	1.03241i	−0.993396	−	0.114737i	$-0.963397\pi$
$857$	−17.4495	−	30.2234i	−0.596063	−	1.03241i	0.397333	−	0.917675i	$-0.369936\pi$
$858$	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
$862$	−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	$0.898247\pi$
$864$	5.00000	−	1.41421i	0.170103	−	0.0481125i
$865$	−2.24745	+	3.89270i	−0.0764155	+	0.132356i
$866$	7.79796			0.264985
$867$	13.0000	+	18.3848i	0.441503	+	0.624380i
$868$		0			0
$869$	1.89898	+	3.28913i	0.0644185	+	0.111576i
$870$	10.0000	+	14.1421i	0.339032	+	0.479463i
$871$	−31.5959	−	54.7257i	−1.07059	−	1.85431i
$872$	−6.34847	+	10.9959i	−0.214986	+	0.372367i
$873$	2.89898	−	8.19955i	0.0981156	−	0.277513i
$874$	2.55051			0.0862723
$875$		0			0
$876$	−5.00000	+	10.8530i	−0.168934	+	0.366689i
$877$	−11.2474	+	19.4812i	−0.379799	+	0.657832i	−0.991033	−	0.133619i	$-0.957340\pi$
$877$	−11.2474	+	19.4812i	−0.379799	+	0.657832i	0.611233	+	0.791450i	$0.290674\pi$
$878$	−2.20204			−0.0743153
$879$	2.75255	+	3.89270i	0.0928413	+	0.131297i
$880$	2.89898			0.0977246
$881$	−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	$0.608104\pi$
$884$	9.79796			0.329541
$885$	−2.10102	+	4.56048i	−0.0706250	+	0.153299i
$886$	−14.8990			−0.500541
$887$	−7.10102	+	12.2993i	−0.238429	+	0.412971i	−0.960264	−	0.279094i	$-0.909966\pi$
$887$	−7.10102	+	12.2993i	−0.238429	+	0.412971i	0.721835	+	0.692065i	$0.243299\pi$
$888$	−11.7980	−	16.6848i	−0.395914	−	0.559906i
$889$		0			0
$890$	24.4949			0.821071
$891$	−14.0000	−	11.3137i	−0.469018	−	0.379023i
$892$	−5.55051	+	9.61377i	−0.185845	+	0.321893i
$893$	−12.4949	−	21.6418i	−0.418126	−	0.724215i
$894$	4.34847	−	9.43879i	0.145435	−	0.315680i
$895$	−15.0000	−	25.9808i	−0.501395	−	0.868441i
$896$		0			0
$897$	8.44949	−	0.778539i	0.282120	−	0.0259947i
$898$	20.5959			0.687295
$899$	−20.6969	+	35.8481i	−0.690282	+	1.19560i
$900$	5.65153	+	6.61037i	0.188384	+	0.220346i
$901$	−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
$905$	−7.50000	+	12.9904i	−0.249308	+	0.431815i
$906$	5.00000	+	7.07107i	0.166114	+	0.234920i
$907$	−1.34847	−	2.33562i	−0.0447752	−	0.0775529i	0.842769	−	0.538275i	$-0.180924\pi$
$907$	−1.34847	−	2.33562i	−0.0447752	−	0.0775529i	−0.887544	+	0.460722i	$0.847590\pi$
$908$	−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	0.00947432	+	0.999955i	$0.496984\pi$
$911$	−25.9949	+	45.0245i	−0.861249	+	1.49173i	−0.870724	+	0.491773i	$0.836349\pi$
$912$	2.55051	+	3.60697i	0.0844558	+	0.119439i
$913$	−4.00000			−0.132381
$914$	−17.4949			−0.578680
$915$	6.88138	−	14.9367i	0.227491	−	0.493793i
$916$	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	$0.694018\pi$
$920$	0.724745	+	1.25529i	0.0238941	+	0.0413858i
$921$	−43.5454	+	4.01229i	−1.43487	+	0.132209i
$922$	2.82577	−	4.89437i	0.0930616	−	0.161187i
$923$	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
$927$	14.0000	−	39.5980i	0.459820	−	1.30057i
$928$	3.44949	−	5.97469i	0.113235	−	0.196129i
$929$	−34.2929			−1.12511			−0.562556	−	0.826759i	$-0.690182\pi$
$929$	−34.2929			−1.12511			−0.562556	+	0.826759i	$0.690182\pi$
$930$	6.30306	−	13.6814i	0.206686	−	0.448632i
$931$		0			0
$932$	3.50000	+	6.06218i	0.114646	+	0.198573i
$933$	−52.9444	+	4.87832i	−1.73332	+	0.159709i
$934$	5.00000	+	8.66025i	0.163605	+	0.283372i
$935$	2.89898	−	5.02118i	0.0948068	−	0.164210i
$936$	9.55051	+	11.1708i	0.312168	+	0.365130i
$937$	−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
$940$	7.10102	−	12.2993i	0.231610	−	0.401160i
$941$	1.44949			0.0472520			0.0236260	−	0.999721i	$-0.492479\pi$
$941$	1.44949			0.0472520			0.0236260	+	0.999721i	$0.492479\pi$
$942$	14.3990	−	1.32673i	0.469144	−	0.0432271i
$943$	9.79796			0.319065
$944$	2.00000			0.0650945
$945$		0			0
$946$	13.7980			0.448610
$947$	52.4949			1.70585			0.852927	−	0.522029i	$-0.174825\pi$
$947$	52.4949			1.70585			0.852927	+	0.522029i	$0.174825\pi$
$948$	−3.27526	+	0.301783i	−0.106375	+	0.00980146i
$949$	−33.7980			−1.09713
$950$	−3.69694	+	6.40329i	−0.119945	+	0.207750i
$951$	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	$0.517506\pi$
$954$	10.8990	−	30.8270i	0.352867	−	0.998060i
$955$	−2.97219	+	5.14799i	−0.0961779	+	0.166585i
$956$	−3.39898	−	5.88721i	−0.109931	−	0.190406i
$957$	−23.7980	+	2.19275i	−0.769279	+	0.0708816i
$958$	4.79796	+	8.31031i	0.155015	+	0.268494i
$959$		0			0
$960$	−1.05051	+	2.28024i	−0.0339051	+	0.0735944i
$961$	5.00000			0.161290
$962$	28.8990	−	50.0545i	0.931740	−	1.61382i
$963$	23.3939	+	27.3629i	0.753857	+	0.881756i
$964$	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	0.597686	−	0.801730i	$-0.296087\pi$
$967$	−12.2980	−	21.3007i	−0.395476	−	0.684984i	−0.993162	+	0.116746i	$0.962754\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	8.79796	−	0.810647i	0.282631	−	0.0260417i
$970$	2.10102	+	3.63907i	0.0674597	+	0.116844i
$971$	−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
$975$	−10.2929	+	22.3417i	−0.329635	+	0.715507i
$976$	−6.55051			−0.209677
$977$	−37.5959			−1.20280			−0.601400	−	0.798948i	$-0.705390\pi$
$977$	−37.5959			−1.20280			−0.601400	+	0.798948i	$0.705390\pi$
$978$	19.7980	+	27.9985i	0.633069	+	0.895295i
$979$	−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
$983$	−16.5959	−	28.7450i	−0.529328	−	0.916822i	−0.999415	−	0.0342024i	$-0.989111\pi$
$983$	−16.5959	−	28.7450i	−0.529328	−	0.916822i	0.470087	−	0.882620i	$-0.344222\pi$
$984$	9.79796	+	13.8564i	0.312348	+	0.441726i
$985$	−12.1010	+	20.9596i	−0.385571	+	0.667828i
$986$	−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
$990$	8.55051	−	1.58919i	0.271753	−	0.0505077i
$991$	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	$0.157575\pi$
$992$	−6.00000			−0.190500
$993$	8.10102	−	0.746431i	0.257078	−	0.0236873i
$994$		0			0
$995$	−2.10102	−	3.63907i	−0.0666068	−	0.115366i
$996$	1.44949	−	3.14626i	0.0459288	−	0.0996932i
$997$	26.0732	+	45.1601i	0.825747	+	1.43024i	0.901347	+	0.433097i	$0.142579\pi$
$997$	26.0732	+	45.1601i	0.825747	+	1.43024i	−0.0756001	+	0.997138i	$0.524087\pi$
$998$	12.6969	−	21.9917i	0.401915	−	0.696136i
$999$	−43.9444	−	42.7442i	−1.39034	−	1.35237i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	7.3	odd	6
126.2.f.c.85.1	yes	4	63.31	odd	6
378.2.f.d.127.1		4	21.17	even	6
378.2.f.d.253.1		4	63.59	even	6
882.2.e.m.373.1		4	63.40	odd	6
882.2.e.m.655.1		4	7.6	odd	2
882.2.e.n.373.2		4	63.58	even	3	inner
882.2.e.n.655.2		4	1.1	even	1	trivial
882.2.f.j.295.1		4	7.4	even	3
882.2.f.j.589.2		4	63.4	even	3
882.2.h.k.67.2		4	63.13	odd	6
882.2.h.k.79.2		4	7.5	odd	6
882.2.h.l.67.1		4	9.4	even	3
882.2.h.l.79.1		4	7.2	even	3
1008.2.r.e.337.2		4	252.31	even	6
1008.2.r.e.673.1		4	28.3	even	6
1134.2.a.i.1.2		2	63.38	even	6
1134.2.a.p.1.1		2	63.52	odd	6
2646.2.e.k.1549.2		4	63.23	odd	6
2646.2.e.k.2125.2		4	3.2	odd	2
2646.2.e.l.1549.1		4	63.5	even	6
2646.2.e.l.2125.1		4	21.20	even	2
2646.2.f.k.883.2		4	21.11	odd	6
2646.2.f.k.1765.2		4	63.32	odd	6
2646.2.h.m.361.2		4	63.41	even	6
2646.2.h.m.667.2		4	21.5	even	6
2646.2.h.n.361.1		4	9.5	odd	6
2646.2.h.n.667.1		4	21.2	odd	6
3024.2.r.e.1009.1		4	252.59	odd	6
3024.2.r.e.2017.1		4	84.59	odd	6
7938.2.a.bm.1.1		2	63.11	odd	6
7938.2.a.bn.1.2		2	63.25	even	3
9072.2.a.bd.1.2		2	252.227	odd	6
9072.2.a.bk.1.1		2	252.115	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.72474 - 0.158919i) q^{3} +1.00000 q^{4} +(-0.724745 + 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.72474 - 0.158919i) q^{3} +1.00000 q^{4} +(-0.724745 + 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(2.94949 - 0.548188i) q^{9} +(-0.724745 + 1.25529i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.72474 - 0.158919i) q^{12} +(2.44949 + 4.24264i) q^{13} +(-1.05051 + 2.28024i) q^{15} +1.00000 q^{16} +(1.00000 - 1.73205i) q^{17} +(2.94949 - 0.548188i) q^{18} +(1.27526 + 2.20881i) q^{19} +(-0.724745 + 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.72474 - 0.158919i) q^{24} +(1.44949 + 2.51059i) q^{25} +(2.44949 + 4.24264i) q^{26} +(5.00000 - 1.41421i) q^{27} +(3.44949 - 5.97469i) q^{29} +(-1.05051 + 2.28024i) q^{30} -6.00000 q^{31} +1.00000 q^{32} +(-2.00000 - 2.82843i) q^{33} +(1.00000 - 1.73205i) q^{34} +(2.94949 - 0.548188i) q^{36} +(-5.89898 - 10.2173i) q^{37} +(1.27526 + 2.20881i) q^{38} +(4.89898 + 6.92820i) q^{39} +(-0.724745 + 1.25529i) q^{40} +(4.89898 + 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.44949 + 4.09978i) q^{45} +(0.500000 - 0.866025i) q^{46} -9.79796 q^{47} +(1.72474 - 0.158919i) q^{48} +(1.44949 + 2.51059i) q^{50} +(1.44949 - 3.14626i) q^{51} +(2.44949 + 4.24264i) q^{52} +(5.44949 - 9.43879i) q^{53} +(5.00000 - 1.41421i) q^{54} +2.89898 q^{55} +(2.55051 + 3.60697i) q^{57} +(3.44949 - 5.97469i) q^{58} +2.00000 q^{59} +(-1.05051 + 2.28024i) q^{60} -6.55051 q^{61} -6.00000 q^{62} +1.00000 q^{64} -7.10102 q^{65} +(-2.00000 - 2.82843i) q^{66} -12.8990 q^{67} +(1.00000 - 1.73205i) q^{68} +(0.724745 - 1.57313i) q^{69} +0.101021 q^{71} +(2.94949 - 0.548188i) q^{72} +(-3.44949 + 5.97469i) q^{73} +(-5.89898 - 10.2173i) q^{74} +(2.89898 + 4.09978i) q^{75} +(1.27526 + 2.20881i) q^{76} +(4.89898 + 6.92820i) q^{78} -1.89898 q^{79} +(-0.724745 + 1.25529i) q^{80} +(8.39898 - 3.23375i) q^{81} +(4.89898 + 8.48528i) q^{82} +(1.00000 - 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} +(-3.44949 + 5.97469i) q^{86} +(5.00000 - 10.8530i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(-8.44949 - 14.6349i) q^{89} +(-1.44949 + 4.09978i) q^{90} +(0.500000 - 0.866025i) q^{92} +(-10.3485 + 0.953512i) q^{93} -9.79796 q^{94} -3.69694 q^{95} +(1.72474 - 0.158919i) q^{96} +(1.44949 - 2.51059i) q^{97} +(-3.89898 - 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} + 2 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 4 q^{32} - 8 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} + 10 q^{38} + 2 q^{40} - 4 q^{43} - 4 q^{44} + 4 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} + 20 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} + 8 q^{59} - 14 q^{60} - 36 q^{61} - 24 q^{62} + 4 q^{64} - 48 q^{65} - 8 q^{66} - 32 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} - 4 q^{74} - 8 q^{75} + 10 q^{76} + 12 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} + 20 q^{87} - 4 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} + 44 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^12 - 14 * q^15 + 4 * q^16 + 4 * q^17 + 2 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 + 2 * q^24 - 4 * q^25 + 20 * q^27 + 4 * q^29 - 14 * q^30 - 24 * q^31 + 4 * q^32 - 8 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 + 10 * q^38 + 2 * q^40 - 4 * q^43 - 4 * q^44 + 4 * q^45 + 2 * q^46 + 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 + 20 * q^54 - 8 * q^55 + 20 * q^57 + 4 * q^58 + 8 * q^59 - 14 * q^60 - 36 * q^61 - 24 * q^62 + 4 * q^64 - 48 * q^65 - 8 * q^66 - 32 * q^67 + 4 * q^68 - 2 * q^69 + 20 * q^71 + 2 * q^72 - 4 * q^73 - 4 * q^74 - 8 * q^75 + 10 * q^76 + 12 * q^79 + 2 * q^80 + 14 * q^81 + 4 * q^83 - 4 * q^85 - 4 * q^86 + 20 * q^87 - 4 * q^88 - 24 * q^89 + 4 * q^90 + 2 * q^92 - 12 * q^93 + 44 * q^95 + 2 * q^96 - 4 * q^97 + 4 * q^99

Introduction

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