LMFDB - Embedded newform 729.2.g.d.55.2

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			55.2
Character	$\chi$	$=$	729.55
Dual form			729.2.g.d.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.677333 + 1.57023i) q^{2} +(-0.634371 - 0.672394i) q^{4} +(-0.0798566 - 1.37108i) q^{5} +(-0.301861 - 0.0715423i) q^{7} +(-1.72842 + 0.629095i) q^{8} +O(q^{10})$	\(q+(-0.677333 + 1.57023i) q^{2} +(-0.634371 - 0.672394i) q^{4} +(-0.0798566 - 1.37108i) q^{5} +(-0.301861 - 0.0715423i) q^{7} +(-1.72842 + 0.629095i) q^{8} +(2.20701 + 0.803287i) q^{10} +(2.01426 + 1.32480i) q^{11} +(4.58584 + 0.536008i) q^{13} +(0.316798 - 0.425534i) q^{14} +(0.290392 - 4.98584i) q^{16} +(0.161307 - 0.135352i) q^{17} +(2.66964 + 2.24009i) q^{19} +(-0.871250 + 0.923471i) q^{20} +(-3.44457 + 2.26553i) q^{22} +(-7.79405 + 1.84722i) q^{23} +(3.09270 - 0.361484i) q^{25} +(-3.94780 + 6.83779i) q^{26} +(0.143387 + 0.248354i) q^{28} +(4.96463 + 6.66865i) q^{29} +(-0.229930 + 0.768019i) q^{31} +(4.34483 + 2.18205i) q^{32} +(0.103276 + 0.344968i) q^{34} +(-0.0739849 + 0.419589i) q^{35} +(1.88786 + 10.7066i) q^{37} +(-5.32570 + 2.67467i) q^{38} +(1.00057 + 2.31958i) q^{40} +(1.86060 + 4.31336i) q^{41} +(6.64705 - 3.33827i) q^{43} +(-0.387001 - 2.19479i) q^{44} +(2.37859 - 13.4897i) q^{46} +(-1.78517 - 5.96289i) q^{47} +(-6.16943 - 3.09840i) q^{49} +(-1.52717 + 5.10110i) q^{50} +(-2.54872 - 3.42352i) q^{52} +(4.27003 + 7.39591i) q^{53} +(1.65556 - 2.86752i) q^{55} +(0.566750 - 0.0662436i) q^{56} +(-13.8340 + 3.27873i) q^{58} +(5.90137 - 3.88139i) q^{59} +(-6.87408 + 7.28610i) q^{61} +(-1.05023 - 0.881248i) q^{62} +(1.28246 - 1.07611i) q^{64} +(0.368703 - 6.33038i) q^{65} +(-0.749408 + 1.00663i) q^{67} +(-0.193338 - 0.0225980i) q^{68} +(-0.608741 - 0.400375i) q^{70} +(-1.68007 - 0.611494i) q^{71} +(-12.6834 + 4.61640i) q^{73} +(-18.0905 - 4.28753i) q^{74} +(-0.187316 - 3.21610i) q^{76} +(-0.513247 - 0.544010i) q^{77} +(-1.25449 + 2.90824i) q^{79} -6.85919 q^{80} -8.03324 q^{82} +(0.317759 - 0.736649i) q^{83} +(-0.198461 - 0.210356i) q^{85} +(0.739606 + 12.6985i) q^{86} +(-4.31493 - 1.02266i) q^{88} +(12.2626 - 4.46322i) q^{89} +(-1.34594 - 0.489881i) q^{91} +(6.18638 + 4.06885i) q^{92} +(10.5723 + 1.23572i) q^{94} +(2.85817 - 3.83919i) q^{95} +(0.387850 - 6.65913i) q^{97} +(9.04397 - 7.58879i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.677333	+	1.57023i	−0.478947	+	1.11032i	0.491907	+	0.870648i	$0.336300\pi$
$2$	−0.677333	+	1.57023i	−0.478947	+	1.11032i	−0.970853	+	0.239675i	$0.922959\pi$
$3$		0			0
$3$		0			0
$4$	−0.634371	−	0.672394i	−0.317186	−	0.336197i
$5$	−0.0798566	−	1.37108i	−0.0357129	−	0.613167i	−0.967923	−	0.251249i	$-0.919159\pi$
$5$	−0.0798566	−	1.37108i	−0.0357129	−	0.613167i	0.932210	−	0.361919i	$-0.117878\pi$
$6$		0			0
$7$	−0.301861	−	0.0715423i	−0.114093	−	0.0270404i	0.173173	−	0.984891i	$-0.444598\pi$
$7$	−0.301861	−	0.0715423i	−0.114093	−	0.0270404i	−0.287266	+	0.957851i	$0.592746\pi$
$8$	−1.72842	+	0.629095i	−0.611091	+	0.222419i
$9$		0			0
$10$	2.20701	+	0.803287i	0.697918	+	0.254022i
$11$	2.01426	+	1.32480i	0.607323	+	0.399442i	0.815591	−	0.578629i	$-0.196412\pi$
$11$	2.01426	+	1.32480i	0.607323	+	0.399442i	−0.208268	+	0.978072i	$0.566783\pi$
$12$		0			0
$13$	4.58584	+	0.536008i	1.27188	+	0.148662i	0.725119	−	0.688624i	$-0.241785\pi$
$13$	4.58584	+	0.536008i	1.27188	+	0.148662i	0.546765	+	0.837286i	$0.315859\pi$
$14$	0.316798	−	0.425534i	0.0846679	−	0.113729i
$15$		0			0
$16$	0.290392	−	4.98584i	0.0725980	−	1.24646i
$17$	0.161307	−	0.135352i	0.0391226	−	0.0328277i	−0.623017	−	0.782209i	$-0.714093\pi$
$17$	0.161307	−	0.135352i	0.0391226	−	0.0328277i	0.662139	+	0.749381i	$0.269649\pi$
$18$		0			0
$19$	2.66964	+	2.24009i	0.612457	+	0.513913i	0.895422	−	0.445218i	$-0.146874\pi$
$19$	2.66964	+	2.24009i	0.612457	+	0.513913i	−0.282965	+	0.959130i	$0.591318\pi$
$20$	−0.871250	+	0.923471i	−0.194817	+	0.206494i
$21$		0			0
$22$	−3.44457	+	2.26553i	−0.734385	+	0.483013i
$23$	−7.79405	+	1.84722i	−1.62517	+	0.385173i	−0.939449	−	0.342689i	$-0.888662\pi$
$23$	−7.79405	+	1.84722i	−1.62517	+	0.385173i	−0.685724	+	0.727862i	$0.740514\pi$
$24$		0			0
$25$	3.09270	−	0.361484i	0.618539	−	0.0722969i
$26$	−3.94780	+	6.83779i	−0.774227	+	1.34100i
$27$		0			0
$28$	0.143387	+	0.248354i	0.0270976	+	0.0469344i
$29$	4.96463	+	6.66865i	0.921908	+	1.23834i	0.970887	+	0.239538i	$0.0769959\pi$
$29$	4.96463	+	6.66865i	0.921908	+	1.23834i	−0.0489788	+	0.998800i	$0.515597\pi$
$30$		0			0
$31$	−0.229930	+	0.768019i	−0.0412966	+	0.137940i	−0.976152	−	0.217089i	$-0.930344\pi$
$31$	−0.229930	+	0.768019i	−0.0412966	+	0.137940i	0.934855	+	0.355029i	$0.115529\pi$
$32$	4.34483	+	2.18205i	0.768064	+	0.385736i
$33$		0			0
$34$	0.103276	+	0.344968i	0.0177118	+	0.0591614i
$35$	−0.0739849	+	0.419589i	−0.0125057	+	0.0709236i
$36$		0			0
$37$	1.88786	+	10.7066i	0.310362	+	1.76015i	0.597126	+	0.802148i	$0.296309\pi$
$37$	1.88786	+	10.7066i	0.310362	+	1.76015i	−0.286764	+	0.958001i	$0.592580\pi$
$38$	−5.32570	+	2.67467i	−0.863943	+	0.433889i
$39$		0			0
$40$	1.00057	+	2.31958i	0.158204	+	0.366758i
$41$	1.86060	+	4.31336i	0.290577	+	0.673634i	0.999499	−	0.0316531i	$-0.0100772\pi$
$41$	1.86060	+	4.31336i	0.290577	+	0.673634i	−0.708921	+	0.705287i	$0.750818\pi$
$42$		0			0
$43$	6.64705	−	3.33827i	1.01367	−	0.509082i	0.137198	−	0.990544i	$-0.456190\pi$
$43$	6.64705	−	3.33827i	1.01367	−	0.509082i	0.876467	+	0.481462i	$0.159894\pi$
$44$	−0.387001	−	2.19479i	−0.0583426	−	0.330877i
$45$		0			0
$46$	2.37859	−	13.4897i	0.350704	−	1.98894i
$47$	−1.78517	−	5.96289i	−0.260394	−	0.869777i	−0.983787	−	0.179341i	$-0.942604\pi$
$47$	−1.78517	−	5.96289i	−0.260394	−	0.869777i	0.723393	−	0.690437i	$-0.242582\pi$
$48$		0			0
$49$	−6.16943	−	3.09840i	−0.881347	−	0.442629i
$50$	−1.52717	+	5.10110i	−0.215974	+	0.721405i
$51$		0			0
$52$	−2.54872	−	3.42352i	−0.353443	−	0.474757i
$53$	4.27003	+	7.39591i	0.586533	+	1.01591i	0.994682	+	0.102990i	$0.0328411\pi$
$53$	4.27003	+	7.39591i	0.586533	+	1.01591i	−0.408149	+	0.912915i	$0.633826\pi$
$54$		0			0
$55$	1.65556	−	2.86752i	0.223236	−	0.386656i
$56$	0.566750	−	0.0662436i	0.0757352	−	0.00885218i
$57$		0			0
$58$	−13.8340	+	3.27873i	−1.81650	+	0.430518i
$59$	5.90137	−	3.88139i	0.768293	−	0.505314i	−0.103834	−	0.994595i	$-0.533111\pi$
$59$	5.90137	−	3.88139i	0.768293	−	0.505314i	0.872126	+	0.489280i	$0.162741\pi$
$60$		0			0
$61$	−6.87408	+	7.28610i	−0.880136	+	0.932889i	−0.998191	−	0.0601177i	$-0.980852\pi$
$61$	−6.87408	+	7.28610i	−0.880136	+	0.932889i	0.118056	+	0.993007i	$0.462334\pi$
$62$	−1.05023	−	0.881248i	−0.133379	−	0.111919i
$63$		0			0
$64$	1.28246	−	1.07611i	0.160308	−	0.134514i
$65$	0.368703	−	6.33038i	0.0457319	−	0.785187i
$66$		0			0
$67$	−0.749408	+	1.00663i	−0.0915548	+	0.122979i	−0.845540	−	0.533912i	$-0.820721\pi$
$67$	−0.749408	+	1.00663i	−0.0915548	+	0.122979i	0.753985	+	0.656891i	$0.228129\pi$
$68$	−0.193338	−	0.0225980i	−0.0234457	−	0.00274041i
$69$		0			0
$70$	−0.608741	−	0.400375i	−0.0727585	−	0.0478540i
$71$	−1.68007	−	0.611494i	−0.199387	−	0.0725710i	0.240396	−	0.970675i	$-0.422723\pi$
$71$	−1.68007	−	0.611494i	−0.199387	−	0.0725710i	−0.439784	+	0.898104i	$0.644945\pi$
$72$		0			0
$73$	−12.6834	+	4.61640i	−1.48448	+	0.540308i	−0.951991	−	0.306126i	$-0.900967\pi$
$73$	−12.6834	+	4.61640i	−1.48448	+	0.540308i	−0.532494	+	0.846434i	$0.678745\pi$
$74$	−18.0905	−	4.28753i	−2.10298	−	0.498415i
$75$		0			0
$76$	−0.187316	−	3.21610i	−0.0214867	−	0.368912i
$77$	−0.513247	−	0.544010i	−0.0584899	−	0.0619957i
$78$		0			0
$79$	−1.25449	+	2.90824i	−0.141142	+	0.327203i	−0.974095	−	0.226141i	$-0.927389\pi$
$79$	−1.25449	+	2.90824i	−0.141142	+	0.327203i	0.832953	+	0.553344i	$0.186648\pi$
$80$	−6.85919			−0.766881
$81$		0			0
$82$	−8.03324			−0.887123
$83$	0.317759	−	0.736649i	0.0348786	−	0.0808578i	−0.899886	−	0.436125i	$-0.856351\pi$
$83$	0.317759	−	0.736649i	0.0348786	−	0.0808578i	0.934765	+	0.355267i	$0.115610\pi$
$84$		0			0
$85$	−0.198461	−	0.210356i	−0.0215261	−	0.0228163i
$86$	0.739606	+	12.6985i	0.0797538	+	1.36932i
$87$		0			0
$88$	−4.31493	−	1.02266i	−0.459973	−	0.109016i
$89$	12.2626	−	4.46322i	1.29983	−	0.473101i	0.402891	−	0.915248i	$-0.368005\pi$
$89$	12.2626	−	4.46322i	1.29983	−	0.473101i	0.896942	+	0.442147i	$0.145783\pi$
$90$		0			0
$91$	−1.34594	−	0.489881i	−0.141093	−	0.0513535i
$92$	6.18638	+	4.06885i	0.644975	+	0.424207i
$93$		0			0
$94$	10.5723	+	1.23572i	1.09045	+	0.127455i
$95$	2.85817	−	3.83919i	0.293242	−	0.393892i
$96$		0			0
$97$	0.387850	−	6.65913i	0.0393802	−	0.676132i	−0.919634	−	0.392775i	$-0.871515\pi$
$97$	0.387850	−	6.65913i	0.0393802	−	0.676132i	0.959015	−	0.283356i	$-0.0914480\pi$
$98$	9.04397	−	7.58879i	0.913579	−	0.766584i
$99$		0			0
$100$	−2.20498	−	1.85020i	−0.220498	−	0.185020i
$101$	6.39584	−	6.77920i	0.636410	−	0.674555i	−0.326245	−	0.945285i	$-0.605784\pi$
$101$	6.39584	−	6.77920i	0.636410	−	0.674555i	0.962655	+	0.270730i	$0.0872650\pi$
$102$		0			0
$103$	1.09702	−	0.721522i	0.108093	−	0.0710936i	−0.494312	−	0.869285i	$-0.664580\pi$
$103$	1.09702	−	0.721522i	0.108093	−	0.0710936i	0.602404	+	0.798191i	$0.294209\pi$
$104$	−8.26349	+	1.95848i	−0.810301	+	0.192045i
$105$		0			0
$106$	−14.5055	+	1.69545i	−1.40890	+	0.164677i
$107$	0.386855	−	0.670052i	0.0373987	−	0.0647764i	−0.846720	−	0.532038i	$-0.821426\pi$
$107$	0.386855	−	0.670052i	0.0373987	−	0.0647764i	0.884119	+	0.467262i	$0.154760\pi$
$108$		0			0
$109$	1.03104	+	1.78582i	0.0987559	+	0.171050i	0.911170	−	0.412031i	$-0.135180\pi$
$109$	1.03104	+	1.78582i	0.0987559	+	0.171050i	−0.812414	+	0.583081i	$0.801847\pi$
$110$	3.38131	+	4.54188i	0.322395	+	0.433051i
$111$		0			0
$112$	−0.444356	+	1.48425i	−0.0419877	+	0.140249i
$113$	−5.25253	−	2.63792i	−0.494116	−	0.248154i	0.184249	−	0.982880i	$-0.441015\pi$
$113$	−5.25253	−	2.63792i	−0.494116	−	0.248154i	−0.678365	+	0.734725i	$0.737311\pi$
$114$		0			0
$115$	3.15511	+	10.5388i	0.294215	+	0.982747i
$116$	1.33455	−	7.56859i	0.123909	−	0.702726i
$117$		0			0
$118$	2.09750	+	11.8955i	0.193091	+	1.09507i
$119$	−0.0583755	+	0.0293173i	−0.00535127	+	0.00268751i
$120$		0			0
$121$	−2.05472	−	4.76339i	−0.186793	−	0.433035i
$122$	−6.78484	−	15.7290i	−0.614270	−	1.42404i
$123$		0			0
$124$	0.662272	−	0.332606i	0.0594738	−	0.0298689i
$125$	−1.93505	−	10.9742i	−0.173076	−	0.981562i
$126$		0			0
$127$	1.81538	−	10.2955i	0.161089	−	0.913580i	−0.791917	−	0.610628i	$-0.790917\pi$
$127$	1.81538	−	10.2955i	0.161089	−	0.913580i	0.953006	−	0.302951i	$-0.0979720\pi$
$128$	3.60996	+	12.0581i	0.319078	+	1.06580i
$129$		0			0
$130$	9.69044	+	4.86672i	0.849908	+	0.426840i
$131$	1.71783	−	5.73796i	0.150088	−	0.501328i	−0.849570	−	0.527475i	$-0.823139\pi$
$131$	1.71783	−	5.73796i	0.150088	−	0.501328i	0.999658	+	0.0261475i	$0.00832394\pi$
$132$		0			0
$133$	−0.645597	−	0.867188i	−0.0559804	−	0.0751947i
$134$	−1.07305	−	1.85857i	−0.0926970	−	0.160556i
$135$		0			0
$136$	−0.193657	+	0.335423i	−0.0166059	+	0.0287623i
$137$	−1.15384	+	0.134865i	−0.0985793	+	0.0115223i	−0.165240	−	0.986253i	$-0.552840\pi$
$137$	−1.15384	+	0.134865i	−0.0985793	+	0.0115223i	0.0666602	+	0.997776i	$0.478766\pi$
$138$		0			0
$139$	15.8687	−	3.76096i	1.34597	−	0.319001i	0.506421	−	0.862286i	$-0.330968\pi$
$139$	15.8687	−	3.76096i	1.34597	−	0.319001i	0.839548	+	0.543285i	$0.182820\pi$
$140$	0.329063	−	0.216428i	0.0278109	−	0.0182915i
$141$		0			0
$142$	2.09815	−	2.22391i	0.176073	−	0.186627i
$143$	8.52698	+	7.15499i	0.713062	+	0.598330i
$144$		0			0
$145$	8.74683	−	7.33946i	0.726384	−	0.609509i
$146$	1.34209	−	23.0428i	0.111072	−	1.90704i
$147$		0			0
$148$	6.00143	−	8.06132i	0.493315	−	0.662636i
$149$	8.86820	+	1.03654i	0.726511	+	0.0849170i	0.471306	−	0.881970i	$-0.343783\pi$
$149$	8.86820	+	1.03654i	0.726511	+	0.0849170i	0.255205	+	0.966887i	$0.417857\pi$
$150$		0			0
$151$	13.0290	+	8.56932i	1.06029	+	0.697361i	0.954857	−	0.297065i	$-0.0960080\pi$
$151$	13.0290	+	8.56932i	1.06029	+	0.697361i	0.105429	+	0.994427i	$0.466378\pi$
$152$	−6.02350	−	2.19238i	−0.488571	−	0.177825i
$153$		0			0
$154$	1.20186	−	0.437442i	0.0968488	−	0.0352501i
$155$	1.07138	+	0.253922i	0.0860553	+	0.0203955i
$156$		0			0
$157$	−0.711632	−	12.2182i	−0.0567944	−	0.975122i	−0.899548	−	0.436822i	$-0.856104\pi$
$157$	−0.711632	−	12.2182i	−0.0567944	−	0.975122i	0.842753	−	0.538300i	$-0.180933\pi$
$158$	−3.71691	−	3.93970i	−0.295702	−	0.313426i
$159$		0			0
$160$	2.64482	−	6.13138i	0.209091	−	0.484728i
$161$	2.48487			0.195835
$162$		0			0
$163$	−25.0816			−1.96454			−0.982271	−	0.187465i	$-0.939973\pi$
$163$	−25.0816			−1.96454			−0.982271	+	0.187465i	$0.939973\pi$
$164$	1.71997	−	3.98733i	0.134307	−	0.311358i
$165$		0			0
$166$	0.941483	+	0.997913i	0.0730732	+	0.0774531i
$167$	−0.468266	−	8.03982i	−0.0362355	−	0.622140i	−0.966724	−	0.255820i	$-0.917655\pi$
$167$	−0.468266	−	8.03982i	−0.0362355	−	0.622140i	0.930489	−	0.366320i	$-0.119382\pi$
$168$		0			0
$169$	8.09307	+	1.91809i	0.622543	+	0.147546i
$170$	0.464732	−	0.169149i	0.0356433	−	0.0129731i
$171$		0			0
$172$	−6.46133	−	2.35173i	−0.492672	−	0.179318i
$173$	14.8606	+	9.77400i	1.12983	+	0.743104i	0.969774	−	0.244004i	$-0.0784609\pi$
$173$	14.8606	+	9.77400i	1.12983	+	0.743104i	0.160060	+	0.987107i	$0.448831\pi$
$174$		0			0
$175$	−0.959425	−	0.112141i	−0.0725257	−	0.00847704i
$176$	7.19017	−	9.65807i	0.541979	−	0.728004i
$177$		0			0
$178$	−1.29756	+	22.2782i	−0.0972562	+	1.66982i
$179$	−13.5735	+	11.3896i	−1.01453	+	0.851295i	−0.988931	−	0.148377i	$-0.952595\pi$
$179$	−13.5735	+	11.3896i	−1.01453	+	0.851295i	−0.0256035	+	0.999672i	$0.508151\pi$
$180$		0			0
$181$	20.5130	+	17.2124i	1.52472	+	1.27939i	0.825340	+	0.564636i	$0.190983\pi$
$181$	20.5130	+	17.2124i	1.52472	+	1.27939i	0.699377	+	0.714753i	$0.253461\pi$
$182$	1.68088	−	1.78162i	0.124595	−	0.132063i
$183$		0			0
$184$	12.3094	−	8.09599i	0.907458	−	0.596844i
$185$	14.5288	−	3.44340i	1.06818	−	0.253164i
$186$		0			0
$187$	0.504228	−	0.0589359i	0.0368728	−	0.00430982i
$188$	−2.87695	+	4.98303i	−0.209823	+	0.363424i
$189$		0			0
$190$	4.09249	+	7.08840i	0.296900	+	0.514246i
$191$	−1.87225	−	2.51487i	−0.135471	−	0.181969i	0.729211	−	0.684289i	$-0.239887\pi$
$191$	−1.87225	−	2.51487i	−0.135471	−	0.181969i	−0.864682	+	0.502320i	$0.832480\pi$
$192$		0			0
$193$	−2.83373	+	9.46533i	−0.203977	+	0.681329i	0.793384	+	0.608722i	$0.208317\pi$
$193$	−2.83373	+	9.46533i	−0.203977	+	0.681329i	−0.997361	+	0.0726078i	$0.976868\pi$
$194$	10.1937	+	5.11946i	0.731864	+	0.367556i
$195$		0			0
$196$	1.83036	+	6.11382i	0.130740	+	0.436702i
$197$	0.354010	−	2.00769i	0.0252221	−	0.143042i	−0.969596	−	0.244711i	$-0.921307\pi$
$197$	0.354010	−	2.00769i	0.0252221	−	0.143042i	0.994818	+	0.101669i	$0.0324182\pi$
$198$		0			0
$199$	−2.26949	−	12.8709i	−0.160880	−	0.912396i	−0.953211	−	0.302305i	$-0.902244\pi$
$199$	−2.26949	−	12.8709i	−0.160880	−	0.912396i	0.792331	−	0.610091i	$-0.208867\pi$
$200$	−5.11809	+	2.57040i	−0.361903	+	0.181755i
$201$		0			0
$202$	6.31281	+	14.6347i	0.444168	+	1.02970i
$203$	−1.02153	−	2.36818i	−0.0716977	−	0.166214i
$204$		0			0
$205$	5.76540	−	2.89549i	0.402673	−	0.202230i
$206$	0.389910	+	2.21129i	0.0271663	+	0.154068i
$207$		0			0
$208$	4.00414	−	22.7086i	0.277637	−	1.57456i
$209$	2.40967	+	8.04887i	0.166681	+	0.556752i
$210$		0			0
$211$	−14.1852	−	7.12406i	−0.976548	−	0.490441i	−0.112391	−	0.993664i	$-0.535851\pi$
$211$	−14.1852	−	7.12406i	−0.976548	−	0.490441i	−0.864156	+	0.503223i	$0.832147\pi$
$212$	2.26418	−	7.56289i	0.155505	−	0.519421i
$213$		0			0
$214$	0.790109	+	1.06130i	0.0540108	+	0.0725490i
$215$	−5.10787	−	8.84708i	−0.348354	−	0.603366i
$216$		0			0
$217$	0.124353	−	0.215385i	0.00844160	−	0.0146213i
$218$	−3.50251	+	0.409385i	−0.237220	+	0.0277270i
$219$		0			0
$220$	−2.97834	+	0.705880i	−0.200800	+	0.0475904i
$221$	0.812276	−	0.534243i	0.0546396	−	0.0359370i
$222$		0			0
$223$	1.30086	−	1.37883i	0.0871121	−	0.0923335i	−0.682351	−	0.731025i	$-0.739042\pi$
$223$	1.30086	−	1.37883i	0.0871121	−	0.0923335i	0.769463	+	0.638691i	$0.220524\pi$
$224$	−1.15542	−	0.969515i	−0.0772000	−	0.0647785i
$225$		0			0
$226$	7.69986	−	6.46095i	0.512187	−	0.429776i
$227$	1.48603	−	25.5142i	0.0986315	−	1.69344i	−0.479538	−	0.877521i	$-0.659196\pi$
$227$	1.48603	−	25.5142i	0.0986315	−	1.69344i	0.578170	−	0.815917i	$-0.303767\pi$
$228$		0			0
$229$	−2.80161	+	3.76321i	−0.185135	+	0.248680i	−0.884995	−	0.465600i	$-0.845838\pi$
$229$	−2.80161	+	3.76321i	−0.185135	+	0.248680i	0.699860	+	0.714280i	$0.253246\pi$
$230$	−18.6854	−	2.18401i	−1.23208	−	0.144010i
$231$		0			0
$232$	−12.7762	−	8.40304i	−0.838799	−	0.551687i
$233$	−10.7706	−	3.92018i	−0.705605	−	0.256819i	−0.0358031	−	0.999359i	$-0.511399\pi$
$233$	−10.7706	−	3.92018i	−0.705605	−	0.256819i	−0.669802	+	0.742540i	$0.733621\pi$
$234$		0			0
$235$	−8.03307	+	2.92380i	−0.524020	+	0.190728i
$236$	−6.35348	−	1.50580i	−0.413577	−	0.0980194i
$237$		0			0
$238$	−0.00649534	−	0.111521i	−0.000421031	−	0.00722882i
$239$	8.06092	+	8.54408i	0.521418	+	0.552671i	0.933547	−	0.358455i	$-0.116696\pi$
$239$	8.06092	+	8.54408i	0.521418	+	0.552671i	−0.412129	+	0.911125i	$0.635215\pi$
$240$		0			0
$241$	1.75025	−	4.05753i	0.112743	−	0.261368i	−0.852497	−	0.522732i	$-0.824913\pi$
$241$	1.75025	−	4.05753i	0.112743	−	0.261368i	0.965240	+	0.261364i	$0.0841721\pi$
$242$	8.87136			0.570273
$243$		0			0
$244$	9.25985			0.592801
$245$	−3.75550	+	8.70623i	−0.239930	+	0.556221i
$246$		0			0
$247$	11.0418	+	11.7037i	0.702575	+	0.744686i
$248$	−0.0857407	−	1.47211i	−0.00544454	−	0.0934792i
$249$		0			0
$250$	18.5427	+	4.39471i	1.17274	+	0.277946i
$251$	−5.90077	+	2.14770i	−0.372453	+	0.135562i	−0.521463	−	0.853274i	$-0.674614\pi$
$251$	−5.90077	+	2.14770i	−0.372453	+	0.135562i	0.149010	+	0.988836i	$0.452391\pi$
$252$		0			0
$253$	−18.1465	−	6.60477i	−1.14086	−	0.415239i
$254$	14.9368	+	9.82406i	0.937216	+	0.616417i
$255$		0			0
$256$	−18.0536	−	2.11016i	−1.12835	−	0.131885i
$257$	−1.41164	+	1.89616i	−0.0880555	+	0.118279i	−0.843968	−	0.536394i	$-0.819786\pi$
$257$	−1.41164	+	1.89616i	−0.0880555	+	0.118279i	0.755912	+	0.654673i	$0.227194\pi$
$258$		0			0
$259$	0.196103	−	3.36695i	0.0121852	−	0.209212i
$260$	−4.49040	+	3.76790i	−0.278483	+	0.233675i
$261$		0			0
$262$	7.84639	+	6.58390i	0.484752	+	0.406755i
$263$	9.60486	−	10.1806i	0.592261	−	0.627760i	−0.360034	−	0.932939i	$-0.617235\pi$
$263$	9.60486	−	10.1806i	0.592261	−	0.627760i	0.952295	+	0.305179i	$0.0987163\pi$
$264$		0			0
$265$	9.79942	−	6.44518i	0.601974	−	0.395924i
$266$	1.79897	−	0.426364i	0.110302	−	0.0261421i
$267$		0			0
$268$	1.15225	−	0.134679i	0.0703851	−	0.00822684i
$269$	12.8630	−	22.2793i	0.784268	−	1.35839i	−0.145167	−	0.989407i	$-0.546372\pi$
$269$	12.8630	−	22.2793i	0.784268	−	1.35839i	0.929435	−	0.368985i	$-0.120295\pi$
$270$		0			0
$271$	−6.52248	−	11.2973i	−0.396212	−	0.686260i	0.597043	−	0.802209i	$-0.296342\pi$
$271$	−6.52248	−	11.2973i	−0.396212	−	0.686260i	−0.993255	+	0.115950i	$0.963009\pi$
$272$	−0.628002	−	0.843553i	−0.0380782	−	0.0511479i
$273$		0			0
$274$	0.569765	−	1.90315i	0.0344208	−	0.114973i
$275$	6.70840	+	3.36908i	0.404532	+	0.203163i
$276$		0			0
$277$	−1.49661	−	4.99901i	−0.0899223	−	0.300361i	0.901183	−	0.433438i	$-0.142700\pi$
$277$	−1.49661	−	4.99901i	−0.0899223	−	0.300361i	−0.991106	+	0.133076i	$0.957514\pi$
$278$	−4.84283	+	27.4651i	−0.290454	+	1.64725i
$279$		0			0
$280$	−0.136084	−	0.771772i	−0.00813259	−	0.0461222i
$281$	−5.07578	+	2.54915i	−0.302795	+	0.152070i	−0.593709	−	0.804680i	$-0.702337\pi$
$281$	−5.07578	+	2.54915i	−0.302795	+	0.152070i	0.290914	+	0.956749i	$0.406041\pi$
$282$		0			0
$283$	−4.49732	−	10.4260i	−0.267338	−	0.619759i	0.730678	−	0.682722i	$-0.239204\pi$
$283$	−4.49732	−	10.4260i	−0.267338	−	0.619759i	−0.998016	+	0.0629635i	$0.979945\pi$
$284$	0.654621	+	1.51758i	0.0388446	+	0.0900519i
$285$		0			0
$286$	−17.0106	+	8.54305i	−1.00586	+	0.505161i
$287$	−0.253055	−	1.43515i	−0.0149374	−	0.0847140i
$288$		0			0
$289$	−2.94432	+	16.6981i	−0.173195	+	0.982239i
$290$	5.60015	+	18.7058i	0.328852	+	1.09844i
$291$		0			0
$292$	11.1500	+	5.59976i	0.652507	+	0.327701i
$293$	−4.95619	+	16.5548i	−0.289544	+	0.967143i	0.682212	+	0.731154i	$0.261018\pi$
$293$	−4.95619	+	16.5548i	−0.289544	+	0.967143i	−0.971756	+	0.235989i	$0.924167\pi$
$294$		0			0
$295$	−5.79298	−	7.78132i	−0.337280	−	0.453046i
$296$	−9.99847	−	17.3179i	−0.581149	−	1.00658i
$297$		0			0
$298$	−7.63434	+	13.2231i	−0.442245	+	0.765991i
$299$	−36.7324	+	4.29341i	−2.12429	+	0.248294i
$300$		0			0
$301$	−2.24531	+	0.532148i	−0.129418	+	0.0306725i
$302$	−22.2808	+	14.6543i	−1.28212	+	0.843261i
$303$		0			0
$304$	11.9440	−	12.6599i	0.685034	−	0.726094i
$305$	10.5388	+	8.84310i	0.603450	+	0.506354i
$306$		0			0
$307$	−6.44460	+	5.40766i	−0.367812	+	0.308631i	−0.807895	−	0.589326i	$-0.799393\pi$
$307$	−6.44460	+	5.40766i	−0.367812	+	0.308631i	0.440083	+	0.897957i	$0.354949\pi$
$308$	−0.0402001	+	0.690208i	−0.00229061	+	0.0393283i
$309$		0			0
$310$	−1.12440	+	1.51033i	−0.0638615	+	0.0857809i
$311$	−6.51107	−	0.761035i	−0.369209	−	0.0431544i	−0.0705345	−	0.997509i	$-0.522470\pi$
$311$	−6.51107	−	0.761035i	−0.369209	−	0.0431544i	−0.298675	+	0.954355i	$0.596545\pi$
$312$		0			0
$313$	−4.55516	−	2.99597i	−0.257473	−	0.169342i	0.414210	−	0.910181i	$-0.364058\pi$
$313$	−4.55516	−	2.99597i	−0.257473	−	0.169342i	−0.671683	+	0.740839i	$0.734428\pi$
$314$	19.6675	+	7.15839i	1.10990	+	0.403971i
$315$		0			0
$316$	2.75130	−	1.00139i	0.154773	−	0.0563327i
$317$	−3.49841	−	0.829137i	−0.196490	−	0.0465690i	0.131192	−	0.991357i	$-0.458119\pi$
$317$	−3.49841	−	0.829137i	−0.196490	−	0.0465690i	−0.327682	+	0.944788i	$0.606268\pi$
$318$		0			0
$319$	1.16542	+	20.0096i	0.0652512	+	1.12032i
$320$	−1.57785	−	1.67243i	−0.0882047	−	0.0934915i
$321$		0			0
$322$	−1.68309	+	3.90183i	−0.0937947	+	0.217441i
$323$	0.733832			0.0408315
$324$		0			0
$325$	14.3764			0.797458
$326$	16.9886	−	39.3840i	0.940911	−	2.18128i
$327$		0			0
$328$	−5.92943	−	6.28483i	−0.327398	−	0.347022i
$329$	0.112274	+	1.92768i	0.00618989	+	0.106276i
$330$		0			0
$331$	−26.0845	−	6.18215i	−1.43374	−	0.339802i	−0.560927	−	0.827865i	$-0.689555\pi$
$331$	−26.0845	−	6.18215i	−1.43374	−	0.339802i	−0.872808	+	0.488063i	$0.837703\pi$
$332$	−0.696896	+	0.253649i	−0.0382471	+	0.0139208i
$333$		0			0
$334$	12.9416	+	4.71034i	0.708131	+	0.257739i
$335$	1.44002	+	0.947115i	0.0786766	+	0.0517464i
$336$		0			0
$337$	−21.4712	−	2.50962i	−1.16961	−	0.136708i	−0.490969	−	0.871177i	$-0.663357\pi$
$337$	−21.4712	−	2.50962i	−1.16961	−	0.136708i	−0.678642	+	0.734469i	$0.737431\pi$
$338$	−8.49355	+	11.4088i	−0.461988	+	0.620558i
$339$		0			0
$340$	−0.0155444	+	0.266888i	−0.000843015	+	0.0144740i
$341$	−1.48061	+	1.24238i	−0.0801796	+	0.0672787i
$342$		0			0
$343$	3.30415	+	2.77251i	0.178407	+	0.149702i
$344$	−9.38883	+	9.95158i	−0.506212	+	0.536553i
$345$		0			0
$346$	−25.4131	+	16.7144i	−1.36622	+	0.898574i
$347$	16.3883	−	3.88409i	0.879768	−	0.208509i	0.234179	−	0.972194i	$-0.424760\pi$
$347$	16.3883	−	3.88409i	0.879768	−	0.208509i	0.645589	+	0.763685i	$0.276612\pi$
$348$		0			0
$349$	1.95794	−	0.228850i	0.104806	−	0.0122501i	−0.0635282	−	0.997980i	$-0.520235\pi$
$349$	1.95794	−	0.228850i	0.104806	−	0.0122501i	0.168334	+	0.985730i	$0.446161\pi$
$350$	0.825937	−	1.43056i	0.0441482	−	0.0764669i
$351$		0			0
$352$	5.86083	+	10.1513i	0.312384	+	0.541064i
$353$	3.47131	+	4.66277i	0.184759	+	0.248174i	0.884847	−	0.465883i	$-0.154263\pi$
$353$	3.47131	+	4.66277i	0.184759	+	0.248174i	−0.700088	+	0.714057i	$0.746856\pi$
$354$		0			0
$355$	−0.704246	+	2.35234i	−0.0373775	+	0.124849i
$356$	−10.7801	−	5.41396i	−0.571343	−	0.286939i
$357$		0			0
$358$	−8.69046	−	29.0282i	−0.459305	−	1.53419i
$359$	3.38611	−	19.2036i	0.178712	−	1.01353i	−0.755059	−	0.655657i	$-0.772392\pi$
$359$	3.38611	−	19.2036i	0.178712	−	1.01353i	0.933771	−	0.357871i	$-0.116497\pi$
$360$		0			0
$361$	−1.19036	−	6.75087i	−0.0626506	−	0.355309i
$362$	−40.9216	+	20.5516i	−2.15079	+	1.08017i
$363$		0			0
$364$	0.524431	+	1.21577i	0.0274876	+	0.0637235i
$365$	7.34232	+	17.0214i	0.384315	+	0.890942i
$366$		0			0
$367$	−16.8818	+	8.47836i	−0.881222	+	0.442567i	−0.831065	−	0.556175i	$-0.812269\pi$
$367$	−16.8818	+	8.47836i	−0.881222	+	0.442567i	−0.0501571	+	0.998741i	$0.515972\pi$
$368$	6.94663	+	39.3963i	0.362118	+	2.05367i
$369$		0			0
$370$	−4.43392	+	25.1460i	−0.230509	+	1.30728i
$371$	−0.759833	−	2.53802i	−0.0394486	−	0.131767i
$372$		0			0
$373$	−19.9239	−	10.0061i	−1.03162	−	0.518098i	−0.149320	−	0.988789i	$-0.547709\pi$
$373$	−19.9239	−	10.0061i	−1.03162	−	0.518098i	−0.882298	+	0.470691i	$0.844005\pi$
$374$	−0.248987	+	0.831676i	−0.0128748	+	0.0430049i
$375$		0			0
$376$	6.83676	+	9.18337i	0.352579	+	0.473596i
$377$	19.1926	+	33.2425i	0.988467	+	1.71207i
$378$		0			0
$379$	5.97107	−	10.3422i	0.306713	−	0.531243i	−0.670928	−	0.741522i	$-0.734104\pi$
$379$	5.97107	−	10.3422i	0.306713	−	0.531243i	0.977641	+	0.210280i	$0.0674374\pi$
$380$	−4.39458	+	0.513653i	−0.225437	+	0.0263499i
$381$		0			0
$382$	5.21706	−	1.23647i	0.266928	−	0.0632631i
$383$	−17.4697	+	11.4900i	−0.892662	+	0.587113i	−0.910857	−	0.412721i	$-0.864578\pi$
$383$	−17.4697	+	11.4900i	−0.892662	+	0.587113i	0.0181952	+	0.999834i	$0.494208\pi$
$384$		0			0
$385$	−0.704897	+	0.747148i	−0.0359249	+	0.0380782i
$386$	−12.9434	−	10.8608i	−0.658802	−	0.552800i
$387$		0			0
$388$	−4.72360	+	3.96357i	−0.239804	+	0.201220i
$389$	−0.558292	+	9.58551i	−0.0283066	+	0.486005i	0.954128	+	0.299398i	$0.0967859\pi$
$389$	−0.558292	+	9.58551i	−0.0283066	+	0.486005i	−0.982435	+	0.186606i	$0.940251\pi$
$390$		0			0
$391$	−1.00721	+	1.35291i	−0.0509366	+	0.0684197i
$392$	12.6126	+	1.47420i	0.637032	+	0.0744583i
$393$		0			0
$394$	2.91276	+	1.91575i	0.146743	+	0.0965141i
$395$	4.08763	+	1.48777i	0.205671	+	0.0748581i
$396$		0			0
$397$	1.93277	−	0.703471i	0.0970030	−	0.0353062i	−0.293063	−	0.956093i	$-0.594674\pi$
$397$	1.93277	−	0.703471i	0.0970030	−	0.0353062i	0.390066	+	0.920787i	$0.372452\pi$
$398$	21.7476	+	5.15427i	1.09011	+	0.258360i
$399$		0			0
$400$	−0.904208	−	15.5247i	−0.0452104	−	0.776233i
$401$	−0.464530	−	0.492373i	−0.0231975	−	0.0245879i	0.715671	−	0.698438i	$-0.246121\pi$
$401$	−0.464530	−	0.492373i	−0.0231975	−	0.0245879i	−0.738869	+	0.673850i	$0.764640\pi$
$402$		0			0
$403$	−1.46609	+	3.39877i	−0.0730310	+	0.169305i
$404$	−8.61563			−0.428644
$405$		0			0
$406$	4.41052			0.218891
$407$	−10.3814	+	24.0669i	−0.514588	+	1.19295i
$408$		0			0
$409$	−11.7714	−	12.4770i	−0.582058	−	0.616945i	0.367695	−	0.929947i	$-0.380147\pi$
$409$	−11.7714	−	12.4770i	−0.582058	−	0.616945i	−0.949753	+	0.313001i	$0.898666\pi$
$410$	0.641507	+	11.0142i	0.0316818	+	0.543955i
$411$		0			0
$412$	−1.18106	−	0.279917i	−0.0581869	−	0.0137905i
$413$	−2.05907	+	0.749442i	−0.101320	+	0.0368776i
$414$		0			0
$415$	−1.03538	−	0.376849i	−0.0508250	−	0.0184988i
$416$	18.7551	+	12.3354i	0.919545	+	0.604794i
$417$		0			0
$418$	−14.2708	−	1.66801i	−0.698006	−	0.0815852i
$419$	−16.7727	+	22.5296i	−0.819399	+	1.10064i	0.173865	+	0.984769i	$0.444374\pi$
$419$	−16.7727	+	22.5296i	−0.819399	+	1.10064i	−0.993264	+	0.115874i	$0.963033\pi$
$420$		0			0
$421$	0.584307	−	10.0322i	0.0284774	−	0.488938i	−0.953674	−	0.300843i	$-0.902732\pi$
$421$	0.584307	−	10.0322i	0.0284774	−	0.488938i	0.982151	−	0.188094i	$-0.0602311\pi$
$422$	20.7945	−	17.4487i	1.01226	−	0.849388i
$423$		0			0
$424$	−12.0332	−	10.0970i	−0.584382	−	0.490354i
$425$	0.449945	−	0.476913i	0.0218255	−	0.0231337i
$426$		0			0
$427$	2.59628	−	1.70760i	0.125643	−	0.0826365i
$428$	−0.695949	+	0.164943i	−0.0336400	+	0.00797282i
$429$		0			0
$430$	17.3517	−	2.02812i	0.836774	−	0.0978048i
$431$	−2.67380	+	4.63116i	−0.128792	+	0.223075i	−0.923209	−	0.384298i	$-0.874443\pi$
$431$	−2.67380	+	4.63116i	−0.128792	+	0.223075i	0.794417	+	0.607373i	$0.207777\pi$
$432$		0			0
$433$	3.44686	+	5.97014i	0.165646	+	0.286906i	0.936884	−	0.349639i	$-0.113696\pi$
$433$	3.44686	+	5.97014i	0.165646	+	0.286906i	−0.771239	+	0.636546i	$0.780363\pi$
$434$	0.253977	+	0.341150i	0.0121913	+	0.0163757i
$435$		0			0
$436$	0.546710	−	1.82614i	0.0261826	−	0.0874561i
$437$	−24.9453	−	12.5280i	−1.19329	−	0.599295i
$438$		0			0
$439$	−4.46624	−	14.9183i	−0.213162	−	0.712011i	−0.995965	−	0.0897416i	$-0.971396\pi$
$439$	−4.46624	−	14.9183i	−0.213162	−	0.712011i	0.782803	−	0.622270i	$-0.213789\pi$
$440$	−1.05757	+	5.99779i	−0.0504178	+	0.285934i
$441$		0			0
$442$	0.288704	+	1.63732i	0.0137323	+	0.0778796i
$443$	−24.9809	+	12.5459i	−1.18688	+	0.596072i	−0.928991	−	0.370103i	$-0.879322\pi$
$443$	−24.9809	+	12.5459i	−1.18688	+	0.596072i	−0.257886	+	0.966175i	$0.583026\pi$
$444$		0			0
$445$	−7.09870	−	16.4566i	−0.336511	−	0.780120i
$446$	1.28397	+	2.97659i	0.0607979	+	0.140945i
$447$		0			0
$448$	−0.464112	+	0.233086i	−0.0219272	+	0.0110123i
$449$	−1.89891	−	10.7693i	−0.0896152	−	0.508233i	−0.996265	−	0.0863489i	$-0.972480\pi$
$449$	−1.89891	−	10.7693i	−0.0896152	−	0.508233i	0.906650	−	0.421884i	$-0.138631\pi$
$450$		0			0
$451$	−1.96661	+	11.1532i	−0.0926038	+	0.525182i
$452$	1.55833	+	5.20519i	0.0732977	+	0.244831i
$453$		0			0
$454$	39.0567	+	19.6150i	1.83302	+	0.920579i
$455$	−0.564187	+	1.88451i	−0.0264495	+	0.0883474i
$456$		0			0
$457$	−9.81178	−	13.1795i	−0.458976	−	0.616511i	0.511039	−	0.859558i	$-0.329261\pi$
$457$	−9.81178	−	13.1795i	−0.458976	−	0.616511i	−0.970015	+	0.243046i	$0.921853\pi$
$458$	−4.01150	−	6.94812i	−0.187445	−	0.324664i
$459$		0			0
$460$	5.08471	−	8.80698i	0.237076	−	0.410627i
$461$	24.8325	−	2.90251i	1.15657	−	0.135183i	0.483896	−	0.875126i	$-0.339221\pi$
$461$	24.8325	−	2.90251i	1.15657	−	0.135183i	0.672670	+	0.739943i	$0.265147\pi$
$462$		0			0
$463$	13.1994	−	3.12832i	0.613429	−	0.145385i	0.0878551	−	0.996133i	$-0.471999\pi$
$463$	13.1994	−	3.12832i	0.613429	−	0.145385i	0.525574	+	0.850748i	$0.323851\pi$
$464$	34.6905	−	22.8163i	1.61047	−	1.05922i
$465$		0			0
$466$	13.4509	−	14.2571i	0.623100	−	0.660447i
$467$	−26.2848	−	22.0556i	−1.21632	−	1.02061i	−0.999009	−	0.0445082i	$-0.985828\pi$
$467$	−26.2848	−	22.0556i	−1.21632	−	1.02061i	−0.217308	−	0.976103i	$-0.569728\pi$
$468$		0			0
$469$	0.298233	−	0.250247i	0.0137711	−	0.0115554i
$470$	0.850014	−	14.5942i	0.0392082	−	0.673179i
$471$		0			0
$472$	−7.75831	+	10.4212i	−0.357105	+	0.479675i
$473$	17.8114	+	2.08186i	0.818971	+	0.0957240i
$474$		0			0
$475$	9.06614	+	5.96290i	0.415983	+	0.273596i
$476$	0.0567445	+	0.0206533i	0.00260088	+	0.000946643i
$477$		0			0
$478$	−18.8761	+	6.87035i	−0.863374	+	0.314242i
$479$	−21.0780	−	4.99558i	−0.963079	−	0.228254i	−0.281143	−	0.959666i	$-0.590714\pi$
$479$	−21.0780	−	4.99558i	−0.963079	−	0.228254i	−0.681936	+	0.731412i	$0.738862\pi$
$480$		0			0
$481$	2.91861	+	50.1105i	0.133077	+	2.28484i
$482$	5.18577	+	5.49659i	0.236205	+	0.250363i
$483$		0			0
$484$	−1.89941	+	4.40334i	−0.0863370	+	0.200152i
$485$	−9.16119			−0.415988
$486$		0			0
$487$	38.8502			1.76047			0.880235	−	0.474538i	$-0.157385\pi$
$487$	38.8502			1.76047			0.880235	+	0.474538i	$0.157385\pi$
$488$	7.29768	−	16.9179i	0.330350	−	0.765838i
$489$		0			0
$490$	−11.1271	−	11.7940i	−0.502671	−	0.532800i
$491$	−1.70264	−	29.2332i	−0.0768391	−	1.31928i	−0.787751	−	0.615994i	$-0.788754\pi$
$491$	−1.70264	−	29.2332i	−0.0768391	−	1.31928i	0.710912	−	0.703281i	$-0.248283\pi$
$492$		0			0
$493$	1.70344	+	0.403724i	0.0767193	+	0.0181828i
$494$	−25.8565	+	9.41099i	−1.16334	+	0.423420i
$495$		0			0
$496$	3.76245	+	1.36942i	0.168939	+	0.0614887i
$497$	0.463398	+	0.304782i	0.0207863	+	0.0136713i
$498$		0			0
$499$	27.2881	+	3.18952i	1.22158	+	0.142783i	0.702339	−	0.711843i	$-0.252139\pi$
$499$	27.2881	+	3.18952i	1.22158	+	0.142783i	0.519245	+	0.854625i	$0.326213\pi$
$500$	−6.15145	+	8.26282i	−0.275101	+	0.369525i
$501$		0			0
$502$	0.624386	−	10.7203i	0.0278677	−	0.478470i
$503$	−25.2177	+	21.1601i	−1.12440	+	0.943484i	−0.998818	−	0.0485988i	$-0.984524\pi$
$503$	−25.2177	+	21.1601i	−1.12440	+	0.943484i	−0.125583	+	0.992083i	$0.540080\pi$
$504$		0			0
$505$	−9.80560	−	8.22788i	−0.436343	−	0.366136i
$506$	22.6622	−	24.0206i	1.00746	−	1.06784i
$507$		0			0
$508$	−8.07427	+	5.31053i	−0.358238	+	0.235617i
$509$	4.99552	−	1.18396i	0.221423	−	0.0524781i	−0.118407	−	0.992965i	$-0.537779\pi$
$509$	4.99552	−	1.18396i	0.221423	−	0.0524781i	0.339830	+	0.940487i	$0.389631\pi$
$510$		0			0
$511$	4.15890	−	0.486106i	0.183979	−	0.0215040i
$512$	2.95483	−	5.11791i	0.130586	−	0.226182i
$513$		0			0
$514$	−2.02126	−	3.50093i	−0.0891541	−	0.154419i
$515$	−1.07687	−	1.44649i	−0.0474526	−	0.0637399i
$516$		0			0
$517$	4.30384	−	14.3758i	0.189283	−	0.632248i
$518$	5.15408	+	2.58847i	0.226457	+	0.113731i
$519$		0			0
$520$	3.34514	+	11.1735i	0.146694	+	0.489992i
$521$	−1.32353	+	7.50611i	−0.0579849	+	0.328849i	−0.999977	−	0.00678637i	$-0.997840\pi$
$521$	−1.32353	+	7.50611i	−0.0579849	+	0.328849i	0.941992	+	0.335635i	$0.108951\pi$
$522$		0			0
$523$	−1.93766	−	10.9890i	−0.0847279	−	0.480516i	−0.997415	−	0.0718566i	$-0.977108\pi$
$523$	−1.93766	−	10.9890i	−0.0847279	−	0.480516i	0.912687	−	0.408659i	$-0.134004\pi$
$524$	−4.94791	+	2.48493i	−0.216151	+	0.108555i
$525$		0			0
$526$	9.48017	+	21.9775i	0.413355	+	0.958265i
$527$	0.0668639	+	0.155008i	0.00291264	+	0.00675226i
$528$		0			0
$529$	36.7815	−	18.4724i	1.59919	−	0.803146i
$530$	3.48297	+	19.7529i	0.151291	+	0.858012i
$531$		0			0
$532$	−0.173544	+	0.984215i	−0.00752407	+	0.0426711i
$533$	6.22044	+	20.7777i	0.269437	+	0.899982i
$534$		0			0
$535$	−0.949591	−	0.476903i	−0.0410544	−	0.0206183i
$536$	0.662030	−	2.21133i	0.0285953	−	0.0955150i
$537$		0			0
$538$	26.2712	+	35.2883i	1.13263	+	1.52139i
$539$	−8.32207	−	14.4143i	−0.358457	−	0.620866i
$540$		0			0
$541$	12.8996	−	22.3428i	0.554598	−	0.960592i	−0.443337	−	0.896355i	$-0.646205\pi$
$541$	12.8996	−	22.3428i	0.554598	−	0.960592i	0.997935	−	0.0642366i	$-0.0204612\pi$
$542$	22.1572	−	2.58981i	0.951735	−	0.111242i
$543$		0			0
$544$	0.996195	−	0.236103i	0.0427115	−	0.0101228i
$545$	2.36617	−	1.55625i	0.101356	−	0.0666626i
$546$		0			0
$547$	−24.8071	+	26.2940i	−1.06068	+	1.12425i	−0.0687241	+	0.997636i	$0.521893\pi$
$547$	−24.8071	+	26.2940i	−1.06068	+	1.12425i	−0.991952	+	0.126615i	$0.959589\pi$
$548$	0.822645	+	0.690281i	0.0351417	+	0.0294874i
$549$		0			0
$550$	−9.83406	+	8.25176i	−0.419326	+	0.351856i
$551$	−1.68464	+	28.9241i	−0.0717680	+	1.23221i
$552$		0			0
$553$	0.586745	−	0.788135i	0.0249509	−	0.0335149i
$554$	8.86331	+	1.03597i	0.376566	+	0.0440143i
$555$		0			0
$556$	−12.5955	−	8.28421i	−0.534169	−	0.351329i
$557$	31.3174	+	11.3986i	1.32696	+	0.482974i	0.905682	−	0.423957i	$-0.139359\pi$
$557$	31.3174	+	11.3986i	1.32696	+	0.482974i	0.421278	+	0.906931i	$0.361582\pi$
$558$		0			0
$559$	32.2717	−	11.7459i	1.36495	−	0.496800i
$560$	2.07052	+	0.490722i	0.0874954	+	0.0207368i
$561$		0			0
$562$	−0.564773	−	9.69678i	−0.0238235	−	0.409034i
$563$	−23.7787	−	25.2040i	−1.00215	−	1.06222i	−0.998062	−	0.0622289i	$-0.980179\pi$
$563$	−23.7787	−	25.2040i	−1.00215	−	1.06222i	−0.00409146	−	0.999992i	$-0.501302\pi$
$564$		0			0
$565$	−3.19736	+	7.41231i	−0.134514	+	0.311838i
$566$	19.4174			0.816173
$567$		0			0
$568$	3.28856			0.137985
$569$	13.0161	−	30.1747i	0.545663	−	1.26499i	−0.392805	−	0.919622i	$-0.628495\pi$
$569$	13.0161	−	30.1747i	0.545663	−	1.26499i	0.938468	−	0.345367i	$-0.112245\pi$
$570$		0			0
$571$	10.4745	+	11.1024i	0.438346	+	0.464620i	0.908451	−	0.417991i	$-0.137266\pi$
$571$	10.4745	+	11.1024i	0.438346	+	0.464620i	−0.470105	+	0.882610i	$0.655784\pi$
$572$	−0.598300	−	10.2724i	−0.0250162	−	0.429511i
$573$		0			0
$574$	2.42492	+	0.574716i	0.101214	+	0.0239882i
$575$	−23.4369	+	8.53034i	−0.977386	+	0.355740i
$576$		0			0
$577$	9.00255	+	3.27666i	0.374781	+	0.136409i	0.522541	−	0.852614i	$-0.324984\pi$
$577$	9.00255	+	3.27666i	0.374781	+	0.136409i	−0.147760	+	0.989023i	$0.547206\pi$
$578$	−24.2256	−	15.9334i	−1.00765	−	0.662743i
$579$		0			0
$580$	−10.4837	−	1.22537i	−0.435314	−	0.0508809i
$581$	−0.148621	+	0.199632i	−0.00616582	+	0.00828214i
$582$		0			0
$583$	−1.19715	+	20.5542i	−0.0495808	+	0.851269i
$584$	19.0182	−	15.9582i	0.786980	−	0.660355i
$585$		0			0
$586$	−22.6380	−	18.9955i	−0.935165	−	0.784697i
$587$	19.5724	−	20.7455i	0.807838	−	0.856258i	−0.184110	−	0.982906i	$-0.558940\pi$
$587$	19.5724	−	20.7455i	0.807838	−	0.856258i	0.991948	+	0.126648i	$0.0404218\pi$
$588$		0			0
$589$	−2.33426	+	1.53527i	−0.0961817	+	0.0632597i
$590$	16.1423	−	3.82579i	0.664567	−	0.157505i
$591$		0			0
$592$	53.9294	−	6.30344i	2.21649	−	0.259070i
$593$	−21.1230	+	36.5862i	−0.867419	+	1.50241i	−0.00279478	+	0.999996i	$0.500890\pi$
$593$	−21.1230	+	36.5862i	−0.867419	+	1.50241i	−0.864625	+	0.502418i	$0.832444\pi$
$594$		0			0
$595$	0.0448581	+	0.0776966i	0.00183900	+	0.00318525i
$596$	−4.92876	−	6.62048i	−0.201890	−	0.271185i
$597$		0			0
$598$	18.1384	−	60.5866i	0.741735	−	2.47757i
$599$	−16.0004	−	8.03568i	−0.653757	−	0.328329i	0.0908185	−	0.995867i	$-0.471052\pi$
$599$	−16.0004	−	8.03568i	−0.653757	−	0.328329i	−0.744575	+	0.667538i	$0.767348\pi$
$600$		0			0
$601$	2.87565	+	9.60533i	0.117300	+	0.391809i	0.996395	−	0.0848376i	$-0.0270372\pi$
$601$	2.87565	+	9.60533i	0.117300	+	0.391809i	−0.879095	+	0.476647i	$0.841852\pi$
$602$	0.685225	−	3.88610i	0.0279277	−	0.158386i
$603$		0			0
$604$	−2.50327	−	14.1968i	−0.101857	−	0.577658i
$605$	−6.36692	+	3.19759i	−0.258852	+	0.130000i
$606$		0			0
$607$	−4.73369	−	10.9739i	−0.192135	−	0.445418i	0.794731	−	0.606962i	$-0.207612\pi$
$607$	−4.73369	−	10.9739i	−0.192135	−	0.445418i	−0.986866	+	0.161544i	$0.948353\pi$
$608$	6.71112	+	15.5581i	0.272172	+	0.630965i
$609$		0			0
$610$	−21.0240	+	10.5587i	−0.851237	+	0.427507i
$611$	−4.99036	−	28.3018i	−0.201888	−	1.14497i
$612$		0			0
$613$	−6.82305	+	38.6954i	−0.275580	+	1.56289i	0.461532	+	0.887124i	$0.347300\pi$
$613$	−6.82305	+	38.6954i	−0.275580	+	1.56289i	−0.737112	+	0.675771i	$0.763811\pi$
$614$	−4.12615	−	13.7823i	−0.166518	−	0.556209i
$615$		0			0
$616$	1.22934	+	0.617399i	0.0495316	+	0.0248757i
$617$	11.7232	−	39.1581i	0.471957	−	1.57644i	−0.308493	−	0.951226i	$-0.599825\pi$
$617$	11.7232	−	39.1581i	0.471957	−	1.57644i	0.780450	−	0.625218i	$-0.214990\pi$
$618$		0			0
$619$	15.2570	+	20.4937i	0.613230	+	0.823711i	0.994929	−	0.100576i	$-0.0320684\pi$
$619$	15.2570	+	20.4937i	0.613230	+	0.823711i	−0.381699	+	0.924287i	$0.624661\pi$
$620$	−0.508917	−	0.881470i	−0.0204386	−	0.0354007i
$621$		0			0
$622$	5.60517	−	9.70843i	0.224747	−	0.389273i
$623$	−4.02091	+	0.469976i	−0.161094	+	0.0188292i
$624$		0			0
$625$	0.257080	−	0.0609291i	0.0102832	−	0.00243716i
$626$	7.78974	−	5.12339i	0.311340	−	0.204772i
$627$		0			0
$628$	−7.76404	+	8.22940i	−0.309819	+	0.328389i
$629$	1.75368	+	1.47151i	0.0699239	+	0.0586731i
$630$		0			0
$631$	−3.09592	+	2.59779i	−0.123247	+	0.103416i	−0.702328	−	0.711854i	$-0.747856\pi$
$631$	−3.09592	+	2.59779i	−0.123247	+	0.103416i	0.579081	+	0.815270i	$0.303411\pi$
$632$	0.338736	−	5.81588i	0.0134742	−	0.231343i
$633$		0			0
$634$	3.67152	−	4.93171i	0.145815	−	0.195863i
$635$	−14.2610	−	1.66687i	−0.565930	−	0.0661478i
$636$		0			0
$637$	−26.6313	−	17.5157i	−1.05517	−	0.693995i
$638$	−32.2091	−	11.7231i	−1.27517	−	0.464123i
$639$		0			0
$640$	16.2444	−	5.91248i	0.642116	−	0.233711i
$641$	11.5063	+	2.72705i	0.454472	+	0.107712i	0.451475	−	0.892284i	$-0.350898\pi$
$641$	11.5063	+	2.72705i	0.454472	+	0.107712i	0.00299679	+	0.999996i	$0.499046\pi$
$642$		0			0
$643$	1.17771	+	20.2204i	0.0464442	+	0.797416i	0.938455	+	0.345402i	$0.112257\pi$
$643$	1.17771	+	20.2204i	0.0464442	+	0.797416i	−0.892011	+	0.452014i	$0.850706\pi$
$644$	−1.57633	−	1.67081i	−0.0621161	−	0.0658393i
$645$		0			0
$646$	−0.497048	+	1.15229i	−0.0195561	+	0.0453361i
$647$	25.4173			0.999257			0.499629	−	0.866240i	$-0.333470\pi$
$647$	25.4173			0.999257			0.499629	+	0.866240i	$0.333470\pi$
$648$		0			0
$649$	17.0290			0.668446
$650$	−9.73759	+	22.5743i	−0.381940	+	0.885436i
$651$		0			0
$652$	15.9110	+	16.8647i	0.623125	+	0.660473i
$653$	−0.380169	−	6.52724i	−0.0148772	−	0.255431i	−0.997544	−	0.0700484i	$-0.977685\pi$
$653$	−0.380169	−	6.52724i	−0.0148772	−	0.255431i	0.982666	−	0.185382i	$-0.0593524\pi$
$654$		0			0
$655$	−8.00440	−	1.89708i	−0.312758	−	0.0741250i
$656$	22.0460	−	8.02410i	0.860753	−	0.313289i
$657$		0			0
$658$	−3.10295	−	1.12938i	−0.120966	−	0.0440279i
$659$	20.8387	+	13.7058i	0.811761	+	0.533904i	0.886190	−	0.463323i	$-0.153343\pi$
$659$	20.8387	+	13.7058i	0.811761	+	0.533904i	−0.0744284	+	0.997226i	$0.523713\pi$
$660$		0			0
$661$	44.7213	+	5.22717i	1.73946	+	0.203313i	0.925795	−	0.378025i	$-0.123397\pi$
$661$	44.7213	+	5.22717i	1.73946	+	0.203313i	0.813662	+	0.581339i	$0.197471\pi$
$662$	27.3753	−	36.7714i	1.06397	−	1.42916i
$663$		0			0
$664$	−0.0858009	+	1.47314i	−0.00332972	+	0.0571691i
$665$	−1.13743	+	0.954419i	−0.0441077	+	0.0370108i
$666$		0			0
$667$	−51.0131	−	42.8051i	−1.97523	−	1.65742i
$668$	−5.10887	+	5.41509i	−0.197668	+	0.209516i
$669$		0			0
$670$	−2.46256	+	1.61965i	−0.0951372	+	0.0625727i
$671$	−23.4988	+	5.56932i	−0.907162	+	0.215001i
$672$		0			0
$673$	−12.0498	+	1.40842i	−0.464485	+	0.0542905i	−0.345117	−	0.938560i	$-0.612161\pi$
$673$	−12.0498	+	1.40842i	−0.464485	+	0.0542905i	−0.119368	+	0.992850i	$0.538087\pi$
$674$	18.4838	−	32.0150i	0.711971	−	1.23317i
$675$		0			0
$676$	−3.84429	−	6.65851i	−0.147857	−	0.256097i
$677$	−3.57201	−	4.79804i	−0.137283	−	0.184404i	0.728165	−	0.685402i	$-0.240374\pi$
$677$	−3.57201	−	4.79804i	−0.137283	−	0.184404i	−0.865448	+	0.500999i	$0.832966\pi$
$678$		0			0
$679$	−0.593486	+	1.98238i	−0.0227759	+	0.0760768i
$680$	0.475359	+	0.238734i	0.0182292	+	0.00915503i
$681$		0			0
$682$	−0.947961	−	3.16641i	−0.0362993	−	0.121248i
$683$	4.79324	−	27.1838i	0.183408	−	1.04016i	−0.744575	−	0.667538i	$-0.767348\pi$
$683$	4.79324	−	27.1838i	0.183408	−	1.04016i	0.927984	−	0.372621i	$-0.121541\pi$
$684$		0			0
$685$	0.277053	+	1.57124i	0.0105856	+	0.0600341i
$686$	−6.59150	+	3.31038i	−0.251665	+	0.126391i
$687$		0			0
$688$	−14.7138	−	34.1105i	−0.560960	−	1.30045i
$689$	15.6174	+	36.2052i	0.594976	+	1.37931i
$690$		0			0
$691$	−26.2115	+	13.1639i	−0.997134	+	0.500779i	−0.871026	−	0.491237i	$-0.836545\pi$
$691$	−26.2115	+	13.1639i	−0.997134	+	0.500779i	−0.126108	+	0.992017i	$0.540248\pi$
$692$	−2.85518	−	16.1926i	−0.108538	−	0.615549i
$693$		0			0
$694$	−5.00138	+	28.3642i	−0.189850	+	1.07669i
$695$	−6.42382	−	21.4571i	−0.243669	−	0.813912i
$696$		0			0
$697$	0.883951	+	0.443937i	0.0334820	+	0.0168153i
$698$	−0.966827	+	3.22943i	−0.0365949	+	0.122236i
$699$		0			0
$700$	0.533229	+	0.716250i	0.0201541	+	0.0270717i
$701$	−1.45226	−	2.51539i	−0.0548512	−	0.0950051i	0.837296	−	0.546750i	$-0.184135\pi$
$701$	−1.45226	−	2.51539i	−0.0548512	−	0.0950051i	−0.892147	+	0.451745i	$0.850802\pi$
$702$		0			0
$703$	−18.9438	+	32.8116i	−0.714479	+	1.23751i
$704$	4.00884	−	0.468567i	0.151089	−	0.0176598i
$705$		0			0
$706$	−9.67287	+	2.29251i	−0.364043	+	0.0862799i
$707$	−2.41565	+	1.58880i	−0.0908500	+	0.0597530i
$708$		0			0
$709$	16.9595	−	17.9760i	0.636927	−	0.675103i	−0.325844	−	0.945424i	$-0.605648\pi$
$709$	16.9595	−	17.9760i	0.636927	−	0.675103i	0.962770	+	0.270321i	$0.0871298\pi$
$710$	−3.21672	−	2.69915i	−0.120721	−	0.101297i
$711$		0			0
$712$	−18.3872	+	15.4287i	−0.689089	+	0.578215i
$713$	0.373382	−	6.41071i	0.0139832	−	0.240083i
$714$		0			0
$715$	9.12916	−	12.2626i	0.341411	−	0.458595i
$716$	16.2689	+	1.90157i	0.607999	+	0.0710648i
$717$		0			0
$718$	27.8606	+	18.3242i	1.03975	+	0.683854i
$719$	23.8425	+	8.67796i	0.889175	+	0.323633i	0.745907	−	0.666051i	$-0.232017\pi$
$719$	23.8425	+	8.67796i	0.889175	+	0.323633i	0.143269	+	0.989684i	$0.454239\pi$
$720$		0			0
$721$	−0.382767	+	0.139316i	−0.0142550	+	0.00518838i
$722$	11.4067	+	2.70344i	0.424514	+	0.100612i
$723$		0			0
$724$	−1.43930	−	24.7119i	−0.0534912	−	0.918409i
$725$	17.7647	+	18.8295i	0.659765	+	0.699310i
$726$		0			0
$727$	7.03503	−	16.3090i	0.260915	−	0.604868i	−0.736523	−	0.676413i	$-0.763534\pi$
$727$	7.03503	−	16.3090i	0.260915	−	0.604868i	0.997437	+	0.0715446i	$0.0227928\pi$
$728$	2.63453			0.0976424
$729$		0			0
$730$	−31.7008			−1.17330
$731$	0.620370	−	1.43818i	0.0229452	−	0.0531930i
$732$		0			0
$733$	−6.35574	−	6.73669i	−0.234755	−	0.248825i	0.599277	−	0.800541i	$-0.295455\pi$
$733$	−6.35574	−	6.73669i	−0.234755	−	0.248825i	−0.834032	+	0.551716i	$0.813973\pi$
$734$	−1.87841	−	32.2510i	−0.0693333	−	1.19041i
$735$		0			0
$736$	−37.8946	−	8.98118i	−1.39681	−	0.331051i
$737$	−2.84309	+	1.03480i	−0.104726	+	0.0381173i
$738$		0			0
$739$	5.02496	+	1.82894i	0.184846	+	0.0672785i	0.432785	−	0.901497i	$-0.357531\pi$
$739$	5.02496	+	1.82894i	0.184846	+	0.0672785i	−0.247939	+	0.968776i	$0.579753\pi$
$740$	−11.5320	−	7.58472i	−0.423925	−	0.278820i
$741$		0			0
$742$	4.49994	+	0.525968i	0.165198	+	0.0193089i
$743$	−15.5402	+	20.8740i	−0.570113	+	0.765795i	−0.989891	−	0.141832i	$-0.954701\pi$
$743$	−15.5402	+	20.8740i	−0.570113	+	0.765795i	0.419778	+	0.907627i	$0.362108\pi$
$744$		0			0
$745$	0.713005	−	12.2418i	0.0261225	−	0.448506i
$746$	29.2071	−	24.5076i	1.06935	−	0.897288i
$747$		0			0
$748$	−0.359496	−	0.301653i	−0.0131445	−	0.0110295i
$749$	−0.164713	+	0.174586i	−0.00601849	+	0.00637923i
$750$		0			0
$751$	3.04582	−	2.00327i	0.111143	−	0.0731002i	−0.492720	−	0.870188i	$-0.663997\pi$
$751$	3.04582	−	2.00327i	0.111143	−	0.0731002i	0.603864	+	0.797088i	$0.293627\pi$
$752$	−30.2484	+	7.16900i	−1.10305	+	0.261427i
$753$		0			0
$754$	−65.1982	+	7.62058i	−2.37438	+	0.277525i
$755$	10.7088	−	18.5482i	0.389733	−	0.675038i
$756$		0			0
$757$	−5.44196	−	9.42576i	−0.197792	−	0.342585i	0.750021	−	0.661415i	$-0.230044\pi$
$757$	−5.44196	−	9.42576i	−0.197792	−	0.342585i	−0.947812	+	0.318830i	$0.896710\pi$
$758$	12.1953	+	16.3811i	0.442952	+	0.594988i
$759$		0			0
$760$	−2.52491	+	8.43380i	−0.0915883	+	0.305926i
$761$	22.0603	+	11.0791i	0.799687	+	0.401618i	0.801212	−	0.598381i	$-0.204189\pi$
$761$	22.0603	+	11.0791i	0.799687	+	0.401618i	−0.00152487	+	0.999999i	$0.500485\pi$
$762$		0			0
$763$	−0.183470	−	0.612831i	−0.00664204	−	0.0221860i
$764$	−0.503281	+	2.85425i	−0.0182081	+	0.103263i
$765$		0			0
$766$	−6.20921	−	35.2142i	−0.224348	−	1.27234i
$767$	29.1432	−	14.6363i	1.05230	−	0.528485i
$768$		0			0
$769$	12.3947	+	28.7342i	0.446965	+	1.03618i	0.981574	+	0.191082i	$0.0611996\pi$
$769$	12.3947	+	28.7342i	0.446965	+	1.03618i	−0.534609	+	0.845099i	$0.679541\pi$
$770$	−0.695746	−	1.61292i	−0.0250730	−	0.0581256i
$771$		0			0
$772$	8.16207	−	4.09915i	0.293759	−	0.147531i
$773$	2.32846	+	13.2054i	0.0837490	+	0.474964i	0.997620	+	0.0689585i	$0.0219676\pi$
$773$	2.32846	+	13.2054i	0.0837490	+	0.474964i	−0.913871	+	0.406006i	$0.866921\pi$
$774$		0			0
$775$	−0.433476	+	2.45837i	−0.0155709	+	0.0883071i
$776$	3.51885	+	11.7538i	0.126320	+	0.421937i
$777$		0			0
$778$	−14.6733	−	7.36923i	−0.526065	−	0.264200i
$779$	−4.69520	+	15.6830i	−0.168223	+	0.561904i
$780$		0			0
$781$	−2.57399	−	3.45746i	−0.0921045	−	0.123718i
$782$	−1.44218	−	2.49792i	−0.0515721	−	0.0893255i
$783$

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)

\(f(q)\)	\(=\)	\(q+(-0.677333 + 1.57023i) q^{2} +(-0.634371 - 0.672394i) q^{4} +(-0.0798566 - 1.37108i) q^{5} +(-0.301861 - 0.0715423i) q^{7} +(-1.72842 + 0.629095i) q^{8} +O(q^{10})\)	\(q+(-0.677333 + 1.57023i) q^{2} +(-0.634371 - 0.672394i) q^{4} +(-0.0798566 - 1.37108i) q^{5} +(-0.301861 - 0.0715423i) q^{7} +(-1.72842 + 0.629095i) q^{8} +(2.20701 + 0.803287i) q^{10} +(2.01426 + 1.32480i) q^{11} +(4.58584 + 0.536008i) q^{13} +(0.316798 - 0.425534i) q^{14} +(0.290392 - 4.98584i) q^{16} +(0.161307 - 0.135352i) q^{17} +(2.66964 + 2.24009i) q^{19} +(-0.871250 + 0.923471i) q^{20} +(-3.44457 + 2.26553i) q^{22} +(-7.79405 + 1.84722i) q^{23} +(3.09270 - 0.361484i) q^{25} +(-3.94780 + 6.83779i) q^{26} +(0.143387 + 0.248354i) q^{28} +(4.96463 + 6.66865i) q^{29} +(-0.229930 + 0.768019i) q^{31} +(4.34483 + 2.18205i) q^{32} +(0.103276 + 0.344968i) q^{34} +(-0.0739849 + 0.419589i) q^{35} +(1.88786 + 10.7066i) q^{37} +(-5.32570 + 2.67467i) q^{38} +(1.00057 + 2.31958i) q^{40} +(1.86060 + 4.31336i) q^{41} +(6.64705 - 3.33827i) q^{43} +(-0.387001 - 2.19479i) q^{44} +(2.37859 - 13.4897i) q^{46} +(-1.78517 - 5.96289i) q^{47} +(-6.16943 - 3.09840i) q^{49} +(-1.52717 + 5.10110i) q^{50} +(-2.54872 - 3.42352i) q^{52} +(4.27003 + 7.39591i) q^{53} +(1.65556 - 2.86752i) q^{55} +(0.566750 - 0.0662436i) q^{56} +(-13.8340 + 3.27873i) q^{58} +(5.90137 - 3.88139i) q^{59} +(-6.87408 + 7.28610i) q^{61} +(-1.05023 - 0.881248i) q^{62} +(1.28246 - 1.07611i) q^{64} +(0.368703 - 6.33038i) q^{65} +(-0.749408 + 1.00663i) q^{67} +(-0.193338 - 0.0225980i) q^{68} +(-0.608741 - 0.400375i) q^{70} +(-1.68007 - 0.611494i) q^{71} +(-12.6834 + 4.61640i) q^{73} +(-18.0905 - 4.28753i) q^{74} +(-0.187316 - 3.21610i) q^{76} +(-0.513247 - 0.544010i) q^{77} +(-1.25449 + 2.90824i) q^{79} -6.85919 q^{80} -8.03324 q^{82} +(0.317759 - 0.736649i) q^{83} +(-0.198461 - 0.210356i) q^{85} +(0.739606 + 12.6985i) q^{86} +(-4.31493 - 1.02266i) q^{88} +(12.2626 - 4.46322i) q^{89} +(-1.34594 - 0.489881i) q^{91} +(6.18638 + 4.06885i) q^{92} +(10.5723 + 1.23572i) q^{94} +(2.85817 - 3.83919i) q^{95} +(0.387850 - 6.65913i) q^{97} +(9.04397 - 7.58879i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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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