LMFDB - Embedded newform 729.2.e.c.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.c.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.688833	−	0.724920i	$-0.741877\pi$
$2$	−2.37939	−	0.866025i	−1.68248	−	0.612372i	−0.993646	+	0.112548i	$0.964099\pi$
$3$		0			0
$3$		0			0
$4$	3.37939	+	2.83564i	1.68969	+	1.41782i
$5$	0.0812519	−	0.460802i	0.0363370	−	0.206077i	−0.961234	−	0.275734i	$-0.911079\pi$
$5$	0.0812519	−	0.460802i	0.0363370	−	0.206077i	0.997571	+	0.0696565i	$0.0221903\pi$
$6$		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	$-0.900438\pi$
$11$	−0.539363	−	3.05888i	−0.162624	−	0.922287i	0.788856	−	0.614577i	$-0.210673\pi$
$12$		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	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		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	0.983378	−	0.181569i	$-0.0581174\pi$
$23$	4.67752	+	3.92490i	0.975330	+	0.818399i	−0.00804825	+	0.999968i	$0.502562\pi$
$24$		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	−0.302651	−	0.953102i	$-0.597872\pi$
$29$	−6.17752	−	2.24843i	−1.14714	−	0.417524i	−0.844486	+	0.535578i	$0.820094\pi$
$30$		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	−0.838422	−	0.545021i	$-0.816522\pi$
$41$	−7.23783	+	2.63435i	−1.13036	+	0.411417i	−0.291936	+	0.956438i	$0.594299\pi$
$42$		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	−0.995875	−	0.0907363i	$-0.971078\pi$
$47$	−7.40033	+	6.20961i	−1.07945	+	0.905765i	−0.0835741	+	0.996502i	$0.526634\pi$
$48$		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	$-0.389395\pi$
$53$	4.95811			0.681049			0.340524	+	0.940236i	$0.389395\pi$
$54$		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	$0.242987\pi$
$59$	−1.48158	+	8.40247i	−0.192886	+	1.09391i	−0.915398	+	0.402550i	$0.868124\pi$
$60$		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	$0.414386\pi$
$71$	−5.91534	+	10.2457i	−0.702022	+	1.21594i	−0.967755	+	0.251892i	$0.918947\pi$
$72$		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	0.418708	−	0.908121i	$-0.362483\pi$
$83$	1.41875	+	0.516382i	0.155728	+	0.0566803i	−0.262980	+	0.964801i	$0.584705\pi$
$84$		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	$0.151510\pi$
$89$	7.93629	+	13.7461i	0.841245	+	1.45708i	−0.0475978	+	0.998867i	$0.515157\pi$
$90$		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	−0.227051	−	0.973883i	$-0.572908\pi$
$101$	6.96064	−	5.84067i	0.692609	−	0.581168i	0.919660	+	0.392715i	$0.128464\pi$
$102$		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	$-0.437409\pi$
$107$	4.04189			0.390744			0.195372	+	0.980729i	$0.437409\pi$
$108$		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	−0.971413	−	0.237395i	$-0.923706\pi$
$113$	0.240352	−	1.36310i	0.0226104	−	0.128230i	0.994024	+	0.109165i	$0.0348176\pi$
$114$		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	0.112869	−	0.993610i	$-0.463996\pi$
$131$	−9.68345	−	8.12538i	−0.846047	−	0.709918i	−0.958915	+	0.283692i	$0.908441\pi$
$132$		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	−0.121309	−	0.992615i	$-0.538709\pi$
$137$	−9.97565	−	3.63084i	−0.852277	−	0.310204i	−0.730969	+	0.682411i	$0.760931\pi$
$138$		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	−0.173045	−	0.984914i	$-0.555361\pi$
$149$	3.99747	−	1.45496i	0.327486	−	0.119195i	0.500531	+	0.865719i	$0.333138\pi$
$150$		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	−0.999359	−	0.0357994i	$-0.988602\pi$
$167$	−0.620615	+	3.51968i	−0.0480246	+	0.272361i	0.951334	+	0.308160i	$0.0997134\pi$
$168$		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	$0.197288\pi$
$173$	3.25877	+	18.4814i	0.247760	+	1.40512i	−0.566235	+	0.824244i	$0.691601\pi$
$174$		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	−0.755257	−	0.655429i	$-0.772488\pi$
$179$	2.54189	−	4.40268i	0.189990	−	0.329072i	0.945247	+	0.326357i	$0.105821\pi$
$180$		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	0.673632	−	0.739067i	$-0.264733\pi$
$191$	9.87598	+	3.59456i	0.714601	+	0.260093i	0.0409690	+	0.999160i	$0.486956\pi$
$192$		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	$-0.999370\pi$
$197$	−7.04189	−	12.1969i	−0.501714	−	0.868994i	0.498284	−	0.867014i	$-0.333964\pi$
$198$		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	$-0.913307\pi$
$227$	−2.26130	−	12.8245i	−0.150088	−	0.851189i	0.813053	−	0.582190i	$-0.197804\pi$
$228$		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	−0.542949	−	0.839765i	$-0.682692\pi$
$233$	6.95723	−	12.0503i	0.455784	−	0.789440i	0.998733	+	0.0503252i	$0.0160258\pi$
$234$		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	0.189732	−	0.981836i	$-0.439238\pi$
$239$	−11.5057	−	9.65441i	−0.744241	−	0.624492i	−0.933973	+	0.357344i	$0.883682\pi$
$240$		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	0.851928	−	0.523659i	$-0.175433\pi$
$251$	−0.436289	−	0.755675i	−0.0275383	−	0.0476978i	−0.879466	+	0.475961i	$0.842100\pi$
$252$		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	−0.472652	−	0.881249i	$-0.656703\pi$
$257$	−4.30066	+	1.56531i	−0.268268	+	0.0976415i	0.204384	+	0.978891i	$0.434481\pi$
$258$		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	−0.535617	−	0.844461i	$-0.679921\pi$
$263$	3.29220	−	2.76249i	0.203006	−	0.170342i	0.738623	+	0.674119i	$0.235476\pi$
$264$		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	$-0.379475\pi$
$269$	12.1257			0.739315			0.369657	+	0.929168i	$0.379475\pi$
$270$		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	$0.237408\pi$
$281$	4.63310	+	26.2756i	0.276388	+	1.56747i	−0.458131	+	0.888885i	$0.651481\pi$
$282$		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	0.0870493	−	0.996204i	$-0.472256\pi$
$293$	−15.0444	−	12.6238i	−0.878904	−	0.737488i	−0.965953	+	0.258716i	$0.916701\pi$
$294$		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	−0.286972	−	0.957939i	$-0.592649\pi$
$311$	1.92127	−	0.699287i	0.108945	−	0.0396529i	0.395918	+	0.918286i	$0.370427\pi$
$312$		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	$-0.383627\pi$
$317$	23.8457	−	20.0089i	1.33931	−	1.12381i	0.981803	−	0.189902i	$-0.0608170\pi$
$318$		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	0.604846	−	0.796342i	$-0.293235\pi$
$347$	−1.38532	−	1.16242i	−0.0743676	−	0.0624018i	−0.679214	+	0.733941i	$0.737679\pi$
$348$		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	0.983305	−	0.181963i	$-0.0582450\pi$
$353$	30.4295	+	11.0754i	1.61960	+	0.589485i	0.636292	+	0.771448i	$0.280467\pi$
$354$		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	0.890180	−	0.455609i	$-0.150579\pi$
$359$	0.957234	+	1.65798i	0.0505209	+	0.0875047i	−0.839659	+	0.543114i	$0.817245\pi$
$360$		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	$0.131742\pi$
$383$	−1.61128	+	9.13803i	−0.0823326	+	0.466932i	−0.997900	+	0.0647678i	$0.979369\pi$
$384$		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	$-0.922801\pi$
$389$	−2.77466	−	15.7359i	−0.140681	−	0.797841i	0.830053	−	0.557684i	$-0.188310\pi$
$390$		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	0.664481	−	0.747305i	$-0.268653\pi$
$401$	0.879385	+	0.737892i	0.0439144	+	0.0368486i	−0.620566	+	0.784154i	$0.713097\pi$
$402$		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	−0.984766	−	0.173886i	$-0.944367\pi$
$419$	−33.3114	+	12.1244i	−1.62737	+	0.592314i	−0.642602	+	0.766200i	$0.722145\pi$
$420$		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	$-0.410037\pi$
$431$	11.5794			0.557758			0.278879	+	0.960326i	$0.410037\pi$
$432$		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	$0.206730\pi$
$443$	5.36437	+	30.4229i	0.254869	+	1.44543i	−0.541540	+	0.840675i	$0.682159\pi$
$444$		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	$-0.459725\pi$
$449$	19.5410	−	33.8460i	0.922197	−	1.59729i	0.796008	−	0.605287i	$-0.206941\pi$
$450$		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	−0.303389	−	0.952867i	$-0.598118\pi$
$461$	−24.6548	−	8.97362i	−1.14829	−	0.417943i	−0.844900	+	0.534924i	$0.820340\pi$
$462$		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	$-0.881473\pi$
$467$	−16.8735	−	29.2257i	−0.780810	−	1.35240i	0.150660	−	0.988586i	$-0.451860\pi$
$468$		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	−0.426951	−	0.904275i	$-0.640412\pi$
$479$	8.52347	−	7.15204i	0.389447	−	0.326785i	0.816398	+	0.577490i	$0.195968\pi$
$480$		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	$-0.776266\pi$
$491$	3.87939	−	22.0011i	0.175074	−	0.992895i	0.938058	−	0.346478i	$-0.112622\pi$
$492$		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	$0.355206\pi$
$503$	−12.5209	+	21.6869i	−0.558281	+	0.966972i	−0.997640	+	0.0686600i	$0.978128\pi$
$504$		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	0.895689	−	0.444682i	$-0.146683\pi$
$509$	13.8366	+	11.6103i	0.613297	+	0.514618i	−0.282391	+	0.959299i	$0.591128\pi$
$510$		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	$0.0258569\pi$
$521$	12.9791	+	22.4804i	0.568623	+	0.984883i	−0.428080	+	0.903741i	$0.640810\pi$
$522$		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	$0.358085\pi$
$557$	−13.3525	+	23.1272i	−0.565764	+	0.979932i	−0.996978	+	0.0776824i	$0.975248\pi$
$558$		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	0.999955	−	0.00946682i	$-0.00301343\pi$
$563$	27.6254	+	23.1805i	1.16427	+	0.976941i	0.164317	+	0.986408i	$0.447458\pi$
$564$		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	0.514018	−	0.857780i	$-0.328157\pi$
$569$	8.50165	+	3.09435i	0.356408	+	0.129722i	−0.157610	+	0.987501i	$0.550379\pi$
$570$		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	−0.250101	−	0.968220i	$-0.580464\pi$
$587$	15.9900	−	13.4172i	0.659979	−	0.553789i	0.910081	+	0.414431i	$0.136019\pi$
$588$		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	$-0.396067\pi$
$593$	15.6212			0.641488			0.320744	+	0.947166i	$0.396067\pi$
$594$		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	−0.986357	−	0.164621i	$-0.947360\pi$
$599$	−0.0778483	+	0.441500i	−0.00318080	+	0.0180392i	0.983176	+	0.182660i	$0.0584709\pi$
$600$		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	0.832853	−	0.553495i	$-0.186706\pi$
$617$	10.7404	+	9.01223i	0.432390	+	0.362819i	−0.400462	+	0.916313i	$0.631151\pi$
$618$		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	−0.975162	−	0.221492i	$-0.928907\pi$
$641$	−23.4538	+	19.6801i	−0.926371	+	0.777317i	0.0487917	+	0.998809i	$0.484463\pi$
$642$		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	$-0.581429\pi$
$647$	−12.8726			−0.506073			−0.253037	+	0.967457i	$0.581429\pi$
$648$		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	$0.126643\pi$
$653$	−1.96555	+	11.1472i	−0.0769178	+	0.436223i	−0.998810	+	0.0487755i	$0.984468\pi$
$654$		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	$-0.969131\pi$
$659$	−2.39100	−	13.5600i	−0.0931400	−	0.528223i	0.902161	−	0.431399i	$-0.141980\pi$
$660$		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	0.408306	−	0.912845i	$-0.366120\pi$
$677$	3.49495	+	1.27206i	0.134322	+	0.0488891i	−0.273985	+	0.961734i	$0.588342\pi$
$678$		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	0.995539	−	0.0943487i	$-0.0300769\pi$
$683$	10.8735	+	18.8334i	0.416061	+	0.720639i	−0.579478	+	0.814988i	$0.696744\pi$
$684$		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	$-0.354738\pi$
$701$	23.3351			0.881355			0.440678	+	0.897665i	$0.354738\pi$
$702$		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	−0.665325	−	0.746554i	$-0.731707\pi$
$719$	8.41622	−	14.5773i	0.313872	−	0.543642i	0.979197	+	0.202911i	$0.0650403\pi$
$720$		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	−0.964194	−	0.265199i	$-0.914562\pi$
$743$	−41.7686	+	15.2025i	−1.53234	+	0.557727i	−0.568149	+	0.822926i	$0.692340\pi$
$744$		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	$0.291051\pi$
$761$	−6.45888	+	36.6301i	−0.234134	+	1.32784i	−0.844429	+	0.535667i	$0.820060\pi$
$762$		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	$0.565615\pi$
$773$	−26.4136	+	45.7497i	−0.950031	+	1.64550i	−0.745351	+	0.666673i	$0.767718\pi$
$774$		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

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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more