LMFDB - Embedded newform 729.2.g.a.109.1

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			109.1
Character	$\chi$	$=$	729.109
Dual form			729.2.g.a.622.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80640 - 1.91467i) q^{2} +(-0.286600 + 4.92073i) q^{4} +(1.22242 - 0.142880i) q^{5} +(3.38572 + 1.70037i) q^{7} +(5.90638 - 4.95604i) q^{8} +O(q^{10})$	\(q+(-1.80640 - 1.91467i) q^{2} +(-0.286600 + 4.92073i) q^{4} +(1.22242 - 0.142880i) q^{5} +(3.38572 + 1.70037i) q^{7} +(5.90638 - 4.95604i) q^{8} +(-2.48175 - 2.08243i) q^{10} +(0.0517889 + 0.120060i) q^{11} +(-1.35400 - 0.320904i) q^{13} +(-2.86031 - 9.55411i) q^{14} +(-10.3670 - 1.21173i) q^{16} +(-0.456801 + 2.59065i) q^{17} +(0.985248 + 5.58762i) q^{19} +(0.352730 + 6.05614i) q^{20} +(0.136325 - 0.316036i) q^{22} +(2.80671 - 1.40958i) q^{23} +(-3.39133 + 0.803761i) q^{25} +(1.83144 + 3.17215i) q^{26} +(-9.33742 + 16.1729i) q^{28} +(-2.69092 + 8.98830i) q^{29} +(0.633750 + 0.416824i) q^{31} +(7.19848 + 9.66923i) q^{32} +(5.78542 - 3.80513i) q^{34} +(4.38171 + 1.59481i) q^{35} +(7.99641 - 2.91045i) q^{37} +(8.91872 - 11.9799i) q^{38} +(6.51194 - 6.90225i) q^{40} +(-2.29682 + 2.43448i) q^{41} +(0.406715 - 0.546314i) q^{43} +(-0.605626 + 0.220430i) q^{44} +(-7.76895 - 2.82767i) q^{46} +(-2.45250 + 1.61304i) q^{47} +(4.39173 + 5.89911i) q^{49} +(7.66505 + 5.04139i) q^{50} +(1.96714 - 6.57070i) q^{52} +(-2.13391 + 3.69605i) q^{53} +(0.0804619 + 0.139364i) q^{55} +(28.4245 - 6.73672i) q^{56} +(22.0706 - 11.0843i) q^{58} +(2.40096 - 5.56606i) q^{59} +(0.416865 + 7.15730i) q^{61} +(-0.346725 - 1.96638i) q^{62} +(1.88515 - 10.6912i) q^{64} +(-1.70101 - 0.198819i) q^{65} +(-0.895189 - 2.99014i) q^{67} +(-12.6170 - 2.99028i) q^{68} +(-4.86159 - 11.2704i) q^{70} +(-2.02173 - 1.69643i) q^{71} +(4.57069 - 3.83527i) q^{73} +(-20.0173 - 10.0531i) q^{74} +(-27.7775 + 3.24673i) q^{76} +(-0.0288043 + 0.494550i) q^{77} +(-0.689346 - 0.730664i) q^{79} -12.8460 q^{80} +8.81022 q^{82} +(-6.22930 - 6.60268i) q^{83} +(-0.188250 + 3.23212i) q^{85} +(-1.78070 + 0.208134i) q^{86} +(0.900907 + 0.452453i) q^{88} +(7.18159 - 6.02607i) q^{89} +(-4.03861 - 3.38880i) q^{91} +(6.13178 + 14.2151i) q^{92} +(7.51865 + 1.78195i) q^{94} +(2.00274 + 6.68963i) q^{95} +(13.9071 + 1.62551i) q^{97} +(3.36166 - 19.0649i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−1.80640	−	1.91467i	−1.27732	−	1.35388i	−0.904789	−	0.425859i	$-0.859972\pi$
$2$	−1.80640	−	1.91467i	−1.27732	−	1.35388i	−0.372530	−	0.928020i	$-0.621510\pi$
$3$		0			0
$3$		0			0
$4$	−0.286600	+	4.92073i	−0.143300	+	2.46037i
$5$	1.22242	−	0.142880i	0.546682	−	0.0638979i	0.161731	−	0.986835i	$-0.448292\pi$
$5$	1.22242	−	0.142880i	0.546682	−	0.0638979i	0.384951	+	0.922937i	$0.374218\pi$
$6$		0			0
$7$	3.38572	+	1.70037i	1.27968	+	0.642680i	0.953148	−	0.302505i	$-0.0978229\pi$
$7$	3.38572	+	1.70037i	1.27968	+	0.642680i	0.326534	+	0.945185i	$0.394119\pi$
$8$	5.90638	−	4.95604i	2.08822	−	1.75222i
$9$		0			0
$10$	−2.48175	−	2.08243i	−0.784798	−	0.658523i
$11$	0.0517889	+	0.120060i	0.0156149	+	0.0361995i	0.925845	−	0.377903i	$-0.123355\pi$
$11$	0.0517889	+	0.120060i	0.0156149	+	0.0361995i	−0.910230	+	0.414103i	$0.864095\pi$
$12$		0			0
$13$	−1.35400	−	0.320904i	−0.375532	−	0.0890028i	0.0385154	−	0.999258i	$-0.487737\pi$
$13$	−1.35400	−	0.320904i	−0.375532	−	0.0890028i	−0.414048	+	0.910255i	$0.635885\pi$
$14$	−2.86031	−	9.55411i	−0.764451	−	2.55344i
$15$		0			0
$16$	−10.3670	−	1.21173i	−2.59175	−	0.302933i
$17$	−0.456801	+	2.59065i	−0.110791	+	0.628325i	0.877958	+	0.478738i	$0.158906\pi$
$17$	−0.456801	+	2.59065i	−0.110791	+	0.628325i	−0.988749	+	0.149587i	$0.952206\pi$
$18$		0			0
$19$	0.985248	+	5.58762i	0.226031	+	1.28189i	0.860704	+	0.509106i	$0.170024\pi$
$19$	0.985248	+	5.58762i	0.226031	+	1.28189i	−0.634672	+	0.772781i	$0.718865\pi$
$20$	0.352730	+	6.05614i	0.0788728	+	1.35419i
$21$		0			0
$22$	0.136325	−	0.316036i	0.0290645	−	0.0673790i
$23$	2.80671	−	1.40958i	0.585240	−	0.293919i	−0.131436	−	0.991325i	$-0.541959\pi$
$23$	2.80671	−	1.40958i	0.585240	−	0.293919i	0.716676	+	0.697406i	$0.245662\pi$
$24$		0			0
$25$	−3.39133	+	0.803761i	−0.678267	+	0.160752i
$26$	1.83144	+	3.17215i	0.359176	+	0.622110i
$27$		0			0
$28$	−9.33742	+	16.1729i	−1.76461	+	3.05639i
$29$	−2.69092	+	8.98830i	−0.499692	+	1.66909i	0.220560	+	0.975373i	$0.429211\pi$
$29$	−2.69092	+	8.98830i	−0.499692	+	1.66909i	−0.720252	+	0.693713i	$0.755974\pi$
$30$		0			0
$31$	0.633750	+	0.416824i	0.113825	+	0.0748637i	0.605145	−	0.796115i	$-0.293115\pi$
$31$	0.633750	+	0.416824i	0.113825	+	0.0748637i	−0.491320	+	0.870979i	$0.663486\pi$
$32$	7.19848	+	9.66923i	1.27252	+	1.70929i
$33$		0			0
$34$	5.78542	−	3.80513i	0.992191	−	0.652574i
$35$	4.38171	+	1.59481i	0.740645	+	0.269573i
$36$		0			0
$37$	7.99641	−	2.91045i	1.31460	−	0.478476i	0.412877	−	0.910787i	$-0.364524\pi$
$37$	7.99641	−	2.91045i	1.31460	−	0.478476i	0.901725	+	0.432311i	$0.142302\pi$
$38$	8.91872	−	11.9799i	1.44681	−	1.94340i
$39$		0			0
$40$	6.51194	−	6.90225i	1.02963	−	1.09134i
$41$	−2.29682	+	2.43448i	−0.358703	+	0.380203i	−0.881444	−	0.472289i	$-0.843428\pi$
$41$	−2.29682	+	2.43448i	−0.358703	+	0.380203i	0.522741	+	0.852491i	$0.324909\pi$
$42$		0			0
$43$	0.406715	−	0.546314i	0.0620235	−	0.0833120i	−0.770029	−	0.638009i	$-0.779758\pi$
$43$	0.406715	−	0.546314i	0.0620235	−	0.0833120i	0.832053	+	0.554697i	$0.187166\pi$
$44$	−0.605626	+	0.220430i	−0.0913016	+	0.0332311i
$45$		0			0
$46$	−7.76895	−	2.82767i	−1.14547	−	0.416917i
$47$	−2.45250	+	1.61304i	−0.357735	+	0.235286i	−0.715636	−	0.698474i	$-0.753863\pi$
$47$	−2.45250	+	1.61304i	−0.357735	+	0.235286i	0.357901	+	0.933760i	$0.383492\pi$
$48$		0			0
$49$	4.39173	+	5.89911i	0.627389	+	0.842730i
$50$	7.66505	+	5.04139i	1.08400	+	0.712960i
$51$		0			0
$52$	1.96714	−	6.57070i	0.272793	−	0.911192i
$53$	−2.13391	+	3.69605i	−0.293116	+	0.507691i	−0.974545	−	0.224193i	$-0.928025\pi$
$53$	−2.13391	+	3.69605i	−0.293116	+	0.507691i	0.681429	+	0.731884i	$0.261359\pi$
$54$		0			0
$55$	0.0804619	+	0.139364i	0.0108495	+	0.0187918i
$56$	28.4245	−	6.73672i	3.79838	−	0.900232i
$57$		0			0
$58$	22.0706	−	11.0843i	2.89801	−	1.45543i
$59$	2.40096	−	5.56606i	0.312579	−	0.724639i	−0.687420	−	0.726260i	$-0.741257\pi$
$59$	2.40096	−	5.56606i	0.312579	−	0.724639i	0.999999	+	0.00162089i	$0.000515944\pi$
$60$		0			0
$61$	0.416865	+	7.15730i	0.0533741	+	0.916398i	0.913633	+	0.406540i	$0.133265\pi$
$61$	0.416865	+	7.15730i	0.0533741	+	0.916398i	−0.860259	+	0.509858i	$0.829698\pi$
$62$	−0.346725	−	1.96638i	−0.0440341	−	0.249730i
$63$		0			0
$64$	1.88515	−	10.6912i	0.235644	−	1.33640i
$65$	−1.70101	−	0.198819i	−0.210984	−	0.0246605i
$66$		0			0
$67$	−0.895189	−	2.99014i	−0.109365	−	0.365304i	0.885734	−	0.464194i	$-0.153656\pi$
$67$	−0.895189	−	2.99014i	−0.109365	−	0.365304i	−0.995098	+	0.0988903i	$0.968471\pi$
$68$	−12.6170	−	2.99028i	−1.53003	−	0.362624i
$69$		0			0
$70$	−4.86159	−	11.2704i	−0.581071	−	1.34707i
$71$	−2.02173	−	1.69643i	−0.239935	−	0.201329i	0.514889	−	0.857257i	$-0.327833\pi$
$71$	−2.02173	−	1.69643i	−0.239935	−	0.201329i	−0.754824	+	0.655928i	$0.772278\pi$
$72$		0			0
$73$	4.57069	−	3.83527i	0.534959	−	0.448884i	−0.334851	−	0.942271i	$-0.608686\pi$
$73$	4.57069	−	3.83527i	0.534959	−	0.448884i	0.869810	+	0.493387i	$0.164241\pi$
$74$	−20.0173	−	10.0531i	−2.32696	−	1.16865i
$75$		0			0
$76$	−27.7775	+	3.24673i	−3.18630	+	0.372425i
$77$	−0.0288043	+	0.494550i	−0.00328255	+	0.0563592i
$78$		0			0
$79$	−0.689346	−	0.730664i	−0.0775574	−	0.0822061i	0.687433	−	0.726248i	$-0.258738\pi$
$79$	−0.689346	−	0.730664i	−0.0775574	−	0.0822061i	−0.764990	+	0.644042i	$0.777256\pi$
$80$	−12.8460			−1.43622
$81$		0			0
$82$	8.81022			0.972926
$83$	−6.22930	−	6.60268i	−0.683755	−	0.724738i	0.288806	−	0.957388i	$-0.406742\pi$
$83$	−6.22930	−	6.60268i	−0.683755	−	0.724738i	−0.972561	+	0.232650i	$0.925260\pi$
$84$		0			0
$85$	−0.188250	+	3.23212i	−0.0204186	+	0.350573i
$86$	−1.78070	+	0.208134i	−0.192018	+	0.0224437i
$87$		0			0
$88$	0.900907	+	0.452453i	0.0960370	+	0.0482316i
$89$	7.18159	−	6.02607i	0.761247	−	0.638762i	−0.177204	−	0.984174i	$-0.556705\pi$
$89$	7.18159	−	6.02607i	0.761247	−	0.638762i	0.938451	+	0.345412i	$0.112261\pi$
$90$		0			0
$91$	−4.03861	−	3.38880i	−0.423361	−	0.355242i
$92$	6.13178	+	14.2151i	0.639283	+	1.48202i
$93$		0			0
$94$	7.51865	+	1.78195i	0.775490	+	0.183794i
$95$	2.00274	+	6.68963i	0.205477	+	0.686342i
$96$		0			0
$97$	13.9071	+	1.62551i	1.41205	+	0.165045i	0.787682	−	0.616082i	$-0.211281\pi$
$97$	13.9071	+	1.62551i	1.41205	+	0.165045i	0.624372	+	0.781128i	$0.285355\pi$
$98$	3.36166	−	19.0649i	0.339578	−	1.92585i
$99$		0			0
$100$	−2.98313	−	16.9182i	−0.298313	−	1.69182i
$101$	−0.421305	−	7.23352i	−0.0419214	−	0.719762i	−0.952145	−	0.305646i	$-0.901128\pi$
$101$	−0.421305	−	7.23352i	−0.0419214	−	0.719762i	0.910224	−	0.414116i	$-0.135909\pi$
$102$		0			0
$103$	−2.23345	+	5.17771i	−0.220068	+	0.510175i	−0.992106	−	0.125401i	$-0.959978\pi$
$103$	−2.23345	+	5.17771i	−0.220068	+	0.510175i	0.772038	+	0.635576i	$0.219237\pi$
$104$	−9.58765	+	4.81510i	−0.940146	+	0.472159i
$105$		0			0
$106$	10.9314	−	2.59080i	1.06175	−	0.251641i
$107$	7.97908	+	13.8202i	0.771366	+	1.33605i	0.936814	+	0.349827i	$0.113760\pi$
$107$	7.97908	+	13.8202i	0.771366	+	1.33605i	−0.165448	+	0.986219i	$0.552907\pi$
$108$		0			0
$109$	9.37030	−	16.2298i	0.897512	−	1.55454i	0.0668480	−	0.997763i	$-0.478706\pi$
$109$	9.37030	−	16.2298i	0.897512	−	1.55454i	0.830664	−	0.556774i	$-0.187961\pi$
$110$	0.121490	−	0.405806i	0.0115836	−	0.0386921i
$111$		0			0
$112$	−33.0394	−	21.7304i	−3.12193	−	2.05333i
$113$	0.167706	+	0.225269i	0.0157765	+	0.0211915i	0.809941	−	0.586511i	$-0.199499\pi$
$113$	0.167706	+	0.225269i	0.0157765	+	0.0211915i	−0.794165	+	0.607702i	$0.792091\pi$
$114$		0			0
$115$	3.22958	−	2.12413i	0.301159	−	0.198076i
$116$	−43.4578	−	15.8173i	−4.03496	−	1.46860i
$117$		0			0
$118$	−14.9943	+	5.45748i	−1.38034	+	0.502402i
$119$	−5.95167	+	7.99448i	−0.545589	+	0.732853i
$120$		0			0
$121$	7.53693	−	7.98867i	0.685175	−	0.726243i
$122$	12.9509	−	13.7271i	1.17252	−	1.24279i
$123$		0			0
$124$	−2.23271	+	2.99905i	−0.200503	+	0.269323i
$125$	−9.81337	+	3.57177i	−0.877735	+	0.319469i
$126$		0			0
$127$	16.6155	+	6.04753i	1.47438	+	0.536632i	0.949287	−	0.314411i	$-0.101807\pi$
$127$	16.6155	+	6.04753i	1.47438	+	0.536632i	0.525097	+	0.851042i	$0.324029\pi$
$128$	−3.73271	+	2.45504i	−0.329928	+	0.216997i
$129$		0			0
$130$	2.69203	+	3.61602i	0.236106	+	0.317146i
$131$	−5.01441	−	3.29803i	−0.438111	−	0.288150i	0.311230	−	0.950335i	$-0.399259\pi$
$131$	−5.01441	−	3.29803i	−0.438111	−	0.288150i	−0.749341	+	0.662185i	$0.769630\pi$
$132$		0			0
$133$	−6.16526	+	20.5934i	−0.534596	+	1.78567i
$134$	−4.10807	+	7.11539i	−0.354883	+	0.614676i
$135$		0			0
$136$	10.1413	+	17.5653i	0.869611	+	1.50621i
$137$	3.74519	−	0.887626i	0.319973	−	0.0758350i	−0.0674909	−	0.997720i	$-0.521499\pi$
$137$	3.74519	−	0.887626i	0.319973	−	0.0758350i	0.387464	+	0.921885i	$0.373351\pi$
$138$		0			0
$139$	8.48155	−	4.25960i	0.719396	−	0.361294i	−0.0511393	−	0.998692i	$-0.516285\pi$
$139$	8.48155	−	4.25960i	0.719396	−	0.361294i	0.770535	+	0.637397i	$0.219989\pi$
$140$	−9.10345	+	21.1042i	−0.769382	+	1.78363i
$141$		0			0
$142$	0.403940	+	6.93538i	0.0338979	+	0.582004i
$143$	−0.0315944	−	0.179181i	−0.00264206	−	0.0149838i
$144$		0			0
$145$	−2.00518	+	11.3719i	−0.166521	+	0.944388i
$146$	−15.5998	−	1.82335i	−1.29105	−	0.150902i
$147$		0			0
$148$	12.0298	+	40.1823i	0.988843	+	3.30297i
$149$	14.3119	+	3.39199i	1.17248	+	0.277883i	0.770302	−	0.637679i	$-0.220105\pi$
$149$	14.3119	+	3.39199i	1.17248	+	0.277883i	0.402177	+	0.915562i	$0.368254\pi$
$150$		0			0
$151$	−4.19116	−	9.71621i	−0.341072	−	0.790694i	−0.999283	−	0.0378602i	$-0.987946\pi$
$151$	−4.19116	−	9.71621i	−0.341072	−	0.790694i	0.658211	−	0.752833i	$-0.271313\pi$
$152$	33.5117	+	28.1197i	2.71816	+	2.28081i
$153$		0			0
$154$	0.998935	−	0.838206i	0.0804965	−	0.0675446i
$155$	0.834263	+	0.418982i	0.0670096	+	0.0336535i
$156$		0			0
$157$	−7.72844	+	0.903325i	−0.616796	+	0.0720932i	−0.418753	−	0.908100i	$-0.637533\pi$
$157$	−7.72844	+	0.903325i	−0.616796	+	0.0720932i	−0.198043	+	0.980193i	$0.563459\pi$
$158$	−0.153748	+	2.63975i	−0.0122315	+	0.210007i
$159$		0			0
$160$	10.1811	+	10.7913i	0.804886	+	0.853129i
$161$	11.8996			0.937817
$162$		0			0
$163$	−16.0980			−1.26089			−0.630446	−	0.776233i	$-0.717128\pi$
$163$	−16.0980			−1.26089			−0.630446	+	0.776233i	$0.717128\pi$
$164$	−11.3212	−	11.9997i	−0.884035	−	0.937022i
$165$		0			0
$166$	−1.38935	+	23.8542i	−0.107834	+	1.85144i
$167$	−4.71360	+	0.550941i	−0.364750	+	0.0426331i	−0.296494	−	0.955035i	$-0.595817\pi$
$167$	−4.71360	+	0.550941i	−0.364750	+	0.0426331i	−0.0682557	+	0.997668i	$0.521743\pi$
$168$		0			0
$169$	−9.88689	−	4.96538i	−0.760530	−	0.381952i
$170$	6.52852	−	5.47808i	0.500715	−	0.420149i
$171$		0			0
$172$	2.57170	+	2.15791i	0.196090	+	0.164539i
$173$	9.46018	+	21.9312i	0.719244	+	1.66740i	0.744420	+	0.667712i	$0.232726\pi$
$173$	9.46018	+	21.9312i	0.719244	+	1.66740i	−0.0251755	+	0.999683i	$0.508014\pi$
$174$		0			0
$175$	−12.8488	−	3.04522i	−0.971278	−	0.230197i
$176$	−0.391416	−	1.30742i	−0.0295041	−	0.0985504i
$177$		0			0
$178$	−24.5108	−	2.86490i	−1.83716	−	0.214734i
$179$	−1.52251	+	8.63457i	−0.113798	+	0.645378i	0.873541	+	0.486751i	$0.161818\pi$
$179$	−1.52251	+	8.63457i	−0.113798	+	0.645378i	−0.987339	+	0.158627i	$0.949293\pi$
$180$		0			0
$181$	0.0939796	+	0.532985i	0.00698545	+	0.0396165i	0.988101	−	0.153805i	$-0.0491527\pi$
$181$	0.0939796	+	0.532985i	0.00698545	+	0.0396165i	−0.981116	+	0.193421i	$0.938042\pi$
$182$	0.806913	+	13.8542i	0.0598124	+	1.02694i
$183$		0			0
$184$	9.59155	−	22.2357i	0.707099	−	1.63924i
$185$	9.35911	−	4.70032i	0.688095	−	0.345574i
$186$		0			0
$187$	−0.334691	+	0.0793232i	−0.0244750	+	0.00580069i
$188$	−7.23444	−	12.5304i	−0.527625	−	0.913874i
$189$		0			0
$190$	9.19071	−	15.9188i	0.666764	−	1.15487i
$191$	0.258769	−	0.864349i	0.0187239	−	0.0625421i	−0.948117	−	0.317921i	$-0.897015\pi$
$191$	0.258769	−	0.864349i	0.0187239	−	0.0625421i	0.966841	+	0.255379i	$0.0822004\pi$
$192$		0			0
$193$	−11.5954	−	7.62641i	−0.834654	−	0.548961i	0.0587197	−	0.998275i	$-0.481298\pi$
$193$	−11.5954	−	7.62641i	−0.834654	−	0.548961i	−0.893374	+	0.449314i	$0.851669\pi$
$194$	−22.0095	−	29.5639i	−1.58019	−	2.12257i
$195$		0			0
$196$	−30.2866	+	19.9198i	−2.16333	+	1.42284i
$197$	20.0246	+	7.28837i	1.42670	+	0.519275i	0.935983	−	0.352047i	$-0.114514\pi$
$197$	20.0246	+	7.28837i	1.42670	+	0.519275i	0.490713	+	0.871321i	$0.336736\pi$
$198$		0			0
$199$	−18.1056	+	6.58992i	−1.28348	+	0.467147i	−0.891580	−	0.452863i	$-0.850403\pi$
$199$	−18.1056	+	6.58992i	−1.28348	+	0.467147i	−0.391895	+	0.920010i	$0.628180\pi$
$200$	−16.0470	+	21.5549i	−1.13470	+	1.52416i
$201$		0			0
$202$	−13.0888	+	13.8733i	−0.920924	+	0.976123i
$203$	−24.3942	+	25.8563i	−1.71214	+	1.81476i
$204$		0			0
$205$	−2.45983	+	3.30413i	−0.171802	+	0.230770i
$206$	13.9481	−	5.07671i	0.971813	−	0.353711i
$207$		0			0
$208$	13.6481	+	4.96750i	0.946325	+	0.344434i
$209$	−0.619825	+	0.407665i	−0.0428742	+	0.0281988i
$210$		0			0
$211$	0.350122	+	0.470295i	0.0241034	+	0.0323765i	0.814012	−	0.580849i	$-0.197279\pi$
$211$	0.350122	+	0.470295i	0.0241034	+	0.0323765i	−0.789908	+	0.613225i	$0.789872\pi$
$212$	−17.5757	−	11.5597i	−1.20710	−	0.793924i
$213$		0			0
$214$	12.0477	−	40.2421i	0.823564	−	2.75089i
$215$	0.419119	−	0.725935i	0.0285837	−	0.0495084i
$216$		0			0
$217$	1.43694	+	2.48886i	0.0975461	+	0.168955i
$218$	−48.0014	+	11.3765i	−3.25107	+	0.770517i
$219$		0			0
$220$	−0.708833	+	0.355989i	−0.0477895	+	0.0240008i
$221$	1.44986	−	3.36115i	0.0975281	−	0.226095i
$222$		0			0
$223$	0.684240	+	11.7480i	0.0458201	+	0.786701i	0.940458	+	0.339909i	$0.110396\pi$
$223$	0.684240	+	11.7480i	0.0458201	+	0.786701i	−0.894638	+	0.446792i	$0.852567\pi$
$224$	7.93073	+	44.9774i	0.529894	+	3.00518i
$225$		0			0
$226$	0.128371	−	0.728029i	0.00853913	−	0.0484278i
$227$	27.5950	+	3.22540i	1.83155	+	0.214077i	0.960721	−	0.277514i	$-0.0895106\pi$
$227$	27.5950	+	3.22540i	1.83155	+	0.214077i	0.870826	+	0.491592i	$0.163585\pi$
$228$		0			0
$229$	−5.22420	−	17.4500i	−0.345225	−	1.15313i	−0.937672	−	0.347522i	$-0.887023\pi$
$229$	−5.22420	−	17.4500i	−0.345225	−	1.15313i	0.592447	−	0.805609i	$-0.298162\pi$
$230$	−9.90092	−	2.34656i	−0.652848	−	0.154728i
$231$		0			0
$232$	28.6528	+	66.4246i	1.88115	+	4.36099i
$233$	−14.3791	−	12.0655i	−0.942004	−	0.790435i	0.0359291	−	0.999354i	$-0.488561\pi$
$233$	−14.3791	−	12.0655i	−0.942004	−	0.790435i	−0.977933	+	0.208919i	$0.933005\pi$
$234$		0			0
$235$	−2.76751	+	2.32222i	−0.180533	+	0.151485i
$236$	26.7010	+	13.4097i	1.73809	+	0.872899i
$237$		0			0
$238$	26.0579	−	3.04574i	1.68909	−	0.197426i
$239$	0.681110	−	11.6942i	0.0440574	−	0.756436i	−0.901860	−	0.432028i	$-0.857798\pi$
$239$	0.681110	−	11.6942i	0.0440574	−	0.756436i	0.945917	−	0.324407i	$-0.105165\pi$
$240$		0			0
$241$	−10.9232	−	11.5779i	−0.703626	−	0.745800i	0.272701	−	0.962099i	$-0.412083\pi$
$241$	−10.9232	−	11.5779i	−0.703626	−	0.745800i	−0.976327	+	0.216299i	$0.930601\pi$
$242$	−28.9104			−1.85843
$243$		0			0
$244$	−35.3386			−2.26232
$245$	6.21139	+	6.58369i	0.396831	+	0.420616i
$246$		0			0
$247$	0.459063	−	7.88181i	0.0292095	−	0.501507i
$248$	5.80896	−	0.678970i	0.368869	−	0.0431146i
$249$		0			0
$250$	24.5657	+	12.3374i	1.55367	+	0.780283i
$251$	−12.0448	+	10.1068i	−0.760259	+	0.637933i	−0.938194	−	0.346109i	$-0.887503\pi$
$251$	−12.0448	+	10.1068i	−0.760259	+	0.637933i	0.177935	+	0.984042i	$0.443058\pi$
$252$		0			0
$253$	0.314591	+	0.263974i	0.0197782	+	0.0165959i
$254$	−18.4352	−	42.7375i	−1.15672	−	2.68159i
$255$		0			0
$256$	−9.68368	−	2.29507i	−0.605230	−	0.143442i
$257$	−0.414732	−	1.38530i	−0.0258703	−	0.0864127i	0.944080	−	0.329718i	$-0.106954\pi$
$257$	−0.414732	−	1.38530i	−0.0258703	−	0.0864127i	−0.969950	+	0.243305i	$0.921768\pi$
$258$		0			0
$259$	32.0225	+	3.74289i	1.98978	+	0.232572i
$260$	1.46584	−	8.31321i	0.0909077	−	0.515563i
$261$		0			0
$262$	2.74339	+	15.5585i	0.169487	+	0.961209i
$263$	−1.14604	−	19.6768i	−0.0706680	−	1.21332i	−0.828165	−	0.560484i	$-0.810615\pi$
$263$	−1.14604	−	19.6768i	−0.0706680	−	1.21332i	0.757497	−	0.652839i	$-0.226422\pi$
$264$		0			0
$265$	−2.08044	+	4.82301i	−0.127801	+	0.296275i
$266$	50.5666	−	25.3955i	3.10044	−	1.55710i
$267$		0			0
$268$	14.9702	−	3.54801i	0.914452	−	0.216729i
$269$	−14.3328	−	24.8251i	−0.873883	−	1.51361i	−0.857948	−	0.513737i	$-0.828261\pi$
$269$	−14.3328	−	24.8251i	−0.873883	−	1.51361i	−0.0159358	−	0.999873i	$-0.505073\pi$
$270$		0			0
$271$	−5.81405	+	10.0702i	−0.353178	+	0.611723i	−0.986804	−	0.161917i	$-0.948232\pi$
$271$	−5.81405	+	10.0702i	−0.353178	+	0.611723i	0.633626	+	0.773639i	$0.281566\pi$
$272$	7.87483	−	26.3038i	0.477482	−	1.59490i
$273$		0			0
$274$	−8.46483	−	5.56741i	−0.511379	−	0.336339i
$275$	−0.272133	−	0.365538i	−0.0164102	−	0.0220428i
$276$		0			0
$277$	1.11501	−	0.733351i	0.0669943	−	0.0440628i	−0.515570	−	0.856847i	$-0.672420\pi$
$277$	1.11501	−	0.733351i	0.0669943	−	0.0440628i	0.582564	+	0.812785i	$0.302049\pi$
$278$	−23.4768	−	8.54487i	−1.40805	−	0.512487i
$279$		0			0
$280$	33.7840	−	12.2964i	2.01898	−	0.734849i
$281$	6.92888	−	9.30711i	0.413343	−	0.555215i	−0.545881	−	0.837862i	$-0.683805\pi$
$281$	6.92888	−	9.30711i	0.413343	−	0.555215i	0.959224	+	0.282647i	$0.0912125\pi$
$282$		0			0
$283$	−6.67381	+	7.07383i	−0.396717	+	0.420495i	−0.894683	−	0.446701i	$-0.852599\pi$
$283$	−6.67381	+	7.07383i	−0.396717	+	0.420495i	0.497966	+	0.867196i	$0.334080\pi$
$284$	8.92710	−	9.46217i	0.529726	−	0.561476i
$285$		0			0
$286$	−0.286001	+	0.384165i	−0.0169116	+	0.0227162i
$287$	−11.9159	+	4.33704i	−0.703374	+	0.256007i
$288$		0			0
$289$	9.47198	+	3.44752i	0.557175	+	0.202795i
$290$	25.3957	−	16.7030i	1.49129	−	0.980836i
$291$		0			0
$292$	17.5623	+	23.5903i	1.02776	+	1.38052i
$293$	24.9955	+	16.4398i	1.46026	+	0.960425i	0.997253	+	0.0740678i	$0.0235981\pi$
$293$	24.9955	+	16.4398i	1.46026	+	0.960425i	0.463002	+	0.886357i	$0.346772\pi$
$294$		0			0
$295$	2.13970	−	7.14710i	0.124578	−	0.416120i
$296$	32.8055	−	56.8207i	1.90678	−	3.30264i
$297$		0			0
$298$	−19.3586	−	33.5300i	−1.12141	−	1.94234i
$299$	−4.25263	+	1.00789i	−0.245936	+	0.0582879i
$300$		0			0
$301$	2.30596	−	1.15810i	0.132913	−	0.0667516i
$302$	−11.0324	+	25.5761i	−0.634846	+	1.47174i
$303$		0			0
$304$	−3.44339	−	59.1208i	−0.197492	−	3.39081i
$305$	1.53222	+	8.68964i	0.0877346	+	0.497568i
$306$		0			0
$307$	5.11689	−	29.0193i	0.292036	−	1.65622i	−0.386974	−	0.922091i	$-0.626480\pi$
$307$	5.11689	−	29.0193i	0.292036	−	1.65622i	0.679010	−	0.734129i	$-0.262409\pi$
$308$	−2.42529	−	0.283476i	−0.138194	−	0.0161526i
$309$		0			0
$310$	−0.704799	−	2.35419i	−0.0400299	−	0.133709i
$311$	−17.3152	−	4.10378i	−0.981854	−	0.232704i	−0.291814	−	0.956475i	$-0.594259\pi$
$311$	−17.3152	−	4.10378i	−0.981854	−	0.232704i	−0.690040	+	0.723771i	$0.742407\pi$
$312$		0			0
$313$	−7.68509	−	17.8160i	−0.434387	−	1.00702i	−0.985046	−	0.172292i	$-0.944883\pi$
$313$	−7.68509	−	17.8160i	−0.434387	−	1.00702i	0.550659	−	0.834730i	$-0.314377\pi$
$314$	15.6902	+	13.1657i	0.885451	+	0.742982i
$315$		0			0
$316$	3.79297	−	3.18268i	0.213371	−	0.179039i
$317$	3.77961	+	1.89819i	0.212284	+	0.106613i	0.551764	−	0.834000i	$-0.313955\pi$
$317$	3.77961	+	1.89819i	0.212284	+	0.106613i	−0.339480	+	0.940613i	$0.610251\pi$
$318$		0			0
$319$	−1.21850	+	0.142422i	−0.0682227	+	0.00797409i
$320$	0.776879	−	13.3385i	0.0434288	−	0.745644i
$321$		0			0
$322$	−21.4954	−	22.7838i	−1.19789	−	1.26969i
$323$	−14.9256			−0.830484
$324$		0			0
$325$	4.84980			0.269018
$326$	29.0795	+	30.8224i	1.61056	+	1.70710i
$327$		0			0
$328$	−1.50047	+	25.7621i	−0.0828497	+	1.42247i
$329$	−11.0463	+	1.29112i	−0.609000	+	0.0711819i
$330$		0			0
$331$	−10.4848	−	5.26567i	−0.576297	−	0.289427i	0.136679	−	0.990615i	$-0.456357\pi$
$331$	−10.4848	−	5.26567i	−0.576297	−	0.289427i	−0.712976	+	0.701188i	$0.752653\pi$
$332$	34.2753	−	28.7604i	1.88110	−	1.57843i
$333$		0			0
$334$	9.56954	+	8.02979i	0.523622	+	0.439371i
$335$	−1.52153	−	3.52729i	−0.0831298	−	0.192717i
$336$		0			0
$337$	0.470154	+	0.111429i	0.0256109	+	0.00606990i	0.243401	−	0.969926i	$-0.421737\pi$
$337$	0.470154	+	0.111429i	0.0256109	+	0.00606990i	−0.217790	+	0.975996i	$0.569885\pi$
$338$	8.35261	+	27.8996i	0.454322	+	1.51754i
$339$		0			0
$340$	−15.8505	−	1.85265i	−0.859612	−	0.100474i
$341$	−0.0172227	+	0.0976749i	−0.000932662	+	0.00528939i
$342$		0			0
$343$	0.233141	+	1.32221i	0.0125884	+	0.0713926i
$344$	−0.305337	−	5.24243i	−0.0164627	−	0.282653i
$345$		0			0
$346$	24.9021	−	57.7297i	1.33875	−	3.10357i
$347$	−26.3002	+	13.2084i	−1.41187	+	0.709066i	−0.981119	−	0.193406i	$-0.938047\pi$
$347$	−26.3002	+	13.2084i	−1.41187	+	0.709066i	−0.430748	+	0.902472i	$0.641750\pi$
$348$		0			0
$349$	−24.8110	+	5.88031i	−1.32810	+	0.314766i	−0.832616	−	0.553851i	$-0.813158\pi$
$349$	−24.8110	+	5.88031i	−1.32810	+	0.314766i	−0.495485	+	0.868616i	$0.665010\pi$
$350$	17.3795	+	30.1022i	0.928973	+	1.60903i
$351$		0			0
$352$	−0.788088	+	1.36501i	−0.0420052	+	0.0727552i
$353$	6.59280	−	22.0215i	0.350900	−	1.17209i	−0.582374	−	0.812921i	$-0.697876\pi$
$353$	6.59280	−	22.0215i	0.350900	−	1.17209i	0.933274	−	0.359165i	$-0.116939\pi$
$354$		0			0
$355$	−2.71378	−	1.78488i	−0.144032	−	0.0947316i
$356$	27.5944	+	37.0657i	1.46250	+	1.96448i
$357$		0			0
$358$	19.2827	−	12.6824i	1.01912	−	0.670286i
$359$	−17.0829	−	6.21766i	−0.901601	−	0.328156i	−0.150707	−	0.988579i	$-0.548155\pi$
$359$	−17.0829	−	6.21766i	−0.901601	−	0.328156i	−0.750894	+	0.660423i	$0.770377\pi$
$360$		0			0
$361$	−12.3966	+	4.51200i	−0.652453	+	0.237473i
$362$	0.850728	−	1.14273i	0.0447133	−	0.0600603i
$363$		0			0
$364$	17.8328	−	18.9017i	0.934694	−	0.990718i
$365$	5.03931	−	5.34136i	0.263770	−	0.279579i
$366$		0			0
$367$	−7.34645	+	9.86800i	−0.383482	+	0.515105i	−0.951391	−	0.307986i	$-0.900345\pi$
$367$	−7.34645	+	9.86800i	−0.383482	+	0.515105i	0.567909	+	0.823091i	$0.307752\pi$
$368$	−30.8053	+	11.2122i	−1.60584	+	0.584477i
$369$		0			0
$370$	−25.9059	−	9.42897i	−1.34678	−	0.490189i
$371$	−13.5095	+	8.88533i	−0.701378	+	0.461304i
$372$		0			0
$373$	1.93432	+	2.59824i	0.100155	+	0.134532i	0.849375	−	0.527789i	$-0.176979\pi$
$373$	1.93432	+	2.59824i	0.100155	+	0.134532i	−0.749220	+	0.662321i	$0.769572\pi$
$374$	0.756465	+	0.497535i	0.0391158	+	0.0257269i
$375$		0			0
$376$	−6.49114	+	21.6819i	−0.334755	+	1.11816i
$377$	6.52789	−	11.3066i	0.336204	−	0.582322i
$378$		0			0
$379$	−15.9961	−	27.7060i	−0.821664	−	1.42316i	−0.904443	−	0.426595i	$-0.859713\pi$
$379$	−15.9961	−	27.7060i	−0.821664	−	1.42316i	0.0827788	−	0.996568i	$-0.473621\pi$
$380$	−33.4919	+	7.93772i	−1.71810	+	0.407196i
$381$		0			0
$382$	−2.12239	+	1.06590i	−0.108591	+	0.0545364i
$383$	5.28390	−	12.2495i	0.269995	−	0.625918i	−0.728239	−	0.685323i	$-0.759661\pi$
$383$	5.28390	−	12.2495i	0.269995	−	0.625918i	0.998234	+	0.0594050i	$0.0189203\pi$
$384$		0			0
$385$	0.0354506	+	0.608663i	0.00180673	+	0.0310203i
$386$	6.34385	+	35.9778i	0.322893	+	1.83122i
$387$		0			0
$388$	−11.9845	+	67.9673i	−0.608419	+	3.45052i
$389$	23.8090	+	2.78288i	1.20717	+	0.141098i	0.695781	−	0.718254i	$-0.255058\pi$
$389$	23.8090	+	2.78288i	1.20717	+	0.141098i	0.511385	+	0.859351i	$0.329132\pi$
$390$		0			0
$391$	2.36963	+	7.91511i	0.119837	+	0.400284i
$392$	55.1754	+	13.0768i	2.78678	+	0.660479i
$393$		0			0
$394$	−22.2177	−	51.5064i	−1.11931	−	2.59485i
$395$	−0.947066	−	0.794682i	−0.0476520	−	0.0399848i
$396$		0			0
$397$	2.87549	−	2.41282i	0.144317	−	0.121096i	−0.567771	−	0.823186i	$-0.692194\pi$
$397$	2.87549	−	2.41282i	0.144317	−	0.121096i	0.712088	+	0.702090i	$0.247750\pi$
$398$	45.3236	+	22.7624i	2.27187	+	1.14098i
$399$		0			0
$400$	36.1319	−	4.22322i	1.80660	−	0.211161i
$401$	0.00360175	−	0.0618397i	0.000179863	−	0.00308812i	−0.998217	−	0.0596888i	$-0.980989\pi$
$401$	0.00360175	−	0.0618397i	0.000179863	−	0.00308812i	0.998397	+	0.0566007i	$0.0180262\pi$
$402$		0			0
$403$	−0.724337	−	0.767752i	−0.0360818	−	0.0382445i
$404$	35.7149			1.77689
$405$		0			0
$406$	93.5721			4.64391
$407$	0.763554	+	0.809320i	0.0378480	+	0.0401165i
$408$		0			0
$409$	0.792100	−	13.5998i	0.0391668	−	0.672468i	−0.920398	−	0.390982i	$-0.872136\pi$
$409$	0.792100	−	13.5998i	0.0391668	−	0.672468i	0.959565	−	0.281486i	$-0.0908274\pi$
$410$	10.7698	−	1.25881i	0.531881	−	0.0621680i
$411$		0			0
$412$	−24.8380	−	12.4741i	−1.22368	−	0.614556i
$413$	17.5934	−	14.7626i	0.865713	−	0.726420i
$414$		0			0
$415$	−8.55820	−	7.18118i	−0.420106	−	0.352510i
$416$	−6.64384	−	15.4022i	−0.325741	−	0.755153i
$417$		0			0
$418$	1.90020	+	0.450356i	0.0929418	+	0.0220276i
$419$	7.14075	+	23.8518i	0.348848	+	1.16523i	0.934885	+	0.354950i	$0.115502\pi$
$419$	7.14075	+	23.8518i	0.348848	+	1.16523i	−0.586037	+	0.810284i	$0.699313\pi$
$420$		0			0
$421$	12.3227	+	1.44031i	0.600571	+	0.0701966i	0.410945	−	0.911660i	$-0.365199\pi$
$421$	12.3227	+	1.44031i	0.600571	+	0.0701966i	0.189625	+	0.981857i	$0.439273\pi$
$422$	0.268002	−	1.51991i	0.0130461	−	0.0739882i
$423$		0			0
$424$	5.71405	+	32.4060i	0.277499	+	1.57377i
$425$	−0.533097	−	9.15291i	−0.0258590	−	0.443982i
$426$		0			0
$427$	−10.7587	+	24.9414i	−0.520649	+	1.20700i
$428$	−70.2921	+	35.3020i	−3.39770	+	1.70639i
$429$		0			0
$430$	−2.14703	+	0.508855i	−0.103539	+	0.0245391i
$431$	4.38452	+	7.59420i	0.211195	+	0.365800i	0.952089	−	0.305822i	$-0.0989313\pi$
$431$	4.38452	+	7.59420i	0.211195	+	0.365800i	−0.740894	+	0.671622i	$0.765598\pi$
$432$		0			0
$433$	−9.78037	+	16.9401i	−0.470015	+	0.814089i	−0.999412	−	0.0342847i	$-0.989085\pi$
$433$	−9.78037	+	16.9401i	−0.470015	+	0.814089i	0.529397	+	0.848374i	$0.322418\pi$
$434$	2.16966	−	7.24716i	0.104147	−	0.347875i
$435$		0			0
$436$	77.1771	+	50.7602i	3.69612	+	2.43097i
$437$	10.6415	+	14.2941i	0.509053	+	0.683777i
$438$		0			0
$439$	12.8254	−	8.43537i	0.612121	−	0.402598i	−0.205250	−	0.978710i	$-0.565801\pi$
$439$	12.8254	−	8.43537i	0.612121	−	0.402598i	0.817371	+	0.576111i	$0.195430\pi$
$440$	1.16593	+	0.424364i	0.0555836	+	0.0202308i
$441$		0			0
$442$	−9.05454	+	3.29558i	−0.430681	+	0.156755i
$443$	−14.7276	+	19.7826i	−0.699730	+	0.939901i	−0.999902	−	0.0139845i	$-0.995548\pi$
$443$	−14.7276	+	19.7826i	−0.699730	+	0.939901i	0.300172	+	0.953885i	$0.402956\pi$
$444$		0			0
$445$	7.91790	−	8.39248i	0.375344	−	0.397842i
$446$	21.2575	−	22.5316i	1.00657	−	1.06690i
$447$		0			0
$448$	24.5617	−	32.9920i	1.16043	−	1.55873i
$449$	4.16042	−	1.51427i	0.196343	−	0.0714628i	−0.241977	−	0.970282i	$-0.577796\pi$
$449$	4.16042	−	1.51427i	0.196343	−	0.0714628i	0.438320	+	0.898819i	$0.355574\pi$
$450$		0			0
$451$	−0.411234	−	0.149677i	−0.0193643	−	0.00704801i
$452$	−1.15655	+	0.760676i	−0.0543996	+	0.0357792i
$453$		0			0
$454$	−43.6722	−	58.6619i	−2.04964	−	2.75314i
$455$	−5.42106	−	3.56549i	−0.254143	−	0.167153i
$456$		0			0
$457$	−6.23593	+	20.8294i	−0.291704	+	0.974360i	0.679011	+	0.734128i	$0.262409\pi$
$457$	−6.23593	+	20.8294i	−0.291704	+	0.974360i	−0.970715	+	0.240232i	$0.922776\pi$
$458$	−23.9742	+	41.5244i	−1.12024	+	1.94031i
$459$		0			0
$460$	9.52665	+	16.5006i	0.444182	+	0.769347i
$461$	−10.5236	+	2.49413i	−0.490131	+	0.116163i	−0.468248	−	0.883597i	$-0.655114\pi$
$461$	−10.5236	+	2.49413i	−0.490131	+	0.116163i	−0.0218836	+	0.999761i	$0.506966\pi$
$462$		0			0
$463$	−15.4236	+	7.74602i	−0.716795	+	0.359988i	−0.769522	−	0.638621i	$-0.779505\pi$
$463$	−15.4236	+	7.74602i	−0.716795	+	0.359988i	0.0527262	+	0.998609i	$0.483209\pi$
$464$	38.7882	−	89.9212i	1.80070	−	4.17449i
$465$		0			0
$466$	2.87293	+	49.3263i	0.133086	+	2.28500i
$467$	−6.62034	−	37.5458i	−0.306353	−	1.73741i	−0.617067	−	0.786911i	$-0.711679\pi$
$467$	−6.62034	−	37.5458i	−0.306353	−	1.73741i	0.310714	−	0.950503i	$-0.399432\pi$
$468$		0			0
$469$	2.05349	−	11.6459i	0.0948214	−	0.537759i
$470$	9.44554	+	1.10403i	0.435690	+	0.0509249i
$471$		0			0
$472$	−13.4046	−	44.7745i	−0.616997	−	2.06091i
$473$	0.0866538	+	0.0205373i	0.00398435	+	0.000944307i
$474$		0			0
$475$	−7.83241	−	18.1576i	−0.359376	−	0.833127i
$476$	−37.6329	−	31.5778i	−1.72490	−	1.44737i
$477$		0			0
$478$	−23.6210	+	19.8203i	−1.08040	+	0.906562i
$479$	−20.8264	−	10.4594i	−0.951583	−	0.477903i	−0.0958929	−	0.995392i	$-0.530571\pi$
$479$	−20.8264	−	10.4594i	−0.951583	−	0.477903i	−0.855690	+	0.517489i	$0.826867\pi$
$480$		0			0
$481$	−11.7611	+	1.37468i	−0.536261	+	0.0626799i
$482$	−2.43625	+	41.8288i	−0.110968	+	1.90525i
$483$		0			0
$484$	37.1500	+	39.3767i	1.68864	+	1.78985i
$485$	17.2326			0.782490
$486$		0			0
$487$	−7.06751			−0.320259			−0.160130	−	0.987096i	$-0.551191\pi$
$487$	−7.06751			−0.320259			−0.160130	+	0.987096i	$0.551191\pi$
$488$	37.9340	+	40.2077i	1.71719	+	1.82012i
$489$		0			0
$490$	1.38535	−	23.7856i	0.0625838	−	1.07452i
$491$	−3.36640	+	0.393475i	−0.151923	+	0.0177573i	−0.191715	−	0.981451i	$-0.561405\pi$
$491$	−3.36640	+	0.393475i	−0.151923	+	0.0177573i	0.0397912	+	0.999208i	$0.487331\pi$
$492$		0			0
$493$	−22.0563	−	11.0771i	−0.993367	−	0.498888i
$494$	−15.9204	+	13.3588i	−0.716291	+	0.601039i
$495$		0			0
$496$	−6.06501	−	5.08915i	−0.272327	−	0.228510i
$497$	−3.96044	−	9.18132i	−0.177650	−	0.411839i
$498$		0			0
$499$	31.2263	+	7.40077i	1.39788	+	0.331304i	0.859388	−	0.511325i	$-0.170845\pi$
$499$	31.2263	+	7.40077i	1.39788	+	0.331304i	0.538495	+	0.842629i	$0.318993\pi$
$500$	−14.7632	−	49.3126i	−0.660232	−	2.20533i
$501$		0			0
$502$	41.1089	+	4.80494i	1.83478	+	0.214455i
$503$	3.47754	−	19.7221i	0.155056	−	0.879366i	−0.803679	−	0.595064i	$-0.797127\pi$
$503$	3.47754	−	19.7221i	0.155056	−	0.879366i	0.958735	−	0.284303i	$-0.0917621\pi$
$504$		0			0
$505$	−1.54854	−	8.78219i	−0.0689090	−	0.390802i
$506$	−0.0628552	−	1.07918i	−0.00279426	−	0.0479755i
$507$		0			0
$508$	−34.5203	+	80.0270i	−1.53159	+	3.55062i
$509$	11.3825	−	5.71652i	0.504522	−	0.253380i	−0.178286	−	0.983979i	$-0.557055\pi$
$509$	11.3825	−	5.71652i	0.504522	−	0.253380i	0.682807	+	0.730598i	$0.260759\pi$
$510$		0			0
$511$	21.9965	−	5.21326i	0.973066	−	0.230621i
$512$	17.5660	+	30.4252i	0.776315	+	1.34462i
$513$		0			0
$514$	−1.90323	+	3.29649i	−0.0839478	+	0.145402i
$515$	−1.99041	+	6.64845i	−0.0877081	+	0.292966i
$516$		0			0
$517$	−0.320674	−	0.210911i	−0.0141032	−	0.00927584i
$518$	−50.6790	−	68.0738i	−2.22671	−	2.99099i
$519$		0			0
$520$	−11.0321	+	7.25595i	−0.483791	+	0.318194i
$521$	12.6173	+	4.59231i	0.552772	+	0.201193i	0.603278	−	0.797531i	$-0.293861\pi$
$521$	12.6173	+	4.59231i	0.552772	+	0.201193i	−0.0505056	+	0.998724i	$0.516083\pi$
$522$		0			0
$523$	12.0309	−	4.37889i	0.526075	−	0.191476i	−0.0653099	−	0.997865i	$-0.520804\pi$
$523$	12.0309	−	4.37889i	0.526075	−	0.191476i	0.591385	+	0.806389i	$0.298581\pi$
$524$	17.6658	−	23.7293i	0.771736	−	1.03662i
$525$		0			0
$526$	−35.6044	+	37.7385i	−1.55243	+	1.64548i
$527$	−1.36934	+	1.45142i	−0.0596495	+	0.0632247i
$528$		0			0
$529$	−7.84393	+	10.5362i	−0.341041	+	0.458097i
$530$	12.9926	−	4.72892i	0.564363	−	0.205411i
$531$		0			0
$532$	−99.5676	−	36.2397i	−4.31680	−	1.57119i
$533$	3.89113	−	2.55923i	0.168543	−	0.110853i
$534$		0			0
$535$	11.7284	+	15.7540i	0.507063	+	0.681103i
$536$	−20.1066	−	13.2243i	−0.868471	−	0.571203i
$537$		0			0
$538$	−21.6412	+	72.2866i	−0.933018	+	3.11650i
$539$	−0.480805	+	0.832779i	−0.0207098	+	0.0358703i
$540$		0			0
$541$	−1.14797	−	1.98835i	−0.0493552	−	0.0854858i	0.840292	−	0.542134i	$-0.182383\pi$
$541$	−1.14797	−	1.98835i	−0.0493552	−	0.0854858i	−0.889648	+	0.456648i	$0.849050\pi$
$542$	29.7837	−	7.05887i	1.27932	−	0.303204i
$543$		0			0
$544$	−28.3379	+	14.2318i	−1.21498	+	0.610184i
$545$	9.13550	−	21.1785i	0.391322	−	0.907186i
$546$		0			0
$547$	−1.47034	−	25.2448i	−0.0628672	−	1.07939i	−0.871284	−	0.490778i	$-0.836712\pi$
$547$	−1.47034	−	25.2448i	−0.0628672	−	1.07939i	0.808417	−	0.588610i	$-0.200325\pi$
$548$	3.29440	+	18.6834i	0.140730	+	0.798117i
$549$		0			0
$550$	−0.208305	+	1.18135i	−0.00888214	+	0.0503731i
$551$	−52.8744	−	6.18014i	−2.25253	−	0.263283i
$552$		0			0
$553$	−1.09153	−	3.64597i	−0.0464166	−	0.155042i
$554$	−3.41828	−	0.810147i	−0.145229	−	0.0344199i
$555$		0			0
$556$	18.5295	+	42.9562i	0.785827	+	1.82175i
$557$	7.86011	+	6.59541i	0.333043	+	0.279457i	0.793939	−	0.607998i	$-0.208027\pi$
$557$	7.86011	+	6.59541i	0.333043	+	0.279457i	−0.460895	+	0.887455i	$0.652472\pi$
$558$		0			0
$559$	−0.726007	+	0.609192i	−0.0307068	+	0.0257661i
$560$	−43.4928	−	21.8429i	−1.83791	−	0.923032i
$561$		0			0
$562$	−30.3364	+	3.54582i	−1.27967	+	0.149571i
$563$	0.695837	−	11.9471i	0.0293260	−	0.503508i	−0.951380	−	0.308020i	$-0.900334\pi$
$563$	0.695837	−	11.9471i	0.0293260	−	0.503508i	0.980706	−	0.195489i	$-0.0626293\pi$
$564$		0			0
$565$	0.237194	+	0.251411i	0.00997882	+	0.0105769i
$566$	25.5997			1.07603
$567$		0			0
$568$	−20.3486			−0.853810
$569$	−0.0931335	−	0.0987157i	−0.00390436	−	0.00413838i	0.725419	−	0.688308i	$-0.241646\pi$
$569$	−0.0931335	−	0.0987157i	−0.00390436	−	0.00413838i	−0.729323	+	0.684170i	$0.760165\pi$
$570$		0			0
$571$	−0.987415	+	16.9533i	−0.0413220	+	0.709472i	0.912496	+	0.409086i	$0.134152\pi$
$571$	−0.987415	+	16.9533i	−0.0413220	+	0.709472i	−0.953818	+	0.300386i	$0.902885\pi$
$572$	0.890755	−	0.104114i	0.0372443	−	0.00435324i
$573$		0			0
$574$	29.8289	+	14.9807i	1.24504	+	0.625281i
$575$	−8.38553	+	7.03630i	−0.349701	+	0.293434i
$576$		0			0
$577$	32.4933	+	27.2651i	1.35271	+	1.13506i	0.978160	+	0.207854i	$0.0666479\pi$
$577$	32.4933	+	27.2651i	1.35271	+	1.13506i	0.374552	+	0.927206i	$0.377797\pi$
$578$	−10.5093	−	24.3634i	−0.437131	−	1.01338i
$579$		0			0
$580$	−55.3836	−	13.1261i	−2.29968	−	0.545034i
$581$	−9.86367	−	32.9470i	−0.409214	−	1.36687i
$582$		0			0
$583$	−0.554261	−	0.0647838i	−0.0229551	−	0.00268307i
$584$	7.98850	−	45.3051i	0.330567	−	1.87474i
$585$		0			0
$586$	−13.6751	−	77.5553i	−0.564913	−	3.20378i
$587$	1.12407	+	19.2995i	0.0463952	+	0.796575i	0.938614	+	0.344970i	$0.112111\pi$
$587$	1.12407	+	19.2995i	0.0463952	+	0.796575i	−0.892218	+	0.451604i	$0.850852\pi$
$588$		0			0
$589$	−1.70465	+	3.95183i	−0.0702389	+	0.162832i
$590$	−17.5495	+	8.81371i	−0.722503	+	0.362855i
$591$		0			0
$592$	−86.4256	+	20.4832i	−3.55207	+	0.841856i
$593$	−5.90567	−	10.2289i	−0.242517	−	0.420051i	0.718914	−	0.695099i	$-0.244640\pi$
$593$	−5.90567	−	10.2289i	−0.242517	−	0.420051i	−0.961431	+	0.275048i	$0.911306\pi$
$594$		0			0
$595$	−6.13318	+	10.6230i	−0.251436	+	0.435499i
$596$	−20.7929	+	69.4530i	−0.851709	+	2.84491i
$597$		0			0
$598$	9.61175	+	6.32175i	0.393054	+	0.258516i
$599$	12.9640	+	17.4136i	0.529693	+	0.711501i	0.983765	−	0.179464i	$-0.0574364\pi$
$599$	12.9640	+	17.4136i	0.529693	+	0.711501i	−0.454072	+	0.890965i	$0.650029\pi$
$600$		0			0
$601$	−1.71752	+	1.12963i	−0.0700591	+	0.0460786i	−0.584055	−	0.811714i	$-0.698535\pi$
$601$	−1.71752	+	1.12963i	−0.0700591	+	0.0460786i	0.513996	+	0.857792i	$0.328165\pi$
$602$	−6.38287	−	2.32318i	−0.260146	−	0.0946856i
$603$		0			0
$604$	49.0120	−	17.8389i	1.99427	−	0.725855i
$605$	8.07185	−	10.8424i	0.328167	−	0.440805i
$606$		0			0
$607$	12.9484	−	13.7245i	0.525557	−	0.557058i	−0.409154	−	0.912465i	$-0.634176\pi$
$607$	12.9484	−	13.7245i	0.525557	−	0.557058i	0.934712	+	0.355407i	$0.115658\pi$
$608$	−46.9357	+	49.7489i	−1.90349	+	2.01759i
$609$		0			0
$610$	13.8700	−	18.6307i	0.561581	−	0.754335i
$611$	3.83832	−	1.39704i	0.155282	−	0.0565180i
$612$		0			0
$613$	−3.39883	−	1.23707i	−0.137277	−	0.0499648i	0.272468	−	0.962165i	$-0.412160\pi$
$613$	−3.39883	−	1.23707i	−0.137277	−	0.0499648i	−0.409745	+	0.912200i	$0.634382\pi$
$614$	−64.8057	+	42.6234i	−2.61535	+	1.72014i
$615$		0			0
$616$	2.28088	+	3.06376i	0.0918993	+	0.123442i
$617$	−32.5525	−	21.4101i	−1.31051	−	0.861939i	−0.314339	−	0.949311i	$-0.601783\pi$
$617$	−32.5525	−	21.4101i	−1.31051	−	0.861939i	−0.996176	+	0.0873715i	$0.972153\pi$
$618$		0			0
$619$	1.26710	−	4.23241i	0.0509291	−	0.170115i	−0.928741	−	0.370728i	$-0.879108\pi$
$619$	1.26710	−	4.23241i	0.0509291	−	0.170115i	0.979671	+	0.200613i	$0.0642934\pi$
$620$	−2.30080	+	3.98510i	−0.0924023	+	0.160046i
$621$		0			0
$622$	23.4208	+	40.5660i	0.939089	+	1.62655i
$623$	34.5614	−	8.19121i	1.38467	−	0.328174i
$624$		0			0
$625$	4.08710	−	2.05262i	0.163484	−	0.0821047i
$626$	−20.2296	+	46.8974i	−0.808536	+	1.87440i
$627$		0			0
$628$	−2.23005	−	38.2884i	−0.0889886	−	1.52788i
$629$	3.88720	+	22.0454i	0.154993	+	0.879007i
$630$		0			0
$631$	−1.55124	+	8.79751i	−0.0617538	+	0.350223i	0.938237	+	0.345993i	$0.112458\pi$
$631$	−1.55124	+	8.79751i	−0.0617538	+	0.350223i	−0.999991	+	0.00423074i	$0.998653\pi$
$632$	−7.69273	−	0.899151i	−0.306000	−	0.0357663i
$633$		0			0
$634$	−3.19307	−	10.6656i	−0.126813	−	0.423586i
$635$	21.1751	+	5.01859i	0.840309	+	0.199157i
$636$		0			0
$637$	−4.05335	−	9.39672i	−0.160600	−	0.372312i
$638$	2.47379	+	2.07575i	0.0979382	+	0.0821799i
$639$		0			0
$640$	−4.21215	+	3.53441i	−0.166500	+	0.139710i
$641$	−21.9359	−	11.0166i	−0.866416	−	0.435130i	−0.0406699	−	0.999173i	$-0.512949\pi$
$641$	−21.9359	−	11.0166i	−0.866416	−	0.435130i	−0.825746	+	0.564042i	$0.809246\pi$
$642$		0			0
$643$	28.2599	−	3.30311i	1.11446	−	0.130262i	0.461130	−	0.887333i	$-0.347444\pi$
$643$	28.2599	−	3.30311i	1.11446	−	0.130262i	0.653333	+	0.757071i	$0.273370\pi$
$644$	−3.41042	+	58.5546i	−0.134389	+	2.30737i
$645$		0			0
$646$	26.9617	+	28.5777i	1.06079	+	1.12438i
$647$	−29.7670			−1.17026			−0.585131	−	0.810939i	$-0.698957\pi$
$647$	−29.7670			−1.17026			−0.585131	+	0.810939i	$0.698957\pi$
$648$		0			0
$649$	0.792605			0.0311125
$650$	−8.76069	−	9.28579i	−0.343622	−	0.364218i
$651$		0			0
$652$	4.61368	−	79.2139i	0.180686	−	3.10226i
$653$	17.5237	−	2.04823i	0.685755	−	0.0801532i	0.233921	−	0.972256i	$-0.424844\pi$
$653$	17.5237	−	2.04823i	0.685755	−	0.0801532i	0.451834	+	0.892102i	$0.350770\pi$
$654$		0			0
$655$	−6.60093	−	3.31511i	−0.257920	−	0.129532i
$656$	26.7611	−	22.4552i	1.04484	−	0.876729i
$657$		0			0
$658$	22.4261	+	18.8177i	0.874259	+	0.733591i
$659$	2.65052	+	6.14459i	0.103249	+	0.239359i	0.962008	−	0.273021i	$-0.0880230\pi$
$659$	2.65052	+	6.14459i	0.103249	+	0.239359i	−0.858758	+	0.512381i	$0.828764\pi$
$660$		0			0
$661$	16.7975	+	3.98109i	0.653348	+	0.154846i	0.543905	−	0.839147i	$-0.316945\pi$
$661$	16.7975	+	3.98109i	0.653348	+	0.154846i	0.109443	+	0.993993i	$0.465093\pi$
$662$	8.85774	+	29.5869i	0.344266	+	1.14993i
$663$		0			0
$664$	−69.5157	−	8.12522i	−2.69773	−	0.315320i
$665$	−4.59414	+	26.0546i	−0.178153	+	1.01036i
$666$		0			0
$667$	5.11713	+	29.0207i	0.198136	+	1.12369i
$668$	−1.36011	−	23.3523i	−0.0526244	−	0.903526i
$669$		0			0
$670$	−4.00513	+	9.28494i	−0.154732	+	0.358709i
$671$	−0.837717	+	0.420717i	−0.0323397	+	0.0162416i
$672$		0			0
$673$	46.6255	−	11.0504i	1.79728	−	0.425963i	0.810196	−	0.586159i	$-0.199361\pi$
$673$	46.6255	−	11.0504i	1.79728	−	0.425963i	0.987085	+	0.160196i	$0.0512126\pi$
$674$	−0.635938	−	1.10148i	−0.0244954	−	0.0424273i
$675$		0			0
$676$	27.2669	−	47.2276i	1.04873	−	1.81645i
$677$	9.63697	−	32.1897i	0.370379	−	1.23715i	−0.546321	−	0.837576i	$-0.683972\pi$
$677$	9.63697	−	32.1897i	0.370379	−	1.23715i	0.916700	−	0.399576i	$-0.130843\pi$
$678$		0			0
$679$	44.3216	+	29.1508i	1.70091	+	1.11870i
$680$	14.9067	+	20.0231i	0.571644	+	0.767851i
$681$		0			0
$682$	0.218127	−	0.143464i	0.00835251	−	0.00549353i
$683$	17.3670	+	6.32106i	0.664529	+	0.241869i	0.652191	−	0.758055i	$-0.273850\pi$
$683$	17.3670	+	6.32106i	0.664529	+	0.241869i	0.0123385	+	0.999924i	$0.496072\pi$
$684$		0			0
$685$	4.45136	−	1.62016i	0.170078	−	0.0619032i
$686$	2.11046	−	2.83483i	0.0805775	−	0.108234i
$687$		0			0
$688$	−4.87841	+	5.17081i	−0.185988	+	0.197135i
$689$	4.07540	−	4.31967i	0.155260	−	0.164566i
$690$		0			0
$691$	−19.9589	+	26.8095i	−0.759274	+	1.01988i	0.239525	+	0.970890i	$0.423008\pi$
$691$	−19.9589	+	26.8095i	−0.759274	+	1.01988i	−0.998799	+	0.0489917i	$0.984399\pi$
$692$	−110.629	+	40.2655i	−4.20547	+	1.53067i
$693$		0			0
$694$	72.7986	+	26.4965i	2.76340	+	1.00579i
$695$	9.75939	−	6.41885i	0.370195	−	0.243481i
$696$		0			0
$697$	−5.25771	−	7.06232i	−0.199150	−	0.267505i
$698$	56.0775	+	36.8827i	2.12256	+	1.39603i
$699$		0			0
$700$	18.6672	−	62.3527i	0.705553	−	2.35671i
$701$	−7.63600	+	13.2259i	−0.288408	+	0.499537i	−0.973430	−	0.228985i	$-0.926459\pi$
$701$	−7.63600	+	13.2259i	−0.288408	+	0.499537i	0.685022	+	0.728522i	$0.259793\pi$
$702$		0			0
$703$	24.1410	+	41.8134i	0.910493	+	1.57702i
$704$	1.38122	−	0.327355i	0.0520567	−	0.0123377i
$705$		0			0
$706$	−54.0733	+	27.1566i	−2.03507	+	1.02205i
$707$	10.8733	−	25.2071i	0.408931	−	0.948009i
$708$		0			0
$709$	1.57683	+	27.0731i	0.0592191	+	1.01675i	0.888779	+	0.458335i	$0.151554\pi$
$709$	1.57683	+	27.0731i	0.0592191	+	1.01675i	−0.829560	+	0.558417i	$0.811409\pi$
$710$	1.48471	+	8.42022i	0.0557202	+	0.316005i
$711$		0			0
$712$	12.5517	−	71.1845i	0.470397	−	2.66775i
$713$	2.36630	+	0.276581i	0.0886187	+	0.0103580i
$714$		0			0
$715$	−0.0642229	−	0.214519i	−0.00240180	−	0.00802257i
$716$	−42.0520	−	9.96652i	−1.57156	−	0.372466i
$717$		0			0
$718$	18.9538	+	43.9398i	0.707349	+	1.63982i
$719$	6.88437	+	5.77667i	0.256744	+	0.215434i	0.762070	−	0.647495i	$-0.224183\pi$
$719$	6.88437	+	5.77667i	0.256744	+	0.215434i	−0.505326	+	0.862929i	$0.668628\pi$
$720$		0			0
$721$	−16.3659	+	13.7326i	−0.609497	+	0.511429i
$722$	31.0323	+	15.5850i	1.15490	+	0.580013i
$723$		0			0
$724$	−2.64961	+	0.309695i	−0.0984720	+	0.0115097i
$725$	1.90137	−	32.6452i	0.0706150	−	1.21241i
$726$		0			0
$727$	−19.0473	−	20.1889i	−0.706425	−	0.748766i	0.270414	−	0.962744i	$-0.412839\pi$
$727$	−19.0473	−	20.1889i	−0.706425	−	0.748766i	−0.976839	+	0.213978i	$0.931358\pi$
$728$	−40.6486			−1.50654
$729$		0			0
$730$	−19.3300			−0.715435
$731$	1.22952	+	1.30321i	0.0454754	+	0.0482011i
$732$		0			0
$733$	0.0139754	−	0.239949i	0.000516194	−	0.00886271i	−0.998040	−	0.0625756i	$-0.980069\pi$
$733$	0.0139754	−	0.239949i	0.000516194	−	0.00886271i	0.998556	+	0.0537129i	$0.0171056\pi$
$734$	32.1647	−	3.75951i	1.18722	−	0.138766i
$735$		0			0
$736$	33.8337	+	16.9919i	1.24713	+	0.626330i
$737$	0.312636	−	0.262332i	0.0115161	−	0.00966314i
$738$		0			0
$739$	−24.3258	−	20.4118i	−0.894840	−	0.750860i	0.0743349	−	0.997233i	$-0.476317\pi$
$739$	−24.3258	−	20.4118i	−0.894840	−	0.750860i	−0.969175	+	0.246373i	$0.920761\pi$
$740$	20.4467	+	47.4007i	0.751635	+	1.74249i
$741$		0			0
$742$	41.4161	+	9.81580i	1.52043	+	0.360349i
$743$	−8.40109	−	28.0616i	−0.308206	−	1.02948i	−0.962055	−	0.272855i	$-0.912032\pi$
$743$	−8.40109	−	28.0616i	−0.308206	−	1.02948i	0.653849	−	0.756625i	$-0.273153\pi$
$744$		0			0
$745$	17.9798	+	2.10154i	0.658729	+	0.0769944i
$746$	1.48063	−	8.39705i	0.0542096	−	0.307438i
$747$		0			0
$748$	−0.294406	−	1.66966i	−0.0107645	−	0.0610487i
$749$	3.51549	+	60.3586i	0.128453	+	2.20546i
$750$		0			0
$751$	18.1925	−	42.1750i	0.663854	−	1.53899i	−0.169072	−	0.985604i	$-0.554077\pi$
$751$	18.1925	−	42.1750i	0.663854	−	1.53899i	0.832926	−	0.553384i	$-0.186664\pi$
$752$	27.3797	−	13.7506i	0.998436	−	0.501433i
$753$		0			0
$754$	−33.4405	+	7.92555i	−1.21783	+	0.288632i
$755$	−6.51160	−	11.2784i	−0.236982	−	0.410464i
$756$		0			0
$757$	2.70356	−	4.68271i	0.0982627	−	0.170196i	−0.812703	−	0.582678i	$-0.802005\pi$
$757$	2.70356	−	4.68271i	0.0982627	−	0.170196i	0.910966	+	0.412482i	$0.135338\pi$
$758$	−24.1527	+	80.6756i	−0.877265	+	2.93027i
$759$		0			0
$760$	44.9830	+	29.5858i	1.63171	+	1.07319i
$761$	26.2960	+	35.3217i	0.953230	+	1.28041i	0.959874	+	0.280433i	$0.0904779\pi$
$761$	26.2960	+	35.3217i	0.953230	+	1.28041i	−0.00664344	+	0.999978i	$0.502115\pi$
$762$		0			0
$763$	59.3220	−	39.0167i	2.14760	−	1.41250i
$764$	4.17907	+	1.52106i	0.151193	+	0.0550299i
$765$		0			0
$766$	−32.9986	+	12.0105i	−1.19229	+	0.433957i
$767$	−5.03708	+	6.76597i	−0.181878	+	0.244305i
$768$		0			0
$769$	3.82377	−	4.05296i	0.137889	−	0.146154i	−0.654749	−	0.755846i	$-0.727226\pi$
$769$	3.82377	−	4.05296i	0.137889	−	0.146154i	0.792638	+	0.609693i	$0.208707\pi$
$770$	1.10135	−	1.16737i	0.0396900	−	0.0420690i
$771$		0			0
$772$	40.8507	−	54.8721i	1.47025	−	1.97489i
$773$	2.57652	−	0.937775i	0.0926708	−	0.0337294i	−0.295269	−	0.955414i	$-0.595409\pi$
$773$	2.57652	−	0.937775i	0.0926708	−	0.0337294i	0.387940	+	0.921685i	$0.373187\pi$
$774$		0			0
$775$	−2.48428	−	0.904205i	−0.0892381	−	0.0324800i
$776$	90.1967	−	59.3233i	3.23787	−	2.12958i
$777$		0			0
$778$	−37.6804	−	50.6136i	−1.35091	−	1.81458i
$779$	−15.8659	−	10.4352i	−0.568455	−	0.373879i
$780$		0			0
$781$	0.0989706	−	0.330585i	0.00354145	−	0.0118293i
$782$	10.8744	−	18.8349i	0.388866	−	0.673536i
$783$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.80640 - 1.91467i) q^{2} +(-0.286600 + 4.92073i) q^{4} +(1.22242 - 0.142880i) q^{5} +(3.38572 + 1.70037i) q^{7} +(5.90638 - 4.95604i) q^{8} +O(q^{10})\)	\(q+(-1.80640 - 1.91467i) q^{2} +(-0.286600 + 4.92073i) q^{4} +(1.22242 - 0.142880i) q^{5} +(3.38572 + 1.70037i) q^{7} +(5.90638 - 4.95604i) q^{8} +(-2.48175 - 2.08243i) q^{10} +(0.0517889 + 0.120060i) q^{11} +(-1.35400 - 0.320904i) q^{13} +(-2.86031 - 9.55411i) q^{14} +(-10.3670 - 1.21173i) q^{16} +(-0.456801 + 2.59065i) q^{17} +(0.985248 + 5.58762i) q^{19} +(0.352730 + 6.05614i) q^{20} +(0.136325 - 0.316036i) q^{22} +(2.80671 - 1.40958i) q^{23} +(-3.39133 + 0.803761i) q^{25} +(1.83144 + 3.17215i) q^{26} +(-9.33742 + 16.1729i) q^{28} +(-2.69092 + 8.98830i) q^{29} +(0.633750 + 0.416824i) q^{31} +(7.19848 + 9.66923i) q^{32} +(5.78542 - 3.80513i) q^{34} +(4.38171 + 1.59481i) q^{35} +(7.99641 - 2.91045i) q^{37} +(8.91872 - 11.9799i) q^{38} +(6.51194 - 6.90225i) q^{40} +(-2.29682 + 2.43448i) q^{41} +(0.406715 - 0.546314i) q^{43} +(-0.605626 + 0.220430i) q^{44} +(-7.76895 - 2.82767i) q^{46} +(-2.45250 + 1.61304i) q^{47} +(4.39173 + 5.89911i) q^{49} +(7.66505 + 5.04139i) q^{50} +(1.96714 - 6.57070i) q^{52} +(-2.13391 + 3.69605i) q^{53} +(0.0804619 + 0.139364i) q^{55} +(28.4245 - 6.73672i) q^{56} +(22.0706 - 11.0843i) q^{58} +(2.40096 - 5.56606i) q^{59} +(0.416865 + 7.15730i) q^{61} +(-0.346725 - 1.96638i) q^{62} +(1.88515 - 10.6912i) q^{64} +(-1.70101 - 0.198819i) q^{65} +(-0.895189 - 2.99014i) q^{67} +(-12.6170 - 2.99028i) q^{68} +(-4.86159 - 11.2704i) q^{70} +(-2.02173 - 1.69643i) q^{71} +(4.57069 - 3.83527i) q^{73} +(-20.0173 - 10.0531i) q^{74} +(-27.7775 + 3.24673i) q^{76} +(-0.0288043 + 0.494550i) q^{77} +(-0.689346 - 0.730664i) q^{79} -12.8460 q^{80} +8.81022 q^{82} +(-6.22930 - 6.60268i) q^{83} +(-0.188250 + 3.23212i) q^{85} +(-1.78070 + 0.208134i) q^{86} +(0.900907 + 0.452453i) q^{88} +(7.18159 - 6.02607i) q^{89} +(-4.03861 - 3.38880i) q^{91} +(6.13178 + 14.2151i) q^{92} +(7.51865 + 1.78195i) q^{94} +(2.00274 + 6.68963i) q^{95} +(13.9071 + 1.62551i) q^{97} +(3.36166 - 19.0649i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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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Database

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