LMFDB - Embedded newform 729.2.c.e.487.2

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			487.2
Root			$0.500000 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.e.244.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.527162 + 0.913072i) q^{2} +(0.444200 + 0.769376i) q^{4} +(0.872894 + 1.51190i) q^{5} +(-1.22962 + 2.12977i) q^{7} -3.04531 q^{8} +O(q^{10})$	\(q+(-0.527162 + 0.913072i) q^{2} +(0.444200 + 0.769376i) q^{4} +(0.872894 + 1.51190i) q^{5} +(-1.22962 + 2.12977i) q^{7} -3.04531 q^{8} -1.84063 q^{10} +(0.627106 - 1.08618i) q^{11} +(2.27451 + 3.93958i) q^{13} +(-1.29642 - 2.24547i) q^{14} +(0.716974 - 1.24184i) q^{16} -6.64717 q^{17} +0.249156 q^{19} +(-0.775478 + 1.34317i) q^{20} +(0.661174 + 1.14519i) q^{22} +(-0.421000 - 0.729194i) q^{23} +(0.976114 - 1.69068i) q^{25} -4.79615 q^{26} -2.18479 q^{28} +(0.256192 - 0.443737i) q^{29} +(0.410002 + 0.710144i) q^{31} +(-2.28939 - 3.96533i) q^{32} +(3.50414 - 6.06935i) q^{34} -4.29332 q^{35} +2.60806 q^{37} +(-0.131346 + 0.227498i) q^{38} +(-2.65823 - 4.60419i) q^{40} +(4.07641 + 7.06054i) q^{41} +(-2.16357 + 3.74742i) q^{43} +1.11424 q^{44} +0.887743 q^{46} +(2.65117 - 4.59196i) q^{47} +(0.476053 + 0.824548i) q^{49} +(1.02914 + 1.78252i) q^{50} +(-2.02068 + 3.49992i) q^{52} -10.4841 q^{53} +2.18959 q^{55} +(3.74459 - 6.48581i) q^{56} +(0.270109 + 0.467843i) q^{58} +(1.50310 + 2.60345i) q^{59} +(-1.44159 + 2.49690i) q^{61} -0.864550 q^{62} +7.69541 q^{64} +(-3.97082 + 6.87766i) q^{65} +(-5.04313 - 8.73496i) q^{67} +(-2.95267 - 5.11417i) q^{68} +(2.26328 - 3.92011i) q^{70} +0.0894756 q^{71} -5.32114 q^{73} +(-1.37487 + 2.38135i) q^{74} +(0.110675 + 0.191695i) q^{76} +(1.54221 + 2.67119i) q^{77} +(-2.38846 + 4.13693i) q^{79} +2.50337 q^{80} -8.59571 q^{82} +(-4.02033 + 6.96342i) q^{83} +(-5.80227 - 10.0498i) q^{85} +(-2.28111 - 3.95099i) q^{86} +(-1.90973 + 3.30776i) q^{88} +6.70377 q^{89} -11.1872 q^{91} +(0.374016 - 0.647816i) q^{92} +(2.79519 + 4.84141i) q^{94} +(0.217487 + 0.376698i) q^{95} +(-2.74529 + 4.75498i) q^{97} -1.00383 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.527162	+	0.913072i	−0.372760	+	0.645639i	−0.989989	−	0.141144i	$-0.954922\pi$
$2$	−0.527162	+	0.913072i	−0.372760	+	0.645639i	0.617229	+	0.786784i	$0.288255\pi$
$3$		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	$-0.0390138\pi$
$5$	0.872894	+	1.51190i	0.390370	+	0.676140i	−0.602128	+	0.798399i	$0.705680\pi$
$6$		0			0
$7$	−1.22962	+	2.12977i	−0.464754	+	0.804977i	−0.999190	−	0.0402312i	$-0.987191\pi$
$7$	−1.22962	+	2.12977i	−0.464754	+	0.804977i	0.534436	+	0.845209i	$0.320524\pi$
$8$	−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	$-0.772783\pi$
$11$	0.627106	−	1.08618i	0.189080	−	0.327496i	0.944944	+	0.327233i	$0.106116\pi$
$12$		0			0
$13$	2.27451	+	3.93958i	0.630837	+	1.09264i	0.987381	+	0.158363i	$0.0506216\pi$
$13$	2.27451	+	3.93958i	0.630837	+	1.09264i	−0.356544	+	0.934279i	$0.616045\pi$
$14$	−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	$-0.798419\pi$
$17$	−6.64717			−1.61218			−0.806088	+	0.591796i	$0.798419\pi$
$18$		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	$-0.194645\pi$
$23$	−0.421000	−	0.729194i	−0.0877847	−	0.152048i	−0.906574	+	0.422046i	$0.861312\pi$
$24$		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	$-0.818184\pi$
$29$	0.256192	−	0.443737i	0.0475736	−	0.0823998i	0.888832	+	0.458234i	$0.151518\pi$
$30$		0			0
$31$	0.410002	+	0.710144i	0.0736385	+	0.127546i	0.900493	−	0.434870i	$-0.143206\pi$
$31$	0.410002	+	0.710144i	0.0736385	+	0.127546i	−0.826855	+	0.562415i	$0.809872\pi$
$32$	−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	0.986168	+	0.165750i	$0.0530046\pi$
$41$	4.07641	+	7.06054i	0.636628	+	1.10267i	−0.349540	+	0.936921i	$0.613662\pi$
$42$		0			0
$43$	−2.16357	+	3.74742i	−0.329942	+	0.571476i	−0.982500	−	0.186263i	$-0.940362\pi$
$43$	−2.16357	+	3.74742i	−0.329942	+	0.571476i	0.652558	+	0.757739i	$0.273696\pi$
$44$	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	$-0.706944\pi$
$47$	2.65117	−	4.59196i	0.386713	−	0.669806i	0.992005	+	0.126197i	$0.0402772\pi$
$48$		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	$-0.755882\pi$
$53$	−10.4841			−1.44010			−0.720052	+	0.693920i	$0.755882\pi$
$54$		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	$-0.103973\pi$
$59$	1.50310	+	2.60345i	0.195687	+	0.338940i	−0.751438	+	0.659803i	$0.770640\pi$
$60$		0			0
$61$	−1.44159	+	2.49690i	−0.184576	+	0.319695i	−0.943434	−	0.331561i	$-0.892425\pi$
$61$	−1.44159	+	2.49690i	−0.184576	+	0.319695i	0.758857	+	0.651257i	$0.225758\pi$
$62$	−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	−0.990187	−	0.139745i	$-0.955372\pi$
$67$	−5.04313	−	8.73496i	−0.616117	−	1.06715i	0.374071	−	0.927400i	$-0.377962\pi$
$68$	−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	$-0.498310\pi$
$71$	0.0894756			0.0106188			0.00530940	+	0.999986i	$0.498310\pi$
$72$		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	−0.968532	−	0.248888i	$-0.919935\pi$
$79$	−2.38846	+	4.13693i	−0.268723	+	0.465441i	0.699810	+	0.714329i	$0.253268\pi$
$80$	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	$-0.978812\pi$
$83$	−4.02033	+	6.96342i	−0.441289	+	0.764334i	0.556497	+	0.830850i	$0.312145\pi$
$84$		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	$-0.384379\pi$
$89$	6.70377			0.710598			0.355299	+	0.934753i	$0.384379\pi$
$90$		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	−0.971072	−	0.238786i	$-0.923251\pi$
$97$	−2.74529	+	4.75498i	−0.278742	+	0.482795i	0.692330	+	0.721581i	$0.256584\pi$
$98$	−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	$-0.913445\pi$
$101$	−2.50273	+	4.33486i	−0.249031	+	0.431335i	0.714226	+	0.699915i	$0.246779\pi$
$102$		0			0
$103$	−5.80958	−	10.0625i	−0.572435	−	0.991486i	−0.996315	−	0.0857682i	$-0.972666\pi$
$103$	−5.80958	−	10.0625i	−0.572435	−	0.991486i	0.423880	−	0.905718i	$-0.360668\pi$
$104$	−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	$-0.110316\pi$
$107$	19.4581			1.88109			0.940544	+	0.339673i	$0.110316\pi$
$108$		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	$-0.0612053\pi$
$113$	3.45786	+	5.98919i	0.325288	+	0.563416i	−0.656282	+	0.754515i	$0.727872\pi$
$114$		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	0.990332	+	0.138715i	$0.0442973\pi$
$131$	7.04240	+	12.1978i	0.615297	+	1.06573i	−0.375035	+	0.927011i	$0.622369\pi$
$132$		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	$-0.864086\pi$
$137$	−1.12907	+	1.95561i	−0.0964630	+	0.167079i	0.813755	+	0.581208i	$0.197420\pi$
$138$		0			0
$139$	3.98755	+	6.90663i	0.338219	+	0.585813i	0.984098	−	0.177627i	$-0.0568421\pi$
$139$	3.98755	+	6.90663i	0.338219	+	0.585813i	−0.645879	+	0.763440i	$0.723509\pi$
$140$	−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	$-0.165272\pi$
$149$	0.0534692	+	0.0926114i	0.00438037	+	0.00758702i	−0.863827	+	0.503789i	$0.831939\pi$
$150$		0			0
$151$	10.1297	−	17.5452i	0.824344	−	1.42781i	−0.0780761	−	0.996947i	$-0.524878\pi$
$151$	10.1297	−	17.5452i	0.824344	−	1.42781i	0.902420	−	0.430858i	$-0.141789\pi$
$152$	−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	0.899598	+	0.436719i	$0.143860\pi$
$157$	10.3749	+	17.9699i	0.828009	+	1.43415i	−0.0715893	+	0.997434i	$0.522807\pi$
$158$	−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	0.938372	+	0.345626i	$0.112333\pi$
$167$	9.93130	+	17.2015i	0.768507	+	1.33109i	−0.169865	+	0.985467i	$0.554333\pi$
$168$		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	0.241803	+	0.970325i	$0.422261\pi$
$173$	−9.46256	+	16.3896i	−0.719425	+	1.24608i	−0.961228	+	0.275755i	$0.911072\pi$
$174$		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	$-0.366274\pi$
$179$	10.9137			0.815725			0.407863	+	0.913043i	$0.366274\pi$
$180$		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	0.297649	−	0.954675i	$-0.403797\pi$
$191$	13.4830	−	23.3533i	0.975598	−	1.68978i	0.677948	−	0.735110i	$-0.262869\pi$
$192$		0			0
$193$	8.57740	+	14.8565i	0.617415	+	1.06939i	0.989956	+	0.141378i	$0.0451534\pi$
$193$	8.57740	+	14.8565i	0.617415	+	1.06939i	−0.372541	+	0.928016i	$0.621513\pi$
$194$	−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	$-0.471475\pi$
$197$	2.51225			0.178990			0.0894951	+	0.995987i	$0.471475\pi$
$198$		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	0.922535	−	0.385914i	$-0.126114\pi$
$211$	1.84559	+	3.19666i	0.127056	+	0.220067i	−0.795479	+	0.605981i	$0.792781\pi$
$212$	−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	−0.253203	−	0.967413i	$-0.581484\pi$
$223$	10.6205	−	18.3953i	0.711203	−	1.23184i	0.964406	−	0.264426i	$-0.0851826\pi$
$224$	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	$-0.675459\pi$
$227$	7.17002	−	12.4188i	0.475891	−	0.824268i	0.999619	+	0.0276182i	$0.00879225\pi$
$228$		0			0
$229$	−8.44291	−	14.6235i	−0.557923	−	0.966351i	−0.997670	−	0.0682290i	$-0.978265\pi$
$229$	−8.44291	−	14.6235i	−0.557923	−	0.966351i	0.439747	−	0.898122i	$-0.355068\pi$
$230$	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	$-0.441284\pi$
$233$	5.59945			0.366832			0.183416	+	0.983035i	$0.441284\pi$
$234$		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	$-0.112102\pi$
$239$	2.63714	+	4.56766i	0.170582	+	0.295457i	−0.768041	+	0.640400i	$0.778768\pi$
$240$		0			0
$241$	4.45124	−	7.70977i	0.286730	−	0.496630i	−0.686298	−	0.727321i	$-0.740765\pi$
$241$	4.45124	−	7.70977i	0.286730	−	0.496630i	0.973027	+	0.230691i	$0.0740986\pi$
$242$	−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	$-0.578966\pi$
$251$	−7.78021			−0.491082			−0.245541	+	0.969386i	$0.578966\pi$
$252$		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	0.986002	+	0.166736i	$0.0533228\pi$
$257$	10.2183	+	17.6986i	0.637399	+	1.10401i	−0.348603	+	0.937270i	$0.613344\pi$
$258$		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	$-0.946395\pi$
$263$	−5.63990	+	9.76860i	−0.347771	+	0.602358i	0.638082	+	0.769969i	$0.279728\pi$
$264$		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	$-0.502987\pi$
$269$	−0.307761			−0.0187645			−0.00938226	+	0.999956i	$0.502987\pi$
$270$		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	−0.267286	−	0.963617i	$-0.586127\pi$
$277$	11.6649	−	20.2041i	0.700874	−	1.21395i	0.968160	−	0.250332i	$-0.0805397\pi$
$278$	−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	$-0.902477\pi$
$281$	−3.61273	+	6.25743i	−0.215517	+	0.373287i	0.737915	+	0.674893i	$0.235810\pi$
$282$		0			0
$283$	−3.56015	−	6.16635i	−0.211629	−	0.366552i	0.740596	−	0.671951i	$-0.234543\pi$
$283$	−3.56015	−	6.16635i	−0.211629	−	0.366552i	−0.952224	+	0.305399i	$0.901210\pi$
$284$	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	$-0.171804\pi$
$293$	−0.276243	−	0.478466i	−0.0161383	−	0.0279523i	−0.873982	+	0.485959i	$0.838471\pi$
$294$		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	$-0.310729\pi$
$311$	−7.71173	−	13.3571i	−0.437292	−	0.757412i	−0.997480	+	0.0709539i	$0.977396\pi$
$312$		0			0
$313$	11.7804	−	20.4043i	0.665870	−	1.15332i	−0.313179	−	0.949694i	$-0.601394\pi$
$313$	11.7804	−	20.4043i	0.665870	−	1.15332i	0.979049	−	0.203626i	$-0.0652726\pi$
$314$	−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	$-0.898616\pi$
$317$	−3.62602	+	6.28045i	−0.203658	+	0.352745i	0.746047	+	0.665894i	$0.231950\pi$
$318$		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	0.123017	+	0.992405i	$0.460743\pi$
$331$	−14.5172	+	25.1446i	−0.797939	+	1.38207i	−0.920956	+	0.389667i	$0.872590\pi$
$332$	−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	0.881379	−	0.472410i	$-0.156616\pi$
$337$	0.579548	+	1.00381i	0.0315700	+	0.0546808i	−0.849809	+	0.527091i	$0.823283\pi$
$338$	−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	$-0.217200\pi$
$347$	−2.94485	−	5.10064i	−0.158088	−	0.273817i	−0.934179	+	0.356804i	$0.883866\pi$
$348$		0			0
$349$	15.2963	−	26.4940i	0.818795	−	1.41819i	−0.0877762	−	0.996140i	$-0.527976\pi$
$349$	15.2963	−	26.4940i	0.818795	−	1.41819i	0.906571	−	0.422054i	$-0.138691\pi$
$350$	−5.06182			−0.270566
$351$		0			0
$352$	−5.74276			−0.306090
$353$	−18.4806	+	32.0094i	−0.983625	+	1.70369i	−0.335731	+	0.941958i	$0.608983\pi$
$353$	−18.4806	+	32.0094i	−0.983625	+	1.70369i	−0.647894	+	0.761731i	$0.724350\pi$
$354$		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	$-0.745055\pi$
$359$	−26.3761			−1.39207			−0.696037	+	0.718006i	$0.745055\pi$
$360$		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	−0.679777	−	0.733418i	$-0.737924\pi$
$367$	5.65657	−	9.79746i	0.295270	−	0.511423i	0.975048	+	0.221995i	$0.0712570\pi$
$368$	−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	0.780407	−	0.625272i	$-0.215012\pi$
$373$	−2.92204	−	5.06112i	−0.151297	−	0.262055i	−0.931705	+	0.363217i	$0.881678\pi$
$374$	−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	$-0.135583\pi$
$383$	1.90803	+	3.30480i	0.0974955	+	0.168867i	−0.813152	+	0.582052i	$0.802250\pi$
$384$		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	$-0.921962\pi$
$389$	−5.42092	+	9.38932i	−0.274852	+	0.476057i	0.695246	+	0.718772i	$0.255295\pi$
$390$		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	$-0.283444\pi$
$401$	−7.18279	−	12.4410i	−0.358691	−	0.621272i	−0.987742	+	0.156092i	$0.950110\pi$
$402$		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	0.560304	−	0.828287i	$-0.310684\pi$
$409$	−8.84113	−	15.3133i	−0.437166	−	0.757193i	−0.997470	+	0.0710938i	$0.977351\pi$
$410$	−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	$-0.238287\pi$
$419$	−4.56688	−	7.91007i	−0.223107	−	0.386432i	−0.955750	+	0.294181i	$0.904953\pi$
$420$		0			0
$421$	−12.0975	+	20.9534i	−0.589594	+	1.02121i	0.404692	+	0.914453i	$0.367379\pi$
$421$	−12.0975	+	20.9534i	−0.589594	+	1.02121i	−0.994286	+	0.106753i	$0.965954\pi$
$422$	−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	$-0.751885\pi$
$431$	−29.5332			−1.42256			−0.711282	+	0.702907i	$0.751885\pi$
$432$		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	−0.780274	−	0.625437i	$-0.784921\pi$
$439$	3.17443	−	5.49828i	0.151507	−	0.262419i	0.931782	+	0.363019i	$0.118254\pi$
$440$	−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	$-0.952177\pi$
$443$	−7.67696	+	13.2969i	−0.364743	+	0.631754i	0.623991	+	0.781431i	$0.285510\pi$
$444$		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	$-0.772862\pi$
$449$	−32.0398			−1.51205			−0.756027	+	0.654541i	$0.772862\pi$
$450$		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	−0.998277	−	0.0586784i	$-0.981311\pi$
$457$	−9.58402	+	16.6000i	−0.448321	+	0.776516i	0.549955	+	0.835194i	$0.314645\pi$
$458$	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	$-0.794542\pi$
$461$	2.61015	−	4.52091i	0.121567	−	0.210560i	0.920386	+	0.391012i	$0.127875\pi$
$462$		0			0
$463$	−0.848695	−	1.46998i	−0.0394422	−	0.0683159i	0.845630	−	0.533769i	$-0.179225\pi$
$463$	−0.848695	−	1.46998i	−0.0394422	−	0.0683159i	−0.885073	+	0.465453i	$0.845891\pi$
$464$	−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	$-0.349495\pi$
$467$	19.6827			0.910808			0.455404	+	0.890285i	$0.349495\pi$
$468$		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	−0.310065	−	0.950716i	$-0.600351\pi$
$479$	14.6267	−	25.3342i	0.668311	−	1.15755i	0.978376	−	0.206834i	$-0.0663160\pi$
$480$		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	$-0.296092\pi$
$491$	−8.76350	−	15.1788i	−0.395491	−	0.685011i	−0.993164	+	0.116730i	$0.962759\pi$
$492$		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	0.996664	−	0.0816157i	$-0.0260080\pi$
$499$	9.55299	+	16.5463i	0.427651	+	0.740713i	−0.569013	+	0.822328i	$0.692675\pi$
$500$	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	$-0.578627\pi$
$503$	−10.9676			−0.489022			−0.244511	+	0.969646i	$0.578627\pi$
$504$		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	$-0.0212864\pi$
$509$	9.94968	+	17.2333i	0.441012	+	0.763855i	−0.556753	+	0.830678i	$0.687953\pi$
$510$		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	$-0.220633\pi$
$521$	35.1167			1.53849			0.769244	+	0.638955i	$0.220633\pi$
$522$		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	−0.637422	−	0.770515i	$-0.719999\pi$
$547$	8.15246	−	14.1205i	0.348574	−	0.603748i	0.985996	+	0.166767i	$0.0533327\pi$
$548$	−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	$-0.272847\pi$
$557$	30.8972			1.30915			0.654577	+	0.755995i	$0.272847\pi$
$558$		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	−0.997120	−	0.0758357i	$-0.975838\pi$
$563$	−13.3880	−	23.1887i	−0.564236	−	0.977285i	0.432884	−	0.901449i	$-0.357496\pi$
$564$		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	$-0.964161\pi$
$569$	−9.53032	+	16.5070i	−0.399532	+	0.692009i	0.594136	+	0.804364i	$0.297494\pi$
$570$		0			0
$571$	9.38710	+	16.2589i	0.392838	+	0.680415i	0.992823	−	0.119596i	$-0.0381600\pi$
$571$	9.38710	+	16.2589i	0.392838	+	0.680415i	−0.599985	+	0.800012i	$0.704827\pi$
$572$	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	−0.299080	−	0.954228i	$-0.596680\pi$
$587$	16.3987	−	28.4033i	0.676846	−	1.17233i	0.975926	−	0.218103i	$-0.0699869\pi$
$588$		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	$-0.384096\pi$
$593$	17.3446			0.712258			0.356129	+	0.934437i	$0.384096\pi$
$594$		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	$-0.332834\pi$
$599$	−12.2040	−	21.1379i	−0.498640	−	0.863670i	−0.999999	+	0.00156953i	$0.999500\pi$
$600$		0			0
$601$	−3.93513	+	6.81585i	−0.160517	+	0.278024i	−0.935054	−	0.354504i	$-0.884650\pi$
$601$	−3.93513	+	6.81585i	−0.160517	+	0.278024i	0.774537	+	0.632529i	$0.217983\pi$
$602$	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	0.951010	−	0.309162i	$-0.100048\pi$
$607$	5.11873	+	8.86591i	0.207763	+	0.359856i	−0.743247	+	0.669018i	$0.766715\pi$
$608$	−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	−0.973780	−	0.227493i	$-0.926947\pi$
$617$	−16.9878	−	29.4238i	−0.683905	−	1.18456i	0.289875	−	0.957065i	$-0.406386\pi$
$618$		0			0
$619$	14.4280	−	24.9900i	0.579910	−	1.00443i	−0.415579	−	0.909557i	$-0.636421\pi$
$619$	14.4280	−	24.9900i	0.579910	−	1.00443i	0.995489	−	0.0948761i	$-0.0302455\pi$
$620$	−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	−0.359404	−	0.933182i	$-0.617020\pi$
$641$	15.9113	−	27.5591i	0.628457	−	1.08852i	0.987861	−	0.155338i	$-0.0496467\pi$
$642$		0			0
$643$	6.42353	+	11.1259i	0.253319	+	0.438762i	0.964438	−	0.264310i	$-0.0851443\pi$
$643$	6.42353	+	11.1259i	0.253319	+	0.438762i	−0.711118	+	0.703072i	$0.751811\pi$
$644$	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	$-0.312642\pi$
$647$	28.2444			1.11040			0.555200	+	0.831717i	$0.312642\pi$
$648$		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	−0.999951	−	0.00989323i	$-0.996851\pi$
$653$	−12.9952	−	22.5084i	−0.508543	−	0.880823i	0.491408	−	0.870930i	$-0.336482\pi$
$654$		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	0.139912	−	0.990164i	$-0.455318\pi$
$659$	23.8089	−	41.2382i	0.927463	−	1.60641i	0.787551	−	0.616250i	$-0.211349\pi$
$660$		0			0
$661$	0.438254	+	0.759078i	0.0170461	+	0.0295247i	0.874423	−	0.485165i	$-0.161240\pi$
$661$	0.438254	+	0.759078i	0.0170461	+	0.0295247i	−0.857377	+	0.514690i	$0.827907\pi$
$662$	−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	0.241468	+	0.970409i	$0.422371\pi$
$673$	−18.6697	+	32.3369i	−0.719665	+	1.24650i	−0.961133	+	0.276087i	$0.910962\pi$
$674$	−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	$-0.748412\pi$
$677$	6.85958	−	11.8811i	0.263635	−	0.456630i	0.967205	+	0.253996i	$0.0817451\pi$
$678$		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	$-0.0943611\pi$
$683$	49.9887			1.91276			0.956381	+	0.292121i	$0.0943611\pi$
$684$		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	−0.998570	−	0.0534640i	$-0.982974\pi$
$691$	−11.9075	+	20.6244i	−0.452984	+	0.784591i	0.545586	+	0.838055i	$0.316307\pi$
$692$	−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	$-0.274532\pi$
$701$	34.4493			1.30113			0.650565	+	0.759450i	$0.274532\pi$
$702$		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	−0.974163	−	0.225845i	$-0.927486\pi$
$709$	−7.76164	+	13.4435i	−0.291494	+	0.504883i	0.682669	+	0.730728i	$0.260819\pi$
$710$	−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	$-0.427839\pi$
$719$	12.0537			0.449528			0.224764	+	0.974413i	$0.427839\pi$
$720$		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	−0.408130	−	0.912924i	$-0.633819\pi$
$727$	15.8151	−	27.3926i	0.586550	−	1.01594i	0.994680	−	0.103011i	$-0.0328478\pi$
$728$	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	0.986505	−	0.163729i	$-0.0523523\pi$
$733$	9.51539	+	16.4811i	0.351459	+	0.608745i	−0.635046	+	0.772474i	$0.719019\pi$
$734$	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	0.991090	+	0.133194i	$0.0425232\pi$
$743$	16.6518	+	28.8417i	0.610894	+	1.05810i	−0.380196	+	0.924906i	$0.624143\pi$
$744$		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	−0.999968	−	0.00796554i	$-0.997464\pi$
$751$	−13.8908	−	24.0596i	−0.506882	−	0.877946i	0.493086	−	0.869981i	$-0.335869\pi$
$752$	−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	0.921716	+	0.387866i	$0.126788\pi$
$761$	21.9796	+	38.0698i	0.796760	+	1.38003i	−0.124956	+	0.992162i	$0.539879\pi$
$762$		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	0.830610	−	0.556854i	$-0.187992\pi$
$769$	−1.85643	−	3.21543i	−0.0669445	−	0.115951i	−0.897555	+	0.440903i	$0.854658\pi$
$770$	−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	$-0.551568\pi$
$773$	−8.96903			−0.322594			−0.161297	+	0.986906i	$0.551568\pi$
$774$		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	−0.931028	−	0.364947i	$-0.881087\pi$
$787$	−21.9257	−	37.9765i	−0.781567	−	1.35371i	0.149461	−	0.988768i	$-0.452246\pi$
$788$	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	$-0.234930\pi$
$797$	−6.00801	−	10.4062i	−0.212815	−	0.368606i	−0.952594	+	0.304243i	$0.901596\pi$
$798$		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	$-0.545080\pi$
$809$	−8.02937			−0.282298			−0.141149	+	0.989988i	$0.545080\pi$
$810$		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	−0.482125	−	0.876103i	$-0.660135\pi$
$821$	14.8327	−	25.6910i	0.517665	−	0.896621i	0.999789	−	0.0205189i	$-0.00653183\pi$
$822$		0			0
$823$	−24.7704	−	42.9035i	−0.863441	−	1.49552i	−0.868587	−	0.495536i	$-0.834972\pi$
$823$	−24.7704	−	42.9035i	−0.863441	−	1.49552i	0.00514683	−	0.999987i	$-0.498362\pi$
$824$	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	$-0.248638\pi$
$827$	40.8431			1.42025			0.710126	+	0.704074i	$0.248638\pi$
$828$		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	$-0.765305\pi$
$839$	6.14344	−	10.6408i	0.212095	−	0.367360i	0.952370	+	0.304945i	$0.0986380\pi$
$840$		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	−0.471038	−	0.882113i	$-0.656120\pi$
$853$	15.4329	−	26.7306i	0.528413	−	0.915239i	0.999451	−	0.0331257i	$-0.0105462\pi$
$854$	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	$-0.894302\pi$
$857$	−5.57302	+	9.65275i	−0.190371	+	0.329731i	0.755003	+	0.655722i	$0.227636\pi$
$858$		0			0
$859$	−2.07434	−	3.59286i	−0.0707755	−	0.122587i	0.828466	−	0.560040i	$-0.189214\pi$
$859$	−2.07434	−	3.59286i	−0.0707755	−	0.122587i	−0.899241	+	0.437453i	$0.855881\pi$
$860$	−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	$-0.797439\pi$
$863$	−47.2534			−1.60852			−0.804262	+	0.594275i	$0.797439\pi$
$864$		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	−0.993760	−	0.111536i	$-0.964423\pi$
$877$	−17.5752	−	30.4412i	−0.593473	−	1.02793i	0.400288	−	0.916390i	$-0.368910\pi$
$878$	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	$-0.605742\pi$
$881$	−19.3596			−0.652242			−0.326121	+	0.945328i	$0.605742\pi$
$882$		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	1.00000		0.000676951i	$0.000215480\pi$
$887$	14.9087	+	25.8227i	0.500586	+	0.867041i	−0.499414	+	0.866364i	$0.666451\pi$
$888$		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	−0.809649	−	0.586914i	$-0.800343\pi$
$907$	3.11579	−	5.39670i	0.103458	−	0.179194i	0.913107	+	0.407720i	$0.133676\pi$
$908$	12.7397			0.422781
$909$		0			0
$910$	20.5914			0.682599
$911$	15.8197	−	27.4006i	0.524131	−	0.907822i	−0.475474	−	0.879730i	$-0.657723\pi$
$911$	15.8197	−	27.4006i	0.524131	−	0.907822i	0.999605	−	0.0280921i	$-0.00894318\pi$
$912$		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	$-0.970412\pi$
$929$	−12.7239	+	22.0384i	−0.417456	+	0.723056i	0.578227	+	0.815876i	$0.303745\pi$
$930$		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	$-0.209833\pi$
$941$	−4.14722	−	7.18320i	−0.135196	−	0.234165i	−0.925672	+	0.378327i	$0.876500\pi$
$942$		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	−0.237881	−	0.971294i	$-0.576453\pi$
$947$	22.2253	−	38.4954i	0.722225	−	1.25093i	0.960106	−	0.279637i	$-0.0902140\pi$
$948$		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	$-0.550068\pi$
$953$	−9.67149			−0.313290			−0.156645	+	0.987655i	$0.550068\pi$
$954$		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	0.999282	+	0.0378900i	$0.0120636\pi$
$967$	16.5575	+	28.6785i	0.532455	+	0.922238i	−0.466827	+	0.884349i	$0.654603\pi$
$968$	−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	$-0.645074\pi$
$971$	−27.4309			−0.880298			−0.440149	+	0.897925i	$0.645074\pi$
$972$		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	−0.995253	−	0.0973232i	$-0.968972\pi$
$977$	−18.1888	−	31.5039i	−0.581911	−	1.00790i	0.413342	−	0.910576i	$-0.364361\pi$
$978$		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	0.305356	+	0.952238i	$0.401224\pi$
$983$	−21.0686	+	36.4919i	−0.671984	+	1.16391i	−0.977341	+	0.211673i	$0.932109\pi$
$984$		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	−0.989972	−	0.141265i	$-0.954883\pi$
$997$	−11.7664	+	20.3801i	−0.372647	+	0.645443i	0.617325	+	0.786708i	$0.288216\pi$
$998$	−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.e.487.2		12
3.2	odd	2		729.2.c.b.487.5		12
9.2	odd	6		729.2.a.d.1.2		6
9.4	even	3	inner	729.2.c.e.244.2		12
9.5	odd	6		729.2.c.b.244.5		12
9.7	even	3		729.2.a.a.1.5		6
27.2	odd	18		243.2.e.b.109.1		12
27.4	even	9		243.2.e.d.55.1		12
27.5	odd	18		243.2.e.b.136.1		12
27.7	even	9		27.2.e.a.13.2	✓	12
27.11	odd	18		243.2.e.a.190.2		12
27.13	even	9		27.2.e.a.25.2	yes	12
27.14	odd	18		81.2.e.a.73.1		12
27.16	even	9		243.2.e.d.190.1		12
27.20	odd	18		81.2.e.a.10.1		12
27.22	even	9		243.2.e.c.136.2		12
27.23	odd	18		243.2.e.a.55.2		12
27.25	even	9		243.2.e.c.109.2		12
108.7	odd	18		432.2.u.c.337.2		12
108.67	odd	18		432.2.u.c.241.2		12
135.7	odd	36		675.2.u.b.499.2		24
135.13	odd	36		675.2.u.b.349.2		24
135.34	even	18		675.2.l.c.526.1		12
135.67	odd	36		675.2.u.b.349.3		24
135.88	odd	36		675.2.u.b.499.3		24
135.94	even	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	27.7	even	9
27.2.e.a.25.2	yes	12	27.13	even	9
81.2.e.a.10.1		12	27.20	odd	18
81.2.e.a.73.1		12	27.14	odd	18
243.2.e.a.55.2		12	27.23	odd	18
243.2.e.a.190.2		12	27.11	odd	18
243.2.e.b.109.1		12	27.2	odd	18
243.2.e.b.136.1		12	27.5	odd	18
243.2.e.c.109.2		12	27.25	even	9
243.2.e.c.136.2		12	27.22	even	9
243.2.e.d.55.1		12	27.4	even	9
243.2.e.d.190.1		12	27.16	even	9
432.2.u.c.241.2		12	108.67	odd	18
432.2.u.c.337.2		12	108.7	odd	18
675.2.l.c.376.1		12	135.94	even	18
675.2.l.c.526.1		12	135.34	even	18
675.2.u.b.349.2		24	135.13	odd	36
675.2.u.b.349.3		24	135.67	odd	36
675.2.u.b.499.2		24	135.7	odd	36
675.2.u.b.499.3		24	135.88	odd	36
729.2.a.a.1.5		6	9.7	even	3
729.2.a.d.1.2		6	9.2	odd	6
729.2.c.b.244.5		12	9.5	odd	6
729.2.c.b.487.5		12	3.2	odd	2
729.2.c.e.244.2		12	9.4	even	3	inner
729.2.c.e.487.2		12	1.1	even	1	trivial

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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