LMFDB - Embedded newform 729.2.e.r.325.2

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			325.2
Root			$-0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.r.406.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.524005 - 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(-0.984808 + 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(1.20805 + 2.09240i) q^{8} +O(q^{10})$	\(q+(0.524005 - 0.439693i) q^{2} +(-0.266044 + 1.50881i) q^{4} +(-0.984808 + 0.358441i) q^{5} +(-0.0209445 - 0.118782i) q^{7} +(1.20805 + 2.09240i) q^{8} +(-0.358441 + 0.620838i) q^{10} +(5.10602 + 1.85844i) q^{11} +(-3.50387 - 2.94010i) q^{13} +(-0.0632028 - 0.0530334i) q^{14} +(-1.32635 - 0.482753i) q^{16} +(-2.38917 + 4.13816i) q^{17} +(0.294263 + 0.509678i) q^{19} +(-0.278817 - 1.58125i) q^{20} +(3.49273 - 1.27125i) q^{22} +(-1.35375 + 7.67752i) q^{23} +(-2.98886 + 2.50795i) q^{25} -3.12879 q^{26} +0.184793 q^{28} +(3.88365 - 3.25877i) q^{29} +(-1.52094 + 8.62571i) q^{31} +(-5.44804 + 1.98293i) q^{32} +(0.567581 + 3.21891i) q^{34} +(0.0632028 + 0.109470i) q^{35} +(1.09240 - 1.89209i) q^{37} +(0.378297 + 0.137689i) q^{38} +(-1.93969 - 1.62760i) q^{40} +(5.79006 + 4.85844i) q^{41} +(1.22668 + 0.446476i) q^{43} +(-4.16247 + 7.20961i) q^{44} +(2.66637 + 4.61830i) q^{46} +(0.419550 + 2.37939i) q^{47} +(6.56418 - 2.38917i) q^{49} +(-0.463450 + 2.62836i) q^{50} +(5.36824 - 4.50449i) q^{52} -3.04628 q^{53} -5.69459 q^{55} +(0.223238 - 0.187319i) q^{56} +(0.602196 - 3.41523i) q^{58} +(0.0412527 - 0.0150147i) q^{59} +(-1.77332 - 10.0570i) q^{61} +(2.99568 + 5.18866i) q^{62} +(-0.571452 + 0.989783i) q^{64} +(4.50449 + 1.63950i) q^{65} +(-1.42468 - 1.19545i) q^{67} +(-5.60808 - 4.70574i) q^{68} +(0.0812519 + 0.0295733i) q^{70} +(3.25519 - 5.63816i) q^{71} +(-6.11721 - 10.5953i) q^{73} +(-0.259515 - 1.47178i) q^{74} +(-0.847296 + 0.308391i) q^{76} +(0.113807 - 0.645430i) q^{77} +(0.538019 - 0.451451i) q^{79} +1.47924 q^{80} +5.17024 q^{82} +(5.19118 - 4.35591i) q^{83} +(0.869585 - 4.93166i) q^{85} +(0.839100 - 0.305407i) q^{86} +(2.27972 + 12.9289i) q^{88} +(-3.42782 - 5.93717i) q^{89} +(-0.275845 + 0.477777i) q^{91} +(-11.2238 - 4.08512i) q^{92} +(1.26604 + 1.06234i) q^{94} +(-0.472482 - 0.396459i) q^{95} +(8.48293 + 3.08753i) q^{97} +(2.38917 - 4.13816i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.438443	−	0.898759i	$-0.644470\pi$
$2$	0.524005	−	0.439693i	0.370528	−	0.310910i	0.808970	+	0.587850i	$0.200025\pi$
$3$		0			0
$3$		0			0
$4$	−0.266044	+	1.50881i	−0.133022	+	0.754407i
$5$	−0.984808	+	0.358441i	−0.440419	+	0.160300i	−0.552706	−	0.833376i	$-0.686405\pi$
$5$	−0.984808	+	0.358441i	−0.440419	+	0.160300i	0.112287	+	0.993676i	$0.464183\pi$
$6$		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	0.965931	−	0.258799i	$-0.0833269\pi$
$11$	5.10602	+	1.85844i	1.53952	+	0.560341i	0.573593	+	0.819140i	$0.305549\pi$
$12$		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	$0.363402\pi$
$17$	−2.38917	+	4.13816i	−0.579458	+	1.00365i	−0.995542	+	0.0943239i	$0.969931\pi$
$18$		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	$0.357605\pi$
$23$	−1.35375	+	7.67752i	−0.282277	+	1.60087i	−0.714852	+	0.699275i	$0.753506\pi$
$24$		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	−0.206534	−	0.978439i	$-0.566219\pi$
$29$	3.88365	−	3.25877i	0.721176	−	0.605138i	0.927710	+	0.373301i	$0.121774\pi$
$30$		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	0.971018	−	0.239008i	$-0.0768222\pi$
$41$	5.79006	+	4.85844i	0.904256	+	0.758761i	−0.0667615	+	0.997769i	$0.521267\pi$
$42$		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	$0.000828726\pi$
$47$	0.419550	+	2.37939i	0.0611976	+	0.347069i	−0.938799	+	0.344465i	$0.888060\pi$
$48$		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	$-0.567092\pi$
$53$	−3.04628			−0.418439			−0.209219	+	0.977869i	$0.567092\pi$
$54$		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	−0.339333	−	0.940666i	$-0.610201\pi$
$59$	0.0412527	−	0.0150147i	0.00537064	−	0.00195475i	0.344704	+	0.938711i	$0.387979\pi$
$60$		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	−0.605631	−	0.795745i	$-0.707079\pi$
$71$	3.25519	−	5.63816i	0.386320	−	0.669126i	0.991951	+	0.126619i	$0.0404127\pi$
$72$		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	−0.311776	−	0.950156i	$-0.600924\pi$
$83$	5.19118	−	4.35591i	0.569806	−	0.478124i	0.881581	+	0.472032i	$0.156479\pi$
$84$		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	0.625161	−	0.780496i	$-0.285033\pi$
$89$	−3.42782	−	5.93717i	−0.363349	−	0.629338i	−0.988510	+	0.151157i	$0.951700\pi$
$90$		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	$0.168163\pi$
$101$	2.25606	+	12.7947i	0.224486	+	1.27312i	−0.639179	+	0.769058i	$0.720726\pi$
$102$		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	$-0.314481\pi$
$107$	11.3865			1.10077			0.550386	+	0.834911i	$0.314481\pi$
$108$		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	0.225003	−	0.974358i	$-0.427761\pi$
$113$	10.8818	−	3.96064i	1.02367	−	0.372585i	0.798667	+	0.601773i	$0.205539\pi$
$114$		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	$-0.746142\pi$
$131$	2.31926	−	13.1532i	0.202635	−	1.14920i	0.901119	−	0.433572i	$-0.142747\pi$
$132$		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	$0.594216\pi$
$137$	−15.0326	+	12.6138i	−1.28432	+	1.07767i	−0.992634	+	0.121156i	$0.961340\pi$
$138$		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	0.919864	−	0.392238i	$-0.128299\pi$
$149$	8.46302	+	7.10132i	0.693318	+	0.581763i	−0.226546	+	0.974000i	$0.572743\pi$
$150$		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	−0.244812	−	0.969571i	$-0.578726\pi$
$167$	2.46669	−	0.897804i	0.190879	−	0.0694741i	0.435691	+	0.900096i	$0.356504\pi$
$168$		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	−0.171502	−	0.985184i	$-0.554862\pi$
$173$	−12.3130	−	4.48158i	−0.936143	−	0.340728i	−0.764642	+	0.644455i	$0.777084\pi$
$174$		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	$-0.524016\pi$
$179$	11.0494	−	19.1382i	0.825872	−	1.43045i	0.901251	−	0.433298i	$-0.142650\pi$
$180$		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	−0.745643	−	0.666346i	$-0.767857\pi$
$191$	−3.02525	+	2.53849i	−0.218899	+	0.183678i	0.526743	+	0.850024i	$0.323413\pi$
$192$		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	0.904004	−	0.427524i	$-0.140614\pi$
$197$	1.14749	+	1.98751i	0.0817553	+	0.141604i	−0.822249	+	0.569128i	$0.807281\pi$
$198$		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	0.776198	−	0.630490i	$-0.217146\pi$
$227$	14.5472	+	5.29473i	0.965528	+	0.351424i	0.189331	+	0.981913i	$0.439368\pi$
$228$		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	−0.767464	−	0.641092i	$-0.778482\pi$
$233$	2.61738	−	4.53343i	0.171470	−	0.296995i	0.938934	+	0.344097i	$0.111815\pi$
$234$		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	$-0.836234\pi$
$239$	1.79028	−	10.1532i	0.115803	−	0.656754i	0.986349	−	0.164667i	$-0.0526548\pi$
$240$		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	0.999612	−	0.0278401i	$-0.00886291\pi$
$251$	7.53644	+	13.0535i	0.475696	+	0.823930i	−0.523916	+	0.851770i	$0.675530\pi$
$252$		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	0.718708	−	0.695312i	$-0.244734\pi$
$257$	2.54514	+	2.13563i	0.158762	+	0.133217i	−0.559946	+	0.828529i	$0.689178\pi$
$258$		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	$-0.967702\pi$
$263$	−1.53482	−	8.70439i	−0.0946410	−	0.536736i	0.900216	−	0.435444i	$-0.143409\pi$
$264$		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	$-0.579349\pi$
$269$	−8.09267			−0.493419			−0.246709	+	0.969090i	$0.579349\pi$
$270$		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	0.538478	−	0.842640i	$-0.318999\pi$
$281$	6.86175	+	2.49747i	0.409338	+	0.148987i	−0.129140	+	0.991626i	$0.541222\pi$
$282$		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	$0.231834\pi$
$293$	−3.12646	+	17.7310i	−0.182650	+	1.03586i	−0.928938	+	0.370235i	$0.879277\pi$
$294$		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	0.212182	−	0.977230i	$-0.431943\pi$
$311$	−12.5802	−	10.5560i	−0.713357	−	0.598577i	−0.925539	+	0.378653i	$0.876387\pi$
$312$		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	$0.184476\pi$
$317$	4.23329	+	24.0082i	0.237766	+	1.34844i	−0.598945	+	0.800790i	$0.704413\pi$
$318$		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	$0.291891\pi$
$347$	−4.37403	+	24.8063i	−0.234810	+	1.33167i	−0.843013	+	0.537893i	$0.819221\pi$
$348$		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	−0.455338	−	0.890319i	$-0.650482\pi$
$353$	6.43285	−	5.39780i	0.342386	−	0.287296i	0.797724	+	0.603023i	$0.206037\pi$
$354$		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	0.898758	−	0.438446i	$-0.144471\pi$
$359$	1.32012	+	2.28652i	0.0696735	+	0.120678i	−0.829084	+	0.559124i	$0.811138\pi$
$360$		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	−0.989246	−	0.146259i	$-0.953277\pi$
$383$	−32.3506	+	11.7747i	−1.65304	+	0.601657i	−0.663793	+	0.747916i	$0.731054\pi$
$384$		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	0.323934	−	0.946080i	$-0.394995\pi$
$389$	−0.710966	−	0.258770i	−0.0360474	−	0.0131202i	−0.359981	+	0.932960i	$0.617217\pi$
$390$		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	$0.131384\pi$
$401$	−1.64111	+	9.30722i	−0.0819533	+	0.464780i	−0.997973	+	0.0636460i	$0.979727\pi$
$402$		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	0.634019	−	0.773317i	$-0.281404\pi$
$419$	−0.357267	−	0.299782i	−0.0174536	−	0.0146453i	−0.651473	+	0.758672i	$0.725848\pi$
$420$		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	$-0.405880\pi$
$431$	12.0992			0.582796			0.291398	+	0.956602i	$0.405880\pi$
$432$		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	0.235495	−	0.971876i	$-0.424329\pi$
$443$	−4.39506	−	1.59967i	−0.208815	−	0.0760026i	−0.444310	+	0.895873i	$0.646551\pi$
$444$		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	$0.383689\pi$
$449$	−13.3534	+	23.1288i	−0.630187	+	1.09152i	−0.987513	+	0.157537i	$0.949645\pi$
$450$		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	−0.932481	−	0.361220i	$-0.882360\pi$
$461$	−15.8600	+	13.3081i	−0.738672	+	0.619820i	0.193808	+	0.981039i	$0.437916\pi$
$462$		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	$0.0450412\pi$
$467$	13.3365	+	23.0994i	0.617138	+	1.06891i	−0.372868	+	0.927884i	$0.621625\pi$
$468$		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	0.994929	−	0.100584i	$-0.0320710\pi$
$479$	0.560282	+	3.17752i	0.0255999	+	0.145185i	−0.969329	+	0.245768i	$0.920960\pi$
$480$		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	0.0457323	−	0.998954i	$-0.485438\pi$
$491$	16.0180	−	5.83006i	0.722880	−	0.263107i	0.677148	+	0.735847i	$0.263216\pi$
$492$		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	$-0.645583\pi$
$503$	12.4748	−	21.6070i	0.556224	−	0.963409i	0.997807	−	0.0661881i	$-0.0210837\pi$
$504$		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	$-0.590274\pi$
$509$	7.02736	−	39.8542i	0.311482	−	1.76650i	0.591300	−	0.806451i	$-0.298615\pi$
$510$		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	$0.0208768\pi$
$521$	12.6837	+	21.9688i	0.555684	+	0.962473i	−0.442166	+	0.896933i	$0.645790\pi$
$522$		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	−0.959322	−	0.282316i	$-0.908897\pi$
$557$	−5.55017	+	9.61318i	−0.235168	+	0.407323i	0.724153	+	0.689639i	$0.242231\pi$
$558$		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	$0.226757\pi$
$563$	−4.22150	+	23.9413i	−0.177915	+	1.00901i	−0.934725	+	0.355372i	$0.884354\pi$
$564$		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	$0.631590\pi$
$569$	−32.7591	+	27.4881i	−1.37333	+	1.15236i	−0.971606	+	0.236603i	$0.923966\pi$
$570$		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	$-0.854877\pi$
$587$	−4.96032	−	28.1313i	−0.204734	−	1.16111i	0.693123	−	0.720819i	$-0.256234\pi$
$588$		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	$-0.639019\pi$
$593$	−20.6009			−0.845977			−0.422989	+	0.906135i	$0.639019\pi$
$594$		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	−0.604603	−	0.796527i	$-0.706668\pi$
$599$	−13.6019	+	4.95067i	−0.555757	+	0.202279i	0.0488454	+	0.998806i	$0.484446\pi$
$600$		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	$-0.621938\pi$
$617$	7.31991	−	41.5133i	0.294688	−	1.67126i	0.668466	−	0.743743i	$-0.266951\pi$
$618$		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	$0.154944\pi$
$641$	5.40009	+	30.6254i	0.213291	+	1.20963i	−0.670558	+	0.741857i	$0.733945\pi$
$642$		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	$-0.529244\pi$
$647$	−4.66717			−0.183485			−0.0917427	+	0.995783i	$0.529244\pi$
$648$		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	−0.283939	−	0.958842i	$-0.591641\pi$
$653$	2.93572	−	1.06851i	0.114884	−	0.0418142i	0.398822	+	0.917028i	$0.369419\pi$
$654$		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	−0.450941	−	0.892554i	$-0.648911\pi$
$659$	−35.1719	−	12.8015i	−1.37010	−	0.498677i	−0.919163	+	0.393877i	$0.871134\pi$
$660$		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	−0.955882	−	0.293751i	$-0.905096\pi$
$677$	−21.6631	+	18.1775i	−0.832581	+	0.698619i	0.123301	+	0.992369i	$0.460652\pi$
$678$		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	0.526691	−	0.850057i	$-0.323433\pi$
$683$	−12.3569	−	21.4029i	−0.472825	−	0.818958i	−0.999516	+	0.0310993i	$0.990099\pi$
$684$		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	$-0.410769\pi$
$701$	14.6504			0.553338			0.276669	+	0.960965i	$0.410769\pi$
$702$		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	−0.911487	−	0.411330i	$-0.865064\pi$
$719$	−2.66858	+	4.62212i	−0.0995213	+	0.172376i	0.811965	+	0.583706i	$0.198398\pi$
$720$		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	$-0.913380\pi$
$743$	−38.0292	−	31.9103i	−1.39516	−	1.17068i	−0.431955	−	0.901895i	$-0.642176\pi$
$744$		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	0.397606	−	0.917556i	$-0.369841\pi$
$761$	35.6410	−	12.9722i	1.29198	−	0.470244i	0.894378	+	0.447313i	$0.147619\pi$
$762$		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	−0.557692	−	0.830048i	$-0.688313\pi$
$773$	12.2332	−	21.1885i	0.439997	−	0.762097i	0.997689	+	0.0679509i	$0.0216461\pi$
$774$		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
$782$	−25.4816			−0.911221
$783$		0			0
$784$	−9.85978			−0.352135
$785$	13.5574	−	11.3760i	0.483883	−	0.406026i
$786$		0			0
$787$	6.52481	−	37.0041i	0.232585	−	1.31905i	−0.615057	−	0.788483i	$-0.710867\pi$
$787$	6.52481	−	37.0041i	0.232585	−	1.31905i	0.847641	−	0.530570i	$-0.178022\pi$
$788$	−3.30407	+	1.20258i	−0.117702	+	0.0428402i
$789$		0			0
$790$	0.0874301	+	0.495841i	0.00311062	+	0.0176412i
$791$	−0.698367	−	1.20961i	−0.0248311	−	0.0430087i
$792$		0			0
$793$	−23.3550	+	40.4521i	−0.829362	+	1.43650i
$794$	−4.50449	−	1.63950i	−0.159858	−	0.0581837i
$795$		0			0
$796$	27.5842	+	23.1459i	0.977698	+	0.820386i
$797$	−1.76568	−	1.48158i	−0.0625436	−	0.0524803i	0.610980	−	0.791646i	$-0.290776\pi$
$797$	−1.76568	−	1.48158i	−0.0625436	−	0.0524803i	−0.673524	+	0.739166i	$0.735220\pi$
$798$		0			0
$799$	−10.8486	−	3.94858i	−0.383797	−	0.139691i
$800$	11.3103	−	19.5901i	0.399881	−	0.692614i
$801$		0			0
$802$	3.23236	+	5.59862i	0.114139	+	0.197694i
$803$	−11.5439	−	65.4684i	−0.407374	−	2.31033i
$804$		0			0
$805$	−0.926022	+	0.337044i	−0.0326380	+	0.0118793i
$806$	4.75871	−	26.9880i	0.167618	−	0.950611i
$807$		0			0
$808$	−24.0462	+	20.1772i	−0.845943	+	0.709831i
$809$	28.8614			1.01471			0.507356	−	0.861736i	$-0.330623\pi$
$809$	28.8614			1.01471			0.507356	+	0.861736i	$0.330623\pi$
$810$		0			0
$811$	−51.8631			−1.82116			−0.910580	−	0.413334i	$-0.864364\pi$
$811$	−51.8631			−1.82116			−0.910580	+	0.413334i	$0.864364\pi$
$812$	0.717670	−	0.602196i	0.0251853	−	0.0211330i
$813$		0			0
$814$	1.41013	−	7.99724i	0.0494250	−	0.280303i
$815$	−8.28368	+	3.01501i	−0.290165	+	0.105611i
$816$		0			0
$817$	0.133408	+	0.756594i	0.00466735	+	0.0264699i
$818$	−1.88711	−	3.26857i	−0.0659813	−	0.114283i
$819$		0			0
$820$	6.06805	−	10.5102i	0.211905	−	0.367031i
$821$	17.3289	+	6.30722i	0.604784	+	0.220123i	0.626220	−	0.779647i	$-0.284601\pi$
$821$	17.3289	+	6.30722i	0.604784	+	0.220123i	−0.0214353	+	0.999770i	$0.506824\pi$
$822$		0			0
$823$	−26.6327	−	22.3475i	−0.928357	−	0.778984i	0.0471645	−	0.998887i	$-0.484982\pi$
$823$	−26.6327	−	22.3475i	−0.928357	−	0.778984i	−0.975522	+	0.219903i	$0.929426\pi$
$824$	−16.7906	−	14.0890i	−0.584929	−	0.490813i
$825$		0			0
$826$	−0.00340357	−	0.00123880i	−0.000118425	−	4.31033e-5i
$827$	−16.3886	+	28.3859i	−0.569889	+	0.987076i	0.426688	+	0.904399i	$0.359680\pi$
$827$	−16.3886	+	28.3859i	−0.569889	+	0.987076i	−0.996576	+	0.0826770i	$0.973653\pi$
$828$		0			0
$829$	−2.67634	−	4.63555i	−0.0929530	−	0.160999i	0.815799	−	0.578335i	$-0.196297\pi$
$829$	−2.67634	−	4.63555i	−0.0929530	−	0.160999i	−0.908752	+	0.417336i	$0.862964\pi$
$830$	0.843586	+	4.78421i	0.0292813	+	0.166063i
$831$		0			0
$832$	4.91235	−	1.78795i	0.170305	−	0.0619860i
$833$	−5.79617	+	32.8717i	−0.200825	+	1.13894i
$834$		0			0
$835$	−2.10741	+	1.76833i	−0.0729300	+	0.0611955i
$836$	−4.89944			−0.169451
$837$		0			0
$838$	−0.319022			−0.0110204
$839$	−4.16604	+	3.49572i	−0.143828	+	0.120686i	−0.711863	−	0.702319i	$-0.752148\pi$
$839$	−4.16604	+	3.49572i	−0.143828	+	0.120686i	0.568035	+	0.823004i	$0.307704\pi$
$840$		0			0
$841$	−0.572634	+	3.24757i	−0.0197460	+	0.111985i
$842$	1.55179	−	0.564807i	0.0534783	−	0.0194645i
$843$		0			0
$844$	0.443563	+	2.51557i	0.0152681	+	0.0865895i
$845$	−4.15079	−	7.18938i	−0.142791	−	0.247322i
$846$		0			0
$847$	1.11721	−	1.93507i	0.0383878	−	0.0664897i
$848$	4.04044	+	1.47060i	0.138749	+	0.0505006i
$849$		0			0
$850$	−9.76929	−	8.19740i	−0.335084	−	0.281169i
$851$	13.0477	+	10.9483i	0.447269	+	0.375303i
$852$		0			0
$853$	44.2756	+	16.1150i	1.51597	+	0.551767i	0.960137	−	0.279529i	$-0.0901782\pi$
$853$	44.2756	+	16.1150i	1.51597	+	0.551767i	0.555830	+	0.831296i	$0.312400\pi$
$854$	−0.421278	+	0.729675i	−0.0144158	+	0.0249690i
$855$		0			0
$856$	13.7554	+	23.8250i	0.470149	+	0.814322i
$857$	8.15382	+	46.2426i	0.278529	+	1.57962i	0.727523	+	0.686083i	$0.240671\pi$
$857$	8.15382	+	46.2426i	0.278529	+	1.57962i	−0.448994	+	0.893535i	$0.648217\pi$
$858$		0			0
$859$	−6.73143	+	2.45004i	−0.229673	+	0.0835943i	−0.454293	−	0.890852i	$-0.650108\pi$
$859$	−6.73143	+	2.45004i	−0.229673	+	0.0835943i	0.224620	+	0.974446i	$0.427886\pi$
$860$	0.363970	−	2.06418i	0.0124113	−	0.0703879i
$861$		0			0
$862$	6.34002	−	5.31991i	0.215942	−	0.181197i
$863$	35.4309			1.20608			0.603041	−	0.797710i	$-0.293955\pi$
$863$	35.4309			1.20608			0.603041	+	0.797710i	$0.293955\pi$
$864$		0			0
$865$	13.7324			0.466914
$866$	17.4761	−	14.6642i	0.593861	−	0.498308i
$867$		0			0
$868$	−0.281059	+	1.59397i	−0.00953977	+	0.0541027i
$869$	3.58613	−	1.30525i	0.121651	−	0.0442774i
$870$		0			0
$871$	1.47716	+	8.37738i	0.0500516	+	0.283857i
$872$	3.50211	+	6.06583i	0.118596	+	0.205415i
$873$		0			0
$874$	−1.56923	+	2.71799i	−0.0530800	+	0.0919373i
$875$	−1.05736	−	0.384848i	−0.0357454	−	0.0130102i
$876$		0			0
$877$	6.26083	+	5.25346i	0.211413	+	0.177397i	0.742345	−	0.670018i	$-0.233714\pi$
$877$	6.26083	+	5.25346i	0.211413	+	0.177397i	−0.530932	+	0.847415i	$0.678158\pi$
$878$	−4.73941	−	3.97683i	−0.159947	−	0.134212i
$879$		0			0
$880$	7.55303	+	2.74908i	0.254613	+	0.0926714i
$881$	−16.6153	+	28.7786i	−0.559785	+	0.969575i	0.437729	+	0.899107i	$0.355783\pi$
$881$	−16.6153	+	28.7786i	−0.559785	+	0.969575i	−0.997514	+	0.0704686i	$0.977551\pi$
$882$		0			0
$883$	−16.5239	−	28.6203i	−0.556075	−	0.963150i	−0.997819	−	0.0660087i	$-0.978973\pi$
$883$	−16.5239	−	28.6203i	−0.556075	−	0.963150i	0.441744	−	0.897141i	$-0.354360\pi$
$884$	5.81466	+	32.9766i	0.195568	+	1.10912i
$885$		0			0
$886$	−3.00640	+	1.09424i	−0.101002	+	0.0367617i
$887$	8.63851	−	48.9914i	0.290053	−	1.64497i	−0.396604	−	0.917990i	$-0.629811\pi$
$887$	8.63851	−	48.9914i	0.290053	−	1.64497i	0.686657	−	0.726982i	$-0.259078\pi$
$888$		0			0
$889$	1.42468	−	1.19545i	0.0477822	−	0.0400940i
$890$	4.91469			0.164741
$891$		0			0
$892$	15.0155			0.502756
$893$	−1.08926	+	0.914000i	−0.0364508	+	0.0305859i
$894$		0			0
$895$	−4.02166	+	22.8080i	−0.134429	+	0.762386i
$896$	−1.22562	+	0.446089i	−0.0409451	+	0.0149028i
$897$		0			0
$898$	3.17230	+	17.9910i	0.105861	+	0.600368i
$899$	22.2024	+	38.4556i	0.740491	+	1.28257i
$900$		0			0
$901$	7.27807	−	12.6060i	0.242468	−	0.419966i
$902$	26.3994	+	9.60859i	0.879004	+	0.319931i
$903$		0			0
$904$	21.4329	+	17.9843i	0.712847	+	0.598150i
$905$	−1.65311	−	1.38713i	−0.0549513	−	0.0461096i
$906$		0			0
$907$	−32.4650	−	11.8163i	−1.07798	−	0.392353i	−0.258826	−	0.965924i	$-0.583336\pi$
$907$	−32.4650	−	11.8163i	−1.07798	−	0.392353i	−0.819156	+	0.573571i	$0.805558\pi$
$908$	−11.8589	+	20.5403i	−0.393553	+	0.681654i
$909$		0			0
$910$	−0.197748	−	0.342509i	−0.00655528	−	0.0113541i
$911$	2.36802	+	13.4297i	0.0784561	+	0.444947i	0.998578	+	0.0533142i	$0.0169785\pi$
$911$	2.36802	+	13.4297i	0.0784561	+	0.444947i	−0.920122	+	0.391633i	$0.871910\pi$
$912$		0			0
$913$	34.6015	−	12.5939i	1.14514	−	0.416798i
$914$	−0.0781298	+	0.443096i	−0.00258430	+	0.0146563i
$915$		0			0
$916$	13.2083	−	11.0830i	0.436413	−	0.366194i
$917$	−1.61094			−0.0531979
$918$		0			0
$919$	32.7701			1.08099			0.540493	−	0.841348i	$-0.318238\pi$
$919$	32.7701			1.08099			0.540493	+	0.841348i	$0.318238\pi$
$920$	15.1218	−	12.6887i	0.498550	−	0.418333i
$921$		0			0
$922$	−2.45924	+	13.9470i	−0.0809906	+	0.459321i
$923$	−27.9825	+	10.1848i	−0.921055	+	0.335237i
$924$		0			0
$925$	1.48024	+	8.39484i	0.0486699	+	0.276021i
$926$	8.49027	+	14.7056i	0.279008	+	0.483255i
$927$		0			0
$928$	−14.6964	+	25.4549i	−0.482433	+	0.835599i
$929$	5.19788	+	1.89187i	0.170537	+	0.0620704i	0.425878	−	0.904781i	$-0.359965\pi$
$929$	5.19788	+	1.89187i	0.170537	+	0.0620704i	−0.255341	+	0.966851i	$0.582188\pi$
$930$		0			0
$931$	3.14930	+	2.64258i	0.103214	+	0.0866069i
$932$	6.14376	+	5.15523i	0.201246	+	0.168865i
$933$		0			0
$934$	17.1450	+	6.24028i	0.561002	+	0.204188i
$935$	13.6053	−	23.5651i	0.444942	−	0.770662i
$936$		0			0
$937$	0.497007	+	0.860841i	0.0162365	+	0.0281225i	0.874029	−	0.485873i	$-0.161498\pi$
$937$	0.497007	+	0.860841i	0.0162365	+	0.0281225i	−0.857793	+	0.513995i	$0.828165\pi$
$938$	0.0266450	+	0.151111i	0.000869989	+	0.00493395i
$939$		0			0
$940$	3.64543	−	1.32683i	0.118901	−	0.0432764i
$941$	−1.98952	+	11.2831i	−0.0648564	+	0.367819i	0.935055	+	0.354503i	$0.115350\pi$
$941$	−1.98952	+	11.2831i	−0.0648564	+	0.367819i	−0.999911	+	0.0133162i	$0.995761\pi$
$942$		0			0
$943$	−45.1391	+	37.8762i	−1.46993	+	1.23342i
$944$	−0.0619640			−0.00201676
$945$		0			0
$946$	4.85204			0.157754
$947$	34.9968	−	29.3658i	1.13724	−	0.954259i	0.137897	−	0.990447i	$-0.455966\pi$
$947$	34.9968	−	29.3658i	1.13724	−	0.954259i	0.999345	+	0.0361872i	$0.0115213\pi$
$948$		0			0
$949$	−9.71735	+	55.1098i	−0.315438	+	1.78894i
$950$	−1.47599	+	0.537217i	−0.0478875	+	0.0174296i
$951$		0			0
$952$	0.241802	+	1.37133i	0.00783685	+	0.0444450i
$953$	−7.25265	−	12.5620i	−0.234936	−	0.406922i	0.724318	−	0.689466i	$-0.242155\pi$
$953$	−7.25265	−	12.5620i	−0.234936	−	0.406922i	−0.959254	+	0.282545i	$0.908822\pi$
$954$		0			0
$955$	2.06939	−	3.58429i	0.0669640	−	0.115985i
$956$	14.8429	+	5.40239i	0.480055	+	0.174726i
$957$		0			0
$958$	1.69072	+	1.41868i	0.0546248	+	0.0458356i
$959$	1.81315	+	1.52141i	0.0585496	+	0.0491289i
$960$		0			0
$961$	−42.9590	−	15.6358i	−1.38578	−	0.504381i
$962$	−3.41787	+	5.91993i	−0.110197	+	0.190866i
$963$		0			0
$964$	8.23055	+	14.2557i	0.265088	+	0.459146i
$965$	−1.53715	−	8.71760i	−0.0494825	−	0.280629i
$966$		0			0
$967$	23.5269	−	8.56310i	0.756575	−	0.275371i	0.0652053	−	0.997872i	$-0.479230\pi$
$967$	23.5269	−	8.56310i	0.756575	−	0.275371i	0.691370	+	0.722501i	$0.257008\pi$
$968$	−7.77228	+	44.0788i	−0.249810	+	1.41675i
$969$		0			0
$970$	−4.95748	+	4.15982i	−0.159175	+	0.133564i
$971$	−27.0907			−0.869383			−0.434692	−	0.900579i	$-0.643143\pi$
$971$	−27.0907			−0.869383			−0.434692	+	0.900579i	$0.643143\pi$
$972$		0			0
$973$	−1.96679			−0.0630522
$974$	−4.07640	+	3.42050i	−0.130616	+	0.109600i
$975$		0			0
$976$	−2.50299	+	14.1952i	−0.0801189	+	0.454377i
$977$	−2.32423	+	0.845952i	−0.0743589	+	0.0270644i	−0.378932	−	0.925425i	$-0.623708\pi$
$977$	−2.32423	+	0.845952i	−0.0743589	+	0.0270644i	0.304573	+	0.952489i	$0.401486\pi$
$978$		0			0
$979$	−6.46868	−	36.6857i	−0.206740	−	1.17248i
$980$	−5.60808	−	9.71348i	−0.179144	−	0.310286i
$981$		0			0
$982$	5.83006	−	10.0980i	0.186045	−	0.322239i
$983$	17.9557	+	6.53533i	0.572697	+	0.208445i	0.612102	−	0.790779i	$-0.290324\pi$
$983$	17.9557	+	6.53533i	0.572697	+	0.208445i	−0.0394052	+	0.999223i	$0.512546\pi$
$984$		0			0
$985$	−1.84246	−	1.54601i	−0.0587057	−	0.0492600i
$986$	12.6940	+	10.6515i	0.404259	+	0.339214i
$987$		0			0
$988$	3.87551	+	1.41057i	0.123297	+	0.0448763i
$989$	−5.08845	+	8.81345i	−0.161803	+	0.280251i
$990$		0			0
$991$	19.1582	+	33.1830i	0.608581	+	1.05409i	0.991475	+	0.130301i	$0.0415943\pi$
$991$	19.1582	+	33.1830i	0.608581	+	1.05409i	−0.382894	+	0.923792i	$0.625072\pi$
$992$	−8.81796	−	50.0091i	−0.279971	−	1.58779i
$993$		0			0
$994$	−0.504748	+	0.183713i	−0.0160096	+	0.00582703i
$995$	−4.27719	+	24.2572i	−0.135596	+	0.769004i
$996$		0			0
$997$	31.6948	−	26.5951i	1.00378	−	0.842275i	0.0162804	−	0.999867i	$-0.494818\pi$
$997$	31.6948	−	26.5951i	1.00378	−	0.842275i	0.987504	+	0.157592i	$0.0503731\pi$
$998$	5.42497			0.171724
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.r.325.2		12
3.2	odd	2	inner	729.2.e.r.325.1		12
9.2	odd	6		729.2.e.m.568.2		12
9.4	even	3		729.2.e.q.82.2		12
9.5	odd	6		729.2.e.q.82.1		12
9.7	even	3		729.2.e.m.568.1		12
27.2	odd	18		729.2.e.m.163.2		12
27.4	even	9		729.2.a.c.1.4	yes	6
27.5	odd	18		729.2.c.c.244.4		12
27.7	even	9		729.2.e.q.649.2		12
27.11	odd	18	inner	729.2.e.r.406.1		12
27.13	even	9		729.2.c.c.487.3		12
27.14	odd	18		729.2.c.c.487.4		12
27.16	even	9	inner	729.2.e.r.406.2		12
27.20	odd	18		729.2.e.q.649.1		12
27.22	even	9		729.2.c.c.244.3		12
27.23	odd	18		729.2.a.c.1.3	✓	6
27.25	even	9		729.2.e.m.163.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.c.1.3	✓	6	27.23	odd	18
729.2.a.c.1.4	yes	6	27.4	even	9
729.2.c.c.244.3		12	27.22	even	9
729.2.c.c.244.4		12	27.5	odd	18
729.2.c.c.487.3		12	27.13	even	9
729.2.c.c.487.4		12	27.14	odd	18
729.2.e.m.163.1		12	27.25	even	9
729.2.e.m.163.2		12	27.2	odd	18
729.2.e.m.568.1		12	9.7	even	3
729.2.e.m.568.2		12	9.2	odd	6
729.2.e.q.82.1		12	9.5	odd	6
729.2.e.q.82.2		12	9.4	even	3
729.2.e.q.649.1		12	27.20	odd	18
729.2.e.q.649.2		12	27.7	even	9
729.2.e.r.325.1		12	3.2	odd	2	inner
729.2.e.r.325.2		12	1.1	even	1	trivial
729.2.e.r.406.1		12	27.11	odd	18	inner
729.2.e.r.406.2		12	27.16	even	9	inner

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

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