LMFDB - Embedded newform 729.2.c.b.244.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.5
Root			$0.500000 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.b.487.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.527162 + 0.913072i) q^{2} +(0.444200 - 0.769376i) q^{4} +(-0.872894 + 1.51190i) q^{5} +(-1.22962 - 2.12977i) q^{7} +3.04531 q^{8} +O(q^{10})$	\(q+(0.527162 + 0.913072i) q^{2} +(0.444200 - 0.769376i) q^{4} +(-0.872894 + 1.51190i) q^{5} +(-1.22962 - 2.12977i) q^{7} +3.04531 q^{8} -1.84063 q^{10} +(-0.627106 - 1.08618i) q^{11} +(2.27451 - 3.93958i) q^{13} +(1.29642 - 2.24547i) q^{14} +(0.716974 + 1.24184i) q^{16} +6.64717 q^{17} +0.249156 q^{19} +(0.775478 + 1.34317i) q^{20} +(0.661174 - 1.14519i) q^{22} +(0.421000 - 0.729194i) q^{23} +(0.976114 + 1.69068i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(-0.256192 - 0.443737i) q^{29} +(0.410002 - 0.710144i) q^{31} +(2.28939 - 3.96533i) q^{32} +(3.50414 + 6.06935i) q^{34} +4.29332 q^{35} +2.60806 q^{37} +(0.131346 + 0.227498i) q^{38} +(-2.65823 + 4.60419i) q^{40} +(-4.07641 + 7.06054i) q^{41} +(-2.16357 - 3.74742i) q^{43} -1.11424 q^{44} +0.887743 q^{46} +(-2.65117 - 4.59196i) q^{47} +(0.476053 - 0.824548i) q^{49} +(-1.02914 + 1.78252i) q^{50} +(-2.02068 - 3.49992i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(-3.74459 - 6.48581i) q^{56} +(0.270109 - 0.467843i) q^{58} +(-1.50310 + 2.60345i) q^{59} +(-1.44159 - 2.49690i) q^{61} +0.864550 q^{62} +7.69541 q^{64} +(3.97082 + 6.87766i) q^{65} +(-5.04313 + 8.73496i) q^{67} +(2.95267 - 5.11417i) q^{68} +(2.26328 + 3.92011i) q^{70} -0.0894756 q^{71} -5.32114 q^{73} +(1.37487 + 2.38135i) q^{74} +(0.110675 - 0.191695i) q^{76} +(-1.54221 + 2.67119i) q^{77} +(-2.38846 - 4.13693i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(4.02033 + 6.96342i) q^{83} +(-5.80227 + 10.0498i) q^{85} +(2.28111 - 3.95099i) q^{86} +(-1.90973 - 3.30776i) q^{88} -6.70377 q^{89} -11.1872 q^{91} +(-0.374016 - 0.647816i) q^{92} +(2.79519 - 4.84141i) q^{94} +(-0.217487 + 0.376698i) q^{95} +(-2.74529 - 4.75498i) q^{97} +1.00383 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8 + 6 * q^10 - 12 * q^11 - 6 * q^14 + 3 * q^16 + 18 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 15 * q^23 + 6 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^29 + 24 * q^35 + 6 * q^37 + 3 * q^38 - 6 * q^40 - 15 * q^41 + 6 * q^44 + 6 * q^46 - 21 * q^47 + 12 * q^49 - 3 * q^50 - 12 * q^52 + 18 * q^53 - 12 * q^55 + 6 * q^56 + 12 * q^58 - 24 * q^59 + 9 * q^61 - 24 * q^62 - 24 * q^64 + 6 * q^65 + 9 * q^67 + 9 * q^68 - 15 * q^70 + 54 * q^71 - 12 * q^73 + 12 * q^74 - 6 * q^76 + 12 * q^77 - 42 * q^80 - 12 * q^82 - 12 * q^83 + 21 * q^86 - 12 * q^88 + 18 * q^89 - 12 * q^91 - 6 * q^92 - 6 * q^94 - 12 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.527162	+	0.913072i	0.372760	+	0.645639i	0.989989	−	0.141144i	$-0.0450781\pi$
$2$	0.527162	+	0.913072i	0.372760	+	0.645639i	−0.617229	+	0.786784i	$0.711745\pi$
$3$		0			0
$3$		0			0
$4$	0.444200	−	0.769376i	0.222100	−	0.384688i
$5$	−0.872894	+	1.51190i	−0.390370	+	0.676140i	−0.992498	−	0.122259i	$-0.960986\pi$
$5$	−0.872894	+	1.51190i	−0.390370	+	0.676140i	0.602128	+	0.798399i	$0.294320\pi$
$6$		0			0
$7$	−1.22962	−	2.12977i	−0.464754	−	0.804977i	0.534436	−	0.845209i	$-0.320524\pi$
$7$	−1.22962	−	2.12977i	−0.464754	−	0.804977i	−0.999190	+	0.0402312i	$0.987191\pi$
$8$	3.04531			1.07668
$9$		0			0
$10$	−1.84063			−0.582057
$11$	−0.627106	−	1.08618i	−0.189080	−	0.327496i	0.755864	−	0.654729i	$-0.227217\pi$
$11$	−0.627106	−	1.08618i	−0.189080	−	0.327496i	−0.944944	+	0.327233i	$0.893884\pi$
$12$		0			0
$13$	2.27451	−	3.93958i	0.630837	−	1.09264i	−0.356544	−	0.934279i	$-0.616045\pi$
$13$	2.27451	−	3.93958i	0.630837	−	1.09264i	0.987381	−	0.158363i	$-0.0506216\pi$
$14$	1.29642	−	2.24547i	0.346483	−	0.600127i
$15$		0			0
$16$	0.716974	+	1.24184i	0.179244	+	0.310459i
$17$	6.64717			1.61218			0.806088	−	0.591796i	$-0.201581\pi$
$17$	6.64717			1.61218			0.806088	+	0.591796i	$0.201581\pi$
$18$		0			0
$19$	0.249156			0.0571604			0.0285802	−	0.999592i	$-0.490901\pi$
$19$	0.249156			0.0571604			0.0285802	+	0.999592i	$0.490901\pi$
$20$	0.775478	+	1.34317i	0.173402	+	0.300341i
$21$		0			0
$22$	0.661174	−	1.14519i	0.140963	−	0.244155i
$23$	0.421000	−	0.729194i	0.0877847	−	0.152048i	−0.818790	−	0.574093i	$-0.805355\pi$
$23$	0.421000	−	0.729194i	0.0877847	−	0.152048i	0.906574	+	0.422046i	$0.138688\pi$
$24$		0			0
$25$	0.976114	+	1.69068i	0.195223	+	0.338136i
$26$	4.79615			0.940603
$27$		0			0
$28$	−2.18479			−0.412887
$29$	−0.256192	−	0.443737i	−0.0475736	−	0.0823998i	0.841258	−	0.540634i	$-0.181816\pi$
$29$	−0.256192	−	0.443737i	−0.0475736	−	0.0823998i	−0.888832	+	0.458234i	$0.848482\pi$
$30$		0			0
$31$	0.410002	−	0.710144i	0.0736385	−	0.127546i	−0.826855	−	0.562415i	$-0.809872\pi$
$31$	0.410002	−	0.710144i	0.0736385	−	0.127546i	0.900493	+	0.434870i	$0.143206\pi$
$32$	2.28939	−	3.96533i	0.404710	−	0.700979i
$33$		0			0
$34$	3.50414	+	6.06935i	0.600955	+	1.04088i
$35$	4.29332			0.725704
$36$		0			0
$37$	2.60806			0.428763			0.214381	−	0.976750i	$-0.431226\pi$
$37$	2.60806			0.428763			0.214381	+	0.976750i	$0.431226\pi$
$38$	0.131346	+	0.227498i	0.0213071	+	0.0369050i
$39$		0			0
$40$	−2.65823	+	4.60419i	−0.420303	+	0.727987i
$41$	−4.07641	+	7.06054i	−0.636628	+	1.10267i	0.349540	+	0.936921i	$0.386338\pi$
$41$	−4.07641	+	7.06054i	−0.636628	+	1.10267i	−0.986168	+	0.165750i	$0.946995\pi$
$42$		0			0
$43$	−2.16357	−	3.74742i	−0.329942	−	0.571476i	0.652558	−	0.757739i	$-0.273696\pi$
$43$	−2.16357	−	3.74742i	−0.329942	−	0.571476i	−0.982500	+	0.186263i	$0.940362\pi$
$44$	−1.11424			−0.167978
$45$		0			0
$46$	0.887743			0.130890
$47$	−2.65117	−	4.59196i	−0.386713	−	0.669806i	0.605293	−	0.796003i	$-0.293056\pi$
$47$	−2.65117	−	4.59196i	−0.386713	−	0.669806i	−0.992005	+	0.126197i	$0.959723\pi$
$48$		0			0
$49$	0.476053	−	0.824548i	0.0680076	−	0.117793i
$50$	−1.02914	+	1.78252i	−0.145543	+	0.252087i
$51$		0			0
$52$	−2.02068	−	3.49992i	−0.280217	−	0.485351i
$53$	10.4841			1.44010			0.720052	−	0.693920i	$-0.244118\pi$
$53$	10.4841			1.44010			0.720052	+	0.693920i	$0.244118\pi$
$54$		0			0
$55$	2.18959			0.295244
$56$	−3.74459	−	6.48581i	−0.500391	−	0.866703i
$57$		0			0
$58$	0.270109	−	0.467843i	0.0354671	−	0.0614307i
$59$	−1.50310	+	2.60345i	−0.195687	+	0.338940i	−0.947126	−	0.320863i	$-0.896027\pi$
$59$	−1.50310	+	2.60345i	−0.195687	+	0.338940i	0.751438	+	0.659803i	$0.229360\pi$
$60$		0			0
$61$	−1.44159	−	2.49690i	−0.184576	−	0.319695i	0.758857	−	0.651257i	$-0.225758\pi$
$61$	−1.44159	−	2.49690i	−0.184576	−	0.319695i	−0.943434	+	0.331561i	$0.892425\pi$
$62$	0.864550			0.109798
$63$		0			0
$64$	7.69541			0.961927
$65$	3.97082	+	6.87766i	0.492519	+	0.853069i
$66$		0			0
$67$	−5.04313	+	8.73496i	−0.616117	+	1.06715i	0.374071	+	0.927400i	$0.377962\pi$
$67$	−5.04313	+	8.73496i	−0.616117	+	1.06715i	−0.990187	+	0.139745i	$0.955372\pi$
$68$	2.95267	−	5.11417i	0.358064	−	0.620185i
$69$		0			0
$70$	2.26328	+	3.92011i	0.270513	+	0.468543i
$71$	−0.0894756			−0.0106188			−0.00530940	−	0.999986i	$-0.501690\pi$
$71$	−0.0894756			−0.0106188			−0.00530940	+	0.999986i	$0.501690\pi$
$72$		0			0
$73$	−5.32114			−0.622792			−0.311396	−	0.950280i	$-0.600797\pi$
$73$	−5.32114			−0.622792			−0.311396	+	0.950280i	$0.600797\pi$
$74$	1.37487	+	2.38135i	0.159826	+	0.276826i
$75$		0			0
$76$	0.110675	−	0.191695i	0.0126953	−	0.0219889i
$77$	−1.54221	+	2.67119i	−0.175751	+	0.304410i
$78$		0			0
$79$	−2.38846	−	4.13693i	−0.268723	−	0.465441i	0.699810	−	0.714329i	$-0.253268\pi$
$79$	−2.38846	−	4.13693i	−0.268723	−	0.465441i	−0.968532	+	0.248888i	$0.919935\pi$
$80$	−2.50337			−0.279885
$81$		0			0
$82$	−8.59571			−0.949238
$83$	4.02033	+	6.96342i	0.441289	+	0.764334i	0.997785	−	0.0665154i	$-0.0211882\pi$
$83$	4.02033	+	6.96342i	0.441289	+	0.764334i	−0.556497	+	0.830850i	$0.687855\pi$
$84$		0			0
$85$	−5.80227	+	10.0498i	−0.629345	+	1.09006i
$86$	2.28111	−	3.95099i	0.245978	−	0.426047i
$87$		0			0
$88$	−1.90973	−	3.30776i	−0.203578	−	0.352608i
$89$	−6.70377			−0.710598			−0.355299	−	0.934753i	$-0.615621\pi$
$89$	−6.70377			−0.710598			−0.355299	+	0.934753i	$0.615621\pi$
$90$		0			0
$91$	−11.1872			−1.17274
$92$	−0.374016	−	0.647816i	−0.0389939	−	0.0675394i
$93$		0			0
$94$	2.79519	−	4.84141i	0.288302	−	0.499354i
$95$	−0.217487	+	0.376698i	−0.0223137	+	0.0386484i
$96$		0			0
$97$	−2.74529	−	4.75498i	−0.278742	−	0.482795i	0.692330	−	0.721581i	$-0.256584\pi$
$97$	−2.74529	−	4.75498i	−0.278742	−	0.482795i	−0.971072	+	0.238786i	$0.923251\pi$
$98$	1.00383			0.101402
$99$		0			0
$100$	1.73436			0.173436
$101$	2.50273	+	4.33486i	0.249031	+	0.431335i	0.963257	−	0.268580i	$-0.0865545\pi$
$101$	2.50273	+	4.33486i	0.249031	+	0.431335i	−0.714226	+	0.699915i	$0.753221\pi$
$102$		0			0
$103$	−5.80958	+	10.0625i	−0.572435	+	0.991486i	0.423880	+	0.905718i	$0.360668\pi$
$103$	−5.80958	+	10.0625i	−0.572435	+	0.991486i	−0.996315	+	0.0857682i	$0.972666\pi$
$104$	6.92660	−	11.9972i	0.679209	−	1.17643i
$105$		0			0
$106$	5.52683	+	9.57275i	0.536813	+	0.929788i
$107$	−19.4581			−1.88109			−0.940544	−	0.339673i	$-0.889684\pi$
$107$	−19.4581			−1.88109			−0.940544	+	0.339673i	$0.889684\pi$
$108$		0			0
$109$	6.31515			0.604881			0.302441	−	0.953168i	$-0.402199\pi$
$109$	6.31515			0.604881			0.302441	+	0.953168i	$0.402199\pi$
$110$	1.15427	+	1.99925i	0.110055	+	0.190621i
$111$		0			0
$112$	1.76322	−	3.05398i	0.166608	−	0.288574i
$113$	−3.45786	+	5.98919i	−0.325288	+	0.563416i	−0.981571	−	0.191099i	$-0.938795\pi$
$113$	−3.45786	+	5.98919i	−0.325288	+	0.563416i	0.656282	+	0.754515i	$0.272128\pi$
$114$		0			0
$115$	0.734977	+	1.27302i	0.0685370	+	0.118710i
$116$	−0.455201			−0.0422643
$117$		0			0
$118$	−3.16951			−0.291777
$119$	−8.17351	−	14.1569i	−0.749265	−	1.29776i
$120$		0			0
$121$	4.71347	−	8.16398i	0.428498	−	0.742180i
$122$	1.51990	−	2.63254i	0.137605	−	0.238339i
$123$		0			0
$124$	−0.364245	−	0.630891i	−0.0327102	−	0.0566557i
$125$	−12.1371			−1.08558
$126$		0			0
$127$	12.0232			1.06689			0.533445	−	0.845835i	$-0.320897\pi$
$127$	12.0232			1.06689			0.533445	+	0.845835i	$0.320897\pi$
$128$	−0.522042	−	0.904203i	−0.0461424	−	0.0799210i
$129$		0			0
$130$	−4.18653	+	7.25129i	−0.367183	+	0.635980i
$131$	−7.04240	+	12.1978i	−0.615297	+	1.06573i	0.375035	+	0.927011i	$0.377631\pi$
$131$	−7.04240	+	12.1978i	−0.615297	+	1.06573i	−0.990332	+	0.138715i	$0.955703\pi$
$132$		0			0
$133$	−0.306368	−	0.530645i	−0.0265655	−	0.0460128i
$134$	−10.6342			−0.918655
$135$		0			0
$136$	20.2427			1.73580
$137$	1.12907	+	1.95561i	0.0964630	+	0.167079i	0.910218	−	0.414129i	$-0.135914\pi$
$137$	1.12907	+	1.95561i	0.0964630	+	0.167079i	−0.813755	+	0.581208i	$0.802580\pi$
$138$		0			0
$139$	3.98755	−	6.90663i	0.338219	−	0.585813i	−0.645879	−	0.763440i	$-0.723509\pi$
$139$	3.98755	−	6.90663i	0.338219	−	0.585813i	0.984098	+	0.177627i	$0.0568421\pi$
$140$	1.90709	−	3.30318i	0.161179	−	0.279170i
$141$		0			0
$142$	−0.0471682	−	0.0816977i	−0.00395827	−	0.00685592i
$143$	−5.70545			−0.477114
$144$		0			0
$145$	0.894512			0.0742851
$146$	−2.80510	−	4.85858i	−0.232152	−	0.402099i
$147$		0			0
$148$	1.15850	−	2.00658i	0.0952281	−	0.164940i
$149$	−0.0534692	+	0.0926114i	−0.00438037	+	0.00758702i	−0.868207	−	0.496202i	$-0.834728\pi$
$149$	−0.0534692	+	0.0926114i	−0.00438037	+	0.00758702i	0.863827	+	0.503789i	$0.168061\pi$
$150$		0			0
$151$	10.1297	+	17.5452i	0.824344	+	1.42781i	0.902420	+	0.430858i	$0.141789\pi$
$151$	10.1297	+	17.5452i	0.824344	+	1.42781i	−0.0780761	+	0.996947i	$0.524878\pi$
$152$	0.758758			0.0615434
$153$		0			0
$154$	−3.25198			−0.262052
$155$	0.715776	+	1.23976i	0.0574925	+	0.0995799i
$156$		0			0
$157$	10.3749	−	17.9699i	0.828009	−	1.43415i	−0.0715893	−	0.997434i	$-0.522807\pi$
$157$	10.3749	−	17.9699i	0.828009	−	1.43415i	0.899598	−	0.436719i	$-0.143860\pi$
$158$	2.51821	−	4.36167i	0.200338	−	0.346996i
$159$		0			0
$160$	3.99678	+	6.92263i	0.315973	+	0.547282i
$161$	−2.07069			−0.163193
$162$		0			0
$163$	−20.1346			−1.57706			−0.788531	−	0.614995i	$-0.789158\pi$
$163$	−20.1346			−1.57706			−0.788531	+	0.614995i	$0.789158\pi$
$164$	3.62148	+	6.27258i	0.282790	+	0.489806i
$165$		0			0
$166$	−4.23873	+	7.34170i	−0.328990	+	0.569827i
$167$	−9.93130	+	17.2015i	−0.768507	+	1.33109i	0.169865	+	0.985467i	$0.445667\pi$
$167$	−9.93130	+	17.2015i	−0.768507	+	1.33109i	−0.938372	+	0.345626i	$0.887667\pi$
$168$		0			0
$169$	−3.84683	−	6.66291i	−0.295910	−	0.512532i
$170$	−12.2350			−0.938378
$171$		0			0
$172$	−3.84423			−0.293120
$173$	9.46256	+	16.3896i	0.719425	+	1.24608i	0.961228	+	0.275755i	$0.0889279\pi$
$173$	9.46256	+	16.3896i	0.719425	+	1.24608i	−0.241803	+	0.970325i	$0.577739\pi$
$174$		0			0
$175$	2.40050	−	4.15780i	0.181461	−	0.314300i
$176$	0.899239	−	1.55753i	0.0677827	−	0.117403i
$177$		0			0
$178$	−3.53398	−	6.12103i	−0.264883	−	0.458790i
$179$	−10.9137			−0.815725			−0.407863	−	0.913043i	$-0.633726\pi$
$179$	−10.9137			−0.815725			−0.407863	+	0.913043i	$0.633726\pi$
$180$		0			0
$181$	−17.9479			−1.33405			−0.667027	−	0.745033i	$-0.732433\pi$
$181$	−17.9479			−1.33405			−0.667027	+	0.745033i	$0.732433\pi$
$182$	−5.89746	−	10.2147i	−0.437149	−	0.757164i
$183$		0			0
$184$	1.28208	−	2.22062i	0.0945160	−	0.163707i
$185$	−2.27656	+	3.94312i	−0.167376	+	0.289904i
$186$		0			0
$187$	−4.16848	−	7.22002i	−0.304830	−	0.527980i
$188$	−4.71059			−0.343555
$189$		0			0
$190$	−0.458604			−0.0332706
$191$	−13.4830	−	23.3533i	−0.975598	−	1.68978i	−0.677948	−	0.735110i	$-0.737131\pi$
$191$	−13.4830	−	23.3533i	−0.975598	−	1.68978i	−0.297649	−	0.954675i	$-0.596203\pi$
$192$		0			0
$193$	8.57740	−	14.8565i	0.617415	−	1.06939i	−0.372541	−	0.928016i	$-0.621513\pi$
$193$	8.57740	−	14.8565i	0.617415	−	1.06939i	0.989956	−	0.141378i	$-0.0451534\pi$
$194$	2.89443	−	5.01329i	0.207808	−	0.359933i
$195$		0			0
$196$	−0.422925	−	0.732528i	−0.0302089	−	0.0523234i
$197$	−2.51225			−0.178990			−0.0894951	−	0.995987i	$-0.528525\pi$
$197$	−2.51225			−0.178990			−0.0894951	+	0.995987i	$0.528525\pi$
$198$		0			0
$199$	18.5388			1.31418			0.657092	−	0.753810i	$-0.271786\pi$
$199$	18.5388			1.31418			0.657092	+	0.753810i	$0.271786\pi$
$200$	2.97257	+	5.14864i	0.210192	+	0.364064i
$201$		0			0
$202$	−2.63869	+	4.57035i	−0.185658	+	0.321569i
$203$	−0.630038	+	1.09126i	−0.0442200	+	0.0765913i
$204$		0			0
$205$	−7.11654	−	12.3262i	−0.497041	−	0.860900i
$206$	−12.2504			−0.853524
$207$		0			0
$208$	6.52307			0.452294
$209$	−0.156247	−	0.270629i	−0.0108079	−	0.0187198i
$210$		0			0
$211$	1.84559	−	3.19666i	0.127056	−	0.220067i	−0.795479	−	0.605981i	$-0.792781\pi$
$211$	1.84559	−	3.19666i	0.127056	−	0.220067i	0.922535	+	0.385914i	$0.126114\pi$
$212$	4.65704	−	8.06623i	0.319847	−	0.553991i
$213$		0			0
$214$	−10.2576	−	17.7667i	−0.701194	−	1.21450i
$215$	7.55427			0.515197
$216$		0			0
$217$	−2.01659			−0.136895
$218$	3.32911	+	5.76619i	0.225476	+	0.390535i
$219$		0			0
$220$	0.972614	−	1.68462i	0.0655736	−	0.113577i
$221$	15.1191	−	26.1870i	1.01702	−	1.76153i
$222$		0			0
$223$	10.6205	+	18.3953i	0.711203	+	1.23184i	0.964406	+	0.264426i	$0.0851826\pi$
$223$	10.6205	+	18.3953i	0.711203	+	1.23184i	−0.253203	+	0.967413i	$0.581484\pi$
$224$	−11.2603			−0.752363
$225$		0			0
$226$	−7.29142			−0.485018
$227$	−7.17002	−	12.4188i	−0.475891	−	0.824268i	0.523727	−	0.851886i	$-0.324541\pi$
$227$	−7.17002	−	12.4188i	−0.475891	−	0.824268i	−0.999619	+	0.0276182i	$0.991208\pi$
$228$		0			0
$229$	−8.44291	+	14.6235i	−0.557923	+	0.966351i	0.439747	+	0.898122i	$0.355068\pi$
$229$	−8.44291	+	14.6235i	−0.557923	+	0.966351i	−0.997670	+	0.0682290i	$0.978265\pi$
$230$	−0.774905	+	1.34217i	−0.0510957	+	0.0885004i
$231$		0			0
$232$	−0.780183	−	1.35132i	−0.0512215	−	0.0887183i
$233$	−5.59945			−0.366832			−0.183416	−	0.983035i	$-0.558716\pi$
$233$	−5.59945			−0.366832			−0.183416	+	0.983035i	$0.558716\pi$
$234$		0			0
$235$	9.25675			0.603844
$236$	1.33535	+	2.31290i	0.0869241	+	0.150557i
$237$		0			0
$238$	8.61754	−	14.9260i	0.558592	−	0.967510i
$239$	−2.63714	+	4.56766i	−0.170582	+	0.295457i	−0.938624	−	0.344943i	$-0.887898\pi$
$239$	−2.63714	+	4.56766i	−0.170582	+	0.295457i	0.768041	+	0.640400i	$0.221232\pi$
$240$		0			0
$241$	4.45124	+	7.70977i	0.286730	+	0.496630i	0.973027	−	0.230691i	$-0.0740986\pi$
$241$	4.45124	+	7.70977i	0.286730	+	0.496630i	−0.686298	+	0.727321i	$0.740765\pi$
$242$	9.93907			0.638907
$243$		0			0
$244$	−2.56141			−0.163977
$245$	0.831087	+	1.43949i	0.0530962	+	0.0919654i
$246$		0			0
$247$	0.566709	−	0.981570i	0.0360589	−	0.0624558i
$248$	1.24858	−	2.16261i	0.0792851	−	0.137326i
$249$		0			0
$250$	−6.39823	−	11.0821i	−0.404659	−	0.700891i
$251$	7.78021			0.491082			0.245541	−	0.969386i	$-0.421034\pi$
$251$	7.78021			0.491082			0.245541	+	0.969386i	$0.421034\pi$
$252$		0			0
$253$	−1.05605			−0.0663932
$254$	6.33820	+	10.9781i	0.397694	+	0.688827i
$255$		0			0
$256$	8.24581	−	14.2822i	0.515363	−	0.892636i
$257$	−10.2183	+	17.6986i	−0.637399	+	1.10401i	0.348603	+	0.937270i	$0.386656\pi$
$257$	−10.2183	+	17.6986i	−0.637399	+	1.10401i	−0.986002	+	0.166736i	$0.946677\pi$
$258$		0			0
$259$	−3.20693	−	5.55457i	−0.199269	−	0.345144i
$260$	7.05534			0.437554
$261$		0			0
$262$	−14.8500			−0.917433
$263$	5.63990	+	9.76860i	0.347771	+	0.602358i	0.985853	−	0.167611i	$-0.0536052\pi$
$263$	5.63990	+	9.76860i	0.347771	+	0.602358i	−0.638082	+	0.769969i	$0.720272\pi$
$264$		0			0
$265$	−9.15152	+	15.8509i	−0.562173	+	0.973712i
$266$	0.323012	−	0.559473i	0.0198051	−	0.0343035i
$267$		0			0
$268$	4.48031	+	7.76013i	0.273679	+	0.474025i
$269$	0.307761			0.0187645			0.00938226	−	0.999956i	$-0.497013\pi$
$269$	0.307761			0.0187645			0.00938226	+	0.999956i	$0.497013\pi$
$270$		0			0
$271$	−2.22251			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$271$	−2.22251			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$272$	4.76585	+	8.25469i	0.288972	+	0.500514i
$273$		0			0
$274$	−1.19041	+	2.06184i	−0.0719151	+	0.124561i
$275$	1.22425	−	2.12047i	0.0738253	−	0.127869i
$276$		0			0
$277$	11.6649	+	20.2041i	0.700874	+	1.21395i	0.968160	+	0.250332i	$0.0805397\pi$
$277$	11.6649	+	20.2041i	0.700874	+	1.21395i	−0.267286	+	0.963617i	$0.586127\pi$
$278$	8.40834			0.504299
$279$		0			0
$280$	13.0745			0.781351
$281$	3.61273	+	6.25743i	0.215517	+	0.373287i	0.953432	−	0.301607i	$-0.0975229\pi$
$281$	3.61273	+	6.25743i	0.215517	+	0.373287i	−0.737915	+	0.674893i	$0.764190\pi$
$282$		0			0
$283$	−3.56015	+	6.16635i	−0.211629	+	0.366552i	−0.952224	−	0.305399i	$-0.901210\pi$
$283$	−3.56015	+	6.16635i	−0.211629	+	0.366552i	0.740596	+	0.671951i	$0.234543\pi$
$284$	−0.0397450	+	0.0688404i	−0.00235843	+	0.00408493i
$285$		0			0
$286$	−3.00770	−	5.20949i	−0.177849	−	0.308044i
$287$	20.0498			1.18350
$288$		0			0
$289$	27.1849			1.59911
$290$	0.471553	+	0.816754i	0.0276905	+	0.0479614i
$291$		0			0
$292$	−2.36365	+	4.09396i	−0.138322	+	0.239581i
$293$	0.276243	−	0.478466i	0.0161383	−	0.0279523i	−0.857843	−	0.513911i	$-0.828196\pi$
$293$	0.276243	−	0.478466i	0.0161383	−	0.0279523i	0.873982	+	0.485959i	$0.161529\pi$
$294$		0			0
$295$	−2.62410	−	4.54507i	−0.152781	−	0.264624i
$296$	7.94236			0.461640
$297$		0			0
$298$	−0.112748			−0.00653131
$299$	−1.91514	−	3.31713i	−0.110756	−	0.191834i
$300$		0			0
$301$	−5.32076	+	9.21582i	−0.306683	+	0.531191i
$302$	−10.6800	+	18.4983i	−0.614565	+	1.06446i
$303$		0			0
$304$	0.178639	+	0.309411i	0.0102456	+	0.0177459i
$305$	5.03340			0.288212
$306$		0			0
$307$	6.72876			0.384031			0.192015	−	0.981392i	$-0.438498\pi$
$307$	6.72876			0.384031			0.192015	+	0.981392i	$0.438498\pi$
$308$	1.37010	+	2.37308i	0.0780686	+	0.135219i
$309$		0			0
$310$	−0.754660	+	1.30711i	−0.0428618	+	0.0742389i
$311$	7.71173	−	13.3571i	0.437292	−	0.757412i	−0.560188	−	0.828366i	$-0.689271\pi$
$311$	7.71173	−	13.3571i	0.437292	−	0.757412i	0.997480	+	0.0709539i	$0.0226043\pi$
$312$		0			0
$313$	11.7804	+	20.4043i	0.665870	+	1.15332i	0.979049	+	0.203626i	$0.0652726\pi$
$313$	11.7804	+	20.4043i	0.665870	+	1.15332i	−0.313179	+	0.949694i	$0.601394\pi$
$314$	21.8771			1.23459
$315$		0			0
$316$	−4.24381			−0.238733
$317$	3.62602	+	6.28045i	0.203658	+	0.352745i	0.949704	−	0.313148i	$-0.101384\pi$
$317$	3.62602	+	6.28045i	0.203658	+	0.352745i	−0.746047	+	0.665894i	$0.768050\pi$
$318$		0			0
$319$	−0.321319	+	0.556540i	−0.0179904	+	0.0311603i
$320$	−6.71728	+	11.6347i	−0.375507	+	0.650397i
$321$		0			0
$322$	−1.09159	−	1.89069i	−0.0608319	−	0.105364i
$323$	1.65618			0.0921525
$324$		0			0
$325$	8.88074			0.492615
$326$	−10.6142	−	18.3843i	−0.587866	−	1.01821i
$327$		0			0
$328$	−12.4139	+	21.5016i	−0.685444	+	1.18722i
$329$	−6.51987	+	11.2928i	−0.359452	+	0.622590i
$330$		0			0
$331$	−14.5172	−	25.1446i	−0.797939	−	1.38207i	−0.920956	−	0.389667i	$-0.872590\pi$
$331$	−14.5172	−	25.1446i	−0.797939	−	1.38207i	0.123017	−	0.992405i	$-0.460743\pi$
$332$	7.14332			0.392040
$333$		0			0
$334$	−20.9416			−1.14588
$335$	−8.80423	−	15.2494i	−0.481027	−	0.833163i
$336$		0			0
$337$	0.579548	−	1.00381i	0.0315700	−	0.0546808i	−0.849809	−	0.527091i	$-0.823283\pi$
$337$	0.579548	−	1.00381i	0.0315700	−	0.0546808i	0.881379	+	0.472410i	$0.156616\pi$
$338$	4.05581	−	7.02487i	0.220607	−	0.382103i
$339$		0			0
$340$	5.15473	+	8.92826i	0.279555	+	0.484203i
$341$	−1.02846			−0.0556942
$342$		0			0
$343$	−19.5562			−1.05594
$344$	−6.58875	−	11.4120i	−0.355242	−	0.615296i
$345$		0			0
$346$	−9.97661	+	17.2800i	−0.536346	+	0.928978i
$347$	2.94485	−	5.10064i	0.158088	−	0.273817i	−0.776091	−	0.630621i	$-0.782800\pi$
$347$	2.94485	−	5.10064i	0.158088	−	0.273817i	0.934179	+	0.356804i	$0.116134\pi$
$348$		0			0
$349$	15.2963	+	26.4940i	0.818795	+	1.41819i	0.906571	+	0.422054i	$0.138691\pi$
$349$	15.2963	+	26.4940i	0.818795	+	1.41819i	−0.0877762	+	0.996140i	$0.527976\pi$
$350$	5.06182			0.270566
$351$		0			0
$352$	−5.74276			−0.306090
$353$	18.4806	+	32.0094i	0.983625	+	1.70369i	0.647894	+	0.761731i	$0.275650\pi$
$353$	18.4806	+	32.0094i	0.983625	+	1.70369i	0.335731	+	0.941958i	$0.391017\pi$
$354$		0			0
$355$	0.0781027	−	0.135278i	0.00414526	−	0.00717980i
$356$	−2.97781	+	5.15772i	−0.157824	+	0.273359i
$357$		0			0
$358$	−5.75327	−	9.96496i	−0.304070	−	0.526664i
$359$	26.3761			1.39207			0.696037	−	0.718006i	$-0.254945\pi$
$359$	26.3761			1.39207			0.696037	+	0.718006i	$0.254945\pi$
$360$		0			0
$361$	−18.9379			−0.996733
$362$	−9.46144	−	16.3877i	−0.497282	−	0.861318i
$363$		0			0
$364$	−4.96934	+	8.60715i	−0.260464	+	0.451137i
$365$	4.64479	−	8.04501i	0.243119	−	0.421095i
$366$		0			0
$367$	5.65657	+	9.79746i	0.295270	+	0.511423i	0.975048	−	0.221995i	$-0.0712570\pi$
$367$	5.65657	+	9.79746i	0.295270	+	0.511423i	−0.679777	+	0.733418i	$0.737924\pi$
$368$	1.20739			0.0629394
$369$		0			0
$370$	−4.80047			−0.249564
$371$	−12.8915	−	22.3288i	−0.669294	−	1.15925i
$372$		0			0
$373$	−2.92204	+	5.06112i	−0.151297	+	0.262055i	−0.931705	−	0.363217i	$-0.881678\pi$
$373$	−2.92204	+	5.06112i	−0.151297	+	0.262055i	0.780407	+	0.625272i	$0.215012\pi$
$374$	4.39494	−	7.61225i	0.227257	−	0.393620i
$375$		0			0
$376$	−8.07363	−	13.9839i	−0.416366	−	0.721166i
$377$	−2.33085			−0.120045
$378$		0			0
$379$	24.3265			1.24957			0.624783	−	0.780798i	$-0.285187\pi$
$379$	24.3265			1.24957			0.624783	+	0.780798i	$0.285187\pi$
$380$	0.193215	+	0.334658i	0.00991173	+	0.0171676i
$381$		0			0
$382$	14.2155	−	24.6220i	0.727328	−	1.25977i
$383$	−1.90803	+	3.30480i	−0.0974955	+	0.168867i	−0.910647	−	0.413184i	$-0.864417\pi$
$383$	−1.90803	+	3.30480i	−0.0974955	+	0.168867i	0.813152	+	0.582052i	$0.197750\pi$
$384$		0			0
$385$	−2.69237	−	4.66332i	−0.137216	−	0.237665i
$386$	18.0867			0.920591
$387$		0			0
$388$	−4.87782			−0.247634
$389$	5.42092	+	9.38932i	0.274852	+	0.476057i	0.970098	−	0.242715i	$-0.0780379\pi$
$389$	5.42092	+	9.38932i	0.274852	+	0.476057i	−0.695246	+	0.718772i	$0.744705\pi$
$390$		0			0
$391$	2.79846	−	4.84708i	0.141524	−	0.245127i
$392$	1.44973	−	2.51101i	0.0732224	−	0.126825i
$393$		0			0
$394$	−1.32436	−	2.29386i	−0.0667204	−	0.115563i
$395$	8.33948			0.419605
$396$		0			0
$397$	−10.5092			−0.527442			−0.263721	−	0.964599i	$-0.584950\pi$
$397$	−10.5092			−0.527442			−0.263721	+	0.964599i	$0.584950\pi$
$398$	9.77298	+	16.9273i	0.489875	+	0.848489i
$399$		0			0
$400$	−1.39970	+	2.42435i	−0.0699849	+	0.121217i
$401$	7.18279	−	12.4410i	0.358691	−	0.621272i	−0.629051	−	0.777364i	$-0.716556\pi$
$401$	7.18279	−	12.4410i	0.358691	−	0.621272i	0.987742	+	0.156092i	$0.0498897\pi$
$402$		0			0
$403$	−1.86511	−	3.23047i	−0.0929078	−	0.160921i
$404$	4.44685			0.221239
$405$		0			0
$406$	−1.32853			−0.0659338
$407$	−1.63553	−	2.83283i	−0.0810703	−	0.140418i
$408$		0			0
$409$	−8.84113	+	15.3133i	−0.437166	+	0.757193i	−0.997470	−	0.0710938i	$-0.977351\pi$
$409$	−8.84113	+	15.3133i	−0.437166	+	0.757193i	0.560304	+	0.828287i	$0.310684\pi$
$410$	7.50314	−	12.9958i	0.370554	−	0.641818i
$411$		0			0
$412$	5.16123	+	8.93951i	0.254275	+	0.440418i
$413$	7.39299			0.363785
$414$		0			0
$415$	−14.0373			−0.689063
$416$	−10.4145	−	18.0384i	−0.510612	−	0.884407i
$417$		0			0
$418$	0.164736	−	0.285330i	0.00805748	−	0.0139560i
$419$	4.56688	−	7.91007i	0.223107	−	0.386432i	−0.732643	−	0.680613i	$-0.761713\pi$
$419$	4.56688	−	7.91007i	0.223107	−	0.386432i	0.955750	+	0.294181i	$0.0950468\pi$
$420$		0			0
$421$	−12.0975	−	20.9534i	−0.589594	−	1.02121i	−0.994286	−	0.106753i	$-0.965954\pi$
$421$	−12.0975	−	20.9534i	−0.589594	−	1.02121i	0.404692	−	0.914453i	$-0.367379\pi$
$422$	3.89170			0.189445
$423$		0			0
$424$	31.9274			1.55053
$425$	6.48839	+	11.2382i	0.314733	+	0.545134i
$426$		0			0
$427$	−3.54522	+	6.14049i	−0.171565	+	0.297159i
$428$	−8.64329	+	14.9706i	−0.417789	+	0.723632i
$429$		0			0
$430$	3.98233	+	6.89760i	0.192045	+	0.332632i
$431$	29.5332			1.42256			0.711282	−	0.702907i	$-0.248115\pi$
$431$	29.5332			1.42256			0.711282	+	0.702907i	$0.248115\pi$
$432$		0			0
$433$	0.669754			0.0321863			0.0160932	−	0.999870i	$-0.494877\pi$
$433$	0.669754			0.0321863			0.0160932	+	0.999870i	$0.494877\pi$
$434$	−1.06307	−	1.84129i	−0.0510290	−	0.0883849i
$435$		0			0
$436$	2.80519	−	4.85872i	0.134344	−	0.232691i
$437$	0.104895	−	0.181683i	0.00501780	−	0.00869109i
$438$		0			0
$439$	3.17443	+	5.49828i	0.151507	+	0.262419i	0.931782	−	0.363019i	$-0.118254\pi$
$439$	3.17443	+	5.49828i	0.151507	+	0.262419i	−0.780274	+	0.625437i	$0.784921\pi$
$440$	6.66798			0.317883
$441$		0			0
$442$	31.8809			1.51642
$443$	7.67696	+	13.2969i	0.364743	+	0.631754i	0.988735	−	0.149677i	$-0.0478233\pi$
$443$	7.67696	+	13.2969i	0.364743	+	0.631754i	−0.623991	+	0.781431i	$0.714490\pi$
$444$		0			0
$445$	5.85168	−	10.1354i	0.277396	−	0.480464i
$446$	−11.1975	+	19.3946i	−0.530216	+	0.918361i
$447$		0			0
$448$	−9.46246	−	16.3895i	−0.447059	−	0.774329i
$449$	32.0398			1.51205			0.756027	−	0.654541i	$-0.227138\pi$
$449$	32.0398			1.51205			0.756027	+	0.654541i	$0.227138\pi$
$450$		0			0
$451$	10.2254			0.481494
$452$	3.07196	+	5.32079i	0.144493	+	0.250269i
$453$		0			0
$454$	7.55954	−	13.0935i	0.354787	−	0.614508i
$455$	9.76522	−	16.9139i	0.457801	−	0.792934i
$456$		0			0
$457$	−9.58402	−	16.6000i	−0.448321	−	0.776516i	0.549955	−	0.835194i	$-0.314645\pi$
$457$	−9.58402	−	16.6000i	−0.448321	−	0.776516i	−0.998277	+	0.0586784i	$0.981311\pi$
$458$	−17.8031			−0.831886
$459$		0			0
$460$	1.30591			0.0608882
$461$	−2.61015	−	4.52091i	−0.121567	−	0.210560i	0.798819	−	0.601571i	$-0.205458\pi$
$461$	−2.61015	−	4.52091i	−0.121567	−	0.210560i	−0.920386	+	0.391012i	$0.872125\pi$
$462$		0			0
$463$	−0.848695	+	1.46998i	−0.0394422	+	0.0683159i	−0.885073	−	0.465453i	$-0.845891\pi$
$463$	−0.848695	+	1.46998i	−0.0394422	+	0.0683159i	0.845630	+	0.533769i	$0.179225\pi$
$464$	0.367365	−	0.636296i	0.0170545	−	0.0295393i
$465$		0			0
$466$	−2.95182	−	5.11270i	−0.136740	−	0.236841i
$467$	−19.6827			−0.910808			−0.455404	−	0.890285i	$-0.650505\pi$
$467$	−19.6827			−0.910808			−0.455404	+	0.890285i	$0.650505\pi$
$468$		0			0
$469$	24.8046			1.14537
$470$	4.87981	+	8.45208i	0.225089	+	0.389865i
$471$		0			0
$472$	−4.57741	+	7.92831i	−0.210692	+	0.364930i
$473$	−2.71358	+	4.70006i	−0.124771	+	0.216109i
$474$		0			0
$475$	0.243205	+	0.421243i	0.0111590	+	0.0193280i
$476$	−14.5227			−0.665646
$477$		0			0
$478$	−5.56080			−0.254345
$479$	−14.6267	−	25.3342i	−0.668311	−	1.15755i	−0.978376	−	0.206834i	$-0.933684\pi$
$479$	−14.6267	−	25.3342i	−0.668311	−	1.15755i	0.310065	−	0.950716i	$-0.399649\pi$
$480$		0			0
$481$	5.93207	−	10.2747i	0.270479	−	0.468484i
$482$	−4.69305	+	8.12861i	−0.213763	+	0.370248i
$483$		0			0
$484$	−4.18745	−	7.25287i	−0.190339	−	0.329676i
$485$	9.58538			0.435250
$486$		0			0
$487$	−20.5056			−0.929199			−0.464600	−	0.885521i	$-0.653802\pi$
$487$	−20.5056			−0.929199			−0.464600	+	0.885521i	$0.653802\pi$
$488$	−4.39008	−	7.60384i	−0.198729	−	0.344210i
$489$		0			0
$490$	−0.876236	+	1.51769i	−0.0395843	+	0.0685620i
$491$	8.76350	−	15.1788i	0.395491	−	0.685011i	−0.597673	−	0.801740i	$-0.703908\pi$
$491$	8.76350	−	15.1788i	0.395491	−	0.685011i	0.993164	+	0.116730i	$0.0372411\pi$
$492$		0			0
$493$	−1.70295	−	2.94959i	−0.0766969	−	0.132843i
$494$	1.19499			0.0537652
$495$		0			0
$496$	1.17584			0.0527969
$497$	0.110021	+	0.190563i	0.00493513	+	0.00854790i
$498$		0			0
$499$	9.55299	−	16.5463i	0.427651	−	0.740713i	−0.569013	−	0.822328i	$-0.692675\pi$
$499$	9.55299	−	16.5463i	0.427651	−	0.740713i	0.996664	+	0.0816157i	$0.0260080\pi$
$500$	−5.39130	+	9.33800i	−0.241106	+	0.417608i
$501$		0			0
$502$	4.10143	+	7.10389i	0.183056	+	0.317062i
$503$	10.9676			0.489022			0.244511	−	0.969646i	$-0.421373\pi$
$503$	10.9676			0.489022			0.244511	+	0.969646i	$0.421373\pi$
$504$		0			0
$505$	−8.73847			−0.388857
$506$	−0.556709	−	0.964248i	−0.0247487	−	0.0428661i
$507$		0			0
$508$	5.34072	−	9.25040i	0.236956	−	0.410420i
$509$	−9.94968	+	17.2333i	−0.441012	+	0.763855i	−0.997765	−	0.0668233i	$-0.978714\pi$
$509$	−9.94968	+	17.2333i	−0.441012	+	0.763855i	0.556753	+	0.830678i	$0.312047\pi$
$510$		0			0
$511$	6.54300	+	11.3328i	0.289445	+	0.501334i
$512$	15.2994			0.676143
$513$		0			0
$514$	−21.5468			−0.950387
$515$	−10.1423	−	17.5670i	−0.446923	−	0.774093i
$516$		0			0
$517$	−3.32513	+	5.75929i	−0.146239	+	0.253293i
$518$	3.38115	−	5.85632i	0.148559	−	0.257312i
$519$		0			0
$520$	12.0924	+	20.9446i	0.530286	+	0.918482i
$521$	−35.1167			−1.53849			−0.769244	−	0.638955i	$-0.779367\pi$
$521$	−35.1167			−1.53849			−0.769244	+	0.638955i	$0.779367\pi$
$522$		0			0
$523$	−14.2454			−0.622907			−0.311453	−	0.950261i	$-0.600816\pi$
$523$	−14.2454			−0.622907			−0.311453	+	0.950261i	$0.600816\pi$
$524$	6.25646	+	10.8365i	0.273315	+	0.473395i
$525$		0			0
$526$	−5.94629	+	10.2993i	−0.259271	+	0.449070i
$527$	2.72535	−	4.72045i	0.118718	−	0.205626i
$528$		0			0
$529$	11.1455	+	19.3046i	0.484588	+	0.839331i
$530$	−19.2973			−0.838223
$531$		0			0
$532$	−0.544355			−0.0236008
$533$	18.5437	+	32.1186i	0.803217	+	1.39121i
$534$		0			0
$535$	16.9849	−	29.4187i	0.734320	−	1.27188i
$536$	−15.3579	+	26.6007i	−0.663360	+	1.14897i
$537$		0			0
$538$	0.162240	+	0.281008i	0.00699466	+	0.0121151i
$539$	−1.19414			−0.0514354
$540$		0			0
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$	−1.17163	−	2.02932i	−0.0503256	−	0.0871666i
$543$		0			0
$544$	15.2179	−	26.3583i	0.652464	−	1.13010i
$545$	−5.51245	+	9.54785i	−0.236127	+	0.408985i
$546$		0			0
$547$	8.15246	+	14.1205i	0.348574	+	0.603748i	0.985996	−	0.166767i	$-0.0533327\pi$
$547$	8.15246	+	14.1205i	0.348574	+	0.603748i	−0.637422	+	0.770515i	$0.719999\pi$
$548$	2.00613			0.0856976
$549$		0			0
$550$	2.58152			0.110077
$551$	−0.0638317	−	0.110560i	−0.00271932	−	0.00471000i
$552$		0			0
$553$	−5.87381	+	10.1737i	−0.249780	+	0.432631i
$554$	−12.2986	+	21.3017i	−0.522516	+	0.905023i
$555$		0			0
$556$	−3.54253	−	6.13585i	−0.150237	−	0.260218i
$557$	−30.8972			−1.30915			−0.654577	−	0.755995i	$-0.727153\pi$
$557$	−30.8972			−1.30915			−0.654577	+	0.755995i	$0.727153\pi$
$558$		0			0
$559$	−19.6843			−0.832557
$560$	3.07820	+	5.33160i	0.130078	+	0.225301i
$561$		0			0
$562$	−3.80899	+	6.59736i	−0.160672	+	0.278293i
$563$	13.3880	−	23.1887i	0.564236	−	0.977285i	−0.432884	−	0.901449i	$-0.642504\pi$
$563$	13.3880	−	23.1887i	0.564236	−	0.977285i	0.997120	−	0.0758357i	$-0.0241625\pi$
$564$		0			0
$565$	−6.03669	−	10.4559i	−0.253966	−	0.439881i
$566$	−7.50710			−0.315547
$567$		0			0
$568$	−0.272481			−0.0114331
$569$	9.53032	+	16.5070i	0.399532	+	0.692009i	0.993668	−	0.112355i	$-0.0358394\pi$
$569$	9.53032	+	16.5070i	0.399532	+	0.692009i	−0.594136	+	0.804364i	$0.702506\pi$
$570$		0			0
$571$	9.38710	−	16.2589i	0.392838	−	0.680415i	−0.599985	−	0.800012i	$-0.704827\pi$
$571$	9.38710	−	16.2589i	0.392838	−	0.680415i	0.992823	+	0.119596i	$0.0381600\pi$
$572$	−2.53436	+	4.38964i	−0.105967	+	0.183540i
$573$		0			0
$574$	10.5695	+	18.3069i	0.441162	+	0.764115i
$575$	1.64378			0.0685503
$576$		0			0
$577$	−4.85962			−0.202309			−0.101154	−	0.994871i	$-0.532254\pi$
$577$	−4.85962			−0.202309			−0.101154	+	0.994871i	$0.532254\pi$
$578$	14.3308	+	24.8217i	0.596084	+	1.03245i
$579$		0			0
$580$	0.397342	−	0.688216i	0.0164987	−	0.0285766i
$581$	9.88698	−	17.1248i	0.410181	−	0.710455i
$582$		0			0
$583$	−6.57466	−	11.3876i	−0.272294	−	0.471628i
$584$	−16.2045			−0.670548
$585$		0			0
$586$	0.582499			0.0240628
$587$	−16.3987	−	28.4033i	−0.676846	−	1.17233i	−0.975926	−	0.218103i	$-0.930013\pi$
$587$	−16.3987	−	28.4033i	−0.676846	−	1.17233i	0.299080	−	0.954228i	$-0.403320\pi$
$588$		0			0
$589$	0.102154	−	0.176937i	0.00420920	−	0.00729055i
$590$	2.76665	−	4.79198i	0.113901	−	0.197283i
$591$		0			0
$592$	1.86991	+	3.23878i	0.0768530	+	0.133113i
$593$	−17.3446			−0.712258			−0.356129	−	0.934437i	$-0.615904\pi$
$593$	−17.3446			−0.712258			−0.356129	+	0.934437i	$0.615904\pi$
$594$		0			0
$595$	28.5384			1.16996
$596$	0.0475020	+	0.0822759i	0.00194576	+	0.00337015i
$597$		0			0
$598$	2.01918	−	3.49733i	0.0825706	−	0.143016i
$599$	12.2040	−	21.1379i	0.498640	−	0.863670i	−0.501359	−	0.865240i	$-0.667166\pi$
$599$	12.2040	−	21.1379i	0.498640	−	0.863670i	0.999999	+	0.00156953i	$0.000499598\pi$
$600$		0			0
$601$	−3.93513	−	6.81585i	−0.160517	−	0.278024i	0.774537	−	0.632529i	$-0.217983\pi$
$601$	−3.93513	−	6.81585i	−0.160517	−	0.278024i	−0.935054	+	0.354504i	$0.884650\pi$
$602$	−11.2196			−0.457277
$603$		0			0
$604$	17.9984			0.732346
$605$	8.22872	+	14.2526i	0.334545	+	0.579449i
$606$		0			0
$607$	5.11873	−	8.86591i	0.207763	−	0.359856i	−0.743247	−	0.669018i	$-0.766715\pi$
$607$	5.11873	−	8.86591i	0.207763	−	0.359856i	0.951010	+	0.309162i	$0.100048\pi$
$608$	0.570415	−	0.987988i	0.0231334	−	0.0400682i
$609$		0			0
$610$	2.65342	+	4.59586i	0.107434	+	0.186081i
$611$	−24.1205			−0.975810
$612$		0			0
$613$	2.23507			0.0902736			0.0451368	−	0.998981i	$-0.485628\pi$
$613$	2.23507			0.0902736			0.0451368	+	0.998981i	$0.485628\pi$
$614$	3.54715	+	6.14384i	0.143151	+	0.247945i
$615$		0			0
$616$	−4.69651	+	8.13459i	−0.189228	+	0.327752i
$617$	16.9878	−	29.4238i	0.683905	−	1.18456i	−0.289875	−	0.957065i	$-0.593614\pi$
$617$	16.9878	−	29.4238i	0.683905	−	1.18456i	0.973780	−	0.227493i	$-0.0730530\pi$
$618$		0			0
$619$	14.4280	+	24.9900i	0.579910	+	1.00443i	0.995489	+	0.0948761i	$0.0302455\pi$
$619$	14.4280	+	24.9900i	0.579910	+	1.00443i	−0.415579	+	0.909557i	$0.636421\pi$
$620$	1.27179			0.0510763
$621$		0			0
$622$	16.2613			0.652020
$623$	8.24311	+	14.2775i	0.330253	+	0.572015i
$624$		0			0
$625$	5.71383	−	9.89665i	0.228553	−	0.395866i
$626$	−12.4204	+	21.5128i	−0.496419	+	0.859823i
$627$		0			0
$628$	−9.21707	−	15.9644i	−0.367801	−	0.637050i
$629$	17.3362			0.691241
$630$		0			0
$631$	−3.14078			−0.125032			−0.0625162	−	0.998044i	$-0.519913\pi$
$631$	−3.14078			−0.125032			−0.0625162	+	0.998044i	$0.519913\pi$
$632$	−7.27360	−	12.5982i	−0.289328	−	0.501131i
$633$		0			0
$634$	−3.82300	+	6.62164i	−0.151831	+	0.262979i
$635$	−10.4950	+	18.1779i	−0.416482	+	0.721368i
$636$		0			0
$637$	−2.16558	−	3.75089i	−0.0858034	−	0.148616i
$638$	−0.677549			−0.0268244
$639$		0			0
$640$	1.82275			0.0720504
$641$	−15.9113	−	27.5591i	−0.628457	−	1.08852i	−0.987861	−	0.155338i	$-0.950353\pi$
$641$	−15.9113	−	27.5591i	−0.628457	−	1.08852i	0.359404	−	0.933182i	$-0.382980\pi$
$642$		0			0
$643$	6.42353	−	11.1259i	0.253319	−	0.438762i	−0.711118	−	0.703072i	$-0.751811\pi$
$643$	6.42353	−	11.1259i	0.253319	−	0.438762i	0.964438	+	0.264310i	$0.0851443\pi$
$644$	−0.919799	+	1.59314i	−0.0362451	+	0.0627784i
$645$		0			0
$646$	0.873078	+	1.51221i	0.0343508	+	0.0594973i
$647$	−28.2444			−1.11040			−0.555200	−	0.831717i	$-0.687358\pi$
$647$	−28.2444			−1.11040			−0.555200	+	0.831717i	$0.687358\pi$
$648$		0			0
$649$	3.77042			0.148002
$650$	4.68159	+	8.10876i	0.183627	+	0.318052i
$651$		0			0
$652$	−8.94377	+	15.4911i	−0.350265	+	0.606677i
$653$	12.9952	−	22.5084i	0.508543	−	0.880823i	−0.491408	−	0.870930i	$-0.663518\pi$
$653$	12.9952	−	22.5084i	0.508543	−	0.880823i	0.999951	−	0.00989323i	$-0.00314916\pi$
$654$		0			0
$655$	−12.2945	−	21.2947i	−0.480387	−	0.832055i
$656$	−11.6907			−0.456446
$657$		0			0
$658$	−13.7481			−0.535958
$659$	−23.8089	−	41.2382i	−0.927463	−	1.60641i	−0.787551	−	0.616250i	$-0.788651\pi$
$659$	−23.8089	−	41.2382i	−0.927463	−	1.60641i	−0.139912	−	0.990164i	$-0.544682\pi$
$660$		0			0
$661$	0.438254	−	0.759078i	0.0170461	−	0.0295247i	−0.857377	−	0.514690i	$-0.827907\pi$
$661$	0.438254	−	0.759078i	0.0170461	−	0.0295247i	0.874423	+	0.485165i	$0.161240\pi$
$662$	15.3059	−	26.5106i	0.594880	−	1.03036i
$663$		0			0
$664$	12.2432	+	21.2058i	0.475127	+	0.822943i
$665$	1.06971			0.0414815
$666$		0			0
$667$	−0.431427			−0.0167049
$668$	8.82296	+	15.2818i	0.341371	+	0.591271i
$669$		0			0
$670$	9.28252	−	16.0778i	0.358615	−	0.621140i
$671$	−1.80806	+	3.13164i	−0.0697992	+	0.120896i
$672$		0			0
$673$	−18.6697	−	32.3369i	−0.719665	−	1.24650i	−0.961133	−	0.276087i	$-0.910962\pi$
$673$	−18.6697	−	32.3369i	−0.719665	−	1.24650i	0.241468	−	0.970409i	$-0.422371\pi$
$674$	1.22206			0.0470721
$675$		0			0
$676$	−6.83505			−0.262886
$677$	−6.85958	−	11.8811i	−0.263635	−	0.456630i	0.703570	−	0.710626i	$-0.251588\pi$
$677$	−6.85958	−	11.8811i	−0.263635	−	0.456630i	−0.967205	+	0.253996i	$0.918255\pi$
$678$		0			0
$679$	−6.75134	+	11.6937i	−0.259093	+	0.448762i
$680$	−17.6697	+	30.6049i	−0.677603	+	1.17364i
$681$		0			0
$682$	−0.542165	−	0.939057i	−0.0207606	−	0.0359584i
$683$	−49.9887			−1.91276			−0.956381	−	0.292121i	$-0.905639\pi$
$683$	−49.9887			−1.91276			−0.956381	+	0.292121i	$0.905639\pi$
$684$		0			0
$685$	−3.94223			−0.150625
$686$	−10.3093	−	17.8562i	−0.393610	−	0.681753i
$687$		0			0
$688$	3.10245	−	5.37360i	0.118280	−	0.204867i
$689$	23.8463	−	41.3030i	0.908471	−	1.57352i
$690$		0			0
$691$	−11.9075	−	20.6244i	−0.452984	−	0.784591i	0.545586	−	0.838055i	$-0.316307\pi$
$691$	−11.9075	−	20.6244i	−0.452984	−	0.784591i	−0.998570	+	0.0534640i	$0.982974\pi$
$692$	16.8131			0.639137
$693$		0			0
$694$	6.20967			0.235716
$695$	6.96141	+	12.0575i	0.264061	+	0.457367i
$696$		0			0
$697$	−27.0966	+	46.9326i	−1.02636	+	1.77770i
$698$	−16.1273	+	27.9333i	−0.610428	+	1.05729i
$699$		0			0
$700$	−2.13261	−	3.69378i	−0.0806049	−	0.139612i
$701$	−34.4493			−1.30113			−0.650565	−	0.759450i	$-0.725468\pi$
$701$	−34.4493			−1.30113			−0.650565	+	0.759450i	$0.725468\pi$
$702$		0			0
$703$	0.649815			0.0245082
$704$	−4.82584	−	8.35861i	−0.181881	−	0.315027i
$705$		0			0
$706$	−19.4846	+	33.7483i	−0.733312	+	1.27013i
$707$	6.15484	−	10.6605i	0.231476	−	0.400929i
$708$		0			0
$709$	−7.76164	−	13.4435i	−0.291494	−	0.504883i	0.682669	−	0.730728i	$-0.260819\pi$
$709$	−7.76164	−	13.4435i	−0.291494	−	0.504883i	−0.974163	+	0.225845i	$0.927486\pi$
$710$	0.164691			0.00618075
$711$		0			0
$712$	−20.4151			−0.765087
$713$	−0.345222	−	0.597942i	−0.0129287	−	0.0223931i
$714$		0			0
$715$	4.98025	−	8.62605i	0.186251	−	0.322596i
$716$	−4.84784	+	8.39671i	−0.181172	+	0.313800i
$717$		0			0
$718$	13.9045	+	24.0832i	0.518910	+	0.898778i
$719$	−12.0537			−0.449528			−0.224764	−	0.974413i	$-0.572161\pi$
$719$	−12.0537			−0.449528			−0.224764	+	0.974413i	$0.572161\pi$
$720$		0			0
$721$	28.5744			1.06417
$722$	−9.98336	−	17.2917i	−0.371542	−	0.643530i
$723$		0			0
$724$	−7.97243	+	13.8087i	−0.296293	+	0.513195i
$725$	0.500144	−	0.866275i	0.0185749	−	0.0321726i
$726$		0			0
$727$	15.8151	+	27.3926i	0.586550	+	1.01594i	0.994680	+	0.103011i	$0.0328478\pi$
$727$	15.8151	+	27.3926i	0.586550	+	1.01594i	−0.408130	+	0.912924i	$0.633819\pi$
$728$	−34.0685			−1.26266
$729$		0			0
$730$	9.79423			0.362501
$731$	−14.3816	−	24.9097i	−0.531924	−	0.921319i
$732$		0			0
$733$	9.51539	−	16.4811i	0.351459	−	0.608745i	−0.635046	−	0.772474i	$-0.719019\pi$
$733$	9.51539	−	16.4811i	0.351459	−	0.608745i	0.986505	+	0.163729i	$0.0523523\pi$
$734$	−5.96386	+	10.3297i	−0.220130	+	0.381276i
$735$		0			0
$736$	−1.92767	−	3.33882i	−0.0710547	−	0.123070i
$737$	12.6503			0.465981
$738$		0			0
$739$	16.6007			0.610668			0.305334	−	0.952245i	$-0.401232\pi$
$739$	16.6007			0.610668			0.305334	+	0.952245i	$0.401232\pi$
$740$	2.02249	+	3.50306i	0.0743484	+	0.128775i
$741$		0			0
$742$	13.5918	−	23.5418i	0.498972	−	0.864245i
$743$	−16.6518	+	28.8417i	−0.610894	+	1.05810i	0.380196	+	0.924906i	$0.375857\pi$
$743$	−16.6518	+	28.8417i	−0.610894	+	1.05810i	−0.991090	+	0.133194i	$0.957477\pi$
$744$		0			0
$745$	−0.0933458	−	0.161680i	−0.00341993	−	0.00592349i
$746$	−6.16156			−0.225591
$747$		0			0
$748$	−7.40655			−0.270810
$749$	23.9262	+	41.4413i	0.874243	+	1.51423i
$750$		0			0
$751$	−13.8908	+	24.0596i	−0.506882	+	0.877946i	0.493086	+	0.869981i	$0.335869\pi$
$751$	−13.8908	+	24.0596i	−0.506882	+	0.877946i	−0.999968	+	0.00796554i	$0.997464\pi$
$752$	3.80164	−	6.58463i	0.138631	−	0.240117i
$753$		0			0
$754$	−1.22873	−	2.12823i	−0.0447479	−	0.0775056i
$755$	−35.3686			−1.28720
$756$		0			0
$757$	−3.12036			−0.113411			−0.0567057	−	0.998391i	$-0.518060\pi$
$757$	−3.12036			−0.113411			−0.0567057	+	0.998391i	$0.518060\pi$
$758$	12.8240	+	22.2118i	0.465789	+	0.806769i
$759$		0			0
$760$	−0.662315	+	1.14716i	−0.0240247	+	0.0416120i
$761$	−21.9796	+	38.0698i	−0.796760	+	1.38003i	0.124956	+	0.992162i	$0.460121\pi$
$761$	−21.9796	+	38.0698i	−0.796760	+	1.38003i	−0.921716	+	0.387866i	$0.873212\pi$
$762$		0			0
$763$	−7.76525	−	13.4498i	−0.281121	−	0.486916i
$764$	−23.9566			−0.866720
$765$		0			0
$766$	−4.02336			−0.145370
$767$	6.83765	+	11.8432i	0.246893	+	0.427632i
$768$		0			0
$769$	−1.85643	+	3.21543i	−0.0669445	+	0.115951i	−0.897555	−	0.440903i	$-0.854658\pi$
$769$	−1.85643	+	3.21543i	−0.0669445	+	0.115951i	0.830610	+	0.556854i	$0.187992\pi$
$770$	2.83863	−	4.91665i	0.102297	−	0.177184i
$771$		0			0
$772$	−7.62016	−	13.1985i	−0.274256	−	0.475024i
$773$	8.96903			0.322594			0.161297	−	0.986906i	$-0.448432\pi$
$773$	8.96903			0.322594			0.161297	+	0.986906i	$0.448432\pi$
$774$		0			0
$775$	1.60083			0.0575036
$776$	−8.36026	−	14.4804i	−0.300116	−	0.519816i
$777$		0			0
$778$	−5.71541	+	9.89939i	−0.204908	+	0.354910i
$779$	−1.01566	+	1.75918i	−0.0363899	+	0.0630291i
$780$		0			0
$781$	0.0561108	+	0.0971867i	0.00200780	+	0.00347761i
$782$	5.90098			0.211018
$783$		0			0
$784$	1.36527			0.0487597
$785$	18.1124	+	31.3716i	0.646459	+	1.11970i
$786$		0			0
$787$	−21.9257	+	37.9765i	−0.781567	+	1.35371i	0.149461	+	0.988768i	$0.452246\pi$
$787$	−21.9257	+	37.9765i	−0.781567	+	1.35371i	−0.931028	+	0.364947i	$0.881087\pi$
$788$	−1.11594	+	1.93286i	−0.0397537	+	0.0688554i
$789$		0			0
$790$	4.39626	+	7.61455i	0.156412	+	0.270914i
$791$	17.0075			0.604716
$792$		0			0
$793$	−13.1156			−0.465750
$794$	−5.54006	−	9.59567i	−0.196609	−	0.340537i
$795$		0			0
$796$	8.23495	−	14.2633i	0.291880	−	0.505551i
$797$	6.00801	−	10.4062i	0.212815	−	0.368606i	−0.739780	−	0.672849i	$-0.765070\pi$
$797$	6.00801	−	10.4062i	0.212815	−	0.368606i	0.952594	+	0.304243i	$0.0984036\pi$
$798$		0			0
$799$	−17.6228	−	30.5235i	−0.623448	−	1.07984i
$800$	8.93881			0.316035
$801$		0			0
$802$	15.1460			0.534823
$803$	3.33692	+	5.77972i	0.117757	+	0.203962i
$804$		0			0
$805$	1.80749	−	3.13066i	0.0637057	−	0.110341i
$806$	1.96643	−	3.40596i	0.0692646	−	0.119970i
$807$		0			0
$808$	7.62160	+	13.2010i	0.268127	+	0.464409i
$809$	8.02937			0.282298			0.141149	−	0.989988i	$-0.454920\pi$
$809$	8.02937			0.282298			0.141149	+	0.989988i	$0.454920\pi$
$810$		0			0
$811$	−12.8345			−0.450681			−0.225341	−	0.974280i	$-0.572349\pi$
$811$	−12.8345			−0.450681			−0.225341	+	0.974280i	$0.572349\pi$
$812$	0.559725	+	0.969473i	0.0196425	+	0.0340218i
$813$		0			0
$814$	1.72438	−	2.98672i	0.0604396	−	0.104684i
$815$	17.5753	−	30.4414i	0.615637	−	1.06632i
$816$		0			0
$817$	−0.539067	−	0.933692i	−0.0188596	−	0.0326658i
$818$	−18.6428			−0.651832
$819$		0			0
$820$	−12.6447			−0.441570
$821$	−14.8327	−	25.6910i	−0.517665	−	0.896621i	−0.999789	−	0.0205189i	$-0.993468\pi$
$821$	−14.8327	−	25.6910i	−0.517665	−	0.896621i	0.482125	−	0.876103i	$-0.339865\pi$
$822$		0			0
$823$	−24.7704	+	42.9035i	−0.863441	+	1.49552i	0.00514683	+	0.999987i	$0.498362\pi$
$823$	−24.7704	+	42.9035i	−0.863441	+	1.49552i	−0.868587	+	0.495536i	$0.834972\pi$
$824$	−17.6920	+	30.6434i	−0.616329	+	1.06751i
$825$		0			0
$826$	3.89731	+	6.75034i	0.135605	+	0.234874i
$827$	−40.8431			−1.42025			−0.710126	−	0.704074i	$-0.751362\pi$
$827$	−40.8431			−1.42025			−0.710126	+	0.704074i	$0.751362\pi$
$828$		0			0
$829$	−9.45276			−0.328308			−0.164154	−	0.986435i	$-0.552489\pi$
$829$	−9.45276			−0.328308			−0.164154	+	0.986435i	$0.552489\pi$
$830$	−7.39993	−	12.8171i	−0.256855	−	0.444886i
$831$		0			0
$832$	17.5033	−	30.3167i	0.606819	−	1.05104i
$833$	3.16441	−	5.48091i	0.109640	−	0.189902i
$834$		0			0
$835$	−17.3379	−	30.0302i	−0.600004	−	1.03924i
$836$	−0.277620			−0.00960170
$837$		0			0
$838$	9.62995			0.332661
$839$	−6.14344	−	10.6408i	−0.212095	−	0.367360i	0.740275	−	0.672304i	$-0.234695\pi$
$839$	−6.14344	−	10.6408i	−0.212095	−	0.367360i	−0.952370	+	0.304945i	$0.901362\pi$
$840$		0			0
$841$	14.3687	−	24.8874i	0.495474	−	0.858185i
$842$	12.7546	−	22.0917i	0.439554	−	0.761330i
$843$		0			0
$844$	−1.63962	−	2.83991i	−0.0564381	−	0.0977536i
$845$	13.4315			0.462058
$846$		0			0
$847$	−23.1832			−0.796584
$848$	7.51684	+	13.0196i	0.258129	+	0.447093i
$849$		0			0
$850$	−6.84087	+	11.8487i	−0.234640	+	0.406409i
$851$	1.09800	−	1.90178i	0.0376388	−	0.0651923i
$852$		0			0
$853$	15.4329	+	26.7306i	0.528413	+	0.915239i	0.999451	+	0.0331257i	$0.0105462\pi$
$853$	15.4329	+	26.7306i	0.528413	+	0.915239i	−0.471038	+	0.882113i	$0.656120\pi$
$854$	−7.47562			−0.255810
$855$		0			0
$856$	−59.2560			−2.02533
$857$	5.57302	+	9.65275i	0.190371	+	0.329731i	0.945373	−	0.325990i	$-0.105698\pi$
$857$	5.57302	+	9.65275i	0.190371	+	0.329731i	−0.755003	+	0.655722i	$0.772364\pi$
$858$		0			0
$859$	−2.07434	+	3.59286i	−0.0707755	+	0.122587i	−0.899241	−	0.437453i	$-0.855881\pi$
$859$	−2.07434	+	3.59286i	−0.0707755	+	0.122587i	0.828466	+	0.560040i	$0.189214\pi$
$860$	3.35560	−	5.81208i	0.114425	−	0.198190i
$861$		0			0
$862$	15.5688	+	26.9659i	0.530275	+	0.918463i
$863$	47.2534			1.60852			0.804262	−	0.594275i	$-0.202561\pi$
$863$	47.2534			1.60852			0.804262	+	0.594275i	$0.202561\pi$
$864$		0			0
$865$	−33.0392			−1.12337
$866$	0.353069	+	0.611534i	0.0119978	+	0.0207808i
$867$		0			0
$868$	−0.895769	+	1.55152i	−0.0304044	+	0.0526619i
$869$	−2.99564	+	5.18860i	−0.101620	+	0.176011i
$870$		0			0
$871$	22.9414	+	39.7356i	0.777338	+	1.34639i
$872$	19.2316			0.651264
$873$		0			0
$874$	0.221187			0.00748175
$875$	14.9241	+	25.8493i	0.504526	+	0.873864i
$876$		0			0
$877$	−17.5752	+	30.4412i	−0.593473	+	1.02793i	0.400288	+	0.916390i	$0.368910\pi$
$877$	−17.5752	+	30.4412i	−0.593473	+	1.02793i	−0.993760	+	0.111536i	$0.964423\pi$
$878$	−3.34689	+	5.79698i	−0.112952	+	0.195638i
$879$		0			0
$880$	1.56988	+	2.71911i	0.0529206	+	0.0916612i
$881$	19.3596			0.652242			0.326121	−	0.945328i	$-0.394258\pi$
$881$	19.3596			0.652242			0.326121	+	0.945328i	$0.394258\pi$
$882$		0			0
$883$	−13.7860			−0.463937			−0.231969	−	0.972723i	$-0.574517\pi$
$883$	−13.7860			−0.463937			−0.231969	+	0.972723i	$0.574517\pi$
$884$	−13.4318	−	23.2645i	−0.451760	−	0.782471i
$885$		0			0
$886$	−8.09401	+	14.0192i	−0.271924	+	0.470986i
$887$	−14.9087	+	25.8227i	−0.500586	+	0.867041i	0.499414	+	0.866364i	$0.333549\pi$
$887$	−14.9087	+	25.8227i	−0.500586	+	0.867041i	−1.00000		0.000676951i	$0.999785\pi$
$888$		0			0
$889$	−14.7841	−	25.6067i	−0.495842	−	0.858823i
$890$	12.3391			0.413609
$891$		0			0
$892$	18.8705			0.631832
$893$	−0.660555	−	1.14411i	−0.0221046	−	0.0382863i
$894$		0			0
$895$	9.52646	−	16.5003i	0.318435	−	0.551545i
$896$	−1.28383	+	2.22366i	−0.0428897	+	0.0742872i
$897$		0			0
$898$	16.8902	+	29.2547i	0.563633	+	0.976241i
$899$	−0.420156			−0.0140130
$900$		0			0
$901$	69.6897			2.32170
$902$	5.39043	+	9.33650i	0.179482	+	0.310871i
$903$		0			0
$904$	−10.5303	+	18.2390i	−0.350231	+	0.606619i
$905$	15.6666	−	27.1353i	0.520775	−	0.902008i
$906$		0			0
$907$	3.11579	+	5.39670i	0.103458	+	0.179194i	0.913107	−	0.407720i	$-0.133676\pi$
$907$	3.11579	+	5.39670i	0.103458	+	0.179194i	−0.809649	+	0.586914i	$0.800343\pi$
$908$	−12.7397			−0.422781
$909$		0			0
$910$	20.5914			0.682599
$911$	−15.8197	−	27.4006i	−0.524131	−	0.907822i	−0.999605	−	0.0280921i	$-0.991057\pi$
$911$	−15.8197	−	27.4006i	−0.524131	−	0.907822i	0.475474	−	0.879730i	$-0.342277\pi$
$912$		0			0
$913$	5.04235	−	8.73361i	0.166877	−	0.289040i
$914$	10.1047	−	17.5018i	0.334233	−	0.578908i
$915$		0			0
$916$	7.50067	+	12.9915i	0.247829	+	0.429253i
$917$	34.6380			1.14385
$918$		0			0
$919$	36.0031			1.18763			0.593816	−	0.804601i	$-0.297621\pi$
$919$	36.0031			1.18763			0.593816	+	0.804601i	$0.297621\pi$
$920$	2.23823	+	3.87674i	0.0737924	+	0.127812i
$921$		0			0
$922$	2.75194	−	4.76650i	0.0906304	−	0.156976i
$923$	−0.203514	+	0.352496i	−0.00669873	+	0.0116025i
$924$		0			0
$925$	2.54576	+	4.40939i	0.0837042	+	0.144980i
$926$	−1.78960			−0.0588099
$927$		0			0
$928$	−2.34609			−0.0770141
$929$	12.7239	+	22.0384i	0.417456	+	0.723056i	0.995683	−	0.0928207i	$-0.0295883\pi$
$929$	12.7239	+	22.0384i	0.417456	+	0.723056i	−0.578227	+	0.815876i	$0.696255\pi$
$930$		0			0
$931$	0.118612	−	0.205441i	0.00388734	−	0.00673307i
$932$	−2.48727	+	4.30808i	−0.0814733	+	0.141116i
$933$		0			0
$934$	−10.3760	−	17.9717i	−0.339513	−	0.588053i
$935$	14.5546			0.475985
$936$		0			0
$937$	28.3048			0.924677			0.462338	−	0.886704i	$-0.347011\pi$
$937$	28.3048			0.924677			0.462338	+	0.886704i	$0.347011\pi$
$938$	13.0761	+	22.6484i	0.426948	+	0.739496i
$939$		0			0
$940$	4.11184	−	7.12192i	0.134114	−	0.232291i
$941$	4.14722	−	7.18320i	0.135196	−	0.234165i	−0.790477	−	0.612492i	$-0.790167\pi$
$941$	4.14722	−	7.18320i	0.135196	−	0.234165i	0.925672	+	0.378327i	$0.123500\pi$
$942$		0			0
$943$	3.43234	+	5.94499i	0.111772	+	0.193595i
$944$	−4.31074			−0.140303
$945$		0			0
$946$	−5.72199			−0.186038
$947$	−22.2253	−	38.4954i	−0.722225	−	1.25093i	−0.960106	−	0.279637i	$-0.909786\pi$
$947$	−22.2253	−	38.4954i	−0.722225	−	1.25093i	0.237881	−	0.971294i	$-0.423547\pi$
$948$		0			0
$949$	−12.1030	+	20.9630i	−0.392880	+	0.680489i
$950$	−0.256417	+	0.444127i	−0.00831926	+	0.0144094i
$951$		0			0
$952$	−24.8909	−	43.1123i	−0.806718	−	1.39728i
$953$	9.67149			0.313290			0.156645	−	0.987655i	$-0.449932\pi$
$953$	9.67149			0.313290			0.156645	+	0.987655i	$0.449932\pi$
$954$		0			0
$955$	47.0770			1.52338
$956$	2.34283	+	4.05790i	0.0757726	+	0.131242i
$957$		0			0
$958$	15.4213	−	26.7105i	0.498240	−	0.862977i
$959$	2.77666	−	4.80932i	0.0896631	−	0.155301i
$960$		0			0
$961$	15.1638	+	26.2645i	0.489155	+	0.847241i
$962$	12.5087			0.403296
$963$		0			0
$964$	7.90895			0.254730
$965$	14.9743	+	25.9363i	0.482040	+	0.834919i
$966$		0			0
$967$	16.5575	−	28.6785i	0.532455	−	0.922238i	−0.466827	−	0.884349i	$-0.654603\pi$
$967$	16.5575	−	28.6785i	0.532455	−	0.922238i	0.999282	−	0.0378900i	$-0.0120636\pi$
$968$	14.3540	−	24.8619i	0.461355	−	0.799090i
$969$		0			0
$970$	5.05305	+	8.75214i	0.162244	+	0.281014i
$971$	27.4309			0.880298			0.440149	−	0.897925i	$-0.354926\pi$
$971$	27.4309			0.880298			0.440149	+	0.897925i	$0.354926\pi$
$972$		0			0
$973$	−19.6127			−0.628755
$974$	−10.8098	−	18.7231i	−0.346368	−	0.599928i
$975$		0			0
$976$	2.06716	−	3.58043i	0.0661682	−	0.114607i
$977$	18.1888	−	31.5039i	0.581911	−	1.00790i	−0.413342	−	0.910576i	$-0.635639\pi$
$977$	18.1888	−	31.5039i	0.581911	−	1.00790i	0.995253	−	0.0973232i	$-0.0310281\pi$
$978$		0			0
$979$	4.20398	+	7.28150i	0.134360	+	0.232718i
$980$	1.47667			0.0471706
$981$		0			0
$982$	18.4791			0.589693
$983$	21.0686	+	36.4919i	0.671984	+	1.16391i	0.977341	+	0.211673i	$0.0678910\pi$
$983$	21.0686	+	36.4919i	0.671984	+	1.16391i	−0.305356	+	0.952238i	$0.598776\pi$
$984$		0			0
$985$	2.19292	−	3.79826i	0.0698724	−	0.121022i
$986$	1.79546	−	3.10983i	0.0571791	−	0.0990371i
$987$		0			0
$988$	−0.503464	−	0.872026i	−0.0160173	−	0.0277428i
$989$	−3.64346			−0.115855
$990$		0			0
$991$	25.5409			0.811333			0.405667	−	0.914021i	$-0.367039\pi$
$991$	25.5409			0.811333			0.405667	+	0.914021i	$0.367039\pi$
$992$	−1.87731	−	3.25159i	−0.0596045	−	0.103238i
$993$		0			0
$994$	−0.115998	+	0.200915i	−0.00367924	+	0.00637263i
$995$	−16.1824	+	28.0288i	−0.513018	+	0.888573i
$996$		0			0
$997$	−11.7664	−	20.3801i	−0.372647	−	0.645443i	0.617325	−	0.786708i	$-0.288216\pi$
$997$	−11.7664	−	20.3801i	−0.372647	−	0.645443i	−0.989972	+	0.141265i	$0.954883\pi$
$998$	20.1439			0.637644
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.c.b.244.5		12
3.2	odd	2		729.2.c.e.244.2		12
9.2	odd	6		729.2.c.e.487.2		12
9.4	even	3		729.2.a.d.1.2		6
9.5	odd	6		729.2.a.a.1.5		6
9.7	even	3	inner	729.2.c.b.487.5		12
27.2	odd	18		27.2.e.a.13.2	✓	12
27.4	even	9		81.2.e.a.73.1		12
27.5	odd	18		243.2.e.d.55.1		12
27.7	even	9		243.2.e.a.190.2		12
27.11	odd	18		243.2.e.c.109.2		12
27.13	even	9		243.2.e.b.136.1		12
27.14	odd	18		243.2.e.c.136.2		12
27.16	even	9		243.2.e.b.109.1		12
27.20	odd	18		243.2.e.d.190.1		12
27.22	even	9		243.2.e.a.55.2		12
27.23	odd	18		27.2.e.a.25.2	yes	12
27.25	even	9		81.2.e.a.10.1		12
108.23	even	18		432.2.u.c.241.2		12
108.83	even	18		432.2.u.c.337.2		12
135.2	even	36		675.2.u.b.499.2		24
135.23	even	36		675.2.u.b.349.2		24
135.29	odd	18		675.2.l.c.526.1		12
135.77	even	36		675.2.u.b.349.3		24
135.83	even	36		675.2.u.b.499.3		24
135.104	odd	18		675.2.l.c.376.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	27.2	odd	18
27.2.e.a.25.2	yes	12	27.23	odd	18
81.2.e.a.10.1		12	27.25	even	9
81.2.e.a.73.1		12	27.4	even	9
243.2.e.a.55.2		12	27.22	even	9
243.2.e.a.190.2		12	27.7	even	9
243.2.e.b.109.1		12	27.16	even	9
243.2.e.b.136.1		12	27.13	even	9
243.2.e.c.109.2		12	27.11	odd	18
243.2.e.c.136.2		12	27.14	odd	18
243.2.e.d.55.1		12	27.5	odd	18
243.2.e.d.190.1		12	27.20	odd	18
432.2.u.c.241.2		12	108.23	even	18
432.2.u.c.337.2		12	108.83	even	18
675.2.l.c.376.1		12	135.104	odd	18
675.2.l.c.526.1		12	135.29	odd	18
675.2.u.b.349.2		24	135.23	even	36
675.2.u.b.349.3		24	135.77	even	36
675.2.u.b.499.2		24	135.2	even	36
675.2.u.b.499.3		24	135.83	even	36
729.2.a.a.1.5		6	9.5	odd	6
729.2.a.d.1.2		6	9.4	even	3
729.2.c.b.244.5		12	1.1	even	1	trivial
729.2.c.b.487.5		12	9.7	even	3	inner
729.2.c.e.244.2		12	3.2	odd	2
729.2.c.e.487.2		12	9.2	odd	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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.527162 + 0.913072i) q^{2} +(0.444200 - 0.769376i) q^{4} +(-0.872894 + 1.51190i) q^{5} +(-1.22962 - 2.12977i) q^{7} +3.04531 q^{8} +O(q^{10})\)	\(q+(0.527162 + 0.913072i) q^{2} +(0.444200 - 0.769376i) q^{4} +(-0.872894 + 1.51190i) q^{5} +(-1.22962 - 2.12977i) q^{7} +3.04531 q^{8} -1.84063 q^{10} +(-0.627106 - 1.08618i) q^{11} +(2.27451 - 3.93958i) q^{13} +(1.29642 - 2.24547i) q^{14} +(0.716974 + 1.24184i) q^{16} +6.64717 q^{17} +0.249156 q^{19} +(0.775478 + 1.34317i) q^{20} +(0.661174 - 1.14519i) q^{22} +(0.421000 - 0.729194i) q^{23} +(0.976114 + 1.69068i) q^{25} +4.79615 q^{26} -2.18479 q^{28} +(-0.256192 - 0.443737i) q^{29} +(0.410002 - 0.710144i) q^{31} +(2.28939 - 3.96533i) q^{32} +(3.50414 + 6.06935i) q^{34} +4.29332 q^{35} +2.60806 q^{37} +(0.131346 + 0.227498i) q^{38} +(-2.65823 + 4.60419i) q^{40} +(-4.07641 + 7.06054i) q^{41} +(-2.16357 - 3.74742i) q^{43} -1.11424 q^{44} +0.887743 q^{46} +(-2.65117 - 4.59196i) q^{47} +(0.476053 - 0.824548i) q^{49} +(-1.02914 + 1.78252i) q^{50} +(-2.02068 - 3.49992i) q^{52} +10.4841 q^{53} +2.18959 q^{55} +(-3.74459 - 6.48581i) q^{56} +(0.270109 - 0.467843i) q^{58} +(-1.50310 + 2.60345i) q^{59} +(-1.44159 - 2.49690i) q^{61} +0.864550 q^{62} +7.69541 q^{64} +(3.97082 + 6.87766i) q^{65} +(-5.04313 + 8.73496i) q^{67} +(2.95267 - 5.11417i) q^{68} +(2.26328 + 3.92011i) q^{70} -0.0894756 q^{71} -5.32114 q^{73} +(1.37487 + 2.38135i) q^{74} +(0.110675 - 0.191695i) q^{76} +(-1.54221 + 2.67119i) q^{77} +(-2.38846 - 4.13693i) q^{79} -2.50337 q^{80} -8.59571 q^{82} +(4.02033 + 6.96342i) q^{83} +(-5.80227 + 10.0498i) q^{85} +(2.28111 - 3.95099i) q^{86} +(-1.90973 - 3.30776i) q^{88} -6.70377 q^{89} -11.1872 q^{91} +(-0.374016 - 0.647816i) q^{92} +(2.79519 - 4.84141i) q^{94} +(-0.217487 + 0.376698i) q^{95} +(-2.74529 - 4.75498i) q^{97} +1.00383 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8 + 6 * q^10 - 12 * q^11 - 6 * q^14 + 3 * q^16 + 18 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 15 * q^23 + 6 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^29 + 24 * q^35 + 6 * q^37 + 3 * q^38 - 6 * q^40 - 15 * q^41 + 6 * q^44 + 6 * q^46 - 21 * q^47 + 12 * q^49 - 3 * q^50 - 12 * q^52 + 18 * q^53 - 12 * q^55 + 6 * q^56 + 12 * q^58 - 24 * q^59 + 9 * q^61 - 24 * q^62 - 24 * q^64 + 6 * q^65 + 9 * q^67 + 9 * q^68 - 15 * q^70 + 54 * q^71 - 12 * q^73 + 12 * q^74 - 6 * q^76 + 12 * q^77 - 42 * q^80 - 12 * q^82 - 12 * q^83 + 21 * q^86 - 12 * q^88 + 18 * q^89 - 12 * q^91 - 6 * q^92 - 6 * q^94 - 12 * q^95 - 90 * q^98

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