LMFDB - Embedded newform 882.2.f.j.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			295.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.j.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +1.44949 q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.724745 + 1.57313i) q^{12} +(2.44949 + 4.24264i) q^{13} +(-1.05051 + 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +(-1.94949 - 2.28024i) q^{18} -2.55051 q^{19} +(-0.724745 + 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(1.44949 - 2.51059i) q^{25} -4.89898 q^{26} +(5.00000 - 1.41421i) q^{27} +(3.44949 - 5.97469i) q^{29} +(-1.44949 - 2.04989i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.44949 - 0.317837i) q^{33} +(1.00000 - 1.73205i) q^{34} +(2.94949 - 0.548188i) q^{36} +11.7980 q^{37} +(1.27526 - 2.20881i) q^{38} +(3.55051 - 7.70674i) q^{39} +(-0.724745 - 1.25529i) q^{40} +(4.89898 + 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} +2.00000 q^{44} +(4.27526 - 0.794593i) q^{45} -1.00000 q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 - 0.158919i) q^{48} +(1.44949 + 2.51059i) q^{50} +(2.00000 + 2.82843i) q^{51} +(2.44949 - 4.24264i) q^{52} -10.8990 q^{53} +(-1.27526 + 5.03723i) q^{54} +2.89898 q^{55} +(2.55051 + 3.60697i) q^{57} +(3.44949 + 5.97469i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(2.50000 - 0.230351i) q^{60} +(3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.55051 - 6.14966i) q^{65} +(-1.44949 + 3.14626i) q^{66} +(6.44949 + 11.1708i) q^{67} +(1.00000 + 1.73205i) q^{68} +(0.724745 - 1.57313i) q^{69} +0.101021 q^{71} +(-1.00000 + 2.82843i) q^{72} +6.89898 q^{73} +(-5.89898 + 10.2173i) q^{74} +(-5.00000 + 0.460702i) q^{75} +(1.27526 + 2.20881i) q^{76} +(4.89898 + 6.92820i) q^{78} +(0.949490 - 1.64456i) q^{79} +1.44949 q^{80} +(-7.00000 - 5.65685i) q^{81} -9.79796 q^{82} +(1.00000 - 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} +(-3.44949 - 5.97469i) q^{86} +(-11.8990 + 1.09638i) q^{87} +(-1.00000 + 1.73205i) q^{88} +16.8990 q^{89} +(-1.44949 + 4.09978i) q^{90} +(0.500000 - 0.866025i) q^{92} +(4.34847 - 9.43879i) q^{93} +(4.89898 + 8.48528i) q^{94} +(1.84847 + 3.20164i) q^{95} +(-0.724745 + 1.57313i) 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} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 20 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} - 4 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} + 4 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 24 q^{39} + 2 q^{40} - 4 q^{43} + 8 q^{44} + 22 q^{45} - 4 q^{46} + 2 q^{48} - 4 q^{50} + 8 q^{51} - 24 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} - 4 q^{59} + 10 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} - 4 q^{72} + 8 q^{73} - 4 q^{74} - 20 q^{75} + 10 q^{76} - 6 q^{79} - 4 q^{80} - 28 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} - 28 q^{87} - 4 q^{88} + 48 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 + 2 * q^12 - 14 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 - 20 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 - 4 * q^24 - 4 * q^25 + 20 * q^27 + 4 * q^29 + 4 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 + 8 * q^37 + 10 * q^38 + 24 * q^39 + 2 * q^40 - 4 * q^43 + 8 * q^44 + 22 * q^45 - 4 * q^46 + 2 * q^48 - 4 * q^50 + 8 * q^51 - 24 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 + 4 * q^58 - 4 * q^59 + 10 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 + 4 * q^68 - 2 * q^69 + 20 * q^71 - 4 * q^72 + 8 * q^73 - 4 * q^74 - 20 * q^75 + 10 * q^76 - 6 * q^79 - 4 * q^80 - 28 * q^81 + 4 * q^83 - 4 * q^85 - 4 * q^86 - 28 * q^87 - 4 * q^88 + 48 * q^89 + 4 * q^90 + 2 * q^92 - 12 * q^93 - 22 * q^95 + 2 * q^96 - 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.724745	−	1.25529i	−0.324116	−	0.561385i	0.657217	−	0.753701i	$-0.271733\pi$
$5$	−0.724745	−	1.25529i	−0.324116	−	0.561385i	−0.981333	+	0.192316i	$0.938400\pi$
$6$	1.72474	−	0.158919i	0.704124	−	0.0648783i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$	1.44949			0.458369
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	−0.724745	+	1.57313i	−0.209216	+	0.454124i
$13$	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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.94949	−	2.28024i	−0.459499	−	0.537457i
$19$	−2.55051			−0.585127			−0.292564	−	0.956246i	$-0.594508\pi$
$19$	−2.55051			−0.585127			−0.292564	+	0.956246i	$0.594508\pi$
$20$	−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	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$	−1.00000	−	1.41421i	−0.204124	−	0.288675i
$25$	1.44949	−	2.51059i	0.289898	−	0.502118i
$26$	−4.89898			−0.960769
$27$	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	$-0.0546286\pi$
$30$	−1.44949	−	2.04989i	−0.264639	−	0.374257i
$31$	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
$33$	3.44949	−	0.317837i	0.600479	−	0.0553284i
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$		0			0
$36$	2.94949	−	0.548188i	0.491582	−	0.0913647i
$37$	11.7980			1.93957			0.969786	−	0.243956i	$-0.0784453\pi$
$37$	11.7980			1.93957			0.969786	+	0.243956i	$0.0784453\pi$
$38$	1.27526	−	2.20881i	0.206874	−	0.358316i
$39$	3.55051	−	7.70674i	0.568537	−	1.23407i
$40$	−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	$0.990342\pi$
$44$	2.00000			0.301511
$45$	4.27526	−	0.794593i	0.637317	−	0.118451i
$46$	−1.00000			−0.147442
$47$	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
$51$	2.00000	+	2.82843i	0.280056	+	0.396059i
$52$	2.44949	−	4.24264i	0.339683	−	0.588348i
$53$	−10.8990			−1.49709			−0.748545	−	0.663084i	$-0.769247\pi$
$53$	−10.8990			−1.49709			−0.748545	+	0.663084i	$0.769247\pi$
$54$	−1.27526	+	5.03723i	−0.173540	+	0.685481i
$55$	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
$59$	−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	$0.874892\pi$
$60$	2.50000	−	0.230351i	0.322749	−	0.0297382i
$61$	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
$66$	−1.44949	+	3.14626i	−0.178420	+	0.387278i
$67$	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	$0.544486\pi$
$68$	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	$0.498092\pi$
$72$	−1.00000	+	2.82843i	−0.117851	+	0.333333i
$73$	6.89898			0.807464			0.403732	−	0.914877i	$-0.367713\pi$
$73$	6.89898			0.807464			0.403732	+	0.914877i	$0.367713\pi$
$74$	−5.89898	+	10.2173i	−0.685742	+	1.18774i
$75$	−5.00000	+	0.460702i	−0.577350	+	0.0531973i
$76$	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	$0.132598\pi$
$80$	1.44949			0.162058
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	−9.79796			−1.08200
$83$	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
$87$	−11.8990	+	1.09638i	−1.27570	+	0.117544i
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	16.8990			1.79129			0.895644	−	0.444771i	$-0.146715\pi$
$89$	16.8990			1.79129			0.895644	+	0.444771i	$0.146715\pi$
$90$	−1.44949	+	4.09978i	−0.152790	+	0.432154i
$91$		0			0
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$	4.34847	−	9.43879i	0.450915	−	0.978757i
$94$	4.89898	+	8.48528i	0.505291	+	0.875190i
$95$	1.84847	+	3.20164i	0.189649	+	0.328482i
$96$	−0.724745	+	1.57313i	−0.0739690	+	0.160557i
$97$	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
$100$	−2.89898			−0.289898
$101$	−8.62372	+	14.9367i	−0.858093	+	1.48626i	0.0156533	+	0.999877i	$0.495017\pi$
$101$	−8.62372	+	14.9367i	−0.858093	+	1.48626i	−0.873746	+	0.486383i	$0.838316\pi$
$102$	−3.44949	+	0.317837i	−0.341550	+	0.0314706i
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$	2.44949	+	4.24264i	0.240192	+	0.416025i
$105$		0			0
$106$	5.44949	−	9.43879i	0.529301	−	0.916777i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−3.72474	−	3.62302i	−0.358414	−	0.348625i
$109$	12.6969			1.21615			0.608073	−	0.793881i	$-0.291943\pi$
$109$	12.6969			1.21615			0.608073	+	0.793881i	$0.291943\pi$
$110$	−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	0.973084	−	0.230449i	$-0.0740194\pi$
$113$	3.05051	+	5.28364i	0.286968	+	0.497043i	−0.686117	+	0.727492i	$0.740686\pi$
$114$	−4.39898	+	0.405324i	−0.412002	+	0.0379620i
$115$	0.724745	−	1.25529i	0.0675828	−	0.117057i
$116$	−6.89898			−0.640554
$117$	−14.4495	+	2.68556i	−1.33586	+	0.248280i
$118$	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
$122$	3.27526	+	5.67291i	0.296528	+	0.513601i
$123$	7.10102	−	15.4135i	0.640277	−	1.38979i
$124$	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
$129$	11.8990	−	1.09638i	1.04765	−	0.0965306i
$130$	3.55051	+	6.14966i	0.311400	+	0.539361i
$131$	−4.27526	−	7.40496i	−0.373531	−	0.646974i	0.616575	−	0.787296i	$-0.288520\pi$
$131$	−4.27526	−	7.40496i	−0.373531	−	0.646974i	−0.990106	+	0.140322i	$0.955186\pi$
$132$	−2.00000	−	2.82843i	−0.174078	−	0.246183i
$133$		0			0
$134$	−12.8990			−1.11430
$135$	−5.39898	−	5.25153i	−0.464670	−	0.451980i
$136$	−2.00000			−0.171499
$137$	−3.89898	+	6.75323i	−0.333112	+	0.576967i	−0.983120	−	0.182960i	$-0.941432\pi$
$137$	−3.89898	+	6.75323i	−0.333112	+	0.576967i	0.650008	+	0.759927i	$0.274765\pi$
$138$	1.00000	+	1.41421i	0.0851257	+	0.120386i
$139$	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
$142$	−0.0505103	+	0.0874863i	−0.00423873	+	0.00734169i
$143$	−9.79796			−0.819346
$144$	−1.94949	−	2.28024i	−0.162457	−	0.190020i
$145$	−10.0000			−0.830455
$146$	−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	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	2.10102	−	4.56048i	0.171548	−	0.372361i
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	−0.746190	−	0.665733i	$-0.768119\pi$
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	0.949637	+	0.313353i	$0.101452\pi$
$152$	−2.55051			−0.206874
$153$	2.00000	−	5.65685i	0.161690	−	0.457330i
$154$		0			0
$155$	4.34847	−	7.53177i	0.349277	−	0.604966i
$156$	−8.44949	+	0.778539i	−0.676501	+	0.0623330i
$157$	−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
$159$	10.8990	+	15.4135i	0.864345	+	1.22237i
$160$	−0.724745	+	1.25529i	−0.0572961	+	0.0992398i
$161$		0			0
$162$	8.39898	−	3.23375i	0.659886	−	0.254067i
$163$	−19.7980			−1.55070			−0.775348	−	0.631534i	$-0.782425\pi$
$163$	−19.7980			−1.55070			−0.775348	+	0.631534i	$0.782425\pi$
$164$	4.89898	−	8.48528i	0.382546	−	0.662589i
$165$	−2.89898	−	4.09978i	−0.225685	−	0.319167i
$166$	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
$170$	−2.89898			−0.222342
$171$	2.55051	−	7.21393i	0.195042	−	0.551663i
$172$	6.89898			0.526042
$173$	−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
$177$	−1.44949	+	3.14626i	−0.108950	+	0.236488i
$178$	−8.44949	+	14.6349i	−0.633316	+	1.09694i
$179$	20.6969			1.54696			0.773481	−	0.633820i	$-0.218514\pi$
$179$	20.6969			1.54696			0.773481	+	0.633820i	$0.218514\pi$
$180$	−2.82577	−	3.30518i	−0.210620	−	0.246354i
$181$	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
$185$	−8.55051	−	14.8099i	−0.628646	−	1.08885i
$186$	6.00000	+	8.48528i	0.439941	+	0.622171i
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	−9.79796			−0.714590
$189$		0			0
$190$	−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	$0.214069\pi$
$192$	−1.00000	−	1.41421i	−0.0721688	−	0.102062i
$193$	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	$0.610524\pi$
$194$	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	$0.297230\pi$
$198$	5.89898	−	1.09638i	0.419222	−	0.0779161i
$199$	2.89898			0.205503			0.102752	−	0.994707i	$-0.467235\pi$
$199$	2.89898			0.205503			0.102752	+	0.994707i	$0.467235\pi$
$200$	1.44949	−	2.51059i	0.102494	−	0.177526i
$201$	9.34847	−	20.2918i	0.659390	−	1.43127i
$202$	−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
$206$	−14.0000			−0.975426
$207$	−2.94949	+	0.548188i	−0.205004	+	0.0381017i
$208$	−4.89898			−0.339683
$209$	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
$213$	−0.101021	−	0.142865i	−0.00692181	−	0.00978892i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	10.0000			0.681994
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$		0			0
$218$	−6.34847	+	10.9959i	−0.429973	+	0.744734i
$219$	−6.89898	−	9.75663i	−0.466190	−	0.659292i
$220$	−1.44949	−	2.51059i	−0.0977246	−	0.169264i
$221$	−4.89898	−	8.48528i	−0.329541	−	0.570782i
$222$	20.3485	−	1.87492i	1.36570	−	0.125836i
$223$	−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
$226$	−6.10102			−0.405834
$227$	−2.72474	+	4.71940i	−0.180848	+	0.313237i	−0.942169	−	0.335137i	$-0.891217\pi$
$227$	−2.72474	+	4.71940i	−0.180848	+	0.313237i	0.761322	+	0.648374i	$0.224551\pi$
$228$	1.84847	−	4.01229i	0.122418	−	0.265720i
$229$	0.623724	+	1.08032i	0.0412169	+	0.0713897i	0.885898	−	0.463880i	$-0.153543\pi$
$229$	0.623724	+	1.08032i	0.0412169	+	0.0713897i	−0.844681	+	0.535270i	$0.820210\pi$
$230$	0.724745	+	1.25529i	0.0477883	+	0.0827717i
$231$		0			0
$232$	3.44949	−	5.97469i	0.226470	−	0.392258i
$233$	−7.00000			−0.458585			−0.229293	−	0.973358i	$-0.573641\pi$
$233$	−7.00000			−0.458585			−0.229293	+	0.973358i	$0.573641\pi$
$234$	4.89898	−	13.8564i	0.320256	−	0.905822i
$235$	−14.2020			−0.926439
$236$	−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	0.734904	−	0.678171i	$-0.237227\pi$
$239$	−3.39898	−	5.88721i	−0.219862	−	0.380812i	−0.954766	+	0.297360i	$0.903894\pi$
$240$	−1.44949	−	2.04989i	−0.0935642	−	0.132320i
$241$	0.449490	−	0.778539i	0.0289542	−	0.0501501i	−0.851185	−	0.524865i	$-0.824116\pi$
$241$	0.449490	−	0.778539i	0.0289542	−	0.0501501i	0.880139	+	0.474715i	$0.157449\pi$
$242$	−7.00000			−0.449977
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$	−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
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$	−3.44949	+	0.317837i	−0.218603	+	0.0201421i
$250$	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
$255$	2.10102	−	4.56048i	0.131571	−	0.285588i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.10102	+	7.10318i	0.255815	+	0.443084i	0.965116	−	0.261821i	$-0.0843230\pi$
$257$	4.10102	+	7.10318i	0.255815	+	0.443084i	−0.709302	+	0.704905i	$0.750990\pi$
$258$	−5.00000	+	10.8530i	−0.311286	+	0.675679i
$259$		0			0
$260$	−7.10102			−0.440387
$261$	13.4495	+	15.7313i	0.832503	+	0.973744i
$262$	8.55051			0.528252
$263$	−12.9495	+	22.4292i	−0.798500	+	1.38304i	0.122093	+	0.992519i	$0.461039\pi$
$263$	−12.9495	+	22.4292i	−0.798500	+	1.38304i	−0.920593	+	0.390523i	$0.872294\pi$
$264$	3.44949	−	0.317837i	0.212301	−	0.0195615i
$265$	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
$269$	18.3485			1.11873			0.559363	−	0.828923i	$-0.311046\pi$
$269$	18.3485			1.11873			0.559363	+	0.828923i	$0.311046\pi$
$270$	7.24745	−	2.04989i	0.441066	−	0.124752i
$271$	−7.10102			−0.431356			−0.215678	−	0.976465i	$-0.569196\pi$
$271$	−7.10102			−0.431356			−0.215678	+	0.976465i	$0.569196\pi$
$272$	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
$276$	−1.72474	+	0.158919i	−0.103817	+	0.00956578i
$277$	9.34847	−	16.1920i	0.561695	−	0.972884i	−0.435654	−	0.900114i	$-0.643483\pi$
$277$	9.34847	−	16.1920i	0.561695	−	0.972884i	0.997349	−	0.0727700i	$-0.0231839\pi$
$278$	−4.55051			−0.272921
$279$	−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	$-0.0251222\pi$
$282$	7.10102	−	15.4135i	0.422860	−	0.917860i
$283$	−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
$285$	2.67934	−	5.81577i	0.158710	−	0.344497i
$286$	4.89898	−	8.48528i	0.289683	−	0.501745i
$287$		0			0
$288$	2.94949	−	0.548188i	0.173800	−	0.0323023i
$289$	−13.0000			−0.764706
$290$	5.00000	−	8.66025i	0.293610	−	0.508548i
$291$	−5.00000	+	0.460702i	−0.293105	+	0.0270068i
$292$	−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
$296$	11.7980			0.685742
$297$	−2.55051	+	10.0745i	−0.147996	+	0.584580i
$298$	−6.00000			−0.347571
$299$	−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
$303$	29.7474	−	2.74094i	1.70895	−	0.157463i
$304$	1.27526	−	2.20881i	0.0731409	−	0.126684i
$305$	−9.49490			−0.543676
$306$	3.89898	+	4.56048i	0.222890	+	0.260705i
$307$	−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
$311$	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	$0.497238\pi$
$312$	3.55051	−	7.70674i	0.201008	−	0.436308i
$313$	−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	$0.969239\pi$
$318$	−18.7980	+	1.73205i	−1.05414	+	0.0971286i
$319$	6.89898	+	11.9494i	0.386269	+	0.669037i
$320$	−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
$324$	−1.39898	+	8.89060i	−0.0777211	+	0.493922i
$325$	14.2020			0.787787
$326$	9.89898	−	17.1455i	0.548254	−	0.949603i
$327$	−12.6969	−	17.9562i	−0.702142	−	0.992979i
$328$	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	$0.207870\pi$
$332$	−2.00000			−0.109764
$333$	−11.7980	+	33.3697i	−0.646524	+	1.82865i
$334$	10.6969			0.585310
$335$	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
$339$	4.42168	−	9.59771i	0.240153	−	0.521276i
$340$	1.44949	−	2.51059i	0.0786096	−	0.136156i
$341$	−12.0000			−0.649836
$342$	4.97219	+	5.81577i	0.268865	+	0.314481i
$343$		0			0
$344$	−3.44949	+	5.97469i	−0.185984	+	0.322134i
$345$	−2.50000	+	0.230351i	−0.134595	+	0.0124017i
$346$	−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	$-0.342969\pi$
$348$	6.89898	+	9.75663i	0.369824	+	0.523010i
$349$	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
$352$	2.00000			0.106600
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$	−2.00000	−	2.82843i	−0.106299	−	0.150329i
$355$	−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
$359$	−8.79796			−0.464339			−0.232169	−	0.972675i	$-0.574582\pi$
$359$	−8.79796			−0.464339			−0.232169	+	0.972675i	$0.574582\pi$
$360$	4.27526	−	0.794593i	0.225326	−	0.0418787i
$361$	−12.4949			−0.657626
$362$	−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
$366$	4.74745	−	10.3048i	0.248153	−	0.538641i
$367$	−6.89898	+	11.9494i	−0.360124	+	0.623753i	−0.987981	−	0.154576i	$-0.950599\pi$
$367$	−6.89898	+	11.9494i	−0.360124	+	0.623753i	0.627857	+	0.778329i	$0.283932\pi$
$368$	−1.00000			−0.0521286
$369$	−28.8990	+	5.37113i	−1.50442	+	0.279610i
$370$	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	0.941404	−	0.337281i	$-0.109507\pi$
$373$	3.44949	+	5.97469i	0.178608	+	0.309358i	−0.762796	+	0.646639i	$0.776174\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	11.4495	+	16.1920i	0.591249	+	0.836153i
$376$	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
$381$	3.00000	+	4.24264i	0.153695	+	0.217357i
$382$	−2.05051	−	3.55159i	−0.104913	−	0.181715i
$383$	−1.44949	−	2.51059i	−0.0740655	−	0.128285i	0.826614	−	0.562769i	$-0.190264\pi$
$383$	−1.44949	−	2.51059i	−0.0740655	−	0.128285i	−0.900679	+	0.434484i	$0.856931\pi$
$384$	1.72474	−	0.158919i	0.0880155	−	0.00810978i
$385$		0			0
$386$	−17.8990			−0.911034
$387$	−13.4495	−	15.7313i	−0.683676	−	0.799668i
$388$	−2.89898			−0.147173
$389$	12.4495	−	21.5631i	0.631214	−	1.09330i	−0.356090	−	0.934452i	$-0.615890\pi$
$389$	12.4495	−	21.5631i	0.631214	−	1.09330i	0.987304	−	0.158843i	$-0.0507764\pi$
$390$	5.14643	−	11.1708i	0.260600	−	0.565658i
$391$	−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
$395$	−2.75255			−0.138496
$396$	−2.00000	+	5.65685i	−0.100504	+	0.284268i
$397$	−38.6969			−1.94214			−0.971072	−	0.238788i	$-0.923250\pi$
$397$	−38.6969			−1.94214			−0.971072	+	0.238788i	$0.923250\pi$
$398$	−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	0.999993	−	0.00362911i	$-0.00115518\pi$
$401$	9.94949	+	17.2330i	0.496854	+	0.860576i	−0.503140	+	0.864205i	$0.667822\pi$
$402$	12.8990	+	18.2419i	0.643343	+	0.909824i
$403$	−14.6969	+	25.4558i	−0.732107	+	1.26805i
$404$	17.2474			0.858093
$405$	−2.02781	+	12.8868i	−0.100763	+	0.640352i
$406$		0			0
$407$	−11.7980	+	20.4347i	−0.584803	+	1.01291i
$408$	2.00000	+	2.82843i	0.0990148	+	0.140028i
$409$	−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
$411$	13.4495	−	1.23924i	0.663414	−	0.0611272i
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$	1.00000	−	2.82843i	0.0491473	−	0.139010i
$415$	−2.89898			−0.142305
$416$	2.44949	−	4.24264i	0.120096	−	0.208013i
$417$	3.29796	−	7.15855i	0.161502	−	0.350556i
$418$	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	$0.978230\pi$
$422$	12.8990			0.627912
$423$	19.1010	+	22.3417i	0.928723	+	1.08629i
$424$	−10.8990			−0.529301
$425$	−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
$429$	9.79796	+	13.8564i	0.473050	+	0.668994i
$430$	−5.00000	+	8.66025i	−0.241121	+	0.417635i
$431$	31.5959			1.52192			0.760961	−	0.648798i	$-0.224728\pi$
$431$	31.5959			1.52192			0.760961	+	0.648798i	$0.224728\pi$
$432$	−1.27526	+	5.03723i	−0.0613557	+	0.242354i
$433$	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
$437$	−1.27526	−	2.20881i	−0.0610037	−	0.105662i
$438$	11.8990	−	1.09638i	0.568555	−	0.0523869i
$439$	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	$0.0515098\pi$
$444$	−8.55051	+	18.5597i	−0.405789	+	0.880807i
$445$	−12.2474	−	21.2132i	−0.580585	−	1.00560i
$446$	−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	$0.338459\pi$
$450$	−8.55051	+	1.58919i	−0.403075	+	0.0749150i
$451$	−19.5959			−0.922736
$452$	3.05051	−	5.28364i	0.143484	−	0.248521i
$453$	−8.62372	+	0.794593i	−0.405178	+	0.0373332i
$454$	−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	$0.0324785\pi$
$458$	−1.24745			−0.0582895
$459$	−10.0000	+	2.82843i	−0.466760	+	0.132020i
$460$	−1.44949			−0.0675828
$461$	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
$465$	−15.0000	+	1.38211i	−0.695608	+	0.0640936i
$466$	3.50000	−	6.06218i	0.162134	−	0.280825i
$467$	−10.0000			−0.462745			−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000			−0.462745			−0.231372	+	0.972865i	$0.574322\pi$
$468$	9.55051	+	11.1708i	0.441472	+	0.516372i
$469$		0			0
$470$	7.10102	−	12.2993i	0.327546	−	0.567326i
$471$	−6.05051	+	13.1332i	−0.278793	+	0.605148i
$472$	−1.00000	−	1.73205i	−0.0460287	−	0.0797241i
$473$	−6.89898	−	11.9494i	−0.317215	−	0.549433i
$474$	1.37628	−	2.98735i	0.0632144	−	0.137213i
$475$	−3.69694	+	6.40329i	−0.169627	+	0.293803i
$476$		0			0
$477$	10.8990	−	30.8270i	0.499030	−	1.41147i
$478$	6.79796			0.310931
$479$	4.79796	−	8.31031i	0.219224	−	0.379708i	−0.735347	−	0.677691i	$-0.762981\pi$
$479$	4.79796	−	8.31031i	0.219224	−	0.379708i	0.954571	+	0.297983i	$0.0963140\pi$
$480$	2.50000	−	0.230351i	0.114109	−	0.0105140i
$481$	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
$485$	−4.20204			−0.190805
$486$	−12.9722	−	8.64420i	−0.588431	−	0.392109i
$487$	−36.3939			−1.64916			−0.824582	−	0.565742i	$-0.808590\pi$
$487$	−36.3939			−1.64916			−0.824582	+	0.565742i	$0.808590\pi$
$488$	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	0.630893	−	0.775869i	$-0.282688\pi$
$491$	−7.89898	−	13.6814i	−0.356476	−	0.617434i	−0.987369	+	0.158435i	$0.949355\pi$
$492$	−16.8990	+	1.55708i	−0.761865	+	0.0701985i
$493$	−6.89898	+	11.9494i	−0.310714	+	0.538173i
$494$	12.4949			0.562172
$495$	−2.89898	+	8.19955i	−0.130299	+	0.368542i
$496$	−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	0.996725	+	0.0808642i	$0.0257680\pi$
$499$	12.6969	+	21.9917i	0.568393	+	0.984486i	−0.428332	+	0.903621i	$0.640899\pi$
$500$	5.72474	+	9.91555i	0.256018	+	0.443437i
$501$	−7.75255	+	16.8277i	−0.346358	+	0.751806i
$502$	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
$507$	18.9722	−	1.74810i	0.842585	−	0.0776361i
$508$	1.50000	+	2.59808i	0.0665517	+	0.115271i
$509$	−3.55051	−	6.14966i	−0.157374	−	0.272579i	0.776547	−	0.630059i	$-0.216969\pi$
$509$	−3.55051	−	6.14966i	−0.157374	−	0.272579i	−0.933921	+	0.357480i	$0.883636\pi$
$510$	2.89898	+	4.09978i	0.128369	+	0.181541i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−12.7526	+	3.60697i	−0.563039	+	0.159251i
$514$	−8.20204			−0.361777
$515$	10.1464	−	17.5741i	0.447105	−	0.774409i
$516$	−6.89898	−	9.75663i	−0.303711	−	0.429512i
$517$	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
$521$	9.30306			0.407575			0.203787	−	0.979015i	$-0.434675\pi$
$521$	9.30306			0.407575			0.203787	+	0.979015i	$0.434675\pi$
$522$	−20.3485	+	3.78194i	−0.890628	+	0.165531i
$523$	14.3485			0.627415			0.313707	−	0.949520i	$-0.398429\pi$
$523$	14.3485			0.627415			0.313707	+	0.949520i	$0.398429\pi$
$524$	−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
$528$	−1.44949	+	3.14626i	−0.0630809	+	0.136924i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−15.7980			−0.686219
$531$	5.89898	−	1.09638i	0.255994	−	0.0475787i
$532$		0			0
$533$	−24.0000	+	41.5692i	−1.03956	+	1.80056i
$534$	29.1464	−	2.68556i	1.26129	−	0.116216i
$535$	8.69694	+	15.0635i	0.376001	+	0.651254i
$536$	6.44949	+	11.1708i	0.278576	+	0.482507i
$537$	−20.6969	−	29.2699i	−0.893139	−	1.26309i
$538$	−9.17423	+	15.8902i	−0.395529	+	0.685077i
$539$		0			0
$540$	−1.84847	+	7.30142i	−0.0795455	+	0.314203i
$541$	−18.4949			−0.795158			−0.397579	−	0.917568i	$-0.630149\pi$
$541$	−18.4949			−0.795158			−0.397579	+	0.917568i	$0.630149\pi$
$542$	3.55051	−	6.14966i	0.152507	−	0.264151i
$543$	−10.3485	−	14.6349i	−0.444095	−	0.628046i
$544$	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	$0.114747\pi$
$548$	7.79796			0.333112
$549$	12.7702	+	14.9367i	0.545017	+	0.637484i
$550$	−5.79796			−0.247226
$551$	−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
$555$	−12.3939	+	26.9022i	−0.526091	+	1.14193i
$556$	2.27526	−	3.94086i	0.0964923	−	0.167130i
$557$	−12.8990			−0.546547			−0.273274	−	0.961936i	$-0.588106\pi$
$557$	−12.8990			−0.546547			−0.273274	+	0.961936i	$0.588106\pi$
$558$	6.00000	−	16.9706i	0.254000	−	0.718421i
$559$	−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
$563$	−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	$-0.485128\pi$
$564$	9.79796	+	13.8564i	0.412568	+	0.583460i
$565$	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	$-0.0498003\pi$
$570$	3.69694	+	5.22826i	0.154848	+	0.218988i
$571$	−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	$-0.416709\pi$
$572$	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
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	15.5959			0.649267			0.324633	−	0.945840i	$-0.394759\pi$
$577$	15.5959			0.649267			0.324633	+	0.945840i	$0.394759\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	12.9722	−	28.1575i	0.539106	−	1.17018i
$580$	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
$584$	6.89898			0.285482
$585$	13.8434	+	16.1920i	0.572353	+	0.669458i
$586$	−2.75255			−0.113707
$587$	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
$591$	−16.6969	−	23.6130i	−0.686820	−	0.971311i
$592$	−5.89898	+	10.2173i	−0.242447	+	0.419930i
$593$	−14.6969			−0.603531			−0.301765	−	0.953382i	$-0.597576\pi$
$593$	−14.6969			−0.603531			−0.301765	+	0.953382i	$0.597576\pi$
$594$	−7.44949	−	7.24604i	−0.305656	−	0.297309i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−2.89898	−	4.09978i	−0.118647	−	0.167793i
$598$	−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	$0.590736\pi$
$600$	−5.00000	+	0.460702i	−0.204124	+	0.0188081i
$601$	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
$604$	−5.00000			−0.203447
$605$	5.07321	−	8.78706i	0.206255	−	0.357245i
$606$	−12.5000	+	27.1325i	−0.507778	+	1.10218i
$607$	10.3485	+	17.9241i	0.420031	+	0.727516i	0.995942	−	0.0899969i	$-0.0286857\pi$
$607$	10.3485	+	17.9241i	0.420031	+	0.727516i	−0.575911	+	0.817513i	$0.695352\pi$
$608$	1.27526	+	2.20881i	0.0517184	+	0.0895789i
$609$		0			0
$610$	4.74745	−	8.22282i	0.192219	−	0.332932i
$611$	48.0000			1.94187
$612$	−5.89898	+	1.09638i	−0.238452	+	0.0443184i
$613$	−14.6969			−0.593604			−0.296802	−	0.954939i	$-0.595920\pi$
$613$	−14.6969			−0.593604			−0.296802	+	0.954939i	$0.595920\pi$
$614$	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	0.978333	−	0.207037i	$-0.0663821\pi$
$617$	7.69694	+	13.3315i	0.309867	+	0.536706i	−0.668466	+	0.743743i	$0.733049\pi$
$618$	14.0000	+	19.7990i	0.563163	+	0.796432i
$619$	15.0732	−	26.1076i	0.605844	−	1.04935i	−0.386074	−	0.922468i	$-0.626169\pi$
$619$	15.0732	−	26.1076i	0.605844	−	1.04935i	0.991918	−	0.126884i	$-0.0404976\pi$
$620$	−8.69694			−0.349277
$621$	3.72474	+	3.62302i	0.149469	+	0.145387i
$622$	−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
$626$	−2.34847	−	4.06767i	−0.0938637	−	0.162577i
$627$	−8.79796	+	0.810647i	−0.351357	+	0.0323741i
$628$	−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
$633$	−9.34847	+	20.2918i	−0.371568	+	0.806527i
$634$	−10.3485	−	17.9241i	−0.410990	−	0.711856i
$635$	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
$639$	−0.101021	+	0.285729i	−0.00399631	+	0.0113033i
$640$	1.44949			0.0572961
$641$	3.74745	−	6.49077i	0.148015	−	0.256370i	−0.782479	−	0.622678i	$-0.786045\pi$
$641$	3.74745	−	6.49077i	0.148015	−	0.256370i	0.930494	+	0.366308i	$0.119378\pi$
$642$	−20.6969	+	1.90702i	−0.816843	+	0.0752642i
$643$	−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
$646$	−2.55051	+	4.41761i	−0.100348	+	0.173809i
$647$	50.6969			1.99310			0.996551	−	0.0829807i	$-0.0264440\pi$
$647$	50.6969			1.99310			0.996551	+	0.0829807i	$0.0264440\pi$
$648$	−7.00000	−	5.65685i	−0.274986	−	0.222222i
$649$	4.00000			0.157014
$650$	−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	0.754106	−	0.656753i	$-0.228071\pi$
$653$	−4.89898	−	8.48528i	−0.191712	−	0.332055i	−0.945818	+	0.324698i	$0.894737\pi$
$654$	21.8990	−	2.01778i	0.856318	−	0.0789014i
$655$	−6.19694	+	10.7334i	−0.242134	+	0.419389i
$656$	−9.79796			−0.382546
$657$	−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	$0.00693018\pi$
$660$	−2.10102	+	4.56048i	−0.0817821	+	0.177516i
$661$	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
$663$	−7.10102	+	15.4135i	−0.275781	+	0.598610i
$664$	1.00000	−	1.73205i	0.0388075	−	0.0672166i
$665$		0			0
$666$	−23.0000	−	26.9022i	−0.891232	−	1.04244i
$667$	6.89898			0.267130
$668$	−5.34847	+	9.26382i	−0.206938	+	0.358428i
$669$	19.1464	−	1.76416i	0.740244	−	0.0682063i
$670$	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	$0.113687\pi$
$674$	−23.3939			−0.901098
$675$	3.69694	−	14.6028i	0.142295	−	0.562063i
$676$	11.0000			0.423077
$677$	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
$681$	9.39898	−	0.866025i	0.360170	−	0.0331862i
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	51.7980			1.98199			0.990997	−	0.133885i	$-0.0427452\pi$
$683$	51.7980			1.98199			0.990997	+	0.133885i	$0.0427452\pi$
$684$	−7.52270	+	1.39816i	−0.287638	+	0.0534600i
$685$	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
$689$	−26.6969	−	46.2405i	−1.01707	−	1.76162i
$690$	1.05051	−	2.28024i	0.0399922	−	0.0868072i
$691$	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
$696$	−11.8990	+	1.09638i	−0.451030	+	0.0415580i
$697$	−9.79796	−	16.9706i	−0.371124	−	0.642806i
$698$	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	$0.544592\pi$
$702$	−24.4949	+	6.92820i	−0.924500	+	0.261488i
$703$	−30.0908			−1.13490
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$	14.2020	+	20.0847i	0.534880	+	0.756434i
$706$	−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	$0.993271\pi$
$710$	0.146428			0.00549535
$711$	3.70204	+	4.33013i	0.138837	+	0.162392i
$712$	16.8990			0.633316
$713$	−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
$717$	−4.92679	+	10.6941i	−0.183994	+	0.399378i
$718$	4.39898	−	7.61926i	0.164168	−	0.284348i
$719$	−9.79796			−0.365402			−0.182701	−	0.983169i	$-0.558484\pi$
$719$	−9.79796			−0.365402			−0.182701	+	0.983169i	$0.558484\pi$
$720$	−1.44949	+	4.09978i	−0.0540193	+	0.152790i
$721$		0			0
$722$	6.24745	−	10.8209i	0.232506	−	0.402712i
$723$	−1.55051	+	0.142865i	−0.0576641	+	0.00531319i
$724$	−5.17423	−	8.96204i	−0.192299	−	0.333071i
$725$	−10.0000	−	17.3205i	−0.371391	−	0.643268i
$726$	7.00000	+	9.89949i	0.259794	+	0.367405i
$727$	−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
$730$	10.0000			0.370117
$731$	6.89898	−	11.9494i	0.255168	−	0.441964i
$732$	6.55051	+	9.26382i	0.242114	+	0.342401i
$733$	−8.72474	−	15.1117i	−0.322256	−	0.558163i	0.658697	−	0.752408i	$-0.271108\pi$
$733$	−8.72474	−	15.1117i	−0.322256	−	0.558163i	−0.980953	+	0.194245i	$0.937774\pi$
$734$	−6.89898	−	11.9494i	−0.254646	−	0.441060i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	−25.7980			−0.950280
$738$	9.79796	−	27.7128i	0.360668	−	1.02012i
$739$	13.5959			0.500134			0.250067	−	0.968229i	$-0.419547\pi$
$739$	13.5959			0.500134			0.250067	+	0.968229i	$0.419547\pi$
$740$	−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	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	4.34847	−	9.43879i	0.159423	−	0.346043i
$745$	4.34847	−	7.53177i	0.159316	−	0.275943i
$746$	−6.89898			−0.252590
$747$	3.89898	+	4.56048i	0.142656	+	0.166859i
$748$	−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	0.852932	−	0.522022i	$-0.174822\pi$
$751$	−0.702041	−	1.21597i	−0.0256178	−	0.0443714i	−0.878550	+	0.477650i	$0.841489\pi$
$752$	4.89898	+	8.48528i	0.178647	+	0.309426i
$753$	17.4495	+	24.6773i	0.635895	+	0.899291i
$754$	−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
$759$	2.00000	+	2.82843i	0.0725954	+	0.102665i
$760$	1.84847	+	3.20164i	0.0670510	+	0.116136i
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	0.883581	−	0.468278i	$-0.155125\pi$
$761$	1.00000	+	1.73205i	0.0362500	+	0.0627868i	−0.847331	+	0.531065i	$0.821792\pi$
$762$	−5.17423	+	0.476756i	−0.187443	+	0.0172710i
$763$		0			0
$764$	4.10102			0.148370
$765$	−8.55051	+	1.58919i	−0.309144	+	0.0574571i
$766$	2.89898			0.104744
$767$	4.89898	−	8.48528i	0.176892	−	0.306386i
$768$	−0.724745	+	1.57313i	−0.0261520	+	0.0567655i
$769$	−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
$772$	8.94949	−	15.5010i	0.322099	−	0.557892i
$773$	−33.9444			−1.22089			−0.610447	−	0.792057i	$-0.709010\pi$
$773$	−33.9444			−1.22089			−0.610447	+	0.792057i	$0.709010\pi$
$774$	20.3485	−	3.78194i	0.731411	−	0.135939i
$775$	17.3939			0.624807
$776$	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
$780$	7.10102	+	10.0424i	0.254257	+	0.359574i
$781$	−0.101021	+	0.174973i	−0.00361480	+	0.00626101i
$782$	2.00000			0.0715199
$783$	8.79796	−	34.7518i	0.314413	−	1.24193i
$784$		0			0
$785$	−6.05051	+	10.4798i	−0.215952	+	0.374040i
$786$	−8.55051	−	12.0922i	−0.304987	−	0.431316i
$787$	−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
$789$	44.6691	−	4.11583i	1.59026	−	0.146527i
$790$	1.37628	−	2.38378i	0.0489657	−	0.0848111i
$791$		0			0
$792$	−3.89898	−	4.56048i	−0.138544	−	0.162050i
$793$	32.0908			1.13958
$794$	19.3485	−	33.5125i	0.686651	−	1.18932i
$795$	11.4495	−	24.8523i	0.406072	−	0.881419i
$796$	−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
$800$	−2.89898			−0.102494
$801$	−16.8990	+	47.7975i	−0.597096	+	1.68884i
$802$	−19.8990			−0.702657
$803$	−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
$807$	−18.3485	−	25.9487i	−0.645897	−	0.913436i
$808$	−8.62372	+	14.9367i	−0.303382	+	0.525472i
$809$	−16.2020			−0.569633			−0.284817	−	0.958582i	$-0.591933\pi$
$809$	−16.2020			−0.569633			−0.284817	+	0.958582i	$0.591933\pi$
$810$	−10.1464	−	8.19955i	−0.356509	−	0.288103i
$811$	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
$815$	14.3485	+	24.8523i	0.502605	+	0.870537i
$816$	−3.44949	+	0.317837i	−0.120756	+	0.0111265i
$817$	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	$0.168911\pi$
$822$	−5.65153	+	12.2672i	−0.197120	+	0.427868i
$823$	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	$0.758335\pi$
$824$	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	$0.718805\pi$
$828$	1.94949	+	2.28024i	0.0677495	+	0.0792438i
$829$	−1.30306			−0.0452572			−0.0226286	−	0.999744i	$-0.507204\pi$
$829$	−1.30306			−0.0452572			−0.0226286	+	0.999744i	$0.507204\pi$
$830$	1.44949	−	2.51059i	0.0503125	−	0.0871438i
$831$	−32.2474	+	2.97129i	−1.11865	+	0.103073i
$832$	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
$836$	−5.10102			−0.176422
$837$	22.3485	+	21.7381i	0.772476	+	0.751379i
$838$	−29.4495			−1.01732
$839$	−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
$843$	−32.7702	+	3.01945i	−1.12866	+	0.103996i
$844$	−6.44949	+	11.1708i	−0.222001	+	0.384516i
$845$	15.9444			0.548504
$846$	−28.8990	+	5.37113i	−0.993567	+	0.184663i
$847$		0			0
$848$	5.44949	−	9.43879i	0.187136	−	0.324129i
$849$	−18.4444	+	40.0354i	−0.633010	+	1.37401i
$850$	−2.89898	−	5.02118i	−0.0994342	−	0.172225i
$851$	5.89898	+	10.2173i	0.202214	+	0.350246i
$852$	−0.0732141	+	0.158919i	−0.00250827	+	0.00544446i
$853$	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
$856$	−12.0000			−0.410152
$857$	−17.4495	+	30.2234i	−0.596063	+	1.03241i	0.397333	+	0.917675i	$0.369936\pi$
$857$	−17.4495	+	30.2234i	−0.596063	+	1.03241i	−0.993396	+	0.114737i	$0.963397\pi$
$858$	−16.8990	+	1.55708i	−0.576922	+	0.0531578i
$859$	−5.00000	−	8.66025i	−0.170598	−	0.295484i	0.768031	−	0.640412i	$-0.221237\pi$
$859$	−5.00000	−	8.66025i	−0.170598	−	0.295484i	−0.938629	+	0.344928i	$0.887903\pi$
$860$	−5.00000	−	8.66025i	−0.170499	−	0.295312i
$861$		0			0
$862$	−15.7980	+	27.3629i	−0.538081	+	0.931983i
$863$	11.8990			0.405046			0.202523	−	0.979278i	$-0.435086\pi$
$863$	11.8990			0.405046			0.202523	+	0.979278i	$0.435086\pi$
$864$	−3.72474	−	3.62302i	−0.126718	−	0.123258i
$865$	4.49490			0.152831
$866$	−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
$870$	−17.2474	+	1.58919i	−0.584743	+	0.0538785i
$871$	−31.5959	+	54.7257i	−1.07059	+	1.85431i
$872$	12.6969			0.429973
$873$	5.65153	+	6.61037i	0.191275	+	0.223727i
$874$	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	0.611233	−	0.791450i	$-0.290674\pi$
$877$	−11.2474	−	19.4812i	−0.379799	−	0.657832i	−0.991033	+	0.133619i	$0.957340\pi$
$878$	1.10102	+	1.90702i	0.0371576	+	0.0643589i
$879$	1.99490	−	4.33013i	0.0672862	−	0.146052i
$880$	−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
$885$	5.00000	−	0.460702i	0.168073	−	0.0154863i
$886$	7.44949	+	12.9029i	0.250271	+	0.433481i
$887$	−7.10102	−	12.2993i	−0.238429	−	0.412971i	0.721835	−	0.692065i	$-0.243299\pi$
$887$	−7.10102	−	12.2993i	−0.238429	−	0.412971i	−0.960264	+	0.279094i	$0.909966\pi$
$888$	−11.7980	−	16.6848i	−0.395914	−	0.559906i
$889$		0			0
$890$	24.4949			0.821071
$891$	16.7980	−	6.46750i	0.562753	−	0.216669i
$892$	11.1010			0.371690
$893$	−12.4949	+	21.6418i	−0.418126	+	0.724215i
$894$	6.00000	+	8.48528i	0.200670	+	0.283790i
$895$	−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
$899$	41.3939			1.38056
$900$	2.89898	−	8.19955i	0.0966326	−	0.273318i
$901$	21.7980			0.726195
$902$	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
$906$	3.62372	−	7.86566i	0.120390	−	0.261319i
$907$	−1.34847	+	2.33562i	−0.0447752	+	0.0775529i	−0.887544	−	0.460722i	$-0.847590\pi$
$907$	−1.34847	+	2.33562i	−0.0447752	+	0.0775529i	0.842769	+	0.538275i	$0.180924\pi$
$908$	5.44949			0.180848
$909$	−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	$0.836349\pi$
$912$	−4.39898	+	0.405324i	−0.145665	+	0.0134216i
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$	8.74745	+	15.1510i	0.289340	+	0.501151i
$915$	9.49490	+	13.4278i	0.313892	+	0.443910i
$916$	0.623724	−	1.08032i	0.0206084	−	0.0356949i
$917$		0			0
$918$	2.55051	−	10.0745i	0.0841794	−	0.332507i
$919$	−25.6969			−0.847664			−0.423832	−	0.905741i	$-0.639315\pi$
$919$	−25.6969			−0.847664			−0.423832	+	0.905741i	$0.639315\pi$
$920$	0.724745	−	1.25529i	0.0238941	−	0.0413858i
$921$	25.2474	+	35.7053i	0.831932	+	1.17653i
$922$	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
$926$	3.69694			0.121489
$927$	−41.2929	+	7.67463i	−1.35624	+	0.252068i
$928$	−6.89898			−0.226470
$929$	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
$933$	22.2474	−	48.2903i	0.728349	−	1.58095i
$934$	5.00000	−	8.66025i	0.163605	−	0.283372i
$935$	−5.79796			−0.189614
$936$	−14.4495	+	2.68556i	−0.472296	+	0.0877804i
$937$	−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
$941$	−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	$0.840854\pi$
$942$	−8.34847	−	11.8065i	−0.272008	−	0.384677i
$943$	−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	$0.841492\pi$
$948$	1.89898	+	2.68556i	0.0616760	+	0.0872230i
$949$	16.8990	+	29.2699i	0.548564	+	0.950141i
$950$	−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	$0.517506\pi$
$954$	21.2474	+	24.8523i	0.687912	+	0.804622i
$955$	5.94439			0.192356
$956$	−3.39898	+	5.88721i	−0.109931	+	0.190406i
$957$	10.0000	−	21.7060i	0.323254	−	0.701656i
$958$	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
$962$	−57.7980			−1.86348
$963$	12.0000	−	33.9411i	0.386695	−	1.09374i
$964$	−0.898979			−0.0289542
$965$	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
$969$	−5.10102	−	7.21393i	−0.163868	−	0.231745i
$970$	2.10102	−	3.63907i	0.0674597	−	0.116844i
$971$	0.0556128			0.00178470			0.000892350	−	1.00000i	$-0.499716\pi$
$971$	0.0556128			0.00178470			0.000892350		1.00000i	$0.499716\pi$
$972$	13.9722	−	6.91215i	0.448158	−	0.221707i
$973$		0			0
$974$	18.1969	−	31.5180i	0.583068	−	1.00990i
$975$	−14.2020	−	20.0847i	−0.454829	−	0.643226i
$976$	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	$0.627943\pi$
$978$	−34.1464	+	3.14626i	−1.09188	+	0.100606i
$979$	−16.8990	+	29.2699i	−0.540094	+	0.935470i
$980$		0			0
$981$	−12.6969	+	35.9124i	−0.405382	+	1.14659i
$982$	15.7980			0.504133
$983$	−16.5959	+	28.7450i	−0.529328	+	0.916822i	0.470087	+	0.882620i	$0.344222\pi$
$983$	−16.5959	+	28.7450i	−0.529328	+	0.916822i	−0.999415	+	0.0342024i	$0.989111\pi$
$984$	7.10102	−	15.4135i	0.226372	−	0.491364i
$985$	−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
$989$	−6.89898			−0.219375
$990$	−5.65153	−	6.61037i	−0.179617	−	0.210091i
$991$	−1.79796			−0.0571140			−0.0285570	−	0.999592i	$-0.509091\pi$
$991$	−1.79796			−0.0571140			−0.0285570	+	0.999592i	$0.509091\pi$
$992$	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
$996$	2.00000	+	2.82843i	0.0633724	+	0.0896221i
$997$	26.0732	−	45.1601i	0.825747	−	1.43024i	−0.0756001	−	0.997138i	$-0.524087\pi$
$997$	26.0732	−	45.1601i	0.825747	−	1.43024i	0.901347	−	0.433097i	$-0.142579\pi$
$998$	−25.3939			−0.803829
$999$	58.9898	−	16.6848i	1.86635	−	0.527885i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	7.6	odd	2
126.2.f.c.85.1	yes	4	63.13	odd	6
378.2.f.d.127.1		4	21.20	even	2
378.2.f.d.253.1		4	63.41	even	6
882.2.e.m.373.1		4	63.31	odd	6
882.2.e.m.655.1		4	7.5	odd	6
882.2.e.n.373.2		4	63.4	even	3
882.2.e.n.655.2		4	7.2	even	3
882.2.f.j.295.1		4	1.1	even	1	trivial
882.2.f.j.589.2		4	9.4	even	3	inner
882.2.h.k.67.2		4	63.40	odd	6
882.2.h.k.79.2		4	7.3	odd	6
882.2.h.l.67.1		4	63.58	even	3
882.2.h.l.79.1		4	7.4	even	3
1008.2.r.e.337.2		4	252.139	even	6
1008.2.r.e.673.1		4	28.27	even	2
1134.2.a.i.1.2		2	63.20	even	6
1134.2.a.p.1.1		2	63.34	odd	6
2646.2.e.k.1549.2		4	63.32	odd	6
2646.2.e.k.2125.2		4	21.2	odd	6
2646.2.e.l.1549.1		4	63.59	even	6
2646.2.e.l.2125.1		4	21.5	even	6
2646.2.f.k.883.2		4	3.2	odd	2
2646.2.f.k.1765.2		4	9.5	odd	6
2646.2.h.m.361.2		4	63.5	even	6
2646.2.h.m.667.2		4	21.17	even	6
2646.2.h.n.361.1		4	63.23	odd	6
2646.2.h.n.667.1		4	21.11	odd	6
3024.2.r.e.1009.1		4	252.167	odd	6
3024.2.r.e.2017.1		4	84.83	odd	2
7938.2.a.bm.1.1		2	9.2	odd	6
7938.2.a.bn.1.2		2	9.7	even	3
9072.2.a.bd.1.2		2	252.83	odd	6
9072.2.a.bk.1.1		2	252.223	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.724745 - 1.25529i) q^{5} +(1.72474 - 0.158919i) q^{6} +1.00000 q^{8} +(-1.00000 + 2.82843i) q^{9} +1.44949 q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.724745 + 1.57313i) q^{12} +(2.44949 + 4.24264i) q^{13} +(-1.05051 + 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} +(-1.94949 - 2.28024i) q^{18} -2.55051 q^{19} +(-0.724745 + 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.00000 - 1.41421i) q^{24} +(1.44949 - 2.51059i) q^{25} -4.89898 q^{26} +(5.00000 - 1.41421i) q^{27} +(3.44949 - 5.97469i) q^{29} +(-1.44949 - 2.04989i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.44949 - 0.317837i) q^{33} +(1.00000 - 1.73205i) q^{34} +(2.94949 - 0.548188i) q^{36} +11.7980 q^{37} +(1.27526 - 2.20881i) q^{38} +(3.55051 - 7.70674i) q^{39} +(-0.724745 - 1.25529i) q^{40} +(4.89898 + 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} +2.00000 q^{44} +(4.27526 - 0.794593i) q^{45} -1.00000 q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 - 0.158919i) q^{48} +(1.44949 + 2.51059i) q^{50} +(2.00000 + 2.82843i) q^{51} +(2.44949 - 4.24264i) q^{52} -10.8990 q^{53} +(-1.27526 + 5.03723i) q^{54} +2.89898 q^{55} +(2.55051 + 3.60697i) q^{57} +(3.44949 + 5.97469i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(2.50000 - 0.230351i) q^{60} +(3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.55051 - 6.14966i) q^{65} +(-1.44949 + 3.14626i) q^{66} +(6.44949 + 11.1708i) q^{67} +(1.00000 + 1.73205i) q^{68} +(0.724745 - 1.57313i) q^{69} +0.101021 q^{71} +(-1.00000 + 2.82843i) q^{72} +6.89898 q^{73} +(-5.89898 + 10.2173i) q^{74} +(-5.00000 + 0.460702i) q^{75} +(1.27526 + 2.20881i) q^{76} +(4.89898 + 6.92820i) q^{78} +(0.949490 - 1.64456i) q^{79} +1.44949 q^{80} +(-7.00000 - 5.65685i) q^{81} -9.79796 q^{82} +(1.00000 - 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} +(-3.44949 - 5.97469i) q^{86} +(-11.8990 + 1.09638i) q^{87} +(-1.00000 + 1.73205i) q^{88} +16.8990 q^{89} +(-1.44949 + 4.09978i) q^{90} +(0.500000 - 0.866025i) q^{92} +(4.34847 - 9.43879i) q^{93} +(4.89898 + 8.48528i) q^{94} +(1.84847 + 3.20164i) q^{95} +(-0.724745 + 1.57313i) q^{96} +(1.44949 - 2.51059i) q^{97} +(-3.89898 - 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 20 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} - 4 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} + 4 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 24 q^{39} + 2 q^{40} - 4 q^{43} + 8 q^{44} + 22 q^{45} - 4 q^{46} + 2 q^{48} - 4 q^{50} + 8 q^{51} - 24 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} - 4 q^{59} + 10 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} - 4 q^{72} + 8 q^{73} - 4 q^{74} - 20 q^{75} + 10 q^{76} - 6 q^{79} - 4 q^{80} - 28 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} - 28 q^{87} - 4 q^{88} + 48 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 + 2 * q^12 - 14 * q^15 - 2 * q^16 - 8 * q^17 + 2 * q^18 - 20 * q^19 + 2 * q^20 - 4 * q^22 + 2 * q^23 - 4 * q^24 - 4 * q^25 + 20 * q^27 + 4 * q^29 + 4 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 + 8 * q^37 + 10 * q^38 + 24 * q^39 + 2 * q^40 - 4 * q^43 + 8 * q^44 + 22 * q^45 - 4 * q^46 + 2 * q^48 - 4 * q^50 + 8 * q^51 - 24 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 + 4 * q^58 - 4 * q^59 + 10 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 + 4 * q^68 - 2 * q^69 + 20 * q^71 - 4 * q^72 + 8 * q^73 - 4 * q^74 - 20 * q^75 + 10 * q^76 - 6 * q^79 - 4 * q^80 - 28 * q^81 + 4 * q^83 - 4 * q^85 - 4 * q^86 - 28 * q^87 - 4 * q^88 + 48 * q^89 + 4 * q^90 + 2 * q^92 - 12 * q^93 - 22 * q^95 + 2 * q^96 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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