LMFDB - Embedded newform 729.2.g.a.55.6

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			55.6
Character	$\chi$	$=$	729.55
Dual form			729.2.g.a.676.6

$q$-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	−0.705980	−	0.708232i	$-0.749493\pi$
$2$	0.415272	−	0.962709i	0.293642	−	0.680738i	0.999622	+	0.0274933i	$0.00875248\pi$
$3$		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	$-0.963934\pi$
$5$	−0.0443725	−	0.761846i	−0.0198440	−	0.340708i	0.973744	−	0.227646i	$-0.0731029\pi$
$6$		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	0.326465	−	0.945209i	$-0.394142\pi$
$11$	−1.36690	−	0.899022i	−0.412135	−	0.271065i	−0.738600	+	0.674144i	$0.764513\pi$
$12$		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	0.100363	−	0.994951i	$-0.468000\pi$
$17$	4.52563	−	3.79745i	1.09763	−	0.921018i	0.997263	+	0.0739329i	$0.0235551\pi$
$18$		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	−0.603038	−	0.797712i	$-0.706043\pi$
$23$	−3.75955	+	0.891030i	−0.783921	+	0.185793i	−0.180882	+	0.983505i	$0.557895\pi$
$24$		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	0.946565	−	0.322514i	$-0.104528\pi$
$29$	1.97163	+	2.64835i	0.366122	+	0.491787i	−0.580443	+	0.814301i	$0.697121\pi$
$30$		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	0.957596	−	0.288115i	$-0.0930286\pi$
$41$	0.581956	+	1.34912i	0.0908862	+	0.210698i	−0.866710	+	0.498813i	$0.833769\pi$
$42$		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	$-0.764917\pi$
$47$	−3.37012	−	11.2570i	−0.491582	−	1.64200i	0.247873	−	0.968793i	$-0.420269\pi$
$48$		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	0.904299	−	0.426899i	$-0.140394\pi$
$53$	0.600204	+	1.03958i	0.0824443	+	0.142798i	−0.821855	+	0.569697i	$0.807061\pi$
$54$		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	−0.104479	−	0.994527i	$-0.533317\pi$
$59$	5.89398	−	3.87653i	0.767330	−	0.504681i	0.871809	+	0.489846i	$0.162947\pi$
$60$		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	−0.345706	−	0.938343i	$-0.612361\pi$
$71$	−10.2267	−	3.72222i	−1.21369	−	0.441746i	−0.867981	+	0.496597i	$0.834583\pi$
$72$		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	$0.523880\pi$
$83$	−6.82230	+	15.8159i	−0.748844	+	1.73602i	−0.673893	+	0.738829i	$0.735379\pi$
$84$		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	−0.156047	−	0.987750i	$-0.549875\pi$
$89$	3.38989	−	1.23382i	0.359327	−	0.130784i	0.515374	+	0.856965i	$0.327653\pi$
$90$		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	−0.958750	−	0.284252i	$-0.908255\pi$
$101$	−6.22321	+	6.59621i	−0.619232	+	0.656348i	0.339517	+	0.940600i	$0.389736\pi$
$102$		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	$0.347348\pi$
$107$	−5.56131	+	9.63248i	−0.537632	+	0.931207i	−0.999031	+	0.0440137i	$0.985985\pi$
$108$		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	0.269150	−	0.963098i	$-0.413257\pi$
$113$	−3.64240	−	1.82928i	−0.342649	−	0.172085i	−0.611798	+	0.791014i	$0.709554\pi$
$114$		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	$0.319114\pi$
$131$	−4.28758	+	14.3215i	−0.374608	+	1.25128i	−0.912783	+	0.408444i	$0.866072\pi$
$132$		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	−0.659586	−	0.751629i	$-0.729268\pi$
$137$	−13.2035	+	1.54327i	−1.12805	+	0.131851i	−0.468469	+	0.883480i	$0.655194\pi$
$138$		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	−0.338385	−	0.941008i	$-0.609881\pi$
$149$	−10.7987	−	1.26218i	−0.884661	−	0.103402i	−0.546275	+	0.837606i	$0.683955\pi$
$150$		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	$0.0805282\pi$
$167$	0.460106	+	7.89972i	0.0356041	+	0.611299i	−0.932565	+	0.361002i	$0.882435\pi$
$168$		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	−0.255631	−	0.966774i	$-0.582283\pi$
$173$	−16.3700	−	10.7667i	−1.24459	−	0.818579i	−0.988958	+	0.148195i	$0.952654\pi$
$174$		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	−0.990674	−	0.136254i	$-0.956494\pi$
$179$	−13.7606	+	11.5465i	−1.02852	+	0.863029i	−0.0378443	+	0.999284i	$0.512049\pi$
$180$		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	0.571513	−	0.820593i	$-0.306357\pi$
$191$	−5.23124	−	7.02677i	−0.378519	−	0.508439i	−0.950031	+	0.312154i	$0.898949\pi$
$192$		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	$0.129984\pi$
$197$	−1.12942	+	6.40526i	−0.0804679	+	0.456356i	−0.998243	+	0.0592552i	$0.981127\pi$
$198$		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	$0.218669\pi$
$227$	−1.03052	+	17.6933i	−0.0683979	+	1.17435i	−0.841569	+	0.540149i	$0.818368\pi$
$228$		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	−0.460217	−	0.887806i	$-0.652228\pi$
$233$	−21.1172	−	7.68604i	−1.38343	−	0.503529i	−0.923218	+	0.384277i	$0.874451\pi$
$234$		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	0.802937	−	0.596064i	$-0.203270\pi$
$239$	2.49200	+	2.64136i	0.161194	+	0.170856i	−0.641743	+	0.766920i	$0.721788\pi$
$240$		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	−0.122474	−	0.992472i	$-0.539083\pi$
$251$	6.68026	−	2.43142i	0.421655	−	0.153470i	0.544128	+	0.839002i	$0.316860\pi$
$252$		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	−0.773143	−	0.634231i	$-0.781317\pi$
$257$	0.900688	−	1.20983i	0.0561833	−	0.0754673i	0.829327	+	0.558764i	$0.188724\pi$
$258$		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	−0.775426	−	0.631438i	$-0.782465\pi$
$263$	−1.62123	+	1.71840i	−0.0999691	+	0.105961i	0.675457	+	0.737399i	$0.263946\pi$
$264$		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	−0.714629	−	0.699504i	$-0.753404\pi$
$269$	4.07527	−	7.05858i	0.248474	−	0.430369i	0.963103	+	0.269135i	$0.0867377\pi$
$270$		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	0.151315	−	0.988486i	$-0.451649\pi$
$281$	17.3424	−	8.70969i	1.03456	−	0.519576i	0.883246	+	0.468909i	$0.155353\pi$
$282$		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	$-0.638664\pi$
$293$	7.33932	−	24.5150i	0.428768	−	1.43218i	0.850746	−	0.525577i	$-0.176151\pi$
$294$		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	0.152211	−	0.988348i	$-0.451361\pi$
$311$	1.27660	+	0.149214i	0.0723895	+	0.00846112i	−0.0798210	+	0.996809i	$0.525435\pi$
$312$		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	0.890648	−	0.454693i	$-0.150251\pi$
$317$	26.3951	+	6.25575i	1.48249	+	0.351358i	0.591847	+	0.806051i	$0.298399\pi$
$318$		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	0.549707	−	0.835357i	$-0.314739\pi$
$347$	26.3744	−	6.25085i	1.41585	−	0.335563i	0.866144	+	0.499794i	$0.166591\pi$
$348$		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	0.352980	−	0.935631i	$-0.385168\pi$
$353$	−12.1106	−	16.2673i	−0.644580	−	0.865822i	−0.997560	+	0.0698092i	$0.977761\pi$
$354$		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	−0.999314	−	0.0370347i	$-0.988209\pi$
$359$	−0.901880	+	5.11482i	−0.0475994	+	0.269950i	0.951715	+	0.306984i	$0.0993199\pi$
$360$		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	0.320758	−	0.947161i	$-0.396062\pi$
$383$	25.7840	−	16.9584i	1.31750	−	0.866535i	0.996744	+	0.0806260i	$0.0256919\pi$
$384$		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	$0.252269\pi$
$389$	−1.53694	+	26.3883i	−0.0779262	+	1.33794i	−0.779974	+	0.625811i	$0.784768\pi$
$390$		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	0.724249	−	0.689539i	$-0.242187\pi$
$401$	−0.124842	−	0.132325i	−0.00623432	−	0.00660799i	−0.730483	+	0.682931i	$0.760705\pi$
$402$		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	−0.994351	−	0.106142i	$-0.966150\pi$
$419$	−12.4349	+	16.7030i	−0.607485	+	0.815994i	0.386866	+	0.922136i	$0.373558\pi$
$420$		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	−0.963086	−	0.269194i	$-0.913243\pi$
$431$	−5.15721	+	8.93256i	−0.248414	+	0.430266i	0.714672	+	0.699460i	$0.246576\pi$
$432$		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	−0.263792	−	0.964580i	$-0.584973\pi$
$443$	7.41704	−	3.72498i	0.352394	−	0.176979i	0.616186	+	0.787601i	$0.288677\pi$
$444$		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	$0.163632\pi$
$449$	4.67637	+	26.5210i	0.220691	+	1.25160i	−0.650061	+	0.759882i	$0.725257\pi$
$450$		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	−0.173384	−	0.984854i	$-0.555470\pi$
$461$	−2.46853	+	0.288530i	−0.114971	+	0.0134382i	0.0584129	+	0.998293i	$0.481396\pi$
$462$		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	0.462668	−	0.886532i	$-0.346892\pi$
$467$	−7.13253	−	5.98491i	−0.330054	−	0.276948i	−0.792722	+	0.609583i	$0.791337\pi$
$468$		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	0.641753	−	0.766911i	$-0.278207\pi$
$479$	19.0640	+	4.51825i	0.871056	+	0.206444i	0.229303	+	0.973355i	$0.426355\pi$
$480$		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	0.999272	−	0.0381548i	$-0.0121480\pi$
$491$	0.0515677	+	0.885383i	0.00232722	+	0.0399568i	−0.996945	+	0.0781116i	$0.975111\pi$
$492$		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	$-0.286061\pi$
$503$	33.6724	−	28.2545i	1.50138	−	1.25981i	0.878742	−	0.477297i	$-0.158383\pi$
$504$		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	0.122495	−	0.992469i	$-0.460911\pi$
$509$	15.2824	−	3.62199i	0.677379	−	0.160542i	0.554885	+	0.831927i	$0.312762\pi$
$510$		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	$-0.859006\pi$
$521$	2.10231	−	11.9228i	0.0921038	−	0.522346i	0.995596	−	0.0937429i	$-0.0298832\pi$
$522$		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	−0.0783156	−	0.996929i	$-0.524954\pi$
$557$	−18.3879	−	6.69266i	−0.779122	−	0.283577i	−0.700807	+	0.713351i	$0.747176\pi$
$558$		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	0.905419	−	0.424519i	$-0.139557\pi$
$563$	10.1785	+	10.7886i	0.428973	+	0.454685i	−0.476446	+	0.879204i	$0.658075\pi$
$564$		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	−0.879017	−	0.476790i	$-0.841800\pi$
$569$	1.69374	−	3.92653i	0.0710053	−	0.164609i	0.950023	+	0.312181i	$0.101060\pi$
$570$		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	−0.688933	−	0.724825i	$-0.741920\pi$
$587$	1.81042	−	1.91894i	0.0747242	−	0.0792030i	0.763657	+	0.645622i	$0.223402\pi$
$588$		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	−0.941814	−	0.336134i	$-0.890881\pi$
$593$	−4.37859	+	7.58393i	−0.179807	+	0.311435i	0.762007	+	0.647568i	$0.224214\pi$
$594$		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	0.701562	−	0.712608i	$-0.252486\pi$
$599$	13.4342	+	6.74691i	0.548906	+	0.275671i	−0.152656	+	0.988279i	$0.548783\pi$
$600$		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	−0.880515	−	0.474017i	$-0.842803\pi$
$617$	2.87197	−	9.59306i	0.115621	−	0.386202i	0.996137	+	0.0878153i	$0.0279885\pi$
$618$		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	$-0.995844\pi$
$641$	−48.0872	−	11.3969i	−1.89933	−	0.450150i	−0.899416	−	0.437094i	$-0.856008\pi$
$642$		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	$-0.410825\pi$
$647$	14.0663			0.553003			0.276501	+	0.961013i	$0.410825\pi$
$648$		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	$-0.944745\pi$
$653$	−0.682581	−	11.7195i	−0.0267115	−	0.458618i	0.958260	−	0.285899i	$-0.0922922\pi$
$654$		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	$0.0257614\pi$
$659$	37.6271	+	24.7477i	1.46574	+	0.964034i	0.469015	+	0.883190i	$0.344609\pi$
$660$		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	0.996702	−	0.0811498i	$-0.0258592\pi$
$677$	16.4729	+	22.1269i	0.633104	+	0.850406i	−0.363598	+	0.931556i	$0.618452\pi$
$678$		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	$-0.861229\pi$
$683$	2.34587	−	13.3041i	0.0897621	−	0.509066i	0.996227	−	0.0867852i	$-0.0276594\pi$
$684$		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	0.986358	−	0.164612i	$-0.0526373\pi$
$701$	9.28318	+	16.0789i	0.350621	+	0.607293i	−0.635738	+	0.771905i	$0.719304\pi$
$702$		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	0.789130	−	0.614226i	$-0.210532\pi$
$719$	26.7826	+	9.74806i	0.998821	+	0.363541i	0.209691	+	0.977768i	$0.432754\pi$
$720$		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	$-0.529324\pi$
$743$	24.2138	−	32.5248i	0.888318	−	1.19322i	0.980311	−	0.197458i	$-0.0632687\pi$
$744$		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	0.397474	−	0.917614i	$-0.369887\pi$
$761$	−2.79203	−	1.40221i	−0.101211	−	0.0508300i	−0.498684	+	0.866784i	$0.666183\pi$
$762$		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	$-0.863072\pi$
$773$	−5.48952	−	31.1326i	−0.197444	−	1.11976i	0.711450	−	0.702737i	$-0.248039\pi$
$774$		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

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

L-functions

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