LMFDB - Embedded newform 729.2.e.h.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			568.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.h.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.37939 + 0.866025i) q^{2} +(3.37939 + 2.83564i) q^{4} +(-0.0812519 + 0.460802i) q^{5} +(-2.47178 + 2.07407i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.592396 + 1.02606i) q^{10} +(0.539363 + 3.05888i) q^{11} +(2.05303 - 0.747243i) q^{13} +(-7.67752 + 2.79439i) q^{14} +(1.15270 + 6.53731i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.0209445 - 0.0362770i) q^{19} +(-1.58125 + 1.32683i) q^{20} +(-1.36571 + 7.74535i) q^{22} +(-4.67752 - 3.92490i) q^{23} +(4.49273 + 1.63522i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(6.17752 + 2.24843i) q^{29} +(-4.76991 - 4.00243i) q^{31} +(-0.798133 + 4.52644i) q^{32} +(5.81908 - 4.88279i) q^{34} +(-0.754900 - 1.30753i) q^{35} +(-1.79813 + 3.11446i) q^{37} +(-0.0184183 - 0.104455i) q^{38} +(-2.68479 + 0.977185i) q^{40} +(7.23783 - 2.63435i) q^{41} +(-0.102196 - 0.579585i) q^{43} +(-6.85117 + 11.8666i) q^{44} +(-7.73055 - 13.3897i) q^{46} +(7.40033 - 6.20961i) q^{47} +(0.592396 - 3.35965i) q^{49} +(9.27379 + 7.78163i) q^{50} +(9.05690 + 3.29644i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(-18.5141 - 6.73859i) q^{56} +(12.7515 + 10.6998i) q^{58} +(1.48158 - 8.40247i) q^{59} +(-0.971782 + 0.815422i) q^{61} +(-7.88326 - 13.6542i) q^{62} +(0.819078 - 1.41868i) q^{64} +(0.177519 + 1.00676i) q^{65} +(-9.40420 + 3.42285i) q^{67} +(12.4363 - 4.52644i) q^{68} +(-0.663848 - 3.76487i) q^{70} +(5.91534 - 10.2457i) q^{71} +(4.11721 + 7.13122i) q^{73} +(-6.97565 + 5.85327i) q^{74} +(0.0320889 - 0.181985i) q^{76} +(-7.67752 - 6.44220i) q^{77} +(-10.3833 - 3.77920i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(-1.41875 - 0.516382i) q^{83} +(1.07532 + 0.902302i) q^{85} +(0.258770 - 1.46756i) q^{86} +(-14.5287 + 12.1910i) q^{88} +(-7.93629 - 13.7461i) q^{89} +(-3.52481 + 6.10516i) q^{91} +(-4.67752 - 26.5275i) q^{92} +(22.9859 - 8.36619i) q^{94} +(0.0184183 - 0.00670372i) q^{95} +(3.23783 + 18.3626i) q^{97} +(4.31908 - 7.48086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8} + 12 q^{11} - 21 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} - 12 q^{20} - 18 q^{22} - 3 q^{23} + 9 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 9 q^{32} + 18 q^{34}+ \cdots + 9 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8 + 12 * q^11 - 21 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 - 12 * q^20 - 18 * q^22 - 3 * q^23 + 9 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 9 * q^32 + 18 * q^34 - 6 * q^35 + 3 * q^37 - 12 * q^38 - 9 * q^40 + 24 * q^41 - 15 * q^44 - 9 * q^46 + 30 * q^47 + 3 * q^50 + 18 * q^52 - 36 * q^53 + 18 * q^55 - 24 * q^56 + 36 * q^58 - 3 * q^59 + 9 * q^61 - 12 * q^62 - 12 * q^64 - 24 * q^65 - 18 * q^67 + 27 * q^68 - 9 * q^71 - 6 * q^73 - 3 * q^74 - 9 * q^76 - 21 * q^77 - 27 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 21 * q^86 - 36 * q^88 + 6 * q^91 - 3 * q^92 + 36 * q^94 + 12 * q^95 + 9 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	2.37939	+	0.866025i	1.68248	+	0.612372i	0.993646	−	0.112548i	$-0.0359011\pi$
$2$	2.37939	+	0.866025i	1.68248	+	0.612372i	0.688833	+	0.724920i	$0.258123\pi$
$3$		0			0
$3$		0			0
$4$	3.37939	+	2.83564i	1.68969	+	1.41782i
$5$	−0.0812519	+	0.460802i	−0.0363370	+	0.206077i	−0.997571	−	0.0696565i	$-0.977810\pi$
$5$	−0.0812519	+	0.460802i	−0.0363370	+	0.206077i	0.961234	+	0.275734i	$0.0889208\pi$
$6$		0			0
$7$	−2.47178	+	2.07407i	−0.934246	+	0.783925i	−0.976575	−	0.215179i	$-0.930967\pi$
$7$	−2.47178	+	2.07407i	−0.934246	+	0.783925i	0.0423291	+	0.999104i	$0.486522\pi$
$8$	3.05303	+	5.28801i	1.07941	+	1.86959i
$9$		0			0
$10$	−0.592396	+	1.02606i	−0.187332	+	0.324469i
$11$	0.539363	+	3.05888i	0.162624	+	0.922287i	0.951480	+	0.307709i	$0.0995624\pi$
$11$	0.539363	+	3.05888i	0.162624	+	0.922287i	−0.788856	+	0.614577i	$0.789327\pi$
$12$		0			0
$13$	2.05303	−	0.747243i	0.569409	−	0.207248i	−0.0412400	−	0.999149i	$-0.513131\pi$
$13$	2.05303	−	0.747243i	0.569409	−	0.207248i	0.610649	+	0.791901i	$0.290909\pi$
$14$	−7.67752	+	2.79439i	−2.05190	+	0.746832i
$15$		0			0
$16$	1.15270	+	6.53731i	0.288176	+	1.63433i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−0.0209445	−	0.0362770i	−0.00480501	−	0.00832251i	0.863613	−	0.504155i	$-0.168196\pi$
$19$	−0.0209445	−	0.0362770i	−0.00480501	−	0.00832251i	−0.868418	+	0.495833i	$0.834863\pi$
$20$	−1.58125	+	1.32683i	−0.353579	+	0.296688i
$21$		0			0
$22$	−1.36571	+	7.74535i	−0.291171	+	1.65131i
$23$	−4.67752	−	3.92490i	−0.975330	−	0.818399i	0.00804825	−	0.999968i	$-0.497438\pi$
$23$	−4.67752	−	3.92490i	−0.975330	−	0.818399i	−0.983378	+	0.181569i	$0.941883\pi$
$24$		0			0
$25$	4.49273	+	1.63522i	0.898545	+	0.327044i
$26$	5.53209			1.08493
$27$		0			0
$28$	−14.2344			−2.69005
$29$	6.17752	+	2.24843i	1.14714	+	0.417524i	0.844486	−	0.535578i	$-0.179906\pi$
$29$	6.17752	+	2.24843i	1.14714	+	0.417524i	0.302651	+	0.953102i	$0.402128\pi$
$30$		0			0
$31$	−4.76991	−	4.00243i	−0.856702	−	0.718858i	0.104553	−	0.994519i	$-0.466659\pi$
$31$	−4.76991	−	4.00243i	−0.856702	−	0.718858i	−0.961255	+	0.275661i	$0.911103\pi$
$32$	−0.798133	+	4.52644i	−0.141091	+	0.800169i
$33$		0			0
$34$	5.81908	−	4.88279i	0.997964	−	0.837391i
$35$	−0.754900	−	1.30753i	−0.127601	−	0.221012i
$36$		0			0
$37$	−1.79813	+	3.11446i	−0.295611	+	0.512014i	−0.975127	−	0.221647i	$-0.928857\pi$
$37$	−1.79813	+	3.11446i	−0.295611	+	0.512014i	0.679516	+	0.733661i	$0.262190\pi$
$38$	−0.0184183	−	0.104455i	−0.00298784	−	0.0169449i
$39$		0			0
$40$	−2.68479	+	0.977185i	−0.424503	+	0.154506i
$41$	7.23783	−	2.63435i	1.13036	−	0.411417i	0.291936	−	0.956438i	$-0.405701\pi$
$41$	7.23783	−	2.63435i	1.13036	−	0.411417i	0.838422	+	0.545021i	$0.183478\pi$
$42$		0			0
$43$	−0.102196	−	0.579585i	−0.0155848	−	0.0883859i	0.976023	−	0.217666i	$-0.0698444\pi$
$43$	−0.102196	−	0.579585i	−0.0155848	−	0.0883859i	−0.991608	+	0.129280i	$0.958733\pi$
$44$	−6.85117	+	11.8666i	−1.03285	+	1.78895i
$45$		0			0
$46$	−7.73055	−	13.3897i	−1.13981	−	1.97420i
$47$	7.40033	−	6.20961i	1.07945	−	0.905765i	0.0835741	−	0.996502i	$-0.473366\pi$
$47$	7.40033	−	6.20961i	1.07945	−	0.905765i	0.995875	+	0.0907363i	$0.0289220\pi$
$48$		0			0
$49$	0.592396	−	3.35965i	0.0846280	−	0.479949i
$50$	9.27379	+	7.78163i	1.31151	+	1.10049i
$51$		0			0
$52$	9.05690	+	3.29644i	1.25597	+	0.457134i
$53$	−4.95811			−0.681049			−0.340524	−	0.940236i	$-0.610605\pi$
$53$	−4.95811			−0.681049			−0.340524	+	0.940236i	$0.610605\pi$
$54$		0			0
$55$	−1.45336			−0.195971
$56$	−18.5141	−	6.73859i	−2.47406	−	0.900483i
$57$		0			0
$58$	12.7515	+	10.6998i	1.67435	+	1.40495i
$59$	1.48158	−	8.40247i	0.192886	−	1.09391i	−0.722512	−	0.691358i	$-0.757013\pi$
$59$	1.48158	−	8.40247i	0.192886	−	1.09391i	0.915398	−	0.402550i	$-0.131876\pi$
$60$		0			0
$61$	−0.971782	+	0.815422i	−0.124424	+	0.104404i	−0.702876	−	0.711312i	$-0.748101\pi$
$61$	−0.971782	+	0.815422i	−0.124424	+	0.104404i	0.578452	+	0.815716i	$0.303657\pi$
$62$	−7.88326	−	13.6542i	−1.00117	−	1.73409i
$63$		0			0
$64$	0.819078	−	1.41868i	0.102385	−	0.177336i
$65$	0.177519	+	1.00676i	0.0220185	+	0.124873i
$66$		0			0
$67$	−9.40420	+	3.42285i	−1.14891	+	0.418168i	−0.845122	−	0.534573i	$-0.820472\pi$
$67$	−9.40420	+	3.42285i	−1.14891	+	0.418168i	−0.303784	+	0.952741i	$0.598250\pi$
$68$	12.4363	−	4.52644i	1.50812	−	0.548911i
$69$		0			0
$70$	−0.663848	−	3.76487i	−0.0793450	−	0.449988i
$71$	5.91534	−	10.2457i	0.702022	−	1.21594i	−0.265733	−	0.964047i	$-0.585614\pi$
$71$	5.91534	−	10.2457i	0.702022	−	1.21594i	0.967755	−	0.251892i	$-0.0810526\pi$
$72$		0			0
$73$	4.11721	+	7.13122i	0.481883	+	0.834646i	0.999784	−	0.0207947i	$-0.00661964\pi$
$73$	4.11721	+	7.13122i	0.481883	+	0.834646i	−0.517901	+	0.855441i	$0.673286\pi$
$74$	−6.97565	+	5.85327i	−0.810903	+	0.680428i
$75$		0			0
$76$	0.0320889	−	0.181985i	0.00368085	−	0.0208751i
$77$	−7.67752	−	6.44220i	−0.874934	−	0.734157i
$78$		0			0
$79$	−10.3833	−	3.77920i	−1.16821	−	0.425193i	−0.316185	−	0.948698i	$-0.602402\pi$
$79$	−10.3833	−	3.77920i	−1.16821	−	0.425193i	−0.852023	+	0.523505i	$0.824624\pi$
$80$	−3.10607			−0.347269
$81$		0			0
$82$	19.5030			2.15375
$83$	−1.41875	−	0.516382i	−0.155728	−	0.0566803i	0.262980	−	0.964801i	$-0.415295\pi$
$83$	−1.41875	−	0.516382i	−0.155728	−	0.0566803i	−0.418708	+	0.908121i	$0.637517\pi$
$84$		0			0
$85$	1.07532	+	0.902302i	0.116635	+	0.0978684i
$86$	0.258770	−	1.46756i	0.0279039	−	0.158251i
$87$		0			0
$88$	−14.5287	+	12.1910i	−1.54876	+	1.29957i
$89$	−7.93629	−	13.7461i	−0.841245	−	1.45708i	−0.888843	−	0.458212i	$-0.848490\pi$
$89$	−7.93629	−	13.7461i	−0.841245	−	1.45708i	0.0475978	−	0.998867i	$-0.484843\pi$
$90$		0			0
$91$	−3.52481	+	6.10516i	−0.369501	+	0.639995i
$92$	−4.67752	−	26.5275i	−0.487665	−	2.76569i
$93$		0			0
$94$	22.9859	−	8.36619i	2.37082	−	0.862907i
$95$	0.0184183	−	0.00670372i	0.00188968	−	0.000687787i
$96$		0			0
$97$	3.23783	+	18.3626i	0.328751	+	1.86444i	0.481882	+	0.876236i	$0.339953\pi$
$97$	3.23783	+	18.3626i	0.328751	+	1.86444i	−0.153131	+	0.988206i	$0.548936\pi$
$98$	4.31908	−	7.48086i	0.436293	−	0.755681i
$99$		0			0
$100$	10.5458	+	18.2658i	1.05458	+	1.82658i
$101$	−6.96064	+	5.84067i	−0.692609	+	0.581168i	−0.919660	−	0.392715i	$-0.871536\pi$
$101$	−6.96064	+	5.84067i	−0.692609	+	0.581168i	0.227051	+	0.973883i	$0.427092\pi$
$102$		0			0
$103$	0.0452926	−	0.256867i	0.00446282	−	0.0253099i	−0.982495	−	0.186289i	$-0.940354\pi$
$103$	0.0452926	−	0.256867i	0.00446282	−	0.0253099i	0.986958	+	0.160979i	$0.0514651\pi$
$104$	10.2194	+	8.57510i	1.00210	+	0.840858i
$105$		0			0
$106$	−11.7973	−	4.29385i	−1.14585	−	0.417056i
$107$	−4.04189			−0.390744			−0.195372	−	0.980729i	$-0.562591\pi$
$107$	−4.04189			−0.390744			−0.195372	+	0.980729i	$0.562591\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	−3.45811	−	1.25865i	−0.329718	−	0.120008i
$111$		0			0
$112$	−16.4081	−	13.7680i	−1.55042	−	1.30095i
$113$	−0.240352	+	1.36310i	−0.0226104	+	0.128230i	−0.994024	−	0.109165i	$-0.965182\pi$
$113$	−0.240352	+	1.36310i	−0.0226104	+	0.128230i	0.971413	+	0.237395i	$0.0762935\pi$
$114$		0			0
$115$	2.18866	−	1.83651i	0.204094	−	0.171255i
$116$	14.5005	+	25.1155i	1.34633	+	2.33192i
$117$		0			0
$118$	10.8020	−	18.7096i	0.994405	−	1.72236i
$119$	1.68092	+	9.53298i	0.154090	+	0.873887i
$120$		0			0
$121$	1.27079	−	0.462531i	0.115527	−	0.0420482i
$122$	−3.01842	+	1.09861i	−0.273275	+	0.0994639i
$123$		0			0
$124$	−4.76991	−	27.0515i	−0.428351	−	2.42930i
$125$	−2.28833	+	3.96351i	−0.204675	+	0.354507i
$126$		0			0
$127$	3.31908	+	5.74881i	0.294521	+	0.510125i	0.974873	−	0.222760i	$-0.0715067\pi$
$127$	3.31908	+	5.74881i	0.294521	+	0.510125i	−0.680353	+	0.732885i	$0.738173\pi$
$128$	10.2194	−	8.57510i	0.903277	−	0.757939i
$129$		0			0
$130$	−0.449493	+	2.54920i	−0.0394231	+	0.223580i
$131$	9.68345	+	8.12538i	0.846047	+	0.709918i	0.958915	−	0.283692i	$-0.0915594\pi$
$131$	9.68345	+	8.12538i	0.846047	+	0.709918i	−0.112869	+	0.993610i	$0.536004\pi$
$132$		0			0
$133$	0.127011	+	0.0462284i	0.0110133	+	0.00400851i
$134$	−25.3405			−2.18908
$135$		0			0
$136$	18.3182			1.57077
$137$	9.97565	+	3.63084i	0.852277	+	0.310204i	0.730969	−	0.682411i	$-0.239069\pi$
$137$	9.97565	+	3.63084i	0.852277	+	0.310204i	0.121309	+	0.992615i	$0.461291\pi$
$138$		0			0
$139$	−5.71554	−	4.79591i	−0.484786	−	0.406783i	0.367368	−	0.930076i	$-0.380259\pi$
$139$	−5.71554	−	4.79591i	−0.484786	−	0.406783i	−0.852153	+	0.523292i	$0.824704\pi$
$140$	1.15657	−	6.55926i	0.0977483	−	0.554358i
$141$		0			0
$142$	22.9479	−	19.2556i	1.92575	−	1.61589i
$143$	3.39306	+	5.87695i	0.283742	+	0.491455i
$144$		0			0
$145$	−1.53802	+	2.66393i	−0.127725	+	0.221227i
$146$	3.62061	+	20.5335i	0.299644	+	1.69937i
$147$		0			0
$148$	−14.9081	+	5.42609i	−1.22544	+	0.446022i
$149$	−3.99747	+	1.45496i	−0.327486	+	0.119195i	−0.500531	−	0.865719i	$-0.666862\pi$
$149$	−3.99747	+	1.45496i	−0.327486	+	0.119195i	0.173045	+	0.984914i	$0.444639\pi$
$150$		0			0
$151$	0.0234708	+	0.133109i	0.00191002	+	0.0108323i	0.985748	−	0.168229i	$-0.0538049\pi$
$151$	0.0234708	+	0.133109i	0.00191002	+	0.0108323i	−0.983838	+	0.179062i	$0.942694\pi$
$152$	0.127889	−	0.221510i	0.0103731	−	0.0179668i
$153$		0			0
$154$	−12.6887	−	21.9774i	−1.02248	−	1.77099i
$155$	2.23190	−	1.87278i	0.179270	−	0.150426i
$156$		0			0
$157$	2.31403	−	13.1235i	0.184679	−	1.04737i	−0.741687	−	0.670746i	$-0.765974\pi$
$157$	2.31403	−	13.1235i	0.184679	−	1.04737i	0.926367	−	0.376623i	$-0.122915\pi$
$158$	−21.4329	−	17.9843i	−1.70511	−	1.43076i
$159$		0			0
$160$	−2.02094	−	0.735564i	−0.159770	−	0.0581514i
$161$	19.7023			1.55276
$162$		0			0
$163$	−9.76382			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$163$	−9.76382			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$164$	31.9295	+	11.6214i	2.49327	+	0.907477i
$165$		0			0
$166$	−2.92855	−	2.45734i	−0.227299	−	0.190727i
$167$	0.620615	−	3.51968i	0.0480246	−	0.272361i	−0.951334	−	0.308160i	$-0.900287\pi$
$167$	0.620615	−	3.51968i	0.0480246	−	0.272361i	0.999359	+	0.0357994i	$0.0113977\pi$
$168$		0			0
$169$	−6.30200	+	5.28801i	−0.484770	+	0.406770i
$170$	1.77719	+	3.07818i	0.136304	+	0.236086i
$171$		0			0
$172$	1.29813	−	2.24843i	0.0989817	−	0.171441i
$173$	−3.25877	−	18.4814i	−0.247760	−	1.40512i	−0.813995	−	0.580872i	$-0.802712\pi$
$173$	−3.25877	−	18.4814i	−0.247760	−	1.40512i	0.566235	−	0.824244i	$-0.308399\pi$
$174$		0			0
$175$	−14.4966	+	5.27633i	−1.09584	+	0.398853i
$176$	−19.3751	+	7.05196i	−1.46045	+	0.531562i
$177$		0			0
$178$	−6.97906	−	39.5802i	−0.523102	−	2.96666i
$179$	−2.54189	+	4.40268i	−0.189990	+	0.329072i	−0.945247	−	0.326357i	$-0.894179\pi$
$179$	−2.54189	+	4.40268i	−0.189990	+	0.329072i	0.755257	+	0.655429i	$0.227512\pi$
$180$		0			0
$181$	−3.57532	−	6.19264i	−0.265752	−	0.460295i	0.702009	−	0.712168i	$-0.252287\pi$
$181$	−3.57532	−	6.19264i	−0.265752	−	0.460295i	−0.967760	+	0.251873i	$0.918953\pi$
$182$	−13.6741	+	11.4739i	−1.01359	+	0.850505i
$183$		0			0
$184$	6.47431	−	36.7176i	0.477292	−	2.70686i
$185$	−1.28905	−	1.08164i	−0.0947727	−	0.0795238i
$186$		0			0
$187$	8.75624	+	3.18701i	0.640320	+	0.233057i
$188$	42.6168			3.10815
$189$		0			0
$190$	0.0496299			0.00360053
$191$	−9.87598	−	3.59456i	−0.714601	−	0.260093i	−0.0409690	−	0.999160i	$-0.513044\pi$
$191$	−9.87598	−	3.59456i	−0.714601	−	0.260093i	−0.673632	+	0.739067i	$0.735267\pi$
$192$		0			0
$193$	−7.76991	−	6.51973i	−0.559291	−	0.469301i	0.318782	−	0.947828i	$-0.396726\pi$
$193$	−7.76991	−	6.51973i	−0.559291	−	0.469301i	−0.878073	+	0.478527i	$0.841171\pi$
$194$	−8.19846	+	46.4958i	−0.588615	+	3.33820i
$195$		0			0
$196$	11.5287	−	9.67372i	0.823478	−	0.690980i
$197$	7.04189	+	12.1969i	0.501714	+	0.868994i	0.999998	+	0.00198008i	$0.000630281\pi$
$197$	7.04189	+	12.1969i	0.501714	+	0.868994i	−0.498284	+	0.867014i	$0.666036\pi$
$198$		0			0
$199$	−5.13816	+	8.89955i	−0.364234	+	0.630872i	−0.988653	−	0.150218i	$-0.952003\pi$
$199$	−5.13816	+	8.89955i	−0.364234	+	0.630872i	0.624419	+	0.781090i	$0.285336\pi$
$200$	5.06939	+	28.7500i	0.358460	+	2.03293i
$201$		0			0
$202$	−21.6202	+	7.86911i	−1.52119	+	0.553669i
$203$	−19.9329	+	7.25498i	−1.39901	+	0.509200i
$204$		0			0
$205$	0.625829	+	3.54925i	0.0437098	+	0.247891i
$206$	0.330222	−	0.571962i	0.0230077	−	0.0398505i
$207$		0			0
$208$	7.25150	+	12.5600i	0.502801	+	0.870877i
$209$	0.0996702	−	0.0836332i	0.00689433	−	0.00578503i
$210$		0			0
$211$	−1.24035	+	7.03439i	−0.0853894	+	0.484267i	0.911883	+	0.410451i	$0.134629\pi$
$211$	−1.24035	+	7.03439i	−0.0853894	+	0.484267i	−0.997272	+	0.0738159i	$0.976482\pi$
$212$	−16.7554	−	14.0594i	−1.15076	−	0.965605i
$213$		0			0
$214$	−9.61721	−	3.50038i	−0.657419	−	0.239281i
$215$	0.275378			0.0187806
$216$		0			0
$217$	20.0915			1.36390
$218$	−12.8576	−	4.67977i	−0.870824	−	0.316954i
$219$		0			0
$220$	−4.91147	−	4.12122i	−0.331132	−	0.277852i
$221$	1.13816	−	6.45480i	0.0765606	−	0.434197i
$222$		0			0
$223$	−7.91740	+	6.64349i	−0.530189	+	0.444881i	−0.868167	−	0.496273i	$-0.834702\pi$
$223$	−7.91740	+	6.64349i	−0.530189	+	0.444881i	0.337978	+	0.941154i	$0.390257\pi$
$224$	−7.41534	−	12.8438i	−0.495459	−	0.858159i
$225$		0			0
$226$	−1.75237	+	3.03520i	−0.116566	+	0.201899i
$227$	2.26130	+	12.8245i	0.150088	+	0.851189i	0.963140	+	0.268999i	$0.0866928\pi$
$227$	2.26130	+	12.8245i	0.150088	+	0.851189i	−0.813053	+	0.582190i	$0.802196\pi$
$228$		0			0
$229$	26.4047	−	9.61051i	1.74487	−	0.635081i	0.745368	−	0.666653i	$-0.232274\pi$
$229$	26.4047	−	9.61051i	1.74487	−	0.635081i	0.999501	+	0.0315726i	$0.0100515\pi$
$230$	6.79813	−	2.47432i	0.448256	−	0.163152i
$231$		0			0
$232$	6.97044	+	39.5313i	0.457632	+	2.59536i
$233$	−6.95723	+	12.0503i	−0.455784	+	0.789440i	−0.998733	−	0.0503252i	$-0.983974\pi$
$233$	−6.95723	+	12.0503i	−0.455784	+	0.789440i	0.542949	+	0.839765i	$0.317308\pi$
$234$		0			0
$235$	2.26011	+	3.91463i	0.147434	+	0.255363i
$236$	28.8332	−	24.1939i	1.87688	−	1.57489i
$237$		0			0
$238$	−4.25624	+	24.1384i	−0.275891	+	1.56466i
$239$	11.5057	+	9.65441i	0.744241	+	0.624492i	0.933973	−	0.357344i	$-0.116318\pi$
$239$	11.5057	+	9.65441i	0.744241	+	0.624492i	−0.189732	+	0.981836i	$0.560762\pi$
$240$		0			0
$241$	12.1912	+	4.43723i	0.785304	+	0.285827i	0.703382	−	0.710812i	$-0.251672\pi$
$241$	12.1912	+	4.43723i	0.785304	+	0.285827i	0.0819212	+	0.996639i	$0.473894\pi$
$242$	3.42427			0.220120
$243$		0			0
$244$	−5.59627			−0.358264
$245$	1.50000	+	0.545955i	0.0958315	+	0.0348798i
$246$		0			0
$247$	−0.0701076	−	0.0588272i	−0.00446084	−	0.00374309i
$248$	6.60220	−	37.4429i	0.419240	−	2.37763i
$249$		0			0
$250$	−8.87733	+	7.44896i	−0.561451	+	0.471114i
$251$	0.436289	+	0.755675i	0.0275383	+	0.0476978i	0.879466	−	0.475961i	$-0.157900\pi$
$251$	0.436289	+	0.755675i	0.0275383	+	0.0476978i	−0.851928	+	0.523659i	$0.824567\pi$
$252$		0			0
$253$	9.48293	−	16.4249i	0.596186	−	1.03263i
$254$	2.91875	+	16.5530i	0.183139	+	1.03863i
$255$		0			0
$256$	28.6634	−	10.4326i	1.79146	−	0.652040i
$257$	4.30066	−	1.56531i	0.268268	−	0.0976415i	−0.204384	−	0.978891i	$-0.565519\pi$
$257$	4.30066	−	1.56531i	0.268268	−	0.0976415i	0.472652	+	0.881249i	$0.343297\pi$
$258$		0			0
$259$	−2.01501	−	11.4277i	−0.125207	−	0.710084i
$260$	−2.25490	+	3.90560i	−0.139843	+	0.242215i
$261$		0			0
$262$	16.0039	+	27.7195i	0.988722	+	1.71252i
$263$	−3.29220	+	2.76249i	−0.203006	+	0.170342i	−0.738623	−	0.674119i	$-0.764524\pi$
$263$	−3.29220	+	2.76249i	−0.203006	+	0.170342i	0.535617	+	0.844461i	$0.320079\pi$
$264$		0			0
$265$	0.402856	−	2.28471i	0.0247472	−	0.140349i
$266$	0.262174	+	0.219990i	0.0160749	+	0.0134885i
$267$		0			0
$268$	−41.4864	−	15.0998i	−2.53418	−	0.922368i
$269$	−12.1257			−0.739315			−0.369657	−	0.929168i	$-0.620525\pi$
$269$	−12.1257			−0.739315			−0.369657	+	0.929168i	$0.620525\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	18.7135	+	6.81115i	1.13467	+	0.412987i
$273$		0			0
$274$	20.5915	+	17.2783i	1.24398	+	1.04382i
$275$	−2.57873	+	14.6247i	−0.155503	+	0.881901i
$276$		0			0
$277$	−20.5462	+	17.2403i	−1.23450	+	1.03587i	−0.236570	+	0.971615i	$0.576023\pi$
$277$	−20.5462	+	17.2403i	−1.23450	+	1.03587i	−0.997933	+	0.0642566i	$0.979532\pi$
$278$	−9.44609	−	16.3611i	−0.566539	−	0.981274i
$279$		0			0
$280$	4.60947	−	7.98384i	0.275469	−	0.477126i
$281$	−4.63310	−	26.2756i	−0.276388	−	1.56747i	−0.734519	−	0.678588i	$-0.762592\pi$
$281$	−4.63310	−	26.2756i	−0.276388	−	1.56747i	0.458131	−	0.888885i	$-0.348519\pi$
$282$		0			0
$283$	8.73308	−	3.17858i	0.519128	−	0.188947i	−0.0691496	−	0.997606i	$-0.522029\pi$
$283$	8.73308	−	3.17858i	0.519128	−	0.188947i	0.588277	+	0.808659i	$0.299806\pi$
$284$	49.0433	−	17.8503i	2.91018	−	1.05922i
$285$		0			0
$286$	2.98380	+	16.9220i	0.176436	+	1.00062i
$287$	−12.4265	+	21.5233i	−0.733512	+	1.27048i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−5.96657	+	5.00654i	−0.350369	+	0.293994i
$291$		0			0
$292$	−6.30793	+	35.7741i	−0.369144	+	2.09352i
$293$	15.0444	+	12.6238i	0.878904	+	0.737488i	0.965953	−	0.258716i	$-0.0832993\pi$
$293$	15.0444	+	12.6238i	0.878904	+	0.737488i	−0.0870493	+	0.996204i	$0.527744\pi$
$294$		0			0
$295$	3.75150	+	1.36543i	0.218421	+	0.0794986i
$296$	−21.9590			−1.27634
$297$		0			0
$298$	−10.7716			−0.623980
$299$	−12.5360	−	4.56272i	−0.724973	−	0.263869i
$300$		0			0
$301$	1.45471	+	1.22064i	0.0838479	+	0.0703568i
$302$	−0.0594300	+	0.337044i	−0.00341981	+	0.0193947i
$303$		0			0
$304$	0.213011	−	0.178737i	0.0122170	−	0.0102513i
$305$	−0.296789	−	0.514054i	−0.0169941	−	0.0294346i
$306$		0			0
$307$	−14.1716	+	24.5459i	−0.808815	+	1.40091i	0.104870	+	0.994486i	$0.466557\pi$
$307$	−14.1716	+	24.5459i	−0.808815	+	1.40091i	−0.913685	+	0.406423i	$0.866776\pi$
$308$	−7.67752	−	43.5414i	−0.437467	−	2.48100i
$309$		0			0
$310$	6.93242	−	2.52319i	0.393735	−	0.143308i
$311$	−1.92127	+	0.699287i	−0.108945	+	0.0396529i	−0.395918	−	0.918286i	$-0.629573\pi$
$311$	−1.92127	+	0.699287i	−0.108945	+	0.0396529i	0.286972	+	0.957939i	$0.407351\pi$
$312$		0			0
$313$	1.46064	+	8.28368i	0.0825601	+	0.468222i	0.997856	+	0.0654405i	$0.0208453\pi$
$313$	1.46064	+	8.28368i	0.0825601	+	0.468222i	−0.915296	+	0.402781i	$0.868044\pi$
$314$	16.8712	−	29.2218i	0.952099	−	1.64908i
$315$		0			0
$316$	−24.3726	−	42.2145i	−1.37106	−	2.37475i
$317$	−23.8457	+	20.0089i	−1.33931	+	1.12381i	−0.357505	+	0.933911i	$0.616373\pi$
$317$	−23.8457	+	20.0089i	−1.33931	+	1.12381i	−0.981803	+	0.189902i	$0.939183\pi$
$318$		0			0
$319$	−3.54576	+	20.1090i	−0.198524	+	1.12589i
$320$	0.587182	+	0.492704i	0.0328245	+	0.0275430i
$321$		0			0
$322$	46.8794	+	17.0627i	2.61249	+	0.950868i
$323$	−0.125667			−0.00699231
$324$		0			0
$325$	10.4456			0.579419
$326$	−23.2319	−	8.45572i	−1.28670	−	0.468319i
$327$		0			0
$328$	36.0278	+	30.2309i	1.98930	+	1.66922i
$329$	−5.41282	+	30.6976i	−0.298418	+	1.69241i
$330$		0			0
$331$	23.7711	−	19.9463i	1.30658	−	1.09635i	0.317609	−	0.948222i	$-0.397120\pi$
$331$	23.7711	−	19.9463i	1.30658	−	1.09635i	0.988968	−	0.148127i	$-0.0473245\pi$
$332$	−3.33022	−	5.76811i	−0.182770	−	0.316566i
$333$		0			0
$334$	4.52481	−	7.83721i	0.247587	−	0.428833i
$335$	−0.813148	−	4.61159i	−0.0444270	−	0.251958i
$336$		0			0
$337$	−22.2986	+	8.11603i	−1.21468	+	0.442108i	−0.868326	−	0.495995i	$-0.834804\pi$
$337$	−22.2986	+	8.11603i	−1.21468	+	0.442108i	−0.346357	+	0.938103i	$0.612581\pi$
$338$	−19.5744	+	7.12452i	−1.06471	+	0.387523i
$339$		0			0
$340$	1.07532	+	6.09845i	0.0583175	+	0.330735i
$341$	9.67024	−	16.7494i	0.523673	−	0.907028i
$342$		0			0
$343$	−5.78952	−	10.0277i	−0.312604	−	0.541447i
$344$	2.75284	−	2.30991i	0.148423	−	0.124542i
$345$		0			0
$346$	8.25150	−	46.7966i	0.443603	−	2.51580i
$347$	1.38532	+	1.16242i	0.0743676	+	0.0624018i	0.679214	−	0.733941i	$-0.262321\pi$
$347$	1.38532	+	1.16242i	0.0743676	+	0.0624018i	−0.604846	+	0.796342i	$0.706765\pi$
$348$		0			0
$349$	−14.3405	−	5.21951i	−0.767629	−	0.279394i	−0.0716245	−	0.997432i	$-0.522818\pi$
$349$	−14.3405	−	5.21951i	−0.767629	−	0.279394i	−0.696004	+	0.718038i	$0.745041\pi$
$350$	−39.0624			−2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	−30.4295	−	11.0754i	−1.61960	−	0.589485i	−0.636292	−	0.771448i	$-0.719533\pi$
$353$	−30.4295	−	11.0754i	−1.61960	−	0.589485i	−0.983305	+	0.181963i	$0.941755\pi$
$354$		0			0
$355$	4.24060	+	3.55829i	0.225068	+	0.188854i
$356$	12.1591	−	68.9577i	0.644431	−	3.65475i
$357$		0			0
$358$	−9.86097	+	8.27433i	−0.521168	+	0.437312i
$359$	−0.957234	−	1.65798i	−0.0505209	−	0.0875047i	0.839659	−	0.543114i	$-0.182755\pi$
$359$	−0.957234	−	1.65798i	−0.0505209	−	0.0875047i	−0.890180	+	0.455609i	$0.849421\pi$
$360$		0			0
$361$	9.49912	−	16.4530i	0.499954	−	0.865945i
$362$	−3.14409	−	17.8310i	−0.165249	−	0.937176i
$363$		0			0
$364$	−29.2237	+	10.6366i	−1.53174	+	0.557508i
$365$	−3.62061	+	1.31780i	−0.189512	+	0.0689766i
$366$		0			0
$367$	−4.66503	−	26.4567i	−0.243513	−	1.38103i	−0.823922	−	0.566704i	$-0.808218\pi$
$367$	−4.66503	−	26.4567i	−0.243513	−	1.38103i	0.580409	−	0.814325i	$-0.302893\pi$
$368$	20.2665	−	35.1026i	1.05646	−	1.82985i
$369$		0			0
$370$	−2.13041	−	3.68999i	−0.110755	−	0.191833i
$371$	12.2554	−	10.2835i	0.636267	−	0.533891i
$372$		0			0
$373$	2.57697	−	14.6147i	0.133431	−	0.756722i	−0.842509	−	0.538682i	$-0.818923\pi$
$373$	2.57697	−	14.6147i	0.133431	−	0.756722i	0.975940	−	0.218040i	$-0.0699664\pi$
$374$	18.0744	+	15.1663i	0.934607	+	0.784229i
$375$		0			0
$376$	55.4299	+	20.1749i	2.85858	+	1.04044i
$377$	14.3628			0.739721
$378$		0			0
$379$	−33.7870			−1.73552			−0.867762	−	0.496980i	$-0.834442\pi$
$379$	−33.7870			−1.73552			−0.867762	+	0.496980i	$0.834442\pi$
$380$	0.0812519	+	0.0295733i	0.00416814	+	0.00151708i
$381$		0			0
$382$	−20.3858	−	17.1057i	−1.04303	−	0.875204i
$383$	1.61128	−	9.13803i	0.0823326	−	0.466932i	−0.915568	−	0.402164i	$-0.868258\pi$
$383$	1.61128	−	9.13803i	0.0823326	−	0.466932i	0.997900	−	0.0647678i	$-0.0206307\pi$
$384$		0			0
$385$	3.59240	−	3.01438i	0.183085	−	0.153627i
$386$	−12.8414	−	22.2419i	−0.653608	−	1.13208i
$387$		0			0
$388$	−41.1279	+	71.2357i	−2.08796	+	3.61644i
$389$	2.77466	+	15.7359i	0.140681	+	0.797841i	0.970734	+	0.240157i	$0.0771989\pi$
$389$	2.77466	+	15.7359i	0.140681	+	0.797841i	−0.830053	+	0.557684i	$0.811690\pi$
$390$		0			0
$391$	−17.2135	+	6.26519i	−0.870523	+	0.316844i
$392$	19.5744	−	7.12452i	0.988659	−	0.359842i
$393$		0			0
$394$	6.19253	+	35.1196i	0.311975	+	1.76930i
$395$	2.58512	−	4.47756i	0.130072	−	0.225291i
$396$		0			0
$397$	−9.85251	−	17.0650i	−0.494483	−	0.856470i	0.505496	−	0.862829i	$-0.331309\pi$
$397$	−9.85251	−	17.0650i	−0.494483	−	0.856470i	−0.999980	+	0.00635841i	$0.997976\pi$
$398$	−19.9329	+	16.7257i	−0.999145	+	0.838382i
$399$		0			0
$400$	−5.51114	+	31.2553i	−0.275557	+	1.56276i
$401$	−0.879385	−	0.737892i	−0.0439144	−	0.0368486i	0.620566	−	0.784154i	$-0.286903\pi$
$401$	−0.879385	−	0.737892i	−0.0439144	−	0.0368486i	−0.664481	+	0.747305i	$0.731347\pi$
$402$		0			0
$403$	−12.7836	−	4.65284i	−0.636796	−	0.231775i
$404$	−40.0847			−1.99429
$405$		0			0
$406$	−53.7110			−2.66563
$407$	−10.4966	−	3.82045i	−0.520297	−	0.189373i
$408$		0			0
$409$	−2.37551	−	1.99329i	−0.117462	−	0.0985620i	0.582165	−	0.813071i	$-0.302206\pi$
$409$	−2.37551	−	1.99329i	−0.117462	−	0.0985620i	−0.699627	+	0.714509i	$0.746650\pi$
$410$	−1.58466	+	8.98703i	−0.0782606	+	0.443838i
$411$		0			0
$412$	0.881445	−	0.739620i	0.0434257	−	0.0364385i
$413$	13.7652	+	23.8420i	0.677340	+	1.17319i
$414$		0			0
$415$	0.353226	−	0.611806i	0.0173392	−	0.0300324i
$416$	1.74376	+	9.88933i	0.0854947	+	0.484864i
$417$		0			0
$418$	0.309582	−	0.112679i	0.0151422	−	0.00551130i
$419$	33.3114	−	12.1244i	1.62737	−	0.592314i	0.642602	−	0.766200i	$-0.277855\pi$
$419$	33.3114	−	12.1244i	1.62737	−	0.592314i	0.984766	+	0.173886i	$0.0556325\pi$
$420$		0			0
$421$	1.60055	+	9.07716i	0.0780059	+	0.442394i	0.998648	+	0.0519855i	$0.0165550\pi$
$421$	1.60055	+	9.07716i	0.0780059	+	0.442394i	−0.920642	+	0.390408i	$0.872334\pi$
$422$	−9.04323	+	15.6633i	−0.440218	+	0.762479i
$423$		0			0
$424$	−15.1373	−	26.2185i	−0.735131	−	1.27328i
$425$	10.9875	−	9.21962i	0.532973	−	0.447217i
$426$		0			0
$427$	0.710790	−	4.03109i	0.0343975	−	0.195078i
$428$	−13.6591	−	11.4613i	−0.660238	−	0.554005i
$429$		0			0
$430$	0.655230	+	0.238484i	0.0315980	+	0.0115007i
$431$	−11.5794			−0.557758			−0.278879	−	0.960326i	$-0.589963\pi$
$431$	−11.5794			−0.557758			−0.278879	+	0.960326i	$0.589963\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	47.8055	+	17.3998i	2.29474	+	0.835215i
$435$		0			0
$436$	−18.2613	−	15.3230i	−0.874557	−	0.733841i
$437$	−0.0444153	+	0.251892i	−0.00212467	+	0.0120496i
$438$		0			0
$439$	22.2199	−	18.6447i	1.06050	−	0.889862i	0.0663388	−	0.997797i	$-0.478868\pi$
$439$	22.2199	−	18.6447i	1.06050	−	0.889862i	0.994158	+	0.107935i	$0.0344238\pi$
$440$	−4.43717	−	7.68540i	−0.211534	−	0.366387i
$441$		0			0
$442$	8.29813	−	14.3728i	0.394702	−	0.683644i
$443$	−5.36437	−	30.4229i	−0.254869	−	1.44543i	−0.796409	−	0.604759i	$-0.793270\pi$
$443$	−5.36437	−	30.4229i	−0.254869	−	1.44543i	0.541540	−	0.840675i	$-0.317841\pi$
$444$		0			0
$445$	6.97906	−	2.54017i	0.330839	−	0.120416i
$446$	−24.5920	+	8.95075i	−1.16446	+	0.423830i
$447$		0			0
$448$	0.917871	+	5.20550i	0.0433653	+	0.245937i
$449$	−19.5410	+	33.8460i	−0.922197	+	1.59729i	−0.126190	+	0.992006i	$0.540275\pi$
$449$	−19.5410	+	33.8460i	−0.922197	+	1.59729i	−0.796008	+	0.605287i	$0.793059\pi$
$450$		0			0
$451$	11.9620	+	20.7188i	0.563268	+	0.975608i
$452$	−4.67752	+	3.92490i	−0.220012	+	0.184612i
$453$		0			0
$454$	−5.72580	+	32.4726i	−0.268725	+	1.52402i
$455$	−2.52687	−	2.12030i	−0.118462	−	0.0994012i
$456$		0			0
$457$	1.41400	+	0.514654i	0.0661441	+	0.0240745i	0.374880	−	0.927073i	$-0.377684\pi$
$457$	1.41400	+	0.514654i	0.0661441	+	0.0240745i	−0.308736	+	0.951148i	$0.599906\pi$
$458$	71.1498			3.32461
$459$		0			0
$460$	12.6040			0.587665
$461$	24.6548	+	8.97362i	1.14829	+	0.417943i	0.844900	−	0.534924i	$-0.179660\pi$
$461$	24.6548	+	8.97362i	1.14829	+	0.417943i	0.303389	+	0.952867i	$0.401882\pi$
$462$		0			0
$463$	5.17571	+	4.34293i	0.240536	+	0.201833i	0.755084	−	0.655628i	$-0.227596\pi$
$463$	5.17571	+	4.34293i	0.240536	+	0.201833i	−0.514549	+	0.857461i	$0.672040\pi$
$464$	−7.57785	+	42.9761i	−0.351793	+	1.99512i
$465$		0			0
$466$	−26.9898	+	22.6471i	−1.25028	+	1.04911i
$467$	16.8735	+	29.2257i	0.780810	+	1.35240i	0.931470	+	0.363818i	$0.118527\pi$
$467$	16.8735	+	29.2257i	0.780810	+	1.35240i	−0.150660	+	0.988586i	$0.548140\pi$
$468$		0			0
$469$	16.1459	−	27.9655i	0.745548	−	1.29133i
$470$	1.98751	+	11.2717i	0.0916771	+	0.519926i
$471$		0			0
$472$	48.9556	−	17.8184i	2.25337	−	0.820158i
$473$	1.71776	−	0.625213i	0.0789826	−	0.0287473i
$474$		0			0
$475$	−0.0347772	−	0.197231i	−0.00159569	−	0.00904960i
$476$	−21.3516	+	36.9821i	−0.978651	+	1.69507i
$477$		0			0
$478$	19.0155	+	32.9358i	0.869748	+	1.50645i
$479$	−8.52347	+	7.15204i	−0.389447	+	0.326785i	−0.816398	−	0.577490i	$-0.804032\pi$
$479$	−8.52347	+	7.15204i	−0.389447	+	0.326785i	0.426951	+	0.904275i	$0.359588\pi$
$480$		0			0
$481$	−1.36437	+	7.73773i	−0.0622099	+	0.352810i
$482$	25.1648	+	21.1158i	1.14622	+	0.961796i
$483$		0			0
$484$	5.60607	+	2.04044i	0.254821	+	0.0927473i
$485$	−8.72462			−0.396165
$486$		0			0
$487$	−4.74691			−0.215103			−0.107552	−	0.994200i	$-0.534301\pi$
$487$	−4.74691			−0.215103			−0.107552	+	0.994200i	$0.534301\pi$
$488$	−7.27884	−	2.64928i	−0.329497	−	0.119927i
$489$		0			0
$490$	3.09627	+	2.59808i	0.139875	+	0.117369i
$491$	−3.87939	+	22.0011i	−0.175074	+	0.992895i	0.762984	+	0.646417i	$0.223734\pi$
$491$	−3.87939	+	22.0011i	−0.175074	+	0.992895i	−0.938058	+	0.346478i	$0.887378\pi$
$492$		0			0
$493$	15.1079	−	12.6770i	0.680425	−	0.570944i
$494$	−0.115867	−	0.200688i	−0.00521310	−	0.00902936i
$495$		0			0
$496$	20.6668	−	35.7960i	0.927969	−	1.60729i
$497$	6.62882	+	37.5939i	0.297343	+	1.68632i
$498$		0			0
$499$	9.83022	−	3.57791i	0.440061	−	0.160169i	−0.112481	−	0.993654i	$-0.535880\pi$
$499$	9.83022	−	3.57791i	0.440061	−	0.160169i	0.552543	+	0.833485i	$0.313658\pi$
$500$	−18.9722	+	6.90533i	−0.848465	+	0.308816i
$501$		0			0
$502$	0.383666	+	2.17588i	0.0171239	+	0.0971142i
$503$	12.5209	−	21.6869i	0.558281	−	0.966972i	−0.439359	−	0.898312i	$-0.644794\pi$
$503$	12.5209	−	21.6869i	0.558281	−	0.966972i	0.997640	−	0.0686600i	$-0.0218723\pi$
$504$		0			0
$505$	−2.12583	−	3.68204i	−0.0945982	−	0.163849i
$506$	36.7879	−	30.8687i	1.63542	−	1.37228i
$507$		0			0
$508$	−5.08512	+	28.8392i	−0.225616	+	1.27953i
$509$	−13.8366	−	11.6103i	−0.613297	−	0.514618i	0.282391	−	0.959299i	$-0.408872\pi$
$509$	−13.8366	−	11.6103i	−0.613297	−	0.514618i	−0.895689	+	0.444682i	$0.853317\pi$
$510$		0			0
$511$	−24.9675	−	9.08743i	−1.10450	−	0.402004i
$512$	50.5553			2.23425
$513$		0			0
$514$	11.5885			0.511148
$515$	0.114685	+	0.0417419i	0.00505362	+	0.00183937i
$516$		0			0
$517$	22.9859	+	19.2875i	1.01092	+	0.848262i
$518$	5.10220	−	28.9360i	0.224178	−	1.27137i
$519$		0			0
$520$	−4.78177	+	4.01239i	−0.209695	+	0.175955i
$521$	−12.9791	−	22.4804i	−0.568623	−	0.984883i	−0.996703	−	0.0811425i	$-0.974143\pi$
$521$	−12.9791	−	22.4804i	−0.568623	−	0.984883i	0.428080	−	0.903741i	$-0.359190\pi$
$522$		0			0
$523$	−12.7973	+	22.1655i	−0.559585	+	0.969230i	0.437946	+	0.899001i	$0.355706\pi$
$523$	−12.7973	+	22.1655i	−0.559585	+	0.969230i	−0.997531	+	0.0702283i	$0.977627\pi$
$524$	9.68345	+	54.9176i	0.423023	+	2.39908i
$525$		0			0
$526$	−10.2258	+	3.72189i	−0.445866	+	0.162282i
$527$	−17.5535	+	6.38895i	−0.764642	+	0.278307i
$528$		0			0
$529$	2.48040	+	14.0670i	0.107843	+	0.611611i
$530$	2.93717	−	5.08732i	0.127582	−	0.220979i
$531$		0			0
$532$	0.298133	+	0.516382i	0.0129257	+	0.0223880i
$533$	12.8910	−	10.8168i	0.558371	−	0.468529i
$534$		0			0
$535$	0.328411	−	1.86251i	0.0141985	−	0.0805234i
$536$	−46.8114	−	39.2794i	−2.02194	−	1.69661i
$537$		0			0
$538$	−28.8516	−	10.5011i	−1.24388	−	0.452736i
$539$	10.5963			0.456414
$540$		0			0
$541$	27.8476			1.19726			0.598631	−	0.801025i	$-0.295712\pi$
$541$	27.8476			1.19726			0.598631	+	0.801025i	$0.295712\pi$
$542$	−0.761297	−	0.277089i	−0.0327005	−	0.0119020i
$543$		0			0
$544$	10.5628	+	8.86327i	0.452878	+	0.380010i
$545$	0.439064	−	2.49005i	0.0188074	−	0.106662i
$546$		0			0
$547$	−4.52616	+	3.79790i	−0.193525	+	0.162386i	−0.734401	−	0.678715i	$-0.762537\pi$
$547$	−4.52616	+	3.79790i	−0.193525	+	0.162386i	0.540877	+	0.841102i	$0.318093\pi$
$548$	23.4158	+	40.5574i	1.00027	+	1.73253i
$549$		0			0
$550$	−18.8011	+	32.5645i	−0.801683	+	1.38856i
$551$	−0.0478189	−	0.271194i	−0.00203715	−	0.0115533i
$552$		0			0
$553$	33.5035	−	12.1943i	1.42471	−	0.518553i
$554$	−63.8180	+	23.2278i	−2.71136	+	0.986856i
$555$		0			0
$556$	−5.71554	−	32.4144i	−0.242393	−	1.37468i
$557$	13.3525	−	23.1272i	0.565764	−	0.979932i	−0.431214	−	0.902250i	$-0.641915\pi$
$557$	13.3525	−	23.1272i	0.565764	−	0.979932i	0.996978	−	0.0776824i	$-0.0247520\pi$
$558$		0			0
$559$	−0.642903	−	1.11354i	−0.0271919	−	0.0470978i
$560$	7.67752	−	6.44220i	0.324434	−	0.272233i
$561$		0			0
$562$	11.7314	−	66.5322i	0.494860	−	2.80649i
$563$	−27.6254	−	23.1805i	−1.16427	−	0.976941i	−0.164317	−	0.986408i	$-0.552542\pi$
$563$	−27.6254	−	23.1805i	−1.16427	−	0.976941i	−0.999955	+	0.00946682i	$0.996987\pi$
$564$		0			0
$565$	−0.608593	−	0.221510i	−0.0256037	−	0.00931899i
$566$	23.5321			0.989127
$567$		0			0
$568$	72.2390			3.03108
$569$	−8.50165	−	3.09435i	−0.356408	−	0.129722i	0.157610	−	0.987501i	$-0.449621\pi$
$569$	−8.50165	−	3.09435i	−0.356408	−	0.129722i	−0.514018	+	0.857780i	$0.671843\pi$
$570$		0			0
$571$	23.4249	+	19.6558i	0.980301	+	0.822571i	0.984135	−	0.177422i	$-0.0567758\pi$
$571$	23.4249	+	19.6558i	0.980301	+	0.822571i	−0.00383345	+	0.999993i	$0.501220\pi$
$572$	−5.19846	+	29.4819i	−0.217359	+	1.23270i
$573$		0			0
$574$	−48.2071	+	40.4506i	−2.01213	+	1.68838i
$575$	−14.5967	−	25.2823i	−0.608726	−	1.05434i
$576$		0			0
$577$	12.5744	−	21.7796i	0.523481	−	0.906696i	−0.476146	−	0.879367i	$-0.657966\pi$
$577$	12.5744	−	21.7796i	0.523481	−	0.906696i	0.999626	−	0.0273292i	$-0.00870022\pi$
$578$	3.51754	+	19.9490i	0.146310	+	0.829768i
$579$		0			0
$580$	−12.7515	+	4.64117i	−0.529477	+	0.192714i
$581$	4.57785	−	1.66620i	0.189921	−	0.0691256i
$582$		0			0
$583$	−2.67422	−	15.1663i	−0.110755	−	0.628122i
$584$	−25.1400	+	43.5437i	−1.04030	+	1.80185i
$585$		0			0
$586$	24.8640	+	43.0656i	1.02712	+	1.77903i
$587$	−15.9900	+	13.4172i	−0.659979	+	0.553789i	−0.910081	−	0.414431i	$-0.863981\pi$
$587$	−15.9900	+	13.4172i	−0.659979	+	0.553789i	0.250101	+	0.968220i	$0.419536\pi$
$588$		0			0
$589$	−0.0452926	+	0.256867i	−0.00186625	+	0.0105840i
$590$	7.74376	+	6.49778i	0.318805	+	0.267509i
$591$		0			0
$592$	−22.4329	−	8.16490i	−0.921986	−	0.335575i
$593$	−15.6212			−0.641488			−0.320744	−	0.947166i	$-0.603933\pi$
$593$	−15.6212			−0.641488			−0.320744	+	0.947166i	$0.603933\pi$
$594$		0			0
$595$	−4.52940			−0.185687
$596$	−17.6348	−	6.41852i	−0.722348	−	0.262913i
$597$		0			0
$598$	−25.8764	−	21.7129i	−1.05817	−	0.887907i
$599$	0.0778483	−	0.441500i	0.00318080	−	0.0180392i	−0.983176	−	0.182660i	$-0.941529\pi$
$599$	0.0778483	−	0.441500i	0.00318080	−	0.0180392i	0.986357	+	0.164621i	$0.0526402\pi$
$600$		0			0
$601$	−13.5378	+	11.3595i	−0.552217	+	0.463365i	−0.875691	−	0.482872i	$-0.839594\pi$
$601$	−13.5378	+	11.3595i	−0.552217	+	0.463365i	0.323474	+	0.946237i	$0.395149\pi$
$602$	2.40420	+	4.16420i	0.0979879	+	0.169720i
$603$		0			0
$604$	−0.298133	+	0.516382i	−0.0121309	+	0.0210113i
$605$	0.109881	+	0.623166i	0.00446729	+	0.0253353i
$606$		0			0
$607$	−24.6186	+	8.96042i	−0.999236	+	0.363692i	−0.789290	−	0.614021i	$-0.789551\pi$
$607$	−24.6186	+	8.96042i	−0.999236	+	0.363692i	−0.209946	+	0.977713i	$0.567329\pi$
$608$	0.180922	−	0.0658503i	0.00733736	−	0.00267058i
$609$		0			0
$610$	−0.260992	−	1.48016i	−0.0105673	−	0.0599299i
$611$	10.5530	−	18.2784i	0.426930	−	0.739465i
$612$		0			0
$613$	−7.27719	−	12.6045i	−0.293923	−	0.509089i	0.680811	−	0.732459i	$-0.261628\pi$
$613$	−7.27719	−	12.6045i	−0.293923	−	0.509089i	−0.974734	+	0.223370i	$0.928294\pi$
$614$	−54.9771	+	46.1312i	−2.21869	+	1.86170i
$615$		0			0
$616$	10.6267	−	60.2670i	0.428162	−	2.42823i
$617$	−10.7404	−	9.01223i	−0.432390	−	0.362819i	0.400462	−	0.916313i	$-0.368849\pi$
$617$	−10.7404	−	9.01223i	−0.432390	−	0.362819i	−0.832853	+	0.553495i	$0.813294\pi$
$618$		0			0
$619$	29.7999	+	10.8463i	1.19776	+	0.435949i	0.862442	−	0.506155i	$-0.168934\pi$
$619$	29.7999	+	10.8463i	1.19776	+	0.435949i	0.335319	+	0.942105i	$0.391156\pi$
$620$	12.8530			0.516188
$621$		0			0
$622$	−5.17705			−0.207581
$623$	48.1271	+	17.5168i	1.92817	+	0.701797i
$624$		0			0
$625$	16.6721	+	13.9895i	0.666882	+	0.559581i
$626$	−3.69846	+	20.9750i	−0.147820	+	0.838331i
$627$		0			0
$628$	45.0335	−	37.7876i	1.79703	−	1.50789i
$629$	5.39440	+	9.34337i	0.215089	+	0.372545i
$630$		0			0
$631$	19.2879	−	33.4077i	0.767840	−	1.32994i	−0.170892	−	0.985290i	$-0.554665\pi$
$631$	19.2879	−	33.4077i	0.767840	−	1.32994i	0.938732	−	0.344648i	$-0.112002\pi$
$632$	−11.7160	−	66.4448i	−0.466038	−	2.64303i
$633$		0			0
$634$	−74.0663	+	26.9579i	−2.94155	+	1.07064i
$635$	−2.91875	+	1.06234i	−0.115827	+	0.0421576i
$636$		0			0
$637$	−1.29426	−	7.34013i	−0.0512806	−	0.290827i
$638$	−25.8516	+	44.7763i	−1.02348	+	1.77271i
$639$		0			0
$640$	3.12108	+	5.40587i	0.123372	+	0.213686i
$641$	23.4538	−	19.6801i	0.926371	−	0.777317i	−0.0487917	−	0.998809i	$-0.515537\pi$
$641$	23.4538	−	19.6801i	0.926371	−	0.777317i	0.975162	+	0.221492i	$0.0710926\pi$
$642$		0			0
$643$	−5.94310	+	33.7050i	−0.234373	+	1.32919i	0.609558	+	0.792742i	$0.291347\pi$
$643$	−5.94310	+	33.7050i	−0.234373	+	1.32919i	−0.843930	+	0.536453i	$0.819764\pi$
$644$	66.5818	+	55.8687i	2.62369	+	2.20154i
$645$		0			0
$646$	−0.299011	−	0.108831i	−0.0117644	−	0.00428190i
$647$	12.8726			0.506073			0.253037	−	0.967457i	$-0.418571\pi$
$647$	12.8726			0.506073			0.253037	+	0.967457i	$0.418571\pi$
$648$		0			0
$649$	26.5012			1.04026
$650$	24.8542	+	9.04617i	0.974860	+	0.354820i
$651$		0			0
$652$	−32.9957	−	27.6867i	−1.29221	−	1.08429i
$653$	1.96555	−	11.1472i	0.0769178	−	0.436223i	−0.921892	−	0.387447i	$-0.873357\pi$
$653$	1.96555	−	11.1472i	0.0769178	−	0.436223i	0.998810	−	0.0487755i	$-0.0155319\pi$
$654$		0			0
$655$	−4.53099	+	3.80195i	−0.177041	+	0.148555i
$656$	25.5646	+	44.2793i	0.998132	+	1.72881i
$657$		0			0
$658$	−39.4641	+	68.3538i	−1.53847	+	2.66471i
$659$	2.39100	+	13.5600i	0.0931400	+	0.528223i	0.995301	+	0.0968246i	$0.0308686\pi$
$659$	2.39100	+	13.5600i	0.0931400	+	0.528223i	−0.902161	+	0.431399i	$0.858020\pi$
$660$		0			0
$661$	19.0446	−	6.93166i	0.740748	−	0.269610i	0.0560409	−	0.998428i	$-0.482152\pi$
$661$	19.0446	−	6.93166i	0.740748	−	0.269610i	0.684707	+	0.728818i	$0.259930\pi$
$662$	73.8346	−	26.8736i	2.86966	−	1.04447i
$663$		0			0
$664$	−1.60085	−	9.07888i	−0.0621251	−	0.352329i
$665$	−0.0316221	+	0.0547710i	−0.00122625	+	0.00212393i
$666$		0			0
$667$	−20.0706	−	34.7633i	−0.777136	−	1.34604i
$668$	12.0778	−	10.1345i	0.467306	−	0.392116i
$669$		0			0
$670$	2.05896	−	11.6770i	0.0795447	−	0.451120i
$671$	−3.01842	−	2.53275i	−0.116525	−	0.0977759i
$672$		0			0
$673$	28.7028	+	10.4470i	1.10641	+	0.402701i	0.829676	−	0.558245i	$-0.188525\pi$
$673$	28.7028	+	10.4470i	1.10641	+	0.402701i	0.276736	+	0.960946i	$0.410747\pi$
$674$	−60.0856			−2.31441
$675$		0			0
$676$	−36.2918			−1.39584
$677$	−3.49495	−	1.27206i	−0.134322	−	0.0488891i	0.273985	−	0.961734i	$-0.411658\pi$
$677$	−3.49495	−	1.27206i	−0.134322	−	0.0488891i	−0.408306	+	0.912845i	$0.633880\pi$
$678$		0			0
$679$	−46.0886	−	38.6729i	−1.76872	−	1.48413i
$680$	−1.48839	+	8.44107i	−0.0570771	+	0.323700i
$681$		0			0
$682$	37.5146	−	31.4785i	1.43651	−	1.20537i
$683$	−10.8735	−	18.8334i	−0.416061	−	0.720639i	0.579478	−	0.814988i	$-0.303256\pi$
$683$	−10.8735	−	18.8334i	−0.416061	−	0.720639i	−0.995539	+	0.0943487i	$0.969923\pi$
$684$		0			0
$685$	−2.48364	+	4.30179i	−0.0948950	+	0.164363i
$686$	−5.09121	−	28.8737i	−0.194383	−	1.10240i
$687$		0			0
$688$	3.67112	−	1.33618i	0.139960	−	0.0509414i
$689$	−10.1792	+	3.70491i	−0.387795	+	0.141146i
$690$		0			0
$691$	−6.52827	−	37.0237i	−0.248347	−	1.40845i	−0.812589	−	0.582838i	$-0.801942\pi$
$691$	−6.52827	−	37.0237i	−0.248347	−	1.40845i	0.564241	−	0.825610i	$-0.309169\pi$
$692$	41.3940	−	71.6965i	1.57356	−	2.72549i
$693$		0			0
$694$	2.28952	+	3.96556i	0.0869088	+	0.150530i
$695$	2.67436	−	2.24406i	0.101444	−	0.0851219i
$696$		0			0
$697$	4.01249	−	22.7560i	0.151984	−	0.861943i
$698$	−29.6013	−	24.8385i	−1.12043	−	0.940149i
$699$		0			0
$700$	−63.9514	−	23.2764i	−2.41713	−	0.879765i
$701$	−23.3351			−0.881355			−0.440678	−	0.897665i	$-0.645262\pi$
$701$	−23.3351			−0.881355			−0.440678	+	0.897665i	$0.645262\pi$
$702$		0			0
$703$	0.150644			0.00568166
$704$	4.78136	+	1.74027i	0.180204	+	0.0655890i
$705$		0			0
$706$	−62.8119	−	52.7054i	−2.36396	−	1.98359i
$707$	5.09121	−	28.8737i	0.191475	−	1.08591i
$708$		0			0
$709$	5.03983	−	4.22892i	0.189275	−	0.158820i	−0.543226	−	0.839586i	$-0.682797\pi$
$709$	5.03983	−	4.22892i	0.189275	−	0.158820i	0.732501	+	0.680766i	$0.238353\pi$
$710$	7.00846	+	12.1390i	0.263023	+	0.455569i
$711$		0			0
$712$	48.4595	−	83.9343i	1.81610	−	3.14557i
$713$	6.60220	+	37.4429i	0.247254	+	1.40225i
$714$		0			0
$715$	−2.98380	+	1.08602i	−0.111588	+	0.0406147i
$716$	−21.0744	+	7.67047i	−0.787589	+	0.286659i
$717$		0			0
$718$	−0.841777	−	4.77396i	−0.0314148	−	0.178162i
$719$	−8.41622	+	14.5773i	−0.313872	+	0.543642i	−0.979197	−	0.202911i	$-0.934960\pi$
$719$	−8.41622	+	14.5773i	−0.313872	+	0.543642i	0.665325	+	0.746554i	$0.268293\pi$
$720$		0			0
$721$	0.420807	+	0.728860i	0.0156717	+	0.0271442i
$722$	36.8508	−	30.9215i	1.37144	−	1.15078i
$723$		0			0
$724$	5.47771	−	31.0656i	0.203578	−	1.15455i
$725$	24.0772	+	20.2032i	0.894205	+	0.750327i
$726$		0			0
$727$	−24.0205	−	8.74276i	−0.890872	−	0.324251i	−0.144283	−	0.989536i	$-0.546088\pi$
$727$	−24.0205	−	8.74276i	−0.890872	−	0.324251i	−0.746589	+	0.665285i	$0.768310\pi$
$728$	−43.0455			−1.59537
$729$		0			0
$730$	−9.75608			−0.361089
$731$	−1.65910	−	0.603863i	−0.0613640	−	0.0223347i
$732$		0			0
$733$	−11.3359	−	9.51195i	−0.418701	−	0.351332i	0.408968	−	0.912549i	$-0.365889\pi$
$733$	−11.3359	−	9.51195i	−0.418701	−	0.351332i	−0.827669	+	0.561217i	$0.810333\pi$
$734$	11.8123	−	66.9907i	0.435999	−	2.47267i
$735$		0			0
$736$	21.4991	−	18.0399i	0.792468	−	0.664960i
$737$	−15.5424	−	26.9202i	−0.572510	−	0.991616i
$738$		0			0
$739$	−4.59539	+	7.95945i	−0.169044	+	0.292793i	−0.938084	−	0.346408i	$-0.887401\pi$
$739$	−4.59539	+	7.95945i	−0.169044	+	0.292793i	0.769040	+	0.639201i	$0.220735\pi$
$740$	−1.28905	−	7.31056i	−0.0473864	−	0.268741i
$741$		0			0
$742$	38.0660	−	13.8549i	1.39745	−	0.508629i
$743$	41.7686	−	15.2025i	1.53234	−	0.557727i	0.568149	−	0.822926i	$-0.307660\pi$
$743$	41.7686	−	15.2025i	1.53234	−	0.557727i	0.964194	+	0.265199i	$0.0854377\pi$
$744$		0			0
$745$	−0.345647	−	1.96026i	−0.0126635	−	0.0718185i
$746$	18.7883	−	32.5423i	0.687890	−	1.19146i
$747$		0			0
$748$	20.5535	+	35.5997i	0.751510	+	1.30165i
$749$	9.99067	−	8.38316i	0.365051	−	0.306314i
$750$		0			0
$751$	−6.21765	+	35.2621i	−0.226885	+	1.28673i	0.632163	+	0.774836i	$0.282167\pi$
$751$	−6.21765	+	35.2621i	−0.226885	+	1.28673i	−0.859048	+	0.511895i	$0.828944\pi$
$752$	49.1245	+	41.2204i	1.79139	+	1.50315i
$753$		0			0
$754$	34.1746	+	12.4385i	1.24456	+	0.452985i
$755$	−0.0632441			−0.00230169
$756$		0			0
$757$	−45.8976			−1.66818			−0.834088	−	0.551632i	$-0.814005\pi$
$757$	−45.8976			−1.66818			−0.834088	+	0.551632i	$0.814005\pi$
$758$	−80.3924	−	29.2604i	−2.91998	−	1.06279i
$759$		0			0
$760$	0.0916810	+	0.0769295i	0.00332562	+	0.00279053i
$761$	6.45888	−	36.6301i	0.234134	−	1.32784i	−0.610295	−	0.792174i	$-0.708949\pi$
$761$	6.45888	−	36.6301i	0.234134	−	1.32784i	0.844429	−	0.535667i	$-0.179940\pi$
$762$		0			0
$763$	13.3568	−	11.2077i	0.483550	−	0.405747i
$764$	−23.1819	−	40.1522i	−0.838690	−	1.45265i
$765$		0			0
$766$	11.7476	−	20.3475i	0.424459	−	0.735185i
$767$	−3.23695	−	18.3576i	−0.116879	−	0.662856i
$768$		0			0
$769$	36.0219	−	13.1109i	1.29898	−	0.472791i	0.402317	−	0.915500i	$-0.368205\pi$
$769$	36.0219	−	13.1109i	1.29898	−	0.472791i	0.896665	+	0.442710i	$0.145983\pi$
$770$	11.1582	−	4.06126i	0.402114	−	0.146358i
$771$		0			0
$772$	−7.76991	−	44.0654i	−0.279645	−	1.58595i
$773$	26.4136	−	45.7497i	0.950031	−	1.64550i	0.204680	−	0.978829i	$-0.434385\pi$
$773$	26.4136	−	45.7497i	0.950031	−	1.64550i	0.745351	−	0.666673i	$-0.232282\pi$
$774$		0			0
$775$	−14.8851	−	25.7817i	−0.534687	−	0.926106i
$776$	−87.2165	+	73.1834i	−3.13089	+	2.62713i
$777$		0			0
$778$	−7.02569	+	39.8447i	−0.251883	+	1.42850i
$779$	−0.247159	−	0.207391i	−0.00885540	−	0.00743056i
$780$		0			0

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.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.37939 + 0.866025i) q^{2} +(3.37939 + 2.83564i) q^{4} +(-0.0812519 + 0.460802i) q^{5} +(-2.47178 + 2.07407i) q^{7} +(3.05303 + 5.28801i) q^{8} +(-0.592396 + 1.02606i) q^{10} +(0.539363 + 3.05888i) q^{11} +(2.05303 - 0.747243i) q^{13} +(-7.67752 + 2.79439i) q^{14} +(1.15270 + 6.53731i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-0.0209445 - 0.0362770i) q^{19} +(-1.58125 + 1.32683i) q^{20} +(-1.36571 + 7.74535i) q^{22} +(-4.67752 - 3.92490i) q^{23} +(4.49273 + 1.63522i) q^{25} +5.53209 q^{26} -14.2344 q^{28} +(6.17752 + 2.24843i) q^{29} +(-4.76991 - 4.00243i) q^{31} +(-0.798133 + 4.52644i) q^{32} +(5.81908 - 4.88279i) q^{34} +(-0.754900 - 1.30753i) q^{35} +(-1.79813 + 3.11446i) q^{37} +(-0.0184183 - 0.104455i) q^{38} +(-2.68479 + 0.977185i) q^{40} +(7.23783 - 2.63435i) q^{41} +(-0.102196 - 0.579585i) q^{43} +(-6.85117 + 11.8666i) q^{44} +(-7.73055 - 13.3897i) q^{46} +(7.40033 - 6.20961i) q^{47} +(0.592396 - 3.35965i) q^{49} +(9.27379 + 7.78163i) q^{50} +(9.05690 + 3.29644i) q^{52} -4.95811 q^{53} -1.45336 q^{55} +(-18.5141 - 6.73859i) q^{56} +(12.7515 + 10.6998i) q^{58} +(1.48158 - 8.40247i) q^{59} +(-0.971782 + 0.815422i) q^{61} +(-7.88326 - 13.6542i) q^{62} +(0.819078 - 1.41868i) q^{64} +(0.177519 + 1.00676i) q^{65} +(-9.40420 + 3.42285i) q^{67} +(12.4363 - 4.52644i) q^{68} +(-0.663848 - 3.76487i) q^{70} +(5.91534 - 10.2457i) q^{71} +(4.11721 + 7.13122i) q^{73} +(-6.97565 + 5.85327i) q^{74} +(0.0320889 - 0.181985i) q^{76} +(-7.67752 - 6.44220i) q^{77} +(-10.3833 - 3.77920i) q^{79} -3.10607 q^{80} +19.5030 q^{82} +(-1.41875 - 0.516382i) q^{83} +(1.07532 + 0.902302i) q^{85} +(0.258770 - 1.46756i) q^{86} +(-14.5287 + 12.1910i) q^{88} +(-7.93629 - 13.7461i) q^{89} +(-3.52481 + 6.10516i) q^{91} +(-4.67752 - 26.5275i) q^{92} +(22.9859 - 8.36619i) q^{94} +(0.0184183 - 0.00670372i) q^{95} +(3.23783 + 18.3626i) q^{97} +(4.31908 - 7.48086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8} + 12 q^{11} - 21 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} - 12 q^{20} - 18 q^{22} - 3 q^{23} + 9 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 9 q^{32} + 18 q^{34}+ \cdots + 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8 + 12 * q^11 - 21 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 - 12 * q^20 - 18 * q^22 - 3 * q^23 + 9 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 9 * q^32 + 18 * q^34 - 6 * q^35 + 3 * q^37 - 12 * q^38 - 9 * q^40 + 24 * q^41 - 15 * q^44 - 9 * q^46 + 30 * q^47 + 3 * q^50 + 18 * q^52 - 36 * q^53 + 18 * q^55 - 24 * q^56 + 36 * q^58 - 3 * q^59 + 9 * q^61 - 12 * q^62 - 12 * q^64 - 24 * q^65 - 18 * q^67 + 27 * q^68 - 9 * q^71 - 6 * q^73 - 3 * q^74 - 9 * q^76 - 21 * q^77 - 27 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 21 * q^86 - 36 * q^88 + 6 * q^91 - 3 * q^92 + 36 * q^94 + 12 * q^95 + 9 * q^98

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