LMFDB - Embedded newform 729.2.e.r.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			325.1
Root			$0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.r.406.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.524005 + 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(0.984808 - 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-1.20805 - 2.09240i) q^{8} +O(q^{10})$	\(q+(-0.524005 + 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(0.984808 - 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-1.20805 - 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(-5.10602 - 1.85844i) q^{11} +(-3.50387 - 2.94010i) q^{13} +(0.0632028 + 0.0530334i) q^{14} +(-1.32635 - 0.482753i) q^{16} +(2.38917 - 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(0.278817 + 1.58125i) q^{20} +(3.49273 - 1.27125i) q^{22} +(1.35375 - 7.67752i) q^{23} +(-2.98886 + 2.50795i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(-3.88365 + 3.25877i) q^{29} +(-1.52094 + 8.62571i) q^{31} +(5.44804 - 1.98293i) q^{32} +(0.567581 + 3.21891i) q^{34} +(-0.0632028 - 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(-0.378297 - 0.137689i) q^{38} +(-1.93969 - 1.62760i) q^{40} +(-5.79006 - 4.85844i) q^{41} +(1.22668 + 0.446476i) q^{43} +(4.16247 - 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(-0.419550 - 2.37939i) q^{47} +(6.56418 - 2.38917i) q^{49} +(0.463450 - 2.62836i) q^{50} +(5.36824 - 4.50449i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(-0.223238 + 0.187319i) q^{56} +(0.602196 - 3.41523i) q^{58} +(-0.0412527 + 0.0150147i) q^{59} +(-1.77332 - 10.0570i) q^{61} +(-2.99568 - 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(-4.50449 - 1.63950i) q^{65} +(-1.42468 - 1.19545i) q^{67} +(5.60808 + 4.70574i) q^{68} +(0.0812519 + 0.0295733i) q^{70} +(-3.25519 + 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(0.259515 + 1.47178i) q^{74} +(-0.847296 + 0.308391i) q^{76} +(-0.113807 + 0.645430i) q^{77} +(0.538019 - 0.451451i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(-5.19118 + 4.35591i) q^{83} +(0.869585 - 4.93166i) q^{85} +(-0.839100 + 0.305407i) q^{86} +(2.27972 + 12.9289i) q^{88} +(3.42782 + 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(11.2238 + 4.08512i) q^{92} +(1.26604 + 1.06234i) q^{94} +(0.472482 + 0.396459i) q^{95} +(8.48293 + 3.08753i) q^{97} +(-2.38917 + 4.13816i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^4 + 6 * q^7	$ 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 + 6 * q^7 + 12 * q^10 + 6 * q^13 - 18 * q^16 + 24 * q^19 + 6 * q^22 - 48 * q^25 - 12 * q^28 - 12 * q^31 + 54 * q^34 + 6 * q^37 - 12 * q^40 - 12 * q^43 - 6 * q^46 + 42 * q^49 + 54 * q^52 - 60 * q^55 + 6 * q^58 - 48 * q^61 - 6 * q^64 - 66 * q^67 + 6 * q^70 - 12 * q^73 - 6 * q^76 + 42 * q^79 - 24 * q^82 - 18 * q^85 - 24 * q^88 + 6 * q^94 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.524005	+	0.439693i	−0.370528	+	0.310910i	−0.808970	−	0.587850i	$-0.799975\pi$
$2$	−0.524005	+	0.439693i	−0.370528	+	0.310910i	0.438443	+	0.898759i	$0.355530\pi$
$3$		0			0
$3$		0			0
$4$	−0.266044	+	1.50881i	−0.133022	+	0.754407i
$5$	0.984808	−	0.358441i	0.440419	−	0.160300i	−0.112287	−	0.993676i	$-0.535817\pi$
$5$	0.984808	−	0.358441i	0.440419	−	0.160300i	0.552706	+	0.833376i	$0.313595\pi$
$6$		0			0
$7$	−0.0209445	−	0.118782i	−0.00791629	−	0.0448955i	0.980594	−	0.196051i	$-0.0628118\pi$
$7$	−0.0209445	−	0.118782i	−0.00791629	−	0.0448955i	−0.988510	+	0.151155i	$0.951701\pi$
$8$	−1.20805	−	2.09240i	−0.427109	−	0.739774i
$9$		0			0
$10$	−0.358441	+	0.620838i	−0.113349	+	0.196326i
$11$	−5.10602	−	1.85844i	−1.53952	−	0.560341i	−0.573593	−	0.819140i	$-0.694451\pi$
$11$	−5.10602	−	1.85844i	−1.53952	−	0.560341i	−0.965931	+	0.258799i	$0.916673\pi$
$12$		0			0
$13$	−3.50387	−	2.94010i	−0.971799	−	0.815436i	0.0110331	−	0.999939i	$-0.496488\pi$
$13$	−3.50387	−	2.94010i	−0.971799	−	0.815436i	−0.982832	+	0.184503i	$0.940932\pi$
$14$	0.0632028	+	0.0530334i	0.0168917	+	0.0141738i
$15$		0			0
$16$	−1.32635	−	0.482753i	−0.331588	−	0.120688i
$17$	2.38917	−	4.13816i	0.579458	−	1.00365i	−0.416084	−	0.909326i	$-0.636598\pi$
$17$	2.38917	−	4.13816i	0.579458	−	1.00365i	0.995542	−	0.0943239i	$-0.0300689\pi$
$18$		0			0
$19$	0.294263	+	0.509678i	0.0675085	+	0.116928i	0.897804	−	0.440395i	$-0.145162\pi$
$19$	0.294263	+	0.509678i	0.0675085	+	0.116928i	−0.830295	+	0.557323i	$0.811828\pi$
$20$	0.278817	+	1.58125i	0.0623455	+	0.353579i
$21$		0			0
$22$	3.49273	−	1.27125i	0.744652	−	0.271031i
$23$	1.35375	−	7.67752i	0.282277	−	1.60087i	−0.432575	−	0.901598i	$-0.642395\pi$
$23$	1.35375	−	7.67752i	0.282277	−	1.60087i	0.714852	−	0.699275i	$-0.246494\pi$
$24$		0			0
$25$	−2.98886	+	2.50795i	−0.597771	+	0.501590i
$26$	3.12879			0.613605
$27$		0			0
$28$	0.184793			0.0349225
$29$	−3.88365	+	3.25877i	−0.721176	+	0.605138i	−0.927710	−	0.373301i	$-0.878226\pi$
$29$	−3.88365	+	3.25877i	−0.721176	+	0.605138i	0.206534	+	0.978439i	$0.433781\pi$
$30$		0			0
$31$	−1.52094	+	8.62571i	−0.273170	+	1.54922i	0.471547	+	0.881841i	$0.343696\pi$
$31$	−1.52094	+	8.62571i	−0.273170	+	1.54922i	−0.744716	+	0.667381i	$0.767415\pi$
$32$	5.44804	−	1.98293i	0.963087	−	0.350535i
$33$		0			0
$34$	0.567581	+	3.21891i	0.0973394	+	0.552039i
$35$	−0.0632028	−	0.109470i	−0.0106832	−	0.0185039i
$36$		0			0
$37$	1.09240	−	1.89209i	0.179589	−	0.311057i	−0.762151	−	0.647399i	$-0.775857\pi$
$37$	1.09240	−	1.89209i	0.179589	−	0.311057i	0.941740	+	0.336342i	$0.109190\pi$
$38$	−0.378297	−	0.137689i	−0.0613679	−	0.0223361i
$39$		0			0
$40$	−1.93969	−	1.62760i	−0.306692	−	0.257345i
$41$	−5.79006	−	4.85844i	−0.904256	−	0.758761i	0.0667615	−	0.997769i	$-0.478733\pi$
$41$	−5.79006	−	4.85844i	−0.904256	−	0.758761i	−0.971018	+	0.239008i	$0.923178\pi$
$42$		0			0
$43$	1.22668	+	0.446476i	0.187067	+	0.0680869i	0.433855	−	0.900983i	$-0.357153\pi$
$43$	1.22668	+	0.446476i	0.187067	+	0.0680869i	−0.246788	+	0.969069i	$0.579375\pi$
$44$	4.16247	−	7.20961i	0.627516	−	1.08689i
$45$		0			0
$46$	2.66637	+	4.61830i	0.393135	+	0.680931i
$47$	−0.419550	−	2.37939i	−0.0611976	−	0.347069i	−0.999997	−	0.00260352i	$-0.999171\pi$
$47$	−0.419550	−	2.37939i	−0.0611976	−	0.347069i	0.938799	−	0.344465i	$-0.111940\pi$
$48$		0			0
$49$	6.56418	−	2.38917i	0.937740	−	0.341309i
$50$	0.463450	−	2.62836i	0.0655417	−	0.371706i
$51$		0			0
$52$	5.36824	−	4.50449i	0.744441	−	0.624660i
$53$	3.04628			0.418439			0.209219	−	0.977869i	$-0.432908\pi$
$53$	3.04628			0.418439			0.209219	+	0.977869i	$0.432908\pi$
$54$		0			0
$55$	−5.69459			−0.767859
$56$	−0.223238	+	0.187319i	−0.0298314	+	0.0250315i
$57$		0			0
$58$	0.602196	−	3.41523i	0.0790723	−	0.448441i
$59$	−0.0412527	+	0.0150147i	−0.00537064	+	0.00195475i	−0.344704	−	0.938711i	$-0.612021\pi$
$59$	−0.0412527	+	0.0150147i	−0.00537064	+	0.00195475i	0.339333	+	0.940666i	$0.389799\pi$
$60$		0			0
$61$	−1.77332	−	10.0570i	−0.227050	−	1.28767i	−0.858727	−	0.512434i	$-0.828744\pi$
$61$	−1.77332	−	10.0570i	−0.227050	−	1.28767i	0.631677	−	0.775232i	$-0.282367\pi$
$62$	−2.99568	−	5.18866i	−0.380451	−	0.658961i
$63$		0			0
$64$	−0.571452	+	0.989783i	−0.0714315	+	0.123723i
$65$	−4.50449	−	1.63950i	−0.558713	−	0.203355i
$66$		0			0
$67$	−1.42468	−	1.19545i	−0.174052	−	0.146047i	0.551600	−	0.834109i	$-0.314017\pi$
$67$	−1.42468	−	1.19545i	−0.174052	−	0.146047i	−0.725652	+	0.688062i	$0.758462\pi$
$68$	5.60808	+	4.70574i	0.680079	+	0.570654i
$69$		0			0
$70$	0.0812519	+	0.0295733i	0.00971146	+	0.00353468i
$71$	−3.25519	+	5.63816i	−0.386320	+	0.669126i	−0.991951	−	0.126619i	$-0.959587\pi$
$71$	−3.25519	+	5.63816i	−0.386320	+	0.669126i	0.605631	+	0.795745i	$0.292921\pi$
$72$		0			0
$73$	−6.11721	−	10.5953i	−0.715965	−	1.24009i	−0.962586	−	0.270976i	$-0.912653\pi$
$73$	−6.11721	−	10.5953i	−0.715965	−	1.24009i	0.246621	−	0.969112i	$-0.420680\pi$
$74$	0.259515	+	1.47178i	0.0301680	+	0.171091i
$75$		0			0
$76$	−0.847296	+	0.308391i	−0.0971916	+	0.0353748i
$77$	−0.113807	+	0.645430i	−0.0129695	+	0.0735535i
$78$		0			0
$79$	0.538019	−	0.451451i	0.0605318	−	0.0507922i	−0.612020	−	0.790842i	$-0.709643\pi$
$79$	0.538019	−	0.451451i	0.0605318	−	0.0507922i	0.672552	+	0.740050i	$0.265198\pi$
$80$	−1.47924			−0.165384
$81$		0			0
$82$	5.17024			0.570958
$83$	−5.19118	+	4.35591i	−0.569806	+	0.478124i	−0.881581	−	0.472032i	$-0.843521\pi$
$83$	−5.19118	+	4.35591i	−0.569806	+	0.478124i	0.311776	+	0.950156i	$0.399076\pi$
$84$		0			0
$85$	0.869585	−	4.93166i	0.0943197	−	0.534914i
$86$	−0.839100	+	0.305407i	−0.0904824	+	0.0329329i
$87$		0			0
$88$	2.27972	+	12.9289i	0.243018	+	1.37823i
$89$	3.42782	+	5.93717i	0.363349	+	0.629338i	0.988510	−	0.151157i	$-0.0483000\pi$
$89$	3.42782	+	5.93717i	0.363349	+	0.629338i	−0.625161	+	0.780496i	$0.714967\pi$
$90$		0			0
$91$	−0.275845	+	0.477777i	−0.0289164	+	0.0500846i
$92$	11.2238	+	4.08512i	1.17016	+	0.425903i
$93$		0			0
$94$	1.26604	+	1.06234i	0.130583	+	0.109572i
$95$	0.472482	+	0.396459i	0.0484756	+	0.0406759i
$96$		0			0
$97$	8.48293	+	3.08753i	0.861311	+	0.313491i	0.734643	−	0.678454i	$-0.237350\pi$
$97$	8.48293	+	3.08753i	0.861311	+	0.313491i	0.126668	+	0.991945i	$0.459572\pi$
$98$	−2.38917	+	4.13816i	−0.241342	+	0.418017i
$99$		0			0
$100$	−2.98886	−	5.17685i	−0.298886	−	0.517685i
$101$	−2.25606	−	12.7947i	−0.224486	−	1.27312i	−0.863665	−	0.504066i	$-0.831837\pi$
$101$	−2.25606	−	12.7947i	−0.224486	−	1.27312i	0.639179	−	0.769058i	$-0.279274\pi$
$102$		0			0
$103$	−8.52481	+	3.10278i	−0.839975	+	0.305726i	−0.725946	−	0.687752i	$-0.758598\pi$
$103$	−8.52481	+	3.10278i	−0.839975	+	0.305726i	−0.114029	+	0.993477i	$0.536376\pi$
$104$	−1.91901	+	10.8833i	−0.188175	+	1.06719i
$105$		0			0
$106$	−1.59627	+	1.33943i	−0.155043	+	0.130097i
$107$	−11.3865			−1.10077			−0.550386	−	0.834911i	$-0.685519\pi$
$107$	−11.3865			−1.10077			−0.550386	+	0.834911i	$0.685519\pi$
$108$		0			0
$109$	2.89899			0.277672			0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89899			0.277672			0.138836	+	0.990315i	$0.455664\pi$
$110$	2.98400	−	2.50387i	0.284513	−	0.238735i
$111$		0			0
$112$	−0.0295627	+	0.167658i	−0.00279341	+	0.0158422i
$113$	−10.8818	+	3.96064i	−1.02367	+	0.372585i	−0.798667	−	0.601773i	$-0.794461\pi$
$113$	−10.8818	+	3.96064i	−1.02367	+	0.372585i	−0.225003	+	0.974358i	$0.572239\pi$
$114$		0			0
$115$	−1.41875	−	8.04612i	−0.132299	−	0.750305i
$116$	−3.88365	−	6.72668i	−0.360588	−	0.624557i
$117$		0			0
$118$	0.0150147	−	0.0260063i	0.00138222	−	0.00239407i
$119$	−0.541580	−	0.197119i	−0.0496465	−	0.0180699i
$120$		0			0
$121$	14.1912	+	11.9078i	1.29011	+	1.08253i
$122$	5.35121	+	4.49020i	0.484476	+	0.406524i
$123$		0			0
$124$	−12.6099	−	4.58964i	−1.13241	−	0.412162i
$125$	−4.66452	+	8.07919i	−0.417208	+	0.722625i
$126$		0			0
$127$	7.70961	+	13.3534i	0.684117	+	1.18493i	0.973713	+	0.227777i	$0.0731456\pi$
$127$	7.70961	+	13.3534i	0.684117	+	1.18493i	−0.289596	+	0.957149i	$0.593521\pi$
$128$	1.87776	+	10.6493i	0.165972	+	0.941274i
$129$		0			0
$130$	3.08125	−	1.12148i	0.270244	−	0.0983607i
$131$	−2.31926	+	13.1532i	−0.202635	+	1.14920i	0.698484	+	0.715625i	$0.253858\pi$
$131$	−2.31926	+	13.1532i	−0.202635	+	1.14920i	−0.901119	+	0.433572i	$0.857253\pi$
$132$		0			0
$133$	0.0543776	−	0.0456282i	0.00471514	−	0.00395647i
$134$	1.27217			0.109899
$135$		0			0
$136$	−11.5449			−0.989965
$137$	15.0326	−	12.6138i	1.28432	−	1.07767i	0.291684	−	0.956515i	$-0.405784\pi$
$137$	15.0326	−	12.6138i	1.28432	−	1.07767i	0.992634	−	0.121156i	$-0.0386600\pi$
$138$		0			0
$139$	2.83157	−	16.0586i	0.240170	−	1.36207i	−0.591276	−	0.806469i	$-0.701376\pi$
$139$	2.83157	−	16.0586i	0.240170	−	1.36207i	0.831447	−	0.555605i	$-0.187513\pi$
$140$	0.181985	−	0.0662372i	0.0153805	−	0.00559806i
$141$		0			0
$142$	−0.773318	−	4.38571i	−0.0648954	−	0.368040i
$143$	12.4269	+	21.5239i	1.03919	+	1.79992i
$144$		0			0
$145$	−2.65657	+	4.60132i	−0.220616	+	0.382119i
$146$	7.86414	+	2.86231i	0.650840	+	0.236887i
$147$		0			0
$148$	2.56418	+	2.15160i	0.210774	+	0.176860i
$149$	−8.46302	−	7.10132i	−0.693318	−	0.581763i	0.226546	−	0.974000i	$-0.427257\pi$
$149$	−8.46302	−	7.10132i	−0.693318	−	0.581763i	−0.919864	+	0.392238i	$0.871701\pi$
$150$		0			0
$151$	6.39053	+	2.32596i	0.520054	+	0.189284i	0.588692	−	0.808357i	$-0.299643\pi$
$151$	6.39053	+	2.32596i	0.520054	+	0.189284i	−0.0686380	+	0.997642i	$0.521865\pi$
$152$	0.710966	−	1.23143i	0.0576670	−	0.0998821i
$153$		0			0
$154$	−0.224155	−	0.388249i	−0.0180630	−	0.0312860i
$155$	1.59397	+	9.03983i	0.128030	+	0.726097i
$156$		0			0
$157$	−15.8687	+	5.77574i	−1.26646	+	0.460954i	−0.885932	−	0.463815i	$-0.846480\pi$
$157$	−15.8687	+	5.77574i	−1.26646	+	0.460954i	−0.380529	+	0.924769i	$0.624258\pi$
$158$	−0.0834248	+	0.473126i	−0.00663692	+	0.0376399i
$159$		0			0
$160$	4.65451	−	3.90560i	0.367972	−	0.308765i
$161$	−0.940307			−0.0741066
$162$		0			0
$163$	8.41147			0.658838			0.329419	−	0.944184i	$-0.393147\pi$
$163$	8.41147			0.658838			0.329419	+	0.944184i	$0.393147\pi$
$164$	8.87089	−	7.44356i	0.692700	−	0.581245i
$165$		0			0
$166$	0.804940	−	4.56504i	0.0624755	−	0.354316i
$167$	−2.46669	+	0.897804i	−0.190879	+	0.0694741i	−0.435691	−	0.900096i	$-0.643496\pi$
$167$	−2.46669	+	0.897804i	−0.190879	+	0.0694741i	0.244812	+	0.969571i	$0.421274\pi$
$168$		0			0
$169$	1.37551	+	7.80093i	0.105809	+	0.600072i
$170$	1.71275	+	2.96657i	0.131362	+	0.227525i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	12.3130	+	4.48158i	0.936143	+	0.340728i	0.764642	−	0.644455i	$-0.222916\pi$
$173$	12.3130	+	4.48158i	0.936143	+	0.340728i	0.171502	+	0.985184i	$0.445138\pi$
$174$		0			0
$175$	0.360500	+	0.302496i	0.0272512	+	0.0228665i
$176$	5.87522	+	4.92989i	0.442861	+	0.371605i
$177$		0			0
$178$	−4.40673	−	1.60392i	−0.330298	−	0.120219i
$179$	−11.0494	+	19.1382i	−0.825872	+	1.43045i	0.0753784	+	0.997155i	$0.475984\pi$
$179$	−11.0494	+	19.1382i	−0.825872	+	1.43045i	−0.901251	+	0.433298i	$0.857350\pi$
$180$		0			0
$181$	1.02956	+	1.78325i	0.0765268	+	0.132548i	0.901749	−	0.432260i	$-0.142284\pi$
$181$	1.02956	+	1.78325i	0.0765268	+	0.132548i	−0.825222	+	0.564808i	$0.808950\pi$
$182$	−0.0655309	−	0.371644i	−0.00485748	−	0.0275481i
$183$		0			0
$184$	−17.6998	+	6.44220i	−1.30485	+	0.474926i
$185$	0.397600	−	2.25490i	0.0292321	−	0.165784i
$186$		0			0
$187$	−19.8897	+	16.6894i	−1.45448	+	1.22045i
$188$	3.70167			0.269972
$189$		0			0
$190$	−0.421903			−0.0306081
$191$	3.02525	−	2.53849i	0.218899	−	0.183678i	−0.526743	−	0.850024i	$-0.676587\pi$
$191$	3.02525	−	2.53849i	0.218899	−	0.183678i	0.745643	+	0.666346i	$0.232143\pi$
$192$		0			0
$193$	−1.46673	+	8.31823i	−0.105577	+	0.598760i	0.885411	+	0.464810i	$0.153877\pi$
$193$	−1.46673	+	8.31823i	−0.105577	+	0.598760i	−0.990988	+	0.133950i	$0.957234\pi$
$194$	−5.80266	+	2.11200i	−0.416607	+	0.151633i
$195$		0			0
$196$	1.85844	+	10.5397i	0.132746	+	0.752839i
$197$	−1.14749	−	1.98751i	−0.0817553	−	0.141604i	0.822249	−	0.569128i	$-0.192719\pi$
$197$	−1.14749	−	1.98751i	−0.0817553	−	0.141604i	−0.904004	+	0.427524i	$0.859386\pi$
$198$		0			0
$199$	11.7515	−	20.3542i	0.833042	−	1.44287i	−0.0625736	−	0.998040i	$-0.519931\pi$
$199$	11.7515	−	20.3542i	0.833042	−	1.44287i	0.895615	−	0.444830i	$-0.146736\pi$
$200$	8.85829	+	3.22416i	0.626376	+	0.227982i
$201$		0			0
$202$	6.80793	+	5.71253i	0.479005	+	0.401933i
$203$	0.468426	+	0.393056i	0.0328770	+	0.0275871i
$204$		0			0
$205$	−7.44356	−	2.70924i	−0.519881	−	0.189221i
$206$	3.10278	−	5.37417i	0.216181	−	0.374436i
$207$		0			0
$208$	3.22803	+	5.59110i	0.223823	+	0.387673i
$209$	−0.555307	−	3.14930i	−0.0384114	−	0.217842i
$210$		0			0
$211$	1.56670	−	0.570234i	0.107856	−	0.0392565i	−0.287528	−	0.957772i	$-0.592834\pi$
$211$	1.56670	−	0.570234i	0.107856	−	0.0392565i	0.395385	+	0.918516i	$0.370611\pi$
$212$	−0.810446	+	4.59627i	−0.0556616	+	0.315673i
$213$		0			0
$214$	5.96657	−	5.00654i	0.407866	−	0.342240i
$215$	1.36808			0.0933023
$216$		0			0
$217$	1.05644			0.0717156
$218$	−1.51908	+	1.27466i	−0.102885	+	0.0863310i
$219$		0			0
$220$	1.51501	−	8.59208i	0.102142	−	0.579278i
$221$	−20.5379	+	7.47519i	−1.38153	+	0.502835i
$222$		0			0
$223$	−1.70187	−	9.65177i	−0.113965	−	0.646330i	−0.987257	−	0.159133i	$-0.949130\pi$
$223$	−1.70187	−	9.65177i	−0.113965	−	0.646330i	0.873292	−	0.487198i	$-0.161981\pi$
$224$	−0.349643	−	0.605600i	−0.0233615	−	0.0404634i
$225$		0			0
$226$	3.96064	−	6.86002i	0.263458	−	0.456322i
$227$	−14.5472	−	5.29473i	−0.965528	−	0.351424i	−0.189331	−	0.981913i	$-0.560632\pi$
$227$	−14.5472	−	5.29473i	−0.965528	−	0.351424i	−0.776198	+	0.630490i	$0.782854\pi$
$228$		0			0
$229$	−8.62108	−	7.23395i	−0.569697	−	0.478033i	0.311848	−	0.950132i	$-0.399052\pi$
$229$	−8.62108	−	7.23395i	−0.569697	−	0.478033i	−0.881545	+	0.472099i	$0.843496\pi$
$230$	4.28125	+	3.59240i	0.282297	+	0.236876i
$231$		0			0
$232$	11.5103	+	4.18939i	0.755686	+	0.275047i
$233$	−2.61738	+	4.53343i	−0.171470	+	0.296995i	−0.938934	−	0.344097i	$-0.888185\pi$
$233$	−2.61738	+	4.53343i	−0.171470	+	0.296995i	0.767464	+	0.641092i	$0.221518\pi$
$234$		0			0
$235$	−1.26604	−	2.19285i	−0.0825876	−	0.143046i
$236$	−0.0116794	−	0.0662372i	−0.000760264	−	0.00431167i
$237$		0			0
$238$	0.370462	−	0.134837i	0.0240135	−	0.00874020i
$239$	−1.79028	+	10.1532i	−0.115803	+	0.656754i	0.870546	+	0.492087i	$0.163766\pi$
$239$	−1.79028	+	10.1532i	−0.115803	+	0.656754i	−0.986349	+	0.164667i	$0.947345\pi$
$240$		0			0
$241$	8.23055	−	6.90625i	0.530176	−	0.444871i	−0.337986	−	0.941151i	$-0.609746\pi$
$241$	8.23055	−	6.90625i	0.530176	−	0.444871i	0.868162	+	0.496280i	$0.165301\pi$
$242$	−12.6720			−0.814590
$243$		0			0
$244$	15.6459			1.00163
$245$	5.60808	−	4.70574i	0.358287	−	0.300639i
$246$		0			0
$247$	0.467444	−	2.65101i	0.0297428	−	0.168680i
$248$	19.8858	−	7.23783i	1.26275	−	0.459602i
$249$		0			0
$250$	−1.10813	−	6.28450i	−0.0700841	−	0.397466i
$251$	−7.53644	−	13.0535i	−0.475696	−	0.823930i	0.523916	−	0.851770i	$-0.324470\pi$
$251$	−7.53644	−	13.0535i	−0.475696	−	0.823930i	−0.999612	+	0.0278401i	$0.991137\pi$
$252$		0			0
$253$	−21.1805	+	36.6857i	−1.33161	+	2.30641i
$254$	−9.91128	−	3.60741i	−0.621889	−	0.226349i
$255$		0			0
$256$	−7.41740	−	6.22394i	−0.463588	−	0.388996i
$257$	−2.54514	−	2.13563i	−0.158762	−	0.133217i	0.559946	−	0.828529i	$-0.310822\pi$
$257$	−2.54514	−	2.13563i	−0.158762	−	0.133217i	−0.718708	+	0.695312i	$0.755266\pi$
$258$		0			0
$259$	−0.247626	−	0.0901285i	−0.0153867	−	0.00560032i
$260$	3.67209	−	6.36025i	0.227734	−	0.394446i
$261$		0			0
$262$	−4.56805	−	7.91209i	−0.282215	−	0.488811i
$263$	1.53482	+	8.70439i	0.0946410	+	0.536736i	0.994857	+	0.101292i	$0.0322975\pi$
$263$	1.53482	+	8.70439i	0.0946410	+	0.536736i	−0.900216	+	0.435444i	$0.856591\pi$
$264$		0			0
$265$	3.00000	−	1.09191i	0.184289	−	0.0670755i
$266$	−0.00843175	+	0.0478189i	−0.000516984	+	0.00293196i
$267$		0			0
$268$	2.18273	−	1.83153i	0.133332	−	0.111879i
$269$	8.09267			0.493419			0.246709	−	0.969090i	$-0.420651\pi$
$269$	8.09267			0.493419			0.246709	+	0.969090i	$0.420651\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−5.16658	+	4.33527i	−0.313270	+	0.262865i
$273$		0			0
$274$	−2.33094	+	13.2194i	−0.140817	+	0.798613i
$275$	19.9220	−	7.25103i	1.20134	−	0.437254i
$276$		0			0
$277$	−0.734422	−	4.16512i	−0.0441272	−	0.250258i	0.954762	−	0.297370i	$-0.0961093\pi$
$277$	−0.734422	−	4.16512i	−0.0441272	−	0.250258i	−0.998890	+	0.0471120i	$0.984998\pi$
$278$	5.57710	+	9.65982i	0.334492	+	0.579357i
$279$		0			0
$280$	−0.152704	+	0.264490i	−0.00912579	+	0.0158063i
$281$	−6.86175	−	2.49747i	−0.409338	−	0.148987i	0.129140	−	0.991626i	$-0.458778\pi$
$281$	−6.86175	−	2.49747i	−0.409338	−	0.148987i	−0.538478	+	0.842640i	$0.681001\pi$
$282$		0			0
$283$	12.2724	+	10.2978i	0.729521	+	0.612141i	0.930001	−	0.367557i	$-0.119806\pi$
$283$	12.2724	+	10.2978i	0.729521	+	0.612141i	−0.200480	+	0.979698i	$0.564250\pi$
$284$	−7.64090	−	6.41147i	−0.453404	−	0.380451i
$285$		0			0
$286$	−15.9757	−	5.81466i	−0.944660	−	0.343828i
$287$	−0.455827	+	0.789515i	−0.0269066	+	0.0466036i
$288$		0			0
$289$	−2.91622	−	5.05104i	−0.171542	−	0.297120i
$290$	−0.631108	−	3.57919i	−0.0370600	−	0.210177i
$291$		0			0
$292$	17.6138	−	6.41090i	1.03077	−	0.375170i
$293$	3.12646	−	17.7310i	0.182650	−	1.03586i	−0.746289	−	0.665622i	$-0.768166\pi$
$293$	3.12646	−	17.7310i	0.182650	−	1.03586i	0.928938	−	0.370235i	$-0.120723\pi$
$294$		0			0
$295$	−0.0352441	+	0.0295733i	−0.00205199	+	0.00172182i
$296$	−5.27866			−0.306816
$297$		0			0
$298$	7.55707			0.437769
$299$	−27.3160	+	22.9209i	−1.57973	+	1.32555i
$300$		0			0
$301$	0.0273411	−	0.155059i	0.00157592	−	0.00893747i
$302$	−4.37138	+	1.59105i	−0.251545	+	0.0915548i
$303$		0			0
$304$	−0.144248	−	0.818069i	−0.00827317	−	0.0469195i
$305$	−5.35121	−	9.26857i	−0.306409	−	0.530717i
$306$		0			0
$307$	6.75537	−	11.7006i	0.385549	−	0.667791i	−0.606296	−	0.795239i	$-0.707345\pi$
$307$	6.75537	−	11.7006i	0.385549	−	0.667791i	0.991845	+	0.127448i	$0.0406787\pi$
$308$	−0.943555	−	0.343426i	−0.0537640	−	0.0195685i
$309$		0			0
$310$	−4.80999	−	4.03606i	−0.273189	−	0.229233i
$311$	12.5802	+	10.5560i	0.713357	+	0.598577i	0.925539	−	0.378653i	$-0.123613\pi$
$311$	12.5802	+	10.5560i	0.713357	+	0.598577i	−0.212182	+	0.977230i	$0.568057\pi$
$312$		0			0
$313$	18.3849	+	6.69156i	1.03918	+	0.378229i	0.804568	−	0.593861i	$-0.202397\pi$
$313$	18.3849	+	6.69156i	1.03918	+	0.378229i	0.234608	+	0.972090i	$0.424619\pi$
$314$	5.77574	−	10.0039i	0.325944	−	0.564551i
$315$		0			0
$316$	0.538019	+	0.931876i	0.0302659	+	0.0524221i
$317$	−4.23329	−	24.0082i	−0.237766	−	1.34844i	−0.836711	−	0.547645i	$-0.815524\pi$
$317$	−4.23329	−	24.0082i	−0.237766	−	1.34844i	0.598945	−	0.800790i	$-0.295587\pi$
$318$		0			0
$319$	25.8862	−	9.42182i	1.44935	−	0.527521i
$320$	−0.207991	+	1.17958i	−0.0116271	+	0.0659404i
$321$		0			0
$322$	0.492726	−	0.413446i	0.0274585	−	0.0230405i
$323$	2.81217			0.156473
$324$		0			0
$325$	17.8462			0.989927
$326$	−4.40766	+	3.69846i	−0.244118	+	0.204839i
$327$		0			0
$328$	−3.17112	+	17.9843i	−0.175096	+	0.993018i
$329$	−0.273842	+	0.0996702i	−0.0150974	+	0.00549500i
$330$		0			0
$331$	4.94878	+	28.0659i	0.272009	+	1.54264i	0.748304	+	0.663356i	$0.230869\pi$
$331$	4.94878	+	28.0659i	0.272009	+	1.54264i	−0.476294	+	0.879286i	$0.658020\pi$
$332$	−5.19118	−	8.99138i	−0.284903	−	0.493466i
$333$		0			0
$334$	0.897804	−	1.55504i	0.0491256	−	0.0850881i
$335$	−1.83153	−	0.666623i	−0.100067	−	0.0364215i
$336$		0			0
$337$	−13.3648	−	11.2144i	−0.728029	−	0.610889i	0.201564	−	0.979475i	$-0.435397\pi$
$337$	−13.3648	−	11.2144i	−0.728029	−	0.610889i	−0.929594	+	0.368586i	$0.879842\pi$
$338$	−4.15079	−	3.48293i	−0.225773	−	0.189446i
$339$		0			0
$340$	7.20961	+	2.62408i	0.390996	+	0.142311i
$341$	23.7963	−	41.2165i	1.28864	−	2.23200i
$342$		0			0
$343$	−0.843426	−	1.46086i	−0.0455407	−	0.0788788i
$344$	−0.547683	−	3.10607i	−0.0295291	−	0.167468i
$345$		0			0
$346$	−8.42262	+	3.06558i	−0.452803	+	0.164807i
$347$	4.37403	−	24.8063i	0.234810	−	1.33167i	−0.608203	−	0.793781i	$-0.708109\pi$
$347$	4.37403	−	24.8063i	0.234810	−	1.33167i	0.843013	−	0.537893i	$-0.180779\pi$
$348$		0			0
$349$	−9.07919	+	7.61835i	−0.485998	+	0.407801i	−0.852589	−	0.522581i	$-0.824969\pi$
$349$	−9.07919	+	7.61835i	−0.485998	+	0.407801i	0.366591	+	0.930382i	$0.380525\pi$
$350$	−0.321909			−0.0172068
$351$		0			0
$352$	−31.5030			−1.67912
$353$	−6.43285	+	5.39780i	−0.342386	+	0.287296i	−0.797724	−	0.603023i	$-0.793963\pi$
$353$	−6.43285	+	5.39780i	−0.342386	+	0.287296i	0.455338	+	0.890319i	$0.349518\pi$
$354$		0			0
$355$	−1.18479	+	6.71929i	−0.0628823	+	0.356623i
$356$	−9.87003	+	3.59240i	−0.523110	+	0.190397i
$357$		0			0
$358$	−2.62495	−	14.8868i	−0.138733	−	0.786794i
$359$	−1.32012	−	2.28652i	−0.0696735	−	0.120678i	0.829084	−	0.559124i	$-0.188862\pi$
$359$	−1.32012	−	2.28652i	−0.0696735	−	0.120678i	−0.898758	+	0.438446i	$0.855529\pi$
$360$		0			0
$361$	9.32682	−	16.1545i	0.490885	−	0.850238i
$362$	−1.32358	−	0.481744i	−0.0695658	−	0.0253199i
$363$		0			0
$364$	−0.647489	−	0.543308i	−0.0339376	−	0.0284771i
$365$	−9.82207	−	8.24170i	−0.514111	−	0.431390i
$366$		0			0
$367$	−8.64290	−	3.14576i	−0.451156	−	0.164207i	0.106441	−	0.994319i	$-0.466054\pi$
$367$	−8.64290	−	3.14576i	−0.451156	−	0.164207i	−0.557597	+	0.830112i	$0.688277\pi$
$368$	−5.50190	+	9.52956i	−0.286806	+	0.496763i
$369$		0			0
$370$	0.783119	+	1.35640i	0.0407124	+	0.0705159i
$371$	−0.0638029	−	0.361844i	−0.00331248	−	0.0187860i
$372$		0			0
$373$	25.1755	−	9.16312i	1.30354	−	0.474448i	0.405389	−	0.914144i	$-0.367136\pi$
$373$	25.1755	−	9.16312i	1.30354	−	0.474448i	0.898147	+	0.439696i	$0.144914\pi$
$374$	3.08408	−	17.4907i	0.159474	−	0.904421i
$375$		0			0
$376$	−4.47178	+	3.75227i	−0.230615	+	0.193509i
$377$	23.1889			1.19429
$378$		0			0
$379$	−27.1242			−1.39328			−0.696639	−	0.717422i	$-0.745322\pi$
$379$	−27.1242			−1.39328			−0.696639	+	0.717422i	$0.745322\pi$
$380$	−0.723884	+	0.607411i	−0.0371345	+	0.0311595i
$381$		0			0
$382$	−0.469093	+	2.66036i	−0.0240009	+	0.136116i
$383$	32.3506	−	11.7747i	1.65304	−	0.601657i	0.663793	−	0.747916i	$-0.268946\pi$
$383$	32.3506	−	11.7747i	1.65304	−	0.601657i	0.989246	+	0.146259i	$0.0467233\pi$
$384$		0			0
$385$	0.119271	+	0.676417i	0.00607859	+	0.0344734i
$386$	−2.88889	−	5.00371i	−0.147041	−	0.254682i
$387$		0			0
$388$	−6.91534	+	11.9777i	−0.351073	+	0.608077i
$389$	0.710966	+	0.258770i	0.0360474	+	0.0131202i	0.359981	−	0.932960i	$-0.382783\pi$
$389$	0.710966	+	0.258770i	0.0360474	+	0.0131202i	−0.323934	+	0.946080i	$0.605005\pi$
$390$		0			0
$391$	−28.5364	−	23.9449i	−1.44315	−	1.21095i
$392$	−12.9289	−	10.8486i	−0.653008	−	0.547939i
$393$		0			0
$394$	1.47519	+	0.536923i	0.0743188	+	0.0270498i
$395$	0.368026	−	0.637441i	0.0185174	−	0.0320731i
$396$		0			0
$397$	−3.50387	−	6.06888i	−0.175854	−	0.304588i	0.764602	−	0.644502i	$-0.222935\pi$
$397$	−3.50387	−	6.06888i	−0.175854	−	0.304588i	−0.940457	+	0.339914i	$0.889602\pi$
$398$	2.79174	+	15.8327i	0.139937	+	0.793624i
$399$		0			0
$400$	5.17499	−	1.88354i	0.258750	−	0.0941772i
$401$	1.64111	−	9.30722i	0.0819533	−	0.464780i	−0.916019	−	0.401134i	$-0.868616\pi$
$401$	1.64111	−	9.30722i	0.0819533	−	0.464780i	0.997973	−	0.0636460i	$-0.0202728\pi$
$402$		0			0
$403$	30.6896	−	25.7516i	1.52876	−	1.28278i
$404$	19.9051			0.990314
$405$		0			0
$406$	−0.418281			−0.0207590
$407$	−9.09413	+	7.63088i	−0.450779	+	0.378249i
$408$		0			0
$409$	0.958111	−	5.43372i	0.0473755	−	0.268680i	−0.951914	−	0.306365i	$-0.900887\pi$
$409$	0.958111	−	5.43372i	0.0473755	−	0.268680i	0.999290	+	0.0376849i	$0.0119983\pi$
$410$	5.09170	−	1.85323i	0.251461	−	0.0915243i
$411$		0			0
$412$	−2.41353	−	13.6878i	−0.118906	−	0.674351i
$413$	0.00264750	+	0.00458561i	0.000130275	+	0.000225643i
$414$		0			0
$415$	−3.55097	+	6.15047i	−0.174310	+	0.301915i
$416$	−24.9192	−	9.06986i	−1.22177	−	0.444686i
$417$		0			0
$418$	1.67571	+	1.40609i	0.0819615	+	0.0687739i
$419$	0.357267	+	0.299782i	0.0174536	+	0.0146453i	0.651473	−	0.758672i	$-0.274152\pi$
$419$	0.357267	+	0.299782i	0.0174536	+	0.0146453i	−0.634019	+	0.773317i	$0.718596\pi$
$420$		0			0
$421$	2.26857	+	0.825692i	0.110563	+	0.0402418i	0.396709	−	0.917944i	$-0.370152\pi$
$421$	2.26857	+	0.825692i	0.110563	+	0.0402418i	−0.286146	+	0.958186i	$0.592374\pi$
$422$	−0.570234	+	0.987674i	−0.0277585	+	0.0480792i
$423$		0			0
$424$	−3.68004	−	6.37402i	−0.178719	−	0.309550i
$425$	3.23741	+	18.3603i	0.157037	+	0.890603i
$426$		0			0
$427$	−1.15745	+	0.421278i	−0.0560130	+	0.0203871i
$428$	3.02931	−	17.1800i	0.146427	−	0.830429i
$429$		0			0
$430$	−0.716881	+	0.601535i	−0.0345711	+	0.0290086i
$431$	−12.0992			−0.582796			−0.291398	−	0.956602i	$-0.594120\pi$
$431$	−12.0992			−0.582796			−0.291398	+	0.956602i	$0.594120\pi$
$432$		0			0
$433$	33.3509			1.60274			0.801371	−	0.598167i	$-0.204104\pi$
$433$	33.3509			1.60274			0.801371	+	0.598167i	$0.204104\pi$
$434$	−0.553579	+	0.464508i	−0.0265726	+	0.0222971i
$435$		0			0
$436$	−0.771259	+	4.37403i	−0.0369366	+	0.209478i
$437$	4.31142	−	1.56923i	0.206243	−	0.0750665i
$438$		0			0
$439$	−1.57057	−	8.90717i	−0.0749594	−	0.425116i	−0.999075	−	0.0430028i	$-0.986308\pi$
$439$	−1.57057	−	8.90717i	−0.0749594	−	0.425116i	0.924116	−	0.382113i	$-0.124804\pi$
$440$	6.87933	+	11.9153i	0.327959	+	0.568042i
$441$		0			0
$442$	7.47519	−	12.9474i	0.355558	−	0.615845i
$443$	4.39506	+	1.59967i	0.208815	+	0.0760026i	0.444310	−	0.895873i	$-0.353449\pi$
$443$	4.39506	+	1.59967i	0.208815	+	0.0760026i	−0.235495	+	0.971876i	$0.575671\pi$
$444$		0			0
$445$	5.50387	+	4.61830i	0.260908	+	0.218928i
$446$	5.13560	+	4.30928i	0.243178	+	0.204050i
$447$		0			0
$448$	0.129538	+	0.0471478i	0.00612008	+	0.00222753i
$449$	13.3534	−	23.1288i	0.630187	−	1.09152i	−0.357326	−	0.933980i	$-0.616311\pi$
$449$	13.3534	−	23.1288i	0.630187	−	1.09152i	0.987513	−	0.157537i	$-0.0503553\pi$
$450$		0			0
$451$	20.5351	+	35.5678i	0.966959	+	1.67482i
$452$	−3.08083	−	17.4722i	−0.144910	−	0.821825i
$453$		0			0
$454$	9.95084	−	3.62181i	0.467016	−	0.169980i
$455$	−0.100399	+	0.569392i	−0.00470679	+	0.0266935i
$456$		0			0
$457$	−0.503870	+	0.422797i	−0.0235701	+	0.0197776i	−0.654497	−	0.756065i	$-0.727119\pi$
$457$	−0.503870	+	0.422797i	−0.0235701	+	0.0197776i	0.630927	+	0.775843i	$0.282675\pi$
$458$	7.69820			0.359713
$459$		0			0
$460$	12.5175			0.583633
$461$	15.8600	−	13.3081i	0.738672	−	0.619820i	−0.193808	−	0.981039i	$-0.562084\pi$
$461$	15.8600	−	13.3081i	0.738672	−	0.619820i	0.932481	+	0.361220i	$0.117640\pi$
$462$		0			0
$463$	−4.31062	+	24.4468i	−0.200332	+	1.13614i	0.704287	+	0.709915i	$0.251267\pi$
$463$	−4.31062	+	24.4468i	−0.200332	+	1.13614i	−0.904619	+	0.426222i	$0.859844\pi$
$464$	6.72427	−	2.44743i	0.312166	−	0.113619i
$465$		0			0
$466$	−0.621797	−	3.52638i	−0.0288042	−	0.163357i
$467$	−13.3365	−	23.0994i	−0.617138	−	1.06891i	−0.990005	−	0.141029i	$-0.954959\pi$
$467$	−13.3365	−	23.0994i	−0.617138	−	1.06891i	0.372868	−	0.927884i	$-0.378375\pi$
$468$		0			0
$469$	−0.112159	+	0.194265i	−0.00517901	+	0.00897031i
$470$	1.62760	+	0.592396i	0.0750754	+	0.0273252i
$471$		0			0
$472$	0.0812519	+	0.0681784i	0.00373992	+	0.00313817i
$473$	−5.43372	−	4.55943i	−0.249843	−	0.209643i
$474$		0			0
$475$	−2.15776	−	0.785359i	−0.0990046	−	0.0360347i
$476$	0.441500	−	0.764700i	0.0202361	−	0.0350500i
$477$		0			0
$478$	−3.52616	−	6.10749i	−0.161283	−	0.279350i
$479$	−0.560282	−	3.17752i	−0.0255999	−	0.145185i	0.969329	−	0.245768i	$-0.0790402\pi$
$479$	−0.560282	−	3.17752i	−0.0255999	−	0.145185i	−0.994929	+	0.100584i	$0.967929\pi$
$480$		0			0
$481$	−9.39053	+	3.41787i	−0.428171	+	0.155842i
$482$	−1.27622	+	7.23783i	−0.0581304	+	0.329674i
$483$		0			0
$484$	−21.7422	+	18.2438i	−0.988280	+	0.829266i
$485$	9.46075			0.429590
$486$		0			0
$487$	−7.77930			−0.352514			−0.176257	−	0.984344i	$-0.556399\pi$
$487$	−7.77930			−0.352514			−0.176257	+	0.984344i	$0.556399\pi$
$488$	−18.9010	+	15.8598i	−0.855606	+	0.717939i
$489$		0			0
$490$	−0.869585	+	4.93166i	−0.0392838	+	0.222790i
$491$	−16.0180	+	5.83006i	−0.722880	+	0.263107i	−0.677148	−	0.735847i	$-0.736784\pi$
$491$	−16.0180	+	5.83006i	−0.722880	+	0.263107i	−0.0457323	+	0.998954i	$0.514562\pi$
$492$		0			0
$493$	4.20661	+	23.8569i	0.189456	+	1.07446i
$494$	0.920686	+	1.59467i	0.0414236	+	0.0717478i
$495$		0			0
$496$	6.18139	−	10.7065i	0.277553	−	0.480735i
$497$	0.737892	+	0.268571i	0.0330990	+	0.0120470i
$498$		0			0
$499$	6.07532	+	5.09780i	0.271969	+	0.228209i	0.768563	−	0.639774i	$-0.220972\pi$
$499$	6.07532	+	5.09780i	0.271969	+	0.228209i	−0.496595	+	0.867983i	$0.665416\pi$
$500$	−10.9490	−	9.18732i	−0.489655	−	0.410869i
$501$		0			0
$502$	9.68866	+	3.52638i	0.432426	+	0.157390i
$503$	−12.4748	+	21.6070i	−0.556224	+	0.963409i	0.441583	+	0.897220i	$0.354417\pi$
$503$	−12.4748	+	21.6070i	−0.556224	+	0.963409i	−0.997807	+	0.0661881i	$0.978916\pi$
$504$		0			0
$505$	−6.80793	−	11.7917i	−0.302949	−	0.524723i
$506$	−5.03174	−	28.5364i	−0.223688	−	1.26860i
$507$		0			0
$508$	−22.1989	+	8.07975i	−0.984918	+	0.358481i
$509$	−7.02736	+	39.8542i	−0.311482	+	1.76650i	0.279818	+	0.960053i	$0.409726\pi$
$509$	−7.02736	+	39.8542i	−0.311482	+	1.76650i	−0.591300	+	0.806451i	$0.701385\pi$
$510$		0			0
$511$	−1.13041	+	0.948531i	−0.0500066	+	0.0419605i
$512$	−15.0038			−0.663080
$513$		0			0
$514$	2.27269			0.100244
$515$	−7.28314	+	6.11128i	−0.320934	+	0.269295i
$516$		0			0
$517$	−2.27972	+	12.9289i	−0.100262	+	0.568613i
$518$	0.169386	−	0.0616516i	0.00744240	−	0.00270881i
$519$		0			0
$520$	2.01114	+	11.4058i	0.0881945	+	0.500176i
$521$	−12.6837	−	21.9688i	−0.555684	−	0.962473i	−0.997850	−	0.0655394i	$-0.979123\pi$
$521$	−12.6837	−	21.9688i	−0.555684	−	0.962473i	0.442166	−	0.896933i	$-0.354210\pi$
$522$		0			0
$523$	−6.36097	+	11.0175i	−0.278146	+	0.481762i	−0.970924	−	0.239388i	$-0.923053\pi$
$523$	−6.36097	+	11.0175i	−0.278146	+	0.481762i	0.692778	+	0.721151i	$0.256386\pi$
$524$	−19.2286	−	6.99866i	−0.840007	−	0.305738i
$525$		0			0
$526$	−4.63151	−	3.88630i	−0.201943	−	0.169451i
$527$	32.0607	+	26.9021i	1.39659	+	1.17188i
$528$		0			0
$529$	−35.4987	−	12.9205i	−1.54342	−	0.561760i
$530$	−1.09191	+	1.89124i	−0.0474296	+	0.0821504i
$531$		0			0
$532$	0.0543776	+	0.0941848i	0.00235757	+	0.00408343i
$533$	6.00335	+	34.0467i	0.260034	+	1.47473i
$534$		0			0
$535$	−11.2135	+	4.08137i	−0.484801	+	0.176453i
$536$	−0.780272	+	4.42514i	−0.0337026	+	0.191137i
$537$		0			0
$538$	−4.24060	+	3.55829i	−0.182825	+	0.153409i
$539$	−37.9570			−1.63492
$540$		0			0
$541$	2.09327			0.0899969			0.0449984	−	0.998987i	$-0.485672\pi$
$541$	2.09327			0.0899969			0.0449984	+	0.998987i	$0.485672\pi$
$542$	9.95610	−	8.35416i	0.427651	−	0.358842i
$543$		0			0
$544$	4.81062	−	27.2824i	0.206254	−	1.16972i
$545$	2.85494	−	1.03911i	0.122292	−	0.0445108i
$546$		0			0
$547$	0.599260	+	3.39857i	0.0256225	+	0.145312i	0.994935	−	0.100519i	$-0.0320502\pi$
$547$	0.599260	+	3.39857i	0.0256225	+	0.145312i	−0.969313	+	0.245831i	$0.920939\pi$
$548$	15.0326	+	26.0371i	0.642159	+	1.11225i
$549$		0			0
$550$	−7.25103	+	12.5592i	−0.309185	+	0.535524i
$551$	−2.80374	−	1.02048i	−0.119443	−	0.0434738i
$552$		0			0
$553$	−0.0648930	−	0.0544517i	−0.00275953	−	0.00231552i
$554$	2.21621	+	1.85962i	0.0941578	+	0.0790078i
$555$		0			0
$556$	23.4761	+	8.54461i	0.995609	+	0.362372i
$557$	5.55017	−	9.61318i	0.235168	−	0.407323i	−0.724153	−	0.689639i	$-0.757769\pi$
$557$	5.55017	−	9.61318i	0.235168	−	0.407323i	0.959322	+	0.282316i	$0.0911025\pi$
$558$		0			0
$559$	−2.98545	−	5.17095i	−0.126271	−	0.218708i
$560$	0.0309820	+	0.175708i	0.00130923	+	0.00742500i
$561$		0			0
$562$	4.69372	−	1.70837i	0.197992	−	0.0720634i
$563$	4.22150	−	23.9413i	0.177915	−	1.00901i	−0.756810	−	0.653635i	$-0.773243\pi$
$563$	4.22150	−	23.9413i	0.177915	−	1.00901i	0.934725	−	0.355372i	$-0.115646\pi$
$564$		0			0
$565$	−9.29679	+	7.80093i	−0.391119	+	0.328188i
$566$	−10.9587			−0.460628
$567$		0			0
$568$	15.7297			0.660002
$569$	32.7591	−	27.4881i	1.37333	−	1.15236i	0.401726	−	0.915760i	$-0.368410\pi$
$569$	32.7591	−	27.4881i	1.37333	−	1.15236i	0.971606	−	0.236603i	$-0.0760340\pi$
$570$		0			0
$571$	3.13058	−	17.7544i	0.131011	−	0.742998i	−0.846545	−	0.532318i	$-0.821321\pi$
$571$	3.13058	−	17.7544i	0.131011	−	0.742998i	0.977555	−	0.210680i	$-0.0675678\pi$
$572$	−35.7817	+	13.0235i	−1.49611	+	0.544539i
$573$		0			0
$574$	−0.108288	−	0.614134i	−0.00451987	−	0.0256334i
$575$	15.2086	+	26.3421i	0.634244	+	1.09854i
$576$		0			0
$577$	−12.6382	+	21.8899i	−0.526133	+	0.911290i	0.473403	+	0.880846i	$0.343025\pi$
$577$	−12.6382	+	21.8899i	−0.526133	+	0.911290i	−0.999536	+	0.0304438i	$0.990308\pi$
$578$	3.74902	+	1.36453i	0.155939	+	0.0567571i
$579$		0			0
$580$	−6.23577	−	5.23243i	−0.258926	−	0.217265i
$581$	0.626133	+	0.525388i	0.0259764	+	0.0217967i
$582$		0			0
$583$	−15.5544	−	5.66133i	−0.644196	−	0.234468i
$584$	−14.7797	+	25.5993i	−0.611590	+	1.05930i
$585$		0			0
$586$	6.15792	+	10.6658i	0.254381	+	0.440601i
$587$	4.96032	+	28.1313i	0.204734	+	1.16111i	0.897858	+	0.440286i	$0.145123\pi$
$587$	4.96032	+	28.1313i	0.204734	+	1.16111i	−0.693123	+	0.720819i	$0.743766\pi$
$588$		0			0
$589$	−4.84389	+	1.76303i	−0.199589	+	0.0726445i
$590$	0.00546492	−	0.0309931i	0.000224987	−	0.00127597i
$591$		0			0
$592$	−2.36231	+	1.98221i	−0.0970904	+	0.0814685i
$593$	20.6009			0.845977			0.422989	−	0.906135i	$-0.360981\pi$
$593$	20.6009			0.845977			0.422989	+	0.906135i	$0.360981\pi$
$594$		0			0
$595$	−0.604007			−0.0247619
$596$	12.9661	−	10.8799i	0.531112	−	0.445656i
$597$		0			0
$598$	4.23560	−	24.0213i	0.173207	−	0.982304i
$599$	13.6019	−	4.95067i	0.555757	−	0.202279i	−0.0488454	−	0.998806i	$-0.515554\pi$
$599$	13.6019	−	4.95067i	0.555757	−	0.202279i	0.604603	+	0.796527i	$0.293332\pi$
$600$		0			0
$601$	−2.31908	−	13.1521i	−0.0945972	−	0.536487i	−0.994870	−	0.101161i	$-0.967744\pi$
$601$	−2.31908	−	13.1521i	−0.0945972	−	0.536487i	0.900273	−	0.435326i	$-0.143367\pi$
$602$	0.0538515	+	0.0932736i	0.00219483	+	0.00380155i
$603$		0			0
$604$	−5.20961	+	9.02330i	−0.211976	+	0.367153i
$605$	18.2438	+	6.64022i	0.741718	+	0.269963i
$606$		0			0
$607$	23.9106	+	20.0634i	0.970501	+	0.814347i	0.982629	−	0.185579i	$-0.0594161\pi$
$607$	23.9106	+	20.0634i	0.970501	+	0.814347i	−0.0121281	+	0.999926i	$0.503861\pi$
$608$	2.61381	+	2.19325i	0.106004	+	0.0889480i
$609$		0			0
$610$	6.87939	+	2.50389i	0.278538	+	0.101380i
$611$	−5.52557	+	9.57057i	−0.223541	+	0.387184i
$612$		0			0
$613$	−15.0326	−	26.0372i	−0.607159	−	1.05163i	−0.991706	−	0.128525i	$-0.958976\pi$
$613$	−15.0326	−	26.0372i	−0.607159	−	1.05163i	0.384547	−	0.923105i	$-0.374358\pi$
$614$	1.60484	+	9.10148i	0.0647659	+	0.367306i
$615$		0			0
$616$	1.48798	−	0.541580i	0.0599524	−	0.0218209i
$617$	−7.31991	+	41.5133i	−0.294688	+	1.67126i	0.373778	+	0.927518i	$0.378062\pi$
$617$	−7.31991	+	41.5133i	−0.294688	+	1.67126i	−0.668466	+	0.743743i	$0.733049\pi$
$618$		0			0
$619$	8.89440	−	7.46329i	0.357496	−	0.299975i	−0.446296	−	0.894886i	$-0.647257\pi$
$619$	8.89440	−	7.46329i	0.357496	−	0.299975i	0.803792	+	0.594911i	$0.202813\pi$
$620$	−14.0635			−0.564803
$621$		0			0
$622$	−11.2335			−0.450422
$623$	0.633436	−	0.531516i	0.0253781	−	0.0212947i
$624$		0			0
$625$	1.68984	−	9.58359i	0.0675938	−	0.383343i
$626$	−12.5760	+	4.57730i	−0.502639	+	0.182946i
$627$		0			0
$628$	−4.49273	−	25.4795i	−0.179279	−	1.01674i
$629$	−5.21983	−	9.04101i	−0.208128	−	0.360489i
$630$		0			0
$631$	14.6552	−	25.3836i	0.583415	−	1.01051i	−0.411655	−	0.911340i	$-0.635049\pi$
$631$	14.6552	−	25.3836i	0.583415	−	1.01051i	0.995071	−	0.0991657i	$-0.0316174\pi$
$632$	−1.59457	−	0.580375i	−0.0634284	−	0.0230861i
$633$		0			0
$634$	12.7745	+	10.7191i	0.507340	+	0.425709i
$635$	12.3789	+	10.3871i	0.491241	+	0.412201i
$636$		0			0
$637$	−30.0244	−	10.9280i	−1.18961	−	0.432983i
$638$	−9.42182	+	16.3191i	−0.373014	+	0.646078i
$639$		0			0
$640$	5.66637	+	9.81445i	0.223983	+	0.387950i
$641$	−5.40009	−	30.6254i	−0.213291	−	1.20963i	−0.883848	−	0.467774i	$-0.845056\pi$
$641$	−5.40009	−	30.6254i	−0.213291	−	1.20963i	0.670558	−	0.741857i	$-0.266055\pi$
$642$		0			0
$643$	−39.5347	+	14.3894i	−1.55910	+	0.567464i	−0.970529	−	0.240985i	$-0.922530\pi$
$643$	−39.5347	+	14.3894i	−1.55910	+	0.567464i	−0.588566	+	0.808449i	$0.700307\pi$
$644$	0.250164	−	1.41875i	0.00985783	−	0.0559065i
$645$		0			0
$646$	−1.47359	+	1.23649i	−0.0579777	+	0.0486491i
$647$	4.66717			0.183485			0.0917427	−	0.995783i	$-0.470756\pi$
$647$	4.66717			0.183485			0.0917427	+	0.995783i	$0.470756\pi$
$648$		0			0
$649$	0.238541			0.00936356
$650$	−9.35149	+	7.84683i	−0.366796	+	0.307778i
$651$		0			0
$652$	−2.23783	+	12.6913i	−0.0876400	+	0.497031i
$653$	−2.93572	+	1.06851i	−0.114884	+	0.0418142i	−0.398822	−	0.917028i	$-0.630581\pi$
$653$	−2.93572	+	1.06851i	−0.114884	+	0.0418142i	0.283939	+	0.958842i	$0.408359\pi$
$654$		0			0
$655$	2.43061	+	13.7847i	0.0949717	+	0.538611i
$656$	5.33424	+	9.23917i	0.208267	+	0.360729i
$657$		0			0
$658$	0.0996702	−	0.172634i	0.00388555	−	0.00672997i
$659$	35.1719	+	12.8015i	1.37010	+	0.498677i	0.919163	−	0.393877i	$-0.128866\pi$
$659$	35.1719	+	12.8015i	1.37010	+	0.498677i	0.450941	+	0.892554i	$0.351089\pi$
$660$		0			0
$661$	20.3004	+	17.0341i	0.789594	+	0.662548i	0.945645	−	0.325201i	$-0.105432\pi$
$661$	20.3004	+	17.0341i	0.789594	+	0.662548i	−0.156051	+	0.987749i	$0.549876\pi$
$662$	−14.9336	−	12.5307i	−0.580409	−	0.487021i
$663$		0			0
$664$	15.3855	+	5.59986i	0.597072	+	0.217317i
$665$	0.0371965	−	0.0644262i	0.00144242	−	0.00249834i
$666$		0			0
$667$	19.7618	+	34.2284i	0.765179	+	1.32533i
$668$	−0.698367	−	3.96064i	−0.0270206	−	0.153242i
$669$		0			0
$670$	1.25284	−	0.455997i	0.0484015	−	0.0176167i
$671$	−9.63571	+	54.6468i	−0.371982	+	2.10962i
$672$		0			0
$673$	1.31836	−	1.10624i	0.0508191	−	0.0426423i	−0.617024	−	0.786944i	$-0.711662\pi$
$673$	1.31836	−	1.10624i	0.0508191	−	0.0426423i	0.667843	+	0.744302i	$0.267218\pi$
$674$	11.9341			0.459686
$675$		0			0
$676$	−12.1361			−0.466773
$677$	21.6631	−	18.1775i	0.832581	−	0.698619i	−0.123301	−	0.992369i	$-0.539348\pi$
$677$	21.6631	−	18.1775i	0.832581	−	0.698619i	0.955882	+	0.293751i	$0.0949035\pi$
$678$		0			0
$679$	0.189073	−	1.07229i	0.00725597	−	0.0411507i
$680$	−11.3695	+	4.13816i	−0.436000	+	0.158691i
$681$		0			0
$682$	5.65317	+	32.0607i	0.216471	+	1.22767i
$683$	12.3569	+	21.4029i	0.472825	+	0.818958i	0.999516	−	0.0310993i	$-0.00990082\pi$
$683$	12.3569	+	21.4029i	0.472825	+	0.818958i	−0.526691	+	0.850057i	$0.676567\pi$
$684$		0			0
$685$	10.2829	−	17.8105i	0.392888	−	0.680502i
$686$	1.08429	+	0.394648i	0.0413983	+	0.0150677i
$687$		0			0
$688$	−1.41147	−	1.18437i	−0.0538119	−	0.0451536i
$689$	−10.6738	−	8.95636i	−0.406638	−	0.341210i
$690$		0			0
$691$	41.1327	+	14.9711i	1.56476	+	0.569527i	0.971821	−	0.235720i	$-0.0757448\pi$
$691$	41.1327	+	14.9711i	1.56476	+	0.569527i	0.592940	+	0.805246i	$0.297967\pi$
$692$	−10.0377	+	17.3858i	−0.381576	+	0.660908i
$693$		0			0
$694$	8.61515	+	14.9219i	0.327027	+	0.566427i
$695$	−2.96751	−	16.8296i	−0.112564	−	0.638383i
$696$		0			0
$697$	−33.9384	+	12.3526i	−1.28551	+	0.467887i
$698$	1.40781	−	7.98411i	0.0532865	−	0.302203i
$699$		0			0
$700$	−0.552318	+	0.463450i	−0.0208757	+	0.0175168i
$701$	−14.6504			−0.553338			−0.276669	−	0.960965i	$-0.589231\pi$
$701$	−14.6504			−0.553338			−0.276669	+	0.960965i	$0.589231\pi$
$702$		0			0
$703$	1.28581			0.0484951
$704$	4.75730	−	3.99185i	0.179297	−	0.150448i
$705$		0			0
$706$	0.997474	−	5.65695i	0.0375404	−	0.212902i
$707$	−1.47254	+	0.535959i	−0.0553804	+	0.0201568i
$708$		0			0
$709$	0.881034	+	4.99659i	0.0330879	+	0.187651i	0.996872	−	0.0790328i	$-0.0251832\pi$
$709$	0.881034	+	4.99659i	0.0330879	+	0.187651i	−0.963784	+	0.266684i	$0.914072\pi$
$710$	−2.33359	−	4.04189i	−0.0875779	−	0.151689i
$711$		0			0
$712$	8.28194	−	14.3447i	0.310379	−	0.537592i
$713$	64.1650	+	23.3542i	2.40300	+	0.874620i
$714$		0			0
$715$	19.9531	+	16.7427i	0.746204	+	0.626140i
$716$	−25.9363	−	21.7631i	−0.969284	−	0.813326i
$717$		0			0
$718$	1.69712	+	0.617701i	0.0633359	+	0.0230524i
$719$	2.66858	−	4.62212i	0.0995213	−	0.172376i	−0.811965	−	0.583706i	$-0.801602\pi$
$719$	2.66858	−	4.62212i	0.0995213	−	0.172376i	0.911487	+	0.411330i	$0.134936\pi$
$720$		0			0
$721$	0.547104	+	0.947611i	0.0203752	+	0.0352909i
$722$	2.21572	+	12.5660i	0.0824607	+	0.467658i
$723$		0			0
$724$	−2.96451	+	1.07899i	−0.110175	+	0.0401004i
$725$	3.43485	−	19.4800i	0.127567	−	0.723469i
$726$		0			0
$727$	28.4354	−	23.8601i	1.05461	−	0.884924i	0.0610401	−	0.998135i	$-0.480558\pi$
$727$	28.4354	−	23.8601i	1.05461	−	0.884924i	0.993571	+	0.113212i	$0.0361138\pi$
$728$	1.33293			0.0494017
$729$		0			0
$730$	8.77063			0.324616
$731$	4.77833	−	4.00950i	0.176733	−	0.148297i
$732$		0			0
$733$	5.20011	−	29.4913i	0.192071	−	1.08929i	−0.724459	−	0.689318i	$-0.757910\pi$
$733$	5.20011	−	29.4913i	0.192071	−	1.08929i	0.916529	−	0.399968i	$-0.130979\pi$
$734$	5.91209	−	2.15183i	0.218219	−	0.0794254i
$735$		0			0
$736$	−7.84864	−	44.5119i	−0.289305	−	1.64073i
$737$	5.05277	+	8.75166i	0.186121	+	0.322371i
$738$		0			0
$739$	14.3050	−	24.7770i	0.526218	−	0.911436i	−0.473316	−	0.880893i	$-0.656943\pi$
$739$	14.3050	−	24.7770i	0.526218	−	0.911436i	0.999533	−	0.0305431i	$-0.00972368\pi$
$740$	3.29644	+	1.19981i	0.121180	+	0.0441058i
$741$		0			0
$742$	0.192533	+	0.161555i	0.00706812	+	0.00593086i
$743$	38.0292	+	31.9103i	1.39516	+	1.17068i	0.963202	+	0.268780i	$0.0866204\pi$
$743$	38.0292	+	31.9103i	1.39516	+	1.17068i	0.431955	+	0.901895i	$0.357824\pi$
$744$		0			0
$745$	−10.8799	−	3.95994i	−0.398607	−	0.145081i
$746$	−9.16312	+	15.8710i	−0.335486	+	0.581078i
$747$		0			0
$748$	−19.8897	−	34.4499i	−0.727238	−	1.25961i
$749$	0.238484	+	1.35251i	0.00871402	+	0.0494197i
$750$		0			0
$751$	29.7165	−	10.8159i	1.08437	−	0.394678i	0.262837	−	0.964840i	$-0.415342\pi$
$751$	29.7165	−	10.8159i	1.08437	−	0.394678i	0.821532	+	0.570162i	$0.193120\pi$
$752$	−0.592184	+	3.35844i	−0.0215947	+	0.122470i
$753$		0			0
$754$	−12.1511	+	10.1960i	−0.442517	+	0.371316i
$755$	7.12716			0.259384
$756$		0			0
$757$	3.04189			0.110559			0.0552797	−	0.998471i	$-0.482395\pi$
$757$	3.04189			0.110559			0.0552797	+	0.998471i	$0.482395\pi$
$758$	14.2132	−	11.9263i	0.516248	−	0.433184i
$759$		0			0
$760$	0.258770	−	1.46756i	0.00938659	−	0.0532340i
$761$	−35.6410	+	12.9722i	−1.29198	+	0.470244i	−0.894378	−	0.447313i	$-0.852381\pi$
$761$	−35.6410	+	12.9722i	−1.29198	+	0.470244i	−0.397606	+	0.917556i	$0.630159\pi$
$762$		0			0
$763$	−0.0607179	−	0.344348i	−0.00219814	−	0.0124662i
$764$	3.02525	+	5.23989i	0.109450	+	0.189572i
$765$		0			0
$766$	−11.7747	+	20.3943i	−0.425436	+	0.736877i
$767$	0.188689	+	0.0686771i	0.00681316	+	0.00247979i
$768$		0			0
$769$	−15.6179	−	13.1050i	−0.563197	−	0.472578i	0.316184	−	0.948698i	$-0.397598\pi$
$769$	−15.6179	−	13.1050i	−0.563197	−	0.472578i	−0.879380	+	0.476120i	$0.842043\pi$
$770$	−0.359914	−	0.302004i	−0.0129704	−	0.0108835i
$771$		0			0
$772$	−12.1604	−	4.42604i	−0.437664	−	0.159297i
$773$	−12.2332	+	21.1885i	−0.439997	+	0.762097i	−0.997689	−	0.0679509i	$-0.978354\pi$
$773$	−12.2332	+	21.1885i	−0.439997	+	0.762097i	0.557692	+	0.830048i	$0.311687\pi$
$774$		0			0
$775$	−17.0869	−	29.5954i	−0.613781	−	1.06310i
$776$	−3.78742	−	21.4795i	−0.135960	−	0.771070i
$777$		0			0
$778$	−0.486329	+	0.177009i	−0.0174358	+	0.00634610i
$779$	0.772441	−	4.38073i	0.0276756	−	0.156956i
$780$		0			0
$781$	27.0993	−	22.7390i	0.969688	−	0.813665i

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.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.524005 + 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(0.984808 - 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-1.20805 - 2.09240i) q^{8} +O(q^{10})\)	\(q+(-0.524005 + 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(0.984808 - 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(-1.20805 - 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(-5.10602 - 1.85844i) q^{11} +(-3.50387 - 2.94010i) q^{13} +(0.0632028 + 0.0530334i) q^{14} +(-1.32635 - 0.482753i) q^{16} +(2.38917 - 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(0.278817 + 1.58125i) q^{20} +(3.49273 - 1.27125i) q^{22} +(1.35375 - 7.67752i) q^{23} +(-2.98886 + 2.50795i) q^{25} +3.12879 q^{26} +0.184793 q^{28} +(-3.88365 + 3.25877i) q^{29} +(-1.52094 + 8.62571i) q^{31} +(5.44804 - 1.98293i) q^{32} +(0.567581 + 3.21891i) q^{34} +(-0.0632028 - 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(-0.378297 - 0.137689i) q^{38} +(-1.93969 - 1.62760i) q^{40} +(-5.79006 - 4.85844i) q^{41} +(1.22668 + 0.446476i) q^{43} +(4.16247 - 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(-0.419550 - 2.37939i) q^{47} +(6.56418 - 2.38917i) q^{49} +(0.463450 - 2.62836i) q^{50} +(5.36824 - 4.50449i) q^{52} +3.04628 q^{53} -5.69459 q^{55} +(-0.223238 + 0.187319i) q^{56} +(0.602196 - 3.41523i) q^{58} +(-0.0412527 + 0.0150147i) q^{59} +(-1.77332 - 10.0570i) q^{61} +(-2.99568 - 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(-4.50449 - 1.63950i) q^{65} +(-1.42468 - 1.19545i) q^{67} +(5.60808 + 4.70574i) q^{68} +(0.0812519 + 0.0295733i) q^{70} +(-3.25519 + 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(0.259515 + 1.47178i) q^{74} +(-0.847296 + 0.308391i) q^{76} +(-0.113807 + 0.645430i) q^{77} +(0.538019 - 0.451451i) q^{79} -1.47924 q^{80} +5.17024 q^{82} +(-5.19118 + 4.35591i) q^{83} +(0.869585 - 4.93166i) q^{85} +(-0.839100 + 0.305407i) q^{86} +(2.27972 + 12.9289i) q^{88} +(3.42782 + 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(11.2238 + 4.08512i) q^{92} +(1.26604 + 1.06234i) q^{94} +(0.472482 + 0.396459i) q^{95} +(8.48293 + 3.08753i) q^{97} +(-2.38917 + 4.13816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^4 + 6 * q^7	\( 12 q + 6 q^{4} + 6 q^{7} + 12 q^{10} + 6 q^{13} - 18 q^{16} + 24 q^{19} + 6 q^{22} - 48 q^{25} - 12 q^{28} - 12 q^{31} + 54 q^{34} + 6 q^{37} - 12 q^{40} - 12 q^{43} - 6 q^{46} + 42 q^{49} + 54 q^{52} - 60 q^{55} + 6 q^{58} - 48 q^{61} - 6 q^{64} - 66 q^{67} + 6 q^{70} - 12 q^{73} - 6 q^{76} + 42 q^{79} - 24 q^{82} - 18 q^{85} - 24 q^{88} + 6 q^{94} + 60 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 + 6 * q^7 + 12 * q^10 + 6 * q^13 - 18 * q^16 + 24 * q^19 + 6 * q^22 - 48 * q^25 - 12 * q^28 - 12 * q^31 + 54 * q^34 + 6 * q^37 - 12 * q^40 - 12 * q^43 - 6 * q^46 + 42 * q^49 + 54 * q^52 - 60 * q^55 + 6 * q^58 - 48 * q^61 - 6 * q^64 - 66 * q^67 + 6 * q^70 - 12 * q^73 - 6 * q^76 + 42 * q^79 - 24 * q^82 - 18 * q^85 - 24 * q^88 + 6 * q^94 + 60 * q^97

Introduction

L-functions

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