LMFDB - Embedded newform 729.2.g.d.55.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			55.3
Character	$\chi$	$=$	729.55
Dual form			729.2.g.d.676.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415272 + 0.962709i) q^{2} +(0.618125 + 0.655174i) q^{4} +(0.0443725 + 0.761846i) q^{5} +(2.82023 + 0.668406i) q^{7} +(-2.85789 + 1.04019i) q^{8} +O(q^{10})$	\(q+(-0.415272 + 0.962709i) q^{2} +(0.618125 + 0.655174i) q^{4} +(0.0443725 + 0.761846i) q^{5} +(2.82023 + 0.668406i) q^{7} +(-2.85789 + 1.04019i) q^{8} +(-0.751863 - 0.273656i) q^{10} +(1.36690 + 0.899022i) q^{11} +(-4.07018 - 0.475735i) q^{13} +(-1.81464 + 2.43749i) q^{14} +(0.0806579 - 1.38484i) q^{16} +(-4.52563 + 3.79745i) q^{17} +(4.77625 + 4.00775i) q^{19} +(-0.471714 + 0.499987i) q^{20} +(-1.43313 + 0.942586i) q^{22} +(3.75955 - 0.891030i) q^{23} +(4.38775 - 0.512855i) q^{25} +(2.14823 - 3.72084i) q^{26} +(1.30533 + 2.26090i) q^{28} +(-1.97163 - 2.64835i) q^{29} +(-0.166718 + 0.556877i) q^{31} +(-4.13590 - 2.07713i) q^{32} +(-1.77648 - 5.93384i) q^{34} +(-0.384082 + 2.17824i) q^{35} +(-0.349184 - 1.98032i) q^{37} +(-5.84174 + 2.93383i) q^{38} +(-0.919272 - 2.13111i) q^{40} +(-0.581956 - 1.34912i) q^{41} +(-6.99844 + 3.51475i) q^{43} +(0.255897 + 1.45126i) q^{44} +(-0.703435 + 3.98938i) q^{46} +(3.37012 + 11.2570i) q^{47} +(1.25148 + 0.628517i) q^{49} +(-1.32838 + 4.43710i) q^{50} +(-2.20419 - 2.96074i) q^{52} +(-0.600204 - 1.03958i) q^{53} +(-0.624264 + 1.08126i) q^{55} +(-8.75515 + 1.02333i) q^{56} +(3.36835 - 0.798315i) q^{58} +(-5.89398 + 3.87653i) q^{59} +(8.34487 - 8.84504i) q^{61} +(-0.466877 - 0.391757i) q^{62} +(5.84249 - 4.90243i) q^{64} +(0.181833 - 3.12196i) q^{65} +(-1.39975 + 1.88018i) q^{67} +(-5.28540 - 0.617774i) q^{68} +(-1.93751 - 1.27432i) q^{70} +(10.2267 + 3.72222i) q^{71} +(-12.9627 + 4.71802i) q^{73} +(2.05148 + 0.486209i) q^{74} +(0.326545 + 5.60657i) q^{76} +(3.25405 + 3.44909i) q^{77} +(-1.70702 + 3.95732i) q^{79} +1.05862 q^{80} +1.54049 q^{82} +(6.82230 - 15.8159i) q^{83} +(-3.09389 - 3.27933i) q^{85} +(-0.477423 - 8.19704i) q^{86} +(-4.84159 - 1.14748i) q^{88} +(-3.38989 + 1.23382i) q^{89} +(-11.1608 - 4.06221i) q^{91} +(2.90765 + 1.91239i) q^{92} +(-12.2367 - 1.43027i) q^{94} +(-2.84135 + 3.81660i) q^{95} +(-0.637153 + 10.9395i) q^{97} +(-1.12478 + 0.943807i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{27}\right)$

Coefficient data

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

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

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

$2$	−0.415272	+	0.962709i	−0.293642	+	0.680738i	−0.999622	−	0.0274933i	$-0.991248\pi$
$2$	−0.415272	+	0.962709i	−0.293642	+	0.680738i	0.705980	+	0.708232i	$0.250507\pi$
$3$		0			0
$3$		0			0
$4$	0.618125	+	0.655174i	0.309062	+	0.327587i
$5$	0.0443725	+	0.761846i	0.0198440	+	0.340708i	0.993588	+	0.113062i	$0.0360658\pi$
$5$	0.0443725	+	0.761846i	0.0198440	+	0.340708i	−0.973744	+	0.227646i	$0.926897\pi$
$6$		0			0
$7$	2.82023	+	0.668406i	1.06595	+	0.252634i	0.725918	−	0.687782i	$-0.241415\pi$
$7$	2.82023	+	0.668406i	1.06595	+	0.252634i	0.340028	+	0.940415i	$0.389564\pi$
$8$	−2.85789	+	1.04019i	−1.01042	+	0.367761i
$9$		0			0
$10$	−0.751863	−	0.273656i	−0.237760	−	0.0865375i
$11$	1.36690	+	0.899022i	0.412135	+	0.271065i	0.738600	−	0.674144i	$-0.235487\pi$
$11$	1.36690	+	0.899022i	0.412135	+	0.271065i	−0.326465	+	0.945209i	$0.605858\pi$
$12$		0			0
$13$	−4.07018	−	0.475735i	−1.12886	−	0.131945i	−0.468906	−	0.883248i	$-0.655352\pi$
$13$	−4.07018	−	0.475735i	−1.12886	−	0.131945i	−0.659958	+	0.751303i	$0.729426\pi$
$14$	−1.81464	+	2.43749i	−0.484984	+	0.651446i
$15$		0			0
$16$	0.0806579	−	1.38484i	0.0201645	−	0.346211i
$17$	−4.52563	+	3.79745i	−1.09763	+	0.921018i	−0.997263	−	0.0739329i	$-0.976445\pi$
$17$	−4.52563	+	3.79745i	−1.09763	+	0.921018i	−0.100363	+	0.994951i	$0.532000\pi$
$18$		0			0
$19$	4.77625	+	4.00775i	1.09575	+	0.919441i	0.997132	−	0.0756846i	$-0.0241142\pi$
$19$	4.77625	+	4.00775i	1.09575	+	0.919441i	0.0986153	+	0.995126i	$0.468559\pi$
$20$	−0.471714	+	0.499987i	−0.105478	+	0.111801i
$21$		0			0
$22$	−1.43313	+	0.942586i	−0.305545	+	0.200960i
$23$	3.75955	−	0.891030i	0.783921	−	0.185793i	0.180882	−	0.983505i	$-0.442105\pi$
$23$	3.75955	−	0.891030i	0.783921	−	0.185793i	0.603038	+	0.797712i	$0.293957\pi$
$24$		0			0
$25$	4.38775	−	0.512855i	0.877550	−	0.102571i
$26$	2.14823	−	3.72084i	0.421302	−	0.729716i
$27$		0			0
$28$	1.30533	+	2.26090i	0.246684	+	0.427269i
$29$	−1.97163	−	2.64835i	−0.366122	−	0.491787i	0.580443	−	0.814301i	$-0.302879\pi$
$29$	−1.97163	−	2.64835i	−0.366122	−	0.491787i	−0.946565	+	0.322514i	$0.895472\pi$
$30$		0			0
$31$	−0.166718	+	0.556877i	−0.0299434	+	0.100018i	−0.971655	−	0.236403i	$-0.924031\pi$
$31$	−0.166718	+	0.556877i	−0.0299434	+	0.100018i	0.941712	+	0.336421i	$0.109217\pi$
$32$	−4.13590	−	2.07713i	−0.731131	−	0.367188i
$33$		0			0
$34$	−1.77648	−	5.93384i	−0.304663	−	1.01765i
$35$	−0.384082	+	2.17824i	−0.0649217	+	0.368189i
$36$		0			0
$37$	−0.349184	−	1.98032i	−0.0574055	−	0.325563i	0.942559	−	0.334041i	$-0.108412\pi$
$37$	−0.349184	−	1.98032i	−0.0574055	−	0.325563i	−0.999964	+	0.00847831i	$0.997301\pi$
$38$	−5.84174	+	2.93383i	−0.947656	+	0.475931i
$39$		0			0
$40$	−0.919272	−	2.13111i	−0.145350	−	0.336958i
$41$	−0.581956	−	1.34912i	−0.0908862	−	0.210698i	0.866710	−	0.498813i	$-0.166231\pi$
$41$	−0.581956	−	1.34912i	−0.0908862	−	0.210698i	−0.957596	+	0.288115i	$0.906971\pi$
$42$		0			0
$43$	−6.99844	+	3.51475i	−1.06725	+	0.535994i	−0.893624	−	0.448817i	$-0.851845\pi$
$43$	−6.99844	+	3.51475i	−1.06725	+	0.535994i	−0.173628	+	0.984811i	$0.555549\pi$
$44$	0.255897	+	1.45126i	0.0385779	+	0.218786i
$45$		0			0
$46$	−0.703435	+	3.98938i	−0.103716	+	0.588201i
$47$	3.37012	+	11.2570i	0.491582	+	1.64200i	0.739455	+	0.673206i	$0.235083\pi$
$47$	3.37012	+	11.2570i	0.491582	+	1.64200i	−0.247873	+	0.968793i	$0.579731\pi$
$48$		0			0
$49$	1.25148	+	0.628517i	0.178783	+	0.0897882i
$50$	−1.32838	+	4.43710i	−0.187862	+	0.627501i
$51$		0			0
$52$	−2.20419	−	2.96074i	−0.305666	−	0.410581i
$53$	−0.600204	−	1.03958i	−0.0824443	−	0.142798i	0.821855	−	0.569697i	$-0.192939\pi$
$53$	−0.600204	−	1.03958i	−0.0824443	−	0.142798i	−0.904299	+	0.426899i	$0.859606\pi$
$54$		0			0
$55$	−0.624264	+	1.08126i	−0.0841757	+	0.145797i
$56$	−8.75515	+	1.02333i	−1.16996	+	0.136748i
$57$		0			0
$58$	3.36835	−	0.798315i	0.442287	−	0.104824i
$59$	−5.89398	+	3.87653i	−0.767330	+	0.504681i	−0.871809	−	0.489846i	$-0.837053\pi$
$59$	−5.89398	+	3.87653i	−0.767330	+	0.504681i	0.104479	+	0.994527i	$0.466683\pi$
$60$		0			0
$61$	8.34487	−	8.84504i	1.06845	−	1.13249i	0.0776755	−	0.996979i	$-0.475250\pi$
$61$	8.34487	−	8.84504i	1.06845	−	1.13249i	0.990776	−	0.135513i	$-0.0432683\pi$
$62$	−0.466877	−	0.391757i	−0.0592935	−	0.0497531i
$63$		0			0
$64$	5.84249	−	4.90243i	0.730312	−	0.612804i
$65$	0.181833	−	3.12196i	0.0225536	−	0.387231i
$66$		0			0
$67$	−1.39975	+	1.88018i	−0.171006	+	0.229701i	−0.879361	−	0.476155i	$-0.842030\pi$
$67$	−1.39975	+	1.88018i	−0.171006	+	0.229701i	0.708355	+	0.705856i	$0.249437\pi$
$68$	−5.28540	−	0.617774i	−0.640949	−	0.0749162i
$69$		0			0
$70$	−1.93751	−	1.27432i	−0.231577	−	0.152310i
$71$	10.2267	+	3.72222i	1.21369	+	0.441746i	0.867981	−	0.496597i	$-0.165417\pi$
$71$	10.2267	+	3.72222i	1.21369	+	0.441746i	0.345706	+	0.938343i	$0.387639\pi$
$72$		0			0
$73$	−12.9627	+	4.71802i	−1.51716	+	0.552202i	−0.960438	−	0.278494i	$-0.910165\pi$
$73$	−12.9627	+	4.71802i	−1.51716	+	0.552202i	−0.556726	+	0.830696i	$0.687943\pi$
$74$	2.05148	+	0.486209i	0.238480	+	0.0565207i
$75$		0			0
$76$	0.326545	+	5.60657i	0.0374573	+	0.643117i
$77$	3.25405	+	3.44909i	0.370833	+	0.393060i
$78$		0			0
$79$	−1.70702	+	3.95732i	−0.192055	+	0.445233i	−0.986849	−	0.161646i	$-0.948320\pi$
$79$	−1.70702	+	3.95732i	−0.192055	+	0.445233i	0.794794	+	0.606879i	$0.207579\pi$
$80$	1.05862			0.118357
$81$		0			0
$82$	1.54049			0.170118
$83$	6.82230	−	15.8159i	0.748844	−	1.73602i	0.0749512	−	0.997187i	$-0.476120\pi$
$83$	6.82230	−	15.8159i	0.748844	−	1.73602i	0.673893	−	0.738829i	$-0.264621\pi$
$84$		0			0
$85$	−3.09389	−	3.27933i	−0.335579	−	0.355693i
$86$	−0.477423	−	8.19704i	−0.0514819	−	0.883909i
$87$		0			0
$88$	−4.84159	−	1.14748i	−0.516115	−	0.122321i
$89$	−3.38989	+	1.23382i	−0.359327	+	0.130784i	−0.515374	−	0.856965i	$-0.672347\pi$
$89$	−3.38989	+	1.23382i	−0.359327	+	0.130784i	0.156047	+	0.987750i	$0.450125\pi$
$90$		0			0
$91$	−11.1608	−	4.06221i	−1.16997	−	0.425836i
$92$	2.90765	+	1.91239i	0.303144	+	0.199381i
$93$		0			0
$94$	−12.2367	−	1.43027i	−1.26212	−	0.147521i
$95$	−2.84135	+	3.81660i	−0.291517	+	0.391575i
$96$		0			0
$97$	−0.637153	+	10.9395i	−0.0646930	+	1.11074i	0.797223	+	0.603685i	$0.206302\pi$
$97$	−0.637153	+	10.9395i	−0.0646930	+	1.11074i	−0.861916	+	0.507051i	$0.830735\pi$
$98$	−1.12478	+	0.943807i	−0.113620	+	0.0953389i
$99$		0			0
$100$	3.04819	+	2.55773i	0.304819	+	0.255773i
$101$	6.22321	−	6.59621i	0.619232	−	0.656348i	−0.339517	−	0.940600i	$-0.610264\pi$
$101$	6.22321	−	6.59621i	0.619232	−	0.656348i	0.958750	+	0.284252i	$0.0917452\pi$
$102$		0			0
$103$	5.43776	−	3.57647i	0.535799	−	0.352400i	−0.252594	−	0.967572i	$-0.581284\pi$
$103$	5.43776	−	3.57647i	0.535799	−	0.352400i	0.788393	+	0.615172i	$0.210913\pi$
$104$	12.1270	−	2.87414i	1.18915	−	0.281833i
$105$		0			0
$106$	1.25006	−	0.146112i	0.121417	−	0.0141916i
$107$	5.56131	−	9.63248i	0.537632	−	0.931207i	−0.461398	−	0.887193i	$-0.652652\pi$
$107$	5.56131	−	9.63248i	0.537632	−	0.931207i	0.999031	−	0.0440137i	$-0.0140145\pi$
$108$		0			0
$109$	4.15761	+	7.20119i	0.398227	+	0.689749i	0.993507	−	0.113769i	$-0.0362923\pi$
$109$	4.15761	+	7.20119i	0.398227	+	0.689749i	−0.595280	+	0.803518i	$0.702959\pi$
$110$	−0.781696	−	1.05000i	−0.0745318	−	0.100114i
$111$		0			0
$112$	1.15311	−	3.85166i	0.108959	−	0.363947i
$113$	3.64240	+	1.82928i	0.342649	+	0.172085i	0.611798	−	0.791014i	$-0.290446\pi$
$113$	3.64240	+	1.82928i	0.342649	+	0.172085i	−0.269150	+	0.963098i	$0.586743\pi$
$114$		0			0
$115$	0.845648	+	2.82466i	0.0788571	+	0.263401i
$116$	0.516421	−	2.92877i	0.0479485	−	0.271929i
$117$		0			0
$118$	−1.28437	−	7.28400i	−0.118235	−	0.670547i
$119$	−15.3015	+	7.68472i	−1.40269	+	0.704457i
$120$		0			0
$121$	−3.29671	−	7.64263i	−0.299701	−	0.694785i
$122$	5.04981	+	11.7068i	0.457189	+	1.05988i
$123$		0			0
$124$	−0.467904	+	0.234990i	−0.0420190	+	0.0211027i
$125$	1.24800	+	7.07775i	0.111624	+	0.633053i
$126$		0			0
$127$	2.35011	−	13.3281i	0.208538	−	1.18268i	−0.683235	−	0.730198i	$-0.739428\pi$
$127$	2.35011	−	13.3281i	0.208538	−	1.18268i	0.891774	−	0.452482i	$-0.149461\pi$
$128$	−0.361365	−	1.20704i	−0.0319405	−	0.106689i
$129$		0			0
$130$	2.93003	+	1.47151i	0.256980	+	0.129060i
$131$	4.28758	−	14.3215i	0.374608	−	1.25128i	−0.538176	−	0.842833i	$-0.680886\pi$
$131$	4.28758	−	14.3215i	0.374608	−	1.25128i	0.912783	−	0.408444i	$-0.133928\pi$
$132$		0			0
$133$	10.7913	+	14.4952i	0.935725	+	1.25690i
$134$	−1.22880	−	2.12834i	−0.106152	−	0.183860i
$135$		0			0
$136$	8.98368	−	15.5602i	0.770344	−	1.33427i
$137$	13.2035	−	1.54327i	1.12805	−	0.131851i	0.468469	−	0.883480i	$-0.344806\pi$
$137$	13.2035	−	1.54327i	1.12805	−	0.131851i	0.659586	+	0.751629i	$0.270732\pi$
$138$		0			0
$139$	12.5063	−	2.96404i	1.06077	−	0.251407i	0.337039	−	0.941491i	$-0.390575\pi$
$139$	12.5063	−	2.96404i	1.06077	−	0.251407i	0.723729	+	0.690084i	$0.242426\pi$
$140$	−1.66453	+	1.09478i	−0.140679	+	0.0925259i
$141$		0			0
$142$	−7.83029	+	8.29962i	−0.657103	+	0.696489i
$143$	−5.13582	−	4.30946i	−0.429479	−	0.360375i
$144$		0			0
$145$	1.93015	−	1.61959i	0.160290	−	0.134499i
$146$	0.840949	−	14.4385i	0.0695974	−	1.19494i
$147$		0			0
$148$	1.08161	−	1.45286i	0.0889082	−	0.119424i
$149$	10.7987	+	1.26218i	0.884661	+	0.103402i	0.546275	−	0.837606i	$-0.316045\pi$
$149$	10.7987	+	1.26218i	0.884661	+	0.103402i	0.338385	+	0.941008i	$0.390119\pi$
$150$		0			0
$151$	−7.10300	−	4.67172i	−0.578034	−	0.380179i	0.226566	−	0.973996i	$-0.427250\pi$
$151$	−7.10300	−	4.67172i	−0.578034	−	0.380179i	−0.804600	+	0.593817i	$0.797620\pi$
$152$	−17.8188	−	6.48551i	−1.44529	−	0.526044i
$153$		0			0
$154$	−4.67179	+	1.70039i	−0.376463	+	0.137021i
$155$	−0.431652	−	0.102303i	−0.0346711	−	0.00821721i
$156$		0			0
$157$	0.827351	+	14.2051i	0.0660298	+	1.13369i	0.854786	+	0.518981i	$0.173688\pi$
$157$	0.827351	+	14.2051i	0.0660298	+	1.13369i	−0.788756	+	0.614706i	$0.789275\pi$
$158$	−3.10087	−	3.28673i	−0.246692	−	0.261478i
$159$		0			0
$160$	1.39893	−	3.24309i	0.110595	−	0.256388i
$161$	11.1984			0.882554
$162$		0			0
$163$	−2.11478			−0.165643			−0.0828213	−	0.996564i	$-0.526393\pi$
$163$	−2.11478			−0.165643			−0.0828213	+	0.996564i	$0.526393\pi$
$164$	0.524190	−	1.21521i	0.0409324	−	0.0948919i
$165$		0			0
$166$	12.3930	+	13.1358i	0.961881	+	1.01953i
$167$	−0.460106	−	7.89972i	−0.0356041	−	0.611299i	−0.968169	−	0.250297i	$-0.919472\pi$
$167$	−0.460106	−	7.89972i	−0.0356041	−	0.611299i	0.932565	−	0.361002i	$-0.117565\pi$
$168$		0			0
$169$	3.69043	+	0.874649i	0.283879	+	0.0672807i
$170$	4.44185	−	1.61670i	0.340674	−	0.123995i
$171$		0			0
$172$	−6.62868	−	2.41264i	−0.505432	−	0.183962i
$173$	16.3700	+	10.7667i	1.24459	+	0.818579i	0.988958	−	0.148195i	$-0.0473465\pi$
$173$	16.3700	+	10.7667i	1.24459	+	0.818579i	0.255631	+	0.966774i	$0.417717\pi$
$174$		0			0
$175$	12.7172	+	1.48643i	0.961334	+	0.112364i
$176$	1.35526	−	1.82042i	0.102156	−	0.137220i
$177$		0			0
$178$	0.219918	−	3.77585i	0.0164836	−	0.283012i
$179$	13.7606	−	11.5465i	1.02852	−	0.863029i	0.0378443	−	0.999284i	$-0.487951\pi$
$179$	13.7606	−	11.5465i	1.02852	−	0.863029i	0.990674	+	0.136254i	$0.0435065\pi$
$180$		0			0
$181$	−2.39235	−	2.00742i	−0.177822	−	0.149210i	0.549532	−	0.835472i	$-0.314806\pi$
$181$	−2.39235	−	2.00742i	−0.177822	−	0.149210i	−0.727354	+	0.686262i	$0.759250\pi$
$182$	8.54552	−	9.05772i	0.633436	−	0.671403i
$183$		0			0
$184$	−9.81753	+	6.45709i	−0.723758	+	0.476023i
$185$	1.49320	−	0.353896i	0.109783	−	0.0260189i
$186$		0			0
$187$	−9.60007	+	1.12209i	−0.702026	+	0.0820551i
$188$	−5.29213	+	9.16623i	−0.385968	+	0.668516i
$189$		0			0
$190$	−2.49434	−	4.32033i	−0.180959	−	0.313429i
$191$	5.23124	+	7.02677i	0.378519	+	0.508439i	0.950031	−	0.312154i	$-0.101051\pi$
$191$	5.23124	+	7.02677i	0.378519	+	0.508439i	−0.571513	+	0.820593i	$0.693643\pi$
$192$		0			0
$193$	5.07494	−	16.9515i	0.365302	−	1.22019i	−0.555946	−	0.831219i	$-0.687644\pi$
$193$	5.07494	−	16.9515i	0.365302	−	1.22019i	0.921248	−	0.388976i	$-0.127171\pi$
$194$	−10.2670	−	5.15626i	−0.737124	−	0.370198i
$195$		0			0
$196$	0.361783	+	1.20844i	0.0258417	+	0.0863171i
$197$	1.12942	−	6.40526i	0.0804679	−	0.456356i	−0.917775	−	0.397101i	$-0.870016\pi$
$197$	1.12942	−	6.40526i	0.0804679	−	0.456356i	0.998243	−	0.0592552i	$-0.0188726\pi$
$198$		0			0
$199$	2.77478	+	15.7366i	0.196699	+	1.11554i	0.909978	+	0.414656i	$0.136098\pi$
$199$	2.77478	+	15.7366i	0.196699	+	1.11554i	−0.713279	+	0.700880i	$0.752791\pi$
$200$	−12.0062	+	6.02976i	−0.848969	+	0.426368i
$201$		0			0
$202$	3.76591	+	8.73037i	0.264969	+	0.614266i
$203$	−3.79025	−	8.78680i	−0.266024	−	0.616712i
$204$		0			0
$205$	1.00200	−	0.503224i	0.0699829	−	0.0351467i
$206$	1.18495	+	6.72019i	0.0825595	+	0.468218i
$207$		0			0
$208$	−0.987111	+	5.59818i	−0.0684438	+	0.388164i
$209$	2.92559	+	9.77214i	0.202367	+	0.675953i
$210$		0			0
$211$	10.9590	+	5.50382i	0.754449	+	0.378899i	0.784078	−	0.620662i	$-0.213136\pi$
$211$	10.9590	+	5.50382i	0.754449	+	0.378899i	−0.0296286	+	0.999561i	$0.509432\pi$
$212$	0.310107	−	1.03583i	0.0212983	−	0.0711411i
$213$		0			0
$214$	6.96382	+	9.35403i	0.476037	+	0.639428i
$215$	−2.98823	−	5.17577i	−0.203796	−	0.352985i
$216$		0			0
$217$	−0.842402	+	1.45908i	−0.0571860	+	0.0990491i
$218$	−8.65920	+	1.01212i	−0.586475	+	0.0685491i
$219$		0			0
$220$	−1.09428	+	0.259350i	−0.0737766	+	0.0174854i
$221$	20.2267	−	13.3033i	1.36059	−	0.894877i
$222$		0			0
$223$	−1.20505	+	1.27728i	−0.0806961	+	0.0855329i	−0.766463	−	0.642288i	$-0.777985\pi$
$223$	−1.20505	+	1.27728i	−0.0806961	+	0.0855329i	0.685767	+	0.727821i	$0.259467\pi$
$224$	−10.2758	−	8.62243i	−0.686582	−	0.576110i
$225$		0			0
$226$	−3.27366	+	2.74693i	−0.217761	+	0.182723i
$227$	1.03052	−	17.6933i	0.0683979	−	1.17435i	−0.773171	−	0.634197i	$-0.781331\pi$
$227$	1.03052	−	17.6933i	0.0683979	−	1.17435i	0.841569	−	0.540149i	$-0.181632\pi$
$228$		0			0
$229$	2.17984	−	2.92804i	0.144048	−	0.193490i	−0.724243	−	0.689544i	$-0.757811\pi$
$229$	2.17984	−	2.92804i	0.144048	−	0.193490i	0.868292	+	0.496054i	$0.165218\pi$
$230$	−3.07050	−	0.358890i	−0.202463	−	0.0236645i
$231$		0			0
$232$	8.38946	+	5.51783i	0.550795	+	0.362263i
$233$	21.1172	+	7.68604i	1.38343	+	0.503529i	0.923218	−	0.384277i	$-0.125549\pi$
$233$	21.1172	+	7.68604i	1.38343	+	0.503529i	0.460217	+	0.887806i	$0.347772\pi$
$234$		0			0
$235$	−8.42654	+	3.06701i	−0.549687	+	0.200070i
$236$	−6.18301	−	1.46540i	−0.402480	−	0.0953895i
$237$		0			0
$238$	−1.04385	−	17.9222i	−0.0676627	−	1.16172i
$239$	−2.49200	−	2.64136i	−0.161194	−	0.170856i	0.641743	−	0.766920i	$-0.278212\pi$
$239$	−2.49200	−	2.64136i	−0.161194	−	0.170856i	−0.802937	+	0.596064i	$0.796730\pi$
$240$		0			0
$241$	2.03864	−	4.72609i	0.131320	−	0.304434i	−0.839851	−	0.542817i	$-0.817358\pi$
$241$	2.03864	−	4.72609i	0.131320	−	0.304434i	0.971171	+	0.238382i	$0.0766172\pi$
$242$	8.72667			0.560972
$243$		0			0
$244$	10.9532			0.701208
$245$	−0.423302	+	0.981324i	−0.0270438	+	0.0626945i
$246$		0			0
$247$	−17.5336	−	18.5845i	−1.11563	−	1.18250i
$248$	−0.102794	−	1.76491i	−0.00652744	−	0.112072i
$249$		0			0
$250$	−7.33207	−	1.73773i	−0.463721	−	0.109904i
$251$	−6.68026	+	2.43142i	−0.421655	+	0.153470i	−0.544128	−	0.839002i	$-0.683140\pi$
$251$	−6.68026	+	2.43142i	−0.421655	+	0.153470i	0.122474	+	0.992472i	$0.460917\pi$
$252$		0			0
$253$	5.93998	+	2.16197i	0.373443	+	0.135922i
$254$	11.8552	+	7.79727i	0.743860	+	0.489244i
$255$		0			0
$256$	16.4626	+	1.92420i	1.02891	+	0.120263i
$257$	−0.900688	+	1.20983i	−0.0561833	+	0.0754673i	−0.829327	−	0.558764i	$-0.811276\pi$
$257$	−0.900688	+	1.20983i	−0.0561833	+	0.0754673i	0.773143	+	0.634231i	$0.218683\pi$
$258$		0			0
$259$	0.338880	−	5.81835i	0.0210570	−	0.361534i
$260$	2.15782	−	1.81063i	0.133822	−	0.112290i
$261$		0			0
$262$	12.0069	+	10.0750i	0.741792	+	0.622437i
$263$	1.62123	−	1.71840i	0.0999691	−	0.105961i	−0.675457	−	0.737399i	$-0.736054\pi$
$263$	1.62123	−	1.71840i	0.0999691	−	0.105961i	0.775426	+	0.631438i	$0.217535\pi$
$264$		0			0
$265$	0.765370	−	0.503392i	0.0470163	−	0.0309231i
$266$	−18.4360	+	4.36942i	−1.13039	+	0.267906i
$267$		0			0
$268$	−2.09707	+	0.245112i	−0.128099	+	0.0149726i
$269$	−4.07527	+	7.05858i	−0.248474	+	0.430369i	−0.963103	−	0.269135i	$-0.913262\pi$
$269$	−4.07527	+	7.05858i	−0.248474	+	0.430369i	0.714629	+	0.699504i	$0.246596\pi$
$270$		0			0
$271$	1.47740	+	2.55894i	0.0897458	+	0.155444i	0.907404	−	0.420260i	$-0.138061\pi$
$271$	1.47740	+	2.55894i	0.0897458	+	0.155444i	−0.817658	+	0.575704i	$0.804728\pi$
$272$	4.89385	+	6.57358i	0.296733	+	0.398582i
$273$		0			0
$274$	−3.99734	+	13.3521i	−0.241488	+	0.806627i
$275$	6.45867	+	3.24367i	0.389473	+	0.195601i
$276$		0			0
$277$	−3.75609	−	12.5462i	−0.225682	−	0.753829i	−0.993567	−	0.113243i	$-0.963876\pi$
$277$	−3.75609	−	12.5462i	−0.225682	−	0.753829i	0.767886	−	0.640587i	$-0.221309\pi$
$278$	−2.34000	+	13.2708i	−0.140344	+	0.795929i
$279$		0			0
$280$	−1.16811	−	6.62467i	−0.0698078	−	0.395900i
$281$	−17.3424	+	8.70969i	−1.03456	+	0.519576i	−0.883246	−	0.468909i	$-0.844647\pi$
$281$	−17.3424	+	8.70969i	−1.03456	+	0.519576i	−0.151315	+	0.988486i	$0.548351\pi$
$282$		0			0
$283$	3.17488	+	7.36020i	0.188727	+	0.437518i	0.986140	−	0.165916i	$-0.0530579\pi$
$283$	3.17488	+	7.36020i	0.188727	+	0.437518i	−0.797413	+	0.603434i	$0.793799\pi$
$284$	3.88268	+	9.00107i	0.230395	+	0.534116i
$285$		0			0
$286$	6.28152	−	3.15470i	0.371434	−	0.186541i
$287$	−0.739484	−	4.19382i	−0.0436503	−	0.247553i
$288$		0			0
$289$	3.10865	−	17.6300i	0.182862	−	1.03706i
$290$	0.757655	+	2.53074i	0.0444910	+	0.148610i
$291$		0			0
$292$	−11.1037	−	5.57647i	−0.649793	−	0.326338i
$293$	−7.33932	+	24.5150i	−0.428768	+	1.43218i	0.421978	+	0.906606i	$0.361336\pi$
$293$	−7.33932	+	24.5150i	−0.428768	+	1.43218i	−0.850746	+	0.525577i	$0.823849\pi$
$294$		0			0
$295$	−3.21485	−	4.31829i	−0.187176	−	0.251420i
$296$	3.05783	+	5.29631i	0.177733	+	0.307842i
$297$		0			0
$298$	−5.69950	+	9.87182i	−0.330163	+	0.571859i
$299$	−15.7259	+	1.83810i	−0.909454	+	0.106300i
$300$		0			0
$301$	−22.0865	+	5.23459i	−1.27304	+	0.301717i
$302$	7.44719	−	4.89809i	0.428538	−	0.281854i
$303$		0			0
$304$	5.93535	−	6.29110i	0.340416	−	0.360819i
$305$	7.10884	+	5.96503i	0.407051	+	0.341556i
$306$		0			0
$307$	2.42628	−	2.03589i	0.138475	−	0.116195i	−0.570919	−	0.821006i	$-0.693413\pi$
$307$	2.42628	−	2.03589i	0.138475	−	0.116195i	0.709394	+	0.704812i	$0.248969\pi$
$308$	−0.248346	+	4.26394i	−0.0141508	+	0.242960i
$309$		0			0
$310$	0.277742	−	0.373072i	0.0157747	−	0.0211891i
$311$	−1.27660	−	0.149214i	−0.0723895	−	0.00846112i	0.0798210	−	0.996809i	$-0.474565\pi$
$311$	−1.27660	−	0.149214i	−0.0723895	−	0.00846112i	−0.152211	+	0.988348i	$0.548639\pi$
$312$		0			0
$313$	−8.71160	−	5.72971i	−0.492408	−	0.323862i	0.278904	−	0.960319i	$-0.410029\pi$
$313$	−8.71160	−	5.72971i	−0.492408	−	0.323862i	−0.771312	+	0.636457i	$0.780399\pi$
$314$	−14.0189	−	5.10247i	−0.791134	−	0.287949i
$315$		0			0
$316$	−3.64788	+	1.32772i	−0.205210	+	0.0746902i
$317$	−26.3951	−	6.25575i	−1.48249	−	0.351358i	−0.591847	−	0.806051i	$-0.701601\pi$
$317$	−26.3951	−	6.25575i	−1.48249	−	0.351358i	−0.890648	+	0.454693i	$0.849749\pi$
$318$		0			0
$319$	−0.314081	−	5.39256i	−0.0175852	−	0.301925i
$320$	3.99414	+	4.23355i	0.223279	+	0.236662i
$321$		0			0
$322$	−4.65037	+	10.7808i	−0.259155	+	0.600788i
$323$	−36.8348			−2.04954
$324$		0			0
$325$	−18.1029			−1.00417
$326$	0.878211	−	2.03592i	0.0486396	−	0.112759i
$327$		0			0
$328$	3.06650	+	3.25030i	0.169319	+	0.179468i
$329$	1.98026	+	33.9998i	0.109176	+	1.87447i
$330$		0			0
$331$	−6.10141	−	1.44606i	−0.335364	−	0.0794827i	0.0594839	−	0.998229i	$-0.481054\pi$
$331$	−6.10141	−	1.44606i	−0.335364	−	0.0794827i	−0.394848	+	0.918747i	$0.629203\pi$
$332$	14.5792	−	5.30638i	0.800136	−	0.291226i
$333$		0			0
$334$	7.79620	+	2.83759i	0.426589	+	0.155266i
$335$	−1.49452	−	0.982961i	−0.0816544	−	0.0537049i
$336$		0			0
$337$	−5.51739	−	0.644890i	−0.300551	−	0.0351294i	−0.0355191	−	0.999369i	$-0.511308\pi$
$337$	−5.51739	−	0.644890i	−0.300551	−	0.0351294i	−0.265032	+	0.964240i	$0.585383\pi$
$338$	−2.37457	+	3.18960i	−0.129159	+	0.173491i
$339$		0			0
$340$	0.236123	−	4.05407i	0.0128055	−	0.219863i
$341$	−0.728531	+	0.611310i	−0.0394522	+	0.0331043i
$342$		0			0
$343$	−12.4325	−	10.4321i	−0.671292	−	0.563281i
$344$	16.3447	−	17.3244i	0.881250	−	0.934070i
$345$		0			0
$346$	−17.1632	+	11.2884i	−0.922702	+	0.606870i
$347$	−26.3744	+	6.25085i	−1.41585	+	0.335563i	−0.866144	−	0.499794i	$-0.833409\pi$
$347$	−26.3744	+	6.25085i	−1.41585	+	0.335563i	−0.549707	+	0.835357i	$0.685261\pi$
$348$		0			0
$349$	20.9161	−	2.44475i	1.11962	−	0.130864i	0.463911	−	0.885882i	$-0.346446\pi$
$349$	20.9161	−	2.44475i	1.11962	−	0.130864i	0.655705	+	0.755018i	$0.272372\pi$
$350$	−6.71212	+	11.6257i	−0.358778	+	0.621422i
$351$		0			0
$352$	−3.78597	−	6.55749i	−0.201793	−	0.349515i
$353$	12.1106	+	16.2673i	0.644580	+	0.865822i	0.997560	−	0.0698092i	$-0.0222390\pi$
$353$	12.1106	+	16.2673i	0.644580	+	0.865822i	−0.352980	+	0.935631i	$0.614832\pi$
$354$		0			0
$355$	−2.38197	+	7.95634i	−0.126422	+	0.422279i
$356$	−2.90374	−	1.45831i	−0.153898	−	0.0772904i
$357$		0			0
$358$	5.40156	+	18.0425i	0.285481	+	0.953573i
$359$	0.901880	−	5.11482i	0.0475994	−	0.269950i	−0.951715	−	0.306984i	$-0.900680\pi$
$359$	0.901880	−	5.11482i	0.0475994	−	0.269950i	0.999314	+	0.0370347i	$0.0117912\pi$
$360$		0			0
$361$	3.45119	+	19.5727i	0.181642	+	1.03014i
$362$	2.92604	−	1.46951i	0.153789	−	0.0772359i
$363$		0			0
$364$	−4.23733	−	9.82324i	−0.222097	−	0.514878i
$365$	−4.16959	−	9.66619i	−0.218246	−	0.505952i
$366$		0			0
$367$	4.98231	−	2.50221i	0.260074	−	0.130614i	−0.313985	−	0.949428i	$-0.601664\pi$
$367$	4.98231	−	2.50221i	0.260074	−	0.130614i	0.574059	+	0.818814i	$0.305368\pi$
$368$	−0.930699	−	5.27826i	−0.0485160	−	0.275148i
$369$		0			0
$370$	−0.279387	+	1.58448i	−0.0145247	+	0.0823734i
$371$	−0.997847	−	3.33304i	−0.0518056	−	0.173043i
$372$		0			0
$373$	−29.5856	−	14.8584i	−1.53188	−	0.769341i	−0.534751	−	0.845010i	$-0.679595\pi$
$373$	−29.5856	−	14.8584i	−1.53188	−	0.769341i	−0.997133	+	0.0756686i	$0.975891\pi$
$374$	2.90640	−	9.70805i	0.150286	−	0.501991i
$375$		0			0
$376$	−21.3408	−	28.6656i	−1.10057	−	1.47832i
$377$	6.76495	+	11.7172i	0.348413	+	0.603468i
$378$		0			0
$379$	0.872014	−	1.51037i	0.0447923	−	0.0775826i	−0.842760	−	0.538289i	$-0.819071\pi$
$379$	0.872014	−	1.51037i	0.0447923	−	0.0775826i	0.887552	+	0.460707i	$0.152404\pi$
$380$	−4.25685	+	0.497554i	−0.218372	+	0.0255240i
$381$		0			0
$382$	−8.93712	+	2.11814i	−0.457263	+	0.108373i
$383$	−25.7840	+	16.9584i	−1.31750	+	0.866535i	−0.996744	−	0.0806260i	$-0.974308\pi$
$383$	−25.7840	+	16.9584i	−1.31750	+	0.866535i	−0.320758	+	0.947161i	$0.603938\pi$
$384$		0			0
$385$	−2.48328	+	2.63213i	−0.126560	+	0.134146i
$386$	14.2119	+	11.9252i	0.723365	+	0.606975i
$387$		0			0
$388$	−7.56111	+	6.34452i	−0.383857	+	0.322094i
$389$	1.53694	−	26.3883i	0.0779262	−	1.33794i	−0.702048	−	0.712129i	$-0.747731\pi$
$389$	1.53694	−	26.3883i	0.0779262	−	1.33794i	0.779974	−	0.625811i	$-0.215232\pi$
$390$		0			0
$391$	−13.6307	+	18.3092i	−0.689334	+	0.925936i
$392$	−4.23036	−	0.494459i	−0.213666	−	0.0249739i
$393$		0			0
$394$	5.69739	+	3.74723i	0.287030	+	0.188783i
$395$	−3.09061	−	1.12489i	−0.155506	−	0.0565994i
$396$		0			0
$397$	32.2517	−	11.7387i	1.61867	−	0.589146i	0.635538	−	0.772069i	$-0.280778\pi$
$397$	32.2517	−	11.7387i	1.61867	−	0.589146i	0.983127	+	0.182923i	$0.0585561\pi$
$398$	−16.3020	−	3.86365i	−0.817147	−	0.193667i
$399$		0			0
$400$	−0.356316	−	6.11771i	−0.0178158	−	0.305886i
$401$	0.124842	+	0.132325i	0.00623432	+	0.00660799i	0.730483	−	0.682931i	$-0.239295\pi$
$401$	0.124842	+	0.132325i	0.00623432	+	0.00660799i	−0.724249	+	0.689539i	$0.757813\pi$
$402$		0			0
$403$	0.943498	−	2.18727i	0.0469990	−	0.108956i
$404$	8.16839			0.406393
$405$		0			0
$406$	10.0331			0.497935
$407$	1.30305	−	3.02082i	0.0645900	−	0.149736i
$408$		0			0
$409$	4.15307	+	4.40200i	0.205356	+	0.217665i	0.821864	−	0.569684i	$-0.192934\pi$
$409$	4.15307	+	4.40200i	0.205356	+	0.217665i	−0.616508	+	0.787349i	$0.711453\pi$
$410$	0.0683551	+	1.17361i	0.00337582	+	0.0579606i
$411$		0			0
$412$	5.70443	+	1.35197i	0.281037	+	0.0666070i
$413$	−19.2134	+	6.99312i	−0.945432	+	0.344109i
$414$		0			0
$415$	12.3520	+	4.49575i	0.606334	+	0.220688i
$416$	15.8457	+	10.4219i	0.776899	+	0.510974i
$417$		0			0
$418$	−10.6226	−	1.24161i	−0.519571	−	0.0607291i
$419$	12.4349	−	16.7030i	0.607485	−	0.815994i	−0.386866	−	0.922136i	$-0.626442\pi$
$419$	12.4349	−	16.7030i	0.607485	−	0.815994i	0.994351	+	0.106142i	$0.0338498\pi$
$420$		0			0
$421$	0.691141	−	11.8664i	0.0336841	−	0.578334i	−0.938669	−	0.344819i	$-0.887940\pi$
$421$	0.691141	−	11.8664i	0.0336841	−	0.578334i	0.972353	−	0.233515i	$-0.0750228\pi$
$422$	−9.84956	+	8.26476i	−0.479469	+	0.402322i
$423$		0			0
$424$	2.79667	+	2.34669i	0.135818	+	0.113965i
$425$	−17.9098	+	18.9833i	−0.868753	+	0.920824i
$426$		0			0
$427$	29.4465	−	19.3673i	1.42502	−	0.937248i
$428$	9.74854	−	2.31045i	0.471213	−	0.111680i
$429$		0			0
$430$	6.22369	−	0.727446i	0.300133	−	0.0350805i
$431$	5.15721	−	8.93256i	0.248414	−	0.430266i	−0.714672	−	0.699460i	$-0.753424\pi$
$431$	5.15721	−	8.93256i	0.248414	−	0.430266i	0.963086	+	0.269194i	$0.0867573\pi$
$432$		0			0
$433$	0.0197177	+	0.0341520i	0.000947570	+	0.00164124i	0.866499	−	0.499179i	$-0.166365\pi$
$433$	0.0197177	+	0.0341520i	0.000947570	+	0.00164124i	−0.865551	+	0.500820i	$0.833032\pi$
$434$	−1.05485	−	1.41691i	−0.0506343	−	0.0680137i
$435$		0			0
$436$	−2.14811	+	7.17520i	−0.102876	+	0.343630i
$437$	21.5276	+	10.8116i	1.02980	+	0.517187i
$438$		0			0
$439$	1.28848	+	4.30381i	0.0614957	+	0.205410i	0.983216	−	0.182445i	$-0.0584012\pi$
$439$	1.28848	+	4.30381i	0.0614957	+	0.205410i	−0.921720	+	0.387855i	$0.873216\pi$
$440$	0.659367	−	3.73946i	0.0314341	−	0.178272i
$441$		0			0
$442$	4.40763	+	24.9969i	0.209650	+	1.18898i
$443$	−7.41704	+	3.72498i	−0.352394	+	0.176979i	−0.616186	−	0.787601i	$-0.711323\pi$
$443$	−7.41704	+	3.72498i	−0.352394	+	0.176979i	0.263792	+	0.964580i	$0.415027\pi$
$444$		0			0
$445$	−1.09040	−	2.52782i	−0.0516898	−	0.119830i
$446$	−0.729224	−	1.69053i	−0.0345297	−	0.0800490i
$447$		0			0
$448$	19.7540	−	9.92082i	0.933287	−	0.468715i
$449$	−4.67637	−	26.5210i	−0.220691	−	1.25160i	−0.870752	−	0.491722i	$-0.836368\pi$
$449$	−4.67637	−	26.5210i	−0.220691	−	1.25160i	0.650061	−	0.759882i	$-0.274743\pi$
$450$		0			0
$451$	0.417420	−	2.36731i	0.0196555	−	0.111472i
$452$	1.05296	+	3.51714i	0.0495271	+	0.165432i
$453$		0			0
$454$	16.6056	+	8.33963i	0.779338	+	0.391398i
$455$	2.59954	−	8.68308i	0.121869	−	0.407069i
$456$		0			0
$457$	−15.5014	−	20.8220i	−0.725126	−	0.974013i	−0.999922	−	0.0125106i	$-0.996018\pi$
$457$	−15.5014	−	20.8220i	−0.725126	−	0.974013i	0.274796	−	0.961503i	$-0.411390\pi$
$458$	1.91362	+	3.31449i	0.0894177	+	0.154876i
$459$		0			0
$460$	−1.32793	+	2.30004i	−0.0619150	+	0.107240i
$461$	2.46853	−	0.288530i	0.114971	−	0.0134382i	−0.0584129	−	0.998293i	$-0.518604\pi$
$461$	2.46853	−	0.288530i	0.114971	−	0.0134382i	0.173384	+	0.984854i	$0.444530\pi$
$462$		0			0
$463$	−19.6502	+	4.65717i	−0.913220	+	0.216437i	−0.660258	−	0.751039i	$-0.729553\pi$
$463$	−19.6502	+	4.65717i	−0.913220	+	0.216437i	−0.252962	+	0.967476i	$0.581405\pi$
$464$	−3.82658	+	2.51678i	−0.177644	+	0.116839i
$465$		0			0
$466$	−16.1688	+	17.1379i	−0.749006	+	0.793900i
$467$	7.13253	+	5.98491i	0.330054	+	0.276948i	0.792722	−	0.609583i	$-0.208663\pi$
$467$	7.13253	+	5.98491i	0.330054	+	0.276948i	−0.462668	+	0.886532i	$0.653108\pi$
$468$		0			0
$469$	−5.20432	+	4.36695i	−0.240313	+	0.201647i
$470$	0.546669	−	9.38595i	0.0252160	−	0.432942i
$471$		0			0
$472$	12.8120	−	17.2095i	0.589720	−	0.792132i
$473$	−12.7260	−	1.48745i	−0.585141	−	0.0683932i
$474$		0			0
$475$	23.0124	+	15.1355i	1.05588	+	0.694464i
$476$	−14.4931	−	5.27505i	−0.664290	−	0.241782i
$477$		0			0
$478$	3.57772	−	1.30218i	0.163641	−	0.0595605i
$479$	−19.0640	−	4.51825i	−0.871056	−	0.206444i	−0.229303	−	0.973355i	$-0.573645\pi$
$479$	−19.0640	−	4.51825i	−0.871056	−	0.206444i	−0.641753	+	0.766911i	$0.721793\pi$
$480$		0			0
$481$	0.479132	+	8.22637i	0.0218465	+	0.375090i
$482$	3.70326	+	3.92523i	0.168679	+	0.178789i
$483$		0			0
$484$	2.96948	−	6.88402i	0.134976	−	0.312910i
$485$	−8.36247			−0.379720
$486$		0			0
$487$	−9.74140			−0.441425			−0.220712	−	0.975339i	$-0.570838\pi$
$487$	−9.74140			−0.441425			−0.220712	+	0.975339i	$0.570838\pi$
$488$	−14.6482	+	33.9583i	−0.663093	+	1.53722i
$489$		0			0
$490$	−0.768944	−	0.815033i	−0.0347374	−	0.0368195i
$491$	−0.0515677	−	0.885383i	−0.00232722	−	0.0399568i	0.996945	−	0.0781116i	$-0.0248890\pi$
$491$	−0.0515677	−	0.885383i	−0.00232722	−	0.0399568i	−0.999272	+	0.0381548i	$0.987852\pi$
$492$		0			0
$493$	18.9798	+	4.49830i	0.854809	+	0.202593i
$494$	25.1727	−	9.16210i	1.13257	−	0.412222i
$495$		0			0
$496$	0.757740	+	0.275795i	0.0340235	+	0.0123836i
$497$	26.3537	+	17.3331i	1.18212	+	0.777496i
$498$		0			0
$499$	20.4062	+	2.38514i	0.913506	+	0.106774i	0.559842	−	0.828599i	$-0.310862\pi$
$499$	20.4062	+	2.38514i	0.913506	+	0.106774i	0.353664	+	0.935373i	$0.384936\pi$
$500$	−3.86574	+	5.19259i	−0.172881	+	0.232220i
$501$		0			0
$502$	0.433380	−	7.44085i	0.0193427	−	0.332102i
$503$	−33.6724	+	28.2545i	−1.50138	+	1.25981i	−0.622638	+	0.782510i	$0.713939\pi$
$503$	−33.6724	+	28.2545i	−1.50138	+	1.25981i	−0.878742	+	0.477297i	$0.841617\pi$
$504$		0			0
$505$	5.30144	+	4.44843i	0.235911	+	0.197953i
$506$	−4.54806	+	4.82066i	−0.202186	+	0.214305i
$507$		0			0
$508$	10.1849	−	6.69871i	0.451882	−	0.297207i
$509$	−15.2824	+	3.62199i	−0.677379	+	0.160542i	−0.554885	−	0.831927i	$-0.687238\pi$
$509$	−15.2824	+	3.62199i	−0.677379	+	0.160542i	−0.122495	+	0.992469i	$0.539089\pi$
$510$		0			0
$511$	−39.7112	+	4.64157i	−1.75672	+	0.205331i
$512$	−7.42895	+	12.8673i	−0.328316	+	0.568660i
$513$		0			0
$514$	−0.790687	−	1.36951i	−0.0348757	−	0.0604065i
$515$	2.96601	+	3.98404i	0.130698	+	0.175558i
$516$		0			0
$517$	−5.51367	+	18.4169i	−0.242491	+	0.809976i
$518$	5.46065	+	2.74244i	0.239927	+	0.120496i
$519$		0			0
$520$	2.72775	+	9.11133i	0.119620	+	0.399558i
$521$	−2.10231	+	11.9228i	−0.0921038	+	0.522346i	0.903493	+	0.428604i	$0.140994\pi$
$521$	−2.10231	+	11.9228i	−0.0921038	+	0.522346i	−0.995596	+	0.0937429i	$0.970117\pi$
$522$		0			0
$523$	−6.56199	−	37.2149i	−0.286936	−	1.62729i	−0.698288	−	0.715817i	$-0.746055\pi$
$523$	−6.56199	−	37.2149i	−0.286936	−	1.62729i	0.411353	−	0.911476i	$-0.365056\pi$
$524$	12.0333	−	6.04337i	0.525679	−	0.264006i
$525$		0			0
$526$	0.981069	+	2.27437i	0.0427766	+	0.0991674i
$527$	−1.36021	−	3.15332i	−0.0592517	−	0.137361i
$528$		0			0
$529$	−7.21326	+	3.62263i	−0.313620	+	0.157506i
$530$	0.166783	+	0.945873i	0.00724459	+	0.0410861i
$531$		0			0
$532$	−2.82653	+	16.0300i	−0.122546	+	0.694991i
$533$	1.72684	+	5.76803i	0.0747976	+	0.249841i
$534$		0			0
$535$	7.58523	+	3.80945i	0.327938	+	0.164697i
$536$	2.04457	−	6.82935i	0.0883121	−	0.294983i
$537$		0			0
$538$	−5.10301	−	6.85454i	−0.220007	−	0.295520i
$539$	1.14559	+	1.98423i	0.0493442	+	0.0854667i
$540$		0			0
$541$	−16.6000	+	28.7521i	−0.713692	+	1.23615i	0.249770	+	0.968305i	$0.419645\pi$
$541$	−16.6000	+	28.7521i	−0.713692	+	1.23615i	−0.963462	+	0.267845i	$0.913688\pi$
$542$	−3.07704	+	0.359654i	−0.132170	+	0.0154485i
$543$		0			0
$544$	26.6054	−	6.30558i	1.14070	−	0.270350i
$545$	−5.30171	+	3.48699i	−0.227101	+	0.149366i
$546$		0			0
$547$	3.03806	−	3.22015i	0.129898	−	0.137684i	−0.659160	−	0.752003i	$-0.729088\pi$
$547$	3.03806	−	3.22015i	0.129898	−	0.137684i	0.789058	+	0.614319i	$0.210569\pi$
$548$	9.17255	+	7.69668i	0.391832	+	0.328786i
$549$		0			0
$550$	−5.80482	+	4.87082i	−0.247518	+	0.207692i
$551$	1.19696	−	20.5510i	0.0509921	−	0.875501i
$552$		0			0
$553$	−7.45928	+	10.0196i	−0.317201	+	0.426075i
$554$	13.6382	+	1.59407i	0.579430	+	0.0677257i
$555$		0			0
$556$	9.67240	+	6.36164i	0.410201	+	0.269794i
$557$	18.3879	+	6.69266i	0.779122	+	0.283577i	0.700807	−	0.713351i	$-0.252824\pi$
$557$	18.3879	+	6.69266i	0.779122	+	0.283577i	0.0783156	+	0.996929i	$0.475046\pi$
$558$		0			0
$559$	30.1570	−	10.9762i	1.27550	−	0.464245i
$560$	2.98554	+	0.707585i	0.126162	+	0.0299009i
$561$		0			0
$562$	−1.18307	−	20.3126i	−0.0499050	−	0.856835i
$563$	−10.1785	−	10.7886i	−0.428973	−	0.454685i	0.476446	−	0.879204i	$-0.341925\pi$
$563$	−10.1785	−	10.7886i	−0.428973	−	0.454685i	−0.905419	+	0.424519i	$0.860443\pi$
$564$		0			0
$565$	−1.23201	+	2.85612i	−0.0518311	+	0.120158i
$566$	−8.40417			−0.353254
$567$		0			0
$568$	−33.0986			−1.38879
$569$	−1.69374	+	3.92653i	−0.0710053	+	0.164609i	−0.950023	−	0.312181i	$-0.898940\pi$
$569$	−1.69374	+	3.92653i	−0.0710053	+	0.164609i	0.879017	+	0.476790i	$0.158200\pi$
$570$		0			0
$571$	5.12217	+	5.42919i	0.214356	+	0.227204i	0.825626	−	0.564218i	$-0.190822\pi$
$571$	5.12217	+	5.42919i	0.214356	+	0.227204i	−0.611269	+	0.791423i	$0.709341\pi$
$572$	−0.351128	−	6.02864i	−0.0146814	−	0.252070i
$573$		0			0
$574$	4.34452	+	1.02967i	0.181337	+	0.0429776i
$575$	16.0390	−	5.83772i	0.668873	−	0.243450i
$576$		0			0
$577$	38.2457	+	13.9203i	1.59219	+	0.579510i	0.977809	−	0.209499i	$-0.0671832\pi$
$577$	38.2457	+	13.9203i	1.59219	+	0.579510i	0.614382	+	0.789009i	$0.289405\pi$
$578$	15.6816	+	10.3140i	0.652270	+	0.429005i
$579$		0			0
$580$	2.25419	+	0.263477i	0.0936000	+	0.0109403i
$581$	29.8118	−	40.0442i	1.23680	−	1.66131i
$582$		0			0
$583$	0.114192	−	1.96060i	0.00472935	−	0.0811998i
$584$	32.1382	−	26.9671i	1.32989	−	1.11591i
$585$		0			0
$586$	−20.5530	−	17.2460i	−0.849038	−	0.712428i
$587$	−1.81042	+	1.91894i	−0.0747242	+	0.0792030i	−0.763657	−	0.645622i	$-0.776598\pi$
$587$	−1.81042	+	1.91894i	−0.0747242	+	0.0792030i	0.688933	+	0.724825i	$0.258080\pi$
$588$		0			0
$589$	−3.02811	+	1.99162i	−0.124771	+	0.0820633i
$590$	5.49229	−	1.30170i	0.226114	−	0.0535900i
$591$		0			0
$592$	−2.77060	+	0.323836i	−0.113871	+	0.0133096i
$593$	4.37859	−	7.58393i	0.179807	−	0.311435i	−0.762007	−	0.647568i	$-0.775786\pi$
$593$	4.37859	−	7.58393i	0.179807	−	0.311435i	0.941814	+	0.336134i	$0.109119\pi$
$594$		0			0
$595$	−6.53354	−	11.3164i	−0.267849	−	0.463928i
$596$	5.84797	+	7.85519i	0.239542	+	0.321761i
$597$		0			0
$598$	4.76099	−	15.9028i	0.194691	−	0.650315i
$599$	−13.4342	−	6.74691i	−0.548906	−	0.275671i	0.152656	−	0.988279i	$-0.451217\pi$
$599$	−13.4342	−	6.74691i	−0.548906	−	0.275671i	−0.701562	+	0.712608i	$0.747514\pi$
$600$		0			0
$601$	−1.44763	−	4.83540i	−0.0590499	−	0.197240i	0.923375	−	0.383900i	$-0.125419\pi$
$601$	−1.44763	−	4.83540i	−0.0590499	−	0.197240i	−0.982425	+	0.186659i	$0.940234\pi$
$602$	4.13251	−	23.4366i	0.168428	−	0.955205i
$603$		0			0
$604$	−1.32975	−	7.54141i	−0.0541069	−	0.306856i
$605$	5.67623	−	2.85071i	0.230771	−	0.115898i
$606$		0			0
$607$	12.6908	+	29.4206i	0.515104	+	1.19414i	0.955137	+	0.296164i	$0.0957073\pi$
$607$	12.6908	+	29.4206i	0.515104	+	1.19414i	−0.440033	+	0.897981i	$0.645033\pi$
$608$	−11.4295	−	26.4965i	−0.463527	−	1.07458i
$609$		0			0
$610$	−8.69469	+	4.36664i	−0.352038	+	0.176800i
$611$	−8.36163	−	47.4212i	−0.338275	−	1.91846i
$612$		0			0
$613$	−4.00790	+	22.7299i	−0.161877	+	0.918052i	0.790348	+	0.612658i	$0.209900\pi$
$613$	−4.00790	+	22.7299i	−0.161877	+	0.918052i	−0.952226	+	0.305395i	$0.901212\pi$
$614$	0.952405	+	3.18125i	0.0384359	+	0.128385i
$615$		0			0
$616$	−12.8874	−	6.47229i	−0.519248	−	0.260776i
$617$	−2.87197	+	9.59306i	−0.115621	+	0.386202i	−0.996137	−	0.0878153i	$-0.972011\pi$
$617$	−2.87197	+	9.59306i	−0.115621	+	0.386202i	0.880515	+	0.474017i	$0.157197\pi$
$618$		0			0
$619$	11.5177	+	15.4710i	0.462935	+	0.621830i	0.970882	−	0.239558i	$-0.0770027\pi$
$619$	11.5177	+	15.4710i	0.462935	+	0.621830i	−0.507947	+	0.861389i	$0.669595\pi$
$620$	−0.199788	−	0.346044i	−0.00802369	−	0.0138974i
$621$		0			0
$622$	0.673787	−	1.16703i	0.0270164	−	0.0467938i
$623$	−10.3849	+	1.21383i	−0.416064	+	0.0486309i
$624$		0			0
$625$	16.1559	−	3.82903i	0.646238	−	0.153161i
$626$	9.13373	−	6.00735i	0.365057	−	0.240102i
$627$		0			0
$628$	−8.79538	+	9.32256i	−0.350974	+	0.372011i
$629$	9.10045	+	7.63618i	0.362859	+	0.304475i
$630$		0			0
$631$	22.1834	−	18.6140i	0.883105	−	0.741013i	−0.0837097	−	0.996490i	$-0.526677\pi$
$631$	22.1834	−	18.6140i	0.883105	−	0.741013i	0.966815	+	0.255477i	$0.0822324\pi$
$632$	0.762125	−	13.0852i	0.0303157	−	0.520501i
$633$		0			0
$634$	16.9836	−	22.8129i	0.674505	−	0.906018i
$635$	10.2583	+	1.19902i	0.407086	+	0.0475816i
$636$		0			0
$637$	−4.79474	−	3.15355i	−0.189975	−	0.124948i
$638$	5.32190	+	1.93701i	0.210696	+	0.0766871i
$639$		0			0
$640$	0.903547	−	0.328864i	0.0357158	−	0.0129995i
$641$	48.0872	+	11.3969i	1.89933	+	0.450150i	0.999915	+	0.0130551i	$0.00415568\pi$
$641$	48.0872	+	11.3969i	1.89933	+	0.450150i	0.899416	+	0.437094i	$0.143992\pi$
$642$		0			0
$643$	−0.833314	−	14.3074i	−0.0328627	−	0.564231i	−0.974048	−	0.226341i	$-0.927324\pi$
$643$	−0.833314	−	14.3074i	−0.0328627	−	0.564231i	0.941186	−	0.337890i	$-0.109713\pi$
$644$	6.92198	+	7.33687i	0.272764	+	0.289113i
$645$		0			0
$646$	15.2965	−	35.4612i	0.601832	−	1.39520i
$647$	−14.0663			−0.553003			−0.276501	−	0.961013i	$-0.589175\pi$
$647$	−14.0663			−0.553003			−0.276501	+	0.961013i	$0.589175\pi$
$648$		0			0
$649$	−11.5415			−0.453045
$650$	7.51764	−	17.4278i	0.294866	−	0.683576i
$651$		0			0
$652$	−1.30720	−	1.38555i	−0.0511939	−	0.0542624i
$653$	0.682581	+	11.7195i	0.0267115	+	0.458618i	0.984971	+	0.172719i	$0.0552552\pi$
$653$	0.682581	+	11.7195i	0.0267115	+	0.458618i	−0.958260	+	0.285899i	$0.907708\pi$
$654$		0			0
$655$	11.1010	+	2.63099i	0.433753	+	0.102801i
$656$	−1.91527	+	0.697100i	−0.0747785	+	0.0272172i
$657$		0			0
$658$	−33.5543	−	12.2128i	−1.30808	−	0.476103i
$659$	−37.6271	−	24.7477i	−1.46574	−	0.964034i	−0.996727	−	0.0808436i	$-0.974239\pi$
$659$	−37.6271	−	24.7477i	−1.46574	−	0.964034i	−0.469015	−	0.883190i	$-0.655391\pi$
$660$		0			0
$661$	−5.54506	−	0.648124i	−0.215678	−	0.0252091i	0.00756779	−	0.999971i	$-0.497591\pi$
$661$	−5.54506	−	0.648124i	−0.215678	−	0.0252091i	−0.223245	+	0.974762i	$0.571665\pi$
$662$	3.92588	−	5.27337i	0.152584	−	0.204956i
$663$		0			0
$664$	−3.04592	+	52.2964i	−0.118204	+	2.02949i
$665$	−10.5643	+	8.86450i	−0.409666	+	0.343750i
$666$		0			0
$667$	−9.77219	−	8.19984i	−0.378381	−	0.317499i
$668$	4.89129	−	5.18446i	0.189250	−	0.200593i
$669$		0			0
$670$	1.56694	−	1.03059i	0.0605361	−	0.0398152i
$671$	19.3585	−	4.58804i	0.747326	−	0.177119i
$672$		0			0
$673$	2.58958	−	0.302678i	0.0998209	−	0.0116674i	−0.0660358	−	0.997817i	$-0.521035\pi$
$673$	2.58958	−	0.302678i	0.0998209	−	0.0116674i	0.165857	+	0.986150i	$0.446961\pi$
$674$	2.91206	−	5.04384i	0.112168	−	0.194281i
$675$		0			0
$676$	1.70810	+	2.95852i	0.0656962	+	0.113789i
$677$	−16.4729	−	22.1269i	−0.633104	−	0.850406i	0.363598	−	0.931556i	$-0.381548\pi$
$677$	−16.4729	−	22.1269i	−0.633104	−	0.850406i	−0.996702	+	0.0811498i	$0.974141\pi$
$678$		0			0
$679$	−9.10893	+	30.4259i	−0.349569	+	1.16764i
$680$	12.2531	+	6.15373i	0.469884	+	0.235985i
$681$		0			0
$682$	−0.285975	−	0.955224i	−0.0109506	−	0.0365774i
$683$	−2.34587	+	13.3041i	−0.0897621	+	0.509066i	0.906465	+	0.422281i	$0.138771\pi$
$683$	−2.34587	+	13.3041i	−0.0897621	+	0.509066i	−0.996227	+	0.0867852i	$0.972341\pi$
$684$		0			0
$685$	1.76161	+	9.99058i	0.0673076	+	0.381720i
$686$	15.2060	−	7.63673i	0.580567	−	0.291572i
$687$		0			0
$688$	4.30289	+	9.97523i	0.164046	+	0.380302i
$689$	1.94837	+	4.51683i	0.0742269	+	0.172077i
$690$		0			0
$691$	−14.5223	+	7.29338i	−0.552455	+	0.277453i	−0.703048	−	0.711143i	$-0.748178\pi$
$691$	−14.5223	+	7.29338i	−0.552455	+	0.277453i	0.150593	+	0.988596i	$0.451882\pi$
$692$	3.06463	+	17.3804i	0.116500	+	0.660703i
$693$		0			0
$694$	4.93481	−	27.9867i	0.187323	−	1.06236i
$695$	2.81308	+	9.39633i	0.106706	+	0.356423i
$696$		0			0
$697$	7.75696	+	3.89569i	0.293816	+	0.147560i
$698$	−6.33231	+	21.1514i	−0.239682	+	0.800592i
$699$		0			0
$700$	6.88697	+	9.25081i	0.260303	+	0.349648i
$701$	−9.28318	−	16.0789i	−0.350621	−	0.607293i	0.635738	−	0.771905i	$-0.280696\pi$
$701$	−9.28318	−	16.0789i	−0.350621	−	0.607293i	−0.986358	+	0.164612i	$0.947363\pi$
$702$		0			0
$703$	6.26884	−	10.8579i	0.236434	−	0.409515i
$704$	12.3935	−	1.44859i	0.467097	−	0.0545958i
$705$		0			0
$706$	−20.6899	+	4.90359i	−0.778674	+	0.184549i
$707$	21.9598	−	14.4432i	0.825883	−	0.543192i
$708$		0			0
$709$	2.41271	−	2.55732i	0.0906111	−	0.0960421i	−0.680481	−	0.732766i	$-0.738229\pi$
$709$	2.41271	−	2.55732i	0.0906111	−	0.0960421i	0.771092	+	0.636723i	$0.219711\pi$
$710$	−6.67048	−	5.59720i	−0.250339	−	0.210059i
$711$		0			0
$712$	8.40451	−	7.05222i	0.314972	−	0.264293i
$713$	−0.130591	+	2.24216i	−0.00489067	+	0.0839695i
$714$		0			0
$715$	3.05526	−	4.10392i	0.114260	−	0.153478i
$716$	16.0708	+	1.87841i	0.600594	+	0.0701993i
$717$		0			0
$718$	4.54956	+	2.99229i	0.169788	+	0.111671i
$719$	−26.7826	−	9.74806i	−0.998821	−	0.363541i	−0.209691	−	0.977768i	$-0.567246\pi$
$719$	−26.7826	−	9.74806i	−0.998821	−	0.363541i	−0.789130	+	0.614226i	$0.789468\pi$
$720$		0			0
$721$	17.7263	−	6.45183i	0.660160	−	0.240279i
$722$	−20.2760	−	4.80550i	−0.754595	−	0.178842i
$723$		0			0
$724$	−0.163562	−	2.80824i	−0.00607872	−	0.104368i
$725$	−10.0092	−	10.6092i	−0.371733	−	0.394014i
$726$		0			0
$727$	−11.9804	+	27.7738i	−0.444330	+	1.03007i	0.538005	+	0.842941i	$0.319178\pi$
$727$	−11.9804	+	27.7738i	−0.444330	+	1.03007i	−0.982335	+	0.187131i	$0.940081\pi$
$728$	36.1218			1.33876
$729$		0			0
$730$	11.0372			0.408507
$731$	18.3252	−	42.4827i	0.677784	−	1.57128i
$732$		0			0
$733$	−1.18301	−	1.25392i	−0.0436955	−	0.0463145i	0.705157	−	0.709051i	$-0.250876\pi$
$733$	−1.18301	−	1.25392i	−0.0436955	−	0.0463145i	−0.748853	+	0.662737i	$0.769395\pi$
$734$	0.339886	+	5.83561i	0.0125454	+	0.215396i
$735$		0			0
$736$	−17.3999	−	4.12386i	−0.641369	−	0.152007i
$737$	−3.60364	+	1.31162i	−0.132742	+	0.0483140i
$738$		0			0
$739$	−1.24530	−	0.453252i	−0.0458091	−	0.0166732i	0.319014	−	0.947750i	$-0.396648\pi$
$739$	−1.24530	−	0.453252i	−0.0458091	−	0.0166732i	−0.364823	+	0.931077i	$0.618871\pi$
$740$	1.15485	+	0.759557i	0.0424531	+	0.0279219i
$741$		0			0
$742$	3.62313	+	0.423483i	0.133009	+	0.0155465i
$743$	−24.2138	+	32.5248i	−0.888318	+	1.19322i	0.0919936	+	0.995760i	$0.470676\pi$
$743$	−24.2138	+	32.5248i	−0.888318	+	1.19322i	−0.980311	+	0.197458i	$0.936731\pi$
$744$		0			0
$745$	−0.482425	+	8.28292i	−0.0176747	+	0.303463i
$746$	26.5904	−	22.3120i	0.973545	−	0.816902i
$747$		0			0
$748$	−6.66920	−	5.59613i	−0.243850	−	0.204615i
$749$	22.1226	−	23.4485i	0.808341	−	0.856791i
$750$		0			0
$751$	11.9765	−	7.87707i	0.437029	−	0.287438i	−0.311867	−	0.950126i	$-0.600954\pi$
$751$	11.9765	−	7.87707i	0.437029	−	0.287438i	0.748896	+	0.662687i	$0.230584\pi$
$752$	15.8610	−	3.75912i	0.578390	−	0.137081i
$753$		0			0
$754$	−14.0896	+	1.64684i	−0.513112	+	0.0599742i
$755$	3.24395	−	5.61869i	0.118059	−	0.204485i
$756$		0			0
$757$	−21.3641	−	37.0037i	−0.776491	−	1.34492i	−0.933953	−	0.357397i	$-0.883664\pi$
$757$	−21.3641	−	37.0037i	−0.776491	−	1.34492i	0.157462	−	0.987525i	$-0.449669\pi$
$758$	1.09193	+	1.46671i	0.0396605	+	0.0532734i
$759$		0			0
$760$	4.15029	−	13.8629i	0.150547	−	0.502862i
$761$	2.79203	+	1.40221i	0.101211	+	0.0508300i	0.498684	−	0.866784i	$-0.333817\pi$
$761$	2.79203	+	1.40221i	0.101211	+	0.0508300i	−0.397474	+	0.917614i	$0.630113\pi$
$762$		0			0
$763$	6.91208	+	23.0880i	0.250234	+	0.835841i
$764$	−1.37020	+	7.77079i	−0.0495721	+	0.281137i
$765$		0			0
$766$	−5.61864	−	31.8649i	−0.203010	−	1.15133i
$767$	25.8337	−	12.9742i	0.932802	−	0.468471i
$768$		0			0
$769$	−4.62658	−	10.7256i	−0.166839	−	0.386776i	0.814201	−	0.580584i	$-0.197176\pi$
$769$	−4.62658	−	10.7256i	−0.166839	−	0.386776i	−0.981040	+	0.193808i	$0.937916\pi$
$770$	−1.50273	−	3.48373i	−0.0541548	−	0.125545i
$771$		0			0
$772$	14.2431	−	7.15316i	0.512621	−	0.257448i
$773$	5.48952	+	31.1326i	0.197444	+	1.11976i	0.908895	+	0.417026i	$0.136928\pi$
$773$	5.48952	+	31.1326i	0.197444	+	1.11976i	−0.711450	+	0.702737i	$0.751961\pi$
$774$		0			0
$775$	−0.445920	+	2.52894i	−0.0160179	+	0.0908422i
$776$	−9.55818	−	31.9266i	−0.343119	−	1.14610i
$777$		0			0
$778$	24.7660	+	12.4380i	0.887905	+	0.445923i
$779$	2.62739	−	8.77609i	0.0941360	−	0.314436i
$780$		0			0
$781$	10.6325	+	14.2819i	0.380461	+	0.511048i
$782$	−11.9660	−	20.7257i	−0.427903	−	0.741149i
$783$		0			0
$784$	0.971340	−	1.68241i	0.0346907	−	0.0600861i
$785$	−10.7854	+	1.26063i	−0.384946	+	0.0449937i
$786$		0			0
$787$	−11.3967	+	2.70107i	−0.406248	+	0.0962826i	−0.428659	−	0.903466i	$-0.641014\pi$
$787$	−11.3967	+	2.70107i	−0.406248	+	0.0962826i	0.0224110	+	0.999749i	$0.492866\pi$
$788$	4.89468	−	3.21928i	0.174366	−	0.114682i
$789$		0			0
$790$	2.36639	−	2.50822i	0.0841923	−	0.0892386i
$791$	9.04970	+	7.59360i	0.321770	+	0.269997i
$792$		0			0
$793$	−38.1730	+	32.0309i	−1.35556	+	1.13745i
$794$	−2.09232	+	35.9237i	−0.0742536	+	1.27489i
$795$		0			0
$796$	−8.59503	+	11.5451i	−0.304643	+	0.409206i
$797$	−29.0061	−	3.39033i	−1.02745	−	0.120092i	−0.414367	−	0.910110i	$-0.635997\pi$
$797$	−29.0061	−	3.39033i	−1.02745	−	0.120092i	−0.613083	+	0.790018i	$0.710071\pi$
$798$		0			0
$799$	−57.9998	−	38.1470i	−2.05188	−	1.34955i
$800$	−19.2126	−	6.99280i	−0.679267	−	0.247233i
$801$		0			0
$802$	−0.179234	+	0.0652358i	−0.00632897	+	0.00230356i
$803$	−21.9602	−	5.20467i	−0.774959	−	0.183669i
$804$		0			0
$805$	0.496899	+	8.53142i	0.0175134	+	0.300693i
$806$	1.71390	+	1.81663i	0.0603696	+	0.0639880i
$807$		0			0
$808$	−10.9239	+	25.3245i	−0.384303	+	0.890913i
$809$	25.8550			0.909015			0.454508	−	0.890743i	$-0.349815\pi$
$809$	25.8550			0.909015			0.454508	+	0.890743i	$0.349815\pi$
$810$		0			0
$811$	44.4567			1.56109			0.780544	−	0.625101i	$-0.214942\pi$
$811$	44.4567			1.56109			0.780544	+	0.625101i	$0.214942\pi$
$812$	3.41403	−	7.91461i	0.119809	−	0.277749i
$813$		0			0
$814$	2.36705	+	2.50892i	0.0829650	+	0.0879377i
$815$	−0.0938381	−	1.61114i	−0.00328701	−	0.0564357i
$816$		0			0
$817$	−47.5125	−	11.2607i	−1.66225	−	0.393961i
$818$	−5.96250	+	2.17017i	−0.208474	+	0.0758783i
$819$		0			0
$820$	0.949062	+	0.345430i	0.0331427	+	0.0120630i
$821$	−5.30694	−	3.49043i	−0.185214	−	0.121817i	0.453516	−	0.891248i	$-0.350169\pi$
$821$	−5.30694	−	3.49043i	−0.185214	−	0.121817i	−0.638730	+	0.769431i	$0.720540\pi$
$822$		0			0
$823$	−12.7230	−	1.48711i	−0.443496	−	0.0518373i	−0.108585	−	0.994087i	$-0.534632\pi$
$823$	−12.7230	−	1.48711i	−0.443496	−	0.0518373i	−0.334911	+	0.942250i	$0.608706\pi$
$824$	−11.8203	+	15.8774i	−0.411780	+	0.553116i
$825$		0			0
$826$	1.24647	−	21.4010i	0.0433701	−	0.744636i
$827$	5.25528	−	4.40970i	0.182744	−	0.153340i	−0.546827	−	0.837246i	$-0.684164\pi$
$827$	5.25528	−	4.40970i	0.182744	−	0.153340i	0.729571	+	0.683905i	$0.239720\pi$
$828$		0			0
$829$	−27.7337	−	23.2713i	−0.963231	−	0.808246i	0.0182451	−	0.999834i	$-0.494192\pi$
$829$	−27.7337	−	23.2713i	−0.963231	−	0.808246i	−0.981476	+	0.191587i	$0.938637\pi$
$830$	−9.45753	+	10.0244i	−0.328276	+	0.347952i
$831$		0			0
$832$	−26.1122	+	17.1743i	−0.905279	+	0.595411i
$833$	−8.05050	+	1.90800i	−0.278933	+	0.0661084i
$834$		0			0
$835$	5.99795	−	0.701060i	0.207568	−	0.0242612i
$836$	−4.59407	+	7.95717i	−0.158889	+	0.275205i
$837$		0			0
$838$	10.9162	+	18.9075i	0.377095	+	0.653149i
$839$	10.9742	+	14.7409i	0.378872	+	0.508913i	0.950129	−	0.311858i	$-0.100951\pi$
$839$	10.9742	+	14.7409i	0.378872	+	0.508913i	−0.571257	+	0.820771i	$0.693544\pi$
$840$		0			0
$841$	5.19083	−	17.3386i	0.178994	−	0.597882i
$842$	11.1369	+	5.59317i	0.383803	+	0.192753i
$843$		0			0
$844$	3.16808	+	10.5821i	0.109050	+	0.364251i
$845$	−0.502594	+	2.85035i	−0.0172897	+	0.0980550i
$846$		0			0
$847$	−4.18909	−	23.7575i	−0.143939	−	0.816317i
$848$	−1.48807	+	0.747337i	−0.0511006	+	0.0256637i
$849$		0			0
$850$	−10.8379	−	25.1252i	−0.371738	−	0.861786i
$851$	−3.07730	−	7.13398i	−0.105488	−	0.244550i
$852$		0			0
$853$	10.7797	−	5.41377i	0.369090	−	0.185364i	−0.254580	−	0.967052i	$-0.581937\pi$
$853$	10.7797	−	5.41377i	0.369090	−	0.185364i	0.623670	+	0.781688i	$0.285641\pi$
$854$	6.41674	+	36.3911i	0.219576	+	1.24528i
$855$		0			0
$856$	−5.87404	+	33.3133i	−0.200770	+	1.13863i
$857$	−5.80165	−	19.3789i	−0.198181	−	0.661970i	−0.998086	−	0.0618432i	$-0.980302\pi$
$857$	−5.80165	−	19.3789i	−0.198181	−	0.661970i	0.799905	−	0.600126i	$-0.204883\pi$
$858$		0			0
$859$	−24.3125	−	12.2102i	−0.829533	−	0.416607i	−0.0172360	−	0.999851i	$-0.505487\pi$
$859$	−24.3125	−	12.2102i	−0.829533	−	0.416607i	−0.812297	+	0.583244i	$0.801783\pi$
$860$	1.54393	−	5.15709i	0.0526476	−	0.175855i
$861$		0			0
$862$	6.45781	+	8.67434i	0.219954	+	0.295449i
$863$	13.5593	+	23.4854i	0.461564	+	0.799452i	0.999039	−	0.0438272i	$-0.0139551\pi$
$863$	13.5593	+	23.4854i	0.461564	+	0.799452i	−0.537475	+	0.843280i	$0.680622\pi$
$864$		0			0
$865$	−7.47621	+	12.9492i	−0.254199	+	0.440285i
$866$	−0.0410667	+	0.00480000i	−0.00139550	+	0.000163111i
$867$		0			0
$868$	−1.47666	+	0.349976i	−0.0501212	+	0.0118790i
$869$	−5.89104	+	3.87460i	−0.199840	+	0.131437i
$870$		0			0
$871$	6.59168	−	6.98677i	0.223351	−	0.236738i
$872$	−19.3726	−	16.2555i	−0.656037	−	0.550481i
$873$		0			0
$874$	−19.3482	+	16.2351i	−0.654463	+	0.549159i
$875$	−1.21117	+	20.7950i	−0.0409451	+	0.703000i
$876$		0			0
$877$	2.65601	−	3.56764i	0.0896871	−	0.120471i	−0.755015	−	0.655708i	$-0.772370\pi$
$877$	2.65601	−	3.56764i	0.0896871	−	0.120471i	0.844702	+	0.535237i	$0.179778\pi$
$878$	−4.67839	−	0.546826i	−0.157888	−	0.0184545i
$879$		0			0
$880$	1.44702	+	0.951719i	0.0487790	+	0.0320824i
$881$	35.6358	+	12.9704i	1.20060	+	0.436983i	0.863434	−	0.504463i	$-0.168309\pi$
$881$	35.6358	+	12.9704i	1.20060	+	0.436983i	0.337166	+	0.941445i	$0.390532\pi$
$882$		0			0
$883$	−25.5461	+	9.29801i	−0.859694	+	0.312903i	−0.733986	−	0.679164i	$-0.762342\pi$
$883$	−25.5461	+	9.29801i	−0.859694	+	0.312903i	−0.125708	+	0.992067i	$0.540120\pi$
$884$	21.2186	+	5.02890i	0.713659	+	0.169140i
$885$		0			0
$886$	−0.505980	−	8.68734i	−0.0169987	−	0.291857i
$887$	−12.7198	−	13.4823i	−0.427091	−	0.452690i	0.477715	−	0.878515i	$-0.341465\pi$
$887$	−12.7198	−	13.4823i	−0.427091	−	0.452690i	−0.904805	+	0.425825i	$0.859984\pi$
$888$		0			0
$889$	15.5364	−	36.0175i	0.521075	−	1.20799i
$890$	2.88637			0.0967514
$891$		0			0
$892$	−1.58171			−0.0529596
$893$	−29.0186	+	67.2727i	−0.971071	+	2.25120i
$894$		0			0
$895$	9.40728	+	9.97113i	0.314451	+	0.333298i
$896$	−0.212336	−	3.64568i	−0.00709366	−	0.121793i
$897$		0			0
$898$	27.4740	+	6.51146i	0.916819	+	0.217290i
$899$	1.80351	−	0.656425i	0.0601505	−	0.0218930i
$900$		0			0
$901$	6.66407	+	2.42552i	0.222012	+	0.0808059i
$902$	2.10569	+	1.38493i	0.0701116	+	0.0461132i
$903$		0			0
$904$	−12.3124	−	1.43911i	−0.409503	−	0.0478641i
$905$	1.42319	−	1.91168i	0.0473085	−	0.0635463i
$906$		0			0
$907$	0.310228	−	5.32641i	0.0103010	−	0.176860i	−0.989233	−	0.146347i	$-0.953249\pi$
$907$	0.310228	−	5.32641i	0.0103010	−	0.176860i	0.999534	−	0.0305140i	$-0.00971441\pi$
$908$	12.2292	−	10.2615i	0.405840	−	0.340540i
$909$		0			0
$910$	7.27977	+	6.10845i	0.241322	+	0.202493i
$911$	−15.1057	+	16.0111i	−0.500473	+	0.530471i	−0.927527	−	0.373755i	$-0.878070\pi$
$911$	−15.1057	+	16.0111i	−0.500473	+	0.530471i	0.427054	+	0.904226i	$0.359551\pi$
$912$		0			0
$913$	23.5442	−	15.4853i	0.779199	−	0.512487i
$914$	26.4829	−	6.27656i	0.875976	−	0.207610i
$915$		0			0
$916$	3.26579	−	0.381716i	0.107905	−	0.0126123i
$917$	21.6645	−	37.5241i	0.715426	−	1.23915i
$918$		0			0
$919$	2.28274	+	3.95382i	0.0753005	+	0.130424i	0.901217	−	0.433368i	$-0.142675\pi$
$919$	2.28274	+	3.95382i	0.0753005	+	0.130424i	−0.825916	+	0.563793i	$0.809342\pi$
$920$	−5.35494	−	7.19293i	−0.176547	−	0.237144i
$921$		0			0
$922$	−0.747342	+	2.49629i	−0.0246124	+	0.0822111i
$923$	−39.8537	−	20.0153i	−1.31180	−	0.658812i
$924$		0			0
$925$	−2.54775	−	8.51007i	−0.0837694	−	0.279809i
$926$	3.67666	−	20.8514i	0.120823	−	0.685219i
$927$		0			0
$928$	2.65348	+	15.0486i	0.0871048	+	0.493996i
$929$	−39.2166	+	19.6953i	−1.28665	+	0.646182i	−0.954828	−	0.297158i	$-0.903961\pi$
$929$	−39.2166	+	19.6953i	−1.28665	+	0.646182i	−0.331826	+	0.943341i	$0.607665\pi$
$930$		0			0
$931$	3.45845	+	8.01758i	0.113346	+	0.262766i
$932$	8.01738	+	18.5864i	0.262618	+	0.608817i
$933$		0			0
$934$	−8.72367	+	4.38119i	−0.285447	+	0.143357i
$935$	−1.28084	−	7.26398i	−0.0418878	−	0.237558i
$936$		0			0
$937$	−5.69877	+	32.3193i	−0.186171	+	1.05583i	0.738271	+	0.674504i	$0.235642\pi$
$937$	−5.69877	+	32.3193i	−0.186171	+	1.05583i	−0.924442	+	0.381323i	$0.875469\pi$
$938$	−2.04289	−	6.82372i	−0.0667027	−	0.222802i
$939$		0			0
$940$	−7.21808	−	3.62505i	−0.235428	−	0.118236i
$941$	−9.50489	+	31.7485i	−0.309850	+	1.03497i	0.651271	+	0.758845i	$0.274236\pi$
$941$	−9.50489	+	31.7485i	−0.309850	+	1.03497i	−0.961121	+	0.276127i	$0.910949\pi$
$942$		0			0
$943$	−3.39000	−	4.55356i	−0.110394	−	0.148284i
$944$	4.89299	+	8.47490i	0.159253	+	0.275835i
$945$		0			0
$946$	6.71673	−	11.6337i	0.218380	−	0.378245i
$947$	45.6739	−	5.33852i	1.48420	−	0.173479i	0.664941	−	0.746896i	$-0.268457\pi$
$947$	45.6739	−	5.33852i	1.48420	−	0.173479i	0.819263	+	0.573418i	$0.194383\pi$
$948$		0			0
$949$	55.0048	−	13.0364i	1.78553	−	0.423179i
$950$	−24.1275	+	15.8689i	−0.782799	+	0.514855i
$951$		0			0
$952$	35.7365	−	37.8785i	1.15823	−	1.22765i
$953$	−39.6249	−	33.2492i	−1.28358	−	1.07705i	−0.992741	−	0.120275i	$-0.961622\pi$
$953$	−39.6249	−	33.2492i	−1.28358	−	1.07705i	−0.290835	−	0.956773i	$-0.593933\pi$
$954$		0			0
$955$	−5.12119	+	4.29719i	−0.165718	+	0.139054i
$956$	0.190187	−	3.26538i	0.00615109	−	0.105610i
$957$		0			0
$958$	12.2665	−	16.4768i	0.396313	−	0.532341i
$959$	38.2685	+	4.47295i	1.23575	+	0.144439i
$960$		0			0
$961$	25.6178	+	16.8491i	0.826381	+	0.543519i
$962$	−8.11857	−	2.95492i	−0.261753	−	0.0952704i
$963$		0			0
$964$	4.35654	−	1.58565i	0.140315	−	0.0510704i
$965$	13.1396	+	3.11414i	0.422979	+	0.100248i
$966$		0			0
$967$	3.61111	+	62.0003i	0.116125	+	1.99380i	0.111108	+	0.993808i	$0.464560\pi$
$967$	3.61111	+	62.0003i	0.116125	+	1.99380i	0.00501741	+	0.999987i	$0.498403\pi$
$968$	17.3714	+	18.4126i	0.558337	+	0.591803i
$969$		0			0
$970$	3.47270	−	8.05063i	0.111502	−	0.258490i
$971$	−21.6241			−0.693949			−0.346975	−	0.937875i	$-0.612791\pi$
$971$	−21.6241			−0.693949			−0.346975	+	0.937875i	$0.612791\pi$
$972$		0			0
$973$	37.2517			1.19423
$974$	4.04533	−	9.37813i	0.129621	−	0.300495i
$975$		0			0
$976$	−11.5759	−	12.2698i	−0.370536	−	0.392745i
$977$	−3.42043	−	58.7266i	−0.109429	−	1.87883i	−0.392529	−	0.919740i	$-0.628400\pi$
$977$	−3.42043	−	58.7266i	−0.109429	−	1.87883i	0.283100	−	0.959091i	$-0.408637\pi$
$978$		0			0
$979$	−5.74286	−	1.36108i	−0.183543	−	0.0435004i
$980$	−0.904592	+	0.329244i	−0.0288961	+	0.0105173i
$981$		0			0
$982$	0.873782	+	0.318031i	0.0278835	+	0.0101488i
$983$	−30.7514	−	20.2255i	−0.980816	−	0.645093i	−0.0455218	−	0.998963i	$-0.514495\pi$
$983$	−30.7514	−	20.2255i	−0.980816	−	0.645093i	−0.935294	+	0.353870i	$0.884865\pi$
$984$		0			0
$985$	4.92994	+	0.576227i	0.157081	+	0.0183601i
$986$	−12.2124	+	16.4041i	−0.388921	+	0.522411i
$987$		0			0
$988$	1.33815	−	22.9751i	0.0425721	−	0.730934i
$989$	−23.1792	+	19.4497i	−0.737057	+	0.618464i
$990$		0			0
$991$	27.7566	+	23.2906i	0.881718	+	0.739850i	0.966532	−	0.256547i	$-0.0825849\pi$
$991$	27.7566	+	23.2906i	0.881718	+	0.739850i	−0.0848132	+	0.996397i	$0.527029\pi$
$992$	1.84623	−	1.95689i	0.0586180	−	0.0621314i
$993$		0			0
$994$	−27.6307	+	18.1730i	−0.876393	+	0.576412i
$995$	−11.8657	+	2.81223i	−0.376168	+	0.0891535i
$996$		0			0
$997$	13.6734	−	1.59819i	0.433040	−	0.0506151i	0.103219	−	0.994659i	$-0.467086\pi$
$997$	13.6734	−	1.59819i	0.433040	−	0.0506151i	0.329821	+	0.944044i	$0.393012\pi$
$998$	−10.7703	+	18.6547i	−0.340928	+	0.590505i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.55.3		144
3.2	odd	2		729.2.g.a.55.6		144
9.2	odd	6		243.2.g.a.19.3		144
9.4	even	3		729.2.g.c.541.3		144
9.5	odd	6		729.2.g.b.541.6		144
9.7	even	3		81.2.g.a.61.6	yes	144
81.4	even	27		729.2.g.c.190.3		144
81.23	odd	54		243.2.g.a.64.3		144
81.29	odd	54		6561.2.a.d.1.45		72
81.31	even	27	inner	729.2.g.d.676.3		144
81.50	odd	54		729.2.g.a.676.6		144
81.52	even	27		6561.2.a.c.1.28		72
81.58	even	27		81.2.g.a.4.6	✓	144
81.77	odd	54		729.2.g.b.190.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.6	✓	144	81.58	even	27
81.2.g.a.61.6	yes	144	9.7	even	3
243.2.g.a.19.3		144	9.2	odd	6
243.2.g.a.64.3		144	81.23	odd	54
729.2.g.a.55.6		144	3.2	odd	2
729.2.g.a.676.6		144	81.50	odd	54
729.2.g.b.190.6		144	81.77	odd	54
729.2.g.b.541.6		144	9.5	odd	6
729.2.g.c.190.3		144	81.4	even	27
729.2.g.c.541.3		144	9.4	even	3
729.2.g.d.55.3		144	1.1	even	1	trivial
729.2.g.d.676.3		144	81.31	even	27	inner
6561.2.a.c.1.28		72	81.52	even	27
6561.2.a.d.1.45		72	81.29	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.415272 + 0.962709i) q^{2} +(0.618125 + 0.655174i) q^{4} +(0.0443725 + 0.761846i) q^{5} +(2.82023 + 0.668406i) q^{7} +(-2.85789 + 1.04019i) q^{8} +O(q^{10})\)	\(q+(-0.415272 + 0.962709i) q^{2} +(0.618125 + 0.655174i) q^{4} +(0.0443725 + 0.761846i) q^{5} +(2.82023 + 0.668406i) q^{7} +(-2.85789 + 1.04019i) q^{8} +(-0.751863 - 0.273656i) q^{10} +(1.36690 + 0.899022i) q^{11} +(-4.07018 - 0.475735i) q^{13} +(-1.81464 + 2.43749i) q^{14} +(0.0806579 - 1.38484i) q^{16} +(-4.52563 + 3.79745i) q^{17} +(4.77625 + 4.00775i) q^{19} +(-0.471714 + 0.499987i) q^{20} +(-1.43313 + 0.942586i) q^{22} +(3.75955 - 0.891030i) q^{23} +(4.38775 - 0.512855i) q^{25} +(2.14823 - 3.72084i) q^{26} +(1.30533 + 2.26090i) q^{28} +(-1.97163 - 2.64835i) q^{29} +(-0.166718 + 0.556877i) q^{31} +(-4.13590 - 2.07713i) q^{32} +(-1.77648 - 5.93384i) q^{34} +(-0.384082 + 2.17824i) q^{35} +(-0.349184 - 1.98032i) q^{37} +(-5.84174 + 2.93383i) q^{38} +(-0.919272 - 2.13111i) q^{40} +(-0.581956 - 1.34912i) q^{41} +(-6.99844 + 3.51475i) q^{43} +(0.255897 + 1.45126i) q^{44} +(-0.703435 + 3.98938i) q^{46} +(3.37012 + 11.2570i) q^{47} +(1.25148 + 0.628517i) q^{49} +(-1.32838 + 4.43710i) q^{50} +(-2.20419 - 2.96074i) q^{52} +(-0.600204 - 1.03958i) q^{53} +(-0.624264 + 1.08126i) q^{55} +(-8.75515 + 1.02333i) q^{56} +(3.36835 - 0.798315i) q^{58} +(-5.89398 + 3.87653i) q^{59} +(8.34487 - 8.84504i) q^{61} +(-0.466877 - 0.391757i) q^{62} +(5.84249 - 4.90243i) q^{64} +(0.181833 - 3.12196i) q^{65} +(-1.39975 + 1.88018i) q^{67} +(-5.28540 - 0.617774i) q^{68} +(-1.93751 - 1.27432i) q^{70} +(10.2267 + 3.72222i) q^{71} +(-12.9627 + 4.71802i) q^{73} +(2.05148 + 0.486209i) q^{74} +(0.326545 + 5.60657i) q^{76} +(3.25405 + 3.44909i) q^{77} +(-1.70702 + 3.95732i) q^{79} +1.05862 q^{80} +1.54049 q^{82} +(6.82230 - 15.8159i) q^{83} +(-3.09389 - 3.27933i) q^{85} +(-0.477423 - 8.19704i) q^{86} +(-4.84159 - 1.14748i) q^{88} +(-3.38989 + 1.23382i) q^{89} +(-11.1608 - 4.06221i) q^{91} +(2.90765 + 1.91239i) q^{92} +(-12.2367 - 1.43027i) q^{94} +(-2.84135 + 3.81660i) q^{95} +(-0.637153 + 10.9395i) q^{97} +(-1.12478 + 0.943807i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

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