LMFDB - Embedded newform 539.2.e.d.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, 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("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	539.177
Dual form			539.2.e.d.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{12} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} -6.00000 q^{20} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(0.500000 - 0.866025i) q^{33} +4.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(2.00000 + 3.46410i) q^{39} +6.00000 q^{41} +8.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(3.00000 + 5.19615i) q^{45} +4.00000 q^{48} +(3.00000 - 5.19615i) q^{51} +(-4.00000 - 6.92820i) q^{52} +(3.00000 + 5.19615i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(4.50000 + 7.79423i) q^{59} +(3.00000 + 5.19615i) q^{60} +(5.00000 - 8.66025i) q^{61} -8.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-6.00000 + 10.3923i) q^{68} +3.00000 q^{69} +9.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(5.00000 - 8.66025i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -18.0000 q^{85} +(3.00000 + 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{89} -6.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(-3.00000 - 5.19615i) q^{95} -1.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q - q^3 + 2 * q^4 - 3 * q^5 + 2 * q^9	$ 2 q - q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{9} + q^{11} + 2 q^{12} - 8 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} - 12 q^{20} - 3 q^{23} - 4 q^{25} - 10 q^{27} - 12 q^{29} - 5 q^{31} + q^{33} + 8 q^{36} - 11 q^{37} + 4 q^{39} + 12 q^{41} + 16 q^{43} - 2 q^{44} + 6 q^{45} + 8 q^{48} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 6 q^{55} + 4 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} - 16 q^{64} + 12 q^{65} - 5 q^{67} - 12 q^{68} + 6 q^{69} + 18 q^{71} - 2 q^{73} - 4 q^{75} - 8 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} + 24 q^{83} - 36 q^{85} + 6 q^{87} + 3 q^{89} - 12 q^{92} - 5 q^{93} - 6 q^{95} - 2 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - q^3 + 2 * q^4 - 3 * q^5 + 2 * q^9 + q^11 + 2 * q^12 - 8 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^19 - 12 * q^20 - 3 * q^23 - 4 * q^25 - 10 * q^27 - 12 * q^29 - 5 * q^31 + q^33 + 8 * q^36 - 11 * q^37 + 4 * q^39 + 12 * q^41 + 16 * q^43 - 2 * q^44 + 6 * q^45 + 8 * q^48 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 6 * q^55 + 4 * q^57 + 9 * q^59 + 6 * q^60 + 10 * q^61 - 16 * q^64 + 12 * q^65 - 5 * q^67 - 12 * q^68 + 6 * q^69 + 18 * q^71 - 2 * q^73 - 4 * q^75 - 8 * q^76 + 10 * q^79 - 12 * q^80 - q^81 + 24 * q^83 - 36 * q^85 + 6 * q^87 + 3 * q^89 - 12 * q^92 - 5 * q^93 - 6 * q^95 - 2 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$2$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−6.00000			−1.34164
$21$		0			0
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	−5.00000			−0.962250
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$		0			0
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$		0			0
$35$		0			0
$36$	4.00000			0.666667
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.0821995	+	0.996616i	$0.526194\pi$
$37$	−5.50000	+	9.52628i	−0.904194	+	1.56611i	−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	3.00000	+	5.19615i	0.447214	+	0.774597i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	4.00000			0.577350
$49$		0			0
$50$		0			0
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−4.00000	−	6.92820i	−0.554700	−	0.960769i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$	3.00000	+	5.19615i	0.387298	+	0.670820i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		0			0
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−6.00000	+	10.3923i	−0.727607	+	1.26025i
$69$	3.00000			0.361158
$70$		0			0
$71$	9.00000			1.06810			0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000			1.06810			0.534052	+	0.845452i	$0.320669\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$		0			0
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	−4.00000			−0.458831
$77$		0			0
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	−6.00000	−	10.3923i	−0.670820	−	1.16190i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−18.0000			−1.95237
$86$		0			0
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$		0			0
$92$	−6.00000			−0.625543
$93$	−2.50000	+	4.33013i	−0.259238	+	0.449013i
$94$		0			0
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$	4.00000	−	6.92820i	0.400000	−	0.692820i
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	−5.00000	−	8.66025i	−0.481125	−	0.833333i
$109$	−10.0000	−	17.3205i	−0.957826	−	1.65900i	−0.727764	−	0.685828i	$-0.759440\pi$
$109$	−10.0000	−	17.3205i	−0.957826	−	1.65900i	−0.230063	−	0.973176i	$-0.573893\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$		0			0
$113$	−3.00000			−0.282216			−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000			−0.282216			−0.141108	+	0.989994i	$0.545067\pi$
$114$		0			0
$115$	−4.50000	−	7.79423i	−0.419627	−	0.726816i
$116$	−6.00000	−	10.3923i	−0.557086	−	0.964901i
$117$	−4.00000	+	6.92820i	−0.369800	+	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	5.00000	−	8.66025i	0.449013	−	0.777714i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$		0			0
$135$	7.50000	−	12.9904i	0.645497	−	1.11803i
$136$		0			0
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$	4.00000	+	6.92820i	0.333333	+	0.577350i
$145$	9.00000	−	15.5885i	0.747409	−	1.29455i
$146$		0			0
$147$		0			0
$148$	−22.0000			−1.80839
$149$	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	$0.0876260\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	15.0000			1.20483
$156$	−4.00000	+	6.92820i	−0.320256	+	0.554700i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$		0			0
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$		0			0
$167$	6.00000			0.464294			0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000			0.464294			0.232147	+	0.972681i	$0.425425\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	8.00000	+	13.8564i	0.609994	+	1.05654i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000			−0.301511
$177$	4.50000	−	7.79423i	0.338241	−	0.585850i
$178$		0			0
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$	−6.00000	+	10.3923i	−0.447214	+	0.774597i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	−16.5000	−	28.5788i	−1.21310	−	2.10116i
$186$		0			0
$187$	−3.00000	+	5.19615i	−0.219382	+	0.379980i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.5000	−	23.3827i	0.976826	−	1.69191i	0.303052	−	0.952974i	$-0.401994\pi$
$191$	13.5000	−	23.3827i	0.976826	−	1.69191i	0.673774	−	0.738938i	$-0.264672\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$		0			0
$195$	−12.0000			−0.859338
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$		0			0
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$		0			0
$203$		0			0
$204$	12.0000			0.840168
$205$	−9.00000	+	15.5885i	−0.628587	+	1.08875i
$206$		0			0
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	8.00000	−	13.8564i	0.554700	−	0.960769i
$209$	−2.00000			−0.138343
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−6.00000	+	10.3923i	−0.412082	+	0.713746i
$213$	−4.50000	−	7.79423i	−0.308335	−	0.534052i
$214$		0			0
$215$	−12.0000	+	20.7846i	−0.818393	+	1.41750i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$	−3.00000	−	5.19615i	−0.202260	−	0.350325i
$221$	−12.0000	−	20.7846i	−0.807207	−	1.39812i
$222$		0			0
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$		0			0
$225$	−8.00000			−0.533333
$226$		0			0
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$	2.00000	+	3.46410i	0.132453	+	0.229416i
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	−0.936728	−	0.350058i	$-0.886162\pi$
$229$	−2.50000	+	4.33013i	−0.165205	+	0.286143i	0.771523	+	0.636201i	$0.219495\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$		0			0
$236$	−9.00000	+	15.5885i	−0.585850	+	1.01472i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−6.00000	+	10.3923i	−0.387298	+	0.670820i
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.825131	+	0.564942i	$0.191101\pi$
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.0766885	+	0.997055i	$0.475565\pi$
$242$		0			0
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	20.0000			1.28037
$245$		0			0
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$		0			0
$255$	9.00000	+	15.5885i	0.563602	+	0.976187i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$		0			0
$259$		0			0
$260$	24.0000			1.48842
$261$	−6.00000	+	10.3923i	−0.371391	+	0.643268i
$262$		0			0
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.791658	+	0.610964i	$0.209218\pi$
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.133281	+	0.991078i	$0.457449\pi$
$264$		0			0
$265$	−18.0000			−1.10573
$266$		0			0
$267$	−3.00000			−0.183597
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.807535	−	0.589819i	$-0.799199\pi$
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.107031	−	0.994256i	$-0.534134\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−24.0000			−1.45521
$273$		0			0
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$		0			0
$279$	−10.0000			−0.598684
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$		0			0
$283$	−16.0000	−	27.7128i	−0.951101	−	1.64736i	−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−16.0000	−	27.7128i	−0.951101	−	1.64736i	−0.208053	−	0.978117i	$-0.566713\pi$
$284$	9.00000	+	15.5885i	0.534052	+	0.925005i
$285$	−3.00000	+	5.19615i	−0.177705	+	0.307794i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	0.500000	+	0.866025i	0.0293105	+	0.0507673i
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	−30.0000			−1.75262			−0.876309	−	0.481749i	$-0.840002\pi$
$293$	−30.0000			−1.75262			−0.876309	+	0.481749i	$0.840002\pi$
$294$		0			0
$295$	−27.0000			−1.57200
$296$		0			0
$297$	−2.50000	−	4.33013i	−0.145065	−	0.251259i
$298$		0			0
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$	−8.00000			−0.461880
$301$		0			0
$302$		0			0
$303$	6.00000	−	10.3923i	0.344691	−	0.597022i
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$	15.0000	+	25.9808i	0.858898	+	1.48765i
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−4.00000			−0.227552
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$		0			0
$315$		0			0
$316$	20.0000			1.12509
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	−0.964281	−	0.264883i	$-0.914667\pi$
$317$	−4.50000	+	7.79423i	−0.252745	+	0.437767i	0.711535	+	0.702650i	$0.248000\pi$
$318$		0			0
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	12.0000	−	20.7846i	0.670820	−	1.16190i
$321$	6.00000			0.334887
$322$		0			0
$323$	−12.0000			−0.667698
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$		0			0
$327$	−10.0000	+	17.3205i	−0.553001	+	0.957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	0.500000	−	0.866025i	0.0274825	−	0.0476011i	0.879440	+	0.476011i	$0.157918\pi$
$332$	12.0000	+	20.7846i	0.658586	+	1.14070i
$333$	11.0000	+	19.0526i	0.602796	+	1.04407i
$334$		0			0
$335$	15.0000			0.819538
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$	−18.0000	−	31.1769i	−0.976187	−	1.69081i
$341$	2.50000	−	4.33013i	0.135383	−	0.234490i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−4.50000	+	7.79423i	−0.242272	+	0.419627i
$346$		0			0
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$		0			0
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$	−13.5000	+	23.3827i	−0.716506	+	1.24102i
$356$	6.00000			0.317999
$357$		0			0
$358$		0			0
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	6.00000			0.314054
$366$		0			0
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	−6.00000	−	10.3923i	−0.312772	−	0.541736i
$369$	6.00000	−	10.3923i	0.312348	−	0.541002i
$370$		0			0
$371$		0			0
$372$	−10.0000			−0.518476
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$		0			0
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$		0			0
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	0.462563	+	0.886586i	$0.346930\pi$
$383$	−10.5000	+	18.1865i	−0.536525	+	0.929288i	−0.999088	+	0.0427020i	$0.986403\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	−0.892735	−	0.450582i	$-0.851216\pi$
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	0.0561516	−	0.998422i	$-0.482117\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$	−6.00000			−0.302660
$394$		0			0
$395$	15.0000	+	25.9808i	0.754732	+	1.30723i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$	10.0000	+	17.3205i	0.498135	+	0.862796i
$404$	−12.0000	+	20.7846i	−0.597022	+	1.03407i
$405$	3.00000			0.149071
$406$		0			0
$407$	−11.0000			−0.545250
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$	1.50000	−	2.59808i	0.0739895	−	0.128154i
$412$	8.00000			0.394132
$413$		0			0
$414$		0			0
$415$	−18.0000	+	31.1769i	−0.883585	+	1.53041i
$416$		0			0
$417$	−7.00000	−	12.1244i	−0.342791	−	0.593732i
$418$		0			0
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.580042
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	10.0000	−	17.3205i	0.481125	−	0.833333i
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$		0			0
$435$	−18.0000			−0.863034
$436$	20.0000	−	34.6410i	0.957826	−	1.65900i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$		0			0
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	0.368945	+	0.929451i	$0.379719\pi$
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	−0.989401	+	0.145210i	$0.953614\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	−0.952901	−	0.303281i	$-0.901918\pi$
$443$	−4.50000	+	7.79423i	−0.213801	+	0.370315i	0.739100	+	0.673596i	$0.235251\pi$
$444$	11.0000	+	19.0526i	0.522037	+	0.904194i
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$		0			0
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	5.00000	−	8.66025i	0.234920	−	0.406894i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−4.00000	+	6.92820i	−0.187112	+	0.324088i	0.757174	+	0.653213i	$0.226579\pi$
$458$		0			0
$459$	−15.0000	−	25.9808i	−0.700140	−	1.21268i
$460$	9.00000	−	15.5885i	0.419627	−	0.726816i
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		0			0
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	12.0000	−	20.7846i	0.557086	−	0.964901i
$465$	−7.50000	−	12.9904i	−0.347804	−	0.602414i
$466$		0			0
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	−0.985726	−	0.168360i	$-0.946153\pi$
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	0.638667	+	0.769483i	$0.279486\pi$
$468$	−16.0000			−0.739600
$469$		0			0
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$		0			0
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$		0			0
$475$	8.00000			0.367065
$476$		0			0
$477$	12.0000			0.549442
$478$		0			0
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	22.0000	−	38.1051i	1.00311	−	1.73744i
$482$		0			0
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$		0			0
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	0.714083	−	0.700061i	$-0.246844\pi$
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	−0.963312	+	0.268384i	$0.913510\pi$
$488$		0			0
$489$	20.0000			0.904431
$490$		0			0
$491$	−30.0000			−1.35388			−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000			−1.35388			−0.676941	+	0.736038i	$0.736695\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$	20.0000			0.898027
$497$		0			0
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−3.00000	−	5.19615i	−0.134164	−	0.232379i
$501$	−3.00000	−	5.19615i	−0.134030	−	0.232147i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−36.0000			−1.60198
$506$		0			0
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	−0.999220	−	0.0394971i	$-0.987424\pi$
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	0.533815	+	0.845601i	$0.320758\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$		0			0
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$	8.00000	−	13.8564i	0.352180	−	0.609994i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$		0			0
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$	−24.0000			−1.03956
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$		0			0
$537$	7.50000	−	12.9904i	0.323649	−	0.560576i
$538$		0			0
$539$		0			0
$540$	30.0000			1.29099
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	−0.641215	−	0.767361i	$-0.721569\pi$
$541$	8.00000	−	13.8564i	0.343947	−	0.595733i	0.985162	+	0.171628i	$0.0549027\pi$
$542$		0			0
$543$	3.50000	+	6.06218i	0.150199	+	0.260153i
$544$		0			0
$545$	60.0000			2.57012
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	−10.0000	−	17.3205i	−0.426790	−	0.739221i
$550$		0			0
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−16.5000	+	28.5788i	−0.700386	+	1.21310i
$556$	14.0000	+	24.2487i	0.593732	+	1.02837i
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	−0.986394	−	0.164399i	$-0.947432\pi$
$557$	−15.0000	−	25.9808i	−0.635570	−	1.10084i	0.350824	−	0.936442i	$-0.385902\pi$
$558$		0			0
$559$	−32.0000			−1.35346
$560$		0			0
$561$	6.00000			0.253320
$562$		0			0
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$		0			0
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$	−27.0000			−1.12794
$574$		0			0
$575$	12.0000			0.500435
$576$	−8.00000	+	13.8564i	−0.333333	+	0.577350i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$		0			0
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$	36.0000			1.49482
$581$		0			0
$582$		0			0
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$		0			0
$585$	−12.0000	−	20.7846i	−0.496139	−	0.859338i
$586$		0			0
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	10.0000			0.412043
$590$		0			0
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$	−22.0000	−	38.1051i	−0.904194	−	1.56611i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$		0			0
$596$	12.0000			0.491539
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$	−10.0000			−0.407231
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	−1.50000	−	2.59808i	−0.0609837	−	0.105627i
$606$		0			0
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	12.0000	+	20.7846i	0.485071	+	0.840168i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$		0			0
$615$	18.0000			0.725830
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$		0			0
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419582\pi$
$619$	9.50000	+	16.4545i	0.381837	+	0.661361i	−0.609488	+	0.792796i	$0.708625\pi$
$620$	15.0000	+	25.9808i	0.602414	+	1.04341i
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$		0			0
$623$		0			0
$624$	−16.0000			−0.640513
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$	1.00000	+	1.73205i	0.0399362	+	0.0691714i
$628$	−13.0000	+	22.5167i	−0.518756	+	0.898513i
$629$	−66.0000			−2.63159
$630$		0			0
$631$	11.0000			0.437903			0.218952	−	0.975736i	$-0.429736\pi$
$631$	11.0000			0.437903			0.218952	+	0.975736i	$0.429736\pi$
$632$		0			0
$633$	−7.00000	−	12.1244i	−0.278225	−	0.481900i
$634$		0			0
$635$	−3.00000	+	5.19615i	−0.119051	+	0.206203i
$636$	12.0000			0.475831
$637$		0			0
$638$		0			0
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$		0			0
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	0.679039	−	0.734103i	$-0.262397\pi$
$641$	−7.50000	−	12.9904i	−0.296232	−	0.513089i	−0.975271	+	0.221013i	$0.929064\pi$
$642$		0			0
$643$	−49.0000			−1.93237			−0.966186	−	0.257847i	$-0.916987\pi$
$643$	−49.0000			−1.93237			−0.966186	+	0.257847i	$0.916987\pi$
$644$		0			0
$645$	24.0000			0.944999
$646$		0			0
$647$	16.5000	+	28.5788i	0.648682	+	1.12355i	0.983438	+	0.181245i	$0.0580128\pi$
$647$	16.5000	+	28.5788i	0.648682	+	1.12355i	−0.334756	+	0.942305i	$0.608654\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$		0			0
$651$		0			0
$652$	−40.0000			−1.56652
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	0.178154	+	0.984003i	$0.442987\pi$
$653$	−19.5000	+	33.7750i	−0.763094	+	1.32172i	−0.941248	+	0.337715i	$0.890346\pi$
$654$		0			0
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	−4.00000			−0.156055
$658$		0			0
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$	−3.00000	+	5.19615i	−0.116775	+	0.202260i
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.739014	+	0.673690i	$0.235292\pi$
$661$	24.5000	+	42.4352i	0.952940	+	1.65054i	0.213925	+	0.976850i	$0.431375\pi$
$662$		0			0
$663$	−12.0000	+	20.7846i	−0.466041	+	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$	9.50000	+	16.4545i	0.367291	+	0.636167i
$670$		0			0
$671$	10.0000			0.386046
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$		0			0
$675$	10.0000	+	17.3205i	0.384900	+	0.666667i
$676$	3.00000	+	5.19615i	0.115385	+	0.199852i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	−4.00000	+	6.92820i	−0.152944	+	0.264906i
$685$	−9.00000			−0.343872
$686$		0			0
$687$	5.00000			0.190762
$688$	−16.0000	+	27.7128i	−0.609994	+	1.05654i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$		0			0
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	0.313355	+	0.949636i	$0.398547\pi$
$691$	−17.5000	+	30.3109i	−0.665731	+	1.15308i	−0.979086	+	0.203445i	$0.934786\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−21.0000	+	36.3731i	−0.796575	+	1.37971i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$	6.00000			0.226941
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−11.0000	−	19.0526i	−0.414873	−	0.718581i
$704$	−4.00000	−	6.92820i	−0.150756	−	0.261116i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	18.0000			0.676481
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	−0.856484	−	0.516174i	$-0.827356\pi$
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	0.875262	+	0.483650i	$0.160689\pi$
$710$		0			0
$711$	−10.0000	−	17.3205i	−0.375029	−	0.649570i
$712$		0			0
$713$	15.0000			0.561754
$714$		0			0
$715$	12.0000			0.448775
$716$	−15.0000	+	25.9808i	−0.560576	+	0.970947i
$717$	6.00000	+	10.3923i	0.224074	+	0.388108i
$718$		0			0
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	−0.230823	−	0.972996i	$-0.574142\pi$
$719$	19.5000	−	33.7750i	0.727227	−	1.25959i	0.958051	−	0.286599i	$-0.0925247\pi$
$720$	−24.0000			−0.894427
$721$		0			0
$722$		0			0
$723$	14.0000	−	24.2487i	0.520666	−	0.901819i
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$		0			0
$727$	17.0000			0.630495			0.315248	−	0.949009i	$-0.397912\pi$
$727$	17.0000			0.630495			0.315248	+	0.949009i	$0.397912\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	−10.0000	−	17.3205i	−0.369611	−	0.640184i
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	−0.826723	−	0.562609i	$-0.809798\pi$
$733$	2.00000	−	3.46410i	0.0738717	−	0.127950i	0.900595	+	0.434659i	$0.143131\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.50000	−	4.33013i	0.0920887	−	0.159502i
$738$		0			0
$739$	17.0000	+	29.4449i	0.625355	+	1.08315i	0.988472	+	0.151403i	$0.0483792\pi$
$739$	17.0000	+	29.4449i	0.625355	+	1.08315i	−0.363117	+	0.931744i	$0.618287\pi$
$740$	33.0000	−	57.1577i	1.21310	−	2.10116i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$		0			0
$747$	12.0000	−	20.7846i	0.439057	−	0.760469i
$748$	−12.0000			−0.438763
$749$		0			0
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$	4.50000	+	7.79423i	0.163989	+	0.284037i
$754$		0			0
$755$	−30.0000			−1.09181
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$		0			0
$759$	1.50000	+	2.59808i	0.0544466	+	0.0943042i
$760$		0			0
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.00800331	+	0.999968i	$0.502548\pi$
$761$	−24.0000	+	41.5692i	−0.869999	+	1.50688i	−0.861996	+	0.506915i	$0.830786\pi$
$762$		0			0
$763$		0			0
$764$	54.0000			1.95365
$765$	−18.0000	+	31.1769i	−0.650791	+	1.12720i
$766$		0			0
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$	−8.00000	+	13.8564i	−0.288675	+	0.500000i
$769$	−40.0000			−1.44244			−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000			−1.44244			−0.721218	+	0.692708i	$0.756418\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	14.0000	−	24.2487i	0.503871	−	0.872730i
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$		0			0
$775$	−10.0000	+	17.3205i	−0.359211	+	0.622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	−12.0000	−	20.7846i	−0.429669	−	0.744208i
$781$	4.50000	+	7.79423i	0.161023	+	0.278899i
$782$		0			0
$783$	30.0000			1.07211
$784$		0			0
$785$	−39.0000			−1.39197
$786$		0			0
$787$	−25.0000	−	43.3013i	−0.891154	−	1.54352i	−0.838494	−	0.544911i	$-0.816563\pi$
$787$	−25.0000	−	43.3013i	−0.891154	−	1.54352i	−0.0526599	−	0.998613i	$-0.516770\pi$
$788$	18.0000	+	31.1769i	0.641223	+	1.11063i
$789$	15.0000	−	25.9808i	0.534014	−	0.924940i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−20.0000	+	34.6410i	−0.710221	+	1.23014i
$794$		0			0
$795$	9.00000	+	15.5885i	0.319197	+	0.552866i
$796$	−16.0000	+	27.7128i	−0.567105	+	0.982255i
$797$	−21.0000			−0.743858			−0.371929	−	0.928261i	$-0.621304\pi$
$797$	−21.0000			−0.743858			−0.371929	+	0.928261i	$0.621304\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$	−10.0000			−0.352673
$805$		0			0
$806$		0			0
$807$	−15.0000	+	25.9808i	−0.528025	+	0.914566i
$808$		0			0
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	−30.0000	−	51.9615i	−1.05085	−	1.82013i
$816$	12.0000	+	20.7846i	0.420084	+	0.727607i
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$		0			0
$819$		0			0
$820$	−36.0000			−1.25717
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$		0			0
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	0.592966	−	0.805228i	$-0.297957\pi$
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	−0.993831	+	0.110910i	$0.964624\pi$
$824$		0			0
$825$	−4.00000			−0.139262
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	−4.00000	+	6.92820i	−0.138758	+	0.240337i
$832$	32.0000			1.10940
$833$		0			0
$834$		0			0
$835$	−9.00000	+	15.5885i	−0.311458	+	0.539461i
$836$	−2.00000	−	3.46410i	−0.0691714	−	0.119808i
$837$	12.5000	+	21.6506i	0.432063	+	0.748355i
$838$		0			0
$839$	−15.0000			−0.517858			−0.258929	−	0.965896i	$-0.583369\pi$
$839$	−15.0000			−0.517858			−0.258929	+	0.965896i	$0.583369\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−6.00000	−	10.3923i	−0.206651	−	0.357930i
$844$	14.0000	+	24.2487i	0.481900	+	0.834675i
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$	−24.0000			−0.824163
$849$	−16.0000	+	27.7128i	−0.549119	+	0.951101i
$850$		0			0
$851$	−16.5000	−	28.5788i	−0.565613	−	0.979670i
$852$	9.00000	−	15.5885i	0.308335	−	0.534052i
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		0			0
$855$	−12.0000			−0.410391
$856$		0			0
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	0.950119	−	0.311888i	$-0.100962\pi$
$857$	6.00000	+	10.3923i	0.204956	+	0.354994i	−0.745163	+	0.666883i	$0.767628\pi$
$858$		0			0
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	−0.733571	−	0.679613i	$-0.762148\pi$
$859$	6.50000	−	11.2583i	0.221777	−	0.384129i	0.955348	+	0.295484i	$0.0954809\pi$
$860$	−48.0000			−1.63679
$861$		0			0
$862$		0			0
$863$	6.00000	−	10.3923i	0.204242	−	0.353758i	−0.745649	−	0.666339i	$-0.767860\pi$
$863$	6.00000	−	10.3923i	0.204242	−	0.353758i	0.949891	+	0.312581i	$0.101194\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	19.0000			0.645274
$868$		0			0
$869$	10.0000			0.339227
$870$		0			0
$871$	10.0000	+	17.3205i	0.338837	+	0.586883i
$872$		0			0
$873$	−1.00000	+	1.73205i	−0.0338449	+	0.0586210i
$874$		0			0
$875$		0			0
$876$	−4.00000			−0.135147
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$		0			0
$879$	15.0000	+	25.9808i	0.505937	+	0.876309i
$880$	6.00000	−	10.3923i	0.202260	−	0.350325i
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	24.0000	−	41.5692i	0.807207	−	1.39812i
$885$	13.5000	+	23.3827i	0.453798	+	0.786000i
$886$		0			0
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	−0.261540	−	0.965193i	$-0.584230\pi$
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	0.966651	−	0.256096i	$-0.0824362\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−19.0000	−	32.9090i	−0.636167	−	1.10187i
$893$		0			0
$894$		0			0
$895$	−45.0000			−1.50418
$896$		0			0
$897$	−12.0000			−0.400668
$898$		0			0
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$	−8.00000	−	13.8564i	−0.266667	−	0.461880i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.5000	−	18.1865i	0.349032	−	0.604541i
$906$		0			0
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	0.791944	−	0.610594i	$-0.209069\pi$
$907$	−4.00000	−	6.92820i	−0.132818	−	0.230047i	−0.924762	+	0.380547i	$0.875736\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	24.0000			0.796030
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	−4.00000	+	6.92820i	−0.132453	+	0.229416i
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$		0			0
$915$	15.0000	−	25.9808i	0.495885	−	0.858898i
$916$	−10.0000			−0.330409
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$		0			0
$923$	−36.0000			−1.18495
$924$		0			0
$925$	44.0000			1.44671
$926$		0			0
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		0			0
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$		0			0
$931$		0			0
$932$	−12.0000			−0.393073
$933$		0			0
$934$		0			0
$935$	−9.00000	−	15.5885i	−0.294331	−	0.509797i
$936$		0			0
$937$	20.0000			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$938$		0			0
$939$	−19.0000			−0.620042
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$	−36.0000			−1.17170
$945$		0			0
$946$		0			0
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	−0.558898	−	0.829237i	$-0.688776\pi$
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	0.997589	+	0.0694014i	$0.0221089\pi$
$948$	−10.0000	−	17.3205i	−0.324785	−	0.562544i
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$		0			0
$951$	9.00000			0.291845
$952$		0			0
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	40.5000	+	70.1481i	1.31055	+	2.26994i
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$	−3.00000	+	5.19615i	−0.0969762	+	0.167968i
$958$		0			0
$959$		0			0
$960$	−24.0000			−0.774597
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−28.0000	+	48.4974i	−0.901819	+	1.56200i
$965$	42.0000			1.35203
$966$		0			0
$967$	14.0000			0.450210			0.225105	−	0.974335i	$-0.427728\pi$
$967$	14.0000			0.450210			0.225105	+	0.974335i	$0.427728\pi$
$968$		0			0
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	−0.362604	−	0.931943i	$-0.618112\pi$
$971$	19.5000	−	33.7750i	0.625785	−	1.08389i	0.988389	−	0.151948i	$-0.0485545\pi$
$972$	−32.0000			−1.02640
$973$		0			0
$974$		0			0
$975$	8.00000	−	13.8564i	0.256205	−	0.443760i
$976$	20.0000	+	34.6410i	0.640184	+	1.10883i
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	0.785020	−	0.619471i	$-0.212653\pi$
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	−0.928987	+	0.370111i	$0.879319\pi$
$978$		0			0
$979$	3.00000			0.0958804
$980$		0			0
$981$	−40.0000			−1.27710
$982$		0			0
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	−0.999532	−	0.0306024i	$-0.990257\pi$
$983$	−16.5000	−	28.5788i	−0.526268	−	0.911523i	0.473263	−	0.880921i	$-0.343076\pi$
$984$		0			0
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$		0			0
$987$		0			0
$988$	16.0000			0.509028
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$		0			0
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	0.964658	−	0.263504i	$-0.0848781\pi$
$991$	8.00000	+	13.8564i	0.254128	+	0.440163i	−0.710530	+	0.703667i	$0.751545\pi$
$992$		0			0
$993$	−1.00000			−0.0317340
$994$		0			0
$995$	−48.0000			−1.52170
$996$	12.0000	−	20.7846i	0.380235	−	0.658586i
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$		0			0
$999$	27.5000	−	47.6314i	0.870061	−	1.50699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.e.d.177.1		2
7.2	even	3		77.2.a.b.1.1	✓	1
7.3	odd	6		539.2.e.e.67.1		2
7.4	even	3	inner	539.2.e.d.67.1		2
7.5	odd	6		539.2.a.b.1.1		1
7.6	odd	2		539.2.e.e.177.1		2
21.2	odd	6		693.2.a.b.1.1		1
21.5	even	6		4851.2.a.k.1.1		1
28.19	even	6		8624.2.a.s.1.1		1
28.23	odd	6		1232.2.a.d.1.1		1
35.2	odd	12		1925.2.b.g.1849.1		2
35.9	even	6		1925.2.a.f.1.1		1
35.23	odd	12		1925.2.b.g.1849.2		2
56.37	even	6		4928.2.a.i.1.1		1
56.51	odd	6		4928.2.a.x.1.1		1
77.2	odd	30		847.2.f.g.323.1		4
77.9	even	15		847.2.f.f.323.1		4
77.16	even	15		847.2.f.f.729.1		4
77.30	odd	30		847.2.f.g.372.1		4
77.37	even	15		847.2.f.f.148.1		4
77.51	odd	30		847.2.f.g.148.1		4
77.54	even	6		5929.2.a.d.1.1		1
77.58	even	15		847.2.f.f.372.1		4
77.65	odd	6		847.2.a.c.1.1		1
77.72	odd	30		847.2.f.g.729.1		4
231.65	even	6		7623.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.b.1.1	✓	1	7.2	even	3
539.2.a.b.1.1		1	7.5	odd	6
539.2.e.d.67.1		2	7.4	even	3	inner
539.2.e.d.177.1		2	1.1	even	1	trivial
539.2.e.e.67.1		2	7.3	odd	6
539.2.e.e.177.1		2	7.6	odd	2
693.2.a.b.1.1		1	21.2	odd	6
847.2.a.c.1.1		1	77.65	odd	6
847.2.f.f.148.1		4	77.37	even	15
847.2.f.f.323.1		4	77.9	even	15
847.2.f.f.372.1		4	77.58	even	15
847.2.f.f.729.1		4	77.16	even	15
847.2.f.g.148.1		4	77.51	odd	30
847.2.f.g.323.1		4	77.2	odd	30
847.2.f.g.372.1		4	77.30	odd	30
847.2.f.g.729.1		4	77.72	odd	30
1232.2.a.d.1.1		1	28.23	odd	6
1925.2.a.f.1.1		1	35.9	even	6
1925.2.b.g.1849.1		2	35.2	odd	12
1925.2.b.g.1849.2		2	35.23	odd	12
4851.2.a.k.1.1		1	21.5	even	6
4928.2.a.i.1.1		1	56.37	even	6
4928.2.a.x.1.1		1	56.51	odd	6
5929.2.a.d.1.1		1	77.54	even	6
7623.2.a.i.1.1		1	231.65	even	6
8624.2.a.s.1.1		1	28.19	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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(1.00000 - 1.73205i) q^{12} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 + 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{19} -6.00000 q^{20} +(-1.50000 + 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(0.500000 - 0.866025i) q^{33} +4.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(2.00000 + 3.46410i) q^{39} +6.00000 q^{41} +8.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(3.00000 + 5.19615i) q^{45} +4.00000 q^{48} +(3.00000 - 5.19615i) q^{51} +(-4.00000 - 6.92820i) q^{52} +(3.00000 + 5.19615i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(4.50000 + 7.79423i) q^{59} +(3.00000 + 5.19615i) q^{60} +(5.00000 - 8.66025i) q^{61} -8.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-6.00000 + 10.3923i) q^{68} +3.00000 q^{69} +9.00000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-2.00000 + 3.46410i) q^{75} -4.00000 q^{76} +(5.00000 - 8.66025i) q^{79} +(-6.00000 - 10.3923i) q^{80} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -18.0000 q^{85} +(3.00000 + 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{89} -6.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(-3.00000 - 5.19615i) q^{95} -1.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q - q^3 + 2 * q^4 - 3 * q^5 + 2 * q^9	\( 2 q - q^{3} + 2 q^{4} - 3 q^{5} + 2 q^{9} + q^{11} + 2 q^{12} - 8 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} - 12 q^{20} - 3 q^{23} - 4 q^{25} - 10 q^{27} - 12 q^{29} - 5 q^{31} + q^{33} + 8 q^{36} - 11 q^{37} + 4 q^{39} + 12 q^{41} + 16 q^{43} - 2 q^{44} + 6 q^{45} + 8 q^{48} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 6 q^{55} + 4 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} - 16 q^{64} + 12 q^{65} - 5 q^{67} - 12 q^{68} + 6 q^{69} + 18 q^{71} - 2 q^{73} - 4 q^{75} - 8 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} + 24 q^{83} - 36 q^{85} + 6 q^{87} + 3 q^{89} - 12 q^{92} - 5 q^{93} - 6 q^{95} - 2 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - q^3 + 2 * q^4 - 3 * q^5 + 2 * q^9 + q^11 + 2 * q^12 - 8 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 2 * q^19 - 12 * q^20 - 3 * q^23 - 4 * q^25 - 10 * q^27 - 12 * q^29 - 5 * q^31 + q^33 + 8 * q^36 - 11 * q^37 + 4 * q^39 + 12 * q^41 + 16 * q^43 - 2 * q^44 + 6 * q^45 + 8 * q^48 + 6 * q^51 - 8 * q^52 + 6 * q^53 - 6 * q^55 + 4 * q^57 + 9 * q^59 + 6 * q^60 + 10 * q^61 - 16 * q^64 + 12 * q^65 - 5 * q^67 - 12 * q^68 + 6 * q^69 + 18 * q^71 - 2 * q^73 - 4 * q^75 - 8 * q^76 + 10 * q^79 - 12 * q^80 - q^81 + 24 * q^83 - 36 * q^85 + 6 * q^87 + 3 * q^89 - 12 * q^92 - 5 * q^93 - 6 * q^95 - 2 * q^97 + 4 * q^99

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