LMFDB - Embedded newform 729.2.g.d.703.8

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			703.8
Character	$\chi$	$=$	729.703
Dual form			729.2.g.d.28.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23012 + 1.46677i) q^{2} +(2.02985 + 4.70573i) q^{4} +(-1.24595 - 1.32063i) q^{5} +(2.56492 - 0.299797i) q^{7} +(-1.44840 + 8.21430i) q^{8} +O(q^{10})$	\(q+(2.23012 + 1.46677i) q^{2} +(2.02985 + 4.70573i) q^{4} +(-1.24595 - 1.32063i) q^{5} +(2.56492 - 0.299797i) q^{7} +(-1.44840 + 8.21430i) q^{8} +(-0.841551 - 4.77267i) q^{10} +(1.04979 + 3.50653i) q^{11} +(-0.0220064 - 0.377836i) q^{13} +(6.15982 + 3.09358i) q^{14} +(-8.24485 + 8.73903i) q^{16} +(2.13907 + 0.778557i) q^{17} +(-1.32149 + 0.480985i) q^{19} +(3.68542 - 8.54376i) q^{20} +(-2.80213 + 9.35978i) q^{22} +(-3.51611 - 0.410974i) q^{23} +(0.0990536 - 1.70069i) q^{25} +(0.505123 - 0.874898i) q^{26} +(6.61718 + 11.4613i) q^{28} +(-5.90521 + 2.96571i) q^{29} +(5.83658 - 7.83989i) q^{31} +(-14.9728 + 3.54862i) q^{32} +(3.62841 + 4.87381i) q^{34} +(-3.59167 - 3.01377i) q^{35} +(-0.463728 + 0.389114i) q^{37} +(-3.65259 - 0.865679i) q^{38} +(12.6526 - 8.32178i) q^{40} +(2.79880 - 1.84080i) q^{41} +(2.59620 + 0.615311i) q^{43} +(-14.3699 + 12.0578i) q^{44} +(-7.23854 - 6.07386i) q^{46} +(0.0900157 + 0.120912i) q^{47} +(-0.322362 + 0.0764011i) q^{49} +(2.71542 - 3.64744i) q^{50} +(1.73333 - 0.870509i) q^{52} +(-6.72572 - 11.6493i) q^{53} +(3.32284 - 5.75532i) q^{55} +(-1.25242 + 21.5033i) q^{56} +(-17.5193 - 2.04772i) q^{58} +(1.21847 - 4.06996i) q^{59} +(2.95087 - 6.84088i) q^{61} +(24.5156 - 8.92296i) q^{62} +(-16.0163 - 5.82946i) q^{64} +(-0.471561 + 0.499826i) q^{65} +(9.01808 + 4.52905i) q^{67} +(0.678316 + 11.6462i) q^{68} +(-3.58935 - 11.9892i) q^{70} +(-0.305263 - 1.73123i) q^{71} +(0.930968 - 5.27978i) q^{73} +(-1.60491 + 0.187587i) q^{74} +(-4.94583 - 5.24227i) q^{76} +(3.74387 + 8.67926i) q^{77} +(-3.55048 - 2.33519i) q^{79} +21.8136 q^{80} +8.94171 q^{82} +(-2.17613 - 1.43126i) q^{83} +(-1.63698 - 3.79495i) q^{85} +(4.88732 + 5.18025i) q^{86} +(-30.3242 + 3.54439i) q^{88} +(-0.553979 + 3.14177i) q^{89} +(-0.169719 - 0.962523i) q^{91} +(-5.20326 - 17.3801i) q^{92} +(0.0233953 + 0.401681i) q^{94} +(2.28171 + 1.14592i) q^{95} +(-10.5487 + 11.1810i) q^{97} +(-0.830968 - 0.302448i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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 $

$2$	2.23012	+	1.46677i	1.57693	+	1.03717i	0.970214	+	0.242249i	$0.0778853\pi$
$2$	2.23012	+	1.46677i	1.57693	+	1.03717i	0.606720	+	0.794916i	$0.292485\pi$
$3$		0			0
$3$		0			0
$4$	2.02985	+	4.70573i	1.01493	+	2.35287i
$5$	−1.24595	−	1.32063i	−0.557204	−	0.590602i	0.386131	−	0.922444i	$-0.373811\pi$
$5$	−1.24595	−	1.32063i	−0.557204	−	0.590602i	−0.943335	+	0.331842i	$0.892330\pi$
$6$		0			0
$7$	2.56492	−	0.299797i	0.969450	−	0.113312i	0.383396	−	0.923584i	$-0.374755\pi$
$7$	2.56492	−	0.299797i	0.969450	−	0.113312i	0.586054	+	0.810272i	$0.300681\pi$
$8$	−1.44840	+	8.21430i	−0.512088	+	2.90419i
$9$		0			0
$10$	−0.841551	−	4.77267i	−0.266122	−	1.50925i
$11$	1.04979	+	3.50653i	0.316522	+	1.05726i	0.957195	+	0.289444i	$0.0934705\pi$
$11$	1.04979	+	3.50653i	0.316522	+	1.05726i	−0.640673	+	0.767814i	$0.721344\pi$
$12$		0			0
$13$	−0.0220064	−	0.377836i	−0.00610349	−	0.104793i	0.993880	−	0.110461i	$-0.0352328\pi$
$13$	−0.0220064	−	0.377836i	−0.00610349	−	0.104793i	−0.999984	+	0.00566826i	$0.998196\pi$
$14$	6.15982	+	3.09358i	1.64628	+	0.826794i
$15$		0			0
$16$	−8.24485	+	8.73903i	−2.06121	+	2.18476i
$17$	2.13907	+	0.778557i	0.518800	+	0.188828i	0.588131	−	0.808766i	$-0.299864\pi$
$17$	2.13907	+	0.778557i	0.518800	+	0.188828i	−0.0693304	+	0.997594i	$0.522086\pi$
$18$		0			0
$19$	−1.32149	+	0.480985i	−0.303172	+	0.110345i	−0.489127	−	0.872213i	$-0.662684\pi$
$19$	−1.32149	+	0.480985i	−0.303172	+	0.110345i	0.185955	+	0.982558i	$0.440462\pi$
$20$	3.68542	−	8.54376i	0.824085	−	1.91044i
$21$		0			0
$22$	−2.80213	+	9.35978i	−0.597417	+	1.99551i
$23$	−3.51611	−	0.410974i	−0.733160	−	0.0856941i	−0.258683	−	0.965962i	$-0.583289\pi$
$23$	−3.51611	−	0.410974i	−0.733160	−	0.0856941i	−0.474476	+	0.880268i	$0.657363\pi$
$24$		0			0
$25$	0.0990536	−	1.70069i	0.0198107	−	0.340137i
$26$	0.505123	−	0.874898i	0.0990627	−	0.171582i
$27$		0			0
$28$	6.61718	+	11.4613i	1.25053	+	2.16598i
$29$	−5.90521	+	2.96571i	−1.09657	+	0.550718i	−0.902683	−	0.430306i	$-0.858406\pi$
$29$	−5.90521	+	2.96571i	−1.09657	+	0.550718i	−0.193887	+	0.981024i	$0.562109\pi$
$30$		0			0
$31$	5.83658	−	7.83989i	1.04828	−	1.40809i	0.139790	−	0.990181i	$-0.455357\pi$
$31$	5.83658	−	7.83989i	1.04828	−	1.40809i	0.908491	−	0.417905i	$-0.137235\pi$
$32$	−14.9728	+	3.54862i	−2.64684	+	0.627313i
$33$		0			0
$34$	3.62841	+	4.87381i	0.622268	+	0.835851i
$35$	−3.59167	−	3.01377i	−0.607104	−	0.509421i
$36$		0			0
$37$	−0.463728	+	0.389114i	−0.0762364	+	0.0639699i	−0.680110	−	0.733111i	$-0.738068\pi$
$37$	−0.463728	+	0.389114i	−0.0762364	+	0.0639699i	0.603873	+	0.797080i	$0.293623\pi$
$38$	−3.65259	−	0.865679i	−0.592528	−	0.140432i
$39$		0			0
$40$	12.6526	−	8.32178i	2.00056	−	1.31579i
$41$	2.79880	−	1.84080i	0.437099	−	0.287485i	−0.311826	−	0.950139i	$-0.600941\pi$
$41$	2.79880	−	1.84080i	0.437099	−	0.287485i	0.748925	+	0.662654i	$0.230570\pi$
$42$		0			0
$43$	2.59620	+	0.615311i	0.395917	+	0.0938340i	0.423751	−	0.905779i	$-0.360713\pi$
$43$	2.59620	+	0.615311i	0.395917	+	0.0938340i	−0.0278346	+	0.999613i	$0.508861\pi$
$44$	−14.3699	+	12.0578i	−2.16634	+	1.81778i
$45$		0			0
$46$	−7.23854	−	6.07386i	−1.06726	−	0.895542i
$47$	0.0900157	+	0.120912i	0.0131301	+	0.0176368i	0.808640	−	0.588304i	$-0.200204\pi$
$47$	0.0900157	+	0.120912i	0.0131301	+	0.0176368i	−0.795510	+	0.605941i	$0.792797\pi$
$48$		0			0
$49$	−0.322362	+	0.0764011i	−0.0460516	+	0.0109144i
$50$	2.71542	−	3.64744i	0.384019	−	0.515826i
$51$		0			0
$52$	1.73333	−	0.870509i	0.240369	−	0.120718i
$53$	−6.72572	−	11.6493i	−0.923849	−	1.60015i	−0.793401	−	0.608699i	$-0.791692\pi$
$53$	−6.72572	−	11.6493i	−0.923849	−	1.60015i	−0.130448	−	0.991455i	$-0.541642\pi$
$54$		0			0
$55$	3.32284	−	5.75532i	0.448051	−	0.776047i
$56$	−1.25242	+	21.5033i	−0.167362	+	2.87350i
$57$		0			0
$58$	−17.5193	−	2.04772i	−2.30040	−	0.268879i
$59$	1.21847	−	4.06996i	0.158631	−	0.529864i	−0.841312	−	0.540550i	$-0.818216\pi$
$59$	1.21847	−	4.06996i	0.158631	−	0.529864i	0.999943	+	0.0106860i	$0.00340151\pi$
$60$		0			0
$61$	2.95087	−	6.84088i	0.377820	−	0.875885i	−0.618138	−	0.786069i	$-0.712113\pi$
$61$	2.95087	−	6.84088i	0.377820	−	0.875885i	0.995958	−	0.0898159i	$-0.0286279\pi$
$62$	24.5156	−	8.92296i	3.11349	−	1.13322i
$63$		0			0
$64$	−16.0163	−	5.82946i	−2.00204	−	0.728682i
$65$	−0.471561	+	0.499826i	−0.0584900	+	0.0619957i
$66$		0			0
$67$	9.01808	+	4.52905i	1.10173	+	0.553311i	0.904254	−	0.426996i	$-0.140428\pi$
$67$	9.01808	+	4.52905i	1.10173	+	0.553311i	0.197480	+	0.980307i	$0.436724\pi$
$68$	0.678316	+	11.6462i	0.0822579	+	1.41231i
$69$		0			0
$70$	−3.58935	−	11.9892i	−0.429009	−	1.43299i
$71$	−0.305263	−	1.73123i	−0.0362281	−	0.205460i	0.961321	−	0.275431i	$-0.0888204\pi$
$71$	−0.305263	−	1.73123i	−0.0362281	−	0.205460i	−0.997549	+	0.0699711i	$0.977709\pi$
$72$		0			0
$73$	0.930968	−	5.27978i	0.108962	−	0.617951i	−0.880602	−	0.473856i	$-0.842862\pi$
$73$	0.930968	−	5.27978i	0.108962	−	0.617951i	0.989564	−	0.144095i	$-0.0460272\pi$
$74$	−1.60491	+	0.187587i	−0.186567	+	0.0218066i
$75$		0			0
$76$	−4.94583	−	5.24227i	−0.567325	−	0.601330i
$77$	3.74387	+	8.67926i	0.426653	+	0.989093i
$78$		0			0
$79$	−3.55048	−	2.33519i	−0.399460	−	0.262729i	0.333846	−	0.942628i	$-0.391653\pi$
$79$	−3.55048	−	2.33519i	−0.399460	−	0.262729i	−0.733306	+	0.679898i	$0.762024\pi$
$80$	21.8136			2.43884
$81$		0			0
$82$	8.94171			0.987446
$83$	−2.17613	−	1.43126i	−0.238861	−	0.157102i	0.424435	−	0.905458i	$-0.360473\pi$
$83$	−2.17613	−	1.43126i	−0.238861	−	0.157102i	−0.663296	+	0.748357i	$0.730843\pi$
$84$		0			0
$85$	−1.63698	−	3.79495i	−0.177556	−	0.411620i
$86$	4.88732	+	5.18025i	0.527013	+	0.558601i
$87$		0			0
$88$	−30.3242	+	3.54439i	−3.23257	+	0.377833i
$89$	−0.553979	+	3.14177i	−0.0587216	+	0.333027i	−0.999989	−	0.00463450i	$-0.998525\pi$
$89$	−0.553979	+	3.14177i	−0.0587216	+	0.333027i	0.941268	+	0.337661i	$0.109636\pi$
$90$		0			0
$91$	−0.169719	−	0.962523i	−0.0177914	−	0.100900i
$92$	−5.20326	−	17.3801i	−0.542477	−	1.81200i
$93$		0			0
$94$	0.0233953	+	0.401681i	0.00241304	+	0.0414302i
$95$	2.28171	+	1.14592i	0.234099	+	0.117569i
$96$		0			0
$97$	−10.5487	+	11.1810i	−1.07106	+	1.13526i	−0.0807017	+	0.996738i	$0.525716\pi$
$97$	−10.5487	+	11.1810i	−1.07106	+	1.13526i	−0.990360	+	0.138520i	$0.955765\pi$
$98$	−0.830968	−	0.302448i	−0.0839405	−	0.0305518i
$99$		0			0
$100$	8.20403	−	2.98602i	0.820403	−	0.298602i
$101$	−5.16679	+	11.9780i	−0.514115	+	1.19185i	0.441508	+	0.897258i	$0.354444\pi$
$101$	−5.16679	+	11.9780i	−0.514115	+	1.19185i	−0.955622	+	0.294594i	$0.904815\pi$
$102$		0			0
$103$	3.93516	−	13.1443i	0.387742	−	1.29515i	−0.512097	−	0.858928i	$-0.671131\pi$
$103$	3.93516	−	13.1443i	0.387742	−	1.29515i	0.899839	−	0.436222i	$-0.143684\pi$
$104$	3.13553	+	0.366491i	0.307464	+	0.0359374i
$105$		0			0
$106$	2.08770	−	35.8445i	0.202776	−	3.48152i
$107$	−1.15268	+	1.99650i	−0.111434	+	0.193009i	−0.916349	−	0.400381i	$-0.868878\pi$
$107$	−1.15268	+	1.99650i	−0.111434	+	0.193009i	0.804915	+	0.593390i	$0.202211\pi$
$108$		0			0
$109$	−4.62468	−	8.01018i	−0.442964	−	0.767236i	0.554944	−	0.831888i	$-0.312740\pi$
$109$	−4.62468	−	8.01018i	−0.442964	−	0.767236i	−0.997908	+	0.0646518i	$0.979406\pi$
$110$	15.8521	−	7.96121i	1.51144	−	0.759072i
$111$		0			0
$112$	−18.5275	+	24.8867i	−1.75068	+	2.35157i
$113$	9.24278	−	2.19058i	0.869487	−	0.206072i	0.228425	−	0.973561i	$-0.426642\pi$
$113$	9.24278	−	2.19058i	0.869487	−	0.206072i	0.641062	+	0.767489i	$0.278494\pi$
$114$		0			0
$115$	3.83814	+	5.15552i	0.357908	+	0.480754i
$116$	−25.9425	−	21.7684i	−2.40870	−	2.02114i
$117$		0			0
$118$	8.68704	−	7.28929i	0.799706	−	0.671033i
$119$	5.71996	+	1.35565i	0.524347	+	0.124273i
$120$		0			0
$121$	−2.00333	+	1.31761i	−0.182121	+	0.119783i
$122$	16.6148	−	10.9277i	1.50424	−	0.989351i
$123$		0			0
$124$	48.7398	+	11.5516i	4.37697	+	1.03736i
$125$	−9.32357	+	7.82340i	−0.833925	+	0.699746i
$126$		0			0
$127$	9.69030	+	8.13112i	0.859875	+	0.721521i	0.961941	−	0.273257i	$-0.0881009\pi$
$127$	9.69030	+	8.13112i	0.859875	+	0.721521i	−0.102066	+	0.994778i	$0.532545\pi$
$128$	−8.79016	−	11.8072i	−0.776948	−	1.04362i
$129$		0			0
$130$	−1.78477	+	0.422998i	−0.156535	+	0.0370994i
$131$	−8.88502	+	11.9347i	−0.776288	+	1.04274i	0.221427	+	0.975177i	$0.428929\pi$
$131$	−8.88502	+	11.9347i	−0.776288	+	1.04274i	−0.997715	+	0.0675591i	$0.978479\pi$
$132$		0			0
$133$	−3.24533	+	1.62987i	−0.281406	+	0.141328i
$134$	13.4683	+	23.3278i	1.16349	+	2.01522i
$135$		0			0
$136$	−9.49354	+	16.4433i	−0.814064	+	1.41000i
$137$	0.944711	−	16.2201i	0.0807121	−	1.38577i	−0.678342	−	0.734746i	$-0.737301\pi$
$137$	0.944711	−	16.2201i	0.0807121	−	1.38577i	0.759054	−	0.651027i	$-0.225662\pi$
$138$		0			0
$139$	16.3959	+	1.91640i	1.39068	+	0.162547i	0.778238	−	0.627969i	$-0.216114\pi$
$139$	16.3959	+	1.91640i	1.39068	+	0.162547i	0.612441	+	0.790516i	$0.290188\pi$
$140$	6.89143	−	23.0190i	0.582432	−	1.94546i
$141$		0			0
$142$	1.85855	−	4.30861i	0.155966	−	0.361570i
$143$	1.30179	−	0.473813i	0.108861	−	0.0396223i
$144$		0			0
$145$	11.2742	+	4.10346i	0.936268	+	0.340774i
$146$	9.82041	−	10.4090i	0.812743	−	0.861457i
$147$		0			0
$148$	−2.77237	−	1.39233i	−0.227887	−	0.114449i
$149$	0.198127	+	3.40171i	0.0162312	+	0.278679i	0.996652	+	0.0817637i	$0.0260553\pi$
$149$	0.198127	+	3.40171i	0.0162312	+	0.278679i	−0.980421	+	0.196915i	$0.936908\pi$
$150$		0			0
$151$	2.47827	+	8.27799i	0.201678	+	0.673653i	0.997662	+	0.0683353i	$0.0217688\pi$
$151$	2.47827	+	8.27799i	0.201678	+	0.673653i	−0.795984	+	0.605318i	$0.793046\pi$
$152$	−2.03690	−	11.5518i	−0.165214	−	0.936976i
$153$		0			0
$154$	−4.38123	+	24.8472i	−0.353050	+	2.00224i
$155$	−17.6256	+	2.06014i	−1.41572	+	0.165474i
$156$		0			0
$157$	−2.66576	−	2.82554i	−0.212751	−	0.225503i	0.612206	−	0.790698i	$-0.290282\pi$
$157$	−2.66576	−	2.82554i	−0.212751	−	0.225503i	−0.824957	+	0.565195i	$0.808801\pi$
$158$	−4.49281	−	10.4155i	−0.357429	−	0.828613i
$159$		0			0
$160$	23.3417	+	15.3521i	1.84532	+	1.21369i
$161$	−9.14176			−0.720472
$162$		0			0
$163$	−23.8379			−1.86713			−0.933564	−	0.358412i	$-0.883318\pi$
$163$	−23.8379			−1.86713			−0.933564	+	0.358412i	$0.883318\pi$
$164$	14.3435	+	9.43385i	1.12004	+	0.736660i
$165$		0			0
$166$	−2.75369	−	6.38378i	−0.213728	−	0.495477i
$167$	−8.77585	−	9.30186i	−0.679096	−	0.719799i	0.292548	−	0.956251i	$-0.405497\pi$
$167$	−8.77585	−	9.30186i	−0.679096	−	0.719799i	−0.971643	+	0.236452i	$0.924016\pi$
$168$		0			0
$169$	12.7698	−	1.49258i	0.982294	−	0.114814i
$170$	1.91566	−	10.8643i	0.146925	−	0.833252i
$171$		0			0
$172$	2.37442	+	13.4660i	0.181048	+	1.02677i
$173$	1.46229	+	4.88437i	0.111176	+	0.371352i	0.995411	−	0.0956887i	$-0.0305053\pi$
$173$	1.46229	+	4.88437i	0.111176	+	0.371352i	−0.884236	+	0.467041i	$0.845320\pi$
$174$		0			0
$175$	−0.255795	−	4.39182i	−0.0193362	−	0.331991i
$176$	−39.2990	−	19.7367i	−2.96227	−	1.48771i
$177$		0			0
$178$	−5.84370	+	6.19397i	−0.438004	+	0.464257i
$179$	1.10838	+	0.403418i	0.0828444	+	0.0301529i	0.383110	−	0.923703i	$-0.374853\pi$
$179$	1.10838	+	0.403418i	0.0828444	+	0.0301529i	−0.300266	+	0.953856i	$0.597075\pi$
$180$		0			0
$181$	−10.7631	+	3.91744i	−0.800013	+	0.291181i	−0.709492	−	0.704714i	$-0.751075\pi$
$181$	−10.7631	+	3.91744i	−0.800013	+	0.291181i	−0.0905211	+	0.995895i	$0.528853\pi$
$182$	1.03331	−	2.39548i	0.0765940	−	0.177565i
$183$		0			0
$184$	8.46861	−	28.2871i	0.624314	−	2.08535i
$185$	1.09165	+	0.127596i	0.0802600	+	0.00938105i
$186$		0			0
$187$	−0.484470	+	8.31803i	−0.0354279	+	0.608274i
$188$	−0.386261	+	0.669024i	−0.0281710	+	0.0487936i
$189$		0			0
$190$	3.40769	+	5.90229i	0.247220	+	0.428197i
$191$	−13.7471	+	6.90406i	−0.994706	+	0.499560i	−0.870221	−	0.492661i	$-0.836024\pi$
$191$	−13.7471	+	6.90406i	−0.994706	+	0.499560i	−0.124485	+	0.992222i	$0.539728\pi$
$192$		0			0
$193$	−10.4188	+	13.9948i	−0.749958	+	1.00737i	0.249283	+	0.968431i	$0.419805\pi$
$193$	−10.4188	+	13.9948i	−0.749958	+	1.00737i	−0.999242	+	0.0389382i	$0.987602\pi$
$194$	−39.9249	+	9.46238i	−2.86644	+	0.679360i
$195$		0			0
$196$	−1.01387	−	1.36186i	−0.0724193	−	0.0972760i
$197$	7.01270	+	5.88435i	0.499634	+	0.419243i	0.857464	−	0.514544i	$-0.172039\pi$
$197$	7.01270	+	5.88435i	0.499634	+	0.419243i	−0.357830	+	0.933787i	$0.616483\pi$
$198$		0			0
$199$	−17.7580	+	14.9007i	−1.25883	+	1.05629i	−0.263026	+	0.964789i	$0.584721\pi$
$199$	−17.7580	+	14.9007i	−1.25883	+	1.05629i	−0.995805	+	0.0914967i	$0.970835\pi$
$200$	13.8265	+	3.27693i	0.977679	+	0.231714i
$201$		0			0
$202$	−29.0915	+	19.1338i	−2.04687	+	1.34625i
$203$	−14.2573	+	9.37717i	−1.00067	+	0.658148i
$204$		0			0
$205$	−5.91817	−	1.40263i	−0.413343	−	0.0979640i
$206$	28.0556	−	23.5415i	1.95473	−	1.64021i
$207$		0			0
$208$	3.48336	+	2.92289i	0.241527	+	0.202666i
$209$	−3.07387	−	4.12893i	−0.212624	−	0.285604i
$210$		0			0
$211$	−25.1316	+	5.95630i	−1.73013	+	0.410048i	−0.970653	−	0.240485i	$-0.922693\pi$
$211$	−25.1316	+	5.95630i	−1.73013	+	0.410048i	−0.759478	+	0.650534i	$0.774545\pi$
$212$	41.1662	−	55.2958i	2.82731	−	3.79773i
$213$		0			0
$214$	−5.49903	+	2.76172i	−0.375906	+	0.188787i
$215$	−2.42213	−	4.19525i	−0.165188	−	0.286114i
$216$		0			0
$217$	12.6200	−	21.8585i	0.856702	−	1.48385i
$218$	1.43553	−	24.6470i	0.0972261	−	1.66931i
$219$		0			0
$220$	33.8279	+	3.95391i	2.28067	+	0.266573i
$221$	0.247094	−	0.825350i	0.0166213	−	0.0555191i
$222$		0			0
$223$	1.61565	−	3.74549i	0.108192	−	0.250816i	−0.855516	−	0.517776i	$-0.826760\pi$
$223$	1.61565	−	3.74549i	0.108192	−	0.250816i	0.963708	+	0.266960i	$0.0860192\pi$
$224$	−37.3402	+	13.5907i	−2.49490	+	0.908069i
$225$		0			0
$226$	23.8256	+	8.67180i	1.58485	+	0.576840i
$227$	14.6081	−	15.4837i	0.969576	−	1.02769i	−0.0300282	−	0.999549i	$-0.509560\pi$
$227$	14.6081	−	15.4837i	0.969576	−	1.02769i	0.999604	−	0.0281412i	$-0.00895881\pi$
$228$		0			0
$229$	10.8317	+	5.43987i	0.715777	+	0.359477i	0.769124	−	0.639099i	$-0.220693\pi$
$229$	10.8317	+	5.43987i	0.715777	+	0.359477i	−0.0533473	+	0.998576i	$0.516989\pi$
$230$	0.997540	+	17.1271i	0.0657758	+	1.12933i
$231$		0			0
$232$	−15.8081	−	52.8027i	−1.03785	−	3.46667i
$233$	4.18661	+	23.7435i	0.274274	+	1.55549i	0.741258	+	0.671220i	$0.234229\pi$
$233$	4.18661	+	23.7435i	0.274274	+	1.55549i	−0.466984	+	0.884266i	$0.654659\pi$
$234$		0			0
$235$	0.0475249	−	0.269527i	0.00310018	−	0.0175820i
$236$	21.6254	−	2.52765i	1.40770	−	0.164536i
$237$		0			0
$238$	10.7678	+	11.4132i	0.697970	+	0.739805i
$239$	−9.40236	−	21.7971i	−0.608188	−	1.40994i	−0.892430	−	0.451186i	$-0.851001\pi$
$239$	−9.40236	−	21.7971i	−0.608188	−	1.40994i	0.284242	−	0.958753i	$-0.408258\pi$
$240$		0			0
$241$	10.5898	+	6.96500i	0.682146	+	0.448655i	0.842708	−	0.538371i	$-0.180960\pi$
$241$	10.5898	+	6.96500i	0.682146	+	0.448655i	−0.160561	+	0.987026i	$0.551330\pi$
$242$	−6.40031			−0.411428
$243$		0			0
$244$	38.1812			2.44430
$245$	0.502542	+	0.330527i	0.0321062	+	0.0211166i
$246$		0			0
$247$	0.210815	+	0.488724i	0.0134138	+	0.0310967i
$248$	55.9455	+	59.2988i	3.55254	+	3.76548i
$249$		0			0
$250$	−32.2678	+	3.77157i	−2.04080	+	0.238535i
$251$	2.35563	−	13.3595i	0.148686	−	0.843242i	−0.815647	−	0.578550i	$-0.803619\pi$
$251$	2.35563	−	13.3595i	0.148686	−	0.843242i	0.964333	−	0.264692i	$-0.0852702\pi$
$252$		0			0
$253$	−2.25007	−	12.7608i	−0.141461	−	0.802263i
$254$	9.68401	+	32.3469i	0.607629	+	2.02962i
$255$		0			0
$256$	−0.302516	−	5.19400i	−0.0189073	−	0.324625i
$257$	2.50132	+	1.25621i	0.156028	+	0.0783603i	0.525100	−	0.851041i	$-0.324028\pi$
$257$	2.50132	+	1.25621i	0.156028	+	0.0783603i	−0.369072	+	0.929401i	$0.620324\pi$
$258$		0			0
$259$	−1.07277	+	1.13707i	−0.0666588	+	0.0706542i
$260$	−3.30925	−	1.20447i	−0.205231	−	0.0746979i
$261$		0			0
$262$	−37.3201	+	13.5834i	−2.30564	+	0.839186i
$263$	−0.588361	+	1.36397i	−0.0362799	+	0.0841063i	−0.935393	−	0.353611i	$-0.884954\pi$
$263$	−0.588361	+	1.36397i	−0.0362799	+	0.0841063i	0.899113	+	0.437717i	$0.144213\pi$
$264$		0			0
$265$	−7.00447	+	23.3966i	−0.430281	+	1.43724i
$266$	−9.62814	−	1.12537i	−0.590339	−	0.0690007i
$267$		0			0
$268$	−3.00710	+	51.6300i	−0.183688	+	3.15380i
$269$	−4.56187	+	7.90140i	−0.278142	+	0.481757i	−0.970923	−	0.239392i	$-0.923052\pi$
$269$	−4.56187	+	7.90140i	−0.278142	+	0.481757i	0.692781	+	0.721148i	$0.256385\pi$
$270$		0			0
$271$	−2.94843	−	5.10683i	−0.179105	−	0.310218i	0.762470	−	0.647024i	$-0.223987\pi$
$271$	−2.94843	−	5.10683i	−0.179105	−	0.310218i	−0.941574	+	0.336806i	$0.890653\pi$
$272$	−24.4401	+	12.2743i	−1.48190	+	0.744238i
$273$		0			0
$274$	25.8980	−	34.7870i	1.56455	−	2.10156i
$275$	6.06749	−	1.43802i	0.365883	−	0.0867159i
$276$		0			0
$277$	−2.95581	−	3.97034i	−0.177597	−	0.238555i	0.704407	−	0.709797i	$-0.251213\pi$
$277$	−2.95581	−	3.97034i	−0.177597	−	0.238555i	−0.882004	+	0.471242i	$0.843806\pi$
$278$	33.7538	+	28.3228i	2.02442	+	1.69869i
$279$		0			0
$280$	29.9582	−	25.1379i	1.79035	−	1.50228i
$281$	13.2418	+	3.13837i	0.789942	+	0.187220i	0.605733	−	0.795668i	$-0.292880\pi$
$281$	13.2418	+	3.13837i	0.789942	+	0.187220i	0.184208	+	0.982887i	$0.441028\pi$
$282$		0			0
$283$	9.88030	−	6.49838i	0.587323	−	0.386289i	−0.220785	−	0.975322i	$-0.570862\pi$
$283$	9.88030	−	6.49838i	0.587323	−	0.386289i	0.808108	+	0.589034i	$0.200492\pi$
$284$	7.52708	−	4.95064i	0.446650	−	0.293766i
$285$		0			0
$286$	3.59813	+	0.852772i	0.212762	+	0.0504255i
$287$	6.62685	−	5.56058i	0.391170	−	0.328231i
$288$		0			0
$289$	−9.05329	−	7.59661i	−0.532547	−	0.446860i
$290$	19.1239	+	25.6878i	1.12299	+	1.50844i
$291$		0			0
$292$	26.7350	−	6.33630i	1.56454	−	0.370804i
$293$	−9.72118	+	13.0578i	−0.567918	+	0.762846i	−0.989592	−	0.143902i	$-0.954035\pi$
$293$	−9.72118	+	13.0578i	−0.567918	+	0.762846i	0.421674	+	0.906747i	$0.361443\pi$
$294$		0			0
$295$	−6.89304	+	3.46181i	−0.401328	+	0.201555i
$296$	−2.52464	−	4.37280i	−0.146741	−	0.254164i
$297$		0			0
$298$	−4.54769	+	7.87683i	−0.263440	+	0.456292i
$299$	−0.0779038	+	1.33756i	−0.00450529	+	0.0773529i
$300$		0			0
$301$	6.84352	+	0.799893i	0.394454	+	0.0461051i
$302$	−6.61510	+	22.0960i	−0.380656	+	1.27148i
$303$		0			0
$304$	6.69218	−	15.5142i	0.383823	−	0.889802i
$305$	−12.7109	+	4.62638i	−0.727822	+	0.264906i
$306$		0			0
$307$	23.4445	+	8.53312i	1.33805	+	0.487011i	0.909198	−	0.416364i	$-0.136696\pi$
$307$	23.4445	+	8.53312i	1.33805	+	0.487011i	0.428853	+	0.903374i	$0.358918\pi$
$308$	−33.2427	+	35.2353i	−1.89418	+	2.00772i
$309$		0			0
$310$	−42.3290	−	21.2584i	−2.40413	−	1.20740i
$311$	−0.482249	−	8.27990i	−0.0273459	−	0.469510i	−0.983987	−	0.178241i	$-0.942959\pi$
$311$	−0.482249	−	8.27990i	−0.0273459	−	0.469510i	0.956641	−	0.291269i	$-0.0940776\pi$
$312$		0			0
$313$	−1.58728	−	5.30188i	−0.0897183	−	0.299680i	0.901340	−	0.433113i	$-0.142585\pi$
$313$	−1.58728	−	5.30188i	−0.0897183	−	0.299680i	−0.991058	+	0.133433i	$0.957400\pi$
$314$	−1.80054	−	10.2114i	−0.101610	−	0.576261i
$315$		0			0
$316$	3.78181	−	21.4477i	0.212743	−	1.20653i
$317$	21.9438	−	2.56486i	1.23249	−	0.144057i	0.525196	−	0.850981i	$-0.323992\pi$
$317$	21.9438	−	2.56486i	1.23249	−	0.144057i	0.707289	+	0.706924i	$0.249918\pi$
$318$		0			0
$319$	−16.5985	−	17.5934i	−0.929340	−	0.985043i
$320$	12.2569	+	28.4147i	0.685183	+	1.58843i
$321$		0			0
$322$	−20.3872	−	13.4089i	−1.13614	−	0.747248i
$323$	−3.20124			−0.178122
$324$		0			0
$325$	−0.644760			−0.0357648
$326$	−53.1614	−	34.9648i	−2.94434	−	1.93652i
$327$		0			0
$328$	11.0671	+	25.6564i	0.611079	+	1.41664i
$329$	0.267132	+	0.283144i	0.0147275	+	0.0156102i
$330$		0			0
$331$	−2.84377	+	0.332389i	−0.156308	+	0.0182698i	−0.193887	−	0.981024i	$-0.562109\pi$
$331$	−2.84377	+	0.332389i	−0.156308	+	0.0182698i	0.0375791	+	0.999294i	$0.488035\pi$
$332$	2.31791	−	13.1455i	0.127212	−	0.721455i
$333$		0			0
$334$	−5.92749	−	33.6165i	−0.324338	−	1.83941i
$335$	−5.25486	−	17.5525i	−0.287104	−	0.958993i
$336$		0			0
$337$	0.939940	+	16.1381i	0.0512018	+	0.879101i	0.921935	+	0.387345i	$0.126608\pi$
$337$	0.939940	+	16.1381i	0.0512018	+	0.879101i	−0.870733	+	0.491756i	$0.836355\pi$
$338$	30.6675	+	15.4018i	1.66809	+	0.837748i
$339$		0			0
$340$	14.5352	−	15.4064i	0.788281	−	0.835529i
$341$	33.6180	+	12.2359i	1.82052	+	0.662613i
$342$		0			0
$343$	−17.7905	+	6.47520i	−0.960595	+	0.349628i
$344$	−8.81469	+	20.4348i	−0.475256	+	1.10177i
$345$		0			0
$346$	−3.90320	+	13.0376i	−0.209837	+	0.700905i
$347$	−14.6404	−	1.71122i	−0.785939	−	0.0918631i	−0.286349	−	0.958125i	$-0.592442\pi$
$347$	−14.6404	−	1.71122i	−0.785939	−	0.0918631i	−0.499590	+	0.866262i	$0.666516\pi$
$348$		0			0
$349$	0.143834	−	2.46953i	0.00769924	−	0.132191i	−0.992268	−	0.124113i	$-0.960392\pi$
$349$	0.143834	−	2.46953i	0.00769924	−	0.132191i	0.999967	−	0.00807818i	$-0.00257139\pi$
$350$	5.87136	−	10.1695i	0.313837	−	0.543582i
$351$		0			0
$352$	−28.1616	−	48.7773i	−1.50102	−	2.59984i
$353$	13.9985	−	7.03032i	0.745066	−	0.374186i	−0.0354092	−	0.999373i	$-0.511273\pi$
$353$	13.9985	−	7.03032i	0.745066	−	0.374186i	0.780475	+	0.625187i	$0.214977\pi$
$354$		0			0
$355$	−1.90597	+	2.56016i	−0.101158	+	0.135879i
$356$	−15.9088	+	3.77046i	−0.843166	+	0.199834i
$357$		0			0
$358$	1.88010	+	2.52542i	0.0993665	+	0.133472i
$359$	−0.180567	−	0.151513i	−0.00952994	−	0.00799657i	0.638010	−	0.770028i	$-0.279758\pi$
$359$	−0.180567	−	0.151513i	−0.00952994	−	0.00799657i	−0.647540	+	0.762031i	$0.724202\pi$
$360$		0			0
$361$	−13.0398	+	10.9417i	−0.686307	+	0.575880i
$362$	−29.7490	−	7.05063i	−1.56357	−	0.370573i
$363$		0			0
$364$	4.18487	−	2.75243i	0.219347	−	0.144267i
$365$	−8.13255	+	5.34886i	−0.425677	+	0.279972i
$366$		0			0
$367$	−9.37480	−	2.22187i	−0.489361	−	0.115981i	−0.0214745	−	0.999769i	$-0.506836\pi$
$367$	−9.37480	−	2.22187i	−0.489361	−	0.115981i	−0.467886	+	0.883789i	$0.654984\pi$
$368$	32.5813	−	27.3390i	1.69842	−	1.42514i
$369$		0			0
$370$	2.24737	+	1.88576i	0.116835	+	0.0980362i
$371$	−20.7434	−	27.8632i	−1.07694	−	1.44659i
$372$		0			0
$373$	−0.0585838	+	0.0138846i	−0.00303336	+	0.000718918i	−0.232132	−	0.972684i	$-0.574570\pi$
$373$	−0.0585838	+	0.0138846i	−0.00303336	+	0.000718918i	0.229099	+	0.973403i	$0.426422\pi$
$374$	−13.2811	+	17.8396i	−0.686749	+	0.922463i
$375$		0			0
$376$	−1.12359	+	0.564287i	−0.0579446	+	0.0291009i
$377$	1.25050	+	2.16594i	0.0644042	+	0.111551i
$378$		0			0
$379$	−1.23614	+	2.14105i	−0.0634961	+	0.109979i	−0.896026	−	0.444002i	$-0.853558\pi$
$379$	−1.23614	+	2.14105i	−0.0634961	+	0.109979i	0.832530	+	0.553980i	$0.186892\pi$
$380$	−0.760843	+	13.0632i	−0.0390304	+	0.670127i
$381$		0			0
$382$	−40.7844	−	4.76701i	−2.08671	−	0.243902i
$383$	7.91287	−	26.4308i	0.404329	−	1.35055i	−0.477355	−	0.878711i	$-0.658404\pi$
$383$	7.91287	−	26.4308i	0.404329	−	1.35055i	0.881684	−	0.471841i	$-0.156410\pi$
$384$		0			0
$385$	6.79739	−	15.7581i	0.346427	−	0.803109i
$386$	−43.7623	+	15.9282i	−2.22744	+	0.810723i
$387$		0			0
$388$	−74.0272	−	26.9437i	−3.75816	−	1.36786i
$389$	−7.41631	+	7.86083i	−0.376022	+	0.398560i	−0.887554	−	0.460705i	$-0.847597\pi$
$389$	−7.41631	+	7.86083i	−0.376022	+	0.398560i	0.511532	+	0.859264i	$0.329078\pi$
$390$		0			0
$391$	−7.20123	−	3.61659i	−0.364182	−	0.182899i
$392$	−0.160672	−	2.75863i	−0.00811517	−	0.139332i
$393$		0			0
$394$	7.00815	+	23.4089i	0.353065	+	1.17932i
$395$	1.33980	+	7.59837i	0.0674126	+	0.382316i
$396$		0			0
$397$	−3.32712	+	18.8690i	−0.166983	+	0.947010i	0.780012	+	0.625764i	$0.215213\pi$
$397$	−3.32712	+	18.8690i	−0.166983	+	0.947010i	−0.946996	+	0.321246i	$0.895898\pi$
$398$	−61.4585	+	7.18347i	−3.08064	+	0.360075i
$399$		0			0
$400$	14.0457	+	14.8875i	0.702283	+	0.744376i
$401$	12.4792	+	28.9301i	0.623182	+	1.44470i	0.878453	+	0.477829i	$0.158576\pi$
$401$	12.4792	+	28.9301i	0.623182	+	1.44470i	−0.255271	+	0.966870i	$0.582165\pi$
$402$		0			0
$403$	−3.09064	−	2.03274i	−0.153956	−	0.101258i
$404$	−66.8529			−3.32606
$405$		0			0
$406$	−45.5497			−2.26059
$407$	−1.85125	−	1.21759i	−0.0917633	−	0.0603537i
$408$		0			0
$409$	−0.362689	−	0.840808i	−0.0179338	−	0.0415753i	0.909014	−	0.416766i	$-0.136837\pi$
$409$	−0.362689	−	0.840808i	−0.0179338	−	0.0415753i	−0.926948	+	0.375191i	$0.877577\pi$
$410$	−11.1409	−	11.8086i	−0.550209	−	0.583187i
$411$		0			0
$412$	69.8415	−	8.16330i	3.44084	−	0.402177i
$413$	1.90511	−	10.8044i	0.0937444	−	0.531651i
$414$		0			0
$415$	0.821178	+	4.65713i	0.0403100	+	0.228609i
$416$	1.67029	+	5.57917i	0.0818929	+	0.273541i
$417$		0			0
$418$	−0.798906	−	13.7167i	−0.0390758	−	0.670905i
$419$	−10.9019	−	5.47513i	−0.532591	−	0.267477i	0.162114	−	0.986772i	$-0.448169\pi$
$419$	−10.9019	−	5.47513i	−0.532591	−	0.267477i	−0.694705	+	0.719295i	$0.744465\pi$
$420$		0			0
$421$	−21.5036	+	22.7925i	−1.04802	+	1.11084i	−0.0543513	+	0.998522i	$0.517309\pi$
$421$	−21.5036	+	22.7925i	−1.04802	+	1.11084i	−0.993672	+	0.112318i	$0.964172\pi$
$422$	−64.7830	−	23.5791i	−3.15359	−	1.14781i
$423$		0			0
$424$	105.432	−	38.3743i	5.12025	−	1.86362i
$425$	1.53596	−	3.56076i	0.0745052	−	0.172722i
$426$		0			0
$427$	5.51788	−	18.4310i	0.267029	−	0.891938i
$428$	−11.7348	−	1.37160i	−0.567221	−	0.0662987i
$429$		0			0
$430$	0.751842	−	12.9086i	0.0362570	−	0.622509i
$431$	6.90324	−	11.9568i	0.332518	−	0.575937i	−0.650487	−	0.759517i	$-0.725435\pi$
$431$	6.90324	−	11.9568i	0.332518	−	0.575937i	0.983005	+	0.183580i	$0.0587686\pi$
$432$		0			0
$433$	12.1413	+	21.0293i	0.583472	+	1.01060i	0.995064	+	0.0992354i	$0.0316397\pi$
$433$	12.1413	+	21.0293i	0.583472	+	1.01060i	−0.411592	+	0.911368i	$0.635027\pi$
$434$	60.2056	−	30.2364i	2.88996	−	1.45139i
$435$		0			0
$436$	28.3063	−	38.0220i	1.35563	−	1.82092i
$437$	4.84419	−	1.14809i	0.231729	−	0.0549208i
$438$		0			0
$439$	7.58958	+	10.1946i	0.362231	+	0.486561i	0.945456	−	0.325750i	$-0.105617\pi$
$439$	7.58958	+	10.1946i	0.362231	+	0.486561i	−0.583225	+	0.812311i	$0.698209\pi$
$440$	42.4631	+	35.6308i	2.02435	+	1.69863i
$441$		0			0
$442$	1.76165	−	1.47820i	0.0837932	−	0.0703108i
$443$	24.8296	+	5.88473i	1.17969	+	0.279592i	0.773260	−	0.634090i	$-0.218625\pi$
$443$	24.8296	+	5.88473i	1.17969	+	0.279592i	0.406431	+	0.913681i	$0.366773\pi$
$444$		0			0
$445$	4.83933	−	3.18288i	0.229406	−	0.150883i
$446$	9.09687	−	5.98310i	0.430749	−	0.283308i
$447$		0			0
$448$	−42.8282	−	10.1505i	−2.02344	−	0.479565i
$449$	2.45881	−	2.06318i	0.116038	−	0.0973677i	−0.582922	−	0.812528i	$-0.698091\pi$
$449$	2.45881	−	2.06318i	0.116038	−	0.0973677i	0.698960	+	0.715160i	$0.253646\pi$
$450$		0			0
$451$	9.39297	+	7.88164i	0.442298	+	0.371132i
$452$	29.0698	+	39.0475i	1.36733	+	1.83664i
$453$		0			0
$454$	55.2890	−	13.1037i	2.59484	−	0.614989i
$455$	−1.05967	+	1.42339i	−0.0496782	+	0.0667294i
$456$		0			0
$457$	−1.90624	+	0.957349i	−0.0891701	+	0.0447829i	−0.492825	−	0.870128i	$-0.664036\pi$
$457$	−1.90624	+	0.957349i	−0.0891701	+	0.0447829i	0.403655	+	0.914911i	$0.367740\pi$
$458$	16.1769	+	28.0192i	0.755896	+	1.30925i
$459$		0			0
$460$	−16.4696	+	28.5262i	−0.767899	+	1.33004i
$461$	−1.33368	+	22.8984i	−0.0621157	+	1.06648i	0.812904	+	0.582398i	$0.197885\pi$
$461$	−1.33368	+	22.8984i	−0.0621157	+	1.06648i	−0.875020	+	0.484087i	$0.839152\pi$
$462$		0			0
$463$	−28.7556	−	3.36105i	−1.33639	−	0.156201i	−0.582298	−	0.812975i	$-0.697846\pi$
$463$	−28.7556	−	3.36105i	−1.33639	−	0.156201i	−0.754088	+	0.656774i	$0.771921\pi$
$464$	22.7701	−	76.0576i	1.05708	−	3.53088i
$465$		0			0
$466$	−25.4896	+	59.0916i	−1.18078	+	2.73737i
$467$	−1.96329	+	0.714577i	−0.0908500	+	0.0330667i	−0.387045	−	0.922061i	$-0.626504\pi$
$467$	−1.96329	+	0.714577i	−0.0908500	+	0.0330667i	0.296195	+	0.955127i	$0.404282\pi$
$468$		0			0
$469$	24.4885	+	8.91307i	1.13077	+	0.411567i
$470$	0.501321	−	0.531369i	0.0231242	−	0.0245102i
$471$		0			0
$472$	31.6671	+	15.9038i	1.45759	+	0.732031i
$473$	0.567849	+	9.74959i	0.0261097	+	0.448287i
$474$		0			0
$475$	0.687105	+	2.29509i	0.0315265	+	0.105306i
$476$	5.23133	+	29.6684i	0.239778	+	1.35985i
$477$		0			0
$478$	11.0030	−	62.4013i	0.503267	−	2.85417i
$479$	21.5915	−	2.52368i	0.986540	−	0.115310i	0.392505	−	0.919750i	$-0.371608\pi$
$479$	21.5915	−	2.52368i	0.986540	−	0.115310i	0.594034	+	0.804440i	$0.297534\pi$
$480$		0			0
$481$	0.157226	+	0.166650i	0.00716890	+	0.00759859i
$482$	13.4004	+	31.0656i	0.610370	+	1.41500i
$483$		0			0
$484$	−10.2668	−	6.75258i	−0.466673	−	0.306936i
$485$	27.9091			1.26729
$486$		0			0
$487$	−3.65843			−0.165779			−0.0828896	−	0.996559i	$-0.526415\pi$
$487$	−3.65843			−0.165779			−0.0828896	+	0.996559i	$0.526415\pi$
$488$	51.9190	+	34.1477i	2.35026	+	1.54579i
$489$		0			0
$490$	0.635921	+	1.47423i	0.0287280	+	0.0665990i
$491$	11.9181	+	12.6324i	0.537855	+	0.570093i	0.938122	−	0.346306i	$-0.112564\pi$
$491$	11.9181	+	12.6324i	0.537855	+	0.570093i	−0.400267	+	0.916399i	$0.631083\pi$
$492$		0			0
$493$	−14.9406	+	1.74631i	−0.672892	+	0.0786498i
$494$	−0.246704	+	1.39913i	−0.0110998	+	0.0629498i
$495$		0			0
$496$	20.3913	+	115.645i	0.915596	+	5.19260i
$497$	−1.30199	−	4.34896i	−0.0584024	−	0.195078i
$498$		0			0
$499$	0.983696	+	16.8894i	0.0440363	+	0.756074i	0.945981	+	0.324222i	$0.105103\pi$
$499$	0.983696	+	16.8894i	0.0440363	+	0.756074i	−0.901945	+	0.431852i	$0.857860\pi$
$500$	−55.7403	−	27.9938i	−2.49278	−	1.25192i
$501$		0			0
$502$	24.8487	−	26.3380i	1.10905	−	1.17552i
$503$	−27.0776	−	9.85546i	−1.20733	−	0.439433i	−0.341555	−	0.939862i	$-0.610953\pi$
$503$	−27.0776	−	9.85546i	−1.20733	−	0.439433i	−0.865778	+	0.500429i	$0.833176\pi$
$504$		0			0
$505$	22.2559	−	8.10050i	0.990377	−	0.360468i
$506$	13.6992	−	31.7584i	0.609006	−	1.41183i
$507$		0			0
$508$	−18.5930	+	62.1049i	−0.824931	+	2.75546i
$509$	11.8969	+	1.39055i	0.527322	+	0.0616351i	0.375589	−	0.926786i	$-0.377440\pi$
$509$	11.8969	+	1.39055i	0.527322	+	0.0616351i	0.151733	+	0.988421i	$0.451515\pi$
$510$		0			0
$511$	0.805001	−	13.8213i	0.0356111	−	0.611420i
$512$	−7.77620	+	13.4688i	−0.343663	+	0.595241i
$513$		0			0
$514$	3.73567	+	6.47037i	0.164773	+	0.285396i
$515$	−22.2617	+	11.1803i	−0.980969	+	0.492661i
$516$		0			0
$517$	−0.329484	+	0.442574i	−0.0144907	+	0.0194644i
$518$	−4.06024	+	0.962294i	−0.178397	+	0.0422808i
$519$		0			0
$520$	−3.42271	−	4.59749i	−0.150096	−	0.201613i
$521$	2.74519	+	2.30349i	0.120269	+	0.100918i	0.700939	−	0.713222i	$-0.252765\pi$
$521$	2.74519	+	2.30349i	0.120269	+	0.100918i	−0.580669	+	0.814139i	$0.697209\pi$
$522$		0			0
$523$	−20.6502	+	17.3276i	−0.902971	+	0.757683i	−0.970769	−	0.240016i	$-0.922847\pi$
$523$	−20.6502	+	17.3276i	−0.902971	+	0.757683i	0.0677978	+	0.997699i	$0.478403\pi$
$524$	−74.1966	−	17.5849i	−3.24129	−	0.768201i
$525$		0			0
$526$	−3.31276	+	2.17884i	−0.144443	+	0.0950018i
$527$	18.5887	−	12.2260i	0.809735	−	0.532571i
$528$		0			0
$529$	−10.1859	−	2.41410i	−0.442865	−	0.104961i
$530$	−49.9383	+	41.9032i	−2.16918	+	1.82016i
$531$		0			0
$532$	−14.2573	−	11.9633i	−0.618132	−	0.518674i
$533$	−0.757113	−	1.01698i	−0.0327942	−	0.0440502i
$534$		0			0
$535$	4.07281	−	0.965273i	0.176083	−	0.0417324i
$536$	−50.2648	+	67.5173i	−2.17111	+	2.91630i
$537$		0			0
$538$	−21.7631	+	10.9298i	−0.938273	+	0.471219i
$539$	−0.606313	−	1.05017i	−0.0261158	−	0.0452338i
$540$		0			0
$541$	8.33503	−	14.4367i	0.358351	−	0.620682i	−0.629335	−	0.777134i	$-0.716672\pi$
$541$	8.33503	−	14.4367i	0.358351	−	0.620682i	0.987685	+	0.156453i	$0.0500058\pi$
$542$	0.915210	−	15.7135i	0.0393116	−	0.674954i
$543$		0			0
$544$	−34.7906	−	4.06644i	−1.49164	−	0.174347i
$545$	−4.81635	+	16.0877i	−0.206310	+	0.689122i
$546$		0			0
$547$	−15.3370	+	35.5553i	−0.655765	+	1.52023i	0.187232	+	0.982316i	$0.440048\pi$
$547$	−15.3370	+	35.5553i	−0.655765	+	1.52023i	−0.842997	+	0.537918i	$0.819211\pi$
$548$	78.2449	−	28.4788i	3.34246	−	1.21655i
$549$		0			0
$550$	15.6405	+	5.69267i	0.666912	+	0.242736i
$551$	6.37724	−	6.75948i	0.271680	−	0.287964i
$552$		0			0
$553$	−9.80679	−	4.92516i	−0.417027	−	0.209439i
$554$	−0.768221	−	13.1898i	−0.0326386	−	0.560383i
$555$		0			0
$556$	24.2632	+	81.0446i	1.02899	+	3.43706i
$557$	3.42298	+	19.4127i	0.145036	+	0.822542i	0.967338	+	0.253490i	$0.0815786\pi$
$557$	3.42298	+	19.4127i	0.145036	+	0.822542i	−0.822302	+	0.569052i	$0.807310\pi$
$558$		0			0
$559$	0.175353	−	0.994479i	0.00741666	−	0.0420620i
$560$	55.9502	−	6.53965i	2.36433	−	0.276350i
$561$		0			0
$562$	24.9276	+	26.4217i	1.05151	+	1.11453i
$563$	0.290922	+	0.674433i	0.0122609	+	0.0284240i	0.924237	−	0.381820i	$-0.124703\pi$
$563$	0.290922	+	0.674433i	0.0122609	+	0.0284240i	−0.911976	+	0.410244i	$0.865443\pi$
$564$		0			0
$565$	−14.4089	−	9.47690i	−0.606188	−	0.398696i
$566$	31.5659			1.32681
$567$		0			0
$568$	14.6630			0.615246
$569$	17.1901	+	11.3061i	0.720647	+	0.473977i	0.856102	−	0.516806i	$-0.172879\pi$
$569$	17.1901	+	11.3061i	0.720647	+	0.473977i	−0.135455	+	0.990784i	$0.543250\pi$
$570$		0			0
$571$	0.929249	+	2.15424i	0.0388878	+	0.0901521i	0.936553	−	0.350526i	$-0.113997\pi$
$571$	0.929249	+	2.15424i	0.0388878	+	0.0901521i	−0.897665	+	0.440678i	$0.854738\pi$
$572$	4.87208	+	5.16411i	0.203712	+	0.215922i
$573$		0			0
$574$	22.9348	−	2.68069i	0.957280	−	0.111890i
$575$	−1.04722	+	5.93909i	−0.0436721	+	0.247677i
$576$		0			0
$577$	−5.62981	−	31.9282i	−0.234372	−	1.32919i	−0.843932	−	0.536449i	$-0.819765\pi$
$577$	−5.62981	−	31.9282i	−0.234372	−	1.32919i	0.609561	−	0.792739i	$-0.291346\pi$
$578$	−9.04742	−	30.2205i	−0.376323	−	1.25701i
$579$		0			0
$580$	3.57513	+	61.3826i	0.148449	+	2.54877i
$581$	−6.01069	−	3.01868i	−0.249366	−	0.125236i
$582$		0			0
$583$	33.7880	−	35.8132i	1.39936	−	1.48323i
$584$	42.0213	+	15.2945i	1.73885	+	0.632891i
$585$		0			0
$586$	−40.8323	+	14.8617i	−1.68677	+	0.613932i
$587$	−7.34958	+	17.0382i	−0.303350	+	0.703244i	−0.999898	−	0.0142660i	$-0.995459\pi$
$587$	−7.34958	+	17.0382i	−0.303350	+	0.703244i	0.696549	+	0.717510i	$0.254718\pi$
$588$		0			0
$589$	−3.94215	+	13.1677i	−0.162433	+	0.542565i
$590$	−20.4500	−	2.39026i	−0.841913	−	0.0984055i
$591$		0			0
$592$	0.422889	−	7.26072i	0.0173806	−	0.298414i
$593$	20.4339	−	35.3926i	0.839120	−	1.45340i	−0.0515108	−	0.998672i	$-0.516404\pi$
$593$	20.4339	−	35.3926i	0.839120	−	1.45340i	0.890631	−	0.454727i	$-0.150263\pi$
$594$		0			0
$595$	−5.33644	−	9.24299i	−0.218773	−	0.378926i
$596$	−15.6054	+	7.83730i	−0.639220	+	0.321028i
$597$		0			0
$598$	−2.13563	+	2.86865i	−0.0873323	+	0.117308i
$599$	8.88883	−	2.10669i	0.363188	−	0.0860771i	−0.0449704	−	0.998988i	$-0.514319\pi$
$599$	8.88883	−	2.10669i	0.363188	−	0.0860771i	0.408158	+	0.912911i	$0.366171\pi$
$600$		0			0
$601$	−22.1512	−	29.7542i	−0.903565	−	1.21370i	−0.976316	−	0.216348i	$-0.930585\pi$
$601$	−22.1512	−	29.7542i	−0.903565	−	1.21370i	0.0727514	−	0.997350i	$-0.476822\pi$
$602$	14.0886	+	11.8218i	0.574209	+	0.481819i
$603$		0			0
$604$	−33.9235	+	28.4652i	−1.38033	+	1.15823i
$605$	4.23612	+	1.00398i	0.172223	+	0.0408175i
$606$		0			0
$607$	27.9450	−	18.3797i	1.13425	−	0.746009i	0.163607	−	0.986526i	$-0.447687\pi$
$607$	27.9450	−	18.3797i	1.13425	−	0.746009i	0.970645	+	0.240516i	$0.0773167\pi$
$608$	18.0796	−	11.8912i	0.733226	−	0.482251i
$609$		0			0
$610$	−35.1326	−	8.32658i	−1.42248	−	0.337133i
$611$	0.0437040	−	0.0366720i	0.00176807	−	0.00148359i
$612$		0			0
$613$	35.2558	+	29.5831i	1.42397	+	1.19485i	0.949173	+	0.314754i	$0.101922\pi$
$613$	35.2558	+	29.5831i	1.42397	+	1.19485i	0.474794	+	0.880097i	$0.342522\pi$
$614$	39.7680	+	53.4177i	1.60491	+	2.15576i
$615$		0			0
$616$	−76.7167	+	18.1822i	−3.09100	+	0.732581i
$617$	25.3857	−	34.0989i	1.02199	−	1.37277i	0.0959295	−	0.995388i	$-0.469418\pi$
$617$	25.3857	−	34.0989i	1.02199	−	1.37277i	0.926059	−	0.377380i	$-0.123175\pi$
$618$		0			0
$619$	37.5931	−	18.8800i	1.51099	−	0.758850i	0.515794	−	0.856713i	$-0.327497\pi$
$619$	37.5931	−	18.8800i	1.51099	−	0.758850i	0.995200	+	0.0978633i	$0.0312008\pi$
$620$	−45.4719	−	78.7597i	−1.82620	−	3.16307i
$621$		0			0
$622$	11.0693	−	19.1725i	0.443837	−	0.768749i
$623$	−0.479021	+	8.22448i	−0.0191916	+	0.329507i
$624$		0			0
$625$	13.4882	+	1.57654i	0.539528	+	0.0630618i
$626$	4.23683	−	14.1520i	0.169338	−	0.565628i
$627$		0			0
$628$	7.88513	−	18.2798i	0.314651	−	0.729443i
$629$	−1.29489	+	0.471303i	−0.0516308	+	0.0187921i
$630$		0			0
$631$	−1.25540	−	0.456928i	−0.0499766	−	0.0181900i	0.316911	−	0.948455i	$-0.397354\pi$
$631$	−1.25540	−	0.456928i	−0.0499766	−	0.0181900i	−0.366888	+	0.930265i	$0.619577\pi$
$632$	24.3245	−	25.7824i	0.967576	−	1.02557i
$633$		0			0
$634$	52.6993	+	26.4666i	2.09296	+	1.05112i
$635$	−1.33542	−	22.9282i	−0.0529943	−	0.909878i
$636$		0			0
$637$	0.0359611	+	0.120118i	0.00142483	+	0.00475927i
$638$	−11.2112	−	63.5818i	−0.443855	−	2.51723i
$639$		0			0
$640$	−4.64087	+	26.3197i	−0.183446	+	1.04038i
$641$	9.56344	−	1.11781i	0.377733	−	0.0441507i	0.0748919	−	0.997192i	$-0.476139\pi$
$641$	9.56344	−	1.11781i	0.377733	−	0.0441507i	0.302841	+	0.953041i	$0.402065\pi$
$642$		0			0
$643$	12.6003	+	13.3556i	0.496909	+	0.526692i	0.926482	−	0.376340i	$-0.122817\pi$
$643$	12.6003	+	13.3556i	0.496909	+	0.526692i	−0.429573	+	0.903032i	$0.641336\pi$
$644$	−18.5564	−	43.0187i	−0.731226	−	1.69517i
$645$		0			0
$646$	−7.13916	−	4.69550i	−0.280886	−	0.184742i
$647$	−24.2705			−0.954170			−0.477085	−	0.878857i	$-0.658307\pi$
$647$	−24.2705			−0.954170			−0.477085	+	0.878857i	$0.658307\pi$
$648$		0			0
$649$	15.5506			0.610413
$650$	−1.43789	−	0.945717i	−0.0563988	−	0.0370941i
$651$		0			0
$652$	−48.3874	−	112.175i	−1.89500	−	4.39310i
$653$	−29.2055	−	30.9560i	−1.14290	−	1.21140i	−0.974188	−	0.225738i	$-0.927521\pi$
$653$	−29.2055	−	30.9560i	−1.14290	−	1.21140i	−0.168712	−	0.985665i	$-0.553961\pi$
$654$		0			0
$655$	26.8315	−	3.13615i	1.04839	−	0.122540i
$656$	−6.98888	+	39.6359i	−0.272870	+	1.54752i
$657$		0			0
$658$	0.180430	+	1.02327i	0.00703388	+	0.0398911i
$659$	−0.540877	−	1.80666i	−0.0210696	−	0.0703773i	0.946808	−	0.321798i	$-0.104287\pi$
$659$	−0.540877	−	1.80666i	−0.0210696	−	0.0703773i	−0.967878	+	0.251421i	$0.919102\pi$
$660$		0			0
$661$	−2.44763	−	42.0242i	−0.0952019	−	1.63455i	−0.620906	−	0.783885i	$-0.713235\pi$
$661$	−2.44763	−	42.0242i	−0.0952019	−	1.63455i	0.525704	−	0.850668i	$-0.323802\pi$
$662$	−6.82949	−	3.42990i	−0.265436	−	0.133307i
$663$		0			0
$664$	14.9087	−	15.8023i	0.578571	−	0.613250i
$665$	6.19596	+	2.25514i	0.240269	+	0.0874507i
$666$		0			0
$667$	21.9822	−	8.00086i	0.851154	−	0.309795i
$668$	25.9584	−	60.1782i	1.00436	−	2.32837i
$669$		0			0
$670$	14.0265	−	46.8518i	0.541891	−	1.81004i
$671$	27.0855	+	3.16585i	1.04563	+	0.122216i
$672$		0			0
$673$	−0.626161	+	10.7508i	−0.0241367	+	0.414412i	0.964500	+	0.264085i	$0.0850698\pi$
$673$	−0.626161	+	10.7508i	−0.0241367	+	0.414412i	−0.988636	+	0.150327i	$0.951967\pi$
$674$	−21.5748	+	37.3687i	−0.831031	+	1.43939i
$675$		0			0
$676$	32.9446	+	57.0616i	1.26710	+	2.19468i
$677$	−9.37345	+	4.70752i	−0.360251	+	0.180925i	−0.619713	−	0.784828i	$-0.712751\pi$
$677$	−9.37345	+	4.70752i	−0.360251	+	0.180925i	0.259462	+	0.965753i	$0.416455\pi$
$678$		0			0
$679$	−23.7047	+	31.8409i	−0.909701	+	1.22194i
$680$	33.5439	−	7.95004i	1.28635	−	0.304870i
$681$		0			0
$682$	57.0248	+	76.5976i	2.18359	+	2.93307i
$683$	−18.5237	−	15.5432i	−0.708789	−	0.594745i	0.215470	−	0.976510i	$-0.430872\pi$
$683$	−18.5237	−	15.5432i	−0.708789	−	0.594745i	−0.924259	+	0.381766i	$0.875316\pi$
$684$		0			0
$685$	−22.5977	+	18.9617i	−0.863413	+	0.724490i
$686$	−49.1725	−	11.6541i	−1.87742	−	0.444956i
$687$		0			0
$688$	−26.7825	+	17.6151i	−1.02107	+	0.671570i
$689$	−4.25351	+	2.79758i	−0.162046	+	0.106579i
$690$		0			0
$691$	−8.33265	−	1.97488i	−0.316989	−	0.0751278i	0.0690415	−	0.997614i	$-0.478006\pi$
$691$	−8.33265	−	1.97488i	−0.316989	−	0.0751278i	−0.386031	+	0.922486i	$0.626154\pi$
$692$	−20.0163	+	16.7957i	−0.760907	+	0.638476i
$693$		0			0
$694$	−30.1399	−	25.2904i	−1.14410	−	0.960011i
$695$	−17.8975	−	24.0405i	−0.678891	−	0.911910i
$696$		0			0
$697$	7.42000	−	1.75857i	0.281053	−	0.0666107i
$698$	3.94301	−	5.29638i	0.149245	−	0.200471i
$699$		0			0
$700$	20.1475	−	10.1185i	0.761504	−	0.382442i
$701$	−1.21019	−	2.09612i	−0.0457084	−	0.0791693i	0.842266	−	0.539062i	$-0.181221\pi$
$701$	−1.21019	−	2.09612i	−0.0457084	−	0.0791693i	−0.887974	+	0.459893i	$0.847888\pi$
$702$		0			0
$703$	0.425656	−	0.737258i	0.0160539	−	0.0278062i
$704$	3.62747	−	62.2813i	0.136716	−	2.34732i
$705$		0			0
$706$	41.5303	+	4.85419i	1.56301	+	0.182690i
$707$	−9.66147	+	32.2715i	−0.363357	+	1.21370i
$708$		0			0
$709$	19.7152	−	45.7050i	0.740420	−	1.71649i	0.0438071	−	0.999040i	$-0.486051\pi$
$709$	19.7152	−	45.7050i	0.740420	−	1.71649i	0.696613	−	0.717447i	$-0.254689\pi$
$710$	−8.00572	+	2.91384i	−0.300449	+	0.109355i
$711$		0			0
$712$	−25.0051	−	9.10110i	−0.937104	−	0.341078i
$713$	−23.7441	+	25.1672i	−0.889222	+	0.942520i
$714$		0			0
$715$	−2.24769	−	1.12883i	−0.0840589	−	0.0422160i
$716$	0.351477	+	6.03463i	0.0131353	+	0.225525i
$717$		0			0
$718$	−0.180450	−	0.602743i	−0.00673432	−	0.0224942i
$719$	−9.09244	−	51.5658i	−0.339091	−	1.92308i	−0.382355	−	0.924015i	$-0.624887\pi$
$719$	−9.09244	−	51.5658i	−0.339091	−	1.92308i	0.0432647	−	0.999064i	$-0.486224\pi$
$720$		0			0
$721$	6.15275	−	34.8940i	0.229140	−	1.29952i
$722$	−45.1295	+	5.27488i	−1.67954	+	0.196311i
$723$		0			0
$724$	−40.2819	−	42.6963i	−1.49706	−	1.58680i
$725$	4.45880	+	10.3367i	0.165596	+	0.383894i
$726$		0			0
$727$	29.4097	+	19.3431i	1.09075	+	0.717396i	0.961662	−	0.274238i	$-0.0884256\pi$
$727$	29.4097	+	19.3431i	1.09075	+	0.717396i	0.129085	+	0.991634i	$0.458796\pi$
$728$	8.15228			0.302143
$729$		0			0
$730$	−25.9821			−0.961642
$731$	5.07439	+	3.33748i	0.187683	+	0.123441i
$732$		0			0
$733$	9.42379	+	21.8468i	0.348076	+	0.806930i	0.998863	+	0.0476702i	$0.0151797\pi$
$733$	9.42379	+	21.8468i	0.348076	+	0.806930i	−0.650787	+	0.759260i	$0.725561\pi$
$734$	−17.6480	−	18.7057i	−0.651398	−	0.690442i
$735$		0			0
$736$	54.1044	−	6.32390i	1.99431	−	0.233102i
$737$	−6.41419	+	36.3767i	−0.236270	+	1.33995i
$738$		0			0
$739$	−7.56827	−	42.9218i	−0.278403	−	1.57890i	−0.727939	−	0.685642i	$-0.759522\pi$
$739$	−7.56827	−	42.9218i	−0.278403	−	1.57890i	0.449536	−	0.893262i	$-0.351589\pi$
$740$	1.61547	+	5.39603i	0.0593857	+	0.198362i
$741$		0			0
$742$	−5.39125	−	92.5642i	−0.197919	−	3.39814i
$743$	9.08770	+	4.56402i	0.333396	+	0.167438i	0.607619	−	0.794228i	$-0.292125\pi$
$743$	9.08770	+	4.56402i	0.333396	+	0.167438i	−0.274224	+	0.961666i	$0.588421\pi$
$744$		0			0
$745$	4.24553	−	4.50000i	0.155544	−	0.164867i
$746$	−0.151015	−	0.0549648i	−0.00552904	−	0.00201240i
$747$		0			0
$748$	−40.1258	+	14.6046i	−1.46714	+	0.533997i
$749$	−2.35799	+	5.46644i	−0.0861591	+	0.199739i
$750$		0			0
$751$	4.79574	−	16.0189i	0.174999	−	0.584537i	−0.824818	−	0.565398i	$-0.808722\pi$
$751$	4.79574	−	16.0189i	0.174999	−	0.584537i	0.999817	−	0.0191386i	$-0.00609236\pi$
$752$	−1.79882	−	0.210252i	−0.0655962	−	0.00766709i
$753$		0			0
$754$	−0.388163	+	6.66450i	−0.0141361	+	0.242707i
$755$	7.84433	−	13.5868i	0.285485	−	0.494474i
$756$		0			0
$757$	20.3289	+	35.2107i	0.738867	+	1.27975i	0.953006	+	0.302951i	$0.0979720\pi$
$757$	20.3289	+	35.2107i	0.738867	+	1.27975i	−0.214139	+	0.976803i	$0.568695\pi$
$758$	−5.89718	+	2.96167i	−0.214195	+	0.107573i
$759$		0			0
$760$	−12.7178	+	17.0829i	−0.461322	+	0.619663i
$761$	13.2491	−	3.14009i	0.480278	−	0.113828i	0.0166566	−	0.999861i	$-0.494698\pi$
$761$	13.2491	−	3.14009i	0.480278	−	0.113828i	0.463622	+	0.886033i	$0.346550\pi$
$762$		0			0
$763$	−14.2634	−	19.1590i	−0.516369	−	0.693603i
$764$	−60.3933	−	50.6760i	−2.18495	−	1.83339i
$765$		0			0
$766$	56.4147	−	47.3375i	2.03835	−	1.71037i
$767$	−1.56459	−	0.370815i	−0.0564941	−	0.0133894i
$768$		0			0
$769$	−37.5321	+	24.6852i	−1.35344	+	0.890172i	−0.998991	−	0.0449035i	$-0.985702\pi$
$769$	−37.5321	+	24.6852i	−1.35344	+	0.890172i	−0.354449	+	0.935075i	$0.615332\pi$
$770$	38.2726	−	25.1723i	1.37925	−	0.907146i
$771$		0			0
$772$	−87.0044	−	20.6204i	−3.13136	−	0.742145i
$773$	17.8408	−	14.9702i	0.641688	−	0.538440i	−0.262848	−	0.964837i	$-0.584662\pi$
$773$	17.8408	−	14.9702i	0.641688	−	0.538440i	0.904536	+	0.426397i	$0.140217\pi$
$774$		0			0
$775$	−12.7551	−	10.7028i	−0.458175	−	0.384454i
$776$	−76.5653	−	102.845i	−2.74853	−	3.69192i
$777$		0			0
$778$	−28.0693	+	6.65255i	−1.00633	+	0.238506i
$779$	−2.81321	+	3.77879i	−0.100794	+	0.135389i
$780$		0			0
$781$	5.75016	−	2.88784i	0.205757	−	0.103335i
$782$	−10.7549	−	18.6280i	−0.384594	−	0.666137i
$783$		0			0
$784$	1.99015	−	3.44704i	0.0710768	−	0.123109i
$785$	−0.410088	+	7.04094i	−0.0146367	+	0.251302i
$786$		0			0
$787$	−2.96226	−	0.346239i	−0.105593	−	0.0123421i	0.0631322	−	0.998005i	$-0.479891\pi$
$787$	−2.96226	−	0.346239i	−0.105593	−	0.0123421i	−0.168725	+	0.985663i	$0.553965\pi$
$788$	−13.4554	+	44.9442i	−0.479330	+	1.60107i
$789$		0			0
$790$	−8.15718	+	18.9105i	−0.290220	+	0.672804i
$791$	23.0503	−	8.38962i	0.819574	−	0.298300i
$792$		0			0
$793$	−2.64967	−	0.964401i	−0.0940925	−	0.0342469i
$794$	−35.0965	+	37.2001i	−1.24553	+	1.32018i
$795$		0			0
$796$	−106.165	−	53.3181i	−3.76292	−	1.88981i
$797$	1.39283	+	23.9140i	0.0493366	+	0.847076i	0.928679	+	0.370885i	$0.120946\pi$
$797$	1.39283	+	23.9140i	0.0493366	+	0.847076i	−0.879342	+	0.476191i	$0.842017\pi$
$798$		0			0
$799$	0.0984128	+	0.328722i	0.00348159	+	0.0116293i
$800$	4.55197	+	25.8155i	0.160937	+	0.912716i
$801$		0			0
$802$	−14.6037	+	82.8217i	−0.515675	+	2.92454i
$803$	19.4910	−	2.27817i	0.687823	−	0.0803950i
$804$		0			0
$805$	11.3901	+	12.0728i	0.401450	+	0.425512i
$806$	−3.91092	−	9.06653i	−0.137756	−	0.319355i
$807$		0			0
$808$	−90.9070	−	59.7905i	−3.19810	−	2.10342i
$809$	36.1049			1.26938			0.634691	−	0.772766i	$-0.281128\pi$
$809$	36.1049			1.26938			0.634691	+	0.772766i	$0.281128\pi$
$810$		0			0
$811$	−41.1368			−1.44451			−0.722255	−	0.691627i	$-0.756894\pi$
$811$	−41.1368			−1.44451			−0.722255	+	0.691627i	$0.756894\pi$
$812$	−73.0667	−	48.0567i	−2.56414	−	1.68646i
$813$		0			0
$814$	−2.34259	−	5.43074i	−0.0821079	−	0.190347i
$815$	29.7007	+	31.4809i	1.04037	+	1.10273i
$816$		0			0
$817$	−3.72682	+	0.435603i	−0.130385	+	0.0152398i
$818$	0.424434	−	2.40709i	0.0148400	−	0.0841618i
$819$		0			0
$820$	−5.41261	−	30.6964i	−0.189017	−	1.07197i
$821$	11.9792	+	40.0134i	0.418078	+	1.39648i	0.864940	+	0.501875i	$0.167356\pi$
$821$	11.9792	+	40.0134i	0.418078	+	1.39648i	−0.446862	+	0.894603i	$0.647459\pi$
$822$		0			0
$823$	−1.08254	−	18.5865i	−0.0377349	−	0.647884i	−0.963156	−	0.268943i	$-0.913326\pi$
$823$	−1.08254	−	18.5865i	−0.0377349	−	0.647884i	0.925421	−	0.378940i	$-0.123711\pi$
$824$	102.272	+	51.3629i	3.56281	+	1.78931i
$825$		0			0
$826$	20.0963	−	21.3008i	0.699239	−	0.741150i
$827$	4.62778	+	1.68437i	0.160924	+	0.0585714i	0.421226	−	0.906956i	$-0.361600\pi$
$827$	4.62778	+	1.68437i	0.160924	+	0.0585714i	−0.260302	+	0.965527i	$0.583822\pi$
$828$		0			0
$829$	8.59129	−	3.12697i	0.298388	−	0.108604i	−0.188488	−	0.982076i	$-0.560359\pi$
$829$	8.59129	−	3.12697i	0.298388	−	0.108604i	0.486876	+	0.873471i	$0.338136\pi$
$830$	−4.99963	+	11.5904i	−0.173540	+	0.402310i
$831$		0			0
$832$	−1.85012	+	6.17982i	−0.0641413	+	0.214247i
$833$	−0.749036	−	0.0875498i	−0.0259526	−	0.00303342i
$834$		0			0
$835$	−1.35004	+	23.1792i	−0.0467199	+	0.802150i
$836$	13.1901	−	22.8460i	0.456190	−	0.790144i
$837$		0			0
$838$	−16.2817	−	28.2008i	−0.562443	−	0.974180i
$839$	32.3604	−	16.2520i	1.11721	−	0.561081i	0.208292	−	0.978067i	$-0.433210\pi$
$839$	32.3604	−	16.2520i	1.11721	−	0.561081i	0.908913	+	0.416985i	$0.136913\pi$
$840$		0			0
$841$	8.75847	−	11.7647i	0.302016	−	0.405678i
$842$	−81.3872	+	19.2891i	−2.80479	+	0.664747i
$843$		0			0
$844$	−79.0422	−	106.172i	−2.72075	−	3.65460i
$845$	−17.8816	−	15.0045i	−0.615147	−	0.516170i
$846$		0			0
$847$	−4.74338	+	3.98017i	−0.162984	+	0.136760i
$848$	157.256	+	37.2704i	5.40020	+	1.27987i
$849$		0			0
$850$	8.64822	−	5.68802i	0.296631	−	0.195098i
$851$	1.79043	−	1.17759i	0.0613753	−	0.0403672i
$852$		0			0
$853$	1.80399	+	0.427554i	0.0617675	+	0.0146392i	0.261383	−	0.965235i	$-0.415821\pi$
$853$	1.80399	+	0.427554i	0.0617675	+	0.0146392i	−0.199616	+	0.979874i	$0.563969\pi$
$854$	39.3396	−	33.0099i	1.34617	−	1.12957i
$855$		0			0
$856$	−14.7303	−	12.3602i	−0.503472	−	0.422463i
$857$	0.604769	+	0.812346i	0.0206585	+	0.0277492i	0.812332	−	0.583195i	$-0.198198\pi$
$857$	0.604769	+	0.812346i	0.0206585	+	0.0277492i	−0.791674	+	0.610944i	$0.790790\pi$
$858$		0			0
$859$	5.71885	−	1.35539i	0.195125	−	0.0462454i	−0.131891	−	0.991264i	$-0.542105\pi$
$859$	5.71885	−	1.35539i	0.195125	−	0.0462454i	0.327016	+	0.945019i	$0.393957\pi$
$860$	14.8252	−	19.9136i	0.505534	−	0.679049i
$861$		0			0
$862$	32.9329	−	16.5395i	1.12170	−	0.563339i
$863$	13.5850	+	23.5299i	0.462438	+	0.800966i	0.999082	−	0.0428431i	$-0.0136416\pi$
$863$	13.5850	+	23.5299i	0.462438	+	0.800966i	−0.536644	+	0.843809i	$0.680308\pi$
$864$		0			0
$865$	4.62850	−	8.01680i	0.157374	−	0.272579i
$866$	−3.76872	+	64.7064i	−0.128066	+	2.19881i
$867$		0			0
$868$	128.477	+	15.0168i	4.36080	+	0.509704i
$869$	4.46116	−	14.9013i	0.151335	−	0.505493i
$870$		0			0
$871$	1.51278	−	3.50702i	0.0512587	−	0.118831i
$872$	72.4964	−	26.3865i	2.45504	−	0.893561i
$873$		0			0
$874$	12.4871	+	4.54494i	0.422383	+	0.153735i
$875$	−21.5688	+	22.8616i	−0.729159	+	0.772863i
$876$		0			0
$877$	5.41496	+	2.71950i	0.182850	+	0.0918309i	0.537869	−	0.843028i	$-0.319229\pi$
$877$	5.41496	+	2.71950i	0.182850	+	0.0918309i	−0.355019	+	0.934859i	$0.615526\pi$
$878$	1.97255	+	33.8673i	0.0665703	+	1.14297i
$879$		0			0
$880$	22.8996	+	76.4901i	0.771946	+	2.57848i
$881$	−4.80252	−	27.2365i	−0.161801	−	0.917620i	−0.952302	−	0.305158i	$-0.901291\pi$
$881$	−4.80252	−	27.2365i	−0.161801	−	0.917620i	0.790500	−	0.612461i	$-0.209821\pi$
$882$		0			0
$883$	8.01388	−	45.4489i	0.269688	−	1.52948i	−0.485656	−	0.874150i	$-0.661419\pi$
$883$	8.01388	−	45.4489i	0.269688	−	1.52948i	0.755344	−	0.655329i	$-0.227470\pi$
$884$	4.38544	−	0.512585i	0.147498	−	0.0172401i
$885$		0			0
$886$	46.7415	+	49.5431i	1.57031	+	1.66443i
$887$	−4.18762	−	9.70799i	−0.140606	−	0.325962i	0.833333	−	0.552772i	$-0.186430\pi$
$887$	−4.18762	−	9.70799i	−0.140606	−	0.325962i	−0.973939	+	0.226809i	$0.927171\pi$
$888$		0			0
$889$	27.2925	+	17.9506i	0.915363	+	0.602044i
$890$	15.4608			0.518249
$891$		0			0
$892$	20.9048			0.699944
$893$	−0.177112	−	0.116488i	−0.00592683	−	0.00389814i
$894$		0			0
$895$	−0.848220	−	1.96639i	−0.0283529	−	0.0657293i
$896$	−26.0859	−	27.6494i	−0.871467	−	0.923701i
$897$		0			0
$898$	8.50966	−	0.994636i	0.283971	−	0.0331914i
$899$	−11.2154	+	63.6058i	−0.374055	+	2.12137i
$900$		0			0
$901$	−5.31714	−	30.1550i	−0.177140	−	1.00461i
$902$	9.38688	+	31.3544i	0.312549	+	1.04399i
$903$		0			0
$904$	4.60681	+	79.0958i	0.153220	+	2.63069i
$905$	18.5837	+	9.33307i	0.617742	+	0.310242i
$906$		0			0
$907$	4.53694	−	4.80888i	0.150647	−	0.159676i	−0.647655	−	0.761933i	$-0.724250\pi$
$907$	4.53694	−	4.80888i	0.150647	−	0.159676i	0.798302	+	0.602257i	$0.205732\pi$
$908$	102.515	+	37.3123i	3.40207	+	1.23825i
$909$		0			0
$910$	−4.45098	+	1.62002i	−0.147549	+	0.0537033i
$911$	−3.63484	+	8.42650i	−0.120428	+	0.279182i	−0.967757	−	0.251885i	$-0.918950\pi$
$911$	−3.63484	+	8.42650i	−0.120428	+	0.279182i	0.847330	+	0.531067i	$0.178209\pi$
$912$		0			0
$913$	2.73430	−	9.13318i	0.0904920	−	0.302264i
$914$	−5.65536	−	0.661017i	−0.187063	−	0.0218645i
$915$		0			0
$916$	−3.61185	+	62.0131i	−0.119339	+	2.04897i
$917$	−19.2114	+	33.2752i	−0.634417	+	1.09884i
$918$		0			0
$919$	7.47487	+	12.9469i	0.246573	+	0.427077i	0.962573	−	0.271023i	$-0.0873621\pi$
$919$	7.47487	+	12.9469i	0.246573	+	0.427077i	−0.716000	+	0.698101i	$0.754029\pi$
$920$	−47.9081	+	24.0604i	−1.57948	+	0.793247i
$921$		0			0
$922$	−36.5610	+	49.1100i	−1.20407	+	1.61735i
$923$	−0.647404	+	0.153438i	−0.0213096	+	0.00505046i
$924$		0			0
$925$	0.615826	+	0.827198i	0.0202482	+	0.0271981i
$926$	−59.1986	−	49.6735i	−1.94539	−	1.63237i
$927$		0			0
$928$	77.8933	−	65.3603i	2.55697	−	2.14556i
$929$	−22.5487	−	5.34414i	−0.739799	−	0.175336i	−0.156597	−	0.987663i	$-0.550052\pi$
$929$	−22.5487	−	5.34414i	−0.739799	−	0.175336i	−0.583202	+	0.812327i	$0.698201\pi$
$930$		0			0
$931$	0.389251	−	0.256015i	0.0127572	−	0.00839054i
$932$	−103.232	+	67.8968i	−3.38148	+	2.22404i
$933$		0			0
$934$	−5.42649	−	1.28610i	−0.177560	−	0.0420825i
$935$	11.5886	−	9.72401i	0.378988	−	0.318009i
$936$		0			0
$937$	18.9849	+	15.9303i	0.620211	+	0.520419i	0.897870	−	0.440261i	$-0.145114\pi$
$937$	18.9849	+	15.9303i	0.620211	+	0.520419i	−0.277659	+	0.960680i	$0.589558\pi$
$938$	41.5388	+	55.7963i	1.35629	+	1.82181i
$939$		0			0
$940$	1.36479	−	0.323461i	0.0445145	−	0.0105501i
$941$	25.0739	−	33.6802i	0.817387	−	1.09794i	−0.176142	−	0.984365i	$-0.556362\pi$
$941$	25.0739	−	33.6802i	0.817387	−	1.09794i	0.993529	−	0.113577i	$-0.0362308\pi$
$942$		0			0
$943$	−10.5974	+	5.32222i	−0.345099	+	0.173315i
$944$	25.5214	+	44.2044i	0.830652	+	1.43873i
$945$		0			0
$946$	−13.0341	+	22.5757i	−0.423774	+	0.733999i
$947$	0.314003	−	5.39122i	0.0102037	−	0.175191i	−0.989356	−	0.145516i	$-0.953516\pi$
$947$	0.314003	−	5.39122i	0.0102037	−	0.175191i	0.999560	−	0.0296750i	$-0.00944723\pi$
$948$		0			0
$949$	−2.01538	−	0.235564i	−0.0654220	−	0.00764673i
$950$	−1.83405	+	6.12615i	−0.0595044	+	0.198759i
$951$		0			0
$952$	−19.4206	+	45.0219i	−0.629424	+	1.45917i
$953$	−25.1832	+	9.16594i	−0.815765	+	0.296914i	−0.716003	−	0.698097i	$-0.754030\pi$
$953$	−25.1832	+	9.16594i	−0.815765	+	0.296914i	−0.0997617	+	0.995011i	$0.531808\pi$
$954$		0			0
$955$	26.2458	+	9.55270i	0.849295	+	0.309118i
$956$	83.4860	−	88.4899i	2.70013	−	2.86197i
$957$		0			0
$958$	51.8533	+	26.0417i	1.67530	+	0.841369i
$959$	−2.43961	−	41.8864i	−0.0787790	−	1.35258i
$960$		0			0
$961$	−18.5073	−	61.8187i	−0.597010	−	1.99415i
$962$	0.106196	+	0.602265i	0.00342388	+	0.0194178i
$963$		0			0
$964$	−11.2797	+	63.9705i	−0.363295	+	2.06035i
$965$	31.4631	−	3.67751i	1.01283	−	0.118383i
$966$		0			0
$967$	−17.2608	−	18.2954i	−0.555070	−	0.588340i	0.387699	−	0.921786i	$-0.373270\pi$
$967$	−17.2608	−	18.2954i	−0.555070	−	0.588340i	−0.942769	+	0.333446i	$0.891788\pi$
$968$	−7.92164	−	18.3644i	−0.254611	−	0.590255i
$969$		0			0
$970$	62.2406	+	40.9363i	1.99842	+	1.31438i
$971$	−42.8042			−1.37365			−0.686826	−	0.726822i	$-0.740997\pi$
$971$	−42.8042			−1.37365			−0.686826	+	0.726822i	$0.740997\pi$
$972$		0			0
$973$	42.6287			1.36661
$974$	−8.15874	−	5.36609i	−0.261423	−	0.171941i
$975$		0			0
$976$	35.4532	+	82.1897i	1.13483	+	2.63083i
$977$	18.2696	+	19.3647i	0.584497	+	0.619530i	0.950365	−	0.311136i	$-0.100710\pi$
$977$	18.2696	+	19.3647i	0.584497	+	0.619530i	−0.365869	+	0.930667i	$0.619228\pi$
$978$		0			0
$979$	−11.5983	+	1.35564i	−0.370682	+	0.0433265i
$980$	−0.535285	+	3.03575i	−0.0170990	+	0.0969735i
$981$		0			0
$982$	8.04984	+	45.6529i	0.256881	+	1.45684i
$983$	−17.0243	−	56.8651i	−0.542990	−	1.81371i	−0.580290	−	0.814410i	$-0.697061\pi$
$983$	−17.0243	−	56.8651i	−0.542990	−	1.81371i	0.0372995	−	0.999304i	$-0.488124\pi$
$984$		0			0
$985$	−0.966416	−	16.5927i	−0.0307926	−	0.528688i
$986$	−35.8808	−	18.0200i	−1.14268	−	0.573875i
$987$		0			0
$988$	−1.87188	+	1.98408i	−0.0595524	+	0.0631219i
$989$	−8.87564	−	3.23047i	−0.282229	−	0.102723i
$990$		0			0
$991$	17.0810	−	6.21699i	0.542597	−	0.197489i	−0.0561572	−	0.998422i	$-0.517885\pi$
$991$	17.0810	−	6.21699i	0.542597	−	0.197489i	0.598754	+	0.800933i	$0.295663\pi$
$992$	−59.5692	+	138.097i	−1.89132	+	4.38458i
$993$		0			0
$994$	3.47534	−	11.6084i	0.110231	−	0.368197i
$995$	41.8038	+	4.88616i	1.32527	+	0.154902i
$996$		0			0
$997$	−0.563902	+	9.68183i	−0.0178590	+	0.306626i	0.977536	+	0.210768i	$0.0675966\pi$
$997$	−0.563902	+	9.68183i	−0.0178590	+	0.306626i	−0.995395	+	0.0958582i	$0.969440\pi$
$998$	−22.5792	+	39.1083i	−0.714731	+	1.23795i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.703.8		144
3.2	odd	2		729.2.g.a.703.1		144
9.2	odd	6		243.2.g.a.235.1		144
9.4	even	3		729.2.g.c.460.1		144
9.5	odd	6		729.2.g.b.460.8		144
9.7	even	3		81.2.g.a.79.8	yes	144
81.13	even	27		81.2.g.a.40.8	✓	144
81.14	odd	54		729.2.g.a.28.1		144
81.38	odd	54		6561.2.a.d.1.70		72
81.40	even	27		729.2.g.c.271.1		144
81.41	odd	54		729.2.g.b.271.8		144
81.43	even	27		6561.2.a.c.1.3		72
81.67	even	27	inner	729.2.g.d.28.8		144
81.68	odd	54		243.2.g.a.91.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.8	✓	144	81.13	even	27
81.2.g.a.79.8	yes	144	9.7	even	3
243.2.g.a.91.1		144	81.68	odd	54
243.2.g.a.235.1		144	9.2	odd	6
729.2.g.a.28.1		144	81.14	odd	54
729.2.g.a.703.1		144	3.2	odd	2
729.2.g.b.271.8		144	81.41	odd	54
729.2.g.b.460.8		144	9.5	odd	6
729.2.g.c.271.1		144	81.40	even	27
729.2.g.c.460.1		144	9.4	even	3
729.2.g.d.28.8		144	81.67	even	27	inner
729.2.g.d.703.8		144	1.1	even	1	trivial
6561.2.a.c.1.3		72	81.43	even	27
6561.2.a.d.1.70		72	81.38	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)

\(f(q)\)	\(=\)	\(q+(2.23012 + 1.46677i) q^{2} +(2.02985 + 4.70573i) q^{4} +(-1.24595 - 1.32063i) q^{5} +(2.56492 - 0.299797i) q^{7} +(-1.44840 + 8.21430i) q^{8} +O(q^{10})\)	\(q+(2.23012 + 1.46677i) q^{2} +(2.02985 + 4.70573i) q^{4} +(-1.24595 - 1.32063i) q^{5} +(2.56492 - 0.299797i) q^{7} +(-1.44840 + 8.21430i) q^{8} +(-0.841551 - 4.77267i) q^{10} +(1.04979 + 3.50653i) q^{11} +(-0.0220064 - 0.377836i) q^{13} +(6.15982 + 3.09358i) q^{14} +(-8.24485 + 8.73903i) q^{16} +(2.13907 + 0.778557i) q^{17} +(-1.32149 + 0.480985i) q^{19} +(3.68542 - 8.54376i) q^{20} +(-2.80213 + 9.35978i) q^{22} +(-3.51611 - 0.410974i) q^{23} +(0.0990536 - 1.70069i) q^{25} +(0.505123 - 0.874898i) q^{26} +(6.61718 + 11.4613i) q^{28} +(-5.90521 + 2.96571i) q^{29} +(5.83658 - 7.83989i) q^{31} +(-14.9728 + 3.54862i) q^{32} +(3.62841 + 4.87381i) q^{34} +(-3.59167 - 3.01377i) q^{35} +(-0.463728 + 0.389114i) q^{37} +(-3.65259 - 0.865679i) q^{38} +(12.6526 - 8.32178i) q^{40} +(2.79880 - 1.84080i) q^{41} +(2.59620 + 0.615311i) q^{43} +(-14.3699 + 12.0578i) q^{44} +(-7.23854 - 6.07386i) q^{46} +(0.0900157 + 0.120912i) q^{47} +(-0.322362 + 0.0764011i) q^{49} +(2.71542 - 3.64744i) q^{50} +(1.73333 - 0.870509i) q^{52} +(-6.72572 - 11.6493i) q^{53} +(3.32284 - 5.75532i) q^{55} +(-1.25242 + 21.5033i) q^{56} +(-17.5193 - 2.04772i) q^{58} +(1.21847 - 4.06996i) q^{59} +(2.95087 - 6.84088i) q^{61} +(24.5156 - 8.92296i) q^{62} +(-16.0163 - 5.82946i) q^{64} +(-0.471561 + 0.499826i) q^{65} +(9.01808 + 4.52905i) q^{67} +(0.678316 + 11.6462i) q^{68} +(-3.58935 - 11.9892i) q^{70} +(-0.305263 - 1.73123i) q^{71} +(0.930968 - 5.27978i) q^{73} +(-1.60491 + 0.187587i) q^{74} +(-4.94583 - 5.24227i) q^{76} +(3.74387 + 8.67926i) q^{77} +(-3.55048 - 2.33519i) q^{79} +21.8136 q^{80} +8.94171 q^{82} +(-2.17613 - 1.43126i) q^{83} +(-1.63698 - 3.79495i) q^{85} +(4.88732 + 5.18025i) q^{86} +(-30.3242 + 3.54439i) q^{88} +(-0.553979 + 3.14177i) q^{89} +(-0.169719 - 0.962523i) q^{91} +(-5.20326 - 17.3801i) q^{92} +(0.0233953 + 0.401681i) q^{94} +(2.28171 + 1.14592i) q^{95} +(-10.5487 + 11.1810i) q^{97} +(-0.830968 - 0.302448i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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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Database

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