LMFDB - Embedded newform 729.2.e.i.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.i.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.93969 + 1.62760i) q^{2} +(0.766044 + 4.34445i) q^{4} +(-0.439693 - 0.160035i) q^{5} +(-0.560307 + 3.17766i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-0.592396 - 1.02606i) q^{10} +(2.91875 - 1.06234i) q^{11} +(-1.67365 + 1.40436i) q^{13} +(-6.25877 + 5.25173i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.0209445 + 0.0362770i) q^{19} +(0.358441 - 2.03282i) q^{20} +(7.39053 + 2.68993i) q^{22} +(1.06031 + 6.01330i) q^{23} +(-3.66250 - 3.07321i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(5.03596 + 4.22567i) q^{29} +(-1.08125 - 6.13208i) q^{31} +(-4.31908 - 1.57202i) q^{32} +(1.31908 - 7.48086i) q^{34} +(0.754900 - 1.30753i) q^{35} +(-1.79813 - 3.11446i) q^{37} +(-0.0996702 + 0.0362770i) q^{38} +(2.18866 - 1.83651i) q^{40} +(5.90033 - 4.95096i) q^{41} +(0.553033 - 0.201288i) q^{43} +(6.85117 + 11.8666i) q^{44} +(-7.73055 + 13.3897i) q^{46} +(-1.67752 + 9.51368i) q^{47} +(-3.20574 - 1.16679i) q^{49} +(-2.10220 - 11.9221i) q^{50} +(-7.38326 - 6.19529i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(-15.0929 - 12.6644i) q^{56} +(2.89053 + 16.3930i) q^{58} +(8.01754 + 2.91815i) q^{59} +(-0.220285 + 1.24930i) q^{61} +(7.88326 - 13.6542i) q^{62} +(0.819078 + 1.41868i) q^{64} +(0.960637 - 0.349643i) q^{65} +(7.66637 - 6.43285i) q^{67} +(10.1382 - 8.50692i) q^{68} +(3.59240 - 1.30753i) q^{70} +(-5.91534 - 10.2457i) q^{71} +(4.11721 - 7.13122i) q^{73} +(1.58125 - 8.96773i) q^{74} +(-0.173648 - 0.0632028i) q^{76} +(1.74035 + 9.87003i) q^{77} +(8.46451 + 7.10257i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(-1.15657 - 0.970481i) q^{83} +(0.243756 + 1.38241i) q^{85} +(1.40033 + 0.509678i) q^{86} +(-3.29339 + 18.6777i) q^{88} +(7.93629 - 13.7461i) q^{89} +(-3.52481 - 6.10516i) q^{91} +(-25.3123 + 9.21291i) q^{92} +(-18.7383 + 15.7233i) q^{94} +(0.0150147 - 0.0125989i) q^{95} +(-17.5214 + 6.37727i) q^{97} +(-4.31908 - 7.48086i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31}+ \cdots - 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8 + 15 * q^11 - 9 * q^13 - 15 * q^14 - 18 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 + 27 * q^22 + 12 * q^23 - 27 * q^25 - 24 * q^26 - 24 * q^28 - 3 * q^29 - 9 * q^31 - 9 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 - 15 * q^38 - 18 * q^40 + 21 * q^41 - 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 - 9 * q^49 - 12 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 21 * q^56 + 3 * q^59 - 27 * q^61 + 12 * q^62 - 12 * q^64 - 3 * q^65 + 27 * q^67 + 27 * q^68 + 18 * q^70 + 9 * q^71 - 6 * q^73 + 12 * q^74 - 24 * q^77 + 18 * q^79 - 6 * q^80 + 36 * q^82 + 15 * q^83 + 9 * q^85 - 6 * q^86 + 27 * q^88 + 6 * q^91 - 51 * q^92 - 27 * q^94 - 30 * q^95 - 36 * q^97 - 9 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.93969	+	1.62760i	1.37157	+	1.15088i	0.972216	+	0.234087i	$0.0752101\pi$
$2$	1.93969	+	1.62760i	1.37157	+	1.15088i	0.399354	+	0.916797i	$0.369234\pi$
$3$		0			0
$3$		0			0
$4$	0.766044	+	4.34445i	0.383022	+	2.17223i
$5$	−0.439693	−	0.160035i	−0.196637	−	0.0715698i	0.241825	−	0.970320i	$-0.422254\pi$
$5$	−0.439693	−	0.160035i	−0.196637	−	0.0715698i	−0.438461	+	0.898750i	$0.644476\pi$
$6$		0			0
$7$	−0.560307	+	3.17766i	−0.211776	+	1.20104i	0.674637	+	0.738149i	$0.264300\pi$
$7$	−0.560307	+	3.17766i	−0.211776	+	1.20104i	−0.886414	+	0.462894i	$0.846811\pi$
$8$	−3.05303	+	5.28801i	−1.07941	+	1.86959i
$9$		0			0
$10$	−0.592396	−	1.02606i	−0.187332	−	0.324469i
$11$	2.91875	−	1.06234i	0.880036	−	0.320307i	0.137811	−	0.990458i	$-0.455993\pi$
$11$	2.91875	−	1.06234i	0.880036	−	0.320307i	0.742224	+	0.670152i	$0.233771\pi$
$12$		0			0
$13$	−1.67365	+	1.40436i	−0.464186	+	0.389499i	−0.844669	−	0.535290i	$-0.820202\pi$
$13$	−1.67365	+	1.40436i	−0.464186	+	0.389499i	0.380482	+	0.924788i	$0.375758\pi$
$14$	−6.25877	+	5.25173i	−1.67273	+	1.40358i
$15$		0			0
$16$	−6.23783	+	2.27038i	−1.55946	+	0.567596i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−0.0209445	+	0.0362770i	−0.00480501	+	0.00832251i	−0.868418	−	0.495833i	$-0.834863\pi$
$19$	−0.0209445	+	0.0362770i	−0.00480501	+	0.00832251i	0.863613	+	0.504155i	$0.168196\pi$
$20$	0.358441	−	2.03282i	0.0801498	−	0.454552i
$21$		0			0
$22$	7.39053	+	2.68993i	1.57567	+	0.573496i
$23$	1.06031	+	6.01330i	0.221089	+	1.25386i	0.870021	+	0.493014i	$0.164105\pi$
$23$	1.06031	+	6.01330i	0.221089	+	1.25386i	−0.648932	+	0.760846i	$0.724784\pi$
$24$		0			0
$25$	−3.66250	−	3.07321i	−0.732501	−	0.614641i
$26$	−5.53209			−1.08493
$27$		0			0
$28$	−14.2344			−2.69005
$29$	5.03596	+	4.22567i	0.935154	+	0.784688i	0.976735	−	0.214448i	$-0.0687951\pi$
$29$	5.03596	+	4.22567i	0.935154	+	0.784688i	−0.0415813	+	0.999135i	$0.513240\pi$
$30$		0			0
$31$	−1.08125	−	6.13208i	−0.194199	−	1.10135i	−0.913555	−	0.406714i	$-0.866674\pi$
$31$	−1.08125	−	6.13208i	−0.194199	−	1.10135i	0.719357	−	0.694641i	$-0.244437\pi$
$32$	−4.31908	−	1.57202i	−0.763512	−	0.277896i
$33$		0			0
$34$	1.31908	−	7.48086i	0.226220	−	1.28296i
$35$	0.754900	−	1.30753i	0.127601	−	0.221012i
$36$		0			0
$37$	−1.79813	−	3.11446i	−0.295611	−	0.512014i	0.679516	−	0.733661i	$-0.262190\pi$
$37$	−1.79813	−	3.11446i	−0.295611	−	0.512014i	−0.975127	+	0.221647i	$0.928857\pi$
$38$	−0.0996702	+	0.0362770i	−0.0161686	+	0.00588491i
$39$		0			0
$40$	2.18866	−	1.83651i	0.346058	−	0.290377i
$41$	5.90033	−	4.95096i	0.921477	−	0.773211i	−0.0527908	−	0.998606i	$-0.516812\pi$
$41$	5.90033	−	4.95096i	0.921477	−	0.773211i	0.974268	+	0.225395i	$0.0723672\pi$
$42$		0			0
$43$	0.553033	−	0.201288i	0.0843368	−	0.0306961i	−0.299507	−	0.954094i	$-0.596822\pi$
$43$	0.553033	−	0.201288i	0.0843368	−	0.0306961i	0.383844	+	0.923398i	$0.374600\pi$
$44$	6.85117	+	11.8666i	1.03285	+	1.78895i
$45$		0			0
$46$	−7.73055	+	13.3897i	−1.13981	+	1.97420i
$47$	−1.67752	+	9.51368i	−0.244691	+	1.38771i	0.576517	+	0.817085i	$0.304411\pi$
$47$	−1.67752	+	9.51368i	−0.244691	+	1.38771i	−0.821209	+	0.570628i	$0.806700\pi$
$48$		0			0
$49$	−3.20574	−	1.16679i	−0.457962	−	0.166685i
$50$	−2.10220	−	11.9221i	−0.297295	−	1.68605i
$51$		0			0
$52$	−7.38326	−	6.19529i	−1.02387	−	0.859132i
$53$	4.95811			0.681049			0.340524	−	0.940236i	$-0.389395\pi$
$53$	4.95811			0.681049			0.340524	+	0.940236i	$0.389395\pi$
$54$		0			0
$55$	−1.45336			−0.195971
$56$	−15.0929	−	12.6644i	−2.01687	−	1.69235i
$57$		0			0
$58$	2.89053	+	16.3930i	0.379545	+	2.15251i
$59$	8.01754	+	2.91815i	1.04379	+	0.379910i	0.806318	−	0.591483i	$-0.201457\pi$
$59$	8.01754	+	2.91815i	1.04379	+	0.379910i	0.237477	+	0.971393i	$0.423679\pi$
$60$		0			0
$61$	−0.220285	+	1.24930i	−0.0282046	+	0.159956i	−0.995657	−	0.0930965i	$-0.970324\pi$
$61$	−0.220285	+	1.24930i	−0.0282046	+	0.159956i	0.967452	+	0.253053i	$0.0814346\pi$
$62$	7.88326	−	13.6542i	1.00117	−	1.73409i
$63$		0			0
$64$	0.819078	+	1.41868i	0.102385	+	0.177336i
$65$	0.960637	−	0.349643i	0.119152	−	0.0433679i
$66$		0			0
$67$	7.66637	−	6.43285i	0.936597	−	0.785898i	−0.0403931	−	0.999184i	$-0.512861\pi$
$67$	7.66637	−	6.43285i	0.936597	−	0.785898i	0.976990	+	0.213286i	$0.0684166\pi$
$68$	10.1382	−	8.50692i	1.22943	−	1.03162i
$69$		0			0
$70$	3.59240	−	1.30753i	0.429373	−	0.156279i
$71$	−5.91534	−	10.2457i	−0.702022	−	1.21594i	−0.967755	−	0.251892i	$-0.918947\pi$
$71$	−5.91534	−	10.2457i	−0.702022	−	1.21594i	0.265733	−	0.964047i	$-0.414386\pi$
$72$		0			0
$73$	4.11721	−	7.13122i	0.481883	−	0.834646i	−0.517901	−	0.855441i	$-0.673286\pi$
$73$	4.11721	−	7.13122i	0.481883	−	0.834646i	0.999784	+	0.0207947i	$0.00661964\pi$
$74$	1.58125	−	8.96773i	0.183817	−	1.04248i
$75$		0			0
$76$	−0.173648	−	0.0632028i	−0.0199188	−	0.00724985i
$77$	1.74035	+	9.87003i	0.198332	+	1.12479i
$78$		0			0
$79$	8.46451	+	7.10257i	0.952332	+	0.799101i	0.979689	−	0.200525i	$-0.0642647\pi$
$79$	8.46451	+	7.10257i	0.952332	+	0.799101i	−0.0273571	+	0.999626i	$0.508709\pi$
$80$	3.10607			0.347269
$81$		0			0
$82$	19.5030			2.15375
$83$	−1.15657	−	0.970481i	−0.126950	−	0.106524i	0.577102	−	0.816672i	$-0.304184\pi$
$83$	−1.15657	−	0.970481i	−0.126950	−	0.106524i	−0.704052	+	0.710148i	$0.748628\pi$
$84$		0			0
$85$	0.243756	+	1.38241i	0.0264390	+	0.149943i
$86$	1.40033	+	0.509678i	0.151001	+	0.0549600i
$87$		0			0
$88$	−3.29339	+	18.6777i	−0.351076	+	1.99105i
$89$	7.93629	−	13.7461i	0.841245	−	1.45708i	−0.0475978	−	0.998867i	$-0.515157\pi$
$89$	7.93629	−	13.7461i	0.841245	−	1.45708i	0.888843	−	0.458212i	$-0.151510\pi$
$90$		0			0
$91$	−3.52481	−	6.10516i	−0.369501	−	0.639995i
$92$	−25.3123	+	9.21291i	−2.63899	+	0.960513i
$93$		0			0
$94$	−18.7383	+	15.7233i	−1.93271	+	1.62173i
$95$	0.0150147	−	0.0125989i	0.00154048	−	0.00129262i
$96$		0			0
$97$	−17.5214	+	6.37727i	−1.77903	+	0.647514i	−0.779246	+	0.626718i	$0.784398\pi$
$97$	−17.5214	+	6.37727i	−1.77903	+	0.647514i	−0.999784	+	0.0207958i	$0.993380\pi$
$98$	−4.31908	−	7.48086i	−0.436293	−	0.755681i
$99$		0			0
$100$	10.5458	−	18.2658i	1.05458	−	1.82658i
$101$	1.57785	−	8.94842i	0.157002	−	0.890401i	−0.799931	−	0.600092i	$-0.795131\pi$
$101$	1.57785	−	8.94842i	0.157002	−	0.890401i	0.956933	−	0.290309i	$-0.0937582\pi$
$102$		0			0
$103$	−0.245100	−	0.0892091i	−0.0241504	−	0.00879003i	0.329917	−	0.944010i	$-0.392979\pi$
$103$	−0.245100	−	0.0892091i	−0.0241504	−	0.00879003i	−0.354067	+	0.935220i	$0.615202\pi$
$104$	−2.31655	−	13.1378i	−0.227157	−	1.28827i
$105$		0			0
$106$	9.61721	+	8.06980i	0.934106	+	0.783808i
$107$	4.04189			0.390744			0.195372	−	0.980729i	$-0.437409\pi$
$107$	4.04189			0.390744			0.195372	+	0.980729i	$0.437409\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	−2.81908	−	2.36549i	−0.268789	−	0.225540i
$111$		0			0
$112$	−3.71941	−	21.0938i	−0.351451	−	1.99318i
$113$	−1.30066	−	0.473401i	−0.122356	−	0.0445339i	0.280117	−	0.959966i	$-0.409627\pi$
$113$	−1.30066	−	0.473401i	−0.122356	−	0.0445339i	−0.402472	+	0.915432i	$0.631849\pi$
$114$		0			0
$115$	0.496130	−	2.81369i	0.0462643	−	0.262378i
$116$	−14.5005	+	25.1155i	−1.34633	+	2.33192i
$117$		0			0
$118$	10.8020	+	18.7096i	0.994405	+	1.72236i
$119$	9.09627	−	3.31077i	0.833853	−	0.303498i
$120$		0			0
$121$	−1.03596	+	0.869273i	−0.0941781	+	0.0790248i
$122$	−2.46064	+	2.06472i	−0.222776	+	0.186931i
$123$		0			0
$124$	25.8123	−	9.39490i	2.31801	−	0.843687i
$125$	2.28833	+	3.96351i	0.204675	+	0.354507i
$126$		0			0
$127$	3.31908	−	5.74881i	0.294521	−	0.510125i	−0.680353	−	0.732885i	$-0.738173\pi$
$127$	3.31908	−	5.74881i	0.294521	−	0.510125i	0.974873	+	0.222760i	$0.0715067\pi$
$128$	−2.31655	+	13.1378i	−0.204756	+	1.16123i
$129$		0			0
$130$	2.43242	+	0.885328i	0.213337	+	0.0776484i
$131$	−2.19506	−	12.4488i	−0.191783	−	1.08766i	−0.916926	−	0.399058i	$-0.869337\pi$
$131$	−2.19506	−	12.4488i	−0.191783	−	1.08766i	0.725142	−	0.688599i	$-0.241774\pi$
$132$		0			0
$133$	−0.103541	−	0.0868809i	−0.00897811	−	0.00753353i
$134$	25.3405			2.18908
$135$		0			0
$136$	18.3182			1.57077
$137$	8.13223	+	6.82375i	0.694783	+	0.582992i	0.920284	−	0.391251i	$-0.127957\pi$
$137$	8.13223	+	6.82375i	0.694783	+	0.582992i	−0.225501	+	0.974243i	$0.572402\pi$
$138$		0			0
$139$	−1.29561	−	7.34775i	−0.109892	−	0.623228i	−0.989153	−	0.146888i	$-0.953074\pi$
$139$	−1.29561	−	7.34775i	−0.109892	−	0.623228i	0.879261	−	0.476340i	$-0.158037\pi$
$140$	6.25877	+	2.27801i	0.528963	+	0.192527i
$141$		0			0
$142$	5.20187	−	29.5013i	0.436531	−	2.47569i
$143$	−3.39306	+	5.87695i	−0.283742	+	0.491455i
$144$		0			0
$145$	−1.53802	−	2.66393i	−0.127725	−	0.221227i
$146$	19.5929	−	7.13122i	1.62152	−	0.590184i
$147$		0			0
$148$	12.1532	−	10.1977i	0.998984	−	0.838247i
$149$	−3.25877	+	2.73443i	−0.266969	+	0.224013i	−0.766438	−	0.642318i	$-0.777973\pi$
$149$	−3.25877	+	2.73443i	−0.266969	+	0.224013i	0.499469	+	0.866332i	$0.333528\pi$
$150$		0			0
$151$	−0.127011	+	0.0462284i	−0.0103360	+	0.00376201i	−0.347183	−	0.937797i	$-0.612862\pi$
$151$	−0.127011	+	0.0462284i	−0.0103360	+	0.00376201i	0.336847	+	0.941559i	$0.390640\pi$
$152$	−0.127889	−	0.221510i	−0.0103731	−	0.0179668i
$153$		0			0
$154$	−12.6887	+	21.9774i	−1.02248	+	1.77099i
$155$	−0.505930	+	2.86927i	−0.0406373	+	0.230465i
$156$		0			0
$157$	−12.5223	−	4.55774i	−0.999387	−	0.363747i	−0.210039	−	0.977693i	$-0.567359\pi$
$157$	−12.5223	−	4.55774i	−0.999387	−	0.363747i	−0.789348	+	0.613946i	$0.789581\pi$
$158$	4.85844	+	27.5536i	0.386517	+	2.19205i
$159$		0			0
$160$	1.64749	+	1.38241i	0.130245	+	0.109289i
$161$	−19.7023			−1.55276
$162$		0			0
$163$	−9.76382			−0.764762			−0.382381	−	0.924005i	$-0.624896\pi$
$163$	−9.76382			−0.764762			−0.382381	+	0.924005i	$0.624896\pi$
$164$	26.0292	+	21.8411i	2.03254	+	1.70550i
$165$		0			0
$166$	−0.663848	−	3.76487i	−0.0515246	−	0.292211i
$167$	3.35844	+	1.22237i	0.259884	+	0.0945900i	0.468676	−	0.883370i	$-0.344731\pi$
$167$	3.35844	+	1.22237i	0.259884	+	0.0945900i	−0.208792	+	0.977960i	$0.566953\pi$
$168$		0			0
$169$	−1.42855	+	8.10170i	−0.109888	+	0.623208i
$170$	−1.77719	+	3.07818i	−0.136304	+	0.236086i
$171$		0			0
$172$	1.29813	+	2.24843i	0.0989817	+	0.171441i
$173$	−17.6348	+	6.41852i	−1.34075	+	0.487991i	−0.910047	−	0.414505i	$-0.863955\pi$
$173$	−17.6348	+	6.41852i	−1.34075	+	0.487991i	−0.430698	+	0.902496i	$0.641733\pi$
$174$		0			0
$175$	11.8177	−	9.91626i	0.893337	−	0.749598i
$176$	−15.7947	+	13.2534i	−1.19057	+	0.999009i
$177$		0			0
$178$	37.7670	−	13.7461i	2.83075	−	1.03031i
$179$	2.54189	+	4.40268i	0.189990	+	0.329072i	0.945247	−	0.326357i	$-0.105821\pi$
$179$	2.54189	+	4.40268i	0.189990	+	0.329072i	−0.755257	+	0.655429i	$0.772488\pi$
$180$		0			0
$181$	−3.57532	+	6.19264i	−0.265752	+	0.460295i	−0.967760	−	0.251873i	$-0.918953\pi$
$181$	−3.57532	+	6.19264i	−0.265752	+	0.460295i	0.702009	+	0.712168i	$0.252287\pi$
$182$	3.09967	−	17.5791i	0.229763	−	1.30305i
$183$		0			0
$184$	−35.0355	−	12.7519i	−2.58285	−	0.940082i
$185$	0.292204	+	1.65717i	0.0214832	+	0.121837i
$186$		0			0
$187$	−7.13816	−	5.98962i	−0.521994	−	0.438005i
$188$	−42.6168			−3.10815
$189$		0			0
$190$	0.0496299			0.00360053
$191$	−8.05097	−	6.75557i	−0.582548	−	0.488816i	0.303235	−	0.952916i	$-0.401933\pi$
$191$	−8.05097	−	6.75557i	−0.582548	−	0.488816i	−0.885783	+	0.464100i	$0.846378\pi$
$192$		0			0
$193$	−1.76130	−	9.98881i	−0.126781	−	0.719010i	−0.980234	−	0.197841i	$-0.936607\pi$
$193$	−1.76130	−	9.98881i	−0.126781	−	0.719010i	0.853453	−	0.521169i	$-0.174504\pi$
$194$	−44.3658	−	16.1478i	−3.18528	−	1.15935i
$195$		0			0
$196$	2.61334	−	14.8210i	0.186667	−	1.05864i
$197$	−7.04189	+	12.1969i	−0.501714	+	0.868994i	0.498284	+	0.867014i	$0.333964\pi$
$197$	−7.04189	+	12.1969i	−0.501714	+	0.868994i	−0.999998	+	0.00198008i	$0.999370\pi$
$198$		0			0
$199$	−5.13816	−	8.89955i	−0.364234	−	0.630872i	0.624419	−	0.781090i	$-0.285336\pi$
$199$	−5.13816	−	8.89955i	−0.364234	−	0.630872i	−0.988653	+	0.150218i	$0.952003\pi$
$200$	27.4329	−	9.98475i	1.93980	−	0.706029i
$201$		0			0
$202$	17.6250	−	14.7891i	1.24009	−	1.04056i
$203$	−16.2494	+	13.6349i	−1.14049	+	0.956982i
$204$		0			0
$205$	−3.38666	+	1.23264i	−0.236535	+	0.0860915i
$206$	−0.330222	−	0.571962i	−0.0230077	−	0.0398505i
$207$		0			0
$208$	7.25150	−	12.5600i	0.502801	−	0.870877i
$209$	−0.0225934	+	0.128134i	−0.00156282	+	0.00886318i
$210$		0			0
$211$	6.71213	+	2.44302i	0.462082	+	0.168184i	0.562562	−	0.826755i	$-0.309816\pi$
$211$	6.71213	+	2.44302i	0.462082	+	0.168184i	−0.100480	+	0.994939i	$0.532038\pi$
$212$	3.79813	+	21.5403i	0.260857	+	1.47939i
$213$		0			0
$214$	7.84002	+	6.57856i	0.535933	+	0.449701i
$215$	−0.275378			−0.0187806
$216$		0			0
$217$	20.0915			1.36390
$218$	−10.4816	−	8.79509i	−0.709902	−	0.595679i
$219$		0			0
$220$	−1.11334	−	6.31407i	−0.0750614	−	0.425694i
$221$	6.15910	+	2.24173i	0.414306	+	0.150795i
$222$		0			0
$223$	−1.79473	+	10.1784i	−0.120184	+	0.681597i	0.863868	+	0.503718i	$0.168035\pi$
$223$	−1.79473	+	10.1784i	−0.120184	+	0.681597i	−0.984052	+	0.177880i	$0.943076\pi$
$224$	7.41534	−	12.8438i	0.495459	−	0.858159i
$225$		0			0
$226$	−1.75237	−	3.03520i	−0.116566	−	0.201899i
$227$	12.2369	−	4.45389i	0.812195	−	0.295615i	0.0976647	−	0.995219i	$-0.468863\pi$
$227$	12.2369	−	4.45389i	0.812195	−	0.295615i	0.714530	+	0.699605i	$0.246641\pi$
$228$		0			0
$229$	−21.5253	+	18.0619i	−1.42243	+	1.19356i	−0.472408	+	0.881380i	$0.656615\pi$
$229$	−21.5253	+	18.0619i	−1.42243	+	1.19356i	−0.950023	+	0.312181i	$0.898940\pi$
$230$	5.54189	−	4.65020i	0.365421	−	0.306625i
$231$		0			0
$232$	−37.7203	+	13.7291i	−2.47646	+	0.901358i
$233$	6.95723	+	12.0503i	0.455784	+	0.789440i	0.998733	−	0.0503252i	$-0.0160258\pi$
$233$	6.95723	+	12.0503i	0.455784	+	0.789440i	−0.542949	+	0.839765i	$0.682692\pi$
$234$		0			0
$235$	2.26011	−	3.91463i	0.147434	−	0.255363i
$236$	−6.53596	+	37.0673i	−0.425455	+	2.41287i
$237$		0			0
$238$	23.0326	+	8.38316i	1.49298	+	0.543400i
$239$	−2.60813	−	14.7914i	−0.168706	−	0.956777i	−0.945161	−	0.326605i	$-0.894095\pi$
$239$	−2.60813	−	14.7914i	−0.168706	−	0.956777i	0.776455	−	0.630172i	$-0.217016\pi$
$240$		0			0
$241$	−9.93835	−	8.33926i	−0.640185	−	0.537179i	0.263890	−	0.964553i	$-0.414994\pi$
$241$	−9.93835	−	8.33926i	−0.640185	−	0.537179i	−0.904075	+	0.427374i	$0.859439\pi$
$242$	−3.42427			−0.220120
$243$		0			0
$244$	−5.59627			−0.358264
$245$	1.22281	+	1.02606i	0.0781225	+	0.0655526i
$246$		0			0
$247$	−0.0158921	−	0.0901285i	−0.00101119	−	0.00573474i
$248$	35.7276	+	13.0038i	2.26871	+	0.825741i
$249$		0			0
$250$	−2.01233	+	11.4125i	−0.127271	+	0.721788i
$251$	−0.436289	+	0.755675i	−0.0275383	+	0.0476978i	−0.879466	−	0.475961i	$-0.842100\pi$
$251$	−0.436289	+	0.755675i	−0.0275383	+	0.0476978i	0.851928	+	0.523659i	$0.175433\pi$
$252$		0			0
$253$	9.48293	+	16.4249i	0.596186	+	1.03263i
$254$	15.7947	−	5.74881i	0.991049	−	0.360713i
$255$		0			0
$256$	−23.3666	+	19.6069i	−1.46042	+	1.22543i
$257$	3.50593	−	2.94182i	0.218694	−	0.183506i	−0.526858	−	0.849953i	$-0.676630\pi$
$257$	3.50593	−	2.94182i	0.218694	−	0.183506i	0.745552	+	0.666447i	$0.232186\pi$
$258$		0			0
$259$	10.9042	−	3.96880i	0.677554	−	0.246609i
$260$	2.25490	+	3.90560i	0.139843	+	0.242215i
$261$		0			0
$262$	16.0039	−	27.7195i	0.988722	−	1.71252i
$263$	0.746282	−	4.23238i	0.0460177	−	0.260979i	−0.953115	−	0.302607i	$-0.902143\pi$
$263$	0.746282	−	4.23238i	0.0460177	−	0.260979i	0.999133	+	0.0416273i	$0.0132542\pi$
$264$		0			0
$265$	−2.18004	−	0.793471i	−0.133919	−	0.0487426i
$266$	−0.0594300	−	0.337044i	−0.00364389	−	0.0206655i
$267$		0			0
$268$	33.8200	+	28.3784i	2.06589	+	1.73348i
$269$	12.1257			0.739315			0.369657	−	0.929168i	$-0.379475\pi$
$269$	12.1257			0.739315			0.369657	+	0.929168i	$0.379475\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	15.2554	+	12.8008i	0.924992	+	0.776161i
$273$		0			0
$274$	4.66772	+	26.4719i	0.281987	+	1.59923i
$275$	−13.9547	−	5.07910i	−0.841501	−	0.306281i
$276$		0			0
$277$	−4.65745	+	26.4137i	−0.279839	+	1.58705i	0.443319	+	0.896364i	$0.353801\pi$
$277$	−4.65745	+	26.4137i	−0.279839	+	1.58705i	−0.723158	+	0.690683i	$0.757310\pi$
$278$	9.44609	−	16.3611i	0.566539	−	0.981274i
$279$		0			0
$280$	4.60947	+	7.98384i	0.275469	+	0.477126i
$281$	−25.0719	+	9.12543i	−1.49567	+	0.544378i	−0.954934	−	0.296818i	$-0.904075\pi$
$281$	−25.0719	+	9.12543i	−1.49567	+	0.544378i	−0.540731	+	0.841195i	$0.681852\pi$
$282$		0			0
$283$	−7.11927	+	5.97378i	−0.423197	+	0.355104i	−0.829378	−	0.558689i	$-0.811305\pi$
$283$	−7.11927	+	5.97378i	−0.423197	+	0.355104i	0.406181	+	0.913793i	$0.366860\pi$
$284$	39.9805	−	33.5476i	2.37240	−	1.99068i
$285$		0			0
$286$	−16.1468	+	5.87695i	−0.954779	+	0.347511i
$287$	12.4265	+	21.5233i	0.733512	+	1.27048i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	1.35251	−	7.67047i	0.0794222	−	0.450426i
$291$		0			0
$292$	34.1352	+	12.4242i	1.99761	+	0.727072i
$293$	−3.41029	−	19.3407i	−0.199231	−	1.12990i	−0.906263	−	0.422715i	$-0.861077\pi$
$293$	−3.41029	−	19.3407i	−0.199231	−	1.12990i	0.707031	−	0.707182i	$-0.250034\pi$
$294$		0			0
$295$	−3.05825	−	2.56617i	−0.178058	−	0.149408i
$296$	21.9590			1.27634
$297$		0			0
$298$	−10.7716			−0.623980
$299$	−10.2194	−	8.57510i	−0.591004	−	0.495911i
$300$		0			0
$301$	0.329755	+	1.87014i	0.0190068	+	0.107793i
$302$	−0.321604	−	0.117054i	−0.0185062	−	0.00673572i
$303$		0			0
$304$	0.0482857	−	0.273842i	0.00276937	−	0.0157059i
$305$	0.296789	−	0.514054i	0.0169941	−	0.0294346i
$306$		0			0
$307$	−14.1716	−	24.5459i	−0.808815	−	1.40091i	−0.913685	−	0.406423i	$-0.866776\pi$
$307$	−14.1716	−	24.5459i	−0.808815	−	1.40091i	0.104870	−	0.994486i	$-0.466557\pi$
$308$	−41.5467	+	15.1218i	−2.36734	+	0.861642i
$309$		0			0
$310$	−5.65136	+	4.74205i	−0.320976	+	0.269331i
$311$	−1.56624	+	1.31423i	−0.0888132	+	0.0745231i	−0.686113	−	0.727495i	$-0.740685\pi$
$311$	−1.56624	+	1.31423i	−0.0888132	+	0.0745231i	0.597300	+	0.802018i	$0.296240\pi$
$312$		0			0
$313$	−7.90420	+	2.87689i	−0.446772	+	0.162612i	−0.555601	−	0.831449i	$-0.687512\pi$
$313$	−7.90420	+	2.87689i	−0.446772	+	0.162612i	0.108830	+	0.994060i	$0.465290\pi$
$314$	−16.8712	−	29.2218i	−0.952099	−	1.64908i
$315$		0			0
$316$	−24.3726	+	42.2145i	−1.37106	+	2.37475i
$317$	5.40538	−	30.6554i	0.303597	−	1.72178i	−0.326442	−	0.945217i	$-0.605850\pi$
$317$	5.40538	−	30.6554i	0.303597	−	1.72178i	0.630038	−	0.776564i	$-0.283039\pi$
$318$		0			0
$319$	19.1878	+	6.98378i	1.07431	+	0.391017i
$320$	−0.133103	−	0.754866i	−0.00744070	−	0.0421983i
$321$		0			0
$322$	−38.2165	−	32.0674i	−2.12972	−	1.78705i
$323$	0.125667			0.00699231
$324$		0			0
$325$	10.4456			0.579419
$326$	−18.9388	−	15.8916i	−1.04892	−	0.880152i
$327$		0			0
$328$	8.16684	+	46.3165i	0.450938	+	2.55740i
$329$	−29.2913	−	10.6612i	−1.61488	−	0.587769i
$330$		0			0
$331$	5.38847	−	30.5595i	0.296177	−	1.67970i	−0.366202	−	0.930535i	$-0.619342\pi$
$331$	5.38847	−	30.5595i	0.296177	−	1.67970i	0.662379	−	0.749169i	$-0.269547\pi$
$332$	3.33022	−	5.76811i	0.182770	−	0.316566i
$333$		0			0
$334$	4.52481	+	7.83721i	0.247587	+	0.428833i
$335$	−4.40033	+	1.60159i	−0.240416	+	0.0875042i
$336$		0			0
$337$	18.1780	−	15.2531i	0.990218	−	0.830892i	0.00461869	−	0.999989i	$-0.498530\pi$
$337$	18.1780	−	15.2531i	0.990218	−	0.830892i	0.985599	+	0.169098i	$0.0540854\pi$
$338$	−15.9572	+	13.3897i	−0.867959	+	0.728304i
$339$		0			0
$340$	−5.81908	+	2.11797i	−0.315584	+	0.114863i
$341$	−9.67024	−	16.7494i	−0.523673	−	0.907028i
$342$		0			0
$343$	−5.78952	+	10.0277i	−0.312604	+	0.541447i
$344$	−0.624018	+	3.53898i	−0.0336448	+	0.190809i
$345$		0			0
$346$	−44.6528	−	16.2523i	−2.40055	−	0.873728i
$347$	−0.314025	−	1.78093i	−0.0168578	−	0.0956052i	0.975218	−	0.221246i	$-0.0710124\pi$
$347$	−0.314025	−	1.78093i	−0.0168578	−	0.0956052i	−0.992076	+	0.125641i	$0.959901\pi$
$348$		0			0
$349$	11.6905	+	9.80947i	0.625777	+	0.525089i	0.899613	−	0.436687i	$-0.143848\pi$
$349$	11.6905	+	9.80947i	0.625777	+	0.525089i	−0.273837	+	0.961776i	$0.588293\pi$
$350$	39.0624			2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	−24.8063	−	20.8150i	−1.32031	−	1.10787i	−0.986240	−	0.165321i	$-0.947134\pi$
$353$	−24.8063	−	20.8150i	−1.32031	−	1.10787i	−0.334069	−	0.942549i	$-0.608422\pi$
$354$		0			0
$355$	0.961266	+	5.45161i	0.0510187	+	0.289341i
$356$	65.7987	+	23.9488i	3.48732	+	1.26928i
$357$		0			0
$358$	−2.23530	+	12.6770i	−0.118139	+	0.670001i
$359$	0.957234	−	1.65798i	0.0505209	−	0.0875047i	−0.839659	−	0.543114i	$-0.817245\pi$
$359$	0.957234	−	1.65798i	0.0505209	−	0.0875047i	0.890180	+	0.455609i	$0.150579\pi$
$360$		0			0
$361$	9.49912	+	16.4530i	0.499954	+	0.865945i
$362$	−17.0141	+	6.19264i	−0.894243	+	0.325478i
$363$		0			0
$364$	23.8234	−	19.9902i	1.24869	−	1.04777i
$365$	−2.95155	+	2.47665i	−0.154491	+	0.129634i
$366$		0			0
$367$	25.2447	−	9.18832i	1.31776	−	0.479626i	0.415022	−	0.909812i	$-0.363774\pi$
$367$	25.2447	−	9.18832i	1.31776	−	0.479626i	0.902741	+	0.430185i	$0.141552\pi$
$368$	−20.2665	−	35.1026i	−1.05646	−	1.82985i
$369$		0			0
$370$	−2.13041	+	3.68999i	−0.110755	+	0.191833i
$371$	−2.77807	+	15.7552i	−0.144230	+	0.817969i
$372$		0			0
$373$	−13.9452	−	5.07564i	−0.722056	−	0.262807i	−0.0452575	−	0.998975i	$-0.514411\pi$
$373$	−13.9452	−	5.07564i	−0.722056	−	0.262807i	−0.676798	+	0.736169i	$0.736633\pi$
$374$	−4.09714	−	23.2361i	−0.211858	−	1.20151i
$375$		0			0
$376$	−45.1869	−	37.9163i	−2.33034	−	1.95538i
$377$	−14.3628			−0.739721
$378$		0			0
$379$	−33.7870			−1.73552			−0.867762	−	0.496980i	$-0.834442\pi$
$379$	−33.7870			−1.73552			−0.867762	+	0.496980i	$0.834442\pi$
$380$	0.0662372	+	0.0555796i	0.00339789	+	0.00285117i
$381$		0			0
$382$	−4.62108	−	26.2075i	−0.236435	−	1.34089i
$383$	8.71941	+	3.17360i	0.445541	+	0.162164i	0.555041	−	0.831823i	$-0.312703\pi$
$383$	8.71941	+	3.17360i	0.445541	+	0.162164i	−0.109500	+	0.993987i	$0.534925\pi$
$384$		0			0
$385$	0.814330	−	4.61830i	0.0415021	−	0.235370i
$386$	12.8414	−	22.2419i	0.653608	−	1.13208i
$387$		0			0
$388$	−41.1279	−	71.2357i	−2.08796	−	3.61644i
$389$	15.0150	−	5.46502i	0.761291	−	0.277087i	0.0679423	−	0.997689i	$-0.478357\pi$
$389$	15.0150	−	5.46502i	0.761291	−	0.277087i	0.693349	+	0.720602i	$0.256134\pi$
$390$		0			0
$391$	14.0326	−	11.7747i	0.709657	−	0.595473i
$392$	15.9572	−	13.3897i	0.805962	−	0.676282i
$393$		0			0
$394$	−33.5107	+	12.1969i	−1.68825	+	0.614471i
$395$	−2.58512	−	4.47756i	−0.130072	−	0.225291i
$396$		0			0
$397$	−9.85251	+	17.0650i	−0.494483	+	0.856470i	−0.999980	−	0.00635841i	$-0.997976\pi$
$397$	−9.85251	+	17.0650i	−0.494483	+	0.856470i	0.505496	+	0.862829i	$0.331309\pi$
$398$	4.51842	−	25.6252i	0.226488	−	1.28448i
$399$		0			0
$400$	29.8234	+	10.8548i	1.49117	+	0.542742i
$401$	0.199340	+	1.13052i	0.00995459	+	0.0564553i	0.989380	−	0.145349i	$-0.0464306\pi$
$401$	0.199340	+	1.13052i	0.00995459	+	0.0564553i	−0.979426	+	0.201804i	$0.935319\pi$
$402$		0			0
$403$	10.4213	+	8.74449i	0.519121	+	0.435594i
$404$	40.0847			1.99429
$405$		0			0
$406$	−53.7110			−2.66563
$407$	−8.55690	−	7.18009i	−0.424150	−	0.355904i
$408$		0			0
$409$	−0.538485	−	3.05390i	−0.0266264	−	0.151006i	0.968596	−	0.248640i	$-0.0799836\pi$
$409$	−0.538485	−	3.05390i	−0.0266264	−	0.151006i	−0.995222	+	0.0976342i	$0.968872\pi$
$410$	−8.57532	−	3.12116i	−0.423505	−	0.154143i
$411$		0			0
$412$	0.199807	−	1.13316i	0.00984380	−	0.0558270i
$413$	−13.7652	+	23.8420i	−0.677340	+	1.17319i
$414$		0			0
$415$	0.353226	+	0.611806i	0.0173392	+	0.0300324i
$416$	9.43629	−	3.43453i	0.462652	−	0.168392i
$417$		0			0
$418$	−0.252374	+	0.211767i	−0.0123440	+	0.0103579i
$419$	27.1557	−	22.7863i	1.32664	−	1.11319i	0.341793	−	0.939775i	$-0.388966\pi$
$419$	27.1557	−	22.7863i	1.32664	−	1.11319i	0.984850	−	0.173410i	$-0.0554786\pi$
$420$		0			0
$421$	−8.66132	+	3.15246i	−0.422127	+	0.153642i	−0.544345	−	0.838862i	$-0.683222\pi$
$421$	−8.66132	+	3.15246i	−0.422127	+	0.153642i	0.122218	+	0.992503i	$0.460999\pi$
$422$	9.04323	+	15.6633i	0.440218	+	0.762479i
$423$		0			0
$424$	−15.1373	+	26.2185i	−0.735131	+	1.27328i
$425$	−2.49067	+	14.1253i	−0.120815	+	0.685176i
$426$		0			0
$427$	−3.84642	−	1.39998i	−0.186141	−	0.0677499i
$428$	3.09627	+	17.5598i	0.149664	+	0.848785i
$429$		0			0
$430$	−0.534148	−	0.448204i	−0.0257589	−	0.0216143i
$431$	11.5794			0.557758			0.278879	−	0.960326i	$-0.410037\pi$
$431$	11.5794			0.557758			0.278879	+	0.960326i	$0.410037\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	38.9714	+	32.7009i	1.87069	+	1.56969i
$435$		0			0
$436$	−4.13950	−	23.4763i	−0.198246	−	1.12431i
$437$	−0.240352	−	0.0874810i	−0.0114976	−	0.00418479i
$438$		0			0
$439$	5.03684	−	28.5653i	0.240395	−	1.36335i	−0.590553	−	0.806999i	$-0.701090\pi$
$439$	5.03684	−	28.5653i	0.240395	−	1.36335i	0.830948	−	0.556350i	$-0.187798\pi$
$440$	4.43717	−	7.68540i	0.211534	−	0.366387i
$441$		0			0
$442$	8.29813	+	14.3728i	0.394702	+	0.683644i
$443$	−29.0292	+	10.5657i	−1.37922	+	0.501994i	−0.921941	−	0.387331i	$-0.873397\pi$
$443$	−29.0292	+	10.5657i	−1.37922	+	0.501994i	−0.457276	+	0.889325i	$0.651175\pi$
$444$		0			0
$445$	−5.68938	+	4.77396i	−0.269702	+	0.226307i
$446$	−20.0476	+	16.8219i	−0.949280	+	0.796540i
$447$		0			0
$448$	−4.96703	+	1.80785i	−0.234670	+	0.0854130i
$449$	19.5410	+	33.8460i	0.922197	+	1.59729i	0.796008	+	0.605287i	$0.206941\pi$
$449$	19.5410	+	33.8460i	0.922197	+	1.59729i	0.126190	+	0.992006i	$0.459725\pi$
$450$		0			0
$451$	11.9620	−	20.7188i	0.563268	−	0.975608i
$452$	1.06031	−	6.01330i	0.0498727	−	0.282842i
$453$		0			0
$454$	30.9850	+	11.2776i	1.45420	+	0.529286i
$455$	0.572796	+	3.24849i	0.0268531	+	0.152291i
$456$		0			0
$457$	−1.15270	−	0.967233i	−0.0539212	−	0.0452453i	0.615429	−	0.788192i	$-0.288983\pi$
$457$	−1.15270	−	0.967233i	−0.0539212	−	0.0452453i	−0.669350	+	0.742947i	$0.733427\pi$
$458$	−71.1498			−3.32461
$459$		0			0
$460$	12.6040			0.587665
$461$	20.0988	+	16.8649i	0.936094	+	0.785476i	0.976901	−	0.213691i	$-0.0685485\pi$
$461$	20.0988	+	16.8649i	0.936094	+	0.785476i	−0.0408072	+	0.999167i	$0.512993\pi$
$462$		0			0
$463$	1.17324	+	6.65376i	0.0545250	+	0.309227i	0.999857	−	0.0168815i	$-0.00537380\pi$
$463$	1.17324	+	6.65376i	0.0545250	+	0.309227i	−0.945333	+	0.326108i	$0.894263\pi$
$464$	−41.0073	−	14.9254i	−1.90372	−	0.692897i
$465$		0			0
$466$	−6.11809	+	34.6974i	−0.283415	+	1.60733i
$467$	−16.8735	+	29.2257i	−0.780810	+	1.35240i	0.150660	+	0.988586i	$0.451860\pi$
$467$	−16.8735	+	29.2257i	−0.780810	+	1.35240i	−0.931470	+	0.363818i	$0.881473\pi$
$468$		0			0
$469$	16.1459	+	27.9655i	0.745548	+	1.29133i
$470$	10.7554	−	3.91463i	0.496108	−	0.180569i
$471$		0			0
$472$	−39.9090	+	33.4876i	−1.83696	+	1.54139i
$473$	1.40033	−	1.17502i	0.0643872	−	0.0540273i
$474$		0			0
$475$	0.188196	−	0.0684978i	0.00863503	−	0.00314289i
$476$	21.3516	+	36.9821i	0.978651	+	1.69507i
$477$		0			0
$478$	19.0155	−	32.9358i	0.869748	−	1.50645i
$479$	1.93211	−	10.9576i	0.0882805	−	0.500664i	−0.908320	−	0.418276i	$-0.862634\pi$
$479$	1.93211	−	10.9576i	0.0882805	−	0.500664i	0.996600	−	0.0823875i	$-0.0262545\pi$
$480$		0			0
$481$	7.38326	+	2.68729i	0.336647	+	0.122530i
$482$	−5.70439	−	32.3512i	−0.259828	−	1.47356i
$483$		0			0
$484$	−4.57011	−	3.83478i	−0.207732	−	0.174308i
$485$	8.72462			0.396165
$486$		0			0
$487$	−4.74691			−0.215103			−0.107552	−	0.994200i	$-0.534301\pi$
$487$	−4.74691			−0.215103			−0.107552	+	0.994200i	$0.534301\pi$
$488$	−5.93376	−	4.97902i	−0.268609	−	0.225390i
$489$		0			0
$490$	0.701867	+	3.98048i	0.0317071	+	0.179820i
$491$	−20.9932	−	7.64090i	−0.947410	−	0.344829i	−0.178322	−	0.983972i	$-0.557067\pi$
$491$	−20.9932	−	7.64090i	−0.947410	−	0.344829i	−0.769088	+	0.639143i	$0.779289\pi$
$492$		0			0
$493$	3.42468	−	19.4223i	0.154240	−	0.874737i
$494$	0.115867	−	0.200688i	0.00521310	−	0.00902936i
$495$		0			0
$496$	20.6668	+	35.7960i	0.927969	+	1.60729i
$497$	35.8717	−	13.0562i	1.60907	−	0.585652i
$498$		0			0
$499$	−8.01367	+	6.72427i	−0.358741	+	0.301020i	−0.804289	−	0.594239i	$-0.797453\pi$
$499$	−8.01367	+	6.72427i	−0.358741	+	0.301020i	0.445548	+	0.895258i	$0.353009\pi$
$500$	−15.4663	+	12.9778i	−0.691675	+	0.580384i
$501$		0			0
$502$	−2.07620	+	0.755675i	−0.0926653	+	0.0337274i
$503$	−12.5209	−	21.6869i	−0.558281	−	0.966972i	−0.997640	−	0.0686600i	$-0.978128\pi$
$503$	−12.5209	−	21.6869i	−0.558281	−	0.966972i	0.439359	−	0.898312i	$-0.355206\pi$
$504$		0			0
$505$	−2.12583	+	3.68204i	−0.0945982	+	0.163849i
$506$	−8.33915	+	47.2936i	−0.370720	+	2.10246i
$507$		0			0
$508$	27.5180	+	10.0157i	1.22091	+	0.444376i
$509$	3.13651	+	17.7880i	0.139023	+	0.788440i	0.971973	+	0.235092i	$0.0755390\pi$
$509$	3.13651	+	17.7880i	0.139023	+	0.788440i	−0.832950	+	0.553348i	$0.813350\pi$
$510$		0			0
$511$	20.3537	+	17.0788i	0.900394	+	0.755521i
$512$	−50.5553			−2.23425
$513$		0			0
$514$	11.5885			0.511148
$515$	0.0934920	+	0.0784491i	0.00411975	+	0.00345688i
$516$		0			0
$517$	5.21048	+	29.5501i	0.229157	+	1.29961i
$518$	27.6104	+	10.0494i	1.21313	+	0.441544i
$519$		0			0
$520$	−1.08394	+	6.14733i	−0.0475339	+	0.269578i
$521$	12.9791	−	22.4804i	0.568623	−	0.984883i	−0.428080	−	0.903741i	$-0.640810\pi$
$521$	12.9791	−	22.4804i	0.568623	−	0.984883i	0.996703	−	0.0811425i	$-0.0258569\pi$
$522$		0			0
$523$	−12.7973	−	22.1655i	−0.559585	−	0.969230i	−0.997531	−	0.0702283i	$-0.977627\pi$
$523$	−12.7973	−	22.1655i	−0.559585	−	0.969230i	0.437946	−	0.899001i	$-0.355706\pi$
$524$	52.4017	−	19.0727i	2.28918	−	0.833193i
$525$		0			0
$526$	8.33615	−	6.99486i	0.363473	−	0.304990i
$527$	−14.3097	+	12.0073i	−0.623342	+	0.523046i
$528$		0			0
$529$	−13.4226	+	4.88543i	−0.583592	+	0.212410i
$530$	−2.93717	−	5.08732i	−0.127582	−	0.220979i
$531$		0			0
$532$	0.298133	−	0.516382i	0.0129257	−	0.0223880i
$533$	−2.92215	+	16.5723i	−0.126572	+	0.717828i
$534$		0			0
$535$	−1.77719	−	0.646844i	−0.0768346	−	0.0279655i
$536$	10.6113	+	60.1796i	0.458338	+	2.59936i
$537$		0			0
$538$	23.5201	+	19.7357i	1.01402	+	0.850866i
$539$	−10.5963			−0.456414
$540$		0			0
$541$	27.8476			1.19726			0.598631	−	0.801025i	$-0.295712\pi$
$541$	27.8476			1.19726			0.598631	+	0.801025i	$0.295712\pi$
$542$	−0.620615	−	0.520758i	−0.0266577	−	0.0223685i
$543$		0			0
$544$	2.39440	+	13.5793i	0.102659	+	0.582208i
$545$	2.37598	+	0.864787i	0.101776	+	0.0370434i
$546$		0			0
$547$	−1.02600	+	5.81872i	−0.0438685	+	0.248790i	−0.998854	−	0.0478621i	$-0.984759\pi$
$547$	−1.02600	+	5.81872i	−0.0438685	+	0.248790i	0.954985	+	0.296653i	$0.0958703\pi$
$548$	−23.4158	+	40.5574i	−1.00027	+	1.73253i
$549$		0			0
$550$	−18.8011	−	32.5645i	−0.801683	−	1.38856i
$551$	−0.258770	+	0.0941848i	−0.0110240	+	0.00401241i
$552$		0			0
$553$	−27.3123	+	22.9177i	−1.16144	+	0.974560i
$554$	−52.0249	+	43.6541i	−2.21032	+	1.85468i
$555$		0			0
$556$	30.9295	−	11.2574i	1.31170	−	0.477421i
$557$	−13.3525	−	23.1272i	−0.565764	−	0.979932i	−0.996978	−	0.0776824i	$-0.975248\pi$
$557$	−13.3525	−	23.1272i	−0.565764	−	0.979932i	0.431214	−	0.902250i	$-0.358085\pi$
$558$		0			0
$559$	−0.642903	+	1.11354i	−0.0271919	+	0.0470978i
$560$	−1.74035	+	9.87003i	−0.0735433	+	0.417085i
$561$		0			0
$562$	−63.4843	−	23.1064i	−2.67792	−	0.974685i
$563$	6.26217	+	35.5146i	0.263919	+	1.49676i	0.772095	+	0.635507i	$0.219209\pi$
$563$	6.26217	+	35.5146i	0.263919	+	1.49676i	−0.508176	+	0.861253i	$0.669680\pi$
$564$		0			0
$565$	0.496130	+	0.416302i	0.0208723	+	0.0175140i
$566$	−23.5321			−0.989127
$567$		0			0
$568$	72.2390			3.03108
$569$	−6.93061	−	5.81547i	−0.290546	−	0.243797i	0.485850	−	0.874042i	$-0.338510\pi$
$569$	−6.93061	−	5.81547i	−0.290546	−	0.243797i	−0.776396	+	0.630245i	$0.782954\pi$
$570$		0			0
$571$	5.30999	+	30.1145i	0.222216	+	1.26025i	0.867936	+	0.496676i	$0.165446\pi$
$571$	5.30999	+	30.1145i	0.222216	+	1.26025i	−0.645719	+	0.763575i	$0.723442\pi$
$572$	−28.1313	−	10.2390i	−1.17623	−	0.428113i
$573$		0			0
$574$	−10.9277	+	61.9739i	−0.456112	+	2.58674i
$575$	14.5967	−	25.2823i	0.608726	−	1.05434i
$576$		0			0
$577$	12.5744	+	21.7796i	0.523481	+	0.906696i	0.999626	+	0.0273292i	$0.00870022\pi$
$577$	12.5744	+	21.7796i	0.523481	+	0.906696i	−0.476146	+	0.879367i	$0.657966\pi$
$578$	19.0351	−	6.92820i	0.791755	−	0.288175i
$579$		0			0
$580$	10.3951	−	8.72254i	0.431634	−	0.362184i
$581$	3.73190	−	3.13143i	0.154825	−	0.129914i
$582$		0			0
$583$	14.4715	−	5.26719i	0.599347	−	0.218145i
$584$	25.1400	+	43.5437i	1.04030	+	1.80185i
$585$		0			0
$586$	24.8640	−	43.0656i	1.02712	−	1.77903i
$587$	3.62465	−	20.5564i	0.149605	−	0.848453i	−0.813948	−	0.580937i	$-0.802686\pi$
$587$	3.62465	−	20.5564i	0.149605	−	0.848453i	0.963553	−	0.267516i	$-0.0862028\pi$
$588$		0			0
$589$	0.245100	+	0.0892091i	0.0100992	+	0.00367580i
$590$	−1.75537	−	9.95518i	−0.0722673	−	0.409848i
$591$		0			0
$592$	18.2875	+	15.3450i	0.751610	+	0.630676i
$593$	15.6212			0.641488			0.320744	−	0.947166i	$-0.396067\pi$
$593$	15.6212			0.641488			0.320744	+	0.947166i	$0.396067\pi$
$594$		0			0
$595$	−4.52940			−0.185687
$596$	−14.3760	−	12.0629i	−0.588863	−	0.494115i
$597$		0			0
$598$	−5.86571	−	33.2661i	−0.239867	−	1.36035i
$599$	0.421274	+	0.153331i	0.0172128	+	0.00626495i	0.350612	−	0.936521i	$-0.385974\pi$
$599$	0.421274	+	0.153331i	0.0172128	+	0.00626495i	−0.333399	+	0.942786i	$0.608196\pi$
$600$		0			0
$601$	−3.06876	+	17.4038i	−0.125177	+	0.709917i	0.856025	+	0.516935i	$0.172927\pi$
$601$	−3.06876	+	17.4038i	−0.125177	+	0.709917i	−0.981202	+	0.192982i	$0.938184\pi$
$602$	−2.40420	+	4.16420i	−0.0979879	+	0.169720i
$603$		0			0
$604$	−0.298133	−	0.516382i	−0.0121309	−	0.0210113i
$605$	0.594618	−	0.216423i	0.0241747	−	0.00879885i
$606$		0			0
$607$	20.0692	−	16.8401i	0.814585	−	0.683518i	−0.137112	−	0.990555i	$-0.543782\pi$
$607$	20.0692	−	16.8401i	0.814585	−	0.683518i	0.951697	+	0.307038i	$0.0993377\pi$
$608$	0.147489	−	0.123758i	0.00598147	−	0.00501905i
$609$		0			0
$610$	1.41235	−	0.514054i	0.0571844	−	0.0208134i
$611$	−10.5530	−	18.2784i	−0.426930	−	0.739465i
$612$		0			0
$613$	−7.27719	+	12.6045i	−0.293923	+	0.509089i	−0.974734	−	0.223370i	$-0.928294\pi$
$613$	−7.27719	+	12.6045i	−0.293923	+	0.509089i	0.680811	+	0.732459i	$0.261628\pi$
$614$	12.4623	−	70.6771i	0.502937	−	2.85230i
$615$		0			0
$616$	−57.5061	−	20.9305i	−2.31699	−	0.843315i
$617$	2.43464	+	13.8075i	0.0980149	+	0.555870i	0.993782	+	0.111346i	$0.0355162\pi$
$617$	2.43464	+	13.8075i	0.0980149	+	0.555870i	−0.895767	+	0.444524i	$0.853373\pi$
$618$		0			0
$619$	−24.2931	−	20.3844i	−0.976424	−	0.819317i	0.00712236	−	0.999975i	$-0.497733\pi$
$619$	−24.2931	−	20.3844i	−0.976424	−	0.819317i	−0.983546	+	0.180658i	$0.942177\pi$
$620$	−12.8530			−0.516188
$621$		0			0
$622$	−5.17705			−0.207581
$623$	39.2335	+	32.9209i	1.57186	+	1.31895i
$624$		0			0
$625$	3.77925	+	21.4332i	0.151170	+	0.857327i
$626$	−20.0141	−	7.28455i	−0.799926	−	0.291149i
$627$		0			0
$628$	10.2083	−	57.8939i	0.407354	−	2.31022i
$629$	−5.39440	+	9.34337i	−0.215089	+	0.372545i
$630$		0			0
$631$	19.2879	+	33.4077i	0.767840	+	1.32994i	0.938732	+	0.344648i	$0.112002\pi$
$631$	19.2879	+	33.4077i	0.767840	+	1.32994i	−0.170892	+	0.985290i	$0.554665\pi$
$632$	−63.4009	+	23.0760i	−2.52195	+	0.917915i
$633$		0			0
$634$	60.3794	−	50.6644i	2.39797	−	2.01214i
$635$	−2.37939	+	1.99654i	−0.0944230	+	0.0792303i
$636$		0			0
$637$	7.00387	−	2.54920i	0.277503	−	0.101003i
$638$	25.8516	+	44.7763i	1.02348	+	1.77271i
$639$		0			0
$640$	3.12108	−	5.40587i	0.123372	−	0.213686i
$641$	−5.31655	+	30.1517i	−0.209991	+	1.19092i	0.679399	+	0.733769i	$0.262241\pi$
$641$	−5.31655	+	30.1517i	−0.209991	+	1.19092i	−0.889390	+	0.457150i	$0.848870\pi$
$642$		0			0
$643$	32.1609	+	11.7056i	1.26830	+	0.461624i	0.886547	−	0.462639i	$-0.153097\pi$
$643$	32.1609	+	11.7056i	1.26830	+	0.461624i	0.381756	+	0.924263i	$0.375320\pi$
$644$	−15.0929	−	85.5959i	−0.594742	−	3.37295i
$645$		0			0
$646$	0.243756	+	0.204535i	0.00959044	+	0.00804734i
$647$	−12.8726			−0.506073			−0.253037	−	0.967457i	$-0.581429\pi$
$647$	−12.8726			−0.506073			−0.253037	+	0.967457i	$0.581429\pi$
$648$		0			0
$649$	26.5012			1.04026
$650$	20.2613	+	17.0012i	0.794713	+	0.666844i
$651$		0			0
$652$	−7.47952	−	42.4185i	−0.292921	−	1.66124i
$653$	10.6365	+	3.87137i	0.416239	+	0.151498i	0.541646	−	0.840607i	$-0.317801\pi$
$653$	10.6365	+	3.87137i	0.416239	+	0.151498i	−0.125407	+	0.992105i	$0.540024\pi$
$654$		0			0
$655$	−1.02709	+	5.82493i	−0.0401318	+	0.227599i
$656$	−25.5646	+	44.2793i	−0.998132	+	1.72881i
$657$		0			0
$658$	−39.4641	−	68.3538i	−1.53847	−	2.66471i
$659$	12.9388	−	4.70934i	0.504025	−	0.183450i	−0.0774786	−	0.996994i	$-0.524687\pi$
$659$	12.9388	−	4.70934i	0.504025	−	0.183450i	0.581503	+	0.813544i	$0.302465\pi$
$660$		0			0
$661$	−15.5253	+	13.0273i	−0.603863	+	0.506702i	−0.892685	−	0.450681i	$-0.851181\pi$
$661$	−15.5253	+	13.0273i	−0.603863	+	0.506702i	0.288821	+	0.957383i	$0.406737\pi$
$662$	60.1905	−	50.5059i	2.33937	−	1.96297i
$663$		0			0
$664$	8.66297	−	3.15306i	0.336188	−	0.122363i
$665$	0.0316221	+	0.0547710i	0.00122625	+	0.00212393i
$666$		0			0
$667$	−20.0706	+	34.7633i	−0.777136	+	1.34604i
$668$	−2.73783	+	15.5270i	−0.105930	+	0.600757i
$669$		0			0
$670$	−11.1420	−	4.05537i	−0.430454	−	0.156672i
$671$	0.684220	+	3.88040i	0.0264140	+	0.149801i
$672$		0			0
$673$	−23.3987	−	19.6339i	−0.901955	−	0.756830i	0.0686165	−	0.997643i	$-0.478142\pi$
$673$	−23.3987	−	19.6339i	−0.901955	−	0.756830i	−0.970572	+	0.240813i	$0.922586\pi$
$674$	60.0856			2.31441
$675$		0			0
$676$	−36.2918			−1.39584
$677$	−2.84911	−	2.39068i	−0.109500	−	0.0918815i	0.586394	−	0.810026i	$-0.300547\pi$
$677$	−2.84911	−	2.39068i	−0.109500	−	0.0918815i	−0.695894	+	0.718145i	$0.744992\pi$
$678$		0			0
$679$	−10.4474	−	59.2503i	−0.400936	−	2.27382i
$680$	−8.05438	−	2.93155i	−0.308871	−	0.112420i
$681$		0			0
$682$	8.50387	−	48.2278i	0.325630	−	1.84674i
$683$	10.8735	−	18.8334i	0.416061	−	0.720639i	−0.579478	−	0.814988i	$-0.696744\pi$
$683$	10.8735	−	18.8334i	0.416061	−	0.720639i	0.995539	+	0.0943487i	$0.0300769\pi$
$684$		0			0
$685$	−2.48364	−	4.30179i	−0.0948950	−	0.164363i
$686$	−27.5510	+	10.0277i	−1.05190	+	0.382861i
$687$		0			0
$688$	−2.99273	+	2.51120i	−0.114097	+	0.0957384i
$689$	−8.29813	+	6.96296i	−0.316134	+	0.265268i
$690$		0			0
$691$	35.3276	−	12.8582i	1.34392	−	0.489149i	0.432878	−	0.901452i	$-0.357498\pi$
$691$	35.3276	−	12.8582i	1.34392	−	0.489149i	0.911046	+	0.412304i	$0.135276\pi$
$692$	−41.3940	−	71.6965i	−1.57356	−	2.72549i
$693$		0			0
$694$	2.28952	−	3.96556i	0.0869088	−	0.150530i
$695$	−0.606229	+	3.43810i	−0.0229956	+	0.130414i
$696$		0			0
$697$	−21.7135	−	7.90306i	−0.822457	−	0.299350i
$698$	6.71007	+	38.0547i	0.253980	+	1.44039i
$699$		0			0
$700$	52.1336	+	43.7453i	1.97047	+	1.65342i
$701$	23.3351			0.881355			0.440678	−	0.897665i	$-0.354738\pi$
$701$	23.3351			0.881355			0.440678	+	0.897665i	$0.354738\pi$
$702$		0			0
$703$	0.150644			0.00568166
$704$	3.89780	+	3.27065i	0.146904	+	0.123267i
$705$		0			0
$706$	−14.2383	−	80.7494i	−0.535865	−	3.03904i
$707$	27.5510	+	10.0277i	1.03616	+	0.377132i
$708$		0			0
$709$	1.14244	−	6.47908i	0.0429051	−	0.243327i	−0.955811	−	0.293981i	$-0.905020\pi$
$709$	1.14244	−	6.47908i	0.0429051	−	0.243327i	0.998716	+	0.0506545i	$0.0161307\pi$
$710$	−7.00846	+	12.1390i	−0.263023	+	0.455569i
$711$		0			0
$712$	48.4595	+	83.9343i	1.81610	+	3.14557i
$713$	35.7276	−	13.0038i	1.33801	−	0.486996i
$714$		0			0
$715$	2.43242	−	2.04104i	0.0909673	−	0.0763306i
$716$	−17.1800	+	14.4158i	−0.642048	+	0.538743i
$717$		0			0
$718$	4.55525	−	1.65798i	0.170001	−	0.0618752i
$719$	8.41622	+	14.5773i	0.313872	+	0.543642i	0.979197	−	0.202911i	$-0.0650403\pi$
$719$	8.41622	+	14.5773i	0.313872	+	0.543642i	−0.665325	+	0.746554i	$0.731707\pi$
$720$		0			0
$721$	0.420807	−	0.728860i	0.0156717	−	0.0271442i
$722$	−8.35339	+	47.3744i	−0.310881	+	1.76309i
$723$		0			0
$724$	−29.6425	−	10.7890i	−1.10165	−	0.400969i
$725$	−5.45786	−	30.9531i	−0.202700	−	1.14957i
$726$		0			0
$727$	19.5817	+	16.4310i	0.726246	+	0.609393i	0.929105	−	0.369815i	$-0.120579\pi$
$727$	19.5817	+	16.4310i	0.726246	+	0.609393i	−0.202860	+	0.979208i	$0.565023\pi$
$728$	43.0455			1.59537
$729$		0			0
$730$	−9.75608			−0.361089
$731$	−1.35251	−	1.13489i	−0.0500244	−	0.0419755i
$732$		0			0
$733$	−2.56964	−	14.5732i	−0.0949118	−	0.538272i	−0.994774	−	0.102098i	$-0.967444\pi$
$733$	−2.56964	−	14.5732i	−0.0949118	−	0.538272i	0.899862	−	0.436174i	$-0.143667\pi$
$734$	63.9218	+	23.2656i	2.35940	+	0.858750i
$735$		0			0
$736$	4.87346	−	27.6387i	0.179638	−	1.01878i
$737$	15.5424	−	26.9202i	0.572510	−	0.991616i
$738$		0			0
$739$	−4.59539	−	7.95945i	−0.169044	−	0.292793i	0.769040	−	0.639201i	$-0.220735\pi$
$739$	−4.59539	−	7.95945i	−0.169044	−	0.292793i	−0.938084	+	0.346408i	$0.887401\pi$
$740$	−6.97565	+	2.53893i	−0.256430	+	0.0933329i
$741$		0			0
$742$	−31.0317	+	26.0387i	−1.13921	+	0.955910i
$743$	34.0501	−	28.5714i	1.24918	−	1.04818i	0.252428	−	0.967616i	$-0.418771\pi$
$743$	34.0501	−	28.5714i	1.24918	−	1.04818i	0.996749	−	0.0805681i	$-0.0256735\pi$
$744$		0			0
$745$	1.87046	−	0.680793i	0.0685284	−	0.0249423i
$746$	−18.7883	−	32.5423i	−0.687890	−	1.19146i
$747$		0			0
$748$	20.5535	−	35.5997i	0.751510	−	1.30165i
$749$	−2.26470	+	12.8438i	−0.0827503	+	0.469301i
$750$		0			0
$751$	33.6467	+	12.2464i	1.22778	+	0.446877i	0.872838	−	0.488010i	$-0.162277\pi$
$751$	33.6467	+	12.2464i	1.22778	+	0.446877i	0.354946	+	0.934887i	$0.384499\pi$
$752$	−11.1356	−	63.1533i	−0.406075	−	2.30296i
$753$		0			0
$754$	−27.8594	−	23.3768i	−1.01458	−	0.851333i
$755$	0.0632441			0.00230169
$756$		0			0
$757$	−45.8976			−1.66818			−0.834088	−	0.551632i	$-0.814005\pi$
$757$	−45.8976			−1.66818			−0.834088	+	0.551632i	$0.814005\pi$
$758$	−65.5365	−	54.9916i	−2.38039	−	1.99739i
$759$		0			0
$760$	0.0207824	+	0.117863i	0.000753857	+	0.00427534i
$761$	34.9521	+	12.7215i	1.26701	+	0.461155i	0.886116	−	0.463463i	$-0.153393\pi$
$761$	34.9521	+	12.7215i	1.26701	+	0.461155i	0.380896	+	0.924618i	$0.375616\pi$
$762$		0			0
$763$	3.02775	−	17.1712i	0.109612	−	0.621640i
$764$	23.1819	−	40.1522i	0.838690	−	1.45265i
$765$		0			0
$766$	11.7476	+	20.3475i	0.424459	+	0.735185i
$767$	−17.5167	+	6.37554i	−0.632490	+	0.230208i
$768$		0			0
$769$	−29.3653	+	24.6404i	−1.05894	+	0.888556i	−0.994005	−	0.109333i	$-0.965128\pi$
$769$	−29.3653	+	24.6404i	−1.05894	+	0.888556i	−0.0649348	+	0.997890i	$0.520684\pi$
$770$	9.09627	−	7.63267i	0.327807	−	0.275062i
$771$		0			0
$772$	42.0467	−	15.3037i	1.51329	−	0.550794i
$773$	−26.4136	−	45.7497i	−0.950031	−	1.64550i	−0.745351	−	0.666673i	$-0.767718\pi$
$773$	−26.4136	−	45.7497i	−0.950031	−	1.64550i	−0.204680	−	0.978829i	$-0.565615\pi$
$774$		0			0
$775$	−14.8851	+	25.7817i	−0.534687	+	0.926106i
$776$	19.7704	−	112.123i	0.709715	−	4.02500i
$777$		0			0
$778$	38.0194	+	13.8379i	1.36306	+	0.496113i
$779$	0.0560265	+	0.317742i	0.00200736	+	0.0113843i
$780$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.93969 + 1.62760i) q^{2} +(0.766044 + 4.34445i) q^{4} +(-0.439693 - 0.160035i) q^{5} +(-0.560307 + 3.17766i) q^{7} +(-3.05303 + 5.28801i) q^{8} +(-0.592396 - 1.02606i) q^{10} +(2.91875 - 1.06234i) q^{11} +(-1.67365 + 1.40436i) q^{13} +(-6.25877 + 5.25173i) q^{14} +(-6.23783 + 2.27038i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.0209445 + 0.0362770i) q^{19} +(0.358441 - 2.03282i) q^{20} +(7.39053 + 2.68993i) q^{22} +(1.06031 + 6.01330i) q^{23} +(-3.66250 - 3.07321i) q^{25} -5.53209 q^{26} -14.2344 q^{28} +(5.03596 + 4.22567i) q^{29} +(-1.08125 - 6.13208i) q^{31} +(-4.31908 - 1.57202i) q^{32} +(1.31908 - 7.48086i) q^{34} +(0.754900 - 1.30753i) q^{35} +(-1.79813 - 3.11446i) q^{37} +(-0.0996702 + 0.0362770i) q^{38} +(2.18866 - 1.83651i) q^{40} +(5.90033 - 4.95096i) q^{41} +(0.553033 - 0.201288i) q^{43} +(6.85117 + 11.8666i) q^{44} +(-7.73055 + 13.3897i) q^{46} +(-1.67752 + 9.51368i) q^{47} +(-3.20574 - 1.16679i) q^{49} +(-2.10220 - 11.9221i) q^{50} +(-7.38326 - 6.19529i) q^{52} +4.95811 q^{53} -1.45336 q^{55} +(-15.0929 - 12.6644i) q^{56} +(2.89053 + 16.3930i) q^{58} +(8.01754 + 2.91815i) q^{59} +(-0.220285 + 1.24930i) q^{61} +(7.88326 - 13.6542i) q^{62} +(0.819078 + 1.41868i) q^{64} +(0.960637 - 0.349643i) q^{65} +(7.66637 - 6.43285i) q^{67} +(10.1382 - 8.50692i) q^{68} +(3.59240 - 1.30753i) q^{70} +(-5.91534 - 10.2457i) q^{71} +(4.11721 - 7.13122i) q^{73} +(1.58125 - 8.96773i) q^{74} +(-0.173648 - 0.0632028i) q^{76} +(1.74035 + 9.87003i) q^{77} +(8.46451 + 7.10257i) q^{79} +3.10607 q^{80} +19.5030 q^{82} +(-1.15657 - 0.970481i) q^{83} +(0.243756 + 1.38241i) q^{85} +(1.40033 + 0.509678i) q^{86} +(-3.29339 + 18.6777i) q^{88} +(7.93629 - 13.7461i) q^{89} +(-3.52481 - 6.10516i) q^{91} +(-25.3123 + 9.21291i) q^{92} +(-18.7383 + 15.7233i) q^{94} +(0.0150147 - 0.0125989i) q^{95} +(-17.5214 + 6.37727i) q^{97} +(-4.31908 - 7.48086i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31}+ \cdots - 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8 + 15 * q^11 - 9 * q^13 - 15 * q^14 - 18 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 + 27 * q^22 + 12 * q^23 - 27 * q^25 - 24 * q^26 - 24 * q^28 - 3 * q^29 - 9 * q^31 - 9 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 - 15 * q^38 - 18 * q^40 + 21 * q^41 - 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 - 9 * q^49 - 12 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 21 * q^56 + 3 * q^59 - 27 * q^61 + 12 * q^62 - 12 * q^64 - 3 * q^65 + 27 * q^67 + 27 * q^68 + 18 * q^70 + 9 * q^71 - 6 * q^73 + 12 * q^74 - 24 * q^77 + 18 * q^79 - 6 * q^80 + 36 * q^82 + 15 * q^83 + 9 * q^85 - 6 * q^86 + 27 * q^88 + 6 * q^91 - 51 * q^92 - 27 * q^94 - 30 * q^95 - 36 * q^97 - 9 * q^98

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