LMFDB - Embedded newform 729.2.c.a.487.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(244,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("729.244");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.c (of order $3$, degree $2$, 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:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			487.3
Root			$1.91182i$ of defining polynomial
Character	$\chi$	$=$	729.487
Dual form			729.2.c.a.244.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.789202 + 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(0.839254 + 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} -2.38124 q^{8} +O(q^{10})$	\(q+(-0.789202 + 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(0.839254 + 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} -2.38124 q^{8} -2.64936 q^{10} +(-2.07561 + 3.59506i) q^{11} +(-3.43802 - 5.95483i) q^{13} +(-2.19342 - 3.79911i) q^{14} +(2.37064 - 4.10607i) q^{16} -0.976551 q^{17} +2.68529 q^{19} +(0.412376 - 0.714256i) q^{20} +(-3.27615 - 5.67446i) q^{22} +(0.806585 + 1.39705i) q^{23} +(1.09131 - 1.89020i) q^{25} +10.8532 q^{26} +1.36563 q^{28} +(-4.11394 + 7.12555i) q^{29} +(-0.522035 - 0.904190i) q^{31} +(1.36059 + 2.35661i) q^{32} +(0.770696 - 1.33489i) q^{34} -4.66505 q^{35} -1.30834 q^{37} +(-2.11924 + 3.67062i) q^{38} +(-1.99847 - 3.46145i) q^{40} +(-2.42408 - 4.19864i) q^{41} +(-4.92011 + 8.52189i) q^{43} +2.03974 q^{44} -2.54623 q^{46} +(6.24885 - 10.8233i) q^{47} +(-0.362204 - 0.627356i) q^{49} +(1.72252 + 2.98350i) q^{50} +(-1.68931 + 2.92596i) q^{52} -7.34280 q^{53} -6.96786 q^{55} +(3.30907 - 5.73148i) q^{56} +(-6.49346 - 11.2470i) q^{58} +(4.52594 + 7.83915i) q^{59} +(0.642871 - 1.11349i) q^{61} +1.64796 q^{62} +5.18745 q^{64} +(5.77075 - 9.99523i) q^{65} +(2.32315 + 4.02381i) q^{67} +(0.239919 + 0.415552i) q^{68} +(3.68166 - 6.37683i) q^{70} -5.62373 q^{71} -4.56144 q^{73} +(1.03255 - 1.78843i) q^{74} +(-0.659722 - 1.14267i) q^{76} +(-5.76871 - 9.99170i) q^{77} +(-2.32840 + 4.03291i) q^{79} +7.95828 q^{80} +7.65237 q^{82} +(2.88220 - 4.99211i) q^{83} +(-0.819574 - 1.41954i) q^{85} +(-7.76593 - 13.4510i) q^{86} +(4.94254 - 8.56072i) q^{88} -4.54442 q^{89} +19.1105 q^{91} +(0.396323 - 0.686452i) q^{92} +(9.86321 + 17.0836i) q^{94} +(2.25364 + 3.90342i) q^{95} +(-4.28772 + 7.42655i) q^{97} +1.14341 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	$ 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.789202	+	1.36694i	−0.558050	+	0.966571i	0.439609	+	0.898189i	$0.355117\pi$
$2$	−0.789202	+	1.36694i	−0.558050	+	0.966571i	−0.997659	+	0.0683820i	$0.978216\pi$
$3$		0			0
$3$		0			0
$4$	−0.245680	−	0.425530i	−0.122840	−	0.212765i
$5$	0.839254	+	1.45363i	0.375326	+	0.650083i	0.990376	−	0.138405i	$-0.0441975\pi$
$5$	0.839254	+	1.45363i	0.375326	+	0.650083i	−0.615050	+	0.788488i	$0.710864\pi$
$6$		0			0
$7$	−1.38964	+	2.40693i	−0.525235	+	0.909734i	0.474333	+	0.880345i	$0.342689\pi$
$7$	−1.38964	+	2.40693i	−0.525235	+	0.909734i	−0.999568	+	0.0293881i	$0.990644\pi$
$8$	−2.38124			−0.841897
$9$		0			0
$10$	−2.64936			−0.837802
$11$	−2.07561	+	3.59506i	−0.625820	+	1.08395i	0.362561	+	0.931960i	$0.381902\pi$
$11$	−2.07561	+	3.59506i	−0.625820	+	1.08395i	−0.988382	+	0.151993i	$0.951431\pi$
$12$		0			0
$13$	−3.43802	−	5.95483i	−0.953536	−	1.65157i	−0.737684	−	0.675147i	$-0.764080\pi$
$13$	−3.43802	−	5.95483i	−0.953536	−	1.65157i	−0.215852	−	0.976426i	$-0.569253\pi$
$14$	−2.19342	−	3.79911i	−0.586215	−	1.01535i
$15$		0			0
$16$	2.37064	−	4.10607i	0.592661	−	1.02652i
$17$	−0.976551			−0.236848			−0.118424	−	0.992963i	$-0.537784\pi$
$17$	−0.976551			−0.236848			−0.118424	+	0.992963i	$0.537784\pi$
$18$		0			0
$19$	2.68529			0.616048			0.308024	−	0.951379i	$-0.400332\pi$
$19$	2.68529			0.616048			0.308024	+	0.951379i	$0.400332\pi$
$20$	0.412376	−	0.714256i	0.0922100	−	0.159712i
$21$		0			0
$22$	−3.27615	−	5.67446i	−0.698478	−	1.20980i
$23$	0.806585	+	1.39705i	0.168185	+	0.291304i	0.937782	−	0.347226i	$-0.112876\pi$
$23$	0.806585	+	1.39705i	0.168185	+	0.291304i	−0.769597	+	0.638530i	$0.779543\pi$
$24$		0			0
$25$	1.09131	−	1.89020i	0.218261	−	0.378040i
$26$	10.8532			2.12848
$27$		0			0
$28$	1.36563			0.258079
$29$	−4.11394	+	7.12555i	−0.763939	+	1.32318i	0.176866	+	0.984235i	$0.443404\pi$
$29$	−4.11394	+	7.12555i	−0.763939	+	1.32318i	−0.940806	+	0.338947i	$0.889929\pi$
$30$		0			0
$31$	−0.522035	−	0.904190i	−0.0937602	−	0.162397i	0.815330	−	0.578996i	$-0.196555\pi$
$31$	−0.522035	−	0.904190i	−0.0937602	−	0.162397i	−0.909090	+	0.416599i	$0.863222\pi$
$32$	1.36059	+	2.35661i	0.240520	+	0.416593i
$33$		0			0
$34$	0.770696	−	1.33489i	0.132173	−	0.228931i
$35$	−4.66505			−0.788537
$36$		0			0
$37$	−1.30834			−0.215091			−0.107545	−	0.994200i	$-0.534299\pi$
$37$	−1.30834			−0.215091			−0.107545	+	0.994200i	$0.534299\pi$
$38$	−2.11924	+	3.67062i	−0.343785	+	0.595454i
$39$		0			0
$40$	−1.99847	−	3.46145i	−0.315986	−	0.547303i
$41$	−2.42408	−	4.19864i	−0.378578	−	0.655717i	0.612277	−	0.790643i	$-0.290254\pi$
$41$	−2.42408	−	4.19864i	−0.378578	−	0.655717i	−0.990856	+	0.134926i	$0.956920\pi$
$42$		0			0
$43$	−4.92011	+	8.52189i	−0.750310	+	1.29958i	0.197362	+	0.980331i	$0.436763\pi$
$43$	−4.92011	+	8.52189i	−0.750310	+	1.29958i	−0.947672	+	0.319245i	$0.896571\pi$
$44$	2.03974			0.307503
$45$		0			0
$46$	−2.54623			−0.375422
$47$	6.24885	−	10.8233i	0.911488	−	1.57874i	0.0995258	−	0.995035i	$-0.468267\pi$
$47$	6.24885	−	10.8233i	0.911488	−	1.57874i	0.811963	−	0.583709i	$-0.198399\pi$
$48$		0			0
$49$	−0.362204	−	0.627356i	−0.0517434	−	0.0896222i
$50$	1.72252	+	2.98350i	0.243601	+	0.421930i
$51$		0			0
$52$	−1.68931	+	2.92596i	−0.234265	+	0.405758i
$53$	−7.34280			−1.00861			−0.504305	−	0.863525i	$-0.668251\pi$
$53$	−7.34280			−1.00861			−0.504305	+	0.863525i	$0.668251\pi$
$54$		0			0
$55$	−6.96786			−0.939546
$56$	3.30907	−	5.73148i	0.442194	−	0.765902i
$57$		0			0
$58$	−6.49346	−	11.2470i	−0.852633	−	1.47680i
$59$	4.52594	+	7.83915i	0.589227	+	1.02057i	0.994334	+	0.106302i	$0.0339009\pi$
$59$	4.52594	+	7.83915i	0.589227	+	1.02057i	−0.405107	+	0.914269i	$0.632766\pi$
$60$		0			0
$61$	0.642871	−	1.11349i	0.0823112	−	0.142567i	−0.821931	−	0.569587i	$-0.807103\pi$
$61$	0.642871	−	1.11349i	0.0823112	−	0.142567i	0.904242	+	0.427020i	$0.140437\pi$
$62$	1.64796			0.209292
$63$		0			0
$64$	5.18745			0.648432
$65$	5.77075	−	9.99523i	0.715773	−	1.23976i
$66$		0			0
$67$	2.32315	+	4.02381i	0.283818	+	0.491587i	0.972322	−	0.233646i	$-0.0750655\pi$
$67$	2.32315	+	4.02381i	0.283818	+	0.491587i	−0.688504	+	0.725233i	$0.741732\pi$
$68$	0.239919	+	0.415552i	0.0290945	+	0.0503931i
$69$		0			0
$70$	3.68166	−	6.37683i	0.440043	−	0.762177i
$71$	−5.62373			−0.667414			−0.333707	−	0.942677i	$-0.608300\pi$
$71$	−5.62373			−0.667414			−0.333707	+	0.942677i	$0.608300\pi$
$72$		0			0
$73$	−4.56144			−0.533877			−0.266938	−	0.963714i	$-0.586012\pi$
$73$	−4.56144			−0.533877			−0.266938	+	0.963714i	$0.586012\pi$
$74$	1.03255	−	1.78843i	0.120031	−	0.207900i
$75$		0			0
$76$	−0.659722	−	1.14267i	−0.0756753	−	0.131073i
$77$	−5.76871	−	9.99170i	−0.657405	−	1.13866i
$78$		0			0
$79$	−2.32840	+	4.03291i	−0.261966	+	0.453738i	−0.966764	−	0.255670i	$-0.917704\pi$
$79$	−2.32840	+	4.03291i	−0.261966	+	0.453738i	0.704799	+	0.709407i	$0.251037\pi$
$80$	7.95828			0.889763
$81$		0			0
$82$	7.65237			0.845063
$83$	2.88220	−	4.99211i	0.316362	−	0.547955i	−0.663364	−	0.748297i	$-0.730872\pi$
$83$	2.88220	−	4.99211i	0.316362	−	0.547955i	0.979726	+	0.200342i	$0.0642052\pi$
$84$		0			0
$85$	−0.819574	−	1.41954i	−0.0888953	−	0.153971i
$86$	−7.76593	−	13.4510i	−0.837422	−	1.45046i
$87$		0			0
$88$	4.94254	−	8.56072i	0.526876	−	0.912576i
$89$	−4.54442			−0.481707			−0.240854	−	0.970561i	$-0.577427\pi$
$89$	−4.54442			−0.481707			−0.240854	+	0.970561i	$0.577427\pi$
$90$		0			0
$91$	19.1105			2.00332
$92$	0.396323	−	0.686452i	0.0413196	−	0.0715676i
$93$		0			0
$94$	9.86321	+	17.0836i	1.01731	+	1.76204i
$95$	2.25364	+	3.90342i	0.231218	+	0.400482i
$96$		0			0
$97$	−4.28772	+	7.42655i	−0.435352	+	0.754052i	−0.997324	−	0.0731042i	$-0.976709\pi$
$97$	−4.28772	+	7.42655i	−0.435352	+	0.754052i	0.561972	+	0.827156i	$0.310043\pi$
$98$	1.14341			0.115502
$99$		0			0
$100$	−1.07245			−0.107245
$101$	−3.90285	+	6.75994i	−0.388348	+	0.672639i	−0.992228	−	0.124437i	$-0.960288\pi$
$101$	−3.90285	+	6.75994i	−0.388348	+	0.672639i	0.603879	+	0.797076i	$0.293621\pi$
$102$		0			0
$103$	1.08307	+	1.87594i	0.106718	+	0.184842i	0.914439	−	0.404724i	$-0.132632\pi$
$103$	1.08307	+	1.87594i	0.106718	+	0.184842i	−0.807721	+	0.589565i	$0.799299\pi$
$104$	8.18677	+	14.1799i	0.802779	+	1.39045i
$105$		0			0
$106$	5.79495	−	10.0371i	0.562855	−	0.974894i
$107$	−12.5849			−1.21663			−0.608317	−	0.793695i	$-0.708155\pi$
$107$	−12.5849			−1.21663			−0.608317	+	0.793695i	$0.708155\pi$
$108$		0			0
$109$	−12.2140			−1.16989			−0.584945	−	0.811073i	$-0.698884\pi$
$109$	−12.2140			−1.16989			−0.584945	+	0.811073i	$0.698884\pi$
$110$	5.49905	−	9.52463i	0.524314	−	0.908138i
$111$		0			0
$112$	6.58868	+	11.4119i	0.622572	+	1.07833i
$113$	0.225417	+	0.390433i	0.0212054	+	0.0367288i	0.876433	−	0.481523i	$-0.159916\pi$
$113$	0.225417	+	0.390433i	0.0212054	+	0.0367288i	−0.855228	+	0.518252i	$0.826583\pi$
$114$		0			0
$115$	−1.35386	+	2.34495i	−0.126248	+	0.218668i
$116$	4.04285			0.375369
$117$		0			0
$118$	−14.2875			−1.31527
$119$	1.35706	−	2.35049i	0.124401	−	0.215469i
$120$		0			0
$121$	−3.11632	−	5.39763i	−0.283302	−	0.490694i
$122$	1.01471	+	1.75753i	0.0918675	+	0.159119i
$123$		0			0
$124$	−0.256507	+	0.444283i	−0.0230350	+	0.0398978i
$125$	12.0561			1.07833
$126$		0			0
$127$	−0.531069			−0.0471247			−0.0235624	−	0.999722i	$-0.507501\pi$
$127$	−0.531069			−0.0471247			−0.0235624	+	0.999722i	$0.507501\pi$
$128$	−6.81513	+	11.8041i	−0.602378	+	1.04335i
$129$		0			0
$130$	9.10857	+	15.7765i	0.798875	+	1.38369i
$131$	−5.70802	−	9.88658i	−0.498712	−	0.863794i	0.501287	−	0.865281i	$-0.332860\pi$
$131$	−5.70802	−	9.88658i	−0.498712	−	0.863794i	−0.999999	+	0.00148672i	$0.999527\pi$
$132$		0			0
$133$	−3.73159	+	6.46330i	−0.323570	+	0.560439i
$134$	−7.33374			−0.633539
$135$		0			0
$136$	2.32541			0.199402
$137$	−2.11462	+	3.66263i	−0.180664	+	0.312920i	−0.942107	−	0.335313i	$-0.891158\pi$
$137$	−2.11462	+	3.66263i	−0.180664	+	0.312920i	0.761443	+	0.648232i	$0.224491\pi$
$138$		0			0
$139$	5.57776	+	9.66097i	0.473100	+	0.819433i	0.999526	−	0.0307879i	$-0.00980165\pi$
$139$	5.57776	+	9.66097i	0.473100	+	0.819433i	−0.526426	+	0.850221i	$0.676468\pi$
$140$	1.14611	+	1.98512i	0.0968638	+	0.167773i
$141$		0			0
$142$	4.43826	−	7.68730i	0.372451	−	0.645104i
$143$	28.5440			2.38697
$144$		0			0
$145$	−13.8106			−1.14690
$146$	3.59990	−	6.23521i	0.297930	−	0.516030i
$147$		0			0
$148$	0.321434	+	0.556740i	0.0264217	+	0.0457638i
$149$	9.73885	+	16.8682i	0.797837	+	1.38189i	0.921022	+	0.389511i	$0.127356\pi$
$149$	9.73885	+	16.8682i	0.797837	+	1.38189i	−0.123184	+	0.992384i	$0.539311\pi$
$150$		0			0
$151$	0.621430	−	1.07635i	0.0505713	−	0.0875920i	−0.839632	−	0.543156i	$-0.817229\pi$
$151$	0.621430	−	1.07635i	0.0505713	−	0.0875920i	0.890203	+	0.455564i	$0.150562\pi$
$152$	−6.39433			−0.518649
$153$		0			0
$154$	18.2107			1.46746
$155$	0.876239	−	1.51769i	0.0703812	−	0.121904i
$156$		0			0
$157$	1.76657	+	3.05979i	0.140988	+	0.244198i	0.927869	−	0.372907i	$-0.121639\pi$
$157$	1.76657	+	3.05979i	0.140988	+	0.244198i	−0.786881	+	0.617105i	$0.788306\pi$
$158$	−3.67516	−	6.36556i	−0.292380	−	0.506417i
$159$		0			0
$160$	−2.28376	+	3.95558i	−0.180547	+	0.312716i
$161$	−4.48345			−0.353346
$162$		0			0
$163$	15.9509			1.24937			0.624685	−	0.780877i	$-0.285228\pi$
$163$	15.9509			1.24937			0.624685	+	0.780877i	$0.285228\pi$
$164$	−1.19110	+	2.06304i	−0.0930091	+	0.161097i
$165$		0			0
$166$	4.54927	+	7.87957i	0.353092	+	0.611573i
$167$	−7.24232	−	12.5441i	−0.560428	−	0.970689i	−0.997459	−	0.0712430i	$-0.977303\pi$
$167$	−7.24232	−	12.5441i	−0.560428	−	0.970689i	0.437031	−	0.899446i	$-0.356030\pi$
$168$		0			0
$169$	−17.1400	+	29.6873i	−1.31846	+	2.28364i
$170$	2.58724			0.198432
$171$		0			0
$172$	4.83509			0.368672
$173$	−6.30870	+	10.9270i	−0.479641	+	0.830763i	−0.999727	−	0.0233506i	$-0.992567\pi$
$173$	−6.30870	+	10.9270i	−0.479641	+	0.830763i	0.520086	+	0.854114i	$0.325900\pi$
$174$		0			0
$175$	3.03305	+	5.25339i	0.229277	+	0.397119i
$176$	9.84106	+	17.0452i	0.741798	+	1.28483i
$177$		0			0
$178$	3.58646	−	6.21194i	0.268817	−	0.465605i
$179$	0.295899			0.0221165			0.0110582	−	0.999939i	$-0.496480\pi$
$179$	0.295899			0.0221165			0.0110582	+	0.999939i	$0.496480\pi$
$180$		0			0
$181$	1.42050			0.105585			0.0527925	−	0.998606i	$-0.483188\pi$
$181$	1.42050			0.105585			0.0527925	+	0.998606i	$0.483188\pi$
$182$	−15.0820	+	26.1228i	−1.11795	+	1.93635i
$183$		0			0
$184$	−1.92068	−	3.32671i	−0.141594	−	0.245248i
$185$	−1.09803	−	1.90185i	−0.0807290	−	0.139827i
$186$		0			0
$187$	2.02694	−	3.51076i	0.148225	−	0.256732i
$188$	−6.14087			−0.447869
$189$		0			0
$190$	−7.11431			−0.516126
$191$	−10.3120	+	17.8610i	−0.746153	+	1.29238i	0.203501	+	0.979075i	$0.434768\pi$
$191$	−10.3120	+	17.8610i	−0.746153	+	1.29238i	−0.949654	+	0.313301i	$0.898565\pi$
$192$		0			0
$193$	10.4780	+	18.1484i	0.754221	+	1.30635i	0.945761	+	0.324864i	$0.105319\pi$
$193$	10.4780	+	18.1484i	0.754221	+	1.30635i	−0.191540	+	0.981485i	$0.561348\pi$
$194$	−6.76776	−	11.7221i	−0.485897	−	0.841598i
$195$		0			0
$196$	−0.177972	+	0.308257i	−0.0127123	+	0.0220184i
$197$	−9.59621			−0.683702			−0.341851	−	0.939754i	$-0.611054\pi$
$197$	−9.59621			−0.683702			−0.341851	+	0.939754i	$0.611054\pi$
$198$		0			0
$199$	−10.6917			−0.757912			−0.378956	−	0.925415i	$-0.623717\pi$
$199$	−10.6917			−0.757912			−0.378956	+	0.925415i	$0.623717\pi$
$200$	−2.59867	+	4.50102i	−0.183753	+	0.318270i
$201$		0			0
$202$	−6.16028	−	10.6699i	−0.433436	−	0.750732i
$203$	−11.4338	−	19.8039i	−0.802495	−	1.38996i
$204$		0			0
$205$	4.06885	−	7.04745i	0.284180	−	0.492215i
$206$	−3.41906			−0.238217
$207$		0			0
$208$	−32.6013			−2.26049
$209$	−5.57362	+	9.65379i	−0.385535	+	0.667766i
$210$		0			0
$211$	7.52512	+	13.0339i	0.518051	+	0.897290i	0.999780	+	0.0209700i	$0.00667546\pi$
$211$	7.52512	+	13.0339i	0.518051	+	0.897290i	−0.481729	+	0.876320i	$0.659991\pi$
$212$	1.80398	+	3.12458i	0.123898	+	0.214597i
$213$		0			0
$214$	9.93207	−	17.2028i	0.678942	−	1.17596i
$215$	−16.5169			−1.12644
$216$		0			0
$217$	2.90176			0.196984
$218$	9.63931	−	16.6958i	0.652857	−	1.13078i
$219$		0			0
$220$	1.71186	+	2.96503i	0.115414	+	0.199903i
$221$	3.35741	+	5.81520i	0.225844	+	0.391172i
$222$		0			0
$223$	6.14405	−	10.6418i	0.411436	−	0.712629i	−0.583611	−	0.812034i	$-0.698361\pi$
$223$	6.14405	−	10.6418i	0.411436	−	0.712629i	0.995047	+	0.0994049i	$0.0316939\pi$
$224$	−7.56292			−0.505319
$225$		0			0
$226$	−0.711597			−0.0473347
$227$	−1.87628	+	3.24981i	−0.124533	+	0.215698i	−0.921550	−	0.388259i	$-0.873077\pi$
$227$	−1.87628	+	3.24981i	−0.124533	+	0.215698i	0.797017	+	0.603957i	$0.206410\pi$
$228$		0			0
$229$	9.30121	+	16.1102i	0.614641	+	1.06459i	0.990447	+	0.137892i	$0.0440326\pi$
$229$	9.30121	+	16.1102i	0.614641	+	1.06459i	−0.375806	+	0.926698i	$0.622634\pi$
$230$	−2.13694	−	3.70128i	−0.140905	−	0.244055i
$231$		0			0
$232$	9.79629	−	16.9677i	0.643158	−	1.11398i
$233$	0.545784			0.0357555			0.0178777	−	0.999840i	$-0.494309\pi$
$233$	0.545784			0.0357555			0.0178777	+	0.999840i	$0.494309\pi$
$234$		0			0
$235$	20.9775			1.36842
$236$	2.22386	−	3.85185i	0.144761	−	0.250734i
$237$		0			0
$238$	2.14198	+	3.71002i	0.138844	+	0.240485i
$239$	10.0474	+	17.4026i	0.649911	+	1.12568i	0.983144	+	0.182834i	$0.0585270\pi$
$239$	10.0474	+	17.4026i	0.649911	+	1.12568i	−0.333233	+	0.942844i	$0.608140\pi$
$240$		0			0
$241$	−7.64565	+	13.2427i	−0.492500	+	0.853034i	−0.999963	−	0.00863907i	$-0.997250\pi$
$241$	−7.64565	+	13.2427i	−0.492500	+	0.853034i	0.507463	+	0.861674i	$0.330583\pi$
$242$	9.83763			0.632387
$243$		0			0
$244$	−0.631762			−0.0404444
$245$	0.607962	−	1.05302i	0.0388413	−	0.0672751i
$246$		0			0
$247$	−9.23208	−	15.9904i	−0.587423	−	1.01745i
$248$	1.24309	+	2.15310i	0.0789364	+	0.136722i
$249$		0			0
$250$	−9.51468	+	16.4799i	−0.601761	+	1.04228i
$251$	12.7563			0.805171			0.402586	−	0.915382i	$-0.368112\pi$
$251$	12.7563			0.805171			0.402586	+	0.915382i	$0.368112\pi$
$252$		0			0
$253$	−6.69663			−0.421013
$254$	0.419121	−	0.725938i	0.0262980	−	0.0455494i
$255$		0			0
$256$	−5.56957	−	9.64678i	−0.348098	−	0.602924i
$257$	6.55235	+	11.3490i	0.408725	+	0.707932i	0.994747	−	0.102363i	$-0.0326403\pi$
$257$	6.55235	+	11.3490i	0.408725	+	0.707932i	−0.586023	+	0.810295i	$0.699307\pi$
$258$		0			0
$259$	1.81813	−	3.14909i	0.112973	−	0.195675i
$260$	−5.67103			−0.351702
$261$		0			0
$262$	18.0191			1.11323
$263$	4.75709	−	8.23952i	0.293335	−	0.508070i	−0.681262	−	0.732040i	$-0.738568\pi$
$263$	4.75709	−	8.23952i	0.293335	−	0.508070i	0.974596	+	0.223970i	$0.0719017\pi$
$264$		0			0
$265$	−6.16247	−	10.6737i	−0.378557	−	0.655681i
$266$	−5.88995	−	10.2017i	−0.361136	−	0.625506i
$267$		0			0
$268$	1.14150	−	1.97714i	0.0697284	−	0.120773i
$269$	22.1408			1.34995			0.674973	−	0.737842i	$-0.264155\pi$
$269$	22.1408			1.34995			0.674973	+	0.737842i	$0.264155\pi$
$270$		0			0
$271$	27.9627			1.69861			0.849307	−	0.527899i	$-0.177020\pi$
$271$	27.9627			1.69861			0.849307	+	0.527899i	$0.177020\pi$
$272$	−2.31505	+	4.00979i	−0.140371	+	0.243129i
$273$		0			0
$274$	−3.33773	−	5.78111i	−0.201639	−	0.349250i
$275$	4.53025	+	7.84663i	0.273185	+	0.473170i
$276$		0			0
$277$	9.44184	−	16.3537i	0.567305	−	0.982601i	−0.429526	−	0.903054i	$-0.641319\pi$
$277$	9.44184	−	16.3537i	0.567305	−	0.982601i	0.996831	−	0.0795468i	$-0.0253473\pi$
$278$	−17.6079			−1.05605
$279$		0			0
$280$	11.1086			0.663867
$281$	10.0009	−	17.3220i	0.596602	−	1.03335i	−0.396717	−	0.917941i	$-0.629850\pi$
$281$	10.0009	−	17.3220i	0.596602	−	1.03335i	0.993319	−	0.115404i	$-0.0368162\pi$
$282$		0			0
$283$	−8.37252	−	14.5016i	−0.497695	−	0.862032i	0.502302	−	0.864692i	$-0.332487\pi$
$283$	−8.37252	−	14.5016i	−0.497695	−	0.862032i	−0.999996	+	0.00266002i	$0.999153\pi$
$284$	1.38164	+	2.39307i	0.0819852	+	0.142002i
$285$		0			0
$286$	−22.5270	+	39.0179i	−1.33205	+	2.30717i
$287$	13.4744			0.795371
$288$		0			0
$289$	−16.0463			−0.943903
$290$	10.8993	−	18.8782i	0.640030	−	1.10856i
$291$		0			0
$292$	1.12066	+	1.94103i	0.0655814	+	0.113590i
$293$	−9.78600	−	16.9499i	−0.571704	−	0.990221i	−0.996391	−	0.0848806i	$-0.972949\pi$
$293$	−9.78600	−	16.9499i	−0.571704	−	0.990221i	0.424687	−	0.905340i	$-0.360384\pi$
$294$		0			0
$295$	−7.59682	+	13.1581i	−0.442304	+	0.766093i
$296$	3.11549			0.181084
$297$		0			0
$298$	−30.7437			−1.78093
$299$	5.54611	−	9.60615i	0.320740	−	0.555538i
$300$		0			0
$301$	−13.6744	−	23.6847i	−0.788178	−	1.36517i
$302$	0.980868	+	1.69891i	0.0564426	+	0.0977614i
$303$		0			0
$304$	6.36586	−	11.0260i	0.365107	−	0.632384i
$305$	2.15813			0.123574
$306$		0			0
$307$	14.8995			0.850357			0.425179	−	0.905109i	$-0.360211\pi$
$307$	14.8995			0.850357			0.425179	+	0.905109i	$0.360211\pi$
$308$	−2.83451	+	4.90952i	−0.161511	+	0.279746i
$309$		0			0
$310$	1.38306	+	2.39553i	0.0785525	+	0.136057i
$311$	−2.29618	−	3.97710i	−0.130204	−	0.225521i	0.793551	−	0.608504i	$-0.208230\pi$
$311$	−2.29618	−	3.97710i	−0.130204	−	0.225521i	−0.923755	+	0.382983i	$0.874897\pi$
$312$		0			0
$313$	−5.93434	+	10.2786i	−0.335429	+	0.580980i	−0.983567	−	0.180543i	$-0.942215\pi$
$313$	−5.93434	+	10.2786i	−0.335429	+	0.580980i	0.648138	+	0.761523i	$0.275548\pi$
$314$	−5.57672			−0.314713
$315$		0			0
$316$	2.28817			0.128719
$317$	7.25867	−	12.5724i	0.407688	−	0.706136i	−0.586943	−	0.809629i	$-0.699669\pi$
$317$	7.25867	−	12.5724i	0.407688	−	0.706136i	0.994630	+	0.103493i	$0.0330019\pi$
$318$		0			0
$319$	−17.0779	−	29.5797i	−0.956177	−	1.65615i
$320$	4.35359	+	7.54064i	0.243373	+	0.421535i
$321$		0			0
$322$	3.53835	−	6.12860i	0.197185	−	0.341534i
$323$	−2.62232			−0.145910
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−12.5885	+	21.8039i	−0.697211	+	1.20760i
$327$		0			0
$328$	5.77234	+	9.99798i	0.318724	+	0.552046i
$329$	17.3673	+	30.0811i	0.957491	+	1.65842i
$330$		0			0
$331$	4.05285	−	7.01974i	0.222765	−	0.385840i	−0.732882	−	0.680356i	$-0.761825\pi$
$331$	4.05285	−	7.01974i	0.222765	−	0.385840i	0.955647	+	0.294516i	$0.0951585\pi$
$332$	−2.83239			−0.155448
$333$		0			0
$334$	22.8626			1.25099
$335$	−3.89942	+	6.75400i	−0.213048	+	0.369010i
$336$		0			0
$337$	9.40398	+	16.2882i	0.512267	+	0.887273i	0.999899	+	0.0142235i	$0.00452764\pi$
$337$	9.40398	+	16.2882i	0.512267	+	0.887273i	−0.487631	+	0.873050i	$0.662139\pi$
$338$	−27.0538	−	46.8586i	−1.47154	−	2.54877i
$339$		0			0
$340$	−0.402706	+	0.697507i	−0.0218398	+	0.0378276i
$341$	4.33416			0.234708
$342$		0			0
$343$	−17.4416			−0.941760
$344$	11.7160	−	20.2927i	0.631684	−	1.09411i
$345$		0			0
$346$	−9.95768	−	17.2472i	−0.535328	−	0.927215i
$347$	8.80881	+	15.2573i	0.472882	+	0.819056i	0.999518	−	0.0310351i	$-0.00988038\pi$
$347$	8.80881	+	15.2573i	0.472882	+	0.819056i	−0.526636	+	0.850091i	$0.676547\pi$
$348$		0			0
$349$	8.49465	−	14.7132i	0.454708	−	0.787577i	−0.543963	−	0.839109i	$-0.683077\pi$
$349$	8.49465	−	14.7132i	0.454708	−	0.787577i	0.998671	+	0.0515316i	$0.0164103\pi$
$350$	−9.57475			−0.511792
$351$		0			0
$352$	−11.2962			−0.602090
$353$	7.57780	−	13.1251i	0.403326	−	0.698580i	−0.590799	−	0.806818i	$-0.701188\pi$
$353$	7.57780	−	13.1251i	0.403326	−	0.698580i	0.994125	+	0.108238i	$0.0345209\pi$
$354$		0			0
$355$	−4.71974	−	8.17483i	−0.250498	−	0.433875i
$356$	1.11647	+	1.93379i	0.0591729	+	0.102491i
$357$		0			0
$358$	−0.233524	+	0.404475i	−0.0123421	+	0.0213772i
$359$	2.45096			0.129357			0.0646783	−	0.997906i	$-0.479398\pi$
$359$	2.45096			0.129357			0.0646783	+	0.997906i	$0.479398\pi$
$360$		0			0
$361$	−11.7892			−0.620485
$362$	−1.12106	+	1.94174i	−0.0589218	+	0.102055i
$363$		0			0
$364$	−4.69506	−	8.13208i	−0.246088	−	0.426237i
$365$	−3.82821	−	6.63065i	−0.200378	−	0.347064i
$366$		0			0
$367$	0.656767	−	1.13755i	0.0342829	−	0.0593798i	−0.848375	−	0.529396i	$-0.822419\pi$
$367$	0.656767	−	1.13755i	0.0342829	−	0.0593798i	0.882658	+	0.470016i	$0.155752\pi$
$368$	7.64850			0.398706
$369$		0			0
$370$	3.46628			0.180203
$371$	10.2039	−	17.6736i	0.529758	−	0.917567i
$372$		0			0
$373$	4.81309	+	8.33651i	0.249212	+	0.431648i	0.963307	−	0.268400i	$-0.0864950\pi$
$373$	4.81309	+	8.33651i	0.249212	+	0.431648i	−0.714095	+	0.700048i	$0.753162\pi$
$374$	3.19933	+	5.54140i	0.165433	+	0.286539i
$375$		0			0
$376$	−14.8800	+	25.7730i	−0.767379	+	1.32914i
$377$	56.5753			2.91377
$378$		0			0
$379$	−8.56311			−0.439857			−0.219929	−	0.975516i	$-0.570582\pi$
$379$	−8.56311			−0.439857			−0.219929	+	0.975516i	$0.570582\pi$
$380$	1.10735	−	1.91798i	0.0568057	−	0.0983904i
$381$		0			0
$382$	−16.2766	−	28.1918i	−0.832782	−	1.44242i
$383$	−16.8173	−	29.1284i	−0.859324	−	1.48839i	−0.872574	−	0.488481i	$-0.837551\pi$
$383$	−16.8173	−	29.1284i	−0.859324	−	1.48839i	0.0132498	−	0.999912i	$-0.495782\pi$
$384$		0			0
$385$	9.68282	−	16.7711i	0.493482	−	0.854736i
$386$	−33.0769			−1.68357
$387$		0			0
$388$	4.21363			0.213915
$389$	7.47699	−	12.9505i	0.379098	−	0.656618i	−0.611833	−	0.790987i	$-0.709567\pi$
$389$	7.47699	−	12.9505i	0.379098	−	0.656618i	0.990931	+	0.134369i	$0.0429008\pi$
$390$		0			0
$391$	−0.787671	−	1.36429i	−0.0398343	−	0.0689950i
$392$	0.862496	+	1.49389i	0.0435626	+	0.0754527i
$393$		0			0
$394$	7.57335	−	13.1174i	0.381540	−	0.660846i
$395$	−7.81648			−0.393290
$396$		0			0
$397$	−16.7788			−0.842102			−0.421051	−	0.907037i	$-0.638339\pi$
$397$	−16.7788			−0.842102			−0.421051	+	0.907037i	$0.638339\pi$
$398$	8.43788	−	14.6148i	0.422953	−	0.732576i
$399$		0			0
$400$	−5.17419	−	8.96197i	−0.258710	−	0.448098i
$401$	−6.56315	−	11.3677i	−0.327748	−	0.567676i	0.654317	−	0.756221i	$-0.272956\pi$
$401$	−6.56315	−	11.3677i	−0.327748	−	0.567676i	−0.982065	+	0.188545i	$0.939623\pi$
$402$		0			0
$403$	−3.58953	+	6.21725i	−0.178807	+	0.309704i
$404$	3.83541			0.190819
$405$		0			0
$406$	36.0943			1.79133
$407$	2.71561	−	4.70358i	0.134608	−	0.233148i
$408$		0			0
$409$	−12.7253	−	22.0408i	−0.629223	−	1.08985i	−0.987708	−	0.156311i	$-0.950040\pi$
$409$	−12.7253	−	22.0408i	−0.629223	−	1.08985i	0.358485	−	0.933536i	$-0.383294\pi$
$410$	6.42228	+	11.1237i	0.317174	+	0.549361i
$411$		0			0
$412$	0.532179	−	0.921761i	0.0262186	−	0.0454119i
$413$	−25.1577			−1.23793
$414$		0			0
$415$	9.67558			0.474955
$416$	9.35547	−	16.2041i	0.458689	−	0.794474i
$417$		0			0
$418$	−8.79742	−	15.2376i	−0.430296	−	0.745294i
$419$	6.33503	+	10.9726i	0.309486	+	0.536046i	0.978250	−	0.207429i	$-0.0665096\pi$
$419$	6.33503	+	10.9726i	0.309486	+	0.536046i	−0.668764	+	0.743475i	$0.733176\pi$
$420$		0			0
$421$	8.83862	−	15.3089i	0.430768	−	0.746112i	−0.566172	−	0.824287i	$-0.691576\pi$
$421$	8.83862	−	15.3089i	0.430768	−	0.746112i	0.996940	+	0.0781752i	$0.0249094\pi$
$422$	−23.7554			−1.15639
$423$		0			0
$424$	17.4850			0.849146
$425$	−1.06572	+	1.84587i	−0.0516948	+	0.0895381i
$426$		0			0
$427$	1.78672	+	3.09469i	0.0864654	+	0.149762i
$428$	3.09187	+	5.35528i	0.149451	+	0.258857i
$429$		0			0
$430$	13.0352	−	22.5776i	0.628612	−	1.08879i
$431$	15.6974			0.756117			0.378059	−	0.925782i	$-0.376592\pi$
$431$	15.6974			0.756117			0.378059	+	0.925782i	$0.376592\pi$
$432$		0			0
$433$	−12.6258			−0.606759			−0.303380	−	0.952870i	$-0.598115\pi$
$433$	−12.6258			−0.606759			−0.303380	+	0.952870i	$0.598115\pi$
$434$	−2.29008	+	3.96653i	−0.109927	+	0.190400i
$435$		0			0
$436$	3.00073	+	5.19742i	0.143709	+	0.248912i
$437$	2.16591	+	3.75147i	0.103610	+	0.179457i
$438$		0			0
$439$	−13.4685	+	23.3281i	−0.642814	+	1.11339i	0.341987	+	0.939705i	$0.388900\pi$
$439$	−13.4685	+	23.3281i	−0.642814	+	1.11339i	−0.984802	+	0.173683i	$0.944433\pi$
$440$	16.5922			0.791001
$441$		0			0
$442$	−10.5987			−0.504128
$443$	−17.3639	+	30.0752i	−0.824986	+	1.42892i	0.0769438	+	0.997035i	$0.475484\pi$
$443$	−17.3639	+	30.0752i	−0.824986	+	1.42892i	−0.901930	+	0.431882i	$0.857850\pi$
$444$		0			0
$445$	−3.81392	−	6.60590i	−0.180797	−	0.313150i
$446$	9.69780	+	16.7971i	0.459204	+	0.795365i
$447$		0			0
$448$	−7.20870	+	12.4858i	−0.340579	+	0.589900i
$449$	−20.7461			−0.979070			−0.489535	−	0.871984i	$-0.662834\pi$
$449$	−20.7461			−0.979070			−0.489535	+	0.871984i	$0.662834\pi$
$450$		0			0
$451$	20.1258			0.947688
$452$	0.110761	−	0.191843i	0.00520974	−	0.00902354i
$453$		0			0
$454$	−2.96153	−	5.12952i	−0.138991	−	0.240740i
$455$	16.0385	+	27.7796i	0.751898	+	1.30233i
$456$		0			0
$457$	3.60387	−	6.24208i	0.168582	−	0.291992i	−0.769340	−	0.638840i	$-0.779415\pi$
$457$	3.60387	−	6.24208i	0.168582	−	0.291992i	0.937921	+	0.346848i	$0.112748\pi$
$458$	−29.3621			−1.37200
$459$		0			0
$460$	1.33046			0.0620332
$461$	−11.5634	+	20.0284i	−0.538562	+	0.932817i	0.460420	+	0.887701i	$0.347699\pi$
$461$	−11.5634	+	20.0284i	−0.538562	+	0.932817i	−0.998982	+	0.0451156i	$0.985634\pi$
$462$		0			0
$463$	−2.48792	−	4.30921i	−0.115623	−	0.200266i	0.802405	−	0.596779i	$-0.203553\pi$
$463$	−2.48792	−	4.30921i	−0.115623	−	0.200266i	−0.918029	+	0.396514i	$0.870220\pi$
$464$	19.5054	+	33.7843i	0.905513	+	1.56840i
$465$		0			0
$466$	−0.430734	+	0.746053i	−0.0199534	+	0.0345602i
$467$	−12.4814			−0.577569			−0.288784	−	0.957394i	$-0.593251\pi$
$467$	−12.4814			−0.577569			−0.288784	+	0.957394i	$0.593251\pi$
$468$		0			0
$469$	−12.9134			−0.596284
$470$	−16.5555	+	28.6749i	−0.763647	+	1.32268i
$471$		0			0
$472$	−10.7774	−	18.6669i	−0.496068	−	0.859216i
$473$	−20.4245	−	35.3762i	−0.939119	−	1.62660i
$474$		0			0
$475$	2.93047	−	5.07573i	0.134459	−	0.232890i
$476$	−1.33361			−0.0611257
$477$		0			0
$478$	−31.7176			−1.45073
$479$	−14.2356	+	24.6568i	−0.650443	+	1.12660i	0.332573	+	0.943078i	$0.392083\pi$
$479$	−14.2356	+	24.6568i	−0.650443	+	1.12660i	−0.983016	+	0.183522i	$0.941250\pi$
$480$		0			0
$481$	4.49812	+	7.79097i	0.205097	+	0.355238i
$482$	−12.0679	−	20.9023i	−0.549679	−	0.952072i
$483$		0			0
$484$	−1.53124	+	2.65218i	−0.0696016	+	0.120554i
$485$	−14.3939			−0.653595
$486$		0			0
$487$	29.6841			1.34511			0.672557	−	0.740045i	$-0.265196\pi$
$487$	29.6841			1.34511			0.672557	+	0.740045i	$0.265196\pi$
$488$	−1.53083	+	2.65148i	−0.0692975	+	0.120027i
$489$		0			0
$490$	0.959610	+	1.66209i	0.0433508	+	0.0750857i
$491$	−6.20248	−	10.7430i	−0.279914	−	0.484825i	0.691449	−	0.722425i	$-0.256973\pi$
$491$	−6.20248	−	10.7430i	−0.279914	−	0.484825i	−0.971363	+	0.237600i	$0.923639\pi$
$492$		0			0
$493$	4.01747	−	6.95846i	0.180938	−	0.313394i
$494$	29.1439			1.31125
$495$		0			0
$496$	−4.95023			−0.222272
$497$	7.81497	−	13.5359i	0.350549	−	0.607169i
$498$		0			0
$499$	1.13991	+	1.97438i	0.0510294	+	0.0883856i	0.890412	−	0.455156i	$-0.150416\pi$
$499$	1.13991	+	1.97438i	0.0510294	+	0.0883856i	−0.839382	+	0.543541i	$0.817083\pi$
$500$	−2.96193	−	5.13022i	−0.132462	−	0.229430i
$501$		0			0
$502$	−10.0673	+	17.4371i	−0.449326	+	0.778256i
$503$	41.2812			1.84064			0.920320	−	0.391167i	$-0.127929\pi$
$503$	41.2812			1.84064			0.920320	+	0.391167i	$0.127929\pi$
$504$		0			0
$505$	−13.1019			−0.583028
$506$	5.28499	−	9.15387i	0.234947	−	0.406939i
$507$		0			0
$508$	0.130473	+	0.225986i	0.00578880	+	0.0100265i
$509$	−8.21208	−	14.2237i	−0.363994	−	0.630456i	0.624620	−	0.780929i	$-0.285254\pi$
$509$	−8.21208	−	14.2237i	−0.363994	−	0.630456i	−0.988614	+	0.150473i	$0.951920\pi$
$510$		0			0
$511$	6.33877	−	10.9791i	0.280411	−	0.485685i
$512$	−9.67844			−0.427731
$513$		0			0
$514$	−20.6845			−0.912355
$515$	−1.81795	+	3.14878i	−0.0801083	+	0.138752i
$516$		0			0
$517$	25.9404	+	44.9300i	1.14086	+	1.97602i
$518$	2.86974	+	4.97054i	0.126089	+	0.218393i
$519$		0			0
$520$	−13.7416	+	23.8011i	−0.602607	+	1.04375i
$521$	−9.29672			−0.407297			−0.203648	−	0.979044i	$-0.565280\pi$
$521$	−9.29672			−0.407297			−0.203648	+	0.979044i	$0.565280\pi$
$522$		0			0
$523$	−22.7471			−0.994662			−0.497331	−	0.867561i	$-0.665686\pi$
$523$	−22.7471			−0.994662			−0.497331	+	0.867561i	$0.665686\pi$
$524$	−2.80469	+	4.85787i	−0.122524	+	0.212217i
$525$		0			0
$526$	7.50861	+	13.0053i	0.327391	+	0.567058i
$527$	0.509794	+	0.882988i	0.0222070	+	0.0384636i
$528$		0			0
$529$	10.1988	−	17.6649i	0.443428	−	0.768040i
$530$	19.4537			0.845016
$531$		0			0
$532$	3.66710			0.158989
$533$	−16.6681	+	28.8700i	−0.721976	+	1.25050i
$534$		0			0
$535$	−10.5620	−	18.2939i	−0.456634	−	0.790913i
$536$	−5.53199	−	9.58168i	−0.238945	−	0.413866i
$537$		0			0
$538$	−17.4735	+	30.2651i	−0.753338	+	1.30482i
$539$	3.00718			0.129528
$540$		0			0
$541$	2.38959			0.102737			0.0513683	−	0.998680i	$-0.483642\pi$
$541$	2.38959			0.102737			0.0513683	+	0.998680i	$0.483642\pi$
$542$	−22.0682	+	38.2233i	−0.947912	+	1.64183i
$543$		0			0
$544$	−1.32868	−	2.30135i	−0.0569669	−	0.0986695i
$545$	−10.2506	−	17.7546i	−0.439089	−	0.760525i
$546$		0			0
$547$	−14.8334	+	25.6922i	−0.634230	+	1.09852i	0.352448	+	0.935832i	$0.385349\pi$
$547$	−14.8334	+	25.6922i	−0.634230	+	1.09852i	−0.986678	+	0.162687i	$0.947984\pi$
$548$	2.07808			0.0887712
$549$		0			0
$550$	−14.3011			−0.609803
$551$	−11.0471	+	19.1342i	−0.470623	+	0.815143i
$552$		0			0
$553$	−6.47128	−	11.2086i	−0.275187	−	0.476638i
$554$	14.9030	+	25.8128i	0.633169	+	1.09668i
$555$		0			0
$556$	2.74069	−	4.74701i	0.116231	−	0.201318i
$557$	8.41413			0.356518			0.178259	−	0.983984i	$-0.442954\pi$
$557$	8.41413			0.356518			0.178259	+	0.983984i	$0.442954\pi$
$558$		0			0
$559$	67.6619			2.86179
$560$	−11.0592	+	19.1550i	−0.467335	+	0.809447i
$561$		0			0
$562$	15.7854	+	27.3411i	0.665868	+	1.15332i
$563$	13.6133	+	23.5788i	0.573730	+	0.993730i	0.996178	+	0.0873428i	$0.0278376\pi$
$563$	13.6133	+	23.5788i	0.573730	+	0.993730i	−0.422448	+	0.906387i	$0.638829\pi$
$564$		0			0
$565$	−0.378363	+	0.655345i	−0.0159179	+	0.0275706i
$566$	26.4304			1.11095
$567$		0			0
$568$	13.3915			0.561894
$569$	10.9747	−	19.0087i	0.460082	−	0.796885i	−0.538883	−	0.842381i	$-0.681154\pi$
$569$	10.9747	−	19.0087i	0.460082	−	0.796885i	0.998965	+	0.0454960i	$0.0144868\pi$
$570$		0			0
$571$	22.4267	+	38.8442i	0.938530	+	1.62558i	0.768216	+	0.640191i	$0.221145\pi$
$571$	22.4267	+	38.8442i	0.938530	+	1.62558i	0.170314	+	0.985390i	$0.445522\pi$
$572$	−7.01269	−	12.1463i	−0.293215	−	0.507863i
$573$		0			0
$574$	−10.6340	+	18.4187i	−0.443857	+	0.768782i
$575$	3.52092			0.146833
$576$		0			0
$577$	12.0191			0.500361			0.250181	−	0.968199i	$-0.419510\pi$
$577$	12.0191			0.500361			0.250181	+	0.968199i	$0.419510\pi$
$578$	12.6638	−	21.9344i	0.526745	−	0.912349i
$579$		0			0
$580$	3.39298	+	5.87681i	0.140886	+	0.244021i
$581$	8.01043	+	13.8745i	0.332329	+	0.575610i
$582$		0			0
$583$	15.2408	−	26.3978i	0.631209	−	1.09329i
$584$	10.8619			0.449469
$585$		0			0
$586$	30.8925			1.27616
$587$	8.51493	−	14.7483i	0.351449	−	0.608727i	−0.635055	−	0.772467i	$-0.719022\pi$
$587$	8.51493	−	14.7483i	0.351449	−	0.608727i	0.986504	+	0.163740i	$0.0523558\pi$
$588$		0			0
$589$	−1.40181	−	2.42801i	−0.0577607	−	0.100045i
$590$	−11.9909	−	20.7688i	−0.493656	−	0.855037i
$591$		0			0
$592$	−3.10162	+	5.37216i	−0.127476	+	0.220794i
$593$	−14.9284			−0.613037			−0.306519	−	0.951865i	$-0.599164\pi$
$593$	−14.9284			−0.613037			−0.306519	+	0.951865i	$0.599164\pi$
$594$		0			0
$595$	4.55566			0.186764
$596$	4.78528	−	8.28835i	0.196013	−	0.339504i
$597$		0			0
$598$	8.75401	+	15.1624i	0.357978	+	0.620036i
$599$	−6.76740	−	11.7215i	−0.276508	−	0.478927i	0.694006	−	0.719969i	$-0.255844\pi$
$599$	−6.76740	−	11.7215i	−0.276508	−	0.478927i	−0.970515	+	0.241042i	$0.922511\pi$
$600$		0			0
$601$	22.6586	−	39.2459i	0.924265	−	1.60087i	0.131525	−	0.991313i	$-0.458013\pi$
$601$	22.6586	−	39.2459i	0.924265	−	1.60087i	0.792739	−	0.609561i	$-0.208654\pi$
$602$	43.1674			1.75937
$603$		0			0
$604$	−0.610691			−0.0248487
$605$	5.23077	−	9.05996i	0.212661	−	0.368340i
$606$		0			0
$607$	−12.2184	−	21.1629i	−0.495929	−	0.858975i	0.504060	−	0.863669i	$-0.331839\pi$
$607$	−12.2184	−	21.1629i	−0.495929	−	0.858975i	−0.999989	+	0.00469404i	$0.998506\pi$
$608$	3.65357	+	6.32817i	0.148172	+	0.256641i
$609$		0			0
$610$	−1.70320	+	2.95003i	−0.0689605	+	0.119443i
$611$	−85.9348			−3.47655
$612$		0			0
$613$	−25.1996			−1.01780			−0.508901	−	0.860825i	$-0.669948\pi$
$613$	−25.1996			−1.01780			−0.508901	+	0.860825i	$0.669948\pi$
$614$	−11.7587	+	20.3666i	−0.474542	+	0.821931i
$615$		0			0
$616$	13.7367	+	23.7927i	0.553467	+	0.958634i
$617$	−2.02093	−	3.50034i	−0.0813594	−	0.140919i	0.822475	−	0.568802i	$-0.192593\pi$
$617$	−2.02093	−	3.50034i	−0.0813594	−	0.140919i	−0.903834	+	0.427883i	$0.859259\pi$
$618$		0			0
$619$	22.3850	−	38.7719i	0.899729	−	1.55838i	0.0718884	−	0.997413i	$-0.477097\pi$
$619$	22.3850	−	38.7719i	0.899729	−	1.55838i	0.827841	−	0.560964i	$-0.189569\pi$
$620$	−0.861097			−0.0345825
$621$		0			0
$622$	7.24860			0.290642
$623$	6.31511	−	10.9381i	0.253010	−	0.438225i
$624$		0			0
$625$	4.66157	+	8.07408i	0.186463	+	0.322963i
$626$	−9.36679	−	16.2238i	−0.374372	−	0.648432i
$627$		0			0
$628$	0.868022	−	1.50346i	0.0346378	−	0.0599945i
$629$	1.27767			0.0509439
$630$		0			0
$631$	31.4116			1.25048			0.625238	−	0.780434i	$-0.285002\pi$
$631$	31.4116			1.25048			0.625238	+	0.780434i	$0.285002\pi$
$632$	5.54449	−	9.60334i	0.220548	−	0.382000i
$633$		0			0
$634$	11.4571	+	19.8443i	0.455020	+	0.788118i
$635$	−0.445701	−	0.771978i	−0.0176871	−	0.0306350i
$636$		0			0
$637$	−2.49053	+	4.31373i	−0.0986784	+	0.170916i
$638$	53.9116			2.13438
$639$		0			0
$640$	−22.8785			−0.904351
$641$	−24.3203	+	42.1240i	−0.960594	+	1.66380i	−0.239581	+	0.970876i	$0.577010\pi$
$641$	−24.3203	+	42.1240i	−0.960594	+	1.66380i	−0.721013	+	0.692922i	$0.756323\pi$
$642$		0			0
$643$	14.0162	+	24.2767i	0.552744	+	0.957381i	0.998075	+	0.0620150i	$0.0197527\pi$
$643$	14.0162	+	24.2767i	0.552744	+	0.957381i	−0.445331	+	0.895366i	$0.646914\pi$
$644$	1.10149	+	1.90784i	0.0434050	+	0.0751796i
$645$		0			0
$646$	2.06954	−	3.58455i	0.0814251	−	0.141032i
$647$	−37.5519			−1.47632			−0.738159	−	0.674627i	$-0.764304\pi$
$647$	−37.5519			−1.47632			−0.738159	+	0.674627i	$0.764304\pi$
$648$		0			0
$649$	−37.5763			−1.47500
$650$	11.8441	−	20.5147i	0.464565	−	0.804651i
$651$		0			0
$652$	−3.91881	−	6.78758i	−0.153472	−	0.265822i
$653$	2.55611	+	4.42731i	0.100028	+	0.173254i	0.911696	−	0.410865i	$-0.134773\pi$
$653$	2.55611	+	4.42731i	0.100028	+	0.173254i	−0.811668	+	0.584119i	$0.801440\pi$
$654$		0			0
$655$	9.58095	−	16.5947i	0.374359	−	0.648408i
$656$	−22.9866			−0.897474
$657$		0			0
$658$	−54.8253			−2.13731
$659$	−17.5030	+	30.3160i	−0.681818	+	1.18094i	0.292607	+	0.956233i	$0.405477\pi$
$659$	−17.5030	+	30.3160i	−0.681818	+	1.18094i	−0.974425	+	0.224711i	$0.927856\pi$
$660$		0			0
$661$	−0.666731	−	1.15481i	−0.0259328	−	0.0449170i	0.852768	−	0.522290i	$-0.174922\pi$
$661$	−0.666731	−	1.15481i	−0.0259328	−	0.0449170i	−0.878701	+	0.477373i	$0.841589\pi$
$662$	6.39704	+	11.0800i	0.248628	+	0.430636i
$663$		0			0
$664$	−6.86321	+	11.8874i	−0.266344	+	0.461322i
$665$	−12.5270			−0.485776
$666$		0			0
$667$	−13.2730			−0.513931
$668$	−3.55859	+	6.16365i	−0.137686	+	0.238479i
$669$		0			0
$670$	−6.15487	−	10.6605i	−0.237783	−	0.411853i
$671$	2.66870	+	4.62232i	0.103024	+	0.178443i
$672$		0			0
$673$	1.78976	−	3.09996i	0.0689904	−	0.119495i	−0.829467	−	0.558556i	$-0.811356\pi$
$673$	1.78976	−	3.09996i	0.0689904	−	0.119495i	0.898457	+	0.439061i	$0.144689\pi$
$674$	−29.6866			−1.14348
$675$		0			0
$676$	16.8438			0.647839
$677$	18.4694	−	31.9900i	0.709839	−	1.22948i	−0.255078	−	0.966920i	$-0.582101\pi$
$677$	18.4694	−	31.9900i	0.709839	−	1.22948i	0.964917	−	0.262556i	$-0.0845654\pi$
$678$		0			0
$679$	−11.9168	−	20.6405i	−0.457324	−	0.792109i
$680$	1.95161	+	3.38028i	0.0748407	+	0.129628i
$681$		0			0
$682$	−3.42053	+	5.92453i	−0.130979	+	0.226862i
$683$	38.0166			1.45466			0.727332	−	0.686286i	$-0.240760\pi$
$683$	38.0166			1.45466			0.727332	+	0.686286i	$0.240760\pi$
$684$		0			0
$685$	−7.09881			−0.271232
$686$	13.7650	−	23.8416i	0.525549	−	0.910278i
$687$		0			0
$688$	23.3277	+	40.4047i	0.889359	+	1.54041i
$689$	25.2447	+	43.7251i	0.961746	+	1.66579i
$690$		0			0
$691$	−0.275232	+	0.476716i	−0.0104703	+	0.0181351i	−0.871213	−	0.490905i	$-0.836666\pi$
$691$	−0.275232	+	0.476716i	−0.0104703	+	0.0181351i	0.860743	+	0.509040i	$0.170000\pi$
$692$	6.19968			0.235677
$693$		0			0
$694$	−27.8077			−1.05557
$695$	−9.36232	+	16.2160i	−0.355133	+	0.615108i
$696$		0			0
$697$	2.36724	+	4.10019i	0.0896657	+	0.155306i
$698$	13.4080	+	23.2233i	0.507500	+	0.879015i
$699$		0			0
$700$	1.49032	−	2.58131i	0.0563287	−	0.0975642i
$701$	19.0242			0.718534			0.359267	−	0.933235i	$-0.383027\pi$
$701$	19.0242			0.718534			0.359267	+	0.933235i	$0.383027\pi$
$702$		0			0
$703$	−3.51328			−0.132506
$704$	−10.7671	+	18.6492i	−0.405802	+	0.702869i
$705$		0			0
$706$	11.9608	+	20.7168i	0.450152	+	0.779686i
$707$	−10.8471	−	18.7878i	−0.407948	−	0.706587i
$708$		0			0
$709$	−6.07839	+	10.5281i	−0.228279	+	0.395390i	−0.957298	−	0.289103i	$-0.906643\pi$
$709$	−6.07839	+	10.5281i	−0.228279	+	0.395390i	0.729019	+	0.684493i	$0.239976\pi$
$710$	14.8993			0.559161
$711$		0			0
$712$	10.8214			0.405548
$713$	0.842130	−	1.45861i	0.0315380	−	0.0546255i
$714$		0			0
$715$	23.9557	+	41.4924i	0.895891	+	1.55173i
$716$	−0.0726963	−	0.125914i	−0.00271679	−	0.00470562i
$717$		0			0
$718$	−1.93430	+	3.35031i	−0.0721875	+	0.125032i
$719$	9.77667			0.364608			0.182304	−	0.983242i	$-0.441644\pi$
$719$	9.77667			0.364608			0.182304	+	0.983242i	$0.441644\pi$
$720$		0			0
$721$	−6.02033			−0.224209
$722$	9.30408	−	16.1151i	0.346262	−	0.599743i
$723$		0			0
$724$	−0.348989	−	0.604466i	−0.0129701	−	0.0224648i
$725$	8.97913	+	15.5523i	0.333477	+	0.577598i
$726$		0			0
$727$	−2.16746	+	3.75416i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$727$	−2.16746	+	3.75416i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$728$	−45.5067			−1.68659
$729$		0			0
$730$	12.0849			0.447283
$731$	4.80474	−	8.32206i	0.177710	−	0.307803i
$732$		0			0
$733$	−14.5968	−	25.2824i	−0.539146	−	0.933829i	−0.998950	−	0.0458082i	$-0.985414\pi$
$733$	−14.5968	−	25.2824i	−0.539146	−	0.933829i	0.459804	−	0.888020i	$-0.347920\pi$
$734$	1.03664	+	1.79552i	0.0382632	+	0.0662738i
$735$		0			0
$736$	−2.19486	+	3.80161i	−0.0809036	+	0.140129i
$737$	−19.2878			−0.710476
$738$		0			0
$739$	41.5553			1.52864			0.764319	−	0.644838i	$-0.223075\pi$
$739$	41.5553			1.52864			0.764319	+	0.644838i	$0.223075\pi$
$740$	−0.539529	+	0.934492i	−0.0198335	+	0.0343526i
$741$		0			0
$742$	16.1058	+	27.8961i	0.591263	+	1.02410i
$743$	−10.6887	−	18.5133i	−0.392130	−	0.679188i	0.600601	−	0.799549i	$-0.294928\pi$
$743$	−10.6887	−	18.5133i	−0.392130	−	0.679188i	−0.992730	+	0.120361i	$0.961595\pi$
$744$		0			0
$745$	−16.3467	+	28.3134i	−0.598898	+	1.03732i
$746$	−15.1940			−0.556291
$747$		0			0
$748$	−1.99191			−0.0728316
$749$	17.4886	−	30.2911i	0.639018	−	1.10681i
$750$		0			0
$751$	19.9838	+	34.6130i	0.729220	+	1.26305i	0.957213	+	0.289383i	$0.0934500\pi$
$751$	19.9838	+	34.6130i	0.729220	+	1.26305i	−0.227994	+	0.973663i	$0.573217\pi$
$752$	−29.6276	−	51.3165i	−1.08041	−	1.87132i
$753$		0			0
$754$	−44.6493	+	77.3349i	−1.62603	+	2.81637i
$755$	2.08615			0.0759228
$756$		0			0
$757$	6.68348			0.242915			0.121458	−	0.992597i	$-0.461243\pi$
$757$	6.68348			0.242915			0.121458	+	0.992597i	$0.461243\pi$
$758$	6.75803	−	11.7052i	0.245463	−	0.425154i
$759$		0			0
$760$	−5.36646	−	9.29499i	−0.194662	−	0.337165i
$761$	−21.0125	−	36.3947i	−0.761703	−	1.31931i	−0.941972	−	0.335691i	$-0.891030\pi$
$761$	−21.0125	−	36.3947i	−0.761703	−	1.31931i	0.180269	−	0.983617i	$-0.442303\pi$
$762$		0			0
$763$	16.9731	−	29.3982i	0.614467	−	1.06429i
$764$	10.1338			0.366630
$765$		0			0
$766$	53.0890			1.91818
$767$	31.1206	−	53.9024i	1.12370	−	1.94630i
$768$		0			0
$769$	−1.20662	−	2.08992i	−0.0435117	−	0.0753644i	0.843449	−	0.537209i	$-0.180521\pi$
$769$	−1.20662	−	2.08992i	−0.0435117	−	0.0753644i	−0.886961	+	0.461844i	$0.847188\pi$
$770$	15.2834	+	26.4716i	0.550776	+	0.953971i
$771$		0			0
$772$	5.14845	−	8.91738i	0.185297	−	0.320944i
$773$	1.39780			0.0502754			0.0251377	−	0.999684i	$-0.491998\pi$
$773$	1.39780			0.0502754			0.0251377	+	0.999684i	$0.491998\pi$
$774$		0			0
$775$	−2.27880			−0.0818569
$776$	10.2101	−	17.6844i	0.366522	−	0.634834i
$777$		0			0
$778$	11.8017	+	20.4412i	0.423112	+	0.732851i
$779$	−6.50937	−	11.2746i	−0.233222	−	0.403953i
$780$		0			0
$781$	11.6727	−	20.2177i	0.417682	−	0.723446i
$782$	2.48653			0.0889181
$783$		0			0
$784$	−3.43462			−0.122665
$785$	−2.96520	+	5.13588i	−0.105833

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.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.789202 + 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(0.839254 + 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} -2.38124 q^{8} +O(q^{10})\)	\(q+(-0.789202 + 1.36694i) q^{2} +(-0.245680 - 0.425530i) q^{4} +(0.839254 + 1.45363i) q^{5} +(-1.38964 + 2.40693i) q^{7} -2.38124 q^{8} -2.64936 q^{10} +(-2.07561 + 3.59506i) q^{11} +(-3.43802 - 5.95483i) q^{13} +(-2.19342 - 3.79911i) q^{14} +(2.37064 - 4.10607i) q^{16} -0.976551 q^{17} +2.68529 q^{19} +(0.412376 - 0.714256i) q^{20} +(-3.27615 - 5.67446i) q^{22} +(0.806585 + 1.39705i) q^{23} +(1.09131 - 1.89020i) q^{25} +10.8532 q^{26} +1.36563 q^{28} +(-4.11394 + 7.12555i) q^{29} +(-0.522035 - 0.904190i) q^{31} +(1.36059 + 2.35661i) q^{32} +(0.770696 - 1.33489i) q^{34} -4.66505 q^{35} -1.30834 q^{37} +(-2.11924 + 3.67062i) q^{38} +(-1.99847 - 3.46145i) q^{40} +(-2.42408 - 4.19864i) q^{41} +(-4.92011 + 8.52189i) q^{43} +2.03974 q^{44} -2.54623 q^{46} +(6.24885 - 10.8233i) q^{47} +(-0.362204 - 0.627356i) q^{49} +(1.72252 + 2.98350i) q^{50} +(-1.68931 + 2.92596i) q^{52} -7.34280 q^{53} -6.96786 q^{55} +(3.30907 - 5.73148i) q^{56} +(-6.49346 - 11.2470i) q^{58} +(4.52594 + 7.83915i) q^{59} +(0.642871 - 1.11349i) q^{61} +1.64796 q^{62} +5.18745 q^{64} +(5.77075 - 9.99523i) q^{65} +(2.32315 + 4.02381i) q^{67} +(0.239919 + 0.415552i) q^{68} +(3.68166 - 6.37683i) q^{70} -5.62373 q^{71} -4.56144 q^{73} +(1.03255 - 1.78843i) q^{74} +(-0.659722 - 1.14267i) q^{76} +(-5.76871 - 9.99170i) q^{77} +(-2.32840 + 4.03291i) q^{79} +7.95828 q^{80} +7.65237 q^{82} +(2.88220 - 4.99211i) q^{83} +(-0.819574 - 1.41954i) q^{85} +(-7.76593 - 13.4510i) q^{86} +(4.94254 - 8.56072i) q^{88} -4.54442 q^{89} +19.1105 q^{91} +(0.396323 - 0.686452i) q^{92} +(9.86321 + 17.0836i) q^{94} +(2.25364 + 3.90342i) q^{95} +(-4.28772 + 7.42655i) q^{97} +1.14341 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8	\( 12 q - 3 q^{2} - 9 q^{4} + 3 q^{5} - 6 q^{7} + 12 q^{8} + 12 q^{10} + 6 q^{11} - 6 q^{13} - 24 q^{14} - 15 q^{16} - 18 q^{17} + 24 q^{19} + 21 q^{20} - 3 q^{22} + 12 q^{23} - 9 q^{25} + 48 q^{26} + 6 q^{28} - 21 q^{29} - 15 q^{31} + 60 q^{35} + 6 q^{37} - 15 q^{38} - 3 q^{40} + 12 q^{41} - 6 q^{43} - 66 q^{44} - 6 q^{46} + 15 q^{47} - 12 q^{49} + 24 q^{50} - 3 q^{52} - 18 q^{53} + 30 q^{55} - 12 q^{56} + 15 q^{58} - 6 q^{59} - 24 q^{61} - 60 q^{62} + 12 q^{64} + 15 q^{65} - 15 q^{67} - 36 q^{68} + 15 q^{70} + 24 q^{73} - 24 q^{74} - 9 q^{76} - 15 q^{77} - 24 q^{79} - 42 q^{80} - 42 q^{82} + 6 q^{83} + 18 q^{85} + 30 q^{86} + 21 q^{88} - 18 q^{89} + 36 q^{91} - 6 q^{92} + 6 q^{94} + 33 q^{95} + 21 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 9 * q^4 + 3 * q^5 - 6 * q^7 + 12 * q^8 + 12 * q^10 + 6 * q^11 - 6 * q^13 - 24 * q^14 - 15 * q^16 - 18 * q^17 + 24 * q^19 + 21 * q^20 - 3 * q^22 + 12 * q^23 - 9 * q^25 + 48 * q^26 + 6 * q^28 - 21 * q^29 - 15 * q^31 + 60 * q^35 + 6 * q^37 - 15 * q^38 - 3 * q^40 + 12 * q^41 - 6 * q^43 - 66 * q^44 - 6 * q^46 + 15 * q^47 - 12 * q^49 + 24 * q^50 - 3 * q^52 - 18 * q^53 + 30 * q^55 - 12 * q^56 + 15 * q^58 - 6 * q^59 - 24 * q^61 - 60 * q^62 + 12 * q^64 + 15 * q^65 - 15 * q^67 - 36 * q^68 + 15 * q^70 + 24 * q^73 - 24 * q^74 - 9 * q^76 - 15 * q^77 - 24 * q^79 - 42 * q^80 - 42 * q^82 + 6 * q^83 + 18 * q^85 + 30 * q^86 + 21 * q^88 - 18 * q^89 + 36 * q^91 - 6 * q^92 + 6 * q^94 + 33 * q^95 + 21 * q^97 + 36 * q^98

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