LMFDB - Embedded newform 729.2.c.b.244.1

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:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			244.1
Root			$0.500000 + 1.00210i$ of defining polynomial
Character	$\chi$	$=$	729.244
Dual form			729.2.c.b.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20081 - 2.07986i) q^{2} +(-1.88389 + 3.26300i) q^{4} +(0.0465417 - 0.0806126i) q^{5} +(0.289931 + 0.502175i) q^{7} +4.24555 q^{8} +O(q^{10})$	\(q+(-1.20081 - 2.07986i) q^{2} +(-1.88389 + 3.26300i) q^{4} +(0.0465417 - 0.0806126i) q^{5} +(0.289931 + 0.502175i) q^{7} +4.24555 q^{8} -0.223551 q^{10} +(-1.54654 - 2.67869i) q^{11} +(-2.10087 + 3.63881i) q^{13} +(0.696304 - 1.20603i) q^{14} +(-1.33032 - 2.30417i) q^{16} +1.99099 q^{17} -3.84542 q^{19} +(0.175359 + 0.303731i) q^{20} +(-3.71421 + 6.43320i) q^{22} +(-2.22641 + 3.85625i) q^{23} +(2.49567 + 4.32262i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(3.19975 + 5.54214i) q^{29} +(-0.828750 + 1.43544i) q^{31} +(1.05064 - 1.81975i) q^{32} +(-2.39080 - 4.14098i) q^{34} +0.0539755 q^{35} +4.03009 q^{37} +(4.61762 + 7.99796i) q^{38} +(0.197595 - 0.342245i) q^{40} +(-0.548078 + 0.949299i) q^{41} +(3.45056 + 5.97655i) q^{43} +11.6541 q^{44} +10.6940 q^{46} +(1.79660 + 3.11180i) q^{47} +(3.33188 - 5.77099i) q^{49} +(5.99365 - 10.3813i) q^{50} +(-7.91561 - 13.7102i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(1.23091 + 2.13201i) q^{56} +(7.68460 - 13.3101i) q^{58} +(-5.14233 + 8.90677i) q^{59} +(6.59816 + 11.4283i) q^{61} +3.98069 q^{62} -10.3677 q^{64} +(0.195556 + 0.338713i) q^{65} +(4.41865 - 7.65332i) q^{67} +(-3.75080 + 6.49658i) q^{68} +(-0.0648143 - 0.112262i) q^{70} -1.14495 q^{71} +0.195472 q^{73} +(-4.83938 - 8.38205i) q^{74} +(7.24436 - 12.5476i) q^{76} +(0.896780 - 1.55327i) q^{77} +(3.60400 + 6.24231i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(-7.45022 - 12.9042i) q^{83} +(0.0926639 - 0.160499i) q^{85} +(8.28694 - 14.3534i) q^{86} +(-6.56592 - 11.3725i) q^{88} +1.55313 q^{89} -2.43642 q^{91} +(-8.38862 - 14.5295i) q^{92} +(4.31475 - 7.47336i) q^{94} +(-0.178973 + 0.309990i) q^{95} +(-2.64777 - 4.58607i) q^{97} -16.0038 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8	$ 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8 + 6 * q^10 - 12 * q^11 - 6 * q^14 + 3 * q^16 + 18 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 15 * q^23 + 6 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^29 + 24 * q^35 + 6 * q^37 + 3 * q^38 - 6 * q^40 - 15 * q^41 + 6 * q^44 + 6 * q^46 - 21 * q^47 + 12 * q^49 - 3 * q^50 - 12 * q^52 + 18 * q^53 - 12 * q^55 + 6 * q^56 + 12 * q^58 - 24 * q^59 + 9 * q^61 - 24 * q^62 - 24 * q^64 + 6 * q^65 + 9 * q^67 + 9 * q^68 - 15 * q^70 + 54 * q^71 - 12 * q^73 + 12 * q^74 - 6 * q^76 + 12 * q^77 - 42 * q^80 - 12 * q^82 - 12 * q^83 + 21 * q^86 - 12 * q^88 + 18 * q^89 - 12 * q^91 - 6 * q^92 - 6 * q^94 - 12 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.20081	−	2.07986i	−0.849101	−	1.47069i	−0.882011	−	0.471228i	$-0.843811\pi$
$2$	−1.20081	−	2.07986i	−0.849101	−	1.47069i	0.0329100	−	0.999458i	$-0.489523\pi$
$3$		0			0
$3$		0			0
$4$	−1.88389	+	3.26300i	−0.941946	+	1.63150i
$5$	0.0465417	−	0.0806126i	0.0208141	−	0.0360511i	−0.855431	−	0.517917i	$-0.826708\pi$
$5$	0.0465417	−	0.0806126i	0.0208141	−	0.0360511i	0.876245	+	0.481866i	$0.160041\pi$
$6$		0			0
$7$	0.289931	+	0.502175i	0.109583	+	0.189804i	0.915602	−	0.402087i	$-0.131715\pi$
$7$	0.289931	+	0.502175i	0.109583	+	0.189804i	−0.806018	+	0.591891i	$0.798382\pi$
$8$	4.24555			1.50103
$9$		0			0
$10$	−0.223551			−0.0706931
$11$	−1.54654	−	2.67869i	−0.466300	−	0.807655i	0.532959	−	0.846141i	$-0.321080\pi$
$11$	−1.54654	−	2.67869i	−0.466300	−	0.807655i	−0.999259	+	0.0384858i	$0.987747\pi$
$12$		0			0
$13$	−2.10087	+	3.63881i	−0.582676	+	1.00922i	0.412485	+	0.910964i	$0.364661\pi$
$13$	−2.10087	+	3.63881i	−0.582676	+	1.00922i	−0.995161	+	0.0982594i	$0.968673\pi$
$14$	0.696304	−	1.20603i	0.186095	−	0.322326i
$15$		0			0
$16$	−1.33032	−	2.30417i	−0.332579	−	0.576043i
$17$	1.99099			0.482885			0.241443	−	0.970415i	$-0.422379\pi$
$17$	1.99099			0.482885			0.241443	+	0.970415i	$0.422379\pi$
$18$		0			0
$19$	−3.84542			−0.882201			−0.441100	−	0.897458i	$-0.645412\pi$
$19$	−3.84542			−0.882201			−0.441100	+	0.897458i	$0.645412\pi$
$20$	0.175359	+	0.303731i	0.0392115	+	0.0679163i
$21$		0			0
$22$	−3.71421	+	6.43320i	−0.791872	+	1.37156i
$23$	−2.22641	+	3.85625i	−0.464238	+	0.804084i	−0.999167	−	0.0408132i	$-0.987005\pi$
$23$	−2.22641	+	3.85625i	−0.464238	+	0.804084i	0.534929	+	0.844897i	$0.320338\pi$
$24$		0			0
$25$	2.49567	+	4.32262i	0.499134	+	0.864525i
$26$	10.0910			1.97900
$27$		0			0
$28$	−2.18479			−0.412887
$29$	3.19975	+	5.54214i	0.594179	+	1.02915i	0.993662	+	0.112408i	$0.0358565\pi$
$29$	3.19975	+	5.54214i	0.594179	+	1.02915i	−0.399483	+	0.916741i	$0.630810\pi$
$30$		0			0
$31$	−0.828750	+	1.43544i	−0.148848	+	0.257812i	−0.930802	−	0.365524i	$-0.880890\pi$
$31$	−0.828750	+	1.43544i	−0.148848	+	0.257812i	0.781954	+	0.623336i	$0.214223\pi$
$32$	1.05064	−	1.81975i	0.185728	−	0.321690i
$33$		0			0
$34$	−2.39080	−	4.14098i	−0.410018	−	0.710173i
$35$	0.0539755			0.00912352
$36$		0			0
$37$	4.03009			0.662543			0.331272	−	0.943535i	$-0.392522\pi$
$37$	4.03009			0.662543			0.331272	+	0.943535i	$0.392522\pi$
$38$	4.61762	+	7.99796i	0.749078	+	1.29744i
$39$		0			0
$40$	0.197595	−	0.342245i	0.0312425	−	0.0541136i
$41$	−0.548078	+	0.949299i	−0.0855954	+	0.148256i	−0.905645	−	0.424037i	$-0.860613\pi$
$41$	−0.548078	+	0.949299i	−0.0855954	+	0.148256i	0.820049	+	0.572293i	$0.193946\pi$
$42$		0			0
$43$	3.45056	+	5.97655i	0.526206	+	0.911415i	0.999534	+	0.0305288i	$0.00971911\pi$
$43$	3.45056	+	5.97655i	0.526206	+	0.911415i	−0.473328	+	0.880886i	$0.656948\pi$
$44$	11.6541			1.75692
$45$		0			0
$46$	10.6940			1.57674
$47$	1.79660	+	3.11180i	0.262061	+	0.453902i	0.966789	−	0.255575i	$-0.0822646\pi$
$47$	1.79660	+	3.11180i	0.262061	+	0.453902i	−0.704729	+	0.709477i	$0.748931\pi$
$48$		0			0
$49$	3.33188	−	5.77099i	0.475983	−	0.824427i
$50$	5.99365	−	10.3813i	0.847630	−	1.46814i
$51$		0			0
$52$	−7.91561	−	13.7102i	−1.09770	−	1.90127i
$53$	−5.40034			−0.741793			−0.370897	−	0.928674i	$-0.620950\pi$
$53$	−5.40034			−0.741793			−0.370897	+	0.928674i	$0.620950\pi$
$54$		0			0
$55$	−0.287915			−0.0388224
$56$	1.23091	+	2.13201i	0.164488	+	0.284901i
$57$		0			0
$58$	7.68460	−	13.3101i	1.00904	−	1.74770i
$59$	−5.14233	+	8.90677i	−0.669474	+	1.15956i	0.308577	+	0.951199i	$0.400147\pi$
$59$	−5.14233	+	8.90677i	−0.669474	+	1.15956i	−0.978051	+	0.208364i	$0.933186\pi$
$60$		0			0
$61$	6.59816	+	11.4283i	0.844808	+	1.46325i	0.885788	+	0.464090i	$0.153619\pi$
$61$	6.59816	+	11.4283i	0.844808	+	1.46325i	−0.0409801	+	0.999160i	$0.513048\pi$
$62$	3.98069			0.505548
$63$		0			0
$64$	−10.3677			−1.29596
$65$	0.195556	+	0.338713i	0.0242557	+	0.0420121i
$66$		0			0
$67$	4.41865	−	7.65332i	0.539824	−	0.935002i	−0.459089	−	0.888390i	$-0.651824\pi$
$67$	4.41865	−	7.65332i	0.539824	−	0.935002i	0.998913	−	0.0466119i	$-0.0148424\pi$
$68$	−3.75080	+	6.49658i	−0.454852	+	0.787826i
$69$		0			0
$70$	−0.0648143	−	0.112262i	−0.00774679	−	0.0134178i
$71$	−1.14495			−0.135880			−0.0679401	−	0.997689i	$-0.521643\pi$
$71$	−1.14495			−0.135880			−0.0679401	+	0.997689i	$0.521643\pi$
$72$		0			0
$73$	0.195472			0.0228783			0.0114391	−	0.999935i	$-0.496359\pi$
$73$	0.195472			0.0228783			0.0114391	+	0.999935i	$0.496359\pi$
$74$	−4.83938	−	8.38205i	−0.562566	−	0.974394i
$75$		0			0
$76$	7.24436	−	12.5476i	0.830985	−	1.43931i
$77$	0.896780	−	1.55327i	0.102198	−	0.177011i
$78$		0			0
$79$	3.60400	+	6.24231i	0.405481	+	0.702314i	0.994377	−	0.105895i	$-0.0337706\pi$
$79$	3.60400	+	6.24231i	0.405481	+	0.702314i	−0.588896	+	0.808209i	$0.700437\pi$
$80$	−0.247661			−0.0276893
$81$		0			0
$82$	2.63255			0.290717
$83$	−7.45022	−	12.9042i	−0.817768	−	1.41642i	−0.907323	−	0.420434i	$-0.861878\pi$
$83$	−7.45022	−	12.9042i	−0.817768	−	1.41642i	0.0895548	−	0.995982i	$-0.471456\pi$
$84$		0			0
$85$	0.0926639	−	0.160499i	0.0100508	−	0.0174085i
$86$	8.28694	−	14.3534i	0.893604	−	1.54777i
$87$		0			0
$88$	−6.56592	−	11.3725i	−0.699929	−	1.21231i
$89$	1.55313			0.164631			0.0823155	−	0.996606i	$-0.473768\pi$
$89$	1.55313			0.164631			0.0823155	+	0.996606i	$0.473768\pi$
$90$		0			0
$91$	−2.43642			−0.255406
$92$	−8.38862	−	14.5295i	−0.874575	−	1.51481i
$93$		0			0
$94$	4.31475	−	7.47336i	0.445032	−	0.770818i
$95$	−0.178973	+	0.309990i	−0.0183622	+	0.0318043i
$96$		0			0
$97$	−2.64777	−	4.58607i	−0.268840	−	0.465645i	0.699723	−	0.714415i	$-0.253307\pi$
$97$	−2.64777	−	4.58607i	−0.268840	−	0.465645i	−0.968563	+	0.248770i	$0.919974\pi$
$98$	−16.0038			−1.61663
$99$		0			0
$100$	−18.8063			−1.88063
$101$	−3.63449	−	6.29512i	−0.361645	−	0.626388i	0.626586	−	0.779352i	$-0.284452\pi$
$101$	−3.63449	−	6.29512i	−0.361645	−	0.626388i	−0.988232	+	0.152964i	$0.951118\pi$
$102$		0			0
$103$	−3.20069	+	5.54375i	−0.315373	+	0.546242i	−0.979517	−	0.201363i	$-0.935463\pi$
$103$	−3.20069	+	5.54375i	−0.315373	+	0.546242i	0.664144	+	0.747605i	$0.268796\pi$
$104$	−8.91933	+	15.4487i	−0.874612	+	1.51487i
$105$		0			0
$106$	6.48478	+	11.2320i	0.629858	+	1.09095i
$107$	5.54365			0.535925			0.267963	−	0.963429i	$-0.413650\pi$
$107$	5.54365			0.535925			0.267963	+	0.963429i	$0.413650\pi$
$108$		0			0
$109$	−6.23137			−0.596857			−0.298428	−	0.954432i	$-0.596462\pi$
$109$	−6.23137			−0.596857			−0.298428	+	0.954432i	$0.596462\pi$
$110$	0.345731	+	0.598824i	0.0329642	+	0.0570956i
$111$		0			0
$112$	0.771398	−	1.33610i	0.0728903	−	0.126250i
$113$	−5.92199	+	10.2572i	−0.557094	+	0.964915i	0.440643	+	0.897682i	$0.354750\pi$
$113$	−5.92199	+	10.2572i	−0.557094	+	0.964915i	−0.997737	+	0.0672328i	$0.978583\pi$
$114$		0			0
$115$	0.207242	+	0.358953i	0.0193254	+	0.0334725i
$116$	−24.1120			−2.23874
$117$		0			0
$118$	24.6998			2.27381
$119$	0.577248	+	0.999823i	0.0529162	+	0.0916536i
$120$		0			0
$121$	0.716417	−	1.24087i	0.0651289	−	0.112806i
$122$	15.8463	−	27.4466i	1.43465	−	2.48490i
$123$		0			0
$124$	−3.12255	−	5.40842i	−0.280413	−	0.485690i
$125$	0.930028			0.0831842
$126$		0			0
$127$	11.5294			1.02307			0.511533	−	0.859263i	$-0.329078\pi$
$127$	11.5294			1.02307			0.511533	+	0.859263i	$0.329078\pi$
$128$	10.3484	+	17.9239i	0.914677	+	1.58427i
$129$		0			0
$130$	0.469651	−	0.813459i	0.0411911	−	0.0713451i
$131$	−4.50589	+	7.80443i	−0.393681	+	0.681876i	−0.992932	−	0.118686i	$-0.962132\pi$
$131$	−4.50589	+	7.80443i	−0.393681	+	0.681876i	0.599251	+	0.800561i	$0.295465\pi$
$132$		0			0
$133$	−1.11491	−	1.93107i	−0.0966746	−	0.167445i
$134$	−21.2238			−1.83346
$135$		0			0
$136$	8.45283			0.724824
$137$	5.76012	+	9.97681i	0.492120	+	0.852377i	0.999959	−	0.00907543i	$-0.00288884\pi$
$137$	5.76012	+	9.97681i	0.492120	+	0.852377i	−0.507839	+	0.861452i	$0.669556\pi$
$138$		0			0
$139$	−0.851917	+	1.47556i	−0.0722587	+	0.125156i	−0.899891	−	0.436115i	$-0.856354\pi$
$139$	−0.851917	+	1.47556i	−0.0722587	+	0.125156i	0.827632	+	0.561271i	$0.189687\pi$
$140$	−0.101684	+	0.176122i	−0.00859386	+	0.0148850i
$141$		0			0
$142$	1.37486	+	2.38133i	0.115376	+	0.199837i
$143$	12.9963			1.08681
$144$		0			0
$145$	0.595688			0.0494692
$146$	−0.234725	−	0.406556i	−0.0194260	−	0.0336468i
$147$		0			0
$148$	−7.59226	+	13.1502i	−0.624080	+	1.08094i
$149$	−10.8264	+	18.7518i	−0.886932	+	1.53621i	−0.0434485	+	0.999056i	$0.513834\pi$
$149$	−10.8264	+	18.7518i	−0.886932	+	1.53621i	−0.843483	+	0.537155i	$0.819499\pi$
$150$		0			0
$151$	2.37076	+	4.10628i	0.192930	+	0.334164i	0.946220	−	0.323524i	$-0.104868\pi$
$151$	2.37076	+	4.10628i	0.192930	+	0.334164i	−0.753290	+	0.657688i	$0.771534\pi$
$152$	−16.3259			−1.32421
$153$		0			0
$154$	−4.30745			−0.347104
$155$	0.0771429	+	0.133615i	0.00619626	+	0.0107322i
$156$		0			0
$157$	0.104603	−	0.181178i	0.00834822	−	0.0144595i	−0.861821	−	0.507212i	$-0.830676\pi$
$157$	0.104603	−	0.181178i	0.00834822	−	0.0144595i	0.870169	+	0.492753i	$0.164009\pi$
$158$	8.65544	−	14.9917i	0.688589	−	1.19267i
$159$		0			0
$160$	−0.0977967	−	0.169389i	−0.00773151	−	0.0133914i
$161$	−2.58202			−0.203491
$162$		0			0
$163$	5.62384			0.440493			0.220247	−	0.975444i	$-0.429314\pi$
$163$	5.62384			0.440493			0.220247	+	0.975444i	$0.429314\pi$
$164$	−2.06504	−	3.57675i	−0.161253	−	0.279298i
$165$		0			0
$166$	−17.8926	+	30.9909i	−1.38874	+	2.40536i
$167$	8.34025	−	14.4457i	0.645388	−	1.11784i	−0.338824	−	0.940850i	$-0.610029\pi$
$167$	8.34025	−	14.4457i	0.645388	−	1.11784i	0.984212	−	0.176995i	$-0.0566375\pi$
$168$		0			0
$169$	−2.32728	−	4.03097i	−0.179022	−	0.310074i
$170$	−0.445087			−0.0341366
$171$		0			0
$172$	−26.0019			−1.98263
$173$	9.50107	+	16.4563i	0.722353	+	1.25115i	0.960054	+	0.279814i	$0.0902728\pi$
$173$	9.50107	+	16.4563i	0.722353	+	1.25115i	−0.237701	+	0.971338i	$0.576394\pi$
$174$		0			0
$175$	−1.44714	+	2.50652i	−0.109394	+	0.189475i
$176$	−4.11478	+	7.12700i	−0.310163	+	0.537218i
$177$		0			0
$178$	−1.86501	−	3.23029i	−0.139788	−	0.242121i
$179$	−16.2352			−1.21348			−0.606739	−	0.794901i	$-0.707523\pi$
$179$	−16.2352			−1.21348			−0.606739	+	0.794901i	$0.707523\pi$
$180$		0			0
$181$	−2.99158			−0.222362			−0.111181	−	0.993800i	$-0.535463\pi$
$181$	−2.99158			−0.222362			−0.111181	+	0.993800i	$0.535463\pi$
$182$	2.92568	+	5.06743i	0.216866	+	0.375623i
$183$		0			0
$184$	−9.45232	+	16.3719i	−0.696834	+	1.20695i
$185$	0.187567	−	0.324876i	0.0137902	−	0.0238854i
$186$		0			0
$187$	−3.07914	−	5.33323i	−0.225169	−	0.390005i
$188$	−13.5384			−0.987388
$189$		0			0
$190$	0.859649			0.0623655
$191$	−1.12691	−	1.95186i	−0.0815402	−	0.141232i	0.822371	−	0.568951i	$-0.192651\pi$
$191$	−1.12691	−	1.95186i	−0.0815402	−	0.141232i	−0.903912	+	0.427719i	$0.859317\pi$
$192$		0			0
$193$	0.440137	−	0.762339i	0.0316817	−	0.0548743i	−0.849750	−	0.527186i	$-0.823247\pi$
$193$	0.440137	−	0.762339i	0.0316817	−	0.0548743i	0.881432	+	0.472312i	$0.156580\pi$
$194$	−6.35893	+	11.0140i	−0.456545	+	0.790759i
$195$		0			0
$196$	12.5538	+	21.7438i	0.896700	+	1.55313i
$197$	−20.2766			−1.44464			−0.722322	−	0.691557i	$-0.756925\pi$
$197$	−20.2766			−1.44464			−0.722322	+	0.691557i	$0.756925\pi$
$198$		0			0
$199$	−19.0094			−1.34754			−0.673772	−	0.738939i	$-0.735327\pi$
$199$	−19.0094			−1.34754			−0.673772	+	0.738939i	$0.735327\pi$
$200$	10.5955	+	18.3519i	0.749213	+	1.29768i
$201$		0			0
$202$	−8.72867	+	15.1185i	−0.614147	+	1.06373i
$203$	−1.85541	+	3.21367i	−0.130225	+	0.225556i
$204$		0			0
$205$	0.0510170	+	0.0883640i	0.00356318	+	0.00617161i
$206$	15.3737			1.07113
$207$		0			0
$208$	11.1793			0.775142
$209$	5.94711	+	10.3007i	0.411370	+	0.712514i
$210$		0			0
$211$	−8.09203	+	14.0158i	−0.557079	+	0.964888i	0.440660	+	0.897674i	$0.354744\pi$
$211$	−8.09203	+	14.0158i	−0.557079	+	0.964888i	−0.997739	+	0.0672143i	$0.978589\pi$
$212$	10.1737	−	17.6213i	0.698729	−	1.21023i
$213$		0			0
$214$	−6.65688	−	11.5300i	−0.455055	−	0.788178i
$215$	0.642380			0.0438100
$216$		0			0
$217$	−0.961120			−0.0652451
$218$	7.48270	+	12.9604i	0.506792	+	0.877790i
$219$		0			0
$220$	0.542400	−	0.939465i	0.0365686	−	0.0633387i
$221$	−4.18280	+	7.24482i	−0.281365	+	0.487339i
$222$		0			0
$223$	−10.7286	−	18.5826i	−0.718443	−	1.24438i	−0.961616	−	0.274398i	$-0.911522\pi$
$223$	−10.7286	−	18.5826i	−0.718443	−	1.24438i	0.243173	−	0.969983i	$-0.421812\pi$
$224$	1.21845			0.0814108
$225$		0			0
$226$	28.4448			1.89212
$227$	−9.55712	−	16.5534i	−0.634329	−	1.09869i	−0.986657	−	0.162813i	$-0.947943\pi$
$227$	−9.55712	−	16.5534i	−0.634329	−	1.09869i	0.352328	−	0.935876i	$-0.385390\pi$
$228$		0			0
$229$	−11.2351	+	19.4597i	−0.742435	+	1.28594i	0.208949	+	0.977927i	$0.432996\pi$
$229$	−11.2351	+	19.4597i	−0.742435	+	1.28594i	−0.951384	+	0.308008i	$0.900337\pi$
$230$	0.497716	−	0.862069i	0.0328184	−	0.0568432i
$231$		0			0
$232$	13.5847	+	23.5294i	0.891880	+	1.54478i
$233$	17.6815			1.15835			0.579176	−	0.815203i	$-0.303374\pi$
$233$	17.6815			1.15835			0.579176	+	0.815203i	$0.303374\pi$
$234$		0			0
$235$	0.334467			0.0218182
$236$	−19.3752	−	33.5588i	−1.26122	−	2.18449i
$237$		0			0
$238$	1.38633	−	2.40120i	0.0898625	−	0.155646i
$239$	−7.71016	+	13.3544i	−0.498729	+	0.863823i	−0.999999	−	0.00146732i	$-0.999533\pi$
$239$	−7.71016	+	13.3544i	−0.498729	+	0.863823i	0.501270	+	0.865291i	$0.332866\pi$
$240$		0			0
$241$	−6.57572	−	11.3895i	−0.423580	−	0.733661i	0.572707	−	0.819760i	$-0.305893\pi$
$241$	−6.57572	−	11.3895i	−0.423580	−	0.733661i	−0.996287	+	0.0860987i	$0.972560\pi$
$242$	−3.44113			−0.221204
$243$		0			0
$244$	−49.7209			−3.18305
$245$	−0.310143	−	0.537183i	−0.0198143	−	0.0343194i
$246$		0			0
$247$	8.07872	−	13.9928i	0.514037	−	0.890338i
$248$	−3.51850	+	6.09422i	−0.223425	+	0.386983i
$249$		0			0
$250$	−1.11679	−	1.93433i	−0.0706318	−	0.122338i
$251$	−17.4166			−1.09933			−0.549663	−	0.835386i	$-0.685244\pi$
$251$	−17.4166			−1.09933			−0.549663	+	0.835386i	$0.685244\pi$
$252$		0			0
$253$	13.7729			0.865897
$254$	−13.8446	−	23.9795i	−0.868687	−	1.50461i
$255$		0			0
$256$	14.4852	−	25.0891i	0.905325	−	1.56807i
$257$	5.59379	−	9.68873i	0.348931	−	0.604366i	−0.637129	−	0.770757i	$-0.719878\pi$
$257$	5.59379	−	9.68873i	0.348931	−	0.604366i	0.986060	+	0.166391i	$0.0532114\pi$
$258$		0			0
$259$	1.16845	+	2.02381i	0.0726038	+	0.125754i
$260$	−1.47362			−0.0913903
$261$		0			0
$262$	21.6429			1.33710
$263$	−10.3554	−	17.9362i	−0.638544	−	1.10599i	−0.985752	−	0.168203i	$-0.946204\pi$
$263$	−10.3554	−	17.9362i	−0.638544	−	1.10599i	0.347209	−	0.937788i	$-0.387130\pi$
$264$		0			0
$265$	−0.251341	+	0.435335i	−0.0154397	+	0.0267424i
$266$	−2.67758	+	4.63771i	−0.164173	+	0.284356i
$267$		0			0
$268$	16.6485	+	28.8361i	1.01697	+	1.76144i
$269$	28.2449			1.72212			0.861060	−	0.508504i	$-0.169801\pi$
$269$	28.2449			1.72212			0.861060	+	0.508504i	$0.169801\pi$
$270$		0			0
$271$	17.2626			1.04863			0.524316	−	0.851524i	$-0.324321\pi$
$271$	17.2626			1.04863			0.524316	+	0.851524i	$0.324321\pi$
$272$	−2.64864	−	4.58758i	−0.160597	−	0.278163i
$273$		0			0
$274$	13.8336	−	23.9605i	0.835719	−	1.44751i
$275$	7.71931	−	13.3702i	0.465492	−	0.806255i
$276$		0			0
$277$	−2.58449	−	4.47647i	−0.155287	−	0.268965i	0.777877	−	0.628417i	$-0.216297\pi$
$277$	−2.58449	−	4.47647i	−0.155287	−	0.268965i	−0.933163	+	0.359452i	$0.882964\pi$
$278$	4.09197			0.245420
$279$		0			0
$280$	0.229155			0.0136947
$281$	−1.64822	−	2.85480i	−0.0983246	−	0.170303i	0.812667	−	0.582729i	$-0.198015\pi$
$281$	−1.64822	−	2.85480i	−0.0983246	−	0.170303i	−0.910991	+	0.412426i	$0.864682\pi$
$282$		0			0
$283$	4.56536	−	7.90744i	0.271382	−	0.470048i	−0.697834	−	0.716260i	$-0.745853\pi$
$283$	4.56536	−	7.90744i	0.271382	−	0.470048i	0.969216	+	0.246212i	$0.0791858\pi$
$284$	2.15696	−	3.73596i	0.127992	−	0.221688i
$285$		0			0
$286$	−15.6061	−	27.0306i	−0.922809	−	1.59835i
$287$	−0.635618			−0.0375194
$288$		0			0
$289$	−13.0360			−0.766822
$290$	−0.715309	−	1.23895i	−0.0420044	−	0.0727537i
$291$		0			0
$292$	−0.368248	+	0.637825i	−0.0215501	+	0.0373259i
$293$	−1.41322	+	2.44776i	−0.0825610	+	0.143000i	−0.904349	−	0.426793i	$-0.859643\pi$
$293$	−1.41322	+	2.44776i	−0.0825610	+	0.143000i	0.821788	+	0.569793i	$0.192977\pi$
$294$		0			0
$295$	0.478665	+	0.829073i	0.0278690	+	0.0482705i
$296$	17.1100			0.994496
$297$		0			0
$298$	52.0017			3.01238
$299$	−9.35477	−	16.2029i	−0.541000	−	0.937040i
$300$		0			0
$301$	−2.00085	+	3.46557i	−0.115327	+	0.199752i
$302$	5.69367	−	9.86173i	0.327634	−	0.567479i
$303$		0			0
$304$	5.11562	+	8.86052i	0.293401	+	0.508186i
$305$	1.22836			0.0703356
$306$		0			0
$307$	6.29446			0.359244			0.179622	−	0.983736i	$-0.442513\pi$
$307$	6.29446			0.359244			0.179622	+	0.983736i	$0.442513\pi$
$308$	3.37887	+	5.85238i	0.192529	+	0.333470i
$309$		0			0
$310$	0.185268	−	0.320894i	0.0105225	−	0.0182255i
$311$	−3.68644	+	6.38511i	−0.209039	+	0.362066i	−0.951412	−	0.307920i	$-0.900367\pi$
$311$	−3.68644	+	6.38511i	−0.209039	+	0.362066i	0.742373	+	0.669987i	$0.233700\pi$
$312$		0			0
$313$	2.13538	+	3.69858i	0.120699	+	0.209056i	0.920043	−	0.391817i	$-0.128153\pi$
$313$	2.13538	+	3.69858i	0.120699	+	0.209056i	−0.799345	+	0.600873i	$0.794820\pi$
$314$	−0.502433			−0.0283539
$315$		0			0
$316$	−27.1582			−1.52777
$317$	8.07379	+	13.9842i	0.453469	+	0.785431i	0.998599	−	0.0529204i	$-0.0168529\pi$
$317$	8.07379	+	13.9842i	0.453469	+	0.785431i	−0.545130	+	0.838352i	$0.683520\pi$
$318$		0			0
$319$	9.89711	−	17.1423i	0.554132	−	0.959784i
$320$	−0.482531	+	0.835769i	−0.0269743	+	0.0467209i
$321$		0			0
$322$	3.10051	+	5.37024i	0.172785	+	0.299272i
$323$	−7.65618			−0.426001
$324$		0			0
$325$	−20.9723			−1.16333
$326$	−6.75317	−	11.6968i	−0.374024	−	0.647828i
$327$		0			0
$328$	−2.32689	+	4.03029i	−0.128481	+	0.222536i
$329$	−1.04178	+	1.80441i	−0.0574350	+	0.0994804i
$330$		0			0
$331$	−9.61412	−	16.6521i	−0.528440	−	0.915284i	−0.999450	−	0.0331567i	$-0.989444\pi$
$331$	−9.61412	−	16.6521i	−0.528440	−	0.915284i	0.471011	−	0.882128i	$-0.343889\pi$
$332$	56.1417			3.08117
$333$		0			0
$334$	−40.0602			−2.19200
$335$	−0.411303	−	0.712397i	−0.0224719	−	0.0389224i
$336$		0			0
$337$	14.7314	−	25.5155i	0.802469	−	1.38992i	−0.115517	−	0.993306i	$-0.536852\pi$
$337$	14.7314	−	25.5155i	0.802469	−	1.38992i	0.917986	−	0.396612i	$-0.129814\pi$
$338$	−5.58925	+	9.68086i	−0.304015	+	0.526569i
$339$		0			0
$340$	0.349138	+	0.604724i	0.0189346	+	0.0327958i
$341$	5.12679			0.277631
$342$		0			0
$343$	7.92309			0.427806
$344$	14.6495	+	25.3737i	0.789849	+	1.36806i
$345$		0			0
$346$	22.8180	−	39.5219i	1.22670	−	2.12471i
$347$	5.69852	−	9.87012i	0.305912	−	0.529856i	−0.671552	−	0.740958i	$-0.734372\pi$
$347$	5.69852	−	9.87012i	0.305912	−	0.529856i	0.977464	+	0.211102i	$0.0677052\pi$
$348$		0			0
$349$	−14.0808	−	24.3887i	−0.753728	−	1.30550i	−0.946004	−	0.324155i	$-0.894920\pi$
$349$	−14.0808	−	24.3887i	−0.753728	−	1.30550i	0.192276	−	0.981341i	$-0.438413\pi$
$350$	6.95097			0.371545
$351$		0			0
$352$	−6.49941			−0.346419
$353$	14.3270	+	24.8152i	0.762552	+	1.32078i	0.941531	+	0.336926i	$0.109387\pi$
$353$	14.3270	+	24.8152i	0.762552	+	1.32078i	−0.178979	+	0.983853i	$0.557280\pi$
$354$		0			0
$355$	−0.0532878	+	0.0922971i	−0.00282822	+	0.00489862i
$356$	−2.92592	+	5.06784i	−0.155074	+	0.268595i
$357$		0			0
$358$	19.4954	+	33.7671i	1.03037	+	1.78465i
$359$	31.0322			1.63782			0.818909	−	0.573923i	$-0.194579\pi$
$359$	31.0322			1.63782			0.818909	+	0.573923i	$0.194579\pi$
$360$		0			0
$361$	−4.21272			−0.221722
$362$	3.59232	+	6.22208i	0.188808	+	0.327025i
$363$		0			0
$364$	4.58996	−	7.95004i	0.240579	−	0.416695i
$365$	0.00909761	−	0.0157575i	0.000476190	−	0.000824786i
$366$		0			0
$367$	−12.0621	−	20.8922i	−0.629637	−	1.09056i	−0.987625	−	0.156837i	$-0.949870\pi$
$367$	−12.0621	−	20.8922i	−0.629637	−	1.09056i	0.357988	−	0.933726i	$-0.383463\pi$
$368$	11.8473			0.617583
$369$		0			0
$370$	−0.900932			−0.0468372
$371$	−1.56572	−	2.71191i	−0.0812883	−	0.140795i
$372$		0			0
$373$	6.29281	−	10.8995i	0.325829	−	0.564353i	−0.655851	−	0.754891i	$-0.727690\pi$
$373$	6.29281	−	10.8995i	0.325829	−	0.564353i	0.981680	+	0.190538i	$0.0610232\pi$
$374$	−7.39494	+	12.8084i	−0.382383	+	0.662307i
$375$		0			0
$376$	7.62754	+	13.2113i	0.393360	+	0.681320i
$377$	−26.8890			−1.38486
$378$		0			0
$379$	−7.70522			−0.395790			−0.197895	−	0.980223i	$-0.563411\pi$
$379$	−7.70522			−0.395790			−0.197895	+	0.980223i	$0.563411\pi$
$380$	−0.674330	−	1.16797i	−0.0345924	−	0.0599158i
$381$		0			0
$382$	−2.70641	+	4.68763i	−0.138472	+	0.239840i
$383$	−8.93081	+	15.4686i	−0.456343	+	0.790410i	−0.998764	−	0.0496970i	$-0.984174\pi$
$383$	−8.93081	+	15.4686i	−0.456343	+	0.790410i	0.542421	+	0.840107i	$0.317508\pi$
$384$		0			0
$385$	−0.0834753	−	0.144584i	−0.00425430	−	0.00736866i
$386$	−2.11408			−0.107604
$387$		0			0
$388$	19.9524			1.01293
$389$	13.6942	+	23.7191i	0.694325	+	1.20261i	0.970408	+	0.241472i	$0.0776303\pi$
$389$	13.6942	+	23.7191i	0.694325	+	1.20261i	−0.276083	+	0.961134i	$0.589036\pi$
$390$		0			0
$391$	−4.43275	+	7.67774i	−0.224174	+	0.388280i
$392$	14.1457	−	24.5010i	0.714464	−	1.23749i
$393$		0			0
$394$	24.3483	+	42.1725i	1.22665	+	2.12462i
$395$	0.670945			0.0337589
$396$		0			0
$397$	4.21599			0.211594			0.105797	−	0.994388i	$-0.466261\pi$
$397$	4.21599			0.211594			0.105797	+	0.994388i	$0.466261\pi$
$398$	22.8267	+	39.5371i	1.14420	+	1.98181i
$399$		0			0
$400$	6.64005	−	11.5009i	0.332002	−	0.575045i
$401$	7.58625	−	13.1398i	0.378839	−	0.656169i	−0.612054	−	0.790816i	$-0.709657\pi$
$401$	7.58625	−	13.1398i	0.378839	−	0.656169i	0.990894	+	0.134647i	$0.0429900\pi$
$402$		0			0
$403$	−3.48219	−	6.03132i	−0.173460	−	0.300442i
$404$	27.3880			1.36260
$405$		0			0
$406$	8.91200			0.442295
$407$	−6.23271	−	10.7954i	−0.308944	−	0.535107i
$408$		0			0
$409$	−2.35481	+	4.07864i	−0.116438	+	0.201676i	−0.918354	−	0.395761i	$-0.870481\pi$
$409$	−2.35481	+	4.07864i	−0.116438	+	0.201676i	0.801916	+	0.597437i	$0.203814\pi$
$410$	0.122523	−	0.212217i	0.00605100	−	0.0104806i
$411$		0			0
$412$	−12.0595	−	20.8877i	−0.594129	−	1.02906i
$413$	−5.96367			−0.293453
$414$		0			0
$415$	−1.38698			−0.0680844
$416$	4.41449	+	7.64612i	0.216438	+	0.374882i
$417$		0			0
$418$	14.2827	−	24.7384i	0.698590	−	1.20999i
$419$	9.89557	−	17.1396i	0.483430	−	0.837325i	−0.516389	−	0.856354i	$-0.672724\pi$
$419$	9.89557	−	17.1396i	0.483430	−	0.837325i	0.999819	+	0.0190288i	$0.00605741\pi$
$420$		0			0
$421$	−14.0929	−	24.4095i	−0.686844	−	1.18965i	−0.972854	−	0.231422i	$-0.925662\pi$
$421$	−14.0929	−	24.4095i	−0.686844	−	1.18965i	0.286010	−	0.958227i	$-0.407671\pi$
$422$	38.8680			1.89206
$423$		0			0
$424$	−22.9274			−1.11345
$425$	4.96884	+	8.60628i	0.241024	+	0.417466i
$426$		0			0
$427$	−3.82602	+	6.62686i	−0.185154	+	0.320696i
$428$	−10.4436	+	18.0889i	−0.504813	+	0.874361i
$429$		0			0
$430$	−0.771377	−	1.33606i	−0.0371991	−	0.0644307i
$431$	5.19681			0.250321			0.125161	−	0.992136i	$-0.460055\pi$
$431$	5.19681			0.250321			0.125161	+	0.992136i	$0.460055\pi$
$432$		0			0
$433$	25.3285			1.21721			0.608605	−	0.793473i	$-0.291730\pi$
$433$	25.3285			1.21721			0.608605	+	0.793473i	$0.291730\pi$
$434$	1.15412	+	1.99900i	0.0553997	+	0.0959551i
$435$		0			0
$436$	11.7392	−	20.3329i	0.562207	−	0.973771i
$437$	8.56148	−	14.8289i	0.409551	−	0.709363i
$438$		0			0
$439$	7.83062	+	13.5630i	0.373735	+	0.647328i	0.990137	−	0.140104i	$-0.0447436\pi$
$439$	7.83062	+	13.5630i	0.373735	+	0.647328i	−0.616402	+	0.787432i	$0.711410\pi$
$440$	−1.22236			−0.0582735
$441$		0			0
$442$	20.0910			0.955631
$443$	−9.12692	−	15.8083i	−0.433633	−	0.751075i	0.563550	−	0.826082i	$-0.309435\pi$
$443$	−9.12692	−	15.8083i	−0.433633	−	0.751075i	−0.997183	+	0.0750074i	$0.976102\pi$
$444$		0			0
$445$	0.0722851	−	0.125202i	0.00342664	−	0.00593512i
$446$	−25.7661	+	44.6283i	−1.22006	+	2.11321i
$447$		0			0
$448$	−3.00592	−	5.20640i	−0.142016	−	0.245979i
$449$	−28.7216			−1.35546			−0.677729	−	0.735312i	$-0.737036\pi$
$449$	−28.7216			−1.35546			−0.677729	+	0.735312i	$0.737036\pi$
$450$		0			0
$451$	3.39050			0.159652
$452$	−22.3128	−	38.6469i	−1.04950	−	1.81780i
$453$		0			0
$454$	−22.9526	+	39.7551i	−1.07722	+	1.86580i
$455$	−0.113395	+	0.196406i	−0.00531605	+	0.00920767i
$456$		0			0
$457$	17.6940	+	30.6468i	0.827688	+	1.43360i	0.899847	+	0.436205i	$0.143678\pi$
$457$	17.6940	+	30.6468i	0.827688	+	1.43360i	−0.0721589	+	0.997393i	$0.522989\pi$
$458$	53.9648			2.52161
$459$		0			0
$460$	−1.56168			−0.0728139
$461$	1.13836	+	1.97171i	0.0530189	+	0.0918315i	0.891317	−	0.453381i	$-0.149782\pi$
$461$	1.13836	+	1.97171i	0.0530189	+	0.0918315i	−0.838298	+	0.545212i	$0.816449\pi$
$462$		0			0
$463$	−9.18726	+	15.9128i	−0.426968	+	0.739531i	−0.996602	−	0.0823678i	$-0.973752\pi$
$463$	−9.18726	+	15.9128i	−0.426968	+	0.739531i	0.569634	+	0.821899i	$0.307085\pi$
$464$	8.51336	−	14.7456i	0.395223	−	0.684546i
$465$		0			0
$466$	−21.2321	−	36.7751i	−0.983558	−	1.70357i
$467$	−4.65870			−0.215579			−0.107789	−	0.994174i	$-0.534377\pi$
$467$	−4.65870			−0.215579			−0.107789	+	0.994174i	$0.534377\pi$
$468$		0			0
$469$	5.12440			0.236623
$470$	−0.401631	−	0.695646i	−0.0185259	−	0.0320877i
$471$		0			0
$472$	−21.8320	+	37.8141i	−1.00490	+	1.74054i
$473$	10.6729	−	18.4860i	0.490739	−	0.849985i
$474$		0			0
$475$	−9.59690	−	16.6223i	−0.440336	−	0.762684i
$476$	−4.34989			−0.199377
$477$		0			0
$478$	37.0338			1.69388
$479$	−7.08795	−	12.2767i	−0.323857	−	0.560936i	0.657424	−	0.753521i	$-0.271646\pi$
$479$	−7.08795	−	12.2767i	−0.323857	−	0.560936i	−0.981280	+	0.192585i	$0.938313\pi$
$480$		0			0
$481$	−8.46669	+	14.6647i	−0.386048	+	0.668654i
$482$	−15.7924	+	27.3532i	−0.719324	+	1.24591i
$483$		0			0
$484$	2.69931	+	4.67534i	0.122696	+	0.212515i
$485$	−0.492926			−0.0223826
$486$		0			0
$487$	−21.4338			−0.971258			−0.485629	−	0.874165i	$-0.661409\pi$
$487$	−21.4338			−0.971258			−0.485629	+	0.874165i	$0.661409\pi$
$488$	28.0128	+	48.5196i	1.26808	+	2.19638i
$489$		0			0
$490$	−0.744846	+	1.29011i	−0.0336487	+	0.0582812i
$491$	−7.04393	+	12.2004i	−0.317888	+	0.550598i	−0.980047	−	0.198765i	$-0.936307\pi$
$491$	−7.04393	+	12.2004i	−0.317888	+	0.550598i	0.662159	+	0.749363i	$0.269640\pi$
$492$		0			0
$493$	6.37067	+	11.0343i	0.286920	+	0.496961i
$494$	−38.8041			−1.74588
$495$		0			0
$496$	4.40999			0.198015
$497$	−0.331955	−	0.574963i	−0.0148902	−	0.0257906i
$498$		0			0
$499$	−7.45467	+	12.9119i	−0.333717	+	0.578014i	−0.983237	−	0.182330i	$-0.941636\pi$
$499$	−7.45467	+	12.9119i	−0.333717	+	0.578014i	0.649521	+	0.760344i	$0.274970\pi$
$500$	−1.75207	+	3.03468i	−0.0783550	+	0.135715i
$501$		0			0
$502$	20.9140	+	36.2242i	0.933440	+	1.61676i
$503$	15.8631			0.707299			0.353650	−	0.935378i	$-0.384941\pi$
$503$	15.8631			0.707299			0.353650	+	0.935378i	$0.384941\pi$
$504$		0			0
$505$	−0.676622			−0.0301093
$506$	−16.5387	−	28.6458i	−0.735234	−	1.27346i
$507$		0			0
$508$	−21.7201	+	37.6203i	−0.963674	+	1.66913i
$509$	16.9633	−	29.3814i	0.751887	−	1.30231i	−0.195020	−	0.980799i	$-0.562477\pi$
$509$	16.9633	−	29.3814i	0.751887	−	1.30231i	0.946907	−	0.321508i	$-0.104190\pi$
$510$		0			0
$511$	0.0566734	+	0.0981611i	0.00250708	+	0.00434239i
$512$	−28.1824			−1.24550
$513$		0			0
$514$	−26.8683			−1.18511
$515$	0.297931	+	0.516031i	0.0131284	+	0.0227391i
$516$		0			0
$517$	5.55702	−	9.62505i	0.244398	−	0.423309i
$518$	2.80617	−	4.86043i	0.123296	−	0.213555i
$519$		0			0
$520$	0.830242	+	1.43802i	0.0364085	+	0.0630614i
$521$	42.7798			1.87422			0.937108	−	0.349039i	$-0.113492\pi$
$521$	42.7798			1.87422			0.937108	+	0.349039i	$0.113492\pi$
$522$		0			0
$523$	−2.77785			−0.121467			−0.0607335	−	0.998154i	$-0.519344\pi$
$523$	−2.77785			−0.121467			−0.0607335	+	0.998154i	$0.519344\pi$
$524$	−16.9772	−	29.4054i	−0.741653	−	1.28458i
$525$		0			0
$526$	−24.8698	+	43.0758i	−1.08438	+	1.87820i
$527$	−1.65003	+	2.85794i	−0.0718764	+	0.124494i
$528$		0			0
$529$	1.58622	+	2.74741i	0.0689660	+	0.119453i
$530$	1.20725			0.0524396
$531$		0			0
$532$	8.40145			0.364249
$533$	−2.30288	−	3.98870i	−0.0997487	−	0.172770i
$534$		0			0
$535$	0.258011	−	0.446888i	0.0111548	−	0.0193207i
$536$	18.7596	−	32.4925i	0.810290	−	1.40346i
$537$		0			0
$538$	−33.9167	−	58.7455i	−1.46225	−	2.53270i
$539$	−20.6116			−0.887803
$540$		0			0
$541$	−3.59390			−0.154514			−0.0772570	−	0.997011i	$-0.524616\pi$
$541$	−3.59390			−0.154514			−0.0772570	+	0.997011i	$0.524616\pi$
$542$	−20.7292	−	35.9040i	−0.890394	−	1.54221i
$543$		0			0
$544$	2.09180	−	3.62310i	0.0896852	−	0.155339i
$545$	−0.290019	+	0.502327i	−0.0124230	+	0.0215173i
$546$		0			0
$547$	19.7929	+	34.2823i	0.846284	+	1.46581i	0.884501	+	0.466537i	$0.154499\pi$
$547$	19.7929	+	34.2823i	0.846284	+	1.46581i	−0.0382175	+	0.999269i	$0.512168\pi$
$548$	−43.4057			−1.85420
$549$		0			0
$550$	−37.0777			−1.58100
$551$	−12.3044	−	21.3119i	−0.524185	−	0.907916i
$552$		0			0
$553$	−2.08982	+	3.61967i	−0.0888681	+	0.153924i
$554$	−6.20696	+	10.7508i	−0.263709	+	0.456757i
$555$		0			0
$556$	−3.20984	−	5.55961i	−0.136128	−	0.235780i
$557$	11.4346			0.484501			0.242250	−	0.970214i	$-0.422114\pi$
$557$	11.4346			0.484501			0.242250	+	0.970214i	$0.422114\pi$
$558$		0			0
$559$	−28.9967			−1.22643
$560$	−0.0718044	−	0.124369i	−0.00303429	−	0.00525554i
$561$		0			0
$562$	−3.95840	+	6.85615i	−0.166975	+	0.289209i
$563$	7.25540	−	12.5667i	0.305778	−	0.529624i	−0.671656	−	0.740863i	$-0.734417\pi$
$563$	7.25540	−	12.5667i	0.305778	−	0.529624i	0.977434	+	0.211239i	$0.0677500\pi$
$564$		0			0
$565$	0.551239	+	0.954774i	0.0231908	+	0.0401676i
$566$	−21.9285			−0.921725
$567$		0			0
$568$	−4.86093			−0.203960
$569$	−0.649591	−	1.12513i	−0.0272323	−	0.0471677i	0.852088	−	0.523398i	$-0.175336\pi$
$569$	−0.649591	−	1.12513i	−0.0272323	−	0.0471677i	−0.879320	+	0.476231i	$0.842003\pi$
$570$		0			0
$571$	−8.02866	+	13.9061i	−0.335989	+	0.581950i	−0.983674	−	0.179958i	$-0.942404\pi$
$571$	−8.02866	+	13.9061i	−0.335989	+	0.581950i	0.647685	+	0.761908i	$0.275737\pi$
$572$	−24.4836	+	42.4069i	−1.02371	+	1.77312i
$573$		0			0
$574$	0.763257	+	1.32200i	0.0318577	+	0.0551792i
$575$	−22.2255			−0.926867
$576$		0			0
$577$	−8.46033			−0.352208			−0.176104	−	0.984372i	$-0.556350\pi$
$577$	−8.46033			−0.352208			−0.176104	+	0.984372i	$0.556350\pi$
$578$	15.6537	+	27.1131i	0.651110	+	1.12775i
$579$		0			0
$580$	−1.12221	+	1.94373i	−0.0465973	+	0.0807089i
$581$	4.32010	−	7.48263i	0.179228	−	0.310432i
$582$		0			0
$583$	8.35184	+	14.4658i	0.345898	+	0.599113i
$584$	0.829886			0.0343409
$585$		0			0
$586$	6.78802			0.280411
$587$	−9.19260	−	15.9221i	−0.379419	−	0.657173i	0.611559	−	0.791199i	$-0.290543\pi$
$587$	−9.19260	−	15.9221i	−0.379419	−	0.657173i	−0.990978	+	0.134026i	$0.957210\pi$
$588$		0			0
$589$	3.18689	−	5.51986i	0.131314	−	0.227442i
$590$	1.14957	−	1.99112i	0.0473272	−	0.0819731i
$591$		0			0
$592$	−5.36130	−	9.28604i	−0.220348	−	0.381654i
$593$	−13.5128			−0.554905			−0.277452	−	0.960739i	$-0.589490\pi$
$593$	−13.5128			−0.554905			−0.277452	+	0.960739i	$0.589490\pi$
$594$		0			0
$595$	0.107464			0.00440561
$596$	−40.7915	−	70.6529i	−1.67088	−	2.89406i
$597$		0			0
$598$	−22.4666	+	38.9133i	−0.918728	+	1.59128i
$599$	5.51386	−	9.55028i	0.225290	−	0.390214i	−0.731116	−	0.682253i	$-0.761000\pi$
$599$	5.51386	−	9.55028i	0.225290	−	0.390214i	0.956406	+	0.292039i	$0.0943337\pi$
$600$		0			0
$601$	−12.8990	−	22.3417i	−0.526160	−	0.911335i	−0.999536	−	0.0304746i	$-0.990298\pi$
$601$	−12.8990	−	22.3417i	−0.526160	−	0.911335i	0.473376	−	0.880860i	$-0.343035\pi$
$602$	9.61055			0.391697
$603$		0			0
$604$	−17.8650			−0.726918
$605$	−0.0666866	−	0.115505i	−0.00271120	−	0.00469593i
$606$		0			0
$607$	7.39494	−	12.8084i	0.300151	−	0.519877i	−0.676019	−	0.736884i	$-0.736296\pi$
$607$	7.39494	−	12.8084i	0.300151	−	0.519877i	0.976170	+	0.217007i	$0.0696295\pi$
$608$	−4.04014	+	6.99772i	−0.163849	+	0.283795i
$609$		0			0
$610$	−1.47503	−	2.55482i	−0.0597221	−	0.103442i
$611$	−15.0976			−0.610785
$612$		0			0
$613$	36.2739			1.46509			0.732545	−	0.680719i	$-0.238332\pi$
$613$	36.2739			1.46509			0.732545	+	0.680719i	$0.238332\pi$
$614$	−7.55846	−	13.0916i	−0.305034	−	0.528335i
$615$		0			0
$616$	3.80732	−	6.59447i	0.153401	−	0.265699i
$617$	−20.1868	+	34.9645i	−0.812689	+	1.40762i	0.0982868	+	0.995158i	$0.468664\pi$
$617$	−20.1868	+	34.9645i	−0.812689	+	1.40762i	−0.910976	+	0.412460i	$0.864670\pi$
$618$		0			0
$619$	3.44665	+	5.96978i	0.138533	+	0.239946i	0.926941	−	0.375206i	$-0.122428\pi$
$619$	3.44665	+	5.96978i	0.138533	+	0.239946i	−0.788409	+	0.615152i	$0.789095\pi$
$620$	−0.581315			−0.0233462
$621$		0			0
$622$	17.7069			0.709981
$623$	0.450299	+	0.779940i	0.0180408	+	0.0312477i
$624$		0			0
$625$	−12.4351	+	21.5381i	−0.497402	+	0.861526i
$626$	5.12836	−	8.88259i	0.204971	−	0.355020i
$627$		0			0
$628$	0.394121	+	0.682638i	0.0157271	+	0.0272402i
$629$	8.02386			0.319932
$630$		0			0
$631$	29.8191			1.18708			0.593539	−	0.804805i	$-0.297730\pi$
$631$	29.8191			1.18708			0.593539	+	0.804805i	$0.297730\pi$
$632$	15.3009	+	26.5020i	0.608639	+	1.05419i
$633$		0			0
$634$	19.3902	−	33.5848i	0.770082	−	1.33382i
$635$	0.536597	−	0.929413i	0.0212942	−	0.0368826i
$636$		0			0
$637$	13.9997	+	24.2481i	0.554687	+	0.960746i
$638$	−47.5382			−1.88206
$639$		0			0
$640$	1.92653			0.0761527
$641$	21.4404	+	37.1358i	0.846844	+	1.46678i	0.884011	+	0.467467i	$0.154833\pi$
$641$	21.4404	+	37.1358i	0.846844	+	1.46678i	−0.0371670	+	0.999309i	$0.511833\pi$
$642$		0			0
$643$	13.7066	−	23.7406i	0.540537	−	0.936237i	−0.458336	−	0.888779i	$-0.651554\pi$
$643$	13.7066	−	23.7406i	0.540537	−	0.936237i	0.998873	−	0.0474584i	$-0.0151122\pi$
$644$	4.86424	−	8.42511i	0.191678	−	0.331996i
$645$		0			0
$646$	9.19363	+	15.9238i	0.361718	+	0.626515i
$647$	16.1623			0.635407			0.317703	−	0.948190i	$-0.397088\pi$
$647$	16.1623			0.635407			0.317703	+	0.948190i	$0.397088\pi$
$648$		0			0
$649$	31.8113			1.24870
$650$	25.1837	+	43.6195i	0.987786	+	1.71090i
$651$		0			0
$652$	−10.5947	+	18.3506i	−0.414921	+	0.718664i
$653$	16.1231	−	27.9261i	0.630947	−	1.09283i	−0.356411	−	0.934329i	$-0.616000\pi$
$653$	16.1231	−	27.9261i	0.630947	−	1.09283i	0.987358	−	0.158504i	$-0.0506670\pi$
$654$		0			0
$655$	0.419423	+	0.726463i	0.0163882	+	0.0283852i
$656$	2.91647			0.113869
$657$		0			0
$658$	5.00391			0.195073
$659$	13.9093	+	24.0916i	0.541829	+	0.938475i	0.998799	+	0.0489934i	$0.0156013\pi$
$659$	13.9093	+	24.0916i	0.541829	+	0.938475i	−0.456970	+	0.889482i	$0.651065\pi$
$660$		0			0
$661$	−15.3943	+	26.6637i	−0.598769	+	1.03710i	0.394234	+	0.919010i	$0.371010\pi$
$661$	−15.3943	+	26.6637i	−0.598769	+	1.03710i	−0.993003	+	0.118088i	$0.962323\pi$
$662$	−23.0895	+	39.9921i	−0.897398	+	1.55434i
$663$		0			0
$664$	−31.6303	−	54.7853i	−1.22749	−	2.12608i
$665$	−0.207559			−0.00804877
$666$		0			0
$667$	−28.4958			−1.10336
$668$	31.4243	+	54.4284i	1.21584	+	2.10590i
$669$		0			0
$670$	−0.987793	+	1.71091i	−0.0381618	+	0.0660982i
$671$	20.4087	−	35.3488i	0.787868	−	1.36463i
$672$		0			0
$673$	13.0653	+	22.6298i	0.503631	+	0.872314i	0.999991	+	0.00419727i	$0.00133604\pi$
$673$	13.0653	+	22.6298i	0.503631	+	0.872314i	−0.496361	+	0.868116i	$0.665331\pi$
$674$	−70.7584			−2.72551
$675$		0			0
$676$	17.5374			0.674515
$677$	9.09725	+	15.7569i	0.349636	+	0.605587i	0.986185	−	0.165650i	$-0.0529720\pi$
$677$	9.09725	+	15.7569i	0.349636	+	0.605587i	−0.636549	+	0.771236i	$0.719639\pi$
$678$		0			0
$679$	1.53534	−	2.65928i	0.0589209	−	0.102054i
$680$	0.393409	−	0.681404i	0.0150865	−	0.0261307i
$681$		0			0
$682$	−6.15630	−	10.6630i	−0.235737	−	0.408308i
$683$	−23.4971			−0.899092			−0.449546	−	0.893257i	$-0.648414\pi$
$683$	−23.4971			−0.899092			−0.449546	+	0.893257i	$0.648414\pi$
$684$		0			0
$685$	1.07234			0.0409721
$686$	−9.51413	−	16.4790i	−0.363251	−	0.629169i
$687$		0			0
$688$	9.18067	−	15.9014i	0.350010	−	0.606235i
$689$	11.3454	−	19.6508i	0.432225	−	0.748635i
$690$		0			0
$691$	22.2690	+	38.5710i	0.847151	+	1.46731i	0.883740	+	0.467979i	$0.155018\pi$
$691$	22.2690	+	38.5710i	0.847151	+	1.46731i	−0.0365885	+	0.999330i	$0.511649\pi$
$692$	−71.5960			−2.72167
$693$		0			0
$694$	−27.3714			−1.03900
$695$	0.0792994	+	0.137351i	0.00300800	+	0.00521000i
$696$		0			0
$697$	−1.09122	+	1.89004i	−0.0413327	+	0.0715904i
$698$	−33.8168	+	58.5724i	−1.27998	+	2.21700i
$699$		0			0
$700$	−5.45252	−	9.44404i	−0.206086	−	0.356951i
$701$	25.2567			0.953934			0.476967	−	0.878921i	$-0.341736\pi$
$701$	25.2567			0.953934			0.476967	+	0.878921i	$0.341736\pi$
$702$		0			0
$703$	−15.4974			−0.584496
$704$	16.0341	+	27.7719i	0.604308	+	1.04669i
$705$		0			0
$706$	34.4081	−	59.5967i	1.29497	−	2.24295i
$707$	2.10750	−	3.65030i	0.0792607	−	0.137284i
$708$		0			0
$709$	7.84201	+	13.5828i	0.294513	+	0.510111i	0.974871	−	0.222768i	$-0.0715093\pi$
$709$	7.84201	+	13.5828i	0.294513	+	0.510111i	−0.680359	+	0.732879i	$0.738176\pi$
$710$	0.255954			0.00960579
$711$		0			0
$712$	6.59387			0.247116
$713$	−3.69027	−	6.39174i	−0.138202	−	0.239372i
$714$		0			0
$715$	0.604871	−	1.04767i	0.0226209	−	0.0391805i
$716$	30.5854	−	52.9755i	1.14303	−	1.97979i
$717$		0			0
$718$	−37.2638	−	64.5429i	−1.39067	−	2.40872i
$719$	53.1607			1.98256			0.991280	−	0.131771i	$-0.0420664\pi$
$719$	53.1607			1.98256			0.991280	+	0.131771i	$0.0420664\pi$
$720$		0			0
$721$	−3.71191			−0.138239
$722$	5.05868	+	8.76190i	0.188265	+	0.326084i
$723$		0			0
$724$	5.63581	−	9.76152i	0.209453	−	0.362784i
$725$	−15.9710	+	27.6627i	−0.593150	+	1.02737i
$726$		0			0
$727$	−0.234586	−	0.406315i	−0.00870032	−	0.0150694i	0.861642	−	0.507516i	$-0.169436\pi$
$727$	−0.234586	−	0.406315i	−0.00870032	−	0.0150694i	−0.870343	+	0.492446i	$0.836103\pi$
$728$	−10.3440			−0.383372
$729$		0			0
$730$	−0.0436980			−0.00161734
$731$	6.87002	+	11.8992i	0.254097	+	0.440109i
$732$		0			0
$733$	23.2031	−	40.1890i	0.857028	−	1.48442i	−0.0177237	−	0.999843i	$-0.505642\pi$
$733$	23.2031	−	40.1890i	0.857028	−	1.48442i	0.874751	−	0.484572i	$-0.161025\pi$
$734$	−28.9686	+	50.1751i	−1.06925	+	1.85200i
$735$		0			0
$736$	4.67829	+	8.10303i	0.172444	+	0.298682i
$737$	−27.3345			−1.00688
$738$		0			0
$739$	25.8093			0.949411			0.474706	−	0.880145i	$-0.342555\pi$
$739$	25.8093			0.949411			0.474706	+	0.880145i	$0.342555\pi$
$740$	0.706714	+	1.22406i	0.0259793	+	0.0449975i
$741$		0			0
$742$	−3.76027	+	6.51298i	−0.138044	+	0.239099i
$743$	17.3548	−	30.0594i	0.636687	−	1.10277i	−0.349469	−	0.936948i	$-0.613638\pi$
$743$	17.3548	−	30.0594i	0.636687	−	1.10277i	0.986155	−	0.165825i	$-0.0530288\pi$
$744$		0			0
$745$	1.00776	+	1.74549i	0.0369213	+	0.0639497i
$746$	−30.2259			−1.10665
$747$		0			0
$748$	23.2031			0.848389
$749$	1.60728	+	2.78388i	0.0587286	+	0.101721i
$750$		0			0
$751$	−11.9929	+	20.7724i	−0.437628	+	0.757994i	−0.997506	−	0.0705811i	$-0.977515\pi$
$751$	−11.9929	+	20.7724i	−0.437628	+	0.757994i	0.559878	+	0.828575i	$0.310848\pi$
$752$	4.78008	−	8.27934i	0.174312	−	0.301917i
$753$		0			0
$754$	32.2886	+	55.9255i	1.17588	+	2.03669i
$755$	0.441357			0.0160626
$756$		0			0
$757$	−8.78780			−0.319398			−0.159699	−	0.987166i	$-0.551052\pi$
$757$	−8.78780			−0.319398			−0.159699	+	0.987166i	$0.551052\pi$
$758$	9.25251	+	16.0258i	0.336066	+	0.582084i
$759$		0			0
$760$	−0.759837	+	1.31608i	−0.0275622	+	0.0477391i
$761$	6.87694	−	11.9112i	0.249289	−	0.431781i	−0.714040	−	0.700105i	$-0.753137\pi$
$761$	6.87694	−	11.9112i	0.249289	−	0.431781i	0.963329	+	0.268324i	$0.0864698\pi$
$762$		0			0
$763$	−1.80667	−	3.12924i	−0.0654057	−	0.113286i
$764$	8.49190			0.307226
$765$		0			0
$766$	42.8969			1.54993
$767$	−21.6067	−	37.4239i	−0.780172	−	1.35130i
$768$		0			0
$769$	15.6790	−	27.1568i	0.565398	−	0.979298i	−0.431615	−	0.902058i	$-0.642056\pi$
$769$	15.6790	−	27.1568i	0.565398	−	0.979298i	0.997013	−	0.0772399i	$-0.0246107\pi$
$770$	−0.200476	+	0.347235i	−0.00722466	+	0.0125135i
$771$		0			0
$772$	1.65834	+	2.87233i	0.0596849	+	0.103377i
$773$	−28.1214			−1.01146			−0.505729	−	0.862693i	$-0.668776\pi$
$773$	−28.1214			−1.01146			−0.505729	+	0.862693i	$0.668776\pi$
$774$		0			0
$775$	−8.27314			−0.297180
$776$	−11.2412	−	19.4704i	−0.403536	−	0.698946i
$777$		0			0
$778$	32.8883	−	56.9643i	1.17910	−	2.04227i
$779$	2.10759	−	3.65046i	0.0755123	−	0.130791i
$780$		0			0
$781$	1.77071	+	3.06696i	0.0633609	+	0.109744i
$782$	21.2916			0.761385
$783$		0			0
$784$	−17.7298			−0.633207
$785$	−0.00973679	−	0.0168646i	−0.000347521	−	0.000601924i
$786$		0			0

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)

\(f(q)\)	\(=\)	\(q+(-1.20081 - 2.07986i) q^{2} +(-1.88389 + 3.26300i) q^{4} +(0.0465417 - 0.0806126i) q^{5} +(0.289931 + 0.502175i) q^{7} +4.24555 q^{8} +O(q^{10})\)	\(q+(-1.20081 - 2.07986i) q^{2} +(-1.88389 + 3.26300i) q^{4} +(0.0465417 - 0.0806126i) q^{5} +(0.289931 + 0.502175i) q^{7} +4.24555 q^{8} -0.223551 q^{10} +(-1.54654 - 2.67869i) q^{11} +(-2.10087 + 3.63881i) q^{13} +(0.696304 - 1.20603i) q^{14} +(-1.33032 - 2.30417i) q^{16} +1.99099 q^{17} -3.84542 q^{19} +(0.175359 + 0.303731i) q^{20} +(-3.71421 + 6.43320i) q^{22} +(-2.22641 + 3.85625i) q^{23} +(2.49567 + 4.32262i) q^{25} +10.0910 q^{26} -2.18479 q^{28} +(3.19975 + 5.54214i) q^{29} +(-0.828750 + 1.43544i) q^{31} +(1.05064 - 1.81975i) q^{32} +(-2.39080 - 4.14098i) q^{34} +0.0539755 q^{35} +4.03009 q^{37} +(4.61762 + 7.99796i) q^{38} +(0.197595 - 0.342245i) q^{40} +(-0.548078 + 0.949299i) q^{41} +(3.45056 + 5.97655i) q^{43} +11.6541 q^{44} +10.6940 q^{46} +(1.79660 + 3.11180i) q^{47} +(3.33188 - 5.77099i) q^{49} +(5.99365 - 10.3813i) q^{50} +(-7.91561 - 13.7102i) q^{52} -5.40034 q^{53} -0.287915 q^{55} +(1.23091 + 2.13201i) q^{56} +(7.68460 - 13.3101i) q^{58} +(-5.14233 + 8.90677i) q^{59} +(6.59816 + 11.4283i) q^{61} +3.98069 q^{62} -10.3677 q^{64} +(0.195556 + 0.338713i) q^{65} +(4.41865 - 7.65332i) q^{67} +(-3.75080 + 6.49658i) q^{68} +(-0.0648143 - 0.112262i) q^{70} -1.14495 q^{71} +0.195472 q^{73} +(-4.83938 - 8.38205i) q^{74} +(7.24436 - 12.5476i) q^{76} +(0.896780 - 1.55327i) q^{77} +(3.60400 + 6.24231i) q^{79} -0.247661 q^{80} +2.63255 q^{82} +(-7.45022 - 12.9042i) q^{83} +(0.0926639 - 0.160499i) q^{85} +(8.28694 - 14.3534i) q^{86} +(-6.56592 - 11.3725i) q^{88} +1.55313 q^{89} -2.43642 q^{91} +(-8.38862 - 14.5295i) q^{92} +(4.31475 - 7.47336i) q^{94} +(-0.178973 + 0.309990i) q^{95} +(-2.64777 - 4.58607i) q^{97} -16.0038 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} - 6 q^{5} + 12 q^{8} + 6 q^{10} - 12 q^{11} - 6 q^{14} + 3 q^{16} + 18 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 15 q^{23} + 6 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{29} + 24 q^{35} + 6 q^{37} + 3 q^{38} - 6 q^{40} - 15 q^{41} + 6 q^{44} + 6 q^{46} - 21 q^{47} + 12 q^{49} - 3 q^{50} - 12 q^{52} + 18 q^{53} - 12 q^{55} + 6 q^{56} + 12 q^{58} - 24 q^{59} + 9 q^{61} - 24 q^{62} - 24 q^{64} + 6 q^{65} + 9 q^{67} + 9 q^{68} - 15 q^{70} + 54 q^{71} - 12 q^{73} + 12 q^{74} - 6 q^{76} + 12 q^{77} - 42 q^{80} - 12 q^{82} - 12 q^{83} + 21 q^{86} - 12 q^{88} + 18 q^{89} - 12 q^{91} - 6 q^{92} - 6 q^{94} - 12 q^{95} - 90 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 - 6 * q^5 + 12 * q^8 + 6 * q^10 - 12 * q^11 - 6 * q^14 + 3 * q^16 + 18 * q^17 + 6 * q^19 - 6 * q^20 - 6 * q^22 - 15 * q^23 + 6 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^29 + 24 * q^35 + 6 * q^37 + 3 * q^38 - 6 * q^40 - 15 * q^41 + 6 * q^44 + 6 * q^46 - 21 * q^47 + 12 * q^49 - 3 * q^50 - 12 * q^52 + 18 * q^53 - 12 * q^55 + 6 * q^56 + 12 * q^58 - 24 * q^59 + 9 * q^61 - 24 * q^62 - 24 * q^64 + 6 * q^65 + 9 * q^67 + 9 * q^68 - 15 * q^70 + 54 * q^71 - 12 * q^73 + 12 * q^74 - 6 * q^76 + 12 * q^77 - 42 * q^80 - 12 * q^82 - 12 * q^83 + 21 * q^86 - 12 * q^88 + 18 * q^89 - 12 * q^91 - 6 * q^92 - 6 * q^94 - 12 * q^95 - 90 * q^98

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