LMFDB - Embedded newform 729.2.e.r.406.2

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			406.2
Root			$-0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.r.325.2

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

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

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	$-0.200025\pi$
$2$	0.524005	+	0.439693i	0.370528	+	0.310910i	−0.438443	+	0.898759i	$0.644470\pi$
$3$		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	$-0.464183\pi$
$5$	−0.984808	−	0.358441i	−0.440419	−	0.160300i	−0.552706	+	0.833376i	$0.686405\pi$
$6$		0			0
$7$	−0.0209445	+	0.118782i	−0.00791629	+	0.0448955i	−0.988510	−	0.151155i	$-0.951701\pi$
$7$	−0.0209445	+	0.118782i	−0.00791629	+	0.0448955i	0.980594	+	0.196051i	$0.0628118\pi$
$8$	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	$-0.305549\pi$
$11$	5.10602	−	1.85844i	1.53952	−	0.560341i	0.965931	+	0.258799i	$0.0833269\pi$
$12$		0			0
$13$	−3.50387	+	2.94010i	−0.971799	+	0.815436i	−0.982832	−	0.184503i	$-0.940932\pi$
$13$	−3.50387	+	2.94010i	−0.971799	+	0.815436i	0.0110331	+	0.999939i	$0.496488\pi$
$14$	−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	−0.995542	−	0.0943239i	$-0.969931\pi$
$17$	−2.38917	−	4.13816i	−0.579458	−	1.00365i	0.416084	−	0.909326i	$-0.363402\pi$
$18$		0			0
$19$	0.294263	−	0.509678i	0.0675085	−	0.116928i	−0.830295	−	0.557323i	$-0.811828\pi$
$19$	0.294263	−	0.509678i	0.0675085	−	0.116928i	0.897804	+	0.440395i	$0.145162\pi$
$20$	−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	−0.714852	−	0.699275i	$-0.753506\pi$
$23$	−1.35375	−	7.67752i	−0.282277	−	1.60087i	0.432575	−	0.901598i	$-0.357605\pi$
$24$		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	$-0.121774\pi$
$29$	3.88365	+	3.25877i	0.721176	+	0.605138i	−0.206534	+	0.978439i	$0.566219\pi$
$30$		0			0
$31$	−1.52094	−	8.62571i	−0.273170	−	1.54922i	−0.744716	−	0.667381i	$-0.767415\pi$
$31$	−1.52094	−	8.62571i	−0.273170	−	1.54922i	0.471547	−	0.881841i	$-0.343696\pi$
$32$	−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	0.941740	−	0.336342i	$-0.109190\pi$
$37$	1.09240	+	1.89209i	0.179589	+	0.311057i	−0.762151	+	0.647399i	$0.775857\pi$
$38$	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	$-0.521267\pi$
$41$	5.79006	−	4.85844i	0.904256	−	0.758761i	0.971018	+	0.239008i	$0.0768222\pi$
$42$		0			0
$43$	1.22668	−	0.446476i	0.187067	−	0.0680869i	−0.246788	−	0.969069i	$-0.579375\pi$
$43$	1.22668	−	0.446476i	0.187067	−	0.0680869i	0.433855	+	0.900983i	$0.357153\pi$
$44$	−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	−0.938799	−	0.344465i	$-0.888060\pi$
$47$	0.419550	−	2.37939i	0.0611976	−	0.347069i	0.999997	−	0.00260352i	$-0.000828726\pi$
$48$		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	0.344704	−	0.938711i	$-0.387979\pi$
$59$	0.0412527	+	0.0150147i	0.00537064	+	0.00195475i	−0.339333	+	0.940666i	$0.610201\pi$
$60$		0			0
$61$	−1.77332	+	10.0570i	−0.227050	+	1.28767i	0.631677	+	0.775232i	$0.282367\pi$
$61$	−1.77332	+	10.0570i	−0.227050	+	1.28767i	−0.858727	+	0.512434i	$0.828744\pi$
$62$	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	−0.725652	−	0.688062i	$-0.758462\pi$
$67$	−1.42468	+	1.19545i	−0.174052	+	0.146047i	0.551600	+	0.834109i	$0.314017\pi$
$68$	−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	$-0.0404127\pi$
$71$	3.25519	+	5.63816i	0.386320	+	0.669126i	−0.605631	+	0.795745i	$0.707079\pi$
$72$		0			0
$73$	−6.11721	+	10.5953i	−0.715965	+	1.24009i	0.246621	+	0.969112i	$0.420680\pi$
$73$	−6.11721	+	10.5953i	−0.715965	+	1.24009i	−0.962586	+	0.270976i	$0.912653\pi$
$74$	−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	0.672552	−	0.740050i	$-0.265198\pi$
$79$	0.538019	+	0.451451i	0.0605318	+	0.0507922i	−0.612020	+	0.790842i	$0.709643\pi$
$80$	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	$-0.156479\pi$
$83$	5.19118	+	4.35591i	0.569806	+	0.478124i	−0.311776	+	0.950156i	$0.600924\pi$
$84$		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	$-0.951700\pi$
$89$	−3.42782	+	5.93717i	−0.363349	+	0.629338i	0.625161	+	0.780496i	$0.285033\pi$
$90$		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	0.126668	−	0.991945i	$-0.459572\pi$
$97$	8.48293	−	3.08753i	0.861311	−	0.313491i	0.734643	+	0.678454i	$0.237350\pi$
$98$	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	−0.639179	−	0.769058i	$-0.720726\pi$
$101$	2.25606	−	12.7947i	0.224486	−	1.27312i	0.863665	−	0.504066i	$-0.168163\pi$
$102$		0			0
$103$	−8.52481	−	3.10278i	−0.839975	−	0.305726i	−0.114029	−	0.993477i	$-0.536376\pi$
$103$	−8.52481	−	3.10278i	−0.839975	−	0.305726i	−0.725946	+	0.687752i	$0.758598\pi$
$104$	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	0.798667	−	0.601773i	$-0.205539\pi$
$113$	10.8818	+	3.96064i	1.02367	+	0.372585i	0.225003	+	0.974358i	$0.427761\pi$
$114$		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	−0.289596	−	0.957149i	$-0.593521\pi$
$127$	7.70961	−	13.3534i	0.684117	−	1.18493i	0.973713	−	0.227777i	$-0.0731456\pi$
$128$	−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	0.901119	+	0.433572i	$0.142747\pi$
$131$	2.31926	+	13.1532i	0.202635	+	1.14920i	−0.698484	+	0.715625i	$0.746142\pi$
$132$		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	−0.992634	−	0.121156i	$-0.961340\pi$
$137$	−15.0326	−	12.6138i	−1.28432	−	1.07767i	−0.291684	−	0.956515i	$-0.594216\pi$
$138$		0			0
$139$	2.83157	+	16.0586i	0.240170	+	1.36207i	0.831447	+	0.555605i	$0.187513\pi$
$139$	2.83157	+	16.0586i	0.240170	+	1.36207i	−0.591276	+	0.806469i	$0.701376\pi$
$140$	−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	$-0.572743\pi$
$149$	8.46302	−	7.10132i	0.693318	−	0.581763i	0.919864	+	0.392238i	$0.128299\pi$
$150$		0			0
$151$	6.39053	−	2.32596i	0.520054	−	0.189284i	−0.0686380	−	0.997642i	$-0.521865\pi$
$151$	6.39053	−	2.32596i	0.520054	−	0.189284i	0.588692	+	0.808357i	$0.299643\pi$
$152$	−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	−0.380529	−	0.924769i	$-0.624258\pi$
$157$	−15.8687	−	5.77574i	−1.26646	−	0.460954i	−0.885932	+	0.463815i	$0.846480\pi$
$158$	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	$-0.356504\pi$
$167$	2.46669	+	0.897804i	0.190879	+	0.0694741i	−0.244812	+	0.969571i	$0.578726\pi$
$168$		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	$-0.777084\pi$
$173$	−12.3130	+	4.48158i	−0.936143	+	0.340728i	−0.171502	+	0.985184i	$0.554862\pi$
$174$		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	0.901251	+	0.433298i	$0.142650\pi$
$179$	11.0494	+	19.1382i	0.825872	+	1.43045i	−0.0753784	+	0.997155i	$0.524016\pi$
$180$		0			0
$181$	1.02956	−	1.78325i	0.0765268	−	0.132548i	−0.825222	−	0.564808i	$-0.808950\pi$
$181$	1.02956	−	1.78325i	0.0765268	−	0.132548i	0.901749	+	0.432260i	$0.142284\pi$
$182$	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	$-0.323413\pi$
$191$	−3.02525	−	2.53849i	−0.218899	−	0.183678i	−0.745643	+	0.666346i	$0.767857\pi$
$192$		0			0
$193$	−1.46673	−	8.31823i	−0.105577	−	0.598760i	−0.990988	−	0.133950i	$-0.957234\pi$
$193$	−1.46673	−	8.31823i	−0.105577	−	0.598760i	0.885411	−	0.464810i	$-0.153877\pi$
$194$	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	$-0.807281\pi$
$197$	1.14749	−	1.98751i	0.0817553	−	0.141604i	0.904004	+	0.427524i	$0.140614\pi$
$198$		0			0
$199$	11.7515	+	20.3542i	0.833042	+	1.44287i	0.895615	+	0.444830i	$0.146736\pi$
$199$	11.7515	+	20.3542i	0.833042	+	1.44287i	−0.0625736	+	0.998040i	$0.519931\pi$
$200$	−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	0.395385	−	0.918516i	$-0.370611\pi$
$211$	1.56670	+	0.570234i	0.107856	+	0.0392565i	−0.287528	+	0.957772i	$0.592834\pi$
$212$	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	0.873292	+	0.487198i	$0.161981\pi$
$223$	−1.70187	+	9.65177i	−0.113965	+	0.646330i	−0.987257	+	0.159133i	$0.949130\pi$
$224$	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	$-0.439368\pi$
$227$	14.5472	−	5.29473i	0.965528	−	0.351424i	0.776198	+	0.630490i	$0.217146\pi$
$228$		0			0
$229$	−8.62108	+	7.23395i	−0.569697	+	0.478033i	−0.881545	−	0.472099i	$-0.843496\pi$
$229$	−8.62108	+	7.23395i	−0.569697	+	0.478033i	0.311848	+	0.950132i	$0.399052\pi$
$230$	−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	$-0.111815\pi$
$233$	2.61738	+	4.53343i	0.171470	+	0.296995i	−0.767464	+	0.641092i	$0.778482\pi$
$234$		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	0.986349	+	0.164667i	$0.0526548\pi$
$239$	1.79028	+	10.1532i	0.115803	+	0.656754i	−0.870546	+	0.492087i	$0.836234\pi$
$240$		0			0
$241$	8.23055	+	6.90625i	0.530176	+	0.444871i	0.868162	−	0.496280i	$-0.165301\pi$
$241$	8.23055	+	6.90625i	0.530176	+	0.444871i	−0.337986	+	0.941151i	$0.609746\pi$
$242$	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	$-0.675530\pi$
$251$	7.53644	−	13.0535i	0.475696	−	0.823930i	0.999612	+	0.0278401i	$0.00886291\pi$
$252$		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	$-0.689178\pi$
$257$	2.54514	−	2.13563i	0.158762	−	0.133217i	0.718708	+	0.695312i	$0.244734\pi$
$258$		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	0.900216	+	0.435444i	$0.143409\pi$
$263$	−1.53482	+	8.70439i	−0.0946410	+	0.536736i	−0.994857	+	0.101292i	$0.967702\pi$
$264$		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	−0.998890	−	0.0471120i	$-0.984998\pi$
$277$	−0.734422	+	4.16512i	−0.0441272	+	0.250258i	0.954762	+	0.297370i	$0.0961093\pi$
$278$	−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	$-0.541222\pi$
$281$	6.86175	−	2.49747i	0.409338	−	0.148987i	0.538478	+	0.842640i	$0.318999\pi$
$282$		0			0
$283$	12.2724	−	10.2978i	0.729521	−	0.612141i	−0.200480	−	0.979698i	$-0.564250\pi$
$283$	12.2724	−	10.2978i	0.729521	−	0.612141i	0.930001	+	0.367557i	$0.119806\pi$
$284$	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	−0.928938	−	0.370235i	$-0.879277\pi$
$293$	−3.12646	−	17.7310i	−0.182650	−	1.03586i	0.746289	−	0.665622i	$-0.231834\pi$
$294$		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	0.991845	−	0.127448i	$-0.0406787\pi$
$307$	6.75537	+	11.7006i	0.385549	+	0.667791i	−0.606296	+	0.795239i	$0.707345\pi$
$308$	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	$-0.876387\pi$
$311$	−12.5802	+	10.5560i	−0.713357	+	0.598577i	0.212182	+	0.977230i	$0.431943\pi$
$312$		0			0
$313$	18.3849	−	6.69156i	1.03918	−	0.378229i	0.234608	−	0.972090i	$-0.424619\pi$
$313$	18.3849	−	6.69156i	1.03918	−	0.378229i	0.804568	+	0.593861i	$0.202397\pi$
$314$	−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	−0.598945	−	0.800790i	$-0.704413\pi$
$317$	4.23329	−	24.0082i	0.237766	−	1.34844i	0.836711	−	0.547645i	$-0.184476\pi$
$318$		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	−0.476294	−	0.879286i	$-0.658020\pi$
$331$	4.94878	−	28.0659i	0.272009	−	1.54264i	0.748304	−	0.663356i	$-0.230869\pi$
$332$	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	−0.929594	−	0.368586i	$-0.879842\pi$
$337$	−13.3648	+	11.2144i	−0.728029	+	0.610889i	0.201564	+	0.979475i	$0.435397\pi$
$338$	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	−0.843013	−	0.537893i	$-0.819221\pi$
$347$	−4.37403	−	24.8063i	−0.234810	−	1.33167i	0.608203	−	0.793781i	$-0.291891\pi$
$348$		0			0
$349$	−9.07919	−	7.61835i	−0.485998	−	0.407801i	0.366591	−	0.930382i	$-0.380525\pi$
$349$	−9.07919	−	7.61835i	−0.485998	−	0.407801i	−0.852589	+	0.522581i	$0.824969\pi$
$350$	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	$-0.206037\pi$
$353$	6.43285	+	5.39780i	0.342386	+	0.287296i	−0.455338	+	0.890319i	$0.650482\pi$
$354$		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	$-0.811138\pi$
$359$	1.32012	−	2.28652i	0.0696735	−	0.120678i	0.898758	+	0.438446i	$0.144471\pi$
$360$		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	−0.557597	−	0.830112i	$-0.688277\pi$
$367$	−8.64290	+	3.14576i	−0.451156	+	0.164207i	0.106441	+	0.994319i	$0.466054\pi$
$368$	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	0.898147	−	0.439696i	$-0.144914\pi$
$373$	25.1755	+	9.16312i	1.30354	+	0.474448i	0.405389	+	0.914144i	$0.367136\pi$
$374$	−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	$-0.731054\pi$
$383$	−32.3506	−	11.7747i	−1.65304	−	0.601657i	−0.989246	+	0.146259i	$0.953277\pi$
$384$		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	$-0.617217\pi$
$389$	−0.710966	+	0.258770i	−0.0360474	+	0.0131202i	0.323934	+	0.946080i	$0.394995\pi$
$390$		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	−0.940457	−	0.339914i	$-0.889602\pi$
$397$	−3.50387	+	6.06888i	−0.175854	+	0.304588i	0.764602	+	0.644502i	$0.222935\pi$
$398$	−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	−0.997973	−	0.0636460i	$-0.979727\pi$
$401$	−1.64111	−	9.30722i	−0.0819533	−	0.464780i	0.916019	−	0.401134i	$-0.131384\pi$
$402$		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	0.999290	−	0.0376849i	$-0.0119983\pi$
$409$	0.958111	+	5.43372i	0.0473755	+	0.268680i	−0.951914	+	0.306365i	$0.900887\pi$
$410$	−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	$-0.725848\pi$
$419$	−0.357267	+	0.299782i	−0.0174536	+	0.0146453i	0.634019	+	0.773317i	$0.281404\pi$
$420$		0			0
$421$	2.26857	−	0.825692i	0.110563	−	0.0402418i	−0.286146	−	0.958186i	$-0.592374\pi$
$421$	2.26857	−	0.825692i	0.110563	−	0.0402418i	0.396709	+	0.917944i	$0.370152\pi$
$422$	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	0.924116	+	0.382113i	$0.124804\pi$
$439$	−1.57057	+	8.90717i	−0.0749594	+	0.425116i	−0.999075	+	0.0430028i	$0.986308\pi$
$440$	−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	$-0.646551\pi$
$443$	−4.39506	+	1.59967i	−0.208815	+	0.0760026i	0.235495	+	0.971876i	$0.424329\pi$
$444$		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	−0.987513	−	0.157537i	$-0.949645\pi$
$449$	−13.3534	−	23.1288i	−0.630187	−	1.09152i	0.357326	−	0.933980i	$-0.383689\pi$
$450$		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	0.630927	−	0.775843i	$-0.282675\pi$
$457$	−0.503870	−	0.422797i	−0.0235701	−	0.0197776i	−0.654497	+	0.756065i	$0.727119\pi$
$458$	−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	$-0.437916\pi$
$461$	−15.8600	−	13.3081i	−0.738672	−	0.619820i	−0.932481	+	0.361220i	$0.882360\pi$
$462$		0			0
$463$	−4.31062	−	24.4468i	−0.200332	−	1.13614i	−0.904619	−	0.426222i	$-0.859844\pi$
$463$	−4.31062	−	24.4468i	−0.200332	−	1.13614i	0.704287	−	0.709915i	$-0.251267\pi$
$464$	−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	−0.372868	−	0.927884i	$-0.621625\pi$
$467$	13.3365	−	23.0994i	0.617138	−	1.06891i	0.990005	−	0.141029i	$-0.0450412\pi$
$468$		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	$-0.920960\pi$
$479$	0.560282	−	3.17752i	0.0255999	−	0.145185i	0.994929	+	0.100584i	$0.0320710\pi$
$480$		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	$-0.263216\pi$
$491$	16.0180	+	5.83006i	0.722880	+	0.263107i	0.0457323	+	0.998954i	$0.485438\pi$
$492$		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	−0.496595	−	0.867983i	$-0.665416\pi$
$499$	6.07532	−	5.09780i	0.271969	−	0.228209i	0.768563	+	0.639774i	$0.220972\pi$
$500$	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	0.997807	+	0.0661881i	$0.0210837\pi$
$503$	12.4748	+	21.6070i	0.556224	+	0.963409i	−0.441583	+	0.897220i	$0.645583\pi$
$504$		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	0.591300	+	0.806451i	$0.298615\pi$
$509$	7.02736	+	39.8542i	0.311482	+	1.76650i	−0.279818	+	0.960053i	$0.590274\pi$
$510$		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	−0.442166	−	0.896933i	$-0.645790\pi$
$521$	12.6837	−	21.9688i	0.555684	−	0.962473i	0.997850	−	0.0655394i	$-0.0208768\pi$
$522$		0			0
$523$	−6.36097	−	11.0175i	−0.278146	−	0.481762i	0.692778	−	0.721151i	$-0.256386\pi$
$523$	−6.36097	−	11.0175i	−0.278146	−	0.481762i	−0.970924	+	0.239388i	$0.923053\pi$
$524$	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	−0.969313	−	0.245831i	$-0.920939\pi$
$547$	0.599260	−	3.39857i	0.0256225	−	0.145312i	0.994935	+	0.100519i	$0.0320502\pi$
$548$	−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	$-0.242231\pi$
$557$	−5.55017	−	9.61318i	−0.235168	−	0.407323i	−0.959322	+	0.282316i	$0.908897\pi$
$558$		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	−0.934725	−	0.355372i	$-0.884354\pi$
$563$	−4.22150	−	23.9413i	−0.177915	−	1.00901i	0.756810	−	0.653635i	$-0.226757\pi$
$564$		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	−0.971606	−	0.236603i	$-0.923966\pi$
$569$	−32.7591	−	27.4881i	−1.37333	−	1.15236i	−0.401726	−	0.915760i	$-0.631590\pi$
$570$		0			0
$571$	3.13058	+	17.7544i	0.131011	+	0.742998i	0.977555	+	0.210680i	$0.0675678\pi$
$571$	3.13058	+	17.7544i	0.131011	+	0.742998i	−0.846545	+	0.532318i	$0.821321\pi$
$572$	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	−0.999536	−	0.0304438i	$-0.990308\pi$
$577$	−12.6382	−	21.8899i	−0.526133	−	0.911290i	0.473403	−	0.880846i	$-0.343025\pi$
$578$	−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	0.693123	+	0.720819i	$0.256234\pi$
$587$	−4.96032	+	28.1313i	−0.204734	+	1.16111i	−0.897858	+	0.440286i	$0.854877\pi$
$588$		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	0.0488454	−	0.998806i	$-0.484446\pi$
$599$	−13.6019	−	4.95067i	−0.555757	−	0.202279i	−0.604603	+	0.796527i	$0.706668\pi$
$600$		0			0
$601$	−2.31908	+	13.1521i	−0.0945972	+	0.536487i	0.900273	+	0.435326i	$0.143367\pi$
$601$	−2.31908	+	13.1521i	−0.0945972	+	0.536487i	−0.994870	+	0.101161i	$0.967744\pi$
$602$	−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	−0.0121281	−	0.999926i	$-0.503861\pi$
$607$	23.9106	−	20.0634i	0.970501	−	0.814347i	0.982629	+	0.185579i	$0.0594161\pi$
$608$	−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	0.384547	+	0.923105i	$0.374358\pi$
$613$	−15.0326	+	26.0372i	−0.607159	+	1.05163i	−0.991706	+	0.128525i	$0.958976\pi$
$614$	−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	0.668466	+	0.743743i	$0.266951\pi$
$617$	7.31991	+	41.5133i	0.294688	+	1.67126i	−0.373778	+	0.927518i	$0.621938\pi$
$618$		0			0
$619$	8.89440	+	7.46329i	0.357496	+	0.299975i	0.803792	−	0.594911i	$-0.202813\pi$
$619$	8.89440	+	7.46329i	0.357496	+	0.299975i	−0.446296	+	0.894886i	$0.647257\pi$
$620$	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	0.995071	+	0.0991657i	$0.0316174\pi$
$631$	14.6552	+	25.3836i	0.583415	+	1.01051i	−0.411655	+	0.911340i	$0.635049\pi$
$632$	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	−0.670558	−	0.741857i	$-0.733945\pi$
$641$	5.40009	−	30.6254i	0.213291	−	1.20963i	0.883848	−	0.467774i	$-0.154944\pi$
$642$		0			0
$643$	−39.5347	−	14.3894i	−1.55910	−	0.567464i	−0.588566	−	0.808449i	$-0.700307\pi$
$643$	−39.5347	−	14.3894i	−1.55910	−	0.567464i	−0.970529	+	0.240985i	$0.922530\pi$
$644$	−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	0.398822	−	0.917028i	$-0.369419\pi$
$653$	2.93572	+	1.06851i	0.114884	+	0.0418142i	−0.283939	+	0.958842i	$0.591641\pi$
$654$		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	$-0.871134\pi$
$659$	−35.1719	+	12.8015i	−1.37010	+	0.498677i	−0.450941	+	0.892554i	$0.648911\pi$
$660$		0			0
$661$	20.3004	−	17.0341i	0.789594	−	0.662548i	−0.156051	−	0.987749i	$-0.549876\pi$
$661$	20.3004	−	17.0341i	0.789594	−	0.662548i	0.945645	+	0.325201i	$0.105432\pi$
$662$	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	0.667843	−	0.744302i	$-0.267218\pi$
$673$	1.31836	+	1.10624i	0.0508191	+	0.0426423i	−0.617024	+	0.786944i	$0.711662\pi$
$674$	−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	$-0.460652\pi$
$677$	−21.6631	−	18.1775i	−0.832581	−	0.698619i	−0.955882	+	0.293751i	$0.905096\pi$
$678$		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	$-0.990099\pi$
$683$	−12.3569	+	21.4029i	−0.472825	+	0.818958i	0.526691	+	0.850057i	$0.323433\pi$
$684$		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	0.592940	−	0.805246i	$-0.297967\pi$
$691$	41.1327	−	14.9711i	1.56476	−	0.569527i	0.971821	+	0.235720i	$0.0757448\pi$
$692$	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	−0.963784	−	0.266684i	$-0.914072\pi$
$709$	0.881034	−	4.99659i	0.0330879	−	0.187651i	0.996872	+	0.0790328i	$0.0251832\pi$
$710$	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	$-0.198398\pi$
$719$	−2.66858	−	4.62212i	−0.0995213	−	0.172376i	−0.911487	+	0.411330i	$0.865064\pi$
$720$		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	0.993571	−	0.113212i	$-0.0361138\pi$
$727$	28.4354	+	23.8601i	1.05461	+	0.884924i	0.0610401	+	0.998135i	$0.480558\pi$
$728$	−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	0.916529	+	0.399968i	$0.130979\pi$
$733$	5.20011	+	29.4913i	0.192071	+	1.08929i	−0.724459	+	0.689318i	$0.757910\pi$
$734$	−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	0.999533	+	0.0305431i	$0.00972368\pi$
$739$	14.3050	+	24.7770i	0.526218	+	0.911436i	−0.473316	+	0.880893i	$0.656943\pi$
$740$	−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	−0.431955	+	0.901895i	$0.642176\pi$
$743$	−38.0292	+	31.9103i	−1.39516	+	1.17068i	−0.963202	+	0.268780i	$0.913380\pi$
$744$		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	0.821532	−	0.570162i	$-0.193120\pi$
$751$	29.7165	+	10.8159i	1.08437	+	0.394678i	0.262837	+	0.964840i	$0.415342\pi$
$752$	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	$-0.147619\pi$
$761$	35.6410	+	12.9722i	1.29198	+	0.470244i	0.397606	+	0.917556i	$0.369841\pi$
$762$		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	−0.879380	−	0.476120i	$-0.842043\pi$
$769$	−15.6179	+	13.1050i	−0.563197	+	0.472578i	0.316184	+	0.948698i	$0.397598\pi$
$770$	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	$-0.0216461\pi$
$773$	12.2332	+	21.1885i	0.439997	+	0.762097i	−0.557692	+	0.830048i	$0.688313\pi$
$774$		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	0.847641	+	0.530570i	$0.178022\pi$
$787$	6.52481	+	37.0041i	0.232585	+	1.31905i	−0.615057	+	0.788483i	$0.710867\pi$
$788$	−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	−0.673524	−	0.739166i	$-0.735220\pi$
$797$	−1.76568	+	1.48158i	−0.0625436	+	0.0524803i	0.610980	+	0.791646i	$0.290776\pi$
$798$		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	−0.0214353	−	0.999770i	$-0.506824\pi$
$821$	17.3289	−	6.30722i	0.604784	−	0.220123i	0.626220	+	0.779647i	$0.284601\pi$
$822$		0			0
$823$	−26.6327	+	22.3475i	−0.928357	+	0.778984i	−0.975522	−	0.219903i	$-0.929426\pi$
$823$	−26.6327	+	22.3475i	−0.928357	+	0.778984i	0.0471645	+	0.998887i	$0.484982\pi$
$824$	−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	−0.996576	−	0.0826770i	$-0.973653\pi$
$827$	−16.3886	−	28.3859i	−0.569889	−	0.987076i	0.426688	−	0.904399i	$-0.359680\pi$
$828$		0			0
$829$	−2.67634	+	4.63555i	−0.0929530	+	0.160999i	−0.908752	−	0.417336i	$-0.862964\pi$
$829$	−2.67634	+	4.63555i	−0.0929530	+	0.160999i	0.815799	+	0.578335i	$0.196297\pi$
$830$	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	0.568035	−	0.823004i	$-0.307704\pi$
$839$	−4.16604	−	3.49572i	−0.143828	−	0.120686i	−0.711863	+	0.702319i	$0.752148\pi$
$840$		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	0.555830	−	0.831296i	$-0.312400\pi$
$853$	44.2756	−	16.1150i	1.51597	−	0.551767i	0.960137	+	0.279529i	$0.0901782\pi$
$854$	−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	−0.448994	−	0.893535i	$-0.648217\pi$
$857$	8.15382	−	46.2426i	0.278529	−	1.57962i	0.727523	−	0.686083i	$-0.240671\pi$
$858$		0			0
$859$	−6.73143	−	2.45004i	−0.229673	−	0.0835943i	0.224620	−	0.974446i	$-0.427886\pi$
$859$	−6.73143	−	2.45004i	−0.229673	−	0.0835943i	−0.454293	+	0.890852i	$0.650108\pi$
$860$	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	−0.530932	−	0.847415i	$-0.678158\pi$
$877$	6.26083	−	5.25346i	0.211413	−	0.177397i	0.742345	+	0.670018i	$0.233714\pi$
$878$	−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	−0.997514	−	0.0704686i	$-0.977551\pi$
$881$	−16.6153	−	28.7786i	−0.559785	−	0.969575i	0.437729	−	0.899107i	$-0.355783\pi$
$882$		0			0
$883$	−16.5239	+	28.6203i	−0.556075	+	0.963150i	0.441744	+	0.897141i	$0.354360\pi$
$883$	−16.5239	+	28.6203i	−0.556075	+	0.963150i	−0.997819	+	0.0660087i	$0.978973\pi$
$884$	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	0.686657	+	0.726982i	$0.259078\pi$
$887$	8.63851	+	48.9914i	0.290053	+	1.64497i	−0.396604	+	0.917990i	$0.629811\pi$
$888$		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	−0.819156	−	0.573571i	$-0.805558\pi$
$907$	−32.4650	+	11.8163i	−1.07798	+	0.392353i	−0.258826	+	0.965924i	$0.583336\pi$
$908$	−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	−0.920122	−	0.391633i	$-0.871910\pi$
$911$	2.36802	−	13.4297i	0.0784561	−	0.444947i	0.998578	−	0.0533142i	$-0.0169785\pi$
$912$		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	−0.255341	−	0.966851i	$-0.582188\pi$
$929$	5.19788	−	1.89187i	0.170537	−	0.0620704i	0.425878	+	0.904781i	$0.359965\pi$
$930$		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	−0.857793	−	0.513995i	$-0.828165\pi$
$937$	0.497007	−	0.860841i	0.0162365	−	0.0281225i	0.874029	+	0.485873i	$0.161498\pi$
$938$	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	−0.999911	−	0.0133162i	$-0.995761\pi$
$941$	−1.98952	−	11.2831i	−0.0648564	−	0.367819i	0.935055	−	0.354503i	$-0.115350\pi$
$942$		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	0.999345	−	0.0361872i	$-0.0115213\pi$
$947$	34.9968	+	29.3658i	1.13724	+	0.954259i	0.137897	+	0.990447i	$0.455966\pi$
$948$		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	−0.959254	−	0.282545i	$-0.908822\pi$
$953$	−7.25265	+	12.5620i	−0.234936	+	0.406922i	0.724318	+	0.689466i	$0.242155\pi$
$954$		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	0.691370	−	0.722501i	$-0.257008\pi$
$967$	23.5269	+	8.56310i	0.756575	+	0.275371i	0.0652053	+	0.997872i	$0.479230\pi$
$968$	−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	0.304573	−	0.952489i	$-0.401486\pi$
$977$	−2.32423	−	0.845952i	−0.0743589	−	0.0270644i	−0.378932	+	0.925425i	$0.623708\pi$
$978$		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	−0.0394052	−	0.999223i	$-0.512546\pi$
$983$	17.9557	−	6.53533i	0.572697	−	0.208445i	0.612102	+	0.790779i	$0.290324\pi$
$984$		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	−0.382894	−	0.923792i	$-0.625072\pi$
$991$	19.1582	−	33.1830i	0.608581	−	1.05409i	0.991475	−	0.130301i	$-0.0415943\pi$
$992$	−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	0.987504	−	0.157592i	$-0.0503731\pi$
$997$	31.6948	+	26.5951i	1.00378	+	0.842275i	0.0162804	+	0.999867i	$0.494818\pi$
$998$	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.406.2		12
3.2	odd	2	inner	729.2.e.r.406.1		12
9.2	odd	6		729.2.e.q.649.1		12
9.4	even	3		729.2.e.m.163.1		12
9.5	odd	6		729.2.e.m.163.2		12
9.7	even	3		729.2.e.q.649.2		12
27.2	odd	18		729.2.c.c.244.4		12
27.4	even	9		729.2.e.q.82.2		12
27.5	odd	18	inner	729.2.e.r.325.1		12
27.7	even	9		729.2.a.c.1.4	yes	6
27.11	odd	18		729.2.c.c.487.4		12
27.13	even	9		729.2.e.m.568.1		12
27.14	odd	18		729.2.e.m.568.2		12
27.16	even	9		729.2.c.c.487.3		12
27.20	odd	18		729.2.a.c.1.3	✓	6
27.22	even	9	inner	729.2.e.r.325.2		12
27.23	odd	18		729.2.e.q.82.1		12
27.25	even	9		729.2.c.c.244.3		12

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

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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