LMFDB - Embedded newform 729.2.e.r.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.r.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	0.438443	−	0.898759i	$-0.355530\pi$
$2$	−0.524005	−	0.439693i	−0.370528	−	0.310910i	−0.808970	+	0.587850i	$0.799975\pi$
$3$		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	$-0.313595\pi$
$5$	0.984808	+	0.358441i	0.440419	+	0.160300i	−0.112287	+	0.993676i	$0.535817\pi$
$6$		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	−0.965931	−	0.258799i	$-0.916673\pi$
$11$	−5.10602	+	1.85844i	−1.53952	+	0.560341i	−0.573593	+	0.819140i	$0.694451\pi$
$12$		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	$0.0300689\pi$
$17$	2.38917	+	4.13816i	0.579458	+	1.00365i	−0.416084	+	0.909326i	$0.636598\pi$
$18$		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	$0.246494\pi$
$23$	1.35375	+	7.67752i	0.282277	+	1.60087i	−0.432575	+	0.901598i	$0.642395\pi$
$24$		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	$-0.433781\pi$
$29$	−3.88365	−	3.25877i	−0.721176	−	0.605138i	−0.927710	+	0.373301i	$0.878226\pi$
$30$		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	−0.971018	−	0.239008i	$-0.923178\pi$
$41$	−5.79006	+	4.85844i	−0.904256	+	0.758761i	0.0667615	+	0.997769i	$0.478733\pi$
$42$		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	$0.111940\pi$
$47$	−0.419550	+	2.37939i	−0.0611976	+	0.347069i	−0.999997	+	0.00260352i	$0.999171\pi$
$48$		0			0
$49$	6.56418	+	2.38917i	0.937740	+	0.341309i
$50$	0.463450	+	2.62836i	0.0655417	+	0.371706i
$51$		0			0
$52$	5.36824	+	4.50449i	0.744441	+	0.624660i
$53$	3.04628			0.418439			0.209219	−	0.977869i	$-0.432908\pi$
$53$	3.04628			0.418439			0.209219	+	0.977869i	$0.432908\pi$
$54$		0			0
$55$	−5.69459			−0.767859
$56$	−0.223238	−	0.187319i	−0.0298314	−	0.0250315i
$57$		0			0
$58$	0.602196	+	3.41523i	0.0790723	+	0.448441i
$59$	−0.0412527	−	0.0150147i	−0.00537064	−	0.00195475i	0.339333	−	0.940666i	$-0.389799\pi$
$59$	−0.0412527	−	0.0150147i	−0.00537064	−	0.00195475i	−0.344704	+	0.938711i	$0.612021\pi$
$60$		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	0.605631	−	0.795745i	$-0.292921\pi$
$71$	−3.25519	−	5.63816i	−0.386320	−	0.669126i	−0.991951	+	0.126619i	$0.959587\pi$
$72$		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	0.311776	−	0.950156i	$-0.399076\pi$
$83$	−5.19118	−	4.35591i	−0.569806	−	0.478124i	−0.881581	+	0.472032i	$0.843521\pi$
$84$		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	$-0.714967\pi$
$89$	3.42782	−	5.93717i	0.363349	−	0.629338i	0.988510	+	0.151157i	$0.0483000\pi$
$90$		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	$0.279274\pi$
$101$	−2.25606	+	12.7947i	−0.224486	+	1.27312i	−0.863665	+	0.504066i	$0.831837\pi$
$102$		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	$-0.685519\pi$
$107$	−11.3865			−1.10077			−0.550386	+	0.834911i	$0.685519\pi$
$108$		0			0
$109$	2.89899			0.277672			0.138836	−	0.990315i	$-0.455664\pi$
$109$	2.89899			0.277672			0.138836	+	0.990315i	$0.455664\pi$
$110$	2.98400	+	2.50387i	0.284513	+	0.238735i
$111$		0			0
$112$	−0.0295627	−	0.167658i	−0.00279341	−	0.0158422i
$113$	−10.8818	−	3.96064i	−1.02367	−	0.372585i	−0.225003	−	0.974358i	$-0.572239\pi$
$113$	−10.8818	−	3.96064i	−1.02367	−	0.372585i	−0.798667	+	0.601773i	$0.794461\pi$
$114$		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	$-0.857253\pi$
$131$	−2.31926	−	13.1532i	−0.202635	−	1.14920i	0.698484	−	0.715625i	$-0.253858\pi$
$132$		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	$0.0386600\pi$
$137$	15.0326	+	12.6138i	1.28432	+	1.07767i	0.291684	+	0.956515i	$0.405784\pi$
$138$		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	−0.919864	−	0.392238i	$-0.871701\pi$
$149$	−8.46302	+	7.10132i	−0.693318	+	0.581763i	0.226546	+	0.974000i	$0.427257\pi$
$150$		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	0.244812	−	0.969571i	$-0.421274\pi$
$167$	−2.46669	−	0.897804i	−0.190879	−	0.0694741i	−0.435691	+	0.900096i	$0.643496\pi$
$168$		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	$-0.445138\pi$
$173$	12.3130	−	4.48158i	0.936143	−	0.340728i	0.764642	+	0.644455i	$0.222916\pi$
$174$		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	$-0.857350\pi$
$179$	−11.0494	−	19.1382i	−0.825872	−	1.43045i	0.0753784	−	0.997155i	$-0.475984\pi$
$180$		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	0.745643	−	0.666346i	$-0.232143\pi$
$191$	3.02525	+	2.53849i	0.218899	+	0.183678i	−0.526743	+	0.850024i	$0.676587\pi$
$192$		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	−0.904004	−	0.427524i	$-0.859386\pi$
$197$	−1.14749	+	1.98751i	−0.0817553	+	0.141604i	0.822249	+	0.569128i	$0.192719\pi$
$198$		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	−0.776198	−	0.630490i	$-0.782854\pi$
$227$	−14.5472	+	5.29473i	−0.965528	+	0.351424i	−0.189331	+	0.981913i	$0.560632\pi$
$228$		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	0.767464	−	0.641092i	$-0.221518\pi$
$233$	−2.61738	−	4.53343i	−0.171470	−	0.296995i	−0.938934	+	0.344097i	$0.888185\pi$
$234$		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	$-0.947345\pi$
$239$	−1.79028	−	10.1532i	−0.115803	−	0.656754i	0.870546	−	0.492087i	$-0.163766\pi$
$240$		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	−0.999612	−	0.0278401i	$-0.991137\pi$
$251$	−7.53644	+	13.0535i	−0.475696	+	0.823930i	0.523916	+	0.851770i	$0.324470\pi$
$252$		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	$-0.755266\pi$
$257$	−2.54514	+	2.13563i	−0.158762	+	0.133217i	0.559946	+	0.828529i	$0.310822\pi$
$258$		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	$-0.856591\pi$
$263$	1.53482	−	8.70439i	0.0946410	−	0.536736i	0.994857	−	0.101292i	$-0.0322975\pi$
$264$		0			0
$265$	3.00000	+	1.09191i	0.184289	+	0.0670755i
$266$	−0.00843175	−	0.0478189i	−0.000516984	−	0.00293196i
$267$		0			0
$268$	2.18273	+	1.83153i	0.133332	+	0.111879i
$269$	8.09267			0.493419			0.246709	−	0.969090i	$-0.420651\pi$
$269$	8.09267			0.493419			0.246709	+	0.969090i	$0.420651\pi$
$270$		0			0
$271$	−19.0000			−1.15417			−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000			−1.15417			−0.577084	+	0.816685i	$0.695809\pi$
$272$	−5.16658	−	4.33527i	−0.313270	−	0.262865i
$273$		0			0
$274$	−2.33094	−	13.2194i	−0.140817	−	0.798613i
$275$	19.9220	+	7.25103i	1.20134	+	0.437254i
$276$		0			0
$277$	−0.734422	+	4.16512i	−0.0441272	+	0.250258i	−0.998890	−	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	−0.538478	−	0.842640i	$-0.681001\pi$
$281$	−6.86175	+	2.49747i	−0.409338	+	0.148987i	0.129140	+	0.991626i	$0.458778\pi$
$282$		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	$0.120723\pi$
$293$	3.12646	+	17.7310i	0.182650	+	1.03586i	−0.746289	+	0.665622i	$0.768166\pi$
$294$		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	−0.212182	−	0.977230i	$-0.568057\pi$
$311$	12.5802	−	10.5560i	0.713357	−	0.598577i	0.925539	+	0.378653i	$0.123613\pi$
$312$		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	$0.295587\pi$
$317$	−4.23329	+	24.0082i	−0.237766	+	1.34844i	−0.836711	+	0.547645i	$0.815524\pi$
$318$		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	$0.180779\pi$
$347$	4.37403	+	24.8063i	0.234810	+	1.33167i	−0.608203	+	0.793781i	$0.708109\pi$
$348$		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	0.455338	−	0.890319i	$-0.349518\pi$
$353$	−6.43285	−	5.39780i	−0.342386	−	0.287296i	−0.797724	+	0.603023i	$0.793963\pi$
$354$		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	$-0.855529\pi$
$359$	−1.32012	+	2.28652i	−0.0696735	+	0.120678i	0.829084	+	0.559124i	$0.188862\pi$
$360$		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	0.989246	−	0.146259i	$-0.0467233\pi$
$383$	32.3506	+	11.7747i	1.65304	+	0.601657i	0.663793	+	0.747916i	$0.268946\pi$
$384$		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	$-0.605005\pi$
$389$	0.710966	−	0.258770i	0.0360474	−	0.0131202i	0.359981	+	0.932960i	$0.382783\pi$
$390$		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	$0.0202728\pi$
$401$	1.64111	+	9.30722i	0.0819533	+	0.464780i	−0.916019	+	0.401134i	$0.868616\pi$
$402$		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	−0.634019	−	0.773317i	$-0.718596\pi$
$419$	0.357267	−	0.299782i	0.0174536	−	0.0146453i	0.651473	+	0.758672i	$0.274152\pi$
$420$		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	$-0.594120\pi$
$431$	−12.0992			−0.582796			−0.291398	+	0.956602i	$0.594120\pi$
$432$		0			0
$433$	33.3509			1.60274			0.801371	−	0.598167i	$-0.204104\pi$
$433$	33.3509			1.60274			0.801371	+	0.598167i	$0.204104\pi$
$434$	−0.553579	−	0.464508i	−0.0265726	−	0.0222971i
$435$		0			0
$436$	−0.771259	−	4.37403i	−0.0369366	−	0.209478i
$437$	4.31142	+	1.56923i	0.206243	+	0.0750665i
$438$		0			0
$439$	−1.57057	+	8.90717i	−0.0749594	+	0.425116i	0.924116	+	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	−0.235495	−	0.971876i	$-0.575671\pi$
$443$	4.39506	−	1.59967i	0.208815	−	0.0760026i	0.444310	+	0.895873i	$0.353449\pi$
$444$		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	$0.0503553\pi$
$449$	13.3534	+	23.1288i	0.630187	+	1.09152i	−0.357326	+	0.933980i	$0.616311\pi$
$450$		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	0.932481	−	0.361220i	$-0.117640\pi$
$461$	15.8600	+	13.3081i	0.738672	+	0.619820i	−0.193808	+	0.981039i	$0.562084\pi$
$462$		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	$0.378375\pi$
$467$	−13.3365	+	23.0994i	−0.617138	+	1.06891i	−0.990005	+	0.141029i	$0.954959\pi$
$468$		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	$-0.967929\pi$
$479$	−0.560282	+	3.17752i	−0.0255999	+	0.145185i	0.969329	+	0.245768i	$0.0790402\pi$
$480$		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	$-0.514562\pi$
$491$	−16.0180	−	5.83006i	−0.722880	−	0.263107i	−0.677148	+	0.735847i	$0.736784\pi$
$492$		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	$-0.978916\pi$
$503$	−12.4748	−	21.6070i	−0.556224	−	0.963409i	0.441583	−	0.897220i	$-0.354417\pi$
$504$		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	$-0.701385\pi$
$509$	−7.02736	−	39.8542i	−0.311482	−	1.76650i	0.279818	−	0.960053i	$-0.409726\pi$
$510$		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	$0.354210\pi$
$521$	−12.6837	+	21.9688i	−0.555684	+	0.962473i	−0.997850	+	0.0655394i	$0.979123\pi$
$522$		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	0.959322	−	0.282316i	$-0.0911025\pi$
$557$	5.55017	+	9.61318i	0.235168	+	0.407323i	−0.724153	+	0.689639i	$0.757769\pi$
$558$		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	$0.115646\pi$
$563$	4.22150	+	23.9413i	0.177915	+	1.00901i	−0.756810	+	0.653635i	$0.773243\pi$
$564$		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	$0.0760340\pi$
$569$	32.7591	+	27.4881i	1.37333	+	1.15236i	0.401726	+	0.915760i	$0.368410\pi$
$570$		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	$-0.743766\pi$
$587$	4.96032	−	28.1313i	0.204734	−	1.16111i	0.897858	−	0.440286i	$-0.145123\pi$
$588$		0			0
$589$	−4.84389	−	1.76303i	−0.199589	−	0.0726445i
$590$	0.00546492	+	0.0309931i	0.000224987	+	0.00127597i
$591$		0			0
$592$	−2.36231	−	1.98221i	−0.0970904	−	0.0814685i
$593$	20.6009			0.845977			0.422989	−	0.906135i	$-0.360981\pi$
$593$	20.6009			0.845977			0.422989	+	0.906135i	$0.360981\pi$
$594$		0			0
$595$	−0.604007			−0.0247619
$596$	12.9661	+	10.8799i	0.531112	+	0.445656i
$597$		0			0
$598$	4.23560	+	24.0213i	0.173207	+	0.982304i
$599$	13.6019	+	4.95067i	0.555757	+	0.202279i	0.604603	−	0.796527i	$-0.293332\pi$
$599$	13.6019	+	4.95067i	0.555757	+	0.202279i	−0.0488454	+	0.998806i	$0.515554\pi$
$600$		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	$-0.733049\pi$
$617$	−7.31991	−	41.5133i	−0.294688	−	1.67126i	0.373778	−	0.927518i	$-0.378062\pi$
$618$		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	$0.266055\pi$
$641$	−5.40009	+	30.6254i	−0.213291	+	1.20963i	−0.883848	+	0.467774i	$0.845056\pi$
$642$		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	$-0.470756\pi$
$647$	4.66717			0.183485			0.0917427	+	0.995783i	$0.470756\pi$
$648$		0			0
$649$	0.238541			0.00936356
$650$	−9.35149	−	7.84683i	−0.366796	−	0.307778i
$651$		0			0
$652$	−2.23783	−	12.6913i	−0.0876400	−	0.497031i
$653$	−2.93572	−	1.06851i	−0.114884	−	0.0418142i	0.283939	−	0.958842i	$-0.408359\pi$
$653$	−2.93572	−	1.06851i	−0.114884	−	0.0418142i	−0.398822	+	0.917028i	$0.630581\pi$
$654$		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	$-0.351089\pi$
$659$	35.1719	−	12.8015i	1.37010	−	0.498677i	0.919163	+	0.393877i	$0.128866\pi$
$660$		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	0.955882	−	0.293751i	$-0.0949035\pi$
$677$	21.6631	+	18.1775i	0.832581	+	0.698619i	−0.123301	+	0.992369i	$0.539348\pi$
$678$		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	$-0.676567\pi$
$683$	12.3569	−	21.4029i	0.472825	−	0.818958i	0.999516	+	0.0310993i	$0.00990082\pi$
$684$		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	$-0.589231\pi$
$701$	−14.6504			−0.553338			−0.276669	+	0.960965i	$0.589231\pi$
$702$		0			0
$703$	1.28581			0.0484951
$704$	4.75730	+	3.99185i	0.179297	+	0.150448i
$705$		0			0
$706$	0.997474	+	5.65695i	0.0375404	+	0.212902i
$707$	−1.47254	−	0.535959i	−0.0553804	−	0.0201568i
$708$		0			0
$709$	0.881034	−	4.99659i	0.0330879	−	0.187651i	−0.963784	−	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	0.911487	−	0.411330i	$-0.134936\pi$
$719$	2.66858	+	4.62212i	0.0995213	+	0.172376i	−0.811965	+	0.583706i	$0.801602\pi$
$720$		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	$-0.357824\pi$
$743$	38.0292	−	31.9103i	1.39516	−	1.17068i	0.963202	−	0.268780i	$-0.0866204\pi$
$744$		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	−0.397606	−	0.917556i	$-0.630159\pi$
$761$	−35.6410	−	12.9722i	−1.29198	−	0.470244i	−0.894378	+	0.447313i	$0.852381\pi$
$762$		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	0.557692	−	0.830048i	$-0.311687\pi$
$773$	−12.2332	−	21.1885i	−0.439997	−	0.762097i	−0.997689	+	0.0679509i	$0.978354\pi$
$774$		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	−0.610980	−	0.791646i	$-0.709224\pi$
$797$	1.76568	−	1.48158i	0.0625436	−	0.0524803i	0.673524	+	0.739166i	$0.264780\pi$
$798$		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	$-0.669377\pi$
$809$	−28.8614			−1.01471			−0.507356	+	0.861736i	$0.669377\pi$
$810$		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	$-0.715399\pi$
$821$	−17.3289	+	6.30722i	−0.604784	+	0.220123i	0.0214353	+	0.999770i	$0.493176\pi$
$822$		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	$0.0263470\pi$
$827$	16.3886	+	28.3859i	0.569889	+	0.987076i	−0.426688	+	0.904399i	$0.640320\pi$
$828$		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	0.711863	−	0.702319i	$-0.247852\pi$
$839$	4.16604	+	3.49572i	0.143828	+	0.120686i	−0.568035	+	0.823004i	$0.692296\pi$
$840$		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	$0.351783\pi$
$857$	−8.15382	+	46.2426i	−0.278529	+	1.57962i	−0.727523	+	0.686083i	$0.759329\pi$
$858$		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	$-0.706045\pi$
$863$	−35.4309			−1.20608			−0.603041	+	0.797710i	$0.706045\pi$
$864$		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	$0.0224494\pi$
$881$	16.6153	+	28.7786i	0.559785	+	0.969575i	−0.437729	+	0.899107i	$0.644217\pi$
$882$		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	$-0.740922\pi$
$887$	−8.63851	−	48.9914i	−0.290053	−	1.64497i	0.396604	−	0.917990i	$-0.370189\pi$
$888$		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	$0.128090\pi$
$911$	−2.36802	+	13.4297i	−0.0784561	+	0.444947i	−0.998578	+	0.0533142i	$0.983022\pi$
$912$		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	$-0.640035\pi$
$929$	−5.19788	+	1.89187i	−0.170537	+	0.0620704i	0.255341	+	0.966851i	$0.417812\pi$
$930$		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	$0.00423880\pi$
$941$	1.98952	+	11.2831i	0.0648564	+	0.367819i	−0.935055	+	0.354503i	$0.884650\pi$
$942$		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	$-0.544034\pi$
$947$	−34.9968	−	29.3658i	−1.13724	−	0.954259i	−0.999345	+	0.0361872i	$0.988479\pi$
$948$		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	$-0.757845\pi$
$953$	7.25265	−	12.5620i	0.234936	−	0.406922i	0.959254	+	0.282545i	$0.0911785\pi$
$954$		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	$-0.356857\pi$
$971$	27.0907			0.869383			0.434692	+	0.900579i	$0.356857\pi$
$972$		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	$-0.376292\pi$
$977$	2.32423	+	0.845952i	0.0743589	+	0.0270644i	−0.304573	+	0.952489i	$0.598514\pi$
$978$		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	$-0.709676\pi$
$983$	−17.9557	+	6.53533i	−0.572697	+	0.208445i	0.0394052	+	0.999223i	$0.487454\pi$
$984$		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.406.1		12
3.2	odd	2	inner	729.2.e.r.406.2		12
9.2	odd	6		729.2.e.q.649.2		12
9.4	even	3		729.2.e.m.163.2		12
9.5	odd	6		729.2.e.m.163.1		12
9.7	even	3		729.2.e.q.649.1		12
27.2	odd	18		729.2.c.c.244.3		12
27.4	even	9		729.2.e.q.82.1		12
27.5	odd	18	inner	729.2.e.r.325.2		12
27.7	even	9		729.2.a.c.1.3	✓	6
27.11	odd	18		729.2.c.c.487.3		12
27.13	even	9		729.2.e.m.568.2		12
27.14	odd	18		729.2.e.m.568.1		12
27.16	even	9		729.2.c.c.487.4		12
27.20	odd	18		729.2.a.c.1.4	yes	6
27.22	even	9	inner	729.2.e.r.325.1		12
27.23	odd	18		729.2.e.q.82.2		12
27.25	even	9		729.2.c.c.244.4		12

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

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