LMFDB - Embedded newform 729.2.g.a.28.1

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			28.1
Character	$\chi$	$=$	729.28
Dual form			729.2.g.a.703.1

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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	−0.606720	+	0.794916i	$0.707515\pi$
$2$	−2.23012	+	1.46677i	−1.57693	+	1.03717i	−0.970214	+	0.242249i	$0.922115\pi$
$3$		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	$-0.626189\pi$
$5$	1.24595	−	1.32063i	0.557204	−	0.590602i	0.943335	+	0.331842i	$0.107670\pi$
$6$		0			0
$7$	2.56492	+	0.299797i	0.969450	+	0.113312i	0.586054	−	0.810272i	$-0.300681\pi$
$7$	2.56492	+	0.299797i	0.969450	+	0.113312i	0.383396	+	0.923584i	$0.374755\pi$
$8$	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	0.640673	+	0.767814i	$0.278656\pi$
$11$	−1.04979	+	3.50653i	−0.316522	+	1.05726i	−0.957195	+	0.289444i	$0.906530\pi$
$12$		0			0
$13$	−0.0220064	+	0.377836i	−0.00610349	+	0.104793i	−0.999984	−	0.00566826i	$-0.998196\pi$
$13$	−0.0220064	+	0.377836i	−0.00610349	+	0.104793i	0.993880	+	0.110461i	$0.0352328\pi$
$14$	−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	$-0.700136\pi$
$17$	−2.13907	+	0.778557i	−0.518800	+	0.188828i	0.0693304	+	0.997594i	$0.477914\pi$
$18$		0			0
$19$	−1.32149	−	0.480985i	−0.303172	−	0.110345i	0.185955	−	0.982558i	$-0.440462\pi$
$19$	−1.32149	−	0.480985i	−0.303172	−	0.110345i	−0.489127	+	0.872213i	$0.662684\pi$
$20$	−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	$-0.416711\pi$
$23$	3.51611	−	0.410974i	0.733160	−	0.0856941i	0.474476	+	0.880268i	$0.342637\pi$
$24$		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	$-0.141594\pi$
$29$	5.90521	+	2.96571i	1.09657	+	0.550718i	0.193887	+	0.981024i	$0.437891\pi$
$30$		0			0
$31$	5.83658	+	7.83989i	1.04828	+	1.40809i	0.908491	+	0.417905i	$0.137235\pi$
$31$	5.83658	+	7.83989i	1.04828	+	1.40809i	0.139790	+	0.990181i	$0.455357\pi$
$32$	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	0.603873	−	0.797080i	$-0.293623\pi$
$37$	−0.463728	−	0.389114i	−0.0762364	−	0.0639699i	−0.680110	+	0.733111i	$0.738068\pi$
$38$	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	$-0.399059\pi$
$41$	−2.79880	−	1.84080i	−0.437099	−	0.287485i	−0.748925	+	0.662654i	$0.769430\pi$
$42$		0			0
$43$	2.59620	−	0.615311i	0.395917	−	0.0938340i	−0.0278346	−	0.999613i	$-0.508861\pi$
$43$	2.59620	−	0.615311i	0.395917	−	0.0938340i	0.423751	+	0.905779i	$0.360713\pi$
$44$	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	$-0.799796\pi$
$47$	−0.0900157	+	0.120912i	−0.0131301	+	0.0176368i	0.795510	+	0.605941i	$0.207203\pi$
$48$		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	0.130448	−	0.991455i	$-0.458358\pi$
$53$	6.72572	−	11.6493i	0.923849	−	1.60015i	0.793401	−	0.608699i	$-0.208308\pi$
$54$		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	$-0.181784\pi$
$59$	−1.21847	−	4.06996i	−0.158631	−	0.529864i	−0.999943	+	0.0106860i	$0.996598\pi$
$60$		0			0
$61$	2.95087	+	6.84088i	0.377820	+	0.875885i	0.995958	+	0.0898159i	$0.0286279\pi$
$61$	2.95087	+	6.84088i	0.377820	+	0.875885i	−0.618138	+	0.786069i	$0.712113\pi$
$62$	−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	0.197480	−	0.980307i	$-0.436724\pi$
$67$	9.01808	−	4.52905i	1.10173	−	0.553311i	0.904254	+	0.426996i	$0.140428\pi$
$68$	−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	$-0.911180\pi$
$71$	0.305263	−	1.73123i	0.0362281	−	0.205460i	0.997549	+	0.0699711i	$0.0222907\pi$
$72$		0			0
$73$	0.930968	+	5.27978i	0.108962	+	0.617951i	0.989564	+	0.144095i	$0.0460272\pi$
$73$	0.930968	+	5.27978i	0.108962	+	0.617951i	−0.880602	+	0.473856i	$0.842862\pi$
$74$	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	−0.733306	−	0.679898i	$-0.762024\pi$
$79$	−3.55048	+	2.33519i	−0.399460	+	0.262729i	0.333846	+	0.942628i	$0.391653\pi$
$80$	−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	$-0.639527\pi$
$83$	2.17613	−	1.43126i	0.238861	−	0.157102i	0.663296	+	0.748357i	$0.269157\pi$
$84$		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	$-0.00147521\pi$
$89$	0.553979	+	3.14177i	0.0587216	+	0.333027i	−0.941268	+	0.337661i	$0.890364\pi$
$90$		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	−0.990360	−	0.138520i	$-0.955765\pi$
$97$	−10.5487	−	11.1810i	−1.07106	−	1.13526i	−0.0807017	−	0.996738i	$-0.525716\pi$
$98$	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	0.955622	+	0.294594i	$0.0951846\pi$
$101$	5.16679	+	11.9780i	0.514115	+	1.19185i	−0.441508	+	0.897258i	$0.645556\pi$
$102$		0			0
$103$	3.93516	+	13.1443i	0.387742	+	1.29515i	0.899839	+	0.436222i	$0.143684\pi$
$103$	3.93516	+	13.1443i	0.387742	+	1.29515i	−0.512097	+	0.858928i	$0.671131\pi$
$104$	−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	$-0.131122\pi$
$107$	1.15268	+	1.99650i	0.111434	+	0.193009i	−0.804915	+	0.593390i	$0.797789\pi$
$108$		0			0
$109$	−4.62468	+	8.01018i	−0.442964	+	0.767236i	−0.997908	−	0.0646518i	$-0.979406\pi$
$109$	−4.62468	+	8.01018i	−0.442964	+	0.767236i	0.554944	+	0.831888i	$0.312740\pi$
$110$	−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	$-0.573358\pi$
$113$	−9.24278	−	2.19058i	−0.869487	−	0.206072i	−0.641062	+	0.767489i	$0.721506\pi$
$114$		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	−0.102066	−	0.994778i	$-0.532545\pi$
$127$	9.69030	−	8.13112i	0.859875	−	0.721521i	0.961941	+	0.273257i	$0.0881009\pi$
$128$	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	0.997715	+	0.0675591i	$0.0215211\pi$
$131$	8.88502	+	11.9347i	0.776288	+	1.04274i	−0.221427	+	0.975177i	$0.571071\pi$
$132$		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	−0.759054	−	0.651027i	$-0.774338\pi$
$137$	−0.944711	−	16.2201i	−0.0807121	−	1.38577i	0.678342	−	0.734746i	$-0.262699\pi$
$138$		0			0
$139$	16.3959	−	1.91640i	1.39068	−	0.162547i	0.612441	−	0.790516i	$-0.290188\pi$
$139$	16.3959	−	1.91640i	1.39068	−	0.162547i	0.778238	+	0.627969i	$0.216114\pi$
$140$	−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	0.980421	+	0.196915i	$0.0630923\pi$
$149$	−0.198127	+	3.40171i	−0.0162312	+	0.278679i	−0.996652	+	0.0817637i	$0.973945\pi$
$150$		0			0
$151$	2.47827	−	8.27799i	0.201678	−	0.673653i	−0.795984	−	0.605318i	$-0.793046\pi$
$151$	2.47827	−	8.27799i	0.201678	−	0.673653i	0.997662	−	0.0683353i	$-0.0217688\pi$
$152$	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	−0.824957	−	0.565195i	$-0.808801\pi$
$157$	−2.66576	+	2.82554i	−0.212751	+	0.225503i	0.612206	+	0.790698i	$0.290282\pi$
$158$	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	$-0.594503\pi$
$167$	8.77585	−	9.30186i	0.679096	−	0.719799i	0.971643	+	0.236452i	$0.0759845\pi$
$168$		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	$-0.969495\pi$
$173$	−1.46229	+	4.88437i	−0.111176	+	0.371352i	0.884236	+	0.467041i	$0.154680\pi$
$174$		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	$-0.625147\pi$
$179$	−1.10838	+	0.403418i	−0.0828444	+	0.0301529i	0.300266	+	0.953856i	$0.402925\pi$
$180$		0			0
$181$	−10.7631	−	3.91744i	−0.800013	−	0.291181i	−0.0905211	−	0.995895i	$-0.528853\pi$
$181$	−10.7631	−	3.91744i	−0.800013	−	0.291181i	−0.709492	+	0.704714i	$0.751075\pi$
$182$	−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	$-0.163976\pi$
$191$	13.7471	+	6.90406i	0.994706	+	0.499560i	0.124485	+	0.992222i	$0.460272\pi$
$192$		0			0
$193$	−10.4188	−	13.9948i	−0.749958	−	1.00737i	−0.999242	−	0.0389382i	$-0.987602\pi$
$193$	−10.4188	−	13.9948i	−0.749958	−	1.00737i	0.249283	−	0.968431i	$-0.419805\pi$
$194$	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	$-0.827961\pi$
$197$	−7.01270	+	5.88435i	−0.499634	+	0.419243i	0.357830	+	0.933787i	$0.383517\pi$
$198$		0			0
$199$	−17.7580	−	14.9007i	−1.25883	−	1.05629i	−0.995805	−	0.0914967i	$-0.970835\pi$
$199$	−17.7580	−	14.9007i	−1.25883	−	1.05629i	−0.263026	−	0.964789i	$-0.584721\pi$
$200$	−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	−0.759478	−	0.650534i	$-0.774545\pi$
$211$	−25.1316	−	5.95630i	−1.73013	−	0.410048i	−0.970653	+	0.240485i	$0.922693\pi$
$212$	−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	0.963708	−	0.266960i	$-0.0860192\pi$
$223$	1.61565	+	3.74549i	0.108192	+	0.250816i	−0.855516	+	0.517776i	$0.826760\pi$
$224$	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	−0.999604	−	0.0281412i	$-0.991041\pi$
$227$	−14.6081	−	15.4837i	−0.969576	−	1.02769i	0.0300282	−	0.999549i	$-0.490440\pi$
$228$		0			0
$229$	10.8317	−	5.43987i	0.715777	−	0.359477i	−0.0533473	−	0.998576i	$-0.516989\pi$
$229$	10.8317	−	5.43987i	0.715777	−	0.359477i	0.769124	+	0.639099i	$0.220693\pi$
$230$	−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	0.466984	+	0.884266i	$0.345341\pi$
$233$	−4.18661	+	23.7435i	−0.274274	+	1.55549i	−0.741258	+	0.671220i	$0.765771\pi$
$234$		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	−0.284242	−	0.958753i	$-0.591742\pi$
$239$	9.40236	−	21.7971i	0.608188	−	1.40994i	0.892430	−	0.451186i	$-0.148999\pi$
$240$		0			0
$241$	10.5898	−	6.96500i	0.682146	−	0.448655i	−0.160561	−	0.987026i	$-0.551330\pi$
$241$	10.5898	−	6.96500i	0.682146	−	0.448655i	0.842708	+	0.538371i	$0.180960\pi$
$242$	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	−0.964333	−	0.264692i	$-0.914730\pi$
$251$	−2.35563	−	13.3595i	−0.148686	−	0.843242i	0.815647	−	0.578550i	$-0.196381\pi$
$252$		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	$-0.675972\pi$
$257$	−2.50132	+	1.25621i	−0.156028	+	0.0783603i	0.369072	+	0.929401i	$0.379676\pi$
$258$		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	$-0.115046\pi$
$263$	0.588361	+	1.36397i	0.0362799	+	0.0841063i	−0.899113	+	0.437717i	$0.855787\pi$
$264$		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	$-0.0769480\pi$
$269$	4.56187	+	7.90140i	0.278142	+	0.481757i	−0.692781	+	0.721148i	$0.743615\pi$
$270$		0			0
$271$	−2.94843	+	5.10683i	−0.179105	+	0.310218i	−0.941574	−	0.336806i	$-0.890653\pi$
$271$	−2.94843	+	5.10683i	−0.179105	+	0.310218i	0.762470	+	0.647024i	$0.223987\pi$
$272$	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	−0.882004	−	0.471242i	$-0.843806\pi$
$277$	−2.95581	+	3.97034i	−0.177597	+	0.238555i	0.704407	+	0.709797i	$0.251213\pi$
$278$	−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	$-0.707120\pi$
$281$	−13.2418	+	3.13837i	−0.789942	+	0.187220i	−0.184208	+	0.982887i	$0.558972\pi$
$282$		0			0
$283$	9.88030	+	6.49838i	0.587323	+	0.386289i	0.808108	−	0.589034i	$-0.200492\pi$
$283$	9.88030	+	6.49838i	0.587323	+	0.386289i	−0.220785	+	0.975322i	$0.570862\pi$
$284$	−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	$-0.0459649\pi$
$293$	9.72118	+	13.0578i	0.567918	+	0.762846i	−0.421674	+	0.906747i	$0.638557\pi$
$294$		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	0.428853	−	0.903374i	$-0.358918\pi$
$307$	23.4445	−	8.53312i	1.33805	−	0.487011i	0.909198	+	0.416364i	$0.136696\pi$
$308$	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	−0.956641	−	0.291269i	$-0.905922\pi$
$311$	0.482249	−	8.27990i	0.0273459	−	0.469510i	0.983987	−	0.178241i	$-0.0570406\pi$
$312$		0			0
$313$	−1.58728	+	5.30188i	−0.0897183	+	0.299680i	−0.991058	−	0.133433i	$-0.957400\pi$
$313$	−1.58728	+	5.30188i	−0.0897183	+	0.299680i	0.901340	+	0.433113i	$0.142585\pi$
$314$	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	$-0.676008\pi$
$317$	−21.9438	−	2.56486i	−1.23249	−	0.144057i	−0.707289	+	0.706924i	$0.750082\pi$
$318$		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	0.0375791	−	0.999294i	$-0.488035\pi$
$331$	−2.84377	−	0.332389i	−0.156308	−	0.0182698i	−0.193887	+	0.981024i	$0.562109\pi$
$332$	−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	−0.870733	−	0.491756i	$-0.836355\pi$
$337$	0.939940	−	16.1381i	0.0512018	−	0.879101i	0.921935	−	0.387345i	$-0.126608\pi$
$338$	−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	$-0.407558\pi$
$347$	14.6404	−	1.71122i	0.785939	−	0.0918631i	0.499590	+	0.866262i	$0.333484\pi$
$348$		0			0
$349$	0.143834	+	2.46953i	0.00769924	+	0.132191i	0.999967	+	0.00807818i	$0.00257139\pi$
$349$	0.143834	+	2.46953i	0.00769924	+	0.132191i	−0.992268	+	0.124113i	$0.960392\pi$
$350$	−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	$-0.488727\pi$
$353$	−13.9985	−	7.03032i	−0.745066	−	0.374186i	−0.780475	+	0.625187i	$0.785023\pi$
$354$		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	$-0.720242\pi$
$359$	0.180567	−	0.151513i	0.00952994	−	0.00799657i	0.647540	+	0.762031i	$0.275798\pi$
$360$		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	−0.467886	−	0.883789i	$-0.654984\pi$
$367$	−9.37480	+	2.22187i	−0.489361	+	0.115981i	−0.0214745	+	0.999769i	$0.506836\pi$
$368$	−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	0.229099	−	0.973403i	$-0.426422\pi$
$373$	−0.0585838	−	0.0138846i	−0.00303336	−	0.000718918i	−0.232132	+	0.972684i	$0.574570\pi$
$374$	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	0.832530	−	0.553980i	$-0.186892\pi$
$379$	−1.23614	−	2.14105i	−0.0634961	−	0.109979i	−0.896026	+	0.444002i	$0.853558\pi$
$380$	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	−0.881684	−	0.471841i	$-0.843590\pi$
$383$	−7.91287	−	26.4308i	−0.404329	−	1.35055i	0.477355	−	0.878711i	$-0.341596\pi$
$384$		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	$-0.152403\pi$
$389$	7.41631	+	7.86083i	0.376022	+	0.398560i	−0.511532	+	0.859264i	$0.670922\pi$
$390$		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	−0.946996	−	0.321246i	$-0.895898\pi$
$397$	−3.32712	−	18.8690i	−0.166983	−	0.947010i	0.780012	−	0.625764i	$-0.215213\pi$
$398$	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	0.255271	+	0.966870i	$0.417835\pi$
$401$	−12.4792	+	28.9301i	−0.623182	+	1.44470i	−0.878453	+	0.477829i	$0.841424\pi$
$402$		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	−0.926948	−	0.375191i	$-0.877577\pi$
$409$	−0.362689	+	0.840808i	−0.0179338	+	0.0415753i	0.909014	+	0.416766i	$0.136837\pi$
$410$	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	$-0.551831\pi$
$419$	10.9019	−	5.47513i	0.532591	−	0.267477i	0.694705	+	0.719295i	$0.255535\pi$
$420$		0			0
$421$	−21.5036	−	22.7925i	−1.04802	−	1.11084i	−0.993672	−	0.112318i	$-0.964172\pi$
$421$	−21.5036	−	22.7925i	−1.04802	−	1.11084i	−0.0543513	−	0.998522i	$-0.517309\pi$
$422$	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	$-0.274565\pi$
$431$	−6.90324	−	11.9568i	−0.332518	−	0.575937i	−0.983005	+	0.183580i	$0.941231\pi$
$432$		0			0
$433$	12.1413	−	21.0293i	0.583472	−	1.01060i	−0.411592	−	0.911368i	$-0.635027\pi$
$433$	12.1413	−	21.0293i	0.583472	−	1.01060i	0.995064	−	0.0992354i	$-0.0316397\pi$
$434$	−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	−0.583225	−	0.812311i	$-0.698209\pi$
$439$	7.58958	−	10.1946i	0.362231	−	0.486561i	0.945456	+	0.325750i	$0.105617\pi$
$440$	−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	$-0.781375\pi$
$443$	−24.8296	+	5.88473i	−1.17969	+	0.279592i	−0.406431	+	0.913681i	$0.633227\pi$
$444$		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	$-0.301909\pi$
$449$	−2.45881	−	2.06318i	−0.116038	−	0.0973677i	−0.698960	+	0.715160i	$0.746354\pi$
$450$		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	0.403655	−	0.914911i	$-0.367740\pi$
$457$	−1.90624	−	0.957349i	−0.0891701	−	0.0447829i	−0.492825	+	0.870128i	$0.664036\pi$
$458$	−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	0.875020	+	0.484087i	$0.160848\pi$
$461$	1.33368	+	22.8984i	0.0621157	+	1.06648i	−0.812904	+	0.582398i	$0.802115\pi$
$462$		0			0
$463$	−28.7556	+	3.36105i	−1.33639	+	0.156201i	−0.754088	−	0.656774i	$-0.771921\pi$
$463$	−28.7556	+	3.36105i	−1.33639	+	0.156201i	−0.582298	+	0.812975i	$0.697846\pi$
$464$	−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	$-0.373496\pi$
$467$	1.96329	+	0.714577i	0.0908500	+	0.0330667i	−0.296195	+	0.955127i	$0.595718\pi$
$468$		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	$-0.628392\pi$
$479$	−21.5915	−	2.52368i	−0.986540	−	0.115310i	−0.594034	+	0.804440i	$0.702466\pi$
$480$		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	$-0.887436\pi$
$491$	−11.9181	+	12.6324i	−0.537855	+	0.570093i	0.400267	+	0.916399i	$0.368917\pi$
$492$		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	−0.901945	−	0.431852i	$-0.857860\pi$
$499$	0.983696	−	16.8894i	0.0440363	−	0.756074i	0.945981	−	0.324222i	$-0.105103\pi$
$500$	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	$-0.389047\pi$
$503$	27.0776	−	9.85546i	1.20733	−	0.439433i	0.865778	+	0.500429i	$0.166824\pi$
$504$		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	$-0.622560\pi$
$509$	−11.8969	+	1.39055i	−0.527322	+	0.0616351i	−0.151733	+	0.988421i	$0.548485\pi$
$510$		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	$-0.747235\pi$
$521$	−2.74519	+	2.30349i	−0.120269	+	0.100918i	0.580669	+	0.814139i	$0.302791\pi$
$522$		0			0
$523$	−20.6502	−	17.3276i	−0.902971	−	0.757683i	0.0677978	−	0.997699i	$-0.478403\pi$
$523$	−20.6502	−	17.3276i	−0.902971	−	0.757683i	−0.970769	+	0.240016i	$0.922847\pi$
$524$	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	0.987685	−	0.156453i	$-0.0500058\pi$
$541$	8.33503	+	14.4367i	0.358351	+	0.620682i	−0.629335	+	0.777134i	$0.716672\pi$
$542$	−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	−0.842997	−	0.537918i	$-0.819211\pi$
$547$	−15.3370	−	35.5553i	−0.655765	−	1.52023i	0.187232	−	0.982316i	$-0.440048\pi$
$548$	−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	0.822302	+	0.569052i	$0.192690\pi$
$557$	−3.42298	+	19.4127i	−0.145036	+	0.822542i	−0.967338	+	0.253490i	$0.918421\pi$
$558$		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	$-0.875297\pi$
$563$	−0.290922	+	0.674433i	−0.0122609	+	0.0284240i	0.911976	+	0.410244i	$0.134557\pi$
$564$		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	$-0.827121\pi$
$569$	−17.1901	+	11.3061i	−0.720647	+	0.473977i	0.135455	+	0.990784i	$0.456750\pi$
$570$		0			0
$571$	0.929249	−	2.15424i	0.0388878	−	0.0901521i	−0.897665	−	0.440678i	$-0.854738\pi$
$571$	0.929249	−	2.15424i	0.0388878	−	0.0901521i	0.936553	+	0.350526i	$0.113997\pi$
$572$	−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	0.609561	+	0.792739i	$0.291346\pi$
$577$	−5.62981	+	31.9282i	−0.234372	+	1.32919i	−0.843932	+	0.536449i	$0.819765\pi$
$578$	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	$-0.00454116\pi$
$587$	7.34958	+	17.0382i	0.303350	+	0.703244i	−0.696549	+	0.717510i	$0.745282\pi$
$588$		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	−0.890631	−	0.454727i	$-0.849737\pi$
$593$	−20.4339	−	35.3926i	−0.839120	−	1.45340i	0.0515108	−	0.998672i	$-0.483596\pi$
$594$		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	$-0.485681\pi$
$599$	−8.88883	−	2.10669i	−0.363188	−	0.0860771i	−0.408158	+	0.912911i	$0.633829\pi$
$600$		0			0
$601$	−22.1512	+	29.7542i	−0.903565	+	1.21370i	0.0727514	+	0.997350i	$0.476822\pi$
$601$	−22.1512	+	29.7542i	−0.903565	+	1.21370i	−0.976316	+	0.216348i	$0.930585\pi$
$602$	−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	0.970645	−	0.240516i	$-0.0773167\pi$
$607$	27.9450	+	18.3797i	1.13425	+	0.746009i	0.163607	+	0.986526i	$0.447687\pi$
$608$	−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	0.474794	−	0.880097i	$-0.342522\pi$
$613$	35.2558	−	29.5831i	1.42397	−	1.19485i	0.949173	−	0.314754i	$-0.101922\pi$
$614$	−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	−0.926059	−	0.377380i	$-0.876825\pi$
$617$	−25.3857	−	34.0989i	−1.02199	−	1.37277i	−0.0959295	−	0.995388i	$-0.530582\pi$
$618$		0			0
$619$	37.5931	+	18.8800i	1.51099	+	0.758850i	0.995200	−	0.0978633i	$-0.0312008\pi$
$619$	37.5931	+	18.8800i	1.51099	+	0.758850i	0.515794	+	0.856713i	$0.327497\pi$
$620$	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	−0.366888	−	0.930265i	$-0.619577\pi$
$631$	−1.25540	+	0.456928i	−0.0499766	+	0.0181900i	0.316911	+	0.948455i	$0.397354\pi$
$632$	−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	$-0.523861\pi$
$641$	−9.56344	−	1.11781i	−0.377733	−	0.0441507i	−0.302841	+	0.953041i	$0.597935\pi$
$642$		0			0
$643$	12.6003	−	13.3556i	0.496909	−	0.526692i	−0.429573	−	0.903032i	$-0.641336\pi$
$643$	12.6003	−	13.3556i	0.496909	−	0.526692i	0.926482	+	0.376340i	$0.122817\pi$
$644$	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	$-0.341693\pi$
$647$	24.2705			0.954170			0.477085	+	0.878857i	$0.341693\pi$
$648$		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	0.168712	−	0.985665i	$-0.446039\pi$
$653$	29.2055	−	30.9560i	1.14290	−	1.21140i	0.974188	−	0.225738i	$-0.0724794\pi$
$654$		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	$-0.895713\pi$
$659$	0.540877	−	1.80666i	0.0210696	−	0.0703773i	0.967878	+	0.251421i	$0.0808979\pi$
$660$		0			0
$661$	−2.44763	+	42.0242i	−0.0952019	+	1.63455i	0.525704	+	0.850668i	$0.323802\pi$
$661$	−2.44763	+	42.0242i	−0.0952019	+	1.63455i	−0.620906	+	0.783885i	$0.713235\pi$
$662$	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	−0.988636	−	0.150327i	$-0.951967\pi$
$673$	−0.626161	−	10.7508i	−0.0241367	−	0.414412i	0.964500	−	0.264085i	$-0.0850698\pi$
$674$	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	$-0.287249\pi$
$677$	9.37345	+	4.70752i	0.360251	+	0.180925i	−0.259462	+	0.965753i	$0.583545\pi$
$678$		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	$-0.569128\pi$
$683$	18.5237	−	15.5432i	0.708789	−	0.594745i	0.924259	+	0.381766i	$0.124684\pi$
$684$		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	−0.386031	−	0.922486i	$-0.626154\pi$
$691$	−8.33265	+	1.97488i	−0.316989	+	0.0751278i	0.0690415	+	0.997614i	$0.478006\pi$
$692$	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	$-0.818779\pi$
$701$	1.21019	−	2.09612i	0.0457084	−	0.0791693i	0.887974	+	0.459893i	$0.152112\pi$
$702$		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	0.696613	+	0.717447i	$0.254689\pi$
$709$	19.7152	+	45.7050i	0.740420	+	1.71649i	0.0438071	+	0.999040i	$0.486051\pi$
$710$	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	−0.0432647	−	0.999064i	$-0.513776\pi$
$719$	9.09244	−	51.5658i	0.339091	−	1.92308i	0.382355	−	0.924015i	$-0.375113\pi$
$720$		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	0.129085	−	0.991634i	$-0.458796\pi$
$727$	29.4097	−	19.3431i	1.09075	−	0.717396i	0.961662	+	0.274238i	$0.0884256\pi$
$728$	−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	−0.650787	−	0.759260i	$-0.725561\pi$
$733$	9.42379	−	21.8468i	0.348076	−	0.806930i	0.998863	−	0.0476702i	$-0.0151797\pi$
$734$	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	0.449536	+	0.893262i	$0.351589\pi$
$739$	−7.56827	+	42.9218i	−0.278403	+	1.57890i	−0.727939	+	0.685642i	$0.759522\pi$
$740$	−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	$-0.707875\pi$
$743$	−9.08770	+	4.56402i	−0.333396	+	0.167438i	0.274224	+	0.961666i	$0.411579\pi$
$744$		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	0.999817	+	0.0191386i	$0.00609236\pi$
$751$	4.79574	+	16.0189i	0.174999	+	0.584537i	−0.824818	+	0.565398i	$0.808722\pi$
$752$	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	−0.214139	−	0.976803i	$-0.568695\pi$
$757$	20.3289	−	35.2107i	0.738867	−	1.27975i	0.953006	−	0.302951i	$-0.0979720\pi$
$758$	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	$-0.505302\pi$
$761$	−13.2491	−	3.14009i	−0.480278	−	0.113828i	−0.463622	+	0.886033i	$0.653450\pi$
$762$		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	−0.354449	−	0.935075i	$-0.615332\pi$
$769$	−37.5321	−	24.6852i	−1.35344	−	0.890172i	−0.998991	+	0.0449035i	$0.985702\pi$
$770$	−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	$-0.415338\pi$
$773$	−17.8408	−	14.9702i	−0.641688	−	0.538440i	−0.904536	+	0.426397i	$0.859783\pi$
$774$		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

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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