LMFDB - Embedded newform 729.2.g.d.676.2

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			676.2
Character	$\chi$	$=$	729.676
Dual form			729.2.g.d.55.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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	−0.970853	−	0.239675i	$-0.922959\pi$
$2$	−0.677333	−	1.57023i	−0.478947	−	1.11032i	0.491907	−	0.870648i	$-0.336300\pi$
$3$		0			0
$3$		0			0
$4$	−0.634371	+	0.672394i	−0.317186	+	0.336197i
$5$	−0.0798566	+	1.37108i	−0.0357129	+	0.613167i	0.932210	+	0.361919i	$0.117878\pi$
$5$	−0.0798566	+	1.37108i	−0.0357129	+	0.613167i	−0.967923	+	0.251249i	$0.919159\pi$
$6$		0			0
$7$	−0.301861	+	0.0715423i	−0.114093	+	0.0270404i	−0.287266	−	0.957851i	$-0.592746\pi$
$7$	−0.301861	+	0.0715423i	−0.114093	+	0.0270404i	0.173173	+	0.984891i	$0.444598\pi$
$8$	−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	−0.208268	−	0.978072i	$-0.566783\pi$
$11$	2.01426	−	1.32480i	0.607323	−	0.399442i	0.815591	+	0.578629i	$0.196412\pi$
$12$		0			0
$13$	4.58584	−	0.536008i	1.27188	−	0.148662i	0.546765	−	0.837286i	$-0.315859\pi$
$13$	4.58584	−	0.536008i	1.27188	−	0.148662i	0.725119	+	0.688624i	$0.241785\pi$
$14$	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	0.662139	−	0.749381i	$-0.269649\pi$
$17$	0.161307	+	0.135352i	0.0391226	+	0.0328277i	−0.623017	+	0.782209i	$0.714093\pi$
$18$		0			0
$19$	2.66964	−	2.24009i	0.612457	−	0.513913i	−0.282965	−	0.959130i	$-0.591318\pi$
$19$	2.66964	−	2.24009i	0.612457	−	0.513913i	0.895422	+	0.445218i	$0.146874\pi$
$20$	−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	−0.685724	−	0.727862i	$-0.740514\pi$
$23$	−7.79405	−	1.84722i	−1.62517	−	0.385173i	−0.939449	+	0.342689i	$0.888662\pi$
$24$		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	−0.0489788	−	0.998800i	$-0.515597\pi$
$29$	4.96463	−	6.66865i	0.921908	−	1.23834i	0.970887	−	0.239538i	$-0.0769959\pi$
$30$		0			0
$31$	−0.229930	−	0.768019i	−0.0412966	−	0.137940i	0.934855	−	0.355029i	$-0.115529\pi$
$31$	−0.229930	−	0.768019i	−0.0412966	−	0.137940i	−0.976152	+	0.217089i	$0.930344\pi$
$32$	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	−0.286764	−	0.958001i	$-0.592580\pi$
$37$	1.88786	−	10.7066i	0.310362	−	1.76015i	0.597126	−	0.802148i	$-0.296309\pi$
$38$	−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	−0.708921	−	0.705287i	$-0.750818\pi$
$41$	1.86060	−	4.31336i	0.290577	−	0.673634i	0.999499	+	0.0316531i	$0.0100772\pi$
$42$		0			0
$43$	6.64705	+	3.33827i	1.01367	+	0.509082i	0.876467	−	0.481462i	$-0.159894\pi$
$43$	6.64705	+	3.33827i	1.01367	+	0.509082i	0.137198	+	0.990544i	$0.456190\pi$
$44$	−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	0.723393	+	0.690437i	$0.242582\pi$
$47$	−1.78517	+	5.96289i	−0.260394	+	0.869777i	−0.983787	+	0.179341i	$0.942604\pi$
$48$		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	−0.408149	−	0.912915i	$-0.633826\pi$
$53$	4.27003	−	7.39591i	0.586533	−	1.01591i	0.994682	−	0.102990i	$-0.0328411\pi$
$54$		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	0.872126	−	0.489280i	$-0.162741\pi$
$59$	5.90137	+	3.88139i	0.768293	+	0.505314i	−0.103834	+	0.994595i	$0.533111\pi$
$60$		0			0
$61$	−6.87408	−	7.28610i	−0.880136	−	0.932889i	0.118056	−	0.993007i	$-0.462334\pi$
$61$	−6.87408	−	7.28610i	−0.880136	−	0.932889i	−0.998191	+	0.0601177i	$0.980852\pi$
$62$	−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	0.753985	−	0.656891i	$-0.228129\pi$
$67$	−0.749408	−	1.00663i	−0.0915548	−	0.122979i	−0.845540	+	0.533912i	$0.820721\pi$
$68$	−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	−0.439784	−	0.898104i	$-0.644945\pi$
$71$	−1.68007	+	0.611494i	−0.199387	+	0.0725710i	0.240396	+	0.970675i	$0.422723\pi$
$72$		0			0
$73$	−12.6834	−	4.61640i	−1.48448	−	0.540308i	−0.532494	−	0.846434i	$-0.678745\pi$
$73$	−12.6834	−	4.61640i	−1.48448	−	0.540308i	−0.951991	+	0.306126i	$0.900967\pi$
$74$	−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	0.832953	−	0.553344i	$-0.186648\pi$
$79$	−1.25449	−	2.90824i	−0.141142	−	0.327203i	−0.974095	+	0.226141i	$0.927389\pi$
$80$	−6.85919			−0.766881
$81$		0			0
$82$	−8.03324			−0.887123
$83$	0.317759	+	0.736649i	0.0348786	+	0.0808578i	0.934765	−	0.355267i	$-0.115610\pi$
$83$	0.317759	+	0.736649i	0.0348786	+	0.0808578i	−0.899886	+	0.436125i	$0.856351\pi$
$84$		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	0.896942	−	0.442147i	$-0.145783\pi$
$89$	12.2626	+	4.46322i	1.29983	+	0.473101i	0.402891	+	0.915248i	$0.368005\pi$
$90$		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	0.959015	+	0.283356i	$0.0914480\pi$
$97$	0.387850	+	6.65913i	0.0393802	+	0.676132i	−0.919634	+	0.392775i	$0.871515\pi$
$98$	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	0.962655	−	0.270730i	$-0.0872650\pi$
$101$	6.39584	+	6.77920i	0.636410	+	0.674555i	−0.326245	+	0.945285i	$0.605784\pi$
$102$		0			0
$103$	1.09702	+	0.721522i	0.108093	+	0.0710936i	0.602404	−	0.798191i	$-0.294209\pi$
$103$	1.09702	+	0.721522i	0.108093	+	0.0710936i	−0.494312	+	0.869285i	$0.664580\pi$
$104$	−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	0.884119	−	0.467262i	$-0.154760\pi$
$107$	0.386855	+	0.670052i	0.0373987	+	0.0647764i	−0.846720	+	0.532038i	$0.821426\pi$
$108$		0			0
$109$	1.03104	−	1.78582i	0.0987559	−	0.171050i	−0.812414	−	0.583081i	$-0.801847\pi$
$109$	1.03104	−	1.78582i	0.0987559	−	0.171050i	0.911170	+	0.412031i	$0.135180\pi$
$110$	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	−0.678365	−	0.734725i	$-0.737311\pi$
$113$	−5.25253	+	2.63792i	−0.494116	+	0.248154i	0.184249	+	0.982880i	$0.441015\pi$
$114$		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	0.953006	+	0.302951i	$0.0979720\pi$
$127$	1.81538	+	10.2955i	0.161089	+	0.913580i	−0.791917	+	0.610628i	$0.790917\pi$
$128$	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	0.999658	−	0.0261475i	$-0.00832394\pi$
$131$	1.71783	+	5.73796i	0.150088	+	0.501328i	−0.849570	+	0.527475i	$0.823139\pi$
$132$		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	0.0666602	−	0.997776i	$-0.478766\pi$
$137$	−1.15384	−	0.134865i	−0.0985793	−	0.0115223i	−0.165240	+	0.986253i	$0.552840\pi$
$138$		0			0
$139$	15.8687	+	3.76096i	1.34597	+	0.319001i	0.839548	−	0.543285i	$-0.182820\pi$
$139$	15.8687	+	3.76096i	1.34597	+	0.319001i	0.506421	+	0.862286i	$0.330968\pi$
$140$	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	0.255205	−	0.966887i	$-0.417857\pi$
$149$	8.86820	−	1.03654i	0.726511	−	0.0849170i	0.471306	+	0.881970i	$0.343783\pi$
$150$		0			0
$151$	13.0290	−	8.56932i	1.06029	−	0.697361i	0.105429	−	0.994427i	$-0.466378\pi$
$151$	13.0290	−	8.56932i	1.06029	−	0.697361i	0.954857	+	0.297065i	$0.0960080\pi$
$152$	−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	0.842753	+	0.538300i	$0.180933\pi$
$157$	−0.711632	+	12.2182i	−0.0567944	+	0.975122i	−0.899548	+	0.436822i	$0.856104\pi$
$158$	−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	0.930489	+	0.366320i	$0.119382\pi$
$167$	−0.468266	+	8.03982i	−0.0362355	+	0.622140i	−0.966724	+	0.255820i	$0.917655\pi$
$168$		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	0.160060	−	0.987107i	$-0.448831\pi$
$173$	14.8606	−	9.77400i	1.12983	−	0.743104i	0.969774	+	0.244004i	$0.0784609\pi$
$174$		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	−0.0256035	−	0.999672i	$-0.508151\pi$
$179$	−13.5735	−	11.3896i	−1.01453	−	0.851295i	−0.988931	+	0.148377i	$0.952595\pi$
$180$		0			0
$181$	20.5130	−	17.2124i	1.52472	−	1.27939i	0.699377	−	0.714753i	$-0.253461\pi$
$181$	20.5130	−	17.2124i	1.52472	−	1.27939i	0.825340	−	0.564636i	$-0.190983\pi$
$182$	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	−0.864682	−	0.502320i	$-0.832480\pi$
$191$	−1.87225	+	2.51487i	−0.135471	+	0.181969i	0.729211	+	0.684289i	$0.239887\pi$
$192$		0			0
$193$	−2.83373	−	9.46533i	−0.203977	−	0.681329i	−0.997361	−	0.0726078i	$-0.976868\pi$
$193$	−2.83373	−	9.46533i	−0.203977	−	0.681329i	0.793384	−	0.608722i	$-0.208317\pi$
$194$	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	0.994818	−	0.101669i	$-0.0324182\pi$
$197$	0.354010	+	2.00769i	0.0252221	+	0.143042i	−0.969596	+	0.244711i	$0.921307\pi$
$198$		0			0
$199$	−2.26949	+	12.8709i	−0.160880	+	0.912396i	0.792331	+	0.610091i	$0.208867\pi$
$199$	−2.26949	+	12.8709i	−0.160880	+	0.912396i	−0.953211	+	0.302305i	$0.902244\pi$
$200$	−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	−0.864156	−	0.503223i	$-0.832147\pi$
$211$	−14.1852	+	7.12406i	−0.976548	+	0.490441i	−0.112391	+	0.993664i	$0.535851\pi$
$212$	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	0.769463	−	0.638691i	$-0.220524\pi$
$223$	1.30086	+	1.37883i	0.0871121	+	0.0923335i	−0.682351	+	0.731025i	$0.739042\pi$
$224$	−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	0.578170	+	0.815917i	$0.303767\pi$
$227$	1.48603	+	25.5142i	0.0986315	+	1.69344i	−0.479538	+	0.877521i	$0.659196\pi$
$228$		0			0
$229$	−2.80161	−	3.76321i	−0.185135	−	0.248680i	0.699860	−	0.714280i	$-0.253246\pi$
$229$	−2.80161	−	3.76321i	−0.185135	−	0.248680i	−0.884995	+	0.465600i	$0.845838\pi$
$230$	−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	−0.669802	−	0.742540i	$-0.733621\pi$
$233$	−10.7706	+	3.92018i	−0.705605	+	0.256819i	−0.0358031	+	0.999359i	$0.511399\pi$
$234$		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	−0.412129	−	0.911125i	$-0.635215\pi$
$239$	8.06092	−	8.54408i	0.521418	−	0.552671i	0.933547	+	0.358455i	$0.116696\pi$
$240$		0			0
$241$	1.75025	+	4.05753i	0.112743	+	0.261368i	0.965240	−	0.261364i	$-0.0841721\pi$
$241$	1.75025	+	4.05753i	0.112743	+	0.261368i	−0.852497	+	0.522732i	$0.824913\pi$
$242$	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	0.149010	−	0.988836i	$-0.452391\pi$
$251$	−5.90077	−	2.14770i	−0.372453	−	0.135562i	−0.521463	+	0.853274i	$0.674614\pi$
$252$		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	0.755912	−	0.654673i	$-0.227194\pi$
$257$	−1.41164	−	1.89616i	−0.0880555	−	0.118279i	−0.843968	+	0.536394i	$0.819786\pi$
$258$		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	0.952295	−	0.305179i	$-0.0987163\pi$
$263$	9.60486	+	10.1806i	0.592261	+	0.627760i	−0.360034	+	0.932939i	$0.617235\pi$
$264$		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	0.929435	+	0.368985i	$0.120295\pi$
$269$	12.8630	+	22.2793i	0.784268	+	1.35839i	−0.145167	+	0.989407i	$0.546372\pi$
$270$		0			0
$271$	−6.52248	+	11.2973i	−0.396212	+	0.686260i	−0.993255	−	0.115950i	$-0.963009\pi$
$271$	−6.52248	+	11.2973i	−0.396212	+	0.686260i	0.597043	+	0.802209i	$0.296342\pi$
$272$	−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	−0.991106	−	0.133076i	$-0.957514\pi$
$277$	−1.49661	+	4.99901i	−0.0899223	+	0.300361i	0.901183	+	0.433438i	$0.142700\pi$
$278$	−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	0.290914	−	0.956749i	$-0.406041\pi$
$281$	−5.07578	−	2.54915i	−0.302795	−	0.152070i	−0.593709	+	0.804680i	$0.702337\pi$
$282$		0			0
$283$	−4.49732	+	10.4260i	−0.267338	+	0.619759i	−0.998016	−	0.0629635i	$-0.979945\pi$
$283$	−4.49732	+	10.4260i	−0.267338	+	0.619759i	0.730678	+	0.682722i	$0.239204\pi$
$284$	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	−0.971756	−	0.235989i	$-0.924167\pi$
$293$	−4.95619	−	16.5548i	−0.289544	−	0.967143i	0.682212	−	0.731154i	$-0.261018\pi$
$294$		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	0.440083	−	0.897957i	$-0.354949\pi$
$307$	−6.44460	−	5.40766i	−0.367812	−	0.308631i	−0.807895	+	0.589326i	$0.799393\pi$
$308$	−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	−0.298675	−	0.954355i	$-0.596545\pi$
$311$	−6.51107	+	0.761035i	−0.369209	+	0.0431544i	−0.0705345	+	0.997509i	$0.522470\pi$
$312$		0			0
$313$	−4.55516	+	2.99597i	−0.257473	+	0.169342i	−0.671683	−	0.740839i	$-0.734428\pi$
$313$	−4.55516	+	2.99597i	−0.257473	+	0.169342i	0.414210	+	0.910181i	$0.364058\pi$
$314$	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	−0.327682	−	0.944788i	$-0.606268\pi$
$317$	−3.49841	+	0.829137i	−0.196490	+	0.0465690i	0.131192	+	0.991357i	$0.458119\pi$
$318$		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	−0.872808	−	0.488063i	$-0.837703\pi$
$331$	−26.0845	+	6.18215i	−1.43374	+	0.339802i	−0.560927	+	0.827865i	$0.689555\pi$
$332$	−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	−0.678642	−	0.734469i	$-0.737431\pi$
$337$	−21.4712	+	2.50962i	−1.16961	+	0.136708i	−0.490969	+	0.871177i	$0.663357\pi$
$338$	−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	0.645589	−	0.763685i	$-0.276612\pi$
$347$	16.3883	+	3.88409i	0.879768	+	0.208509i	0.234179	+	0.972194i	$0.424760\pi$
$348$		0			0
$349$	1.95794	+	0.228850i	0.104806	+	0.0122501i	0.168334	−	0.985730i	$-0.446161\pi$
$349$	1.95794	+	0.228850i	0.104806	+	0.0122501i	−0.0635282	+	0.997980i	$0.520235\pi$
$350$	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	−0.700088	−	0.714057i	$-0.746856\pi$
$353$	3.47131	−	4.66277i	0.184759	−	0.248174i	0.884847	+	0.465883i	$0.154263\pi$
$354$		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	0.933771	+	0.357871i	$0.116497\pi$
$359$	3.38611	+	19.2036i	0.178712	+	1.01353i	−0.755059	+	0.655657i	$0.772392\pi$
$360$		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	−0.0501571	−	0.998741i	$-0.515972\pi$
$367$	−16.8818	−	8.47836i	−0.881222	−	0.442567i	−0.831065	+	0.556175i	$0.812269\pi$
$368$	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	−0.882298	−	0.470691i	$-0.844005\pi$
$373$	−19.9239	+	10.0061i	−1.03162	+	0.518098i	−0.149320	+	0.988789i	$0.547709\pi$
$374$	−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	0.977641	−	0.210280i	$-0.0674374\pi$
$379$	5.97107	+	10.3422i	0.306713	+	0.531243i	−0.670928	+	0.741522i	$0.734104\pi$
$380$	−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	0.0181952	−	0.999834i	$-0.494208\pi$
$383$	−17.4697	−	11.4900i	−0.892662	−	0.587113i	−0.910857	+	0.412721i	$0.864578\pi$
$384$		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	−0.982435	−	0.186606i	$-0.940251\pi$
$389$	−0.558292	−	9.58551i	−0.0283066	−	0.486005i	0.954128	−	0.299398i	$-0.0967859\pi$
$390$		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	0.390066	−	0.920787i	$-0.372452\pi$
$397$	1.93277	+	0.703471i	0.0970030	+	0.0353062i	−0.293063	+	0.956093i	$0.594674\pi$
$398$	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	−0.738869	−	0.673850i	$-0.764640\pi$
$401$	−0.464530	+	0.492373i	−0.0231975	+	0.0245879i	0.715671	+	0.698438i	$0.246121\pi$
$402$		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	−0.949753	−	0.313001i	$-0.898666\pi$
$409$	−11.7714	+	12.4770i	−0.582058	+	0.616945i	0.367695	+	0.929947i	$0.380147\pi$
$410$	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	−0.993264	−	0.115874i	$-0.963033\pi$
$419$	−16.7727	−	22.5296i	−0.819399	−	1.10064i	0.173865	−	0.984769i	$-0.444374\pi$
$420$		0			0
$421$	0.584307	+	10.0322i	0.0284774	+	0.488938i	0.982151	+	0.188094i	$0.0602311\pi$
$421$	0.584307	+	10.0322i	0.0284774	+	0.488938i	−0.953674	+	0.300843i	$0.902732\pi$
$422$	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	0.794417	−	0.607373i	$-0.207777\pi$
$431$	−2.67380	−	4.63116i	−0.128792	−	0.223075i	−0.923209	+	0.384298i	$0.874443\pi$
$432$		0			0
$433$	3.44686	−	5.97014i	0.165646	−	0.286906i	−0.771239	−	0.636546i	$-0.780363\pi$
$433$	3.44686	−	5.97014i	0.165646	−	0.286906i	0.936884	+	0.349639i	$0.113696\pi$
$434$	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	0.782803	+	0.622270i	$0.213789\pi$
$439$	−4.46624	+	14.9183i	−0.213162	+	0.712011i	−0.995965	+	0.0897416i	$0.971396\pi$
$440$	−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	−0.257886	−	0.966175i	$-0.583026\pi$
$443$	−24.9809	−	12.5459i	−1.18688	−	0.596072i	−0.928991	+	0.370103i	$0.879322\pi$
$444$		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	0.906650	+	0.421884i	$0.138631\pi$
$449$	−1.89891	+	10.7693i	−0.0896152	+	0.508233i	−0.996265	+	0.0863489i	$0.972480\pi$
$450$		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	−0.970015	−	0.243046i	$-0.921853\pi$
$457$	−9.81178	+	13.1795i	−0.458976	+	0.616511i	0.511039	+	0.859558i	$0.329261\pi$
$458$	−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	0.672670	−	0.739943i	$-0.265147\pi$
$461$	24.8325	+	2.90251i	1.15657	+	0.135183i	0.483896	+	0.875126i	$0.339221\pi$
$462$		0			0
$463$	13.1994	+	3.12832i	0.613429	+	0.145385i	0.525574	−	0.850748i	$-0.323851\pi$
$463$	13.1994	+	3.12832i	0.613429	+	0.145385i	0.0878551	+	0.996133i	$0.471999\pi$
$464$	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	−0.217308	+	0.976103i	$0.569728\pi$
$467$	−26.2848	+	22.0556i	−1.21632	+	1.02061i	−0.999009	+	0.0445082i	$0.985828\pi$
$468$		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	−0.681936	−	0.731412i	$-0.738862\pi$
$479$	−21.0780	+	4.99558i	−0.963079	+	0.228254i	−0.281143	+	0.959666i	$0.590714\pi$
$480$		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	0.710912	+	0.703281i	$0.248283\pi$
$491$	−1.70264	+	29.2332i	−0.0768391	+	1.31928i	−0.787751	+	0.615994i	$0.788754\pi$
$492$		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	0.519245	−	0.854625i	$-0.326213\pi$
$499$	27.2881	−	3.18952i	1.22158	−	0.142783i	0.702339	+	0.711843i	$0.252139\pi$
$500$	−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	−0.125583	−	0.992083i	$-0.540080\pi$
$503$	−25.2177	−	21.1601i	−1.12440	−	0.943484i	−0.998818	+	0.0485988i	$0.984524\pi$
$504$		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	0.339830	−	0.940487i	$-0.389631\pi$
$509$	4.99552	+	1.18396i	0.221423	+	0.0524781i	−0.118407	+	0.992965i	$0.537779\pi$
$510$		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	0.941992	−	0.335635i	$-0.108951\pi$
$521$	−1.32353	−	7.50611i	−0.0579849	−	0.328849i	−0.999977	+	0.00678637i	$0.997840\pi$
$522$		0			0
$523$	−1.93766	+	10.9890i	−0.0847279	+	0.480516i	0.912687	+	0.408659i	$0.134004\pi$
$523$	−1.93766	+	10.9890i	−0.0847279	+	0.480516i	−0.997415	+	0.0718566i	$0.977108\pi$
$524$	−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	0.997935	+	0.0642366i	$0.0204612\pi$
$541$	12.8996	+	22.3428i	0.554598	+	0.960592i	−0.443337	+	0.896355i	$0.646205\pi$
$542$	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	−0.991952	−	0.126615i	$-0.959589\pi$
$547$	−24.8071	−	26.2940i	−1.06068	−	1.12425i	−0.0687241	−	0.997636i	$-0.521893\pi$
$548$	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	0.421278	−	0.906931i	$-0.361582\pi$
$557$	31.3174	−	11.3986i	1.32696	−	0.482974i	0.905682	+	0.423957i	$0.139359\pi$
$558$		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	−0.00409146	+	0.999992i	$0.501302\pi$
$563$	−23.7787	+	25.2040i	−1.00215	+	1.06222i	−0.998062	+	0.0622289i	$0.980179\pi$
$564$		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	0.938468	+	0.345367i	$0.112245\pi$
$569$	13.0161	+	30.1747i	0.545663	+	1.26499i	−0.392805	+	0.919622i	$0.628495\pi$
$570$		0			0
$571$	10.4745	−	11.1024i	0.438346	−	0.464620i	−0.470105	−	0.882610i	$-0.655784\pi$
$571$	10.4745	−	11.1024i	0.438346	−	0.464620i	0.908451	+	0.417991i	$0.137266\pi$
$572$	−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	−0.147760	−	0.989023i	$-0.547206\pi$
$577$	9.00255	−	3.27666i	0.374781	−	0.136409i	0.522541	+	0.852614i	$0.324984\pi$
$578$	−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	0.991948	−	0.126648i	$-0.0404218\pi$
$587$	19.5724	+	20.7455i	0.807838	+	0.856258i	−0.184110	+	0.982906i	$0.558940\pi$
$588$		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	−0.864625	−	0.502418i	$-0.832444\pi$
$593$	−21.1230	−	36.5862i	−0.867419	−	1.50241i	−0.00279478	−	0.999996i	$-0.500890\pi$
$594$		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	−0.744575	−	0.667538i	$-0.767348\pi$
$599$	−16.0004	+	8.03568i	−0.653757	+	0.328329i	0.0908185	+	0.995867i	$0.471052\pi$
$600$		0			0
$601$	2.87565	−	9.60533i	0.117300	−	0.391809i	−0.879095	−	0.476647i	$-0.841852\pi$
$601$	2.87565	−	9.60533i	0.117300	−	0.391809i	0.996395	+	0.0848376i	$0.0270372\pi$
$602$	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	−0.986866	−	0.161544i	$-0.948353\pi$
$607$	−4.73369	+	10.9739i	−0.192135	+	0.445418i	0.794731	+	0.606962i	$0.207612\pi$
$608$	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	−0.737112	−	0.675771i	$-0.763811\pi$
$613$	−6.82305	−	38.6954i	−0.275580	−	1.56289i	0.461532	−	0.887124i	$-0.347300\pi$
$614$	−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	0.780450	+	0.625218i	$0.214990\pi$
$617$	11.7232	+	39.1581i	0.471957	+	1.57644i	−0.308493	+	0.951226i	$0.599825\pi$
$618$		0			0
$619$	15.2570	−	20.4937i	0.613230	−	0.823711i	−0.381699	−	0.924287i	$-0.624661\pi$
$619$	15.2570	−	20.4937i	0.613230	−	0.823711i	0.994929	+	0.100576i	$0.0320684\pi$
$620$	−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	0.579081	−	0.815270i	$-0.303411\pi$
$631$	−3.09592	−	2.59779i	−0.123247	−	0.103416i	−0.702328	+	0.711854i	$0.747856\pi$
$632$	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	0.00299679	−	0.999996i	$-0.499046\pi$
$641$	11.5063	−	2.72705i	0.454472	−	0.107712i	0.451475	+	0.892284i	$0.350898\pi$
$642$		0			0
$643$	1.17771	−	20.2204i	0.0464442	−	0.797416i	−0.892011	−	0.452014i	$-0.850706\pi$
$643$	1.17771	−	20.2204i	0.0464442	−	0.797416i	0.938455	−	0.345402i	$-0.112257\pi$
$644$	−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	0.982666	+	0.185382i	$0.0593524\pi$
$653$	−0.380169	+	6.52724i	−0.0148772	+	0.255431i	−0.997544	+	0.0700484i	$0.977685\pi$
$654$		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	−0.0744284	−	0.997226i	$-0.523713\pi$
$659$	20.8387	−	13.7058i	0.811761	−	0.533904i	0.886190	+	0.463323i	$0.153343\pi$
$660$		0			0
$661$	44.7213	−	5.22717i	1.73946	−	0.203313i	0.813662	−	0.581339i	$-0.197471\pi$
$661$	44.7213	−	5.22717i	1.73946	−	0.203313i	0.925795	+	0.378025i	$0.123397\pi$
$662$	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	−0.119368	−	0.992850i	$-0.538087\pi$
$673$	−12.0498	−	1.40842i	−0.464485	−	0.0542905i	−0.345117	+	0.938560i	$0.612161\pi$
$674$	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	−0.865448	−	0.500999i	$-0.832966\pi$
$677$	−3.57201	+	4.79804i	−0.137283	+	0.184404i	0.728165	+	0.685402i	$0.240374\pi$
$678$		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	0.927984	+	0.372621i	$0.121541\pi$
$683$	4.79324	+	27.1838i	0.183408	+	1.04016i	−0.744575	+	0.667538i	$0.767348\pi$
$684$		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	−0.126108	−	0.992017i	$-0.540248\pi$
$691$	−26.2115	−	13.1639i	−0.997134	−	0.500779i	−0.871026	+	0.491237i	$0.836545\pi$
$692$	−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	−0.892147	−	0.451745i	$-0.850802\pi$
$701$	−1.45226	+	2.51539i	−0.0548512	+	0.0950051i	0.837296	+	0.546750i	$0.184135\pi$
$702$		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	0.962770	−	0.270321i	$-0.0871298\pi$
$709$	16.9595	+	17.9760i	0.636927	+	0.675103i	−0.325844	+	0.945424i	$0.605648\pi$
$710$	−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	0.143269	−	0.989684i	$-0.454239\pi$
$719$	23.8425	−	8.67796i	0.889175	−	0.323633i	0.745907	+	0.666051i	$0.232017\pi$
$720$		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	0.997437	−	0.0715446i	$-0.0227928\pi$
$727$	7.03503	+	16.3090i	0.260915	+	0.604868i	−0.736523	+	0.676413i	$0.763534\pi$
$728$	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	−0.834032	−	0.551716i	$-0.813973\pi$
$733$	−6.35574	+	6.73669i	−0.234755	+	0.248825i	0.599277	+	0.800541i	$0.295455\pi$
$734$	−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	−0.247939	−	0.968776i	$-0.579753\pi$
$739$	5.02496	−	1.82894i	0.184846	−	0.0672785i	0.432785	+	0.901497i	$0.357531\pi$
$740$	−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	0.419778	−	0.907627i	$-0.362108\pi$
$743$	−15.5402	−	20.8740i	−0.570113	−	0.765795i	−0.989891	+	0.141832i	$0.954701\pi$
$744$		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	0.603864	−	0.797088i	$-0.293627\pi$
$751$	3.04582	+	2.00327i	0.111143	+	0.0731002i	−0.492720	+	0.870188i	$0.663997\pi$
$752$	−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	−0.947812	−	0.318830i	$-0.896710\pi$
$757$	−5.44196	+	9.42576i	−0.197792	+	0.342585i	0.750021	+	0.661415i	$0.230044\pi$
$758$	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	−0.00152487	−	0.999999i	$-0.500485\pi$
$761$	22.0603	−	11.0791i	0.799687	−	0.401618i	0.801212	+	0.598381i	$0.204189\pi$
$762$		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	−0.534609	−	0.845099i	$-0.679541\pi$
$769$	12.3947	−	28.7342i	0.446965	−	1.03618i	0.981574	−	0.191082i	$-0.0611996\pi$
$770$	−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	−0.913871	−	0.406006i	$-0.866921\pi$
$773$	2.32846	−	13.2054i	0.0837490	−	0.474964i	0.997620	−	0.0689585i	$-0.0219676\pi$
$774$		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
$783$		0			0
$784$	−17.2397	−	29.8600i	−0.615703	−	1.06643i
$785$	−16.6954	−	1.95141i	−0.595885	−	0.0696490i
$786$		0			0
$787$	20.3175	+	4.81533i	0.724240	+	0.171648i	0.576171	−	0.817329i	$-0.304546\pi$
$787$	20.3175	+	4.81533i	0.724240	+	0.171648i	0.148069	+	0.988977i	$0.452694\pi$
$788$	−1.57453	−	1.03559i	−0.0560904	−	0.0368912i
$789$		0			0
$790$	−5.10484	−	5.41081i	−0.181622	−	0.192508i
$791$	1.39681	−	1.17206i	0.0496648	−	0.0416737i
$792$		0			0
$793$	−35.4289	−	29.7283i	−1.25812	−	1.05568i
$794$	−0.204515	−	3.51138i	−0.00725796	−	0.124614i
$795$		0			0
$796$	−7.21463	−	9.69093i	−0.255716	−	0.343486i
$797$	−51.7224	+	6.04548i	−1.83210	+	0.214142i	−0.960921	−	0.276824i	$-0.910718\pi$
$797$	−51.7224	+	6.04548i	−1.83210	+	0.214142i	−0.871179	+	0.490965i	$0.836644\pi$
$798$		0			0
$799$	−1.09505	+	0.720226i	−0.0387401	+	0.0254798i
$800$	14.2260	−	5.17785i	0.502966	−	0.183065i
$801$		0			0
$802$	1.08778	+	0.395920i	0.0384109	+	0.0139804i
$803$	−31.6636	+	7.50441i	−1.11738	+	0.264825i
$804$		0			0
$805$	−0.198433	+	3.40697i	−0.00699386	+	0.120080i
$806$	−4.34384	+	4.60420i	−0.153005	+	0.162176i
$807$		0			0
$808$	−6.78997	−	15.7409i	−0.238870	−	0.553764i
$809$	−41.7858			−1.46911			−0.734554	−	0.678550i	$-0.762609\pi$
$809$	−41.7858			−1.46911			−0.734554	+	0.678550i	$0.762609\pi$
$810$		0			0
$811$	5.44750			0.191287			0.0956437	−	0.995416i	$-0.469509\pi$
$811$	5.44750			0.191287			0.0956437	+	0.995416i	$0.469509\pi$
$812$	−0.944321	−	2.18918i	−0.0331392	−	0.0768252i
$813$		0			0
$814$	−30.7589	+	32.6025i	−1.07810	+	1.14272i
$815$	2.00293	−	34.3890i	0.0701596	−	1.20459i
$816$		0			0
$817$	25.2233	−	5.97802i	0.882450	−	0.209145i
$818$	27.5649	+	10.0328i	0.963783	+	0.350788i
$819$		0			0
$820$	−5.60432	+	2.03981i	−0.195711	+	0.0712331i
$821$	−25.7159	+	16.9136i	−0.897493	+	0.590290i	−0.912265	−	0.409601i	$-0.865668\pi$
$821$	−25.7159	+	16.9136i	−0.897493	+	0.590290i	0.0147722	+	0.999891i	$0.495298\pi$
$822$		0			0
$823$	−18.5561	+	2.16890i	−0.646825	+	0.0756030i	−0.433178	−	0.901308i	$-0.642608\pi$
$823$	−18.5561	+	2.16890i	−0.646825	+	0.0756030i	−0.213646	+	0.976911i	$0.568534\pi$
$824$	−1.44221	−	1.93723i	−0.0502418	−	0.0674865i
$825$		0			0
$826$	0.217880	+	3.74085i	0.00758100	+	0.130161i
$827$	−1.28456	−	1.07787i	−0.0446686	−	0.0374814i	0.620180	−	0.784459i	$-0.287060\pi$
$827$	−1.28456	−	1.07787i	−0.0446686	−	0.0374814i	−0.664849	+	0.746978i	$0.731504\pi$
$828$		0			0
$829$	23.5451	−	19.7567i	0.817755	−	0.686178i	−0.134690	−	0.990888i	$-0.543004\pi$
$829$	23.5451	−	19.7567i	0.817755	−	0.686178i	0.952445	+	0.304710i	$0.0985595\pi$
$830$	1.29304	+	1.37054i	0.0448821	+	0.0475722i
$831$		0			0
$832$	6.45797	+	4.24747i	0.223890	+	0.147255i
$833$	−1.41454	−	0.335253i	−0.0490111	−	0.0116158i
$834$		0			0
$835$	−10.9859	−	1.28406i	−0.380182	−	0.0444369i
$836$	3.88339	+	6.72622i	0.134310	+	0.232631i
$837$		0			0
$838$	−24.0161	+	41.5971i	−0.829622	+	1.43695i
$839$	−7.27821	+	9.77633i	−0.251272	+	0.337516i	−0.909806	−	0.415035i	$-0.863769\pi$
$839$	−7.27821	+	9.77633i	−0.251272	+	0.337516i	0.658534	+	0.752551i	$0.271177\pi$
$840$		0			0
$841$	−11.5061	−	38.4331i	−0.396762	−	1.32528i
$842$	15.3571	−	7.71261i	0.529240	−	0.265794i
$843$		0			0
$844$	4.20849	−	14.0573i	0.144862	−	0.483873i
$845$	1.98358	+	11.2494i	0.0682373	+	0.386993i
$846$		0			0
$847$	0.279457	−	1.58488i	0.00960225	−	0.0544571i
$848$	38.1148	+	19.1420i	1.30887	+	0.657337i
$849$		0			0
$850$	0.444103	−	1.02955i	0.0152326	−	0.0353132i
$851$	−34.4915	+	79.9603i	−1.18235	+	2.74100i
$852$		0			0
$853$	−8.11031	−	4.07315i	−0.277692	−	0.139462i	0.304503	−	0.952511i	$-0.401510\pi$
$853$	−8.11031	−	4.07315i	−0.277692	−	0.139462i	−0.582195	+	0.813049i	$0.697806\pi$
$854$	0.922785	−	5.23338i	0.0315771	−	0.179082i
$855$		0			0
$856$	−0.247123	−	1.40150i	−0.00844649	−	0.0479024i
$857$	−7.28250	+	24.3252i	−0.248766	+	0.830935i	0.738827	+	0.673895i	$0.235380\pi$
$857$	−7.28250	+	24.3252i	−0.248766	+	0.830935i	−0.987592	+	0.157039i	$0.949805\pi$
$858$		0			0
$859$	−0.382504	+	0.192101i	−0.0130509	+	0.00655439i	−0.455313	−	0.890332i	$-0.650473\pi$
$859$	−0.382504	+	0.192101i	−0.0130509	+	0.00655439i	0.442262	+	0.896886i	$0.354176\pi$
$860$	−2.70844	−	9.04683i	−0.0923572	−	0.308494i
$861$		0			0
$862$	−5.46095	+	7.33532i	−0.186001	+	0.249842i
$863$	20.6116	−	35.7004i	0.701628	−	1.21526i	−0.266267	−	0.963899i	$-0.585790\pi$
$863$	20.6116	−	35.7004i	0.701628	−	1.21526i	0.967895	−	0.251356i	$-0.0808764\pi$
$864$		0			0
$865$	12.2143	+	21.1557i	0.415297	+	0.719316i
$866$	−11.7092	−	1.36861i	−0.397894	−	0.0465072i
$867$		0			0
$868$	−0.223709	−	0.0530201i	−0.00759319	−	0.00179962i
$869$	−6.37972	−	4.19601i	−0.216417	−	0.142340i
$870$		0			0
$871$	−3.97623	−	4.21456i	−0.134729	−	0.142805i
$872$	−2.90553	+	2.43803i	−0.0983936	+	0.0825620i
$873$		0			0
$874$	36.5681	+	30.6843i	1.23693	+	1.03791i
$875$	−0.201005	−	3.45111i	−0.00679519	−	0.116669i
$876$		0			0
$877$	−22.4967	−	30.2183i	−0.759659	−	1.02040i	−0.998779	−	0.0494088i	$-0.984266\pi$
$877$	−22.4967	−	30.2183i	−0.759659	−	1.02040i	0.239120	−	0.970990i	$-0.423141\pi$
$878$	26.4503	−	3.09160i	0.892656	−	0.104337i
$879$		0			0
$880$	−13.8162	+	9.08706i	−0.465744	+	0.306325i
$881$	2.94091	−	1.07040i	0.0990817	−	0.0360628i	−0.292004	−	0.956417i	$-0.594322\pi$
$881$	2.94091	−	1.07040i	0.0990817	−	0.0360628i	0.391085	+	0.920354i	$0.372100\pi$
$882$		0			0
$883$	46.2681	+	16.8402i	1.55705	+	0.566719i	0.970057	−	0.242876i	$-0.0780909\pi$
$883$	46.2681	+	16.8402i	1.55705	+	0.566719i	0.586989	+	0.809595i	$0.300313\pi$
$884$	−0.874506	+	0.207262i	−0.0294128	+	0.00697097i
$885$		0			0
$886$	−2.77958	+	47.7235i	−0.0933818	+	1.60330i
$887$	37.2737	−	39.5078i	1.25153	−	1.32654i	0.327194	−	0.944957i	$-0.393897\pi$
$887$	37.2737	−	39.5078i	1.25153	−	1.32654i	0.924334	−	0.381584i	$-0.124621\pi$
$888$		0			0
$889$	−1.28456	−	2.97794i	−0.0430826	−	0.0998768i
$890$	30.6490			1.02736
$891$		0			0
$892$	−1.75235			−0.0586730
$893$	8.59167	+	19.9177i	0.287509	+	0.666521i
$894$		0			0
$895$	16.7000	−	17.7009i	0.558219	−	0.591677i
$896$	−0.227040	+	3.89813i	−0.00758489	+	0.130227i
$897$		0			0
$898$	18.1965	−	4.31264i	0.607224	−	0.143915i
$899$	−6.26317	−	2.27961i	−0.208888	−	0.0760291i
$900$		0			0
$901$	1.68984	−	0.615050i	0.0562966	−	0.0204903i
$902$	−16.1810	+	10.6424i	−0.538770	+	0.354354i
$903$		0			0
$904$	10.7381	−	1.25510i	0.357144	−	0.0417441i
$905$	21.9616	+	29.4995i	0.730028	+	0.980597i
$906$		0			0
$907$	−2.73676	−	46.9884i	−0.0908728	−	1.56023i	−0.668368	−	0.743831i	$-0.733007\pi$
$907$	−2.73676	−	46.9884i	−0.0908728	−	1.56023i	0.577495	−	0.816394i	$-0.304030\pi$
$908$	−18.0983	−	15.1863i	−0.600613	−	0.503974i
$909$		0			0
$910$	−2.57699	+	2.16235i	−0.0854263	+	0.0716811i
$911$	−35.5213	−	37.6504i	−1.17687	−	1.24741i	−0.962686	−	0.270620i	$-0.912771\pi$
$911$	−35.5213	−	37.6504i	−1.17687	−	1.24741i	−0.214187	−	0.976793i	$-0.568710\pi$
$912$		0			0
$913$	1.61596	+	1.06284i	0.0534806	+	0.0351748i
$914$	27.3407	+	6.47988i	0.904351	+	0.214335i
$915$		0			0
$916$	4.30762	+	0.503488i	0.142328	+	0.0166357i
$917$	−0.929052	−	1.60917i	−0.0306800	−	0.0531393i
$918$		0			0
$919$	−6.58049	+	11.3977i	−0.217070	+	0.375977i	−0.953911	−	0.300090i	$-0.902983\pi$
$919$	−6.58049	+	11.3977i	−0.217070	+	0.375977i	0.736841	+	0.676066i	$0.236317\pi$
$920$	−12.0833	+	16.2306i	−0.398374	+	0.535109i
$921$		0			0
$922$	−12.2623	−	40.9588i	−0.403836	−	1.34891i
$923$	−7.37676	+	3.70475i	−0.242809	+	0.121943i
$924$		0			0
$925$	9.70883	−	32.4297i	0.319224	−	1.06628i
$926$	−4.02821	−	22.8451i	−0.132375	−	0.750736i
$927$		0			0
$928$	7.01909	−	39.8072i	0.230413	−	1.30674i
$929$	15.3938	+	7.73104i	0.505053	+	0.253647i	0.683034	−	0.730387i	$-0.260660\pi$
$929$	15.3938	+	7.73104i	0.505053	+	0.253647i	−0.177981	+	0.984034i	$0.556956\pi$
$930$		0			0
$931$	−9.52943	+	22.0917i	−0.312314	+	0.724026i
$932$	4.19665	−	9.72893i	0.137466	−	0.318682i
$933$		0			0
$934$	52.4360	+	26.3344i	1.71576	+	0.861687i
$935$	−0.121072	+	0.686633i	−0.00395948	+	0.0224553i
$936$		0			0
$937$	6.62799	+	37.5892i	0.216527	+	1.22799i	0.878237	+	0.478226i	$0.158720\pi$
$937$	6.62799	+	37.5892i	0.216527	+	1.22799i	−0.661710	+	0.749760i	$0.730169\pi$
$938$	0.190944	−	0.637797i	0.00623454	−	0.0208248i
$939$		0			0
$940$	7.06189	−	3.54661i	0.230333	−	0.115678i
$941$	6.10319	+	20.3861i	0.198958	+	0.664567i	0.997995	+	0.0632853i	$0.0201578\pi$
$941$	6.10319	+	20.3861i	0.198958	+	0.664567i	−0.799037	+	0.601282i	$0.794657\pi$
$942$		0			0
$943$	−22.4694	+	30.1816i	−0.731704	+	0.982849i
$944$	−17.6383	+	30.5504i	−0.574077	+	0.994331i
$945$		0			0
$946$	−15.3333	−	26.5580i	−0.498528	−	0.863476i
$947$	7.73360	+	0.903928i	0.251308	+	0.0293737i	0.240814	−	0.970571i	$-0.422586\pi$
$947$	7.73360	+	0.903928i	0.251308	+	0.0293737i	0.0104939	+	0.999945i	$0.496660\pi$
$948$		0			0
$949$	−60.6387	−	14.3716i	−1.96842	−	0.466523i
$950$	−15.5039	−	10.1971i	−0.503014	−	0.330838i
$951$		0			0
$952$	0.0824543	+	0.0873965i	0.00267236	+	0.00283254i
$953$	29.0892	−	24.4088i	0.942292	−	0.790677i	−0.0356905	−	0.999363i	$-0.511363\pi$
$953$	29.0892	−	24.4088i	0.942292	−	0.790677i	0.977983	+	0.208686i	$0.0669186\pi$
$954$		0			0
$955$	−3.29858	−	2.76784i	−0.106740	−	0.0895652i
$956$	0.631372	+	10.8402i	0.0204200	+	0.350598i
$957$		0			0
$958$	22.1211	+	29.7137i	0.714699	+	0.960007i
$959$	0.357948	−	0.0418381i	0.0115587	−	0.00135102i
$960$		0			0
$961$	25.3631	−	16.6816i	0.818166	−	0.538116i
$962$	−80.6621	+	29.3586i	−2.60065	+	0.946560i
$963$		0			0
$964$	−3.83856	−	1.39712i	−0.123632	−	0.0449983i
$965$	13.2041	−	3.12942i	0.425054	−	0.100740i
$966$		0			0
$967$	0.314986	−	5.40810i	0.0101293	−	0.173913i	−0.989449	−	0.144880i	$-0.953720\pi$
$967$	0.314986	−	5.40810i	0.0101293	−	0.173913i	0.999578	−	0.0290325i	$-0.00924262\pi$
$968$	6.54806	−	6.94054i	0.210463	−	0.223077i
$969$		0			0
$970$	6.20518	+	14.3852i	0.199236	+	0.461881i
$971$	−45.8419			−1.47114			−0.735568	−	0.677451i	$-0.763085\pi$
$971$	−45.8419			−1.47114			−0.735568	+	0.677451i	$0.763085\pi$
$972$		0			0
$973$	−5.05922			−0.162191
$974$	−26.3145	−	61.0039i	−0.843171	−	1.95469i
$975$		0			0
$976$	34.3311	−	36.3889i	1.09891	−	1.16478i
$977$	2.94958	−	50.6423i	0.0943653	−	1.62019i	−0.536226	−	0.844075i	$-0.680150\pi$
$977$	2.94958	−	50.6423i	0.0943653	−	1.62019i	0.630591	−	0.776115i	$-0.282813\pi$
$978$		0			0
$979$	30.6130	−	7.25541i	0.978395	−	0.231884i
$980$	8.23640	+	2.99780i	0.263102	+	0.0957613i
$981$		0			0
$982$	47.0562	−	17.1271i	1.50162	−	0.546546i
$983$	29.5172	−	19.4138i	0.941453	−	0.619203i	0.0167362	−	0.999860i	$-0.494672\pi$
$983$	29.5172	−	19.4138i	0.941453	−	0.619203i	0.924716	+	0.380657i	$0.124302\pi$
$984$		0			0
$985$	−2.78098	+	0.325050i	−0.0886094	+	0.0103570i
$986$	−1.78774	−	2.40135i	−0.0569332	−	0.0764746i
$987$		0			0
$988$	0.864852	+	14.8489i	0.0275146	+	0.472407i
$989$	−45.6409	−	38.2973i	−1.45130	−	1.21778i
$990$		0			0
$991$	−3.21935	+	2.70136i	−0.102266	+	0.0858114i	−0.692487	−	0.721430i	$-0.743485\pi$
$991$	−3.21935	+	2.70136i	−0.102266	+	0.0858114i	0.590221	+	0.807242i	$0.299041\pi$
$992$	−2.67487	−	2.83519i	−0.0849271	−	0.0900174i
$993$		0			0
$994$	−0.792453	−	0.521205i	−0.0251351	−	0.0165316i
$995$	−17.4659	−	4.13949i	−0.553706	−	0.131231i
$996$		0			0
$997$	−6.83816	−	0.799266i	−0.216567	−	0.0253130i	0.00711765	−	0.999975i	$-0.497734\pi$
$997$	−6.83816	−	0.799266i	−0.216567	−	0.0253130i	−0.223684	+	0.974662i	$0.571808\pi$
$998$	−23.4914	−	40.6884i	−0.743608	−	1.28797i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.676.2		144
3.2	odd	2		729.2.g.a.676.7		144
9.2	odd	6		729.2.g.b.190.7		144
9.4	even	3		81.2.g.a.4.7	✓	144
9.5	odd	6		243.2.g.a.64.2		144
9.7	even	3		729.2.g.c.190.2		144
81.7	even	27		81.2.g.a.61.7	yes	144
81.14	odd	54		6561.2.a.d.1.55		72
81.20	odd	54		729.2.g.b.541.7		144
81.34	even	27	inner	729.2.g.d.55.2		144
81.47	odd	54		729.2.g.a.55.7		144
81.61	even	27		729.2.g.c.541.2		144
81.67	even	27		6561.2.a.c.1.18		72
81.74	odd	54		243.2.g.a.19.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.4.7	✓	144	9.4	even	3
81.2.g.a.61.7	yes	144	81.7	even	27
243.2.g.a.19.2		144	81.74	odd	54
243.2.g.a.64.2		144	9.5	odd	6
729.2.g.a.55.7		144	81.47	odd	54
729.2.g.a.676.7		144	3.2	odd	2
729.2.g.b.190.7		144	9.2	odd	6
729.2.g.b.541.7		144	81.20	odd	54
729.2.g.c.190.2		144	9.7	even	3
729.2.g.c.541.2		144	81.61	even	27
729.2.g.d.55.2		144	81.34	even	27	inner
729.2.g.d.676.2		144	1.1	even	1	trivial
6561.2.a.c.1.18		72	81.67	even	27
6561.2.a.d.1.55		72	81.14	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Modular forms

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