LMFDB - Embedded newform 729.2.e.a.325.1

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:	$1$
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			325.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.a.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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	−0.399354	+	0.916797i	$0.630766\pi$
$2$	−1.93969	+	1.62760i	−1.37157	+	1.15088i	−0.972216	+	0.234087i	$0.924790\pi$
$3$		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	$-0.577746\pi$
$5$	0.439693	−	0.160035i	0.196637	−	0.0715698i	0.438461	+	0.898750i	$0.355524\pi$
$6$		0			0
$7$	−0.560307	−	3.17766i	−0.211776	−	1.20104i	−0.886414	−	0.462894i	$-0.846811\pi$
$7$	−0.560307	−	3.17766i	−0.211776	−	1.20104i	0.674637	−	0.738149i	$-0.264300\pi$
$8$	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	$-0.544007\pi$
$11$	−2.91875	−	1.06234i	−0.880036	−	0.320307i	−0.742224	+	0.670152i	$0.766229\pi$
$12$		0			0
$13$	−1.67365	−	1.40436i	−0.464186	−	0.389499i	0.380482	−	0.924788i	$-0.375758\pi$
$13$	−1.67365	−	1.40436i	−0.464186	−	0.389499i	−0.844669	+	0.535290i	$0.820202\pi$
$14$	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	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	−0.0209445	−	0.0362770i	−0.00480501	−	0.00832251i	0.863613	−	0.504155i	$-0.168196\pi$
$19$	−0.0209445	−	0.0362770i	−0.00480501	−	0.00832251i	−0.868418	+	0.495833i	$0.834863\pi$
$20$	−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	0.648932	+	0.760846i	$0.275216\pi$
$23$	−1.06031	+	6.01330i	−0.221089	+	1.25386i	−0.870021	+	0.493014i	$0.835895\pi$
$24$		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	$-0.931205\pi$
$29$	−5.03596	+	4.22567i	−0.935154	+	0.784688i	0.0415813	+	0.999135i	$0.486760\pi$
$30$		0			0
$31$	−1.08125	+	6.13208i	−0.194199	+	1.10135i	0.719357	+	0.694641i	$0.244437\pi$
$31$	−1.08125	+	6.13208i	−0.194199	+	1.10135i	−0.913555	+	0.406714i	$0.866674\pi$
$32$	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	−0.975127	−	0.221647i	$-0.928857\pi$
$37$	−1.79813	+	3.11446i	−0.295611	+	0.512014i	0.679516	+	0.733661i	$0.262190\pi$
$38$	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	$-0.483188\pi$
$41$	−5.90033	−	4.95096i	−0.921477	−	0.773211i	−0.974268	+	0.225395i	$0.927633\pi$
$42$		0			0
$43$	0.553033	+	0.201288i	0.0843368	+	0.0306961i	0.383844	−	0.923398i	$-0.374600\pi$
$43$	0.553033	+	0.201288i	0.0843368	+	0.0306961i	−0.299507	+	0.954094i	$0.596822\pi$
$44$	−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	0.821209	+	0.570628i	$0.193300\pi$
$47$	1.67752	+	9.51368i	0.244691	+	1.38771i	−0.576517	+	0.817085i	$0.695589\pi$
$48$		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	$-0.610605\pi$
$53$	−4.95811			−0.681049			−0.340524	+	0.940236i	$0.610605\pi$
$54$		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	$-0.798543\pi$
$59$	−8.01754	+	2.91815i	−1.04379	+	0.379910i	−0.237477	+	0.971393i	$0.576321\pi$
$60$		0			0
$61$	−0.220285	−	1.24930i	−0.0282046	−	0.159956i	0.967452	−	0.253053i	$-0.0814346\pi$
$61$	−0.220285	−	1.24930i	−0.0282046	−	0.159956i	−0.995657	+	0.0930965i	$0.970324\pi$
$62$	−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	0.976990	−	0.213286i	$-0.0684166\pi$
$67$	7.66637	+	6.43285i	0.936597	+	0.785898i	−0.0403931	+	0.999184i	$0.512861\pi$
$68$	−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	−0.265733	−	0.964047i	$-0.585614\pi$
$71$	5.91534	−	10.2457i	0.702022	−	1.21594i	0.967755	−	0.251892i	$-0.0810526\pi$
$72$		0			0
$73$	4.11721	+	7.13122i	0.481883	+	0.834646i	0.999784	−	0.0207947i	$-0.00661964\pi$
$73$	4.11721	+	7.13122i	0.481883	+	0.834646i	−0.517901	+	0.855441i	$0.673286\pi$
$74$	−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	−0.0273571	−	0.999626i	$-0.508709\pi$
$79$	8.46451	−	7.10257i	0.952332	−	0.799101i	0.979689	+	0.200525i	$0.0642647\pi$
$80$	−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	$-0.695816\pi$
$83$	1.15657	−	0.970481i	0.126950	−	0.106524i	0.704052	+	0.710148i	$0.251372\pi$
$84$		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	−0.888843	−	0.458212i	$-0.848490\pi$
$89$	−7.93629	−	13.7461i	−0.841245	−	1.45708i	0.0475978	−	0.998867i	$-0.484843\pi$
$90$		0			0
$91$	−3.52481	+	6.10516i	−0.369501	+	0.639995i
$92$	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	−0.999784	−	0.0207958i	$-0.993380\pi$
$97$	−17.5214	−	6.37727i	−1.77903	−	0.647514i	−0.779246	−	0.626718i	$-0.784398\pi$
$98$	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	−0.956933	−	0.290309i	$-0.906242\pi$
$101$	−1.57785	−	8.94842i	−0.157002	−	0.890401i	0.799931	−	0.600092i	$-0.204869\pi$
$102$		0			0
$103$	−0.245100	+	0.0892091i	−0.0241504	+	0.00879003i	−0.354067	−	0.935220i	$-0.615202\pi$
$103$	−0.245100	+	0.0892091i	−0.0241504	+	0.00879003i	0.329917	+	0.944010i	$0.392979\pi$
$104$	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	$-0.562591\pi$
$107$	−4.04189			−0.390744			−0.195372	+	0.980729i	$0.562591\pi$
$108$		0			0
$109$	−5.40373			−0.517584			−0.258792	−	0.965933i	$-0.583324\pi$
$109$	−5.40373			−0.517584			−0.258792	+	0.965933i	$0.583324\pi$
$110$	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	$-0.590373\pi$
$113$	1.30066	−	0.473401i	0.122356	−	0.0445339i	0.402472	+	0.915432i	$0.368151\pi$
$114$		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	0.974873	−	0.222760i	$-0.0715067\pi$
$127$	3.31908	+	5.74881i	0.294521	+	0.510125i	−0.680353	+	0.732885i	$0.738173\pi$
$128$	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	−0.725142	−	0.688599i	$-0.758226\pi$
$131$	2.19506	−	12.4488i	0.191783	−	1.08766i	0.916926	−	0.399058i	$-0.130663\pi$
$132$		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	$-0.872043\pi$
$137$	−8.13223	+	6.82375i	−0.694783	+	0.582992i	0.225501	+	0.974243i	$0.427598\pi$
$138$		0			0
$139$	−1.29561	+	7.34775i	−0.109892	+	0.623228i	0.879261	+	0.476340i	$0.158037\pi$
$139$	−1.29561	+	7.34775i	−0.109892	+	0.623228i	−0.989153	+	0.146888i	$0.953074\pi$
$140$	−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	$-0.222027\pi$
$149$	3.25877	+	2.73443i	0.266969	+	0.224013i	−0.499469	+	0.866332i	$0.666472\pi$
$150$		0			0
$151$	−0.127011	−	0.0462284i	−0.0103360	−	0.00376201i	0.336847	−	0.941559i	$-0.390640\pi$
$151$	−0.127011	−	0.0462284i	−0.0103360	−	0.00376201i	−0.347183	+	0.937797i	$0.612862\pi$
$152$	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	−0.789348	−	0.613946i	$-0.789581\pi$
$157$	−12.5223	+	4.55774i	−0.999387	+	0.363747i	−0.210039	+	0.977693i	$0.567359\pi$
$158$	−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	$-0.655269\pi$
$167$	−3.35844	+	1.22237i	−0.259884	+	0.0945900i	0.208792	+	0.977960i	$0.433047\pi$
$168$		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	$-0.136045\pi$
$173$	17.6348	+	6.41852i	1.34075	+	0.487991i	0.430698	+	0.902496i	$0.358267\pi$
$174$		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	$-0.894179\pi$
$179$	−2.54189	+	4.40268i	−0.189990	+	0.329072i	0.755257	+	0.655429i	$0.227512\pi$
$180$		0			0
$181$	−3.57532	−	6.19264i	−0.265752	−	0.460295i	0.702009	−	0.712168i	$-0.252287\pi$
$181$	−3.57532	−	6.19264i	−0.265752	−	0.460295i	−0.967760	+	0.251873i	$0.918953\pi$
$182$	−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	$-0.598067\pi$
$191$	8.05097	−	6.75557i	0.582548	−	0.488816i	0.885783	+	0.464100i	$0.153622\pi$
$192$		0			0
$193$	−1.76130	+	9.98881i	−0.126781	+	0.719010i	0.853453	+	0.521169i	$0.174504\pi$
$193$	−1.76130	+	9.98881i	−0.126781	+	0.719010i	−0.980234	+	0.197841i	$0.936607\pi$
$194$	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	0.999998	+	0.00198008i	$0.000630281\pi$
$197$	7.04189	+	12.1969i	0.501714	+	0.868994i	−0.498284	+	0.867014i	$0.666036\pi$
$198$		0			0
$199$	−5.13816	+	8.89955i	−0.364234	+	0.630872i	−0.988653	−	0.150218i	$-0.952003\pi$
$199$	−5.13816	+	8.89955i	−0.364234	+	0.630872i	0.624419	+	0.781090i	$0.285336\pi$
$200$	−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	−0.100480	−	0.994939i	$-0.532038\pi$
$211$	6.71213	−	2.44302i	0.462082	−	0.168184i	0.562562	+	0.826755i	$0.309816\pi$
$212$	−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	−0.984052	−	0.177880i	$-0.943076\pi$
$223$	−1.79473	−	10.1784i	−0.120184	−	0.681597i	0.863868	−	0.503718i	$-0.168035\pi$
$224$	−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	$-0.531137\pi$
$227$	−12.2369	−	4.45389i	−0.812195	−	0.295615i	−0.714530	+	0.699605i	$0.753359\pi$
$228$		0			0
$229$	−21.5253	−	18.0619i	−1.42243	−	1.19356i	−0.950023	−	0.312181i	$-0.898940\pi$
$229$	−21.5253	−	18.0619i	−1.42243	−	1.19356i	−0.472408	−	0.881380i	$-0.656615\pi$
$230$	−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	$-0.983974\pi$
$233$	−6.95723	+	12.0503i	−0.455784	+	0.789440i	0.542949	+	0.839765i	$0.317308\pi$
$234$		0			0
$235$	2.26011	+	3.91463i	0.147434	+	0.255363i
$236$	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	−0.776455	−	0.630172i	$-0.782984\pi$
$239$	2.60813	−	14.7914i	0.168706	−	0.956777i	0.945161	−	0.326605i	$-0.105905\pi$
$240$		0			0
$241$	−9.93835	+	8.33926i	−0.640185	+	0.537179i	−0.904075	−	0.427374i	$-0.859439\pi$
$241$	−9.93835	+	8.33926i	−0.640185	+	0.537179i	0.263890	+	0.964553i	$0.414994\pi$
$242$	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	$-0.157900\pi$
$251$	0.436289	+	0.755675i	0.0275383	+	0.0476978i	−0.851928	+	0.523659i	$0.824567\pi$
$252$		0			0
$253$	9.48293	−	16.4249i	0.596186	−	1.03263i
$254$	−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	$-0.323370\pi$
$257$	−3.50593	−	2.94182i	−0.218694	−	0.183506i	−0.745552	+	0.666447i	$0.767814\pi$
$258$		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	$-0.0978569\pi$
$263$	−0.746282	−	4.23238i	−0.0460177	−	0.260979i	−0.999133	+	0.0416273i	$0.986746\pi$
$264$		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	$-0.620525\pi$
$269$	−12.1257			−0.739315			−0.369657	+	0.929168i	$0.620525\pi$
$270$		0			0
$271$	−0.319955			−0.0194359			−0.00971795	−	0.999953i	$-0.503093\pi$
$271$	−0.319955			−0.0194359			−0.00971795	+	0.999953i	$0.503093\pi$
$272$	−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	−0.723158	−	0.690683i	$-0.757310\pi$
$277$	−4.65745	−	26.4137i	−0.279839	−	1.58705i	0.443319	−	0.896364i	$-0.353801\pi$
$278$	−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	$-0.0959254\pi$
$281$	25.0719	+	9.12543i	1.49567	+	0.544378i	0.540731	+	0.841195i	$0.318148\pi$
$282$		0			0
$283$	−7.11927	−	5.97378i	−0.423197	−	0.355104i	0.406181	−	0.913793i	$-0.366860\pi$
$283$	−7.11927	−	5.97378i	−0.423197	−	0.355104i	−0.829378	+	0.558689i	$0.811305\pi$
$284$	−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	−0.707031	−	0.707182i	$-0.749966\pi$
$293$	3.41029	−	19.3407i	0.199231	−	1.12990i	0.906263	−	0.422715i	$-0.138923\pi$
$294$		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	0.104870	+	0.994486i	$0.466557\pi$
$307$	−14.1716	+	24.5459i	−0.808815	+	1.40091i	−0.913685	+	0.406423i	$0.866776\pi$
$308$	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	$-0.259315\pi$
$311$	1.56624	+	1.31423i	0.0888132	+	0.0745231i	−0.597300	+	0.802018i	$0.703760\pi$
$312$		0			0
$313$	−7.90420	−	2.87689i	−0.446772	−	0.162612i	0.108830	−	0.994060i	$-0.465290\pi$
$313$	−7.90420	−	2.87689i	−0.446772	−	0.162612i	−0.555601	+	0.831449i	$0.687512\pi$
$314$	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	−0.630038	−	0.776564i	$-0.716961\pi$
$317$	−5.40538	−	30.6554i	−0.303597	−	1.72178i	0.326442	−	0.945217i	$-0.394150\pi$
$318$		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	0.662379	+	0.749169i	$0.269547\pi$
$331$	5.38847	+	30.5595i	0.296177	+	1.67970i	−0.366202	+	0.930535i	$0.619342\pi$
$332$	−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	0.985599	−	0.169098i	$-0.0540854\pi$
$337$	18.1780	+	15.2531i	0.990218	+	0.830892i	0.00461869	+	0.999989i	$0.498530\pi$
$338$	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	$-0.928988\pi$
$347$	0.314025	−	1.78093i	0.0168578	−	0.0956052i	0.992076	+	0.125641i	$0.0400987\pi$
$348$		0			0
$349$	11.6905	−	9.80947i	0.625777	−	0.525089i	−0.273837	−	0.961776i	$-0.588293\pi$
$349$	11.6905	−	9.80947i	0.625777	−	0.525089i	0.899613	+	0.436687i	$0.143848\pi$
$350$	−39.0624			−2.08797
$351$		0			0
$352$	−14.2763			−0.760930
$353$	24.8063	−	20.8150i	1.32031	−	1.10787i	0.334069	−	0.942549i	$-0.391578\pi$
$353$	24.8063	−	20.8150i	1.32031	−	1.10787i	0.986240	−	0.165321i	$-0.0528662\pi$
$354$		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	$-0.182755\pi$
$359$	−0.957234	−	1.65798i	−0.0505209	−	0.0875047i	−0.890180	+	0.455609i	$0.849421\pi$
$360$		0			0
$361$	9.49912	−	16.4530i	0.499954	−	0.865945i
$362$	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	0.902741	−	0.430185i	$-0.141552\pi$
$367$	25.2447	+	9.18832i	1.31776	+	0.479626i	0.415022	+	0.909812i	$0.363774\pi$
$368$	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	−0.676798	−	0.736169i	$-0.736633\pi$
$373$	−13.9452	+	5.07564i	−0.722056	+	0.262807i	−0.0452575	+	0.998975i	$0.514411\pi$
$374$	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	$-0.687297\pi$
$383$	−8.71941	+	3.17360i	−0.445541	+	0.162164i	0.109500	+	0.993987i	$0.465075\pi$
$384$		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	$-0.521643\pi$
$389$	−15.0150	−	5.46502i	−0.761291	−	0.277087i	−0.693349	+	0.720602i	$0.743866\pi$
$390$		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	0.505496	−	0.862829i	$-0.331309\pi$
$397$	−9.85251	−	17.0650i	−0.494483	−	0.856470i	−0.999980	+	0.00635841i	$0.997976\pi$
$398$	−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	$-0.953569\pi$
$401$	−0.199340	+	1.13052i	−0.00995459	+	0.0564553i	0.979426	+	0.201804i	$0.0646806\pi$
$402$		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	−0.995222	−	0.0976342i	$-0.968872\pi$
$409$	−0.538485	+	3.05390i	−0.0266264	+	0.151006i	0.968596	+	0.248640i	$0.0799836\pi$
$410$	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	−0.984850	−	0.173410i	$-0.944521\pi$
$419$	−27.1557	−	22.7863i	−1.32664	−	1.11319i	−0.341793	−	0.939775i	$-0.611034\pi$
$420$		0			0
$421$	−8.66132	−	3.15246i	−0.422127	−	0.153642i	0.122218	−	0.992503i	$-0.460999\pi$
$421$	−8.66132	−	3.15246i	−0.422127	−	0.153642i	−0.544345	+	0.838862i	$0.683222\pi$
$422$	−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	$-0.589963\pi$
$431$	−11.5794			−0.557758			−0.278879	+	0.960326i	$0.589963\pi$
$432$		0			0
$433$	6.06511			0.291471			0.145735	−	0.989324i	$-0.453445\pi$
$433$	6.06511			0.291471			0.145735	+	0.989324i	$0.453445\pi$
$434$	−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	0.830948	+	0.556350i	$0.187798\pi$
$439$	5.03684	+	28.5653i	0.240395	+	1.36335i	−0.590553	+	0.806999i	$0.701090\pi$
$440$	−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	$-0.126603\pi$
$443$	29.0292	+	10.5657i	1.37922	+	0.501994i	0.457276	+	0.889325i	$0.348825\pi$
$444$		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	−0.126190	+	0.992006i	$0.540275\pi$
$449$	−19.5410	+	33.8460i	−0.922197	+	1.59729i	−0.796008	+	0.605287i	$0.793059\pi$
$450$		0			0
$451$	11.9620	+	20.7188i	0.563268	+	0.975608i
$452$	−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	−0.669350	−	0.742947i	$-0.733427\pi$
$457$	−1.15270	+	0.967233i	−0.0539212	+	0.0452453i	0.615429	+	0.788192i	$0.288983\pi$
$458$	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	$-0.931451\pi$
$461$	−20.0988	+	16.8649i	−0.936094	+	0.785476i	0.0408072	+	0.999167i	$0.487007\pi$
$462$		0			0
$463$	1.17324	−	6.65376i	0.0545250	−	0.309227i	−0.945333	−	0.326108i	$-0.894263\pi$
$463$	1.17324	−	6.65376i	0.0545250	−	0.309227i	0.999857	+	0.0168815i	$0.00537380\pi$
$464$	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	0.931470	+	0.363818i	$0.118527\pi$
$467$	16.8735	+	29.2257i	0.780810	+	1.35240i	−0.150660	+	0.988586i	$0.548140\pi$
$468$		0			0
$469$	16.1459	−	27.9655i	0.745548	−	1.29133i
$470$	−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	−0.996600	−	0.0823875i	$-0.973745\pi$
$479$	−1.93211	−	10.9576i	−0.0882805	−	0.500664i	0.908320	−	0.418276i	$-0.137366\pi$
$480$		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	$-0.442933\pi$
$491$	20.9932	−	7.64090i	0.947410	−	0.344829i	0.769088	+	0.639143i	$0.220711\pi$
$492$		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	0.445548	−	0.895258i	$-0.353009\pi$
$499$	−8.01367	−	6.72427i	−0.358741	−	0.301020i	−0.804289	+	0.594239i	$0.797453\pi$
$500$	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	−0.439359	−	0.898312i	$-0.644794\pi$
$503$	12.5209	−	21.6869i	0.558281	−	0.966972i	0.997640	−	0.0686600i	$-0.0218723\pi$
$504$		0			0
$505$	−2.12583	−	3.68204i	−0.0945982	−	0.163849i
$506$	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	0.832950	+	0.553348i	$0.186650\pi$
$509$	−3.13651	+	17.7880i	−0.139023	+	0.788440i	−0.971973	+	0.235092i	$0.924461\pi$
$510$		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	−0.996703	−	0.0811425i	$-0.974143\pi$
$521$	−12.9791	−	22.4804i	−0.568623	−	0.984883i	0.428080	−	0.903741i	$-0.359190\pi$
$522$		0			0
$523$	−12.7973	+	22.1655i	−0.559585	+	0.969230i	0.437946	+	0.899001i	$0.355706\pi$
$523$	−12.7973	+	22.1655i	−0.559585	+	0.969230i	−0.997531	+	0.0702283i	$0.977627\pi$
$524$	−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	0.954985	−	0.296653i	$-0.0958703\pi$
$547$	−1.02600	−	5.81872i	−0.0438685	−	0.248790i	−0.998854	+	0.0478621i	$0.984759\pi$
$548$	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	−0.431214	−	0.902250i	$-0.641915\pi$
$557$	13.3525	−	23.1272i	0.565764	−	0.979932i	0.996978	−	0.0776824i	$-0.0247520\pi$
$558$		0			0
$559$	−0.642903	−	1.11354i	−0.0271919	−	0.0470978i
$560$	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	0.508176	+	0.861253i	$0.330320\pi$
$563$	−6.26217	+	35.5146i	−0.263919	+	1.49676i	−0.772095	+	0.635507i	$0.780791\pi$
$564$		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	$-0.661490\pi$
$569$	6.93061	−	5.81547i	0.290546	−	0.243797i	0.776396	+	0.630245i	$0.217046\pi$
$570$		0			0
$571$	5.30999	−	30.1145i	0.222216	−	1.26025i	−0.645719	−	0.763575i	$-0.723442\pi$
$571$	5.30999	−	30.1145i	0.222216	−	1.26025i	0.867936	−	0.496676i	$-0.165446\pi$
$572$	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	−0.476146	−	0.879367i	$-0.657966\pi$
$577$	12.5744	−	21.7796i	0.523481	−	0.906696i	0.999626	−	0.0273292i	$-0.00870022\pi$
$578$	−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	−0.963553	−	0.267516i	$-0.913797\pi$
$587$	−3.62465	−	20.5564i	−0.149605	−	0.848453i	0.813948	−	0.580937i	$-0.197314\pi$
$588$		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	$-0.603933\pi$
$593$	−15.6212			−0.641488			−0.320744	+	0.947166i	$0.603933\pi$
$594$		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	$-0.614026\pi$
$599$	−0.421274	+	0.153331i	−0.0172128	+	0.00626495i	0.333399	+	0.942786i	$0.391804\pi$
$600$		0			0
$601$	−3.06876	−	17.4038i	−0.125177	−	0.709917i	−0.981202	−	0.192982i	$-0.938184\pi$
$601$	−3.06876	−	17.4038i	−0.125177	−	0.709917i	0.856025	−	0.516935i	$-0.172927\pi$
$602$	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	0.951697	−	0.307038i	$-0.0993377\pi$
$607$	20.0692	+	16.8401i	0.814585	+	0.683518i	−0.137112	+	0.990555i	$0.543782\pi$
$608$	−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	0.680811	−	0.732459i	$-0.261628\pi$
$613$	−7.27719	−	12.6045i	−0.293923	−	0.509089i	−0.974734	+	0.223370i	$0.928294\pi$
$614$	−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	0.895767	+	0.444524i	$0.146627\pi$
$617$	−2.43464	+	13.8075i	−0.0980149	+	0.555870i	−0.993782	+	0.111346i	$0.964484\pi$
$618$		0			0
$619$	−24.2931	+	20.3844i	−0.976424	+	0.819317i	−0.983546	−	0.180658i	$-0.942177\pi$
$619$	−24.2931	+	20.3844i	−0.976424	+	0.819317i	0.00712236	+	0.999975i	$0.497733\pi$
$620$	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	−0.170892	−	0.985290i	$-0.554665\pi$
$631$	19.2879	−	33.4077i	0.767840	−	1.32994i	0.938732	−	0.344648i	$-0.112002\pi$
$632$	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	0.889390	+	0.457150i	$0.151130\pi$
$641$	5.31655	+	30.1517i	0.209991	+	1.19092i	−0.679399	+	0.733769i	$0.737759\pi$
$642$		0			0
$643$	32.1609	−	11.7056i	1.26830	−	0.461624i	0.381756	−	0.924263i	$-0.375320\pi$
$643$	32.1609	−	11.7056i	1.26830	−	0.461624i	0.886547	+	0.462639i	$0.153097\pi$
$644$	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	$-0.418571\pi$
$647$	12.8726			0.506073			0.253037	+	0.967457i	$0.418571\pi$
$648$		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	$-0.682199\pi$
$653$	−10.6365	+	3.87137i	−0.416239	+	0.151498i	0.125407	+	0.992105i	$0.459976\pi$
$654$		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	$-0.475313\pi$
$659$	−12.9388	−	4.70934i	−0.504025	−	0.183450i	−0.581503	+	0.813544i	$0.697535\pi$
$660$		0			0
$661$	−15.5253	−	13.0273i	−0.603863	−	0.506702i	0.288821	−	0.957383i	$-0.406737\pi$
$661$	−15.5253	−	13.0273i	−0.603863	−	0.506702i	−0.892685	+	0.450681i	$0.851181\pi$
$662$	−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	−0.970572	−	0.240813i	$-0.922586\pi$
$673$	−23.3987	+	19.6339i	−0.901955	+	0.756830i	0.0686165	+	0.997643i	$0.478142\pi$
$674$	−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	$-0.699453\pi$
$677$	2.84911	−	2.39068i	0.109500	−	0.0918815i	0.695894	+	0.718145i	$0.255008\pi$
$678$		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	$-0.303256\pi$
$683$	−10.8735	−	18.8334i	−0.416061	−	0.720639i	−0.995539	+	0.0943487i	$0.969923\pi$
$684$		0			0
$685$	−2.48364	+	4.30179i	−0.0948950	+	0.164363i
$686$	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	0.911046	−	0.412304i	$-0.135276\pi$
$691$	35.3276	+	12.8582i	1.34392	+	0.489149i	0.432878	+	0.901452i	$0.357498\pi$
$692$	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	$-0.645262\pi$
$701$	−23.3351			−0.881355			−0.440678	+	0.897665i	$0.645262\pi$
$702$		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	0.998716	−	0.0506545i	$-0.0161307\pi$
$709$	1.14244	+	6.47908i	0.0429051	+	0.243327i	−0.955811	+	0.293981i	$0.905020\pi$
$710$	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	$-0.934960\pi$
$719$	−8.41622	+	14.5773i	−0.313872	+	0.543642i	0.665325	+	0.746554i	$0.268293\pi$
$720$		0			0
$721$	0.420807	+	0.728860i	0.0156717	+	0.0271442i
$722$	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	−0.202860	−	0.979208i	$-0.565023\pi$
$727$	19.5817	−	16.4310i	0.726246	−	0.609393i	0.929105	+	0.369815i	$0.120579\pi$
$728$	−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	0.899862	+	0.436174i	$0.143667\pi$
$733$	−2.56964	+	14.5732i	−0.0949118	+	0.538272i	−0.994774	+	0.102098i	$0.967444\pi$
$734$	−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	−0.938084	−	0.346408i	$-0.887401\pi$
$739$	−4.59539	+	7.95945i	−0.169044	+	0.292793i	0.769040	+	0.639201i	$0.220735\pi$
$740$	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	−0.996749	−	0.0805681i	$-0.974327\pi$
$743$	−34.0501	−	28.5714i	−1.24918	−	1.04818i	−0.252428	−	0.967616i	$-0.581229\pi$
$744$		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	0.354946	−	0.934887i	$-0.384499\pi$
$751$	33.6467	−	12.2464i	1.22778	−	0.446877i	0.872838	+	0.488010i	$0.162277\pi$
$752$	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	$-0.846607\pi$
$761$	−34.9521	+	12.7215i	−1.26701	+	0.461155i	−0.380896	+	0.924618i	$0.624384\pi$
$762$		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	−0.0649348	−	0.997890i	$-0.520684\pi$
$769$	−29.3653	−	24.6404i	−1.05894	−	0.888556i	−0.994005	+	0.109333i	$0.965128\pi$
$770$	−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	0.204680	−	0.978829i	$-0.434385\pi$
$773$	26.4136	−	45.7497i	0.950031	−	1.64550i	0.745351	−	0.666673i	$-0.232282\pi$
$774$		0			0
$775$	−14.8851	−	25.7817i	−0.534687	−	0.926106i
$776$	−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
$781$	−28.1498	+	23.6205i	−1.00728	+	0.845206i
$782$	−46.3833			−1.65866
$783$		0			0
$784$	22.6459			0.808782
$785$	−4.77656	+	4.00801i	−0.170483	+	0.143052i
$786$		0			0
$787$	7.85591	−	44.5531i	0.280033	−	1.58815i	−0.442473	−	0.896782i	$-0.645899\pi$
$787$	7.85591	−	44.5531i	0.280033	−	1.58815i	0.722506	−	0.691365i	$-0.242990\pi$
$788$	58.3833	−	21.2498i	2.07982	−	0.756992i
$789$		0			0
$790$	2.27332	+	12.8926i	0.0808810	+	0.458699i
$791$	−2.23308	−	3.86780i	−0.0793991	−	0.137523i
$792$		0			0
$793$	−1.38578	+	2.40024i	−0.0492106	+	0.0852352i
$794$	46.8858	+	17.0650i	1.66392	+	0.605616i
$795$		0			0
$796$	34.7276	+	29.1399i	1.23089	+	1.03284i
$797$	12.9606	+	10.8753i	0.459089	+	0.385222i	0.842796	−	0.538233i	$-0.180908\pi$
$797$	12.9606	+	10.8753i	0.459089	+	0.385222i	−0.383706	+	0.923455i	$0.625353\pi$
$798$		0			0
$799$	27.2335	+	9.91220i	0.963454	+	0.350668i
$800$	−10.9875	+	19.0309i	−0.388467	+	0.672845i
$801$		0			0
$802$	−1.45336	−	2.51730i	−0.0513200	−	0.0888889i
$803$	−4.44134	−	25.1881i	−0.156732	−	0.888869i
$804$		0			0
$805$	8.66297	−	3.15306i	0.305330	−	0.111131i
$806$	−5.98158	+	33.9232i	−0.210692	+	1.19490i
$807$		0			0
$808$	42.5021	−	35.6635i	1.49522	−	1.25464i
$809$	34.9145			1.22753			0.613764	−	0.789490i	$-0.289655\pi$
$809$	34.9145			1.22753			0.613764	+	0.789490i	$0.289655\pi$
$810$		0			0
$811$	18.0419			0.633536			0.316768	−	0.948503i	$-0.397402\pi$
$811$	18.0419			0.633536			0.316768	+	0.948503i	$0.397402\pi$
$812$	71.6840	−	60.1500i	2.51561	−	2.11085i
$813$		0			0
$814$	−4.91147	+	27.8544i	−0.172147	+	0.976295i
$815$	−4.29308	+	1.56255i	−0.150380	+	0.0547339i
$816$		0			0
$817$	−0.00428091	−	0.0242783i	−0.000149770	−	0.000849389i
$818$	−3.92602	−	6.80007i	−0.137270	−	0.237759i
$819$		0			0
$820$	−7.94949	+	13.7689i	−0.277608	+	0.480832i
$821$	38.1883	+	13.8994i	1.33278	+	0.485092i	0.907531	−	0.419985i	$-0.137965\pi$
$821$	38.1883	+	13.8994i	1.33278	+	0.485092i	0.425248	+	0.905077i	$0.360187\pi$
$822$		0			0
$823$	19.9552	+	16.7444i	0.695594	+	0.583672i	0.920516	−	0.390704i	$-0.127768\pi$
$823$	19.9552	+	16.7444i	0.695594	+	0.583672i	−0.224923	+	0.974377i	$0.572213\pi$
$824$	−1.22004	−	1.02373i	−0.0425020	−	0.0356634i
$825$		0			0
$826$	−65.5053	−	23.8420i	−2.27922	−	0.829568i
$827$	−18.8097	+	32.5794i	−0.654079	+	1.13290i	0.328045	+	0.944662i	$0.393610\pi$
$827$	−18.8097	+	32.5794i	−0.654079	+	1.13290i	−0.982124	+	0.188236i	$0.939723\pi$
$828$		0			0
$829$	17.5107	+	30.3295i	0.608173	+	1.05339i	0.991541	+	0.129791i	$0.0414306\pi$
$829$	17.5107	+	30.3295i	0.608173	+	1.05339i	−0.383368	+	0.923595i	$0.625236\pi$
$830$	0.310622	+	1.76162i	0.0107818	+	0.0611469i
$831$		0			0
$832$	−3.36319	+	1.22410i	−0.116598	+	0.0424380i
$833$	−1.77719	+	10.0789i	−0.0615759	+	0.349215i
$834$		0			0
$835$	−1.28106	+	1.07494i	−0.0443329	+	0.0371997i
$836$	0.573978			0.0198514
$837$		0			0
$838$	89.7606			3.10073
$839$	−20.3876	+	17.1072i	−0.703858	+	0.590607i	−0.922868	−	0.385116i	$-0.874162\pi$
$839$	−20.3876	+	17.1072i	−0.703858	+	0.590607i	0.219010	+	0.975723i	$0.429717\pi$
$840$		0			0
$841$	2.46879	−	14.0012i	0.0851306	−	0.482800i
$842$	21.9312	−	7.98232i	0.755800	−	0.275089i
$843$		0			0
$844$	−5.47178	−	31.0320i	−0.188346	−	1.06817i
$845$	−1.92468	−	3.33364i	−0.0662109	−	0.114681i
$846$		0			0
$847$	−2.18180	+	3.77899i	−0.0749675	+	0.129848i
$848$	30.9278	+	11.2568i	1.06207	+	0.386560i
$849$		0			0
$850$	−27.8214	−	23.3449i	−0.954265	−	0.800723i
$851$	−16.8216	−	14.1150i	−0.576637	−	0.483856i
$852$		0			0
$853$	−2.30706	−	0.839700i	−0.0789921	−	0.0287508i	0.302222	−	0.953238i	$-0.402272\pi$
$853$	−2.30706	−	0.839700i	−0.0789921	−	0.0287508i	−0.381214	+	0.924487i	$0.624494\pi$
$854$	5.18227	−	8.97595i	0.177334	−	0.307151i
$855$		0			0
$856$	−12.3400	−	21.3735i	−0.421773	−	0.730533i
$857$	1.70692	+	9.68042i	0.0583072	+	0.330677i	0.999983	−	0.00584499i	$-0.00186053\pi$
$857$	1.70692	+	9.68042i	0.0583072	+	0.330677i	−0.941676	+	0.336522i	$0.890749\pi$
$858$		0			0
$859$	−8.28523	+	3.01558i	−0.282689	+	0.102890i	−0.479473	−	0.877557i	$-0.659172\pi$
$859$	−8.28523	+	3.01558i	−0.282689	+	0.102890i	0.196785	+	0.980447i	$0.436950\pi$
$860$	0.210952	−	1.19637i	0.00719339	−	0.0407957i
$861$		0			0
$862$	22.4604	−	18.8465i	0.765004	−	0.641914i
$863$	6.62124			0.225390			0.112695	−	0.993630i	$-0.464052\pi$
$863$	6.62124			0.225390			0.112695	+	0.993630i	$0.464052\pi$
$864$		0			0
$865$	8.78106			0.298565
$866$	−11.7645	+	9.87155i	−0.399772	+	0.335449i
$867$		0			0
$868$	15.3910	−	87.2867i	0.522404	−	2.96270i
$869$	−32.2511	+	11.7384i	−1.09404	+	0.398199i
$870$		0			0
$871$	−3.79679	−	21.5327i	−0.128649	−	0.729606i
$872$	−16.4978	−	28.5750i	−0.558685	−	0.967671i
$873$		0			0
$874$	−0.323826	+	0.560882i	−0.0109536	+	0.0189721i
$875$	13.8769	+	5.05076i	0.469123	+	0.170747i
$876$		0			0
$877$	−3.12243	−	2.62003i	−0.105437	−	0.0884720i	0.588545	−	0.808464i	$-0.299701\pi$
$877$	−3.12243	−	2.62003i	−0.105437	−	0.0884720i	−0.693982	+	0.719992i	$0.744145\pi$
$878$	−56.2627	−	47.2100i	−1.89877	−	1.59326i
$879$		0			0
$880$	9.06583	+	3.29969i	0.305609	+	0.111233i
$881$	4.62567	−	8.01189i	0.155843	−	0.269927i	−0.777523	−	0.628855i	$-0.783524\pi$
$881$	4.62567	−	8.01189i	0.155843	−	0.269927i	0.933366	+	0.358927i	$0.116857\pi$
$882$		0			0
$883$	18.8851	+	32.7099i	0.635533	+	1.10078i	0.986402	+	0.164351i	$0.0525530\pi$
$883$	18.8851	+	32.7099i	0.635533	+	1.10078i	−0.350869	+	0.936425i	$0.614114\pi$
$884$	5.02094	+	28.4752i	0.168873	+	0.957724i
$885$		0			0
$886$	−73.5044	+	26.7534i	−2.46943	+	0.898798i
$887$	−3.29561	+	18.6903i	−0.110656	+	0.627559i	0.878154	+	0.478378i	$0.158775\pi$
$887$	−3.29561	+	18.6903i	−0.110656	+	0.627559i	−0.988810	+	0.149182i	$0.952336\pi$
$888$		0			0
$889$	16.4081	−	13.7680i	0.550309	−	0.461764i
$890$	18.8057			0.630369
$891$		0			0
$892$	−45.5945			−1.52662
$893$	0.309993	−	0.260115i	0.0103735	−	0.00870441i
$894$		0			0
$895$	−0.413067	+	2.34262i	−0.0138073	+	0.0783051i
$896$	40.4495	−	14.7224i	1.35132	−	0.491842i
$897$		0			0
$898$	−17.1841	−	97.4557i	−0.573440	−	3.25214i
$899$	−20.4670	−	35.4499i	−0.682614	−	1.18232i
$900$		0			0
$901$	−7.43717	+	12.8816i	−0.247768	+	0.429147i
$902$	−56.9243	−	20.7188i	−1.89537	−	0.689859i
$903$		0			0
$904$	6.47431	+	5.43259i	0.215332	+	0.180685i
$905$	−2.56308	−	2.15068i	−0.0851997	−	0.0714911i
$906$		0			0
$907$	−9.06418	−	3.29909i	−0.300971	−	0.109545i	0.187120	−	0.982337i	$-0.440085\pi$
$907$	−9.06418	−	3.29909i	−0.300971	−	0.109545i	−0.488091	+	0.872792i	$0.662307\pi$
$908$	−28.7237	+	49.7510i	−0.953231	+	1.65104i
$909$		0			0
$910$	−4.17617	−	7.23335i	−0.138439	−	0.239783i
$911$	1.13475	+	6.43550i	0.0375960	+	0.213218i	0.997818	−	0.0660189i	$-0.0210298\pi$
$911$	1.13475	+	6.43550i	0.0375960	+	0.213218i	−0.960222	+	0.279237i	$0.909919\pi$
$912$		0			0
$913$	−4.40673	+	1.60392i	−0.145841	+	0.0530819i
$914$	0.661626	−	3.75227i	0.0218847	−	0.124114i
$915$		0			0
$916$	−94.9582	+	79.6794i	−3.13751	+	2.63268i
$917$	−40.7880			−1.34694
$918$		0			0
$919$	3.89124			0.128360			0.0641802	−	0.997938i	$-0.479557\pi$
$919$	3.89124			0.128360			0.0641802	+	0.997938i	$0.479557\pi$
$920$	−13.3641	+	11.2138i	−0.440602	+	0.369709i
$921$		0			0
$922$	11.5363	−	65.4254i	0.379927	−	2.15467i
$923$	−24.2888	+	8.84040i	−0.799476	+	0.290985i
$924$		0			0
$925$	−2.98570	−	16.9327i	−0.0981692	−	0.556745i
$926$	8.55391	+	14.8158i	0.281099	+	0.486878i
$927$		0			0
$928$	−15.1079	+	26.1676i	−0.495940	+	0.858994i
$929$	−37.4495	−	13.6305i	−1.22868	−	0.447203i	−0.355535	−	0.934663i	$-0.615701\pi$
$929$	−37.4495	−	13.6305i	−1.22868	−	0.447203i	−0.873145	+	0.487460i	$0.837923\pi$
$930$		0			0
$931$	0.109470	+	0.0918566i	0.00358775	+	0.00301048i
$932$	47.0223	+	39.4564i	1.54027	+	1.29244i
$933$		0			0
$934$	−80.2969	−	29.2257i	−2.62739	−	0.956294i
$935$	−2.18004	+	3.77595i	−0.0712951	+	0.123487i
$936$		0			0
$937$	−16.5326	−	28.6352i	−0.540095	−	0.935472i	−0.998898	−	0.0469340i	$-0.985055\pi$
$937$	−16.5326	−	28.6352i	−0.540095	−	0.935472i	0.458803	−	0.888538i	$-0.348278\pi$
$938$	14.1985	+	80.5235i	0.463596	+	2.62919i
$939$		0			0
$940$	18.7383	−	6.82018i	0.611176	−	0.222450i
$941$	9.34343	−	52.9892i	0.304587	−	1.72740i	−0.320855	−	0.947128i	$-0.603970\pi$
$941$	9.34343	−	52.9892i	0.304587	−	1.72740i	0.625442	−	0.780270i	$-0.284919\pi$
$942$		0			0
$943$	36.0278	−	30.2309i	1.17323	−	0.984454i
$944$	56.6373			1.84339
$945$		0			0
$946$	4.62866			0.150491
$947$	−32.3542	+	27.1484i	−1.05137	+	0.882203i	−0.993237	−	0.116106i	$-0.962959\pi$
$947$	−32.3542	+	27.1484i	−1.05137	+	0.882203i	−0.0581321	+	0.998309i	$0.518514\pi$
$948$		0			0
$949$	3.12402	−	17.7172i	0.101410	−	0.575124i
$950$	−0.476529	+	0.173442i	−0.0154607	+	0.00562722i
$951$		0			0
$952$	−10.2638	−	58.2090i	−0.332652	−	1.88657i
$953$	12.2888	+	21.2848i	0.398073	+	0.689483i	0.993488	−	0.113935i	$-0.0363456\pi$
$953$	12.2888	+	21.2848i	0.398073	+	0.689483i	−0.595415	+	0.803418i	$0.703012\pi$
$954$		0			0
$955$	2.45883	−	4.25881i	0.0795657	−	0.137812i
$956$	−62.2627	−	22.6618i	−2.01372	−	0.732934i
$957$		0			0
$958$	21.5822	+	18.1096i	0.697289	+	0.585095i
$959$	26.2401	+	22.0181i	0.847337	+	0.711000i
$960$		0			0
$961$	−7.30288	−	2.65803i	−0.235577	−	0.0857429i
$962$	−9.94743	+	17.2295i	−0.320718	+	0.555500i
$963$		0			0
$964$	28.6163	+	49.5649i	0.921670	+	1.59638i
$965$	0.824130	+	4.67388i	0.0265297	+	0.150457i
$966$		0			0
$967$	−4.20233	+	1.52952i	−0.135138	+	0.0491862i	−0.408704	−	0.912667i	$-0.634019\pi$
$967$	−4.20233	+	1.52952i	−0.135138	+	0.0491862i	0.273566	+	0.961853i	$0.411797\pi$
$968$	1.43391	−	8.13208i	0.0460875	−	0.261375i
$969$		0			0
$970$	16.9231	−	14.2002i	0.543368	−	0.455939i
$971$	4.61949			0.148246			0.0741232	−	0.997249i	$-0.476384\pi$
$971$	4.61949			0.148246			0.0741232	+	0.997249i	$0.476384\pi$
$972$		0			0
$973$	24.0746			0.771796
$974$	9.20755	−	7.72605i	0.295029	−	0.247559i
$975$		0			0
$976$	−1.46229	+	8.29304i	−0.0468066	+	0.265454i
$977$	−10.6004	+	3.85825i	−0.339138	+	0.123436i	−0.505975	−	0.862548i	$-0.668867\pi$
$977$	−10.6004	+	3.85825i	−0.339138	+	0.123436i	0.166836	+	0.985985i	$0.446645\pi$
$978$		0			0
$979$	8.56108	+	48.5523i	0.273613	+	1.55174i
$980$	3.52094	+	6.09845i	0.112472	+	0.194808i
$981$		0			0
$982$	−28.2841	+	48.9894i	−0.902580	+	1.56332i
$983$	−16.0351	−	5.83629i	−0.511440	−	0.186149i	0.0733925	−	0.997303i	$-0.476617\pi$
$983$	−16.0351	−	5.83629i	−0.511440	−	0.186149i	−0.584832	+	0.811154i	$0.698840\pi$
$984$		0			0
$985$	5.04820	+	4.23594i	0.160849	+	0.134968i
$986$	−38.2545	−	32.0993i	−1.21827	−	1.02225i
$987$		0			0
$988$	0.379385	+	0.138085i	0.0120699	+	0.00439307i
$989$	−1.79679	+	3.11213i	−0.0571346	+	0.0989600i
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	4.96972	+	28.1847i	0.157789	+	0.894865i
$993$		0			0
$994$	90.8303	−	33.0595i	2.88096	−	1.04858i
$995$	−0.834970	+	4.73535i	−0.0264703	+	0.150121i
$996$		0			0
$997$	17.1477	−	14.3886i	0.543073	−	0.455693i	−0.329514	−	0.944151i	$-0.606885\pi$
$997$	17.1477	−	14.3886i	0.543073	−	0.455693i	0.872587	+	0.488458i	$0.162440\pi$
$998$	26.4884			0.838477
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.a.325.1		6
3.2	odd	2		729.2.e.i.325.1		6
9.2	odd	6		729.2.e.c.568.1		6
9.4	even	3		729.2.e.g.82.1		6
9.5	odd	6		729.2.e.b.82.1		6
9.7	even	3		729.2.e.h.568.1		6
27.2	odd	18		729.2.e.c.163.1		6
27.4	even	9		243.2.a.e.1.1	✓	3
27.5	odd	18		243.2.c.e.82.1		6
27.7	even	9		729.2.e.g.649.1		6
27.11	odd	18		729.2.e.i.406.1		6
27.13	even	9		243.2.c.f.163.3		6
27.14	odd	18		243.2.c.e.163.1		6
27.16	even	9	inner	729.2.e.a.406.1		6
27.20	odd	18		729.2.e.b.649.1		6
27.22	even	9		243.2.c.f.82.3		6
27.23	odd	18		243.2.a.f.1.3	yes	3
27.25	even	9		729.2.e.h.163.1		6
108.23	even	18		3888.2.a.bk.1.1		3
108.31	odd	18		3888.2.a.bd.1.3		3
135.4	even	18		6075.2.a.bv.1.3		3
135.104	odd	18		6075.2.a.bq.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.1	✓	3	27.4	even	9
243.2.a.f.1.3	yes	3	27.23	odd	18
243.2.c.e.82.1		6	27.5	odd	18
243.2.c.e.163.1		6	27.14	odd	18
243.2.c.f.82.3		6	27.22	even	9
243.2.c.f.163.3		6	27.13	even	9
729.2.e.a.325.1		6	1.1	even	1	trivial
729.2.e.a.406.1		6	27.16	even	9	inner
729.2.e.b.82.1		6	9.5	odd	6
729.2.e.b.649.1		6	27.20	odd	18
729.2.e.c.163.1		6	27.2	odd	18
729.2.e.c.568.1		6	9.2	odd	6
729.2.e.g.82.1		6	9.4	even	3
729.2.e.g.649.1		6	27.7	even	9
729.2.e.h.163.1		6	27.25	even	9
729.2.e.h.568.1		6	9.7	even	3
729.2.e.i.325.1		6	3.2	odd	2
729.2.e.i.406.1		6	27.11	odd	18
3888.2.a.bd.1.3		3	108.31	odd	18
3888.2.a.bk.1.1		3	108.23	even	18
6075.2.a.bq.1.1		3	135.104	odd	18
6075.2.a.bv.1.3		3	135.4	even	18

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)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more