LMFDB - Embedded newform 729.2.g.a.28.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, 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:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.4
Character	$\chi$	$=$	729.28
Dual form			729.2.g.a.703.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.463223 + 0.304667i) q^{2} +(-0.670406 + 1.55417i) q^{4} +(0.355980 - 0.377317i) q^{5} +(-2.24586 - 0.262503i) q^{7} +(-0.355511 - 2.01620i) q^{8} +O(q^{10})$	\(q+(-0.463223 + 0.304667i) q^{2} +(-0.670406 + 1.55417i) q^{4} +(0.355980 - 0.377317i) q^{5} +(-2.24586 - 0.262503i) q^{7} +(-0.355511 - 2.01620i) q^{8} +(-0.0499424 + 0.283238i) q^{10} +(0.352258 - 1.17662i) q^{11} +(0.226512 - 3.88906i) q^{13} +(1.12031 - 0.562641i) q^{14} +(-1.54412 - 1.63667i) q^{16} +(6.74697 - 2.45569i) q^{17} +(1.31557 + 0.478829i) q^{19} +(0.347766 + 0.806212i) q^{20} +(0.195304 + 0.652361i) q^{22} +(1.91236 - 0.223523i) q^{23} +(0.275078 + 4.72291i) q^{25} +(1.07994 + 1.87051i) q^{26} +(1.91361 - 3.31448i) q^{28} +(6.18810 + 3.10778i) q^{29} +(-4.11811 - 5.53158i) q^{31} +(5.19815 + 1.23198i) q^{32} +(-2.37718 + 3.19311i) q^{34} +(-0.898529 + 0.753956i) q^{35} +(3.62954 + 3.04555i) q^{37} +(-0.755286 + 0.179006i) q^{38} +(-0.887303 - 0.583588i) q^{40} +(1.26157 + 0.829746i) q^{41} +(-2.33285 + 0.552895i) q^{43} +(1.59252 + 1.33629i) q^{44} +(-0.817749 + 0.686173i) q^{46} +(6.75172 - 9.06914i) q^{47} +(-1.83633 - 0.435219i) q^{49} +(-1.56633 - 2.10395i) q^{50} +(5.89243 + 2.95929i) q^{52} +(-3.04317 + 5.27093i) q^{53} +(-0.318564 - 0.551769i) q^{55} +(0.269168 + 4.62143i) q^{56} +(-3.81331 + 0.445712i) q^{58} +(-3.69936 - 12.3567i) q^{59} +(2.26328 + 5.24688i) q^{61} +(3.59289 + 1.30771i) q^{62} +(1.44557 - 0.526145i) q^{64} +(-1.38678 - 1.46990i) q^{65} +(12.0102 - 6.03174i) q^{67} +(-0.706625 + 12.1323i) q^{68} +(0.186514 - 0.623002i) q^{70} +(-0.376160 + 2.13331i) q^{71} +(0.161233 + 0.914398i) q^{73} +(-2.60917 - 0.304968i) q^{74} +(-1.62615 + 1.72362i) q^{76} +(-1.09999 + 2.55007i) q^{77} +(6.48739 - 4.26682i) q^{79} -1.16722 q^{80} -0.837183 q^{82} +(3.50271 - 2.30377i) q^{83} +(1.47521 - 3.41993i) q^{85} +(0.912180 - 0.966854i) q^{86} +(-2.49755 - 0.291921i) q^{88} +(-2.46858 - 14.0000i) q^{89} +(-1.52961 + 8.67483i) q^{91} +(-0.934663 + 3.12199i) q^{92} +(-0.364490 + 6.25806i) q^{94} +(0.648988 - 0.325934i) q^{95} +(-10.6772 - 11.3172i) q^{97} +(0.983230 - 0.357866i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

Coefficient data

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

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

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

$2$	−0.463223	+	0.304667i	−0.327548	+	0.215432i	−0.702622	−	0.711563i	$-0.747988\pi$
$2$	−0.463223	+	0.304667i	−0.327548	+	0.215432i	0.375074	+	0.926995i	$0.377617\pi$
$3$		0			0
$3$		0			0
$4$	−0.670406	+	1.55417i	−0.335203	+	0.777087i
$5$	0.355980	−	0.377317i	0.159199	−	0.168741i	−0.642864	−	0.765980i	$-0.722254\pi$
$5$	0.355980	−	0.377317i	0.159199	−	0.168741i	0.802063	+	0.597239i	$0.203736\pi$
$6$		0			0
$7$	−2.24586	−	0.262503i	−0.848855	−	0.0992170i	−0.319468	−	0.947597i	$-0.603504\pi$
$7$	−2.24586	−	0.262503i	−0.848855	−	0.0992170i	−0.529387	+	0.848380i	$0.677578\pi$
$8$	−0.355511	−	2.01620i	−0.125692	−	0.712835i
$9$		0			0
$10$	−0.0499424	+	0.283238i	−0.0157932	+	0.0895676i
$11$	0.352258	−	1.17662i	0.106210	−	0.354766i	−0.888319	−	0.459227i	$-0.848127\pi$
$11$	0.352258	−	1.17662i	0.106210	−	0.354766i	0.994529	+	0.104461i	$0.0333117\pi$
$12$		0			0
$13$	0.226512	−	3.88906i	0.0628232	−	1.07863i	−0.808682	−	0.588246i	$-0.799819\pi$
$13$	0.226512	−	3.88906i	0.0628232	−	1.07863i	0.871505	−	0.490386i	$-0.163144\pi$
$14$	1.12031	−	0.562641i	0.299416	−	0.150372i
$15$		0			0
$16$	−1.54412	−	1.63667i	−0.386029	−	0.409167i
$17$	6.74697	−	2.45569i	1.63638	−	0.595593i	0.649979	−	0.759952i	$-0.274778\pi$
$17$	6.74697	−	2.45569i	1.63638	−	0.595593i	0.986401	+	0.164359i	$0.0525555\pi$
$18$		0			0
$19$	1.31557	+	0.478829i	0.301813	+	0.109851i	0.488487	−	0.872571i	$-0.337549\pi$
$19$	1.31557	+	0.478829i	0.301813	+	0.109851i	−0.186675	+	0.982422i	$0.559771\pi$
$20$	0.347766	+	0.806212i	0.0777628	+	0.180274i
$21$		0			0
$22$	0.195304	+	0.652361i	0.0416390	+	0.139084i
$23$	1.91236	−	0.223523i	0.398755	−	0.0466077i	0.0856474	−	0.996326i	$-0.472704\pi$
$23$	1.91236	−	0.223523i	0.398755	−	0.0466077i	0.313107	+	0.949718i	$0.398630\pi$
$24$		0			0
$25$	0.275078	+	4.72291i	0.0550156	+	0.944581i
$26$	1.07994	+	1.87051i	0.211794	+	0.366838i
$27$		0			0
$28$	1.91361	−	3.31448i	0.361639	−	0.626377i
$29$	6.18810	+	3.10778i	1.14910	+	0.577100i	0.918294	−	0.395899i	$-0.129567\pi$
$29$	6.18810	+	3.10778i	1.14910	+	0.577100i	0.230807	+	0.972999i	$0.425863\pi$
$30$		0			0
$31$	−4.11811	−	5.53158i	−0.739635	−	0.993502i	−0.999611	−	0.0278867i	$-0.991122\pi$
$31$	−4.11811	−	5.53158i	−0.739635	−	0.993502i	0.259977	−	0.965615i	$-0.416285\pi$
$32$	5.19815	+	1.23198i	0.918912	+	0.217786i
$33$		0			0
$34$	−2.37718	+	3.19311i	−0.407683	+	0.547614i
$35$	−0.898529	+	0.753956i	−0.151879	+	0.127442i
$36$		0			0
$37$	3.62954	+	3.04555i	0.596693	+	0.500685i	0.890381	−	0.455216i	$-0.150438\pi$
$37$	3.62954	+	3.04555i	0.596693	+	0.500685i	−0.293688	+	0.955901i	$0.594883\pi$
$38$	−0.755286	+	0.179006i	−0.122524	+	0.0290386i
$39$		0			0
$40$	−0.887303	−	0.583588i	−0.140295	−	0.0922734i
$41$	1.26157	+	0.829746i	0.197024	+	0.129585i	0.644188	−	0.764867i	$-0.277196\pi$
$41$	1.26157	+	0.829746i	0.197024	+	0.129585i	−0.447164	+	0.894452i	$0.647566\pi$
$42$		0			0
$43$	−2.33285	+	0.552895i	−0.355756	+	0.0843157i	−0.404608	−	0.914490i	$-0.632592\pi$
$43$	−2.33285	+	0.552895i	−0.355756	+	0.0843157i	0.0488519	+	0.998806i	$0.484444\pi$
$44$	1.59252	+	1.33629i	0.240082	+	0.201453i
$45$		0			0
$46$	−0.817749	+	0.686173i	−0.120571	+	0.101171i
$47$	6.75172	−	9.06914i	0.984840	−	1.32287i	0.0386515	−	0.999253i	$-0.487694\pi$
$47$	6.75172	−	9.06914i	0.984840	−	1.32287i	0.946188	−	0.323617i	$-0.104899\pi$
$48$		0			0
$49$	−1.83633	−	0.435219i	−0.262334	−	0.0621742i
$50$	−1.56633	−	2.10395i	−0.221513	−	0.297544i
$51$		0			0
$52$	5.89243	+	2.95929i	0.817133	+	0.410380i
$53$	−3.04317	+	5.27093i	−0.418012	+	0.724018i	−0.995739	−	0.0922118i	$-0.970606\pi$
$53$	−3.04317	+	5.27093i	−0.418012	+	0.724018i	0.577728	+	0.816230i	$0.303940\pi$
$54$		0			0
$55$	−0.318564	−	0.551769i	−0.0429551	−	0.0744005i
$56$	0.269168	+	4.62143i	0.0359691	+	0.617565i
$57$		0			0
$58$	−3.81331	+	0.445712i	−0.500712	+	0.0585248i
$59$	−3.69936	−	12.3567i	−0.481616	−	1.60871i	−0.761152	−	0.648574i	$-0.775366\pi$
$59$	−3.69936	−	12.3567i	−0.481616	−	1.60871i	0.279536	−	0.960135i	$-0.409819\pi$
$60$		0			0
$61$	2.26328	+	5.24688i	0.289784	+	0.671794i	0.999464	−	0.0327296i	$-0.0104200\pi$
$61$	2.26328	+	5.24688i	0.289784	+	0.671794i	−0.709681	+	0.704524i	$0.751161\pi$
$62$	3.59289	+	1.30771i	0.456298	+	0.166079i
$63$		0			0
$64$	1.44557	−	0.526145i	0.180696	−	0.0657681i
$65$	−1.38678	−	1.46990i	−0.172008	−	0.182318i
$66$		0			0
$67$	12.0102	−	6.03174i	1.46728	−	0.736894i	0.477382	−	0.878696i	$-0.341586\pi$
$67$	12.0102	−	6.03174i	1.46728	−	0.736894i	0.989895	+	0.141802i	$0.0452895\pi$
$68$	−0.706625	+	12.1323i	−0.0856908	+	1.47125i
$69$		0			0
$70$	0.186514	−	0.623002i	0.0222927	−	0.0744630i
$71$	−0.376160	+	2.13331i	−0.0446419	+	0.253177i	−0.998959	−	0.0456192i	$-0.985474\pi$
$71$	−0.376160	+	2.13331i	−0.0446419	+	0.253177i	0.954317	+	0.298796i	$0.0965850\pi$
$72$		0			0
$73$	0.161233	+	0.914398i	0.0188709	+	0.107022i	0.992788	−	0.119881i	$-0.0382512\pi$
$73$	0.161233	+	0.914398i	0.0188709	+	0.107022i	−0.973917	+	0.226903i	$0.927140\pi$
$74$	−2.60917	−	0.304968i	−0.303309	−	0.0354518i
$75$		0			0
$76$	−1.62615	+	1.72362i	−0.186532	+	0.197713i
$77$	−1.09999	+	2.55007i	−0.125356	+	0.290607i
$78$		0			0
$79$	6.48739	−	4.26682i	0.729888	−	0.480055i	−0.129371	−	0.991596i	$-0.541296\pi$
$79$	6.48739	−	4.26682i	0.729888	−	0.480055i	0.859259	+	0.511542i	$0.170925\pi$
$80$	−1.16722			−0.130499
$81$		0			0
$82$	−0.837183			−0.0924514
$83$	3.50271	−	2.30377i	0.384473	−	0.252872i	−0.342529	−	0.939507i	$-0.611284\pi$
$83$	3.50271	−	2.30377i	0.384473	−	0.252872i	0.727002	+	0.686636i	$0.240913\pi$
$84$		0			0
$85$	1.47521	−	3.41993i	0.160009	−	0.370943i
$86$	0.912180	−	0.966854i	0.0983629	−	0.104259i
$87$		0			0
$88$	−2.49755	−	0.291921i	−0.266239	−	0.0311189i
$89$	−2.46858	−	14.0000i	−0.261669	−	1.48400i	−0.778356	−	0.627824i	$-0.783946\pi$
$89$	−2.46858	−	14.0000i	−0.261669	−	1.48400i	0.516687	−	0.856175i	$-0.327165\pi$
$90$		0			0
$91$	−1.52961	+	8.67483i	−0.160346	+	0.909369i
$92$	−0.934663	+	3.12199i	−0.0974454	+	0.325490i
$93$		0			0
$94$	−0.364490	+	6.25806i	−0.0375943	+	0.645469i
$95$	0.648988	−	0.325934i	0.0665848	−	0.0334401i
$96$		0			0
$97$	−10.6772	−	11.3172i	−1.08410	−	1.14908i	−0.988118	−	0.153700i	$-0.950881\pi$
$97$	−10.6772	−	11.3172i	−1.08410	−	1.14908i	−0.0959862	−	0.995383i	$-0.530600\pi$
$98$	0.983230	−	0.357866i	0.0993212	−	0.0361500i
$99$		0			0
$100$	−7.52463	−	2.73874i	−0.752463	−	0.273874i
$101$	−3.61117	−	8.37164i	−0.359325	−	0.833010i	−0.997981	−	0.0635169i	$-0.979768\pi$
$101$	−3.61117	−	8.37164i	−0.359325	−	0.833010i	0.638655	−	0.769493i	$-0.279491\pi$
$102$		0			0
$103$	3.02856	+	10.1161i	0.298413	+	0.996769i	0.967349	+	0.253449i	$0.0815649\pi$
$103$	3.02856	+	10.1161i	0.298413	+	0.996769i	−0.668936	+	0.743320i	$0.733250\pi$
$104$	−7.92167	+	0.925910i	−0.776783	+	0.0907929i
$105$		0			0
$106$	−0.196209	−	3.36877i	−0.0190575	−	0.327204i
$107$	−5.34166	−	9.25202i	−0.516398	−	0.894427i	−0.999819	−	0.0190389i	$-0.993939\pi$
$107$	−5.34166	−	9.25202i	−0.516398	−	0.894427i	0.483421	−	0.875388i	$-0.339394\pi$
$108$		0			0
$109$	5.00123	−	8.66239i	0.479031	−	0.829707i	−0.520680	−	0.853752i	$-0.674321\pi$
$109$	5.00123	−	8.66239i	0.479031	−	0.829707i	0.999711	+	0.0240456i	$0.00765470\pi$
$110$	0.315672	+	0.158536i	0.0300981	+	0.0151158i
$111$		0			0
$112$	3.03824	+	4.08107i	0.287087	+	0.385625i
$113$	16.6744	+	3.95190i	1.56859	+	0.371764i	0.920795	−	0.390047i	$-0.127541\pi$
$113$	16.6744	+	3.95190i	1.56859	+	0.371764i	0.647799	+	0.761811i	$0.275689\pi$
$114$		0			0
$115$	0.596424	−	0.801136i	0.0556168	−	0.0747063i
$116$	−8.97857	+	7.53392i	−0.833640	+	0.699507i
$117$		0			0
$118$	5.47831	+	4.59685i	0.504320	+	0.423174i
$119$	−15.7974	+	3.74405i	−1.44814	+	0.343216i
$120$		0			0
$121$	7.93001	+	5.21565i	0.720910	+	0.474150i
$122$	−2.64695	−	1.74093i	−0.239644	−	0.157616i
$123$		0			0
$124$	11.3579	−	2.69186i	1.01997	−	0.241736i
$125$	3.86684	+	3.24467i	0.345861	+	0.290212i
$126$		0			0
$127$	−9.19946	+	7.71927i	−0.816320	+	0.684974i	−0.952107	−	0.305764i	$-0.901088\pi$
$127$	−9.19946	+	7.71927i	−0.816320	+	0.684974i	0.135787	+	0.990738i	$0.456644\pi$
$128$	−6.88954	+	9.25426i	−0.608955	+	0.817969i
$129$		0			0
$130$	1.09022	+	0.258386i	0.0956183	+	0.0226619i
$131$	−9.49207	−	12.7501i	−0.829326	−	1.11398i	−0.991867	−	0.127277i	$-0.959376\pi$
$131$	−9.49207	−	12.7501i	−0.829326	−	1.11398i	0.162541	−	0.986702i	$-0.448031\pi$
$132$		0			0
$133$	−2.82889	−	1.42072i	−0.245296	−	0.123192i
$134$	−3.72572	+	6.45314i	−0.321854	+	0.557467i
$135$		0			0
$136$	−7.34980	−	12.7302i	−0.630240	−	1.09161i
$137$	0.0263322	+	0.452106i	0.00224971	+	0.0386260i	0.999246	−	0.0388209i	$-0.0123602\pi$
$137$	0.0263322	+	0.452106i	0.00224971	+	0.0386260i	−0.996996	+	0.0774470i	$0.975323\pi$
$138$		0			0
$139$	−5.70831	+	0.667205i	−0.484172	+	0.0565916i	−0.354678	−	0.934989i	$-0.615409\pi$
$139$	−5.70831	+	0.667205i	−0.484172	+	0.0565916i	−0.129494	+	0.991580i	$0.541335\pi$
$140$	−0.569400	−	1.90193i	−0.0481231	−	0.160742i
$141$		0			0
$142$	−0.475702	−	1.10280i	−0.0399200	−	0.0925450i
$143$	−4.49618	−	1.63647i	−0.375989	−	0.136849i
$144$		0			0
$145$	3.37546	−	1.22857i	0.280317	−	0.102027i
$146$	−0.353274	−	0.374448i	−0.0292371	−	0.0309896i
$147$		0			0
$148$	−7.16658	+	3.59919i	−0.589089	+	0.295852i
$149$	−0.769758	+	13.2162i	−0.0630611	+	1.08272i	0.807249	+	0.590212i	$0.200956\pi$
$149$	−0.769758	+	13.2162i	−0.0630611	+	1.08272i	−0.870310	+	0.492505i	$0.836081\pi$
$150$		0			0
$151$	−0.813561	+	2.71748i	−0.0662067	+	0.221146i	−0.984690	−	0.174314i	$-0.944229\pi$
$151$	−0.813561	+	2.71748i	−0.0662067	+	0.221146i	0.918484	+	0.395459i	$0.129415\pi$
$152$	0.497716	−	2.82269i	0.0403701	−	0.228950i
$153$		0			0
$154$	−0.267379	−	1.51638i	−0.0215460	−	0.122193i
$155$	−3.55313	−	0.415301i	−0.285394	−	0.0333578i
$156$		0			0
$157$	−9.58966	+	10.1644i	−0.765338	+	0.811211i	−0.986454	−	0.164036i	$-0.947549\pi$
$157$	−9.58966	+	10.1644i	−0.765338	+	0.811211i	0.221116	+	0.975247i	$0.429030\pi$
$158$	−1.70515	+	3.95298i	−0.135654	+	0.314482i
$159$		0			0
$160$	2.31529	−	1.52279i	0.183040	−	0.120387i
$161$	−4.35357			−0.343109
$162$		0			0
$163$	2.66700			0.208896			0.104448	−	0.994530i	$-0.466692\pi$
$163$	2.66700			0.208896			0.104448	+	0.994530i	$0.466692\pi$
$164$	−2.13533	+	1.40443i	−0.166741	+	0.109668i
$165$		0			0
$166$	−0.920655	+	2.13432i	−0.0714567	+	0.165655i
$167$	−14.2643	+	15.1193i	−1.10381	+	1.16997i	−0.119622	+	0.992820i	$0.538168\pi$
$167$	−14.2643	+	15.1193i	−1.10381	+	1.16997i	−0.984184	+	0.177147i	$0.943313\pi$
$168$		0			0
$169$	−2.16140	−	0.252632i	−0.166262	−	0.0194332i
$170$	0.358585	+	2.03364i	0.0275022	+	0.155973i
$171$		0			0
$172$	0.704658	−	3.99631i	0.0537297	−	0.304716i
$173$	−3.83764	+	12.8186i	−0.291770	+	0.974580i	0.678913	+	0.734218i	$0.262451\pi$
$173$	−3.83764	+	12.8186i	−0.291770	+	0.974580i	−0.970683	+	0.240362i	$0.922734\pi$
$174$		0			0
$175$	0.621992	−	10.6792i	0.0470182	−	0.807271i
$176$	−2.46967	+	1.24032i	−0.186159	+	0.0934924i
$177$		0			0
$178$	5.40884	+	5.73304i	0.405410	+	0.429709i
$179$	−3.77200	+	1.37290i	−0.281932	+	0.102615i	−0.479116	−	0.877752i	$-0.659043\pi$
$179$	−3.77200	+	1.37290i	−0.281932	+	0.102615i	0.197184	+	0.980367i	$0.436820\pi$
$180$		0			0
$181$	−12.3224	−	4.48500i	−0.915920	−	0.333368i	−0.159306	−	0.987229i	$-0.550926\pi$
$181$	−12.3224	−	4.48500i	−0.915920	−	0.333368i	−0.756614	+	0.653862i	$0.773148\pi$
$182$	−1.93438	−	4.48440i	−0.143386	−	0.332406i
$183$		0			0
$184$	−1.13053	−	3.77624i	−0.0833439	−	0.278388i
$185$	2.44118	−	0.285334i	0.179479	−	0.0209781i
$186$		0			0
$187$	−0.512756	−	8.80369i	−0.0374965	−	0.643789i
$188$	9.56863	+	16.5734i	0.697864	+	1.20874i
$189$		0			0
$190$	−0.201325	+	0.348705i	−0.0146057	+	0.0252977i
$191$	−0.0543345	−	0.0272878i	−0.00393151	−	0.00197448i	0.446832	−	0.894618i	$-0.352552\pi$
$191$	−0.0543345	−	0.0272878i	−0.00393151	−	0.00197448i	−0.450764	+	0.892643i	$0.648848\pi$
$192$		0			0
$193$	−1.97643	−	2.65481i	−0.142267	−	0.191097i	0.725279	−	0.688455i	$-0.241711\pi$
$193$	−1.97643	−	2.65481i	−0.142267	−	0.191097i	−0.867545	+	0.497358i	$0.834304\pi$
$194$	8.39388	+	1.98939i	0.602645	+	0.142830i
$195$		0			0
$196$	1.90750	−	2.56221i	0.136250	−	0.183015i
$197$	11.5875	−	9.72308i	0.825576	−	0.692740i	−0.128695	−	0.991684i	$-0.541079\pi$
$197$	11.5875	−	9.72308i	0.825576	−	0.692740i	0.954271	+	0.298944i	$0.0966343\pi$
$198$		0			0
$199$	−6.76072	−	5.67291i	−0.479254	−	0.402142i	0.370902	−	0.928672i	$-0.379048\pi$
$199$	−6.76072	−	5.67291i	−0.479254	−	0.402142i	−0.850157	+	0.526530i	$0.823493\pi$
$200$	9.42454	−	2.23366i	0.666416	−	0.157943i
$201$		0			0
$202$	4.22334	+	2.77774i	0.297153	+	0.195441i
$203$	−13.0818	−	8.60404i	−0.918163	−	0.603885i
$204$		0			0
$205$	0.762171	−	0.180638i	0.0532323	−	0.0126163i
$206$	−4.48494	−	3.76331i	−0.312480	−	0.262202i
$207$		0			0
$208$	−6.71487	+	5.63445i	−0.465593	+	0.390679i
$209$	1.02682	−	1.37926i	0.0710268	−	0.0954056i
$210$		0			0
$211$	16.0628	+	3.80695i	1.10581	+	0.262081i	0.742672	−	0.669655i	$-0.233558\pi$
$211$	16.0628	+	3.80695i	1.10581	+	0.262081i	0.363135	+	0.931736i	$0.381706\pi$
$212$	−6.15179	−	8.26328i	−0.422506	−	0.567525i
$213$		0			0
$214$	5.29316	+	2.65833i	0.361833	+	0.181719i
$215$	−0.621831	+	1.07704i	−0.0424085	+	0.0734537i
$216$		0			0
$217$	7.79664	+	13.5042i	0.529270	+	0.916723i
$218$	0.322454	+	5.53633i	0.0218394	+	0.374968i
$219$		0			0
$220$	1.07111	−	0.125195i	0.0722143	−	0.00844065i
$221$	−8.02208	−	26.7956i	−0.539624	−	1.80247i
$222$		0			0
$223$	2.08802	+	4.84058i	0.139824	+	0.324149i	0.973711	−	0.227786i	$-0.0731487\pi$
$223$	2.08802	+	4.84058i	0.139824	+	0.324149i	−0.833887	+	0.551936i	$0.813889\pi$
$224$	−11.3509	−	4.13140i	−0.758415	−	0.276041i
$225$		0			0
$226$	−8.92798	+	3.24952i	−0.593880	+	0.216155i
$227$	−4.65004	−	4.92876i	−0.308634	−	0.327133i	0.554427	−	0.832232i	$-0.312937\pi$
$227$	−4.65004	−	4.92876i	−0.308634	−	0.327133i	−0.863061	+	0.505099i	$0.831456\pi$
$228$		0			0
$229$	−7.65641	+	3.84519i	−0.505950	+	0.254097i	−0.683416	−	0.730029i	$-0.739506\pi$
$229$	−7.65641	+	3.84519i	−0.505950	+	0.254097i	0.177466	+	0.984127i	$0.443210\pi$
$230$	−0.0321978	+	0.552815i	−0.00212306	+	0.0364516i
$231$		0			0
$232$	4.06598	−	13.5813i	0.266945	−	0.891657i
$233$	−1.32146	+	7.49440i	−0.0865720	+	0.490974i	0.910434	+	0.413654i	$0.135748\pi$
$233$	−1.32146	+	7.49440i	−0.0865720	+	0.490974i	−0.997006	+	0.0773205i	$0.975364\pi$
$234$		0			0
$235$	−1.01846	−	5.77598i	−0.0664370	−	0.376783i
$236$	21.6846	+	2.53457i	1.41155	+	0.164986i
$237$		0			0
$238$	6.17702	−	6.54726i	0.400397	−	0.424396i
$239$	−4.56879	+	10.5916i	−0.295530	+	0.685116i	−0.999689	−	0.0249260i	$-0.992065\pi$
$239$	−4.56879	+	10.5916i	−0.295530	+	0.685116i	0.704159	+	0.710042i	$0.251324\pi$
$240$		0			0
$241$	0.299604	−	0.197052i	0.0192992	−	0.0126933i	−0.539823	−	0.841779i	$-0.681509\pi$
$241$	0.299604	−	0.197052i	0.0192992	−	0.0126933i	0.559122	+	0.829085i	$0.311138\pi$
$242$	−5.26240			−0.338280
$243$		0			0
$244$	−9.67188			−0.619179
$245$	−0.817915	+	0.537951i	−0.0522547	+	0.0343684i
$246$		0			0
$247$	2.16019	−	5.00788i	0.137449	−	0.318644i
$248$	−9.68876	+	10.2695i	−0.615237	+	0.652113i
$249$		0			0
$250$	−2.77975	−	0.324907i	−0.175807	−	0.0205489i
$251$	1.46695	+	8.31946i	0.0925927	+	0.525120i	0.995458	+	0.0951969i	$0.0303481\pi$
$251$	1.46695	+	8.31946i	0.0925927	+	0.525120i	−0.902866	+	0.429923i	$0.858541\pi$
$252$		0			0
$253$	0.410642	−	2.32887i	0.0258169	−	0.146415i
$254$	1.90960	−	6.37851i	0.119819	−	0.400224i
$255$		0			0
$256$	0.193037	−	3.31432i	0.0120648	−	0.207145i
$257$	27.9893	−	14.0567i	1.74592	−	0.876835i	0.776988	−	0.629516i	$-0.216747\pi$
$257$	27.9893	−	14.0567i	1.74592	−	0.876835i	0.968934	−	0.247319i	$-0.0795495\pi$
$258$		0			0
$259$	−7.35198	−	7.79264i	−0.456830	−	0.484211i
$260$	3.21418	−	1.16987i	0.199335	−	0.0725520i
$261$		0			0
$262$	8.28147	+	3.01421i	0.511631	+	0.186218i
$263$	0.790541	+	1.83268i	0.0487468	+	0.113008i	0.940849	−	0.338825i	$-0.110030\pi$
$263$	0.790541	+	1.83268i	0.0487468	+	0.113008i	−0.892103	+	0.451833i	$0.850770\pi$
$264$		0			0
$265$	0.905503	+	3.02459i	0.0556246	+	0.185799i
$266$	1.74326	−	0.203757i	0.106886	−	0.0124932i
$267$		0			0
$268$	1.32269	+	22.7096i	0.0807959	+	1.38721i
$269$	−1.73160	−	2.99923i	−0.105578	−	0.182866i	0.808396	−	0.588639i	$-0.200336\pi$
$269$	−1.73160	−	2.99923i	−0.105578	−	0.182866i	−0.913974	+	0.405772i	$0.867003\pi$
$270$		0			0
$271$	−14.7474	+	25.5433i	−0.895843	+	1.55165i	−0.0630854	+	0.998008i	$0.520094\pi$
$271$	−14.7474	+	25.5433i	−0.895843	+	1.55165i	−0.832758	+	0.553638i	$0.813239\pi$
$272$	−14.4373	−	7.25067i	−0.875388	−	0.439636i
$273$		0			0
$274$	−0.149939	−	0.201403i	−0.00905817	−	0.0121672i
$275$	5.65399	+	1.34002i	0.340948	+	0.0808062i
$276$		0			0
$277$	−3.71802	+	4.99417i	−0.223394	+	0.300071i	−0.899664	−	0.436584i	$-0.856188\pi$
$277$	−3.71802	+	4.99417i	−0.223394	+	0.300071i	0.676269	+	0.736655i	$0.263596\pi$
$278$	2.44094	−	2.04820i	0.146398	−	0.122843i
$279$		0			0
$280$	1.83956	+	1.54358i	0.109935	+	0.0922464i
$281$	3.61985	−	0.857919i	0.215942	−	0.0511792i	−0.121221	−	0.992626i	$-0.538681\pi$
$281$	3.61985	−	0.857919i	0.215942	−	0.0511792i	0.337163	+	0.941446i	$0.390533\pi$
$282$		0			0
$283$	−11.4175	−	7.50939i	−0.678698	−	0.446387i	0.162791	−	0.986661i	$-0.447950\pi$
$283$	−11.4175	−	7.50939i	−0.678698	−	0.446387i	−0.841489	+	0.540274i	$0.818321\pi$
$284$	−3.06335	−	2.01480i	−0.181777	−	0.119556i
$285$		0			0
$286$	2.58131	−	0.611782i	0.152636	−	0.0361754i
$287$	−2.61549	−	2.19466i	−0.154388	−	0.129547i
$288$		0			0
$289$	26.4684	−	22.2096i	1.55696	−	1.30645i
$290$	−1.18929	+	1.59749i	−0.0698374	+	0.0938080i
$291$		0			0
$292$	−1.52923	−	0.362433i	−0.0894912	−	0.0212098i
$293$	10.1627	+	13.6509i	0.593712	+	0.797494i	0.992846	−	0.119399i	$-0.0380967\pi$
$293$	10.1627	+	13.6509i	0.593712	+	0.797494i	−0.399134	+	0.916893i	$0.630689\pi$
$294$		0			0
$295$	−5.97931	−	3.00292i	−0.348129	−	0.174837i
$296$	4.85010	−	8.40062i	0.281906	−	0.488276i
$297$		0			0
$298$	−3.66998	−	6.35659i	−0.212596	−	0.368227i
$299$	−0.436122	−	7.48792i	−0.0252216	−	0.433037i
$300$		0			0
$301$	5.38438	−	0.629344i	0.310351	−	0.0362748i
$302$	−0.451066	−	1.50667i	−0.0259559	−	0.0866989i
$303$		0			0
$304$	−1.24771	−	2.89252i	−0.0715612	−	0.165898i
$305$	2.78542	+	1.01381i	0.159493	+	0.0580506i
$306$		0			0
$307$	2.43196	−	0.885161i	0.138799	−	0.0505188i	−0.271686	−	0.962386i	$-0.587581\pi$
$307$	2.43196	−	0.885161i	0.138799	−	0.0505188i	0.410486	+	0.911867i	$0.365359\pi$
$308$	−3.22581	−	3.41916i	−0.183807	−	0.194825i
$309$		0			0
$310$	1.77242	−	0.890143i	0.100667	−	0.0505567i
$311$	0.615800	−	10.5729i	0.0349188	−	0.599533i	−0.934780	−	0.355228i	$-0.884403\pi$
$311$	0.615800	−	10.5729i	0.0349188	−	0.599533i	0.969698	−	0.244305i	$-0.0785598\pi$
$312$		0			0
$313$	−6.25206	+	20.8833i	−0.353388	+	1.18040i	0.577899	+	0.816108i	$0.303873\pi$
$313$	−6.25206	+	20.8833i	−0.353388	+	1.18040i	−0.931286	+	0.364288i	$0.881312\pi$
$314$	1.34538	−	7.63006i	0.0759245	−	0.430589i
$315$		0			0
$316$	2.28221	+	12.9430i	0.128384	+	0.728102i
$317$	−3.56102	−	0.416224i	−0.200007	−	0.0233775i	0.0154994	−	0.999880i	$-0.495066\pi$
$317$	−3.56102	−	0.416224i	−0.200007	−	0.0233775i	−0.215507	+	0.976502i	$0.569140\pi$
$318$		0			0
$319$	5.83650	−	6.18633i	0.326781	−	0.346368i
$320$	0.316072	−	0.732736i	0.0176689	−	0.0409612i
$321$		0			0
$322$	2.01667	−	1.32639i	0.112385	−	0.0739167i
$323$	10.0520			0.559307
$324$		0			0
$325$	18.4300			1.02231
$326$	−1.23542	+	0.812546i	−0.0684234	+	0.0450028i
$327$		0			0
$328$	1.22443	−	2.83856i	0.0676081	−	0.156733i
$329$	−17.5441	+	18.5957i	−0.967238	+	1.02521i
$330$		0			0
$331$	4.12316	+	0.481928i	0.226629	+	0.0264892i	0.228650	−	0.973509i	$-0.426569\pi$
$331$	4.12316	+	0.481928i	0.226629	+	0.0264892i	−0.00202025	+	0.999998i	$0.500643\pi$
$332$	1.23222	+	6.98829i	0.0676270	+	0.383532i
$333$		0			0
$334$	2.00122	−	11.3495i	0.109502	−	0.621016i
$335$	1.99951	−	6.67883i	0.109245	−	0.364903i
$336$		0			0
$337$	−1.19137	+	20.4551i	−0.0648982	+	1.11426i	0.795939	+	0.605377i	$0.206978\pi$
$337$	−1.19137	+	20.4551i	−0.0648982	+	1.11426i	−0.860837	+	0.508881i	$0.830059\pi$
$338$	1.07818	−	0.541483i	0.0586453	−	0.0294528i
$339$		0			0
$340$	4.32617	+	4.58548i	0.234620	+	0.248682i
$341$	−7.95924	+	2.89692i	−0.431017	+	0.156877i
$342$		0			0
$343$	18.8834	+	6.87300i	1.01961	+	0.371107i
$344$	1.94410	+	4.50693i	0.104819	+	0.242997i
$345$		0			0
$346$	−2.12772	−	7.10707i	−0.114387	−	0.382079i
$347$	31.0030	−	3.62373i	1.66433	−	0.194532i	0.768785	−	0.639508i	$-0.220862\pi$
$347$	31.0030	−	3.62373i	1.66433	−	0.194532i	0.895543	+	0.444976i	$0.146788\pi$
$348$		0			0
$349$	−0.686708	−	11.7903i	−0.0367586	−	0.631122i	−0.965502	−	0.260397i	$-0.916146\pi$
$349$	−0.686708	−	11.7903i	−0.0367586	−	0.631122i	0.928743	−	0.370724i	$-0.120891\pi$
$350$	2.96547	+	5.13635i	0.158511	+	0.274549i
$351$		0			0
$352$	3.28068	−	5.68230i	0.174861	−	0.302867i
$353$	8.47948	+	4.25856i	0.451317	+	0.226660i	0.659913	−	0.751342i	$-0.270593\pi$
$353$	8.47948	+	4.25856i	0.451317	+	0.226660i	−0.208596	+	0.978002i	$0.566889\pi$
$354$		0			0
$355$	0.671028	+	0.901347i	0.0356145	+	0.0478385i
$356$	23.4134	+	5.54908i	1.24091	+	0.294101i
$357$		0			0
$358$	1.32900	−	1.78516i	0.0702399	−	0.0943486i
$359$	11.7812	−	9.88558i	0.621787	−	0.521741i	−0.276578	−	0.960992i	$-0.589200\pi$
$359$	11.7812	−	9.88558i	0.621787	−	0.521741i	0.898365	+	0.439250i	$0.144756\pi$
$360$		0			0
$361$	−13.0534	−	10.9531i	−0.687021	−	0.576479i
$362$	7.07447	−	1.67668i	0.371826	−	0.0881244i
$363$		0			0
$364$	−12.4567	−	8.19293i	−0.652911	−	0.429426i
$365$	0.402414	+	0.264672i	0.0210633	+	0.0138536i
$366$		0			0
$367$	−3.45240	+	0.818233i	−0.180214	+	0.0427114i	−0.319732	−	0.947508i	$-0.603593\pi$
$367$	−3.45240	+	0.818233i	−0.180214	+	0.0427114i	0.139518	+	0.990220i	$0.455445\pi$
$368$	−3.31874	−	2.78476i	−0.173001	−	0.145165i
$369$		0			0
$370$	−1.04388	+	0.875921i	−0.0542688	+	0.0455369i
$371$	8.21818	−	11.0389i	0.426666	−	0.573113i
$372$		0			0
$373$	−29.2434	−	6.93082i	−1.51417	−	0.358865i	−0.612213	−	0.790693i	$-0.709720\pi$
$373$	−29.2434	−	6.93082i	−1.51417	−	0.358865i	−0.901956	+	0.431829i	$0.857869\pi$
$374$	2.91971	+	3.92185i	0.150975	+	0.202794i
$375$		0			0
$376$	−20.6855	−	10.3887i	−1.06677	−	0.535754i
$377$	13.4880	−	23.3620i	0.694669	−	1.20320i
$378$		0			0
$379$	11.7966	+	20.4324i	0.605953	+	1.04954i	0.991900	+	0.127020i	$0.0405414\pi$
$379$	11.7966	+	20.4324i	0.605953	+	1.04954i	−0.385947	+	0.922521i	$0.626125\pi$
$380$	0.0714733	+	1.22715i	0.00366650	+	0.0629514i
$381$		0			0
$382$	0.0334827	−	0.00391357i	0.00171312	−	0.000200236i
$383$	−0.0831461	−	0.277727i	−0.00424857	−	0.0141912i	0.955839	−	0.293891i	$-0.0949503\pi$
$383$	−0.0831461	−	0.277727i	−0.00424857	−	0.0141912i	−0.960088	+	0.279700i	$0.909765\pi$
$384$		0			0
$385$	0.570608	+	1.32282i	0.0290809	+	0.0674171i
$386$	1.72436	+	0.627616i	0.0877676	+	0.0319448i
$387$		0			0
$388$	24.7469	−	9.00713i	1.25633	−	0.457268i
$389$	19.2691	+	20.4240i	0.976982	+	1.03554i	0.999359	+	0.0357904i	$0.0113949\pi$
$389$	19.2691	+	20.4240i	0.976982	+	1.03554i	−0.0223777	+	0.999750i	$0.507124\pi$
$390$		0			0
$391$	12.3537	−	6.20427i	0.624755	−	0.313764i
$392$	−0.224653	+	3.85715i	−0.0113467	+	0.194815i
$393$		0			0
$394$	−2.40531	+	8.03428i	−0.121178	+	0.404761i
$395$	0.699438	−	3.96671i	0.0351925	−	0.199587i
$396$		0			0
$397$	−0.686472	−	3.89317i	−0.0344530	−	0.195393i	0.962723	−	0.270488i	$-0.0871850\pi$
$397$	−0.686472	−	3.89317i	−0.0344530	−	0.195393i	−0.997176	+	0.0750952i	$0.976074\pi$
$398$	4.86007	+	0.568061i	0.243613	+	0.0284743i
$399$		0			0
$400$	7.30508	−	7.74293i	0.365254	−	0.387147i
$401$	0.790666	−	1.83297i	0.0394840	−	0.0915341i	−0.897333	−	0.441355i	$-0.854498\pi$
$401$	0.790666	−	1.83297i	0.0394840	−	0.0915341i	0.936817	+	0.349820i	$0.113757\pi$
$402$		0			0
$403$	−22.4455	+	14.7626i	−1.11809	+	0.735379i
$404$	15.4320			0.767768
$405$		0			0
$406$	8.68116			0.430839
$407$	4.86200	−	3.19779i	0.241001	−	0.158509i
$408$		0			0
$409$	−4.74536	+	11.0010i	−0.234643	+	0.543963i	−0.994332	−	0.106324i	$-0.966092\pi$
$409$	−4.74536	+	11.0010i	−0.234643	+	0.543963i	0.759689	+	0.650287i	$0.225351\pi$
$410$	−0.298021	+	0.315884i	−0.0147182	+	0.0156004i
$411$		0			0
$412$	−17.7526	−	2.07498i	−0.874605	−	0.102227i
$413$	5.06457	+	28.7226i	0.249211	+	1.41335i
$414$		0			0
$415$	0.377645	−	2.14173i	0.0185379	−	0.105133i
$416$	5.96871	−	19.9369i	0.292640	−	0.977486i
$417$		0			0
$418$	−0.0554328	+	0.951745i	−0.00271131	+	0.0465514i
$419$	16.5709	−	8.32220i	0.809540	−	0.406566i	0.00464887	−	0.999989i	$-0.498520\pi$
$419$	16.5709	−	8.32220i	0.809540	−	0.406566i	0.804891	+	0.593423i	$0.202224\pi$
$420$		0			0
$421$	26.5846	+	28.1780i	1.29565	+	1.37331i	0.887776	+	0.460276i	$0.152250\pi$
$421$	26.5846	+	28.1780i	1.29565	+	1.37331i	0.407878	+	0.913036i	$0.366269\pi$
$422$	−8.60050	+	3.13033i	−0.418666	+	0.152382i
$423$		0			0
$424$	11.7091	+	4.26178i	0.568646	+	0.206970i
$425$	13.4540	+	31.1898i	0.652613	+	1.51293i
$426$		0			0
$427$	−3.70569	−	12.3779i	−0.179331	−	0.599007i
$428$	17.9603	−	2.09926i	0.868146	−	0.101472i
$429$		0			0
$430$	−0.0400925	−	0.688362i	−0.00193343	−	0.0331958i
$431$	−4.62147	−	8.00461i	−0.222608	−	0.385569i	0.732991	−	0.680238i	$-0.238124\pi$
$431$	−4.62147	−	8.00461i	−0.222608	−	0.385569i	−0.955599	+	0.294670i	$0.904790\pi$
$432$		0			0
$433$	5.80798	−	10.0597i	0.279114	−	0.483439i	−0.692051	−	0.721848i	$-0.743293\pi$
$433$	5.80798	−	10.0597i	0.279114	−	0.483439i	0.971165	+	0.238410i	$0.0766261\pi$
$434$	−7.72586	−	3.88007i	−0.370853	−	0.186249i
$435$		0			0
$436$	10.1100	+	13.5801i	0.484182	+	0.650369i
$437$	2.62287	+	0.621633i	0.125469	+	0.0297367i
$438$		0			0
$439$	9.55626	−	12.8363i	0.456095	−	0.612642i	−0.513282	−	0.858220i	$-0.671570\pi$
$439$	9.55626	−	12.8363i	0.456095	−	0.612642i	0.969377	+	0.245578i	$0.0789777\pi$
$440$	−0.999224	+	0.838449i	−0.0476362	+	0.0399715i
$441$		0			0
$442$	11.8797	+	9.96829i	0.565062	+	0.474143i
$443$	3.87119	−	0.917488i	0.183926	−	0.0435912i	−0.137621	−	0.990485i	$-0.543946\pi$
$443$	3.87119	−	0.917488i	0.183926	−	0.0435912i	0.321546	+	0.946894i	$0.395797\pi$
$444$		0			0
$445$	−6.16121	−	4.05229i	−0.292070	−	0.192097i
$446$	−2.44199	−	1.60612i	−0.115631	−	0.0760520i
$447$		0			0
$448$	−3.38467	+	0.802181i	−0.159910	+	0.0378995i
$449$	21.2890	+	17.8636i	1.00469	+	0.843035i	0.987627	−	0.156819i	$-0.0501240\pi$
$449$	21.2890	+	17.8636i	1.00469	+	0.843035i	0.0170628	+	0.999854i	$0.494568\pi$
$450$		0			0
$451$	1.42070	−	1.19211i	0.0668980	−	0.0561341i
$452$	−17.3205	+	23.2655i	−0.814690	+	1.09432i
$453$		0			0
$454$	3.65564	+	0.866402i	0.171567	+	0.0406622i
$455$	2.72865	+	3.66522i	0.127921	+	0.171828i
$456$		0			0
$457$	1.41493	+	0.710606i	0.0661877	+	0.0332407i	0.481585	−	0.876399i	$-0.340061\pi$
$457$	1.41493	+	0.710606i	0.0661877	+	0.0332407i	−0.415397	+	0.909640i	$0.636357\pi$
$458$	2.37512	−	4.11383i	0.110982	−	0.192227i
$459$		0			0
$460$	0.845260	+	1.46403i	0.0394104	+	0.0682609i
$461$	−1.67892	−	28.8259i	−0.0781950	−	1.34256i	−0.778019	−	0.628241i	$-0.783775\pi$
$461$	−1.67892	−	28.8259i	−0.0781950	−	1.34256i	0.699824	−	0.714315i	$-0.253262\pi$
$462$		0			0
$463$	13.9507	−	1.63060i	0.648344	−	0.0757805i	0.214436	−	0.976738i	$-0.431209\pi$
$463$	13.9507	−	1.63060i	0.648344	−	0.0757805i	0.433907	+	0.900957i	$0.357135\pi$
$464$	−4.46875	−	14.9267i	−0.207456	−	0.692953i
$465$		0			0
$466$	−1.67116	−	3.87418i	−0.0774150	−	0.179468i
$467$	8.66429	+	3.15354i	0.400935	+	0.145929i	0.534614	−	0.845096i	$-0.320457\pi$
$467$	8.66429	+	3.15354i	0.400935	+	0.145929i	−0.133679	+	0.991025i	$0.542679\pi$
$468$		0			0
$469$	−28.5565	+	10.3937i	−1.31862	+	0.479938i
$470$	2.23152	+	2.36528i	0.102932	+	0.109102i
$471$		0			0
$472$	−23.5985	+	11.8516i	−1.08621	+	0.545515i
$473$	−0.171215	+	2.93965i	−0.00787247	+	0.135165i
$474$		0			0
$475$	−1.89958	+	6.34503i	−0.0871586	+	0.291130i
$476$	4.77174	−	27.0619i	0.218713	−	1.24038i
$477$		0			0
$478$	−1.11055	−	6.29825i	−0.0507954	−	0.288075i
$479$	−38.0552	−	4.44802i	−1.73879	−	0.203235i	−0.813256	−	0.581906i	$-0.802307\pi$
$479$	−38.0552	−	4.44802i	−1.73879	−	0.203235i	−0.925532	+	0.378670i	$0.876381\pi$
$480$		0			0
$481$	12.6665	−	13.4257i	0.577541	−	0.612158i
$482$	−0.0787481	+	0.182559i	−0.00358688	+	0.00831531i
$483$		0			0
$484$	−13.4223	+	8.82802i	−0.610107	+	0.401274i
$485$	−8.07103			−0.366486
$486$		0			0
$487$	−31.8391			−1.44277			−0.721384	−	0.692535i	$-0.756494\pi$
$487$	−31.8391			−1.44277			−0.721384	+	0.692535i	$0.756494\pi$
$488$	9.77415	−	6.42856i	0.442455	−	0.291007i
$489$		0			0
$490$	0.214981	−	0.498383i	0.00971187	−	0.0225146i
$491$	−18.1984	+	19.2891i	−0.821280	+	0.870506i	−0.993416	−	0.114567i	$-0.963452\pi$
$491$	−18.1984	+	19.2891i	−0.821280	+	0.870506i	0.172135	+	0.985073i	$0.444933\pi$
$492$		0			0
$493$	49.3827	+	5.77201i	2.22408	+	0.259958i
$494$	0.525085	+	2.97790i	0.0236247	+	0.133982i
$495$		0			0
$496$	−2.69452	+	15.2814i	−0.120988	+	0.686155i
$497$	1.40480	−	4.69237i	0.0630140	−	0.210481i
$498$		0			0
$499$	0.394547	−	6.77412i	0.0176624	−	0.303251i	−0.977895	−	0.209096i	$-0.932948\pi$
$499$	0.394547	−	6.77412i	0.0176624	−	0.303251i	0.995558	−	0.0941553i	$-0.0300150\pi$
$500$	−7.63513	+	3.83451i	−0.341453	+	0.171484i
$501$		0			0
$502$	−3.21418	−	3.40684i	−0.143456	−	0.152055i
$503$	−24.9170	+	9.06903i	−1.11099	+	0.404368i	−0.831357	−	0.555738i	$-0.812436\pi$
$503$	−24.9170	+	9.06903i	−1.11099	+	0.404368i	−0.279635	+	0.960106i	$0.590213\pi$
$504$		0			0
$505$	−4.44427	−	1.61758i	−0.197768	−	0.0719815i
$506$	0.519309	+	1.20389i	0.0230861	+	0.0535196i
$507$		0			0
$508$	−5.82972	−	19.4726i	−0.258652	−	0.863958i
$509$	−6.91186	+	0.807881i	−0.306363	+	0.0358087i	−0.267885	−	0.963451i	$-0.586325\pi$
$509$	−6.91186	+	0.807881i	−0.306363	+	0.0358087i	−0.0384775	+	0.999259i	$0.512251\pi$
$510$		0			0
$511$	−0.122074	−	2.09594i	−0.00540025	−	0.0927187i
$512$	−10.6169	−	18.3890i	−0.469204	−	0.812685i
$513$		0			0
$514$	−8.68265	+	15.0388i	−0.382975	+	0.663333i
$515$	4.89509	+	2.45841i	0.215703	+	0.108330i
$516$		0			0
$517$	−8.29262	−	11.1389i	−0.364709	−	0.489889i
$518$	5.77977	+	1.36983i	0.253948	+	0.0601869i
$519$		0			0
$520$	−2.47060	+	3.31859i	−0.108343	+	0.145530i
$521$	−5.56140	+	4.66657i	−0.243649	+	0.204446i	−0.756432	−	0.654073i	$-0.773059\pi$
$521$	−5.56140	+	4.66657i	−0.243649	+	0.204446i	0.512783	+	0.858518i	$0.328615\pi$
$522$		0			0
$523$	−18.0663	−	15.1594i	−0.789983	−	0.662875i	0.155758	−	0.987795i	$-0.450218\pi$
$523$	−18.0663	−	15.1594i	−0.789983	−	0.662875i	−0.945741	+	0.324920i	$0.894662\pi$
$524$	26.1794	−	6.20463i	1.14365	−	0.271050i
$525$		0			0
$526$	−0.924553	−	0.608088i	−0.0403124	−	0.0265139i
$527$	−41.3686	−	27.2086i	−1.80205	−	1.18522i
$528$		0			0
$529$	−18.7729	+	4.44925i	−0.816212	+	0.193446i
$530$	−1.34094	−	1.12518i	−0.0582468	−	0.0488749i
$531$		0			0
$532$	4.10456	−	3.44414i	0.177955	−	0.149322i
$533$	3.51269	−	4.71837i	0.152152	−	0.204375i
$534$		0			0
$535$	−5.39247	−	1.27804i	−0.233137	−	0.0552545i
$536$	−16.4310	−	22.0706i	−0.709709	−	0.953305i
$537$		0			0
$538$	1.71588	+	0.861749i	0.0739770	+	0.0371527i
$539$	−1.15895	+	2.00737i	−0.0499197	+	0.0864634i
$540$		0			0
$541$	−10.4179	−	18.0443i	−0.447900	−	0.775785i	0.550349	−	0.834935i	$-0.314495\pi$
$541$	−10.4179	−	18.0443i	−0.447900	−	0.775785i	−0.998249	+	0.0591491i	$0.981161\pi$
$542$	−0.950841	−	16.3253i	−0.0408421	−	0.701232i
$543$		0			0
$544$	38.0971	−	4.45292i	1.63340	−	0.190917i
$545$	−1.48813	−	4.97069i	−0.0637444	−	0.212921i
$546$		0			0
$547$	−8.27790	−	19.1903i	−0.353937	−	0.820519i	−0.998436	−	0.0559131i	$-0.982193\pi$
$547$	−8.27790	−	19.1903i	−0.353937	−	0.820519i	0.644498	−	0.764606i	$-0.277066\pi$
$548$	−0.720305	−	0.262170i	−0.0307699	−	0.0111993i
$549$		0			0
$550$	−3.02732	+	1.10185i	−0.129085	+	0.0469832i
$551$	6.65279	+	7.05155i	0.283418	+	0.300406i
$552$		0			0
$553$	−15.6898	+	7.87972i	−0.667199	+	0.335080i
$554$	0.200717	−	3.44617i	0.00852764	−	0.146414i
$555$		0			0
$556$	2.78993	−	9.31900i	0.118319	−	0.395214i
$557$	−5.21184	+	29.5578i	−0.220833	+	1.25240i	0.649661	+	0.760224i	$0.274911\pi$
$557$	−5.21184	+	29.5578i	−0.220833	+	1.25240i	−0.870493	+	0.492180i	$0.836200\pi$
$558$		0			0
$559$	1.62182	+	9.19782i	0.0685959	+	0.389026i
$560$	2.62141	+	0.306399i	0.110775	+	0.0129477i
$561$		0			0
$562$	−1.41542	+	1.50025i	−0.0597058	+	0.0632844i
$563$	−1.65639	+	3.83994i	−0.0698085	+	0.161834i	−0.949548	−	0.313622i	$-0.898458\pi$
$563$	−1.65639	+	3.83994i	−0.0698085	+	0.161834i	0.879740	+	0.475456i	$0.157717\pi$
$564$		0			0
$565$	7.42688	−	4.88473i	0.312451	−	0.205502i
$566$	7.57670			0.318472
$567$		0			0
$568$	4.43491			0.186085
$569$	−23.6347	+	15.5448i	−0.990818	+	0.651671i	−0.937892	−	0.346927i	$-0.887225\pi$
$569$	−23.6347	+	15.5448i	−0.990818	+	0.651671i	−0.0529260	+	0.998598i	$0.516855\pi$
$570$		0			0
$571$	−4.09054	+	9.48294i	−0.171184	+	0.396849i	−0.982112	−	0.188297i	$-0.939703\pi$
$571$	−4.09054	+	9.48294i	−0.171184	+	0.396849i	0.810928	+	0.585146i	$0.198963\pi$
$572$	5.55763	−	5.89074i	0.232376	−	0.246304i
$573$		0			0
$574$	1.88020	+	0.219763i	0.0784779	+	0.00917275i
$575$	1.58173	+	8.97041i	0.0659625	+	0.374092i
$576$		0			0
$577$	1.09162	−	6.19086i	0.0454446	−	0.257729i	−0.953618	−	0.301020i	$-0.902673\pi$
$577$	1.09162	−	6.19086i	0.0454446	−	0.257729i	0.999063	+	0.0432907i	$0.0137842\pi$
$578$	−5.49424	+	18.3520i	−0.228530	+	0.763344i
$579$		0			0
$580$	−0.353520	+	6.06970i	−0.0146791	+	0.252030i
$581$	−8.47135	+	4.25447i	−0.351451	+	0.176505i
$582$		0			0
$583$	5.12992	+	5.43740i	0.212460	+	0.225194i
$584$	1.78629	−	0.650157i	0.0739173	−	0.0269037i
$585$		0			0
$586$	−8.86658	−	3.22717i	−0.366275	−	0.133313i
$587$	1.75202	+	4.06163i	0.0723135	+	0.167642i	0.950539	−	0.310605i	$-0.100532\pi$
$587$	1.75202	+	4.06163i	0.0723135	+	0.167642i	−0.878225	+	0.478247i	$0.841272\pi$
$588$		0			0
$589$	−2.76899	−	9.24906i	−0.114094	−	0.381101i
$590$	3.68464	−	0.430673i	0.151694	−	0.0177305i
$591$		0			0
$592$	−0.619887	−	10.6430i	−0.0254772	−	0.437427i
$593$	2.41323	+	4.17983i	0.0990993	+	0.171645i	0.911312	−	0.411716i	$-0.135071\pi$
$593$	2.41323	+	4.17983i	0.0990993	+	0.171645i	−0.812213	+	0.583361i	$0.801737\pi$
$594$		0			0
$595$	−4.21086	+	7.29343i	−0.172629	+	0.299001i
$596$	−20.0243	−	10.0566i	−0.820227	−	0.411934i
$597$		0			0
$598$	2.48334	+	3.33571i	0.101551	+	0.136407i
$599$	−25.1459	−	5.95970i	−1.02744	−	0.243507i	−0.317861	−	0.948137i	$-0.602965\pi$
$599$	−25.1459	−	5.95970i	−1.02744	−	0.243507i	−0.709574	+	0.704631i	$0.751113\pi$
$600$		0			0
$601$	20.2678	−	27.2243i	0.826739	−	1.11050i	−0.165506	−	0.986209i	$-0.552926\pi$
$601$	20.2678	−	27.2243i	0.826739	−	1.11050i	0.992245	−	0.124295i	$-0.0396668\pi$
$602$	−2.30243	+	1.93197i	−0.0938401	+	0.0787412i
$603$		0			0
$604$	−3.67803	−	3.08623i	−0.149657	−	0.125577i
$605$	4.79088	−	1.13546i	0.194777	−	0.0461630i
$606$		0			0
$607$	34.8325	+	22.9097i	1.41381	+	0.929875i	0.999808	+	0.0195968i	$0.00623825\pi$
$607$	34.8325	+	22.9097i	1.41381	+	0.929875i	0.413998	+	0.910278i	$0.364132\pi$
$608$	6.24863	+	4.10979i	0.253415	+	0.166674i
$609$		0			0
$610$	−1.59915	+	0.379005i	−0.0647476	+	0.0153455i
$611$	−33.7411	−	28.3121i	−1.36502	−	1.14539i
$612$		0			0
$613$	1.53038	−	1.28414i	0.0618116	−	0.0518661i	−0.611358	−	0.791354i	$-0.709377\pi$
$613$	1.53038	−	1.28414i	0.0618116	−	0.0518661i	0.673170	+	0.739488i	$0.264932\pi$
$614$	−0.856862	+	1.15096i	−0.0345801	+	0.0464492i
$615$		0			0
$616$	5.53251	+	1.31123i	0.222911	+	0.0528309i
$617$	18.7421	+	25.1750i	0.754527	+	1.01351i	0.999038	+	0.0438590i	$0.0139652\pi$
$617$	18.7421	+	25.1750i	0.754527	+	1.01351i	−0.244511	+	0.969647i	$0.578627\pi$
$618$		0			0
$619$	−5.02506	−	2.52368i	−0.201974	−	0.101435i	0.344937	−	0.938626i	$-0.387900\pi$
$619$	−5.02506	−	2.52368i	−0.201974	−	0.101435i	−0.546911	+	0.837190i	$0.684197\pi$
$620$	3.02749	−	5.24376i	0.121587	−	0.210595i
$621$		0			0
$622$	2.93595	+	5.08522i	0.117721	+	0.203899i
$623$	1.86903	+	32.0901i	0.0748813	+	1.28566i
$624$		0			0
$625$	−20.8938	+	2.44214i	−0.835753	+	0.0976855i
$626$	−3.46636	−	11.5784i	−0.138544	−	0.462768i
$627$		0			0
$628$	−9.36836	−	21.7183i	−0.373838	−	0.866655i
$629$	31.9673	+	11.6352i	1.27462	+	0.463924i
$630$		0			0
$631$	−0.397697	+	0.144750i	−0.0158321	+	0.00576240i	−0.349924	−	0.936778i	$-0.613793\pi$
$631$	−0.397697	+	0.144750i	−0.0158321	+	0.00576240i	0.334092	+	0.942540i	$0.391570\pi$
$632$	−10.9091	−	11.5630i	−0.433941	−	0.459951i
$633$		0			0
$634$	1.77636	−	0.892121i	0.0705482	−	0.0354307i
$635$	−0.362217	+	6.21902i	−0.0143741	+	0.246794i
$636$		0			0
$637$	−2.10855	+	7.04304i	−0.0835437	+	0.279055i
$638$	−0.818834	+	4.64384i	−0.0324180	+	0.183851i
$639$		0			0
$640$	1.03925	+	5.89388i	0.0410800	+	0.232976i
$641$	−11.5838	−	1.35395i	−0.457532	−	0.0534778i	−0.115794	−	0.993273i	$-0.536941\pi$
$641$	−11.5838	−	1.35395i	−0.457532	−	0.0534778i	−0.341738	+	0.939795i	$0.611015\pi$
$642$		0			0
$643$	−29.1862	+	30.9355i	−1.15099	+	1.21998i	−0.179281	+	0.983798i	$0.557377\pi$
$643$	−29.1862	+	30.9355i	−1.15099	+	1.21998i	−0.971709	+	0.236181i	$0.924104\pi$
$644$	2.91866	−	6.76621i	0.115011	−	0.266626i
$645$		0			0
$646$	−4.65631	+	3.06250i	−0.183200	+	0.120492i
$647$	−14.1553			−0.556501			−0.278251	−	0.960508i	$-0.589755\pi$
$647$	−14.1553			−0.556501			−0.278251	+	0.960508i	$0.589755\pi$
$648$		0			0
$649$	−15.8424			−0.621867
$650$	−8.53720	+	5.61500i	−0.334856	+	0.220239i
$651$		0			0
$652$	−1.78797	+	4.14498i	−0.0700224	+	0.162330i
$653$	−7.94103	+	8.41700i	−0.310756	+	0.329383i	−0.863862	−	0.503729i	$-0.831961\pi$
$653$	−7.94103	+	8.41700i	−0.310756	+	0.329383i	0.553106	+	0.833111i	$0.313443\pi$
$654$		0			0
$655$	−8.18981	−	0.957252i	−0.320002	−	0.0374029i
$656$	−0.589989	−	3.34599i	−0.0230352	−	0.130639i
$657$		0			0
$658$	2.46136	−	13.9590i	0.0959536	−	0.544180i
$659$	1.23393	−	4.12161i	0.0480670	−	0.160555i	−0.930587	−	0.366072i	$-0.880702\pi$
$659$	1.23393	−	4.12161i	0.0480670	−	0.160555i	0.978654	+	0.205517i	$0.0658876\pi$
$660$		0			0
$661$	−0.170582	+	2.92879i	−0.00663489	+	0.113917i	−0.999999	−	0.00109179i	$-0.999652\pi$
$661$	−0.170582	+	2.92879i	−0.00663489	+	0.113917i	0.993365	+	0.115008i	$0.0366895\pi$
$662$	−2.05677	+	1.03295i	−0.0799387	+	0.0401467i
$663$		0			0
$664$	−5.89012	−	6.24316i	−0.228581	−	0.242282i
$665$	−1.54309	+	0.561641i	−0.0598387	+	0.0217795i
$666$		0			0
$667$	12.5285	+	4.56001i	0.485107	+	0.176564i
$668$	−13.9352	−	32.3053i	−0.539167	−	1.24993i
$669$		0			0
$670$	1.10860	+	3.70297i	0.0428289	+	0.143058i
$671$	6.97087	−	0.814778i	0.269107	−	0.0314541i
$672$		0			0
$673$	−0.936690	−	16.0824i	−0.0361068	−	0.619929i	−0.967022	−	0.254693i	$-0.918025\pi$
$673$	−0.936690	−	16.0824i	−0.0361068	−	0.619929i	0.930915	−	0.365236i	$-0.119012\pi$
$674$	−5.68011	−	9.83823i	−0.218790	−	0.378955i
$675$		0			0
$676$	1.84165	−	3.18983i	0.0708327	−	0.122686i
$677$	18.1338	+	9.10714i	0.696939	+	0.350016i	0.761740	−	0.647882i	$-0.224345\pi$
$677$	18.1338	+	9.10714i	0.696939	+	0.350016i	−0.0648017	+	0.997898i	$0.520641\pi$
$678$		0			0
$679$	21.0087	+	28.2195i	0.806239	+	1.08297i
$680$	−7.41972	−	1.75851i	−0.284533	−	0.0674356i
$681$		0			0
$682$	2.80431	−	3.76684i	0.107382	−	0.144240i
$683$	−25.4821	+	21.3820i	−0.975044	+	0.818159i	−0.983334	−	0.181806i	$-0.941806\pi$
$683$	−25.4821	+	21.3820i	−0.975044	+	0.818159i	0.00829016	+	0.999966i	$0.497361\pi$
$684$		0			0
$685$	0.179961	+	0.151005i	0.00687596	+	0.00576962i
$686$	−10.8412	+	2.56941i	−0.413919	+	0.0981006i
$687$		0			0
$688$	4.50710	+	2.96436i	0.171831	+	0.113015i
$689$	19.8097	+	13.0290i	0.754688	+	0.496366i
$690$		0			0
$691$	5.78847	−	1.37189i	0.220204	−	0.0521893i	−0.119033	−	0.992890i	$-0.537979\pi$
$691$	5.78847	−	1.37189i	0.220204	−	0.0521893i	0.339237	+	0.940701i	$0.389831\pi$
$692$	−17.3496	−	14.5580i	−0.659532	−	0.553413i
$693$		0			0
$694$	−13.2573	+	11.1242i	−0.503239	+	0.422268i
$695$	−1.78030	+	2.39135i	−0.0675305	+	0.0907092i
$696$		0			0
$697$	10.5494	+	2.50024i	0.399585	+	0.0947035i
$698$	3.91022	+	5.25233i	0.148004	+	0.198804i
$699$		0			0
$700$	16.1803	+	8.12608i	0.611560	+	0.307137i
$701$	−2.41414	+	4.18141i	−0.0911806	+	0.157929i	−0.908008	−	0.418952i	$-0.862397\pi$
$701$	−2.41414	+	4.18141i	−0.0911806	+	0.157929i	0.816828	+	0.576882i	$0.195731\pi$
$702$		0			0
$703$	3.31663	+	5.74456i	0.125089	+	0.216660i
$704$	−0.109861	−	1.88623i	−0.00414053	−	0.0710901i
$705$		0			0
$706$	−5.22533	+	0.610754i	−0.196658	+	0.0229860i
$707$	5.91261	+	19.7495i	0.222367	+	0.742756i
$708$		0			0
$709$	12.5159	+	29.0152i	0.470046	+	1.08969i	0.974120	+	0.226029i	$0.0725745\pi$
$709$	12.5159	+	29.0152i	0.470046	+	1.08969i	−0.504074	+	0.863660i	$0.668166\pi$
$710$	−0.585446	−	0.213085i	−0.0219714	−	0.00799694i
$711$		0			0
$712$	−27.3493	+	9.95432i	−1.02496	+	0.373054i
$713$	−9.11174	−	9.65788i	−0.341238	−	0.361691i
$714$		0			0
$715$	−2.21802	+	1.11393i	−0.0829493	+	0.0416587i
$716$	0.395050	−	6.78274i	0.0147637	−	0.253483i
$717$		0			0
$718$	−2.44551	+	8.16856i	−0.0912655	+	0.304848i
$719$	−0.209547	+	1.18840i	−0.00781477	+	0.0443198i	−0.988466	−	0.151444i	$-0.951608\pi$
$719$	−0.209547	+	1.18840i	−0.00781477	+	0.0443198i	0.980651	+	0.195764i	$0.0627187\pi$
$720$		0			0
$721$	−4.14621	−	23.5144i	−0.154413	−	0.875720i
$722$	9.38368	+	1.09679i	0.349224	+	0.0408185i
$723$		0			0
$724$	15.2315	−	16.1445i	0.566075	−	0.600004i
$725$	−12.9755	+	30.0807i	−0.481900	+	1.11717i
$726$		0			0
$727$	22.6307	−	14.8845i	0.839328	−	0.552034i	−0.0554936	−	0.998459i	$-0.517673\pi$
$727$	22.6307	−	14.8845i	0.839328	−	0.552034i	0.894821	+	0.446425i	$0.147303\pi$
$728$	18.0340			0.668385
$729$		0			0
$730$	−0.267044			−0.00988375
$731$	−14.3819	+	9.45912i	−0.531934	+	0.349858i
$732$		0			0
$733$	7.72184	−	17.9012i	0.285213	−	0.661198i	−0.714030	−	0.700116i	$-0.753132\pi$
$733$	7.72184	−	17.9012i	0.285213	−	0.661198i	0.999242	+	0.0389179i	$0.0123911\pi$
$734$	1.34994	−	1.43085i	0.0498272	−	0.0528138i
$735$		0			0
$736$	10.2161	+	1.19409i	0.376571	+	0.0440148i
$737$	−2.86641	−	16.2562i	−0.105585	−	0.598805i
$738$		0			0
$739$	2.48150	−	14.0733i	0.0912834	−	0.517694i	−0.904540	−	0.426390i	$-0.859785\pi$
$739$	2.48150	−	14.0733i	0.0912834	−	0.517694i	0.995823	−	0.0913044i	$-0.0291036\pi$
$740$	−1.19313	+	3.98532i	−0.0438602	+	0.146503i
$741$		0			0
$742$	−0.443657	+	7.61729i	−0.0162872	+	0.279640i
$743$	−11.7806	+	5.91644i	−0.432189	+	0.217053i	−0.651574	−	0.758585i	$-0.725891\pi$
$743$	−11.7806	+	5.91644i	−0.432189	+	0.217053i	0.219386	+	0.975638i	$0.429595\pi$
$744$		0			0
$745$	4.71270	+	4.99517i	0.172660	+	0.183009i
$746$	15.6578	−	5.69899i	0.573274	−	0.208655i
$747$		0			0
$748$	14.0262	+	5.10513i	0.512849	+	0.186662i
$749$	9.56793	+	22.1810i	0.349605	+	0.810474i
$750$		0			0
$751$	12.8223	+	42.8296i	0.467894	+	1.56287i	0.788113	+	0.615530i	$0.211058\pi$
$751$	12.8223	+	42.8296i	0.467894	+	1.56287i	−0.320220	+	0.947343i	$0.603757\pi$
$752$	−25.2686	+	2.95348i	−0.921452	+	0.107702i
$753$		0			0
$754$	0.869641	+	14.9312i	0.0316705	+	0.543761i
$755$	0.735741	+	1.27434i	0.0267764	+	0.0463780i
$756$		0			0
$757$	4.72638	−	8.18632i	0.171783	−	0.297537i	−0.767260	−	0.641336i	$-0.778381\pi$
$757$	4.72638	−	8.18632i	0.171783	−	0.297537i	0.939043	+	0.343799i	$0.111714\pi$
$758$	−11.6895	−	5.87071i	−0.424583	−	0.213234i
$759$		0			0
$760$	−0.887871	−	1.19262i	−0.0322065	−	0.0432608i
$761$	1.90438	+	0.451347i	0.0690338	+	0.0163613i	0.264988	−	0.964252i	$-0.414632\pi$
$761$	1.90438	+	0.451347i	0.0690338	+	0.0163613i	−0.195954	+	0.980613i	$0.562780\pi$
$762$		0			0
$763$	−13.5060	+	18.1417i	−0.488949	+	0.656773i
$764$	0.0788362	−	0.0661515i	0.00285219	−	0.00239328i
$765$		0			0
$766$	0.123129	+	0.103318i	0.00444885	+	0.00373303i
$767$	−48.8940	+	11.5881i	−1.76546	+	0.418422i
$768$		0			0
$769$	−18.2670	−	12.0144i	−0.658725	−	0.433250i	0.175646	−	0.984453i	$-0.443799\pi$
$769$	−18.2670	−	12.0144i	−0.658725	−	0.433250i	−0.834371	+	0.551203i	$0.814169\pi$
$770$	−0.667338	−	0.438915i	−0.0240492	−	0.0158174i
$771$		0			0
$772$	5.45105	−	1.29192i	0.196187	−	0.0464973i
$773$	13.5712	+	11.3876i	0.488122	+	0.409583i	0.853353	−	0.521334i	$-0.174565\pi$
$773$	13.5712	+	11.3876i	0.488122	+	0.409583i	−0.365231	+	0.930917i	$0.619010\pi$
$774$		0			0
$775$	24.9923	−	20.9711i	0.897751	−	0.753303i
$776$	−19.0218	+	25.5507i	−0.682844	+	0.917218i
$777$		0			0
$778$	−15.1484	−	3.59024i	−0.543097	−	0.128716i
$779$	1.26238	+	1.69566i	0.0452293	+	0.0607535i
$780$		0			0
$781$	2.37760	+	1.19407i	0.0850771	+	0.0427273i
$782$	−3.83230	+	6.63773i	−0.137043	+	0.237365i
$783$

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.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.463223 + 0.304667i) q^{2} +(-0.670406 + 1.55417i) q^{4} +(0.355980 - 0.377317i) q^{5} +(-2.24586 - 0.262503i) q^{7} +(-0.355511 - 2.01620i) q^{8} +O(q^{10})\)	\(q+(-0.463223 + 0.304667i) q^{2} +(-0.670406 + 1.55417i) q^{4} +(0.355980 - 0.377317i) q^{5} +(-2.24586 - 0.262503i) q^{7} +(-0.355511 - 2.01620i) q^{8} +(-0.0499424 + 0.283238i) q^{10} +(0.352258 - 1.17662i) q^{11} +(0.226512 - 3.88906i) q^{13} +(1.12031 - 0.562641i) q^{14} +(-1.54412 - 1.63667i) q^{16} +(6.74697 - 2.45569i) q^{17} +(1.31557 + 0.478829i) q^{19} +(0.347766 + 0.806212i) q^{20} +(0.195304 + 0.652361i) q^{22} +(1.91236 - 0.223523i) q^{23} +(0.275078 + 4.72291i) q^{25} +(1.07994 + 1.87051i) q^{26} +(1.91361 - 3.31448i) q^{28} +(6.18810 + 3.10778i) q^{29} +(-4.11811 - 5.53158i) q^{31} +(5.19815 + 1.23198i) q^{32} +(-2.37718 + 3.19311i) q^{34} +(-0.898529 + 0.753956i) q^{35} +(3.62954 + 3.04555i) q^{37} +(-0.755286 + 0.179006i) q^{38} +(-0.887303 - 0.583588i) q^{40} +(1.26157 + 0.829746i) q^{41} +(-2.33285 + 0.552895i) q^{43} +(1.59252 + 1.33629i) q^{44} +(-0.817749 + 0.686173i) q^{46} +(6.75172 - 9.06914i) q^{47} +(-1.83633 - 0.435219i) q^{49} +(-1.56633 - 2.10395i) q^{50} +(5.89243 + 2.95929i) q^{52} +(-3.04317 + 5.27093i) q^{53} +(-0.318564 - 0.551769i) q^{55} +(0.269168 + 4.62143i) q^{56} +(-3.81331 + 0.445712i) q^{58} +(-3.69936 - 12.3567i) q^{59} +(2.26328 + 5.24688i) q^{61} +(3.59289 + 1.30771i) q^{62} +(1.44557 - 0.526145i) q^{64} +(-1.38678 - 1.46990i) q^{65} +(12.0102 - 6.03174i) q^{67} +(-0.706625 + 12.1323i) q^{68} +(0.186514 - 0.623002i) q^{70} +(-0.376160 + 2.13331i) q^{71} +(0.161233 + 0.914398i) q^{73} +(-2.60917 - 0.304968i) q^{74} +(-1.62615 + 1.72362i) q^{76} +(-1.09999 + 2.55007i) q^{77} +(6.48739 - 4.26682i) q^{79} -1.16722 q^{80} -0.837183 q^{82} +(3.50271 - 2.30377i) q^{83} +(1.47521 - 3.41993i) q^{85} +(0.912180 - 0.966854i) q^{86} +(-2.49755 - 0.291921i) q^{88} +(-2.46858 - 14.0000i) q^{89} +(-1.52961 + 8.67483i) q^{91} +(-0.934663 + 3.12199i) q^{92} +(-0.364490 + 6.25806i) q^{94} +(0.648988 - 0.325934i) q^{95} +(-10.6772 - 11.3172i) q^{97} +(0.983230 - 0.357866i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

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