LMFDB - Embedded newform 729.2.e.n.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$-0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.n.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32683 - 1.11334i) q^{2} +(0.173648 + 0.984808i) q^{4} +(3.25519 + 1.18479i) q^{5} +(-0.173648 + 0.984808i) q^{7} +(-0.866025 + 1.50000i) q^{8} +(-3.00000 - 5.19615i) q^{10} +(-3.25519 + 1.18479i) q^{11} +(3.83022 - 3.21394i) q^{13} +(1.32683 - 1.11334i) q^{14} +(4.69846 - 1.71010i) q^{16} +(0.500000 - 0.866025i) q^{19} +(-0.601535 + 3.41147i) q^{20} +(5.63816 + 2.05212i) q^{22} +(1.20307 + 6.82295i) q^{23} +(5.36231 + 4.49951i) q^{25} -8.66025 q^{26} -1.00000 q^{28} +(2.65366 + 2.22668i) q^{29} +(0.868241 + 4.92404i) q^{31} +(-4.88279 - 1.77719i) q^{32} +(-1.73205 + 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.62760 + 0.592396i) q^{38} +(-4.59627 + 3.85673i) q^{40} +(-2.65366 + 2.22668i) q^{41} +(0.939693 - 0.342020i) q^{43} +(-1.73205 - 3.00000i) q^{44} +(6.00000 - 10.3923i) q^{46} +(0.601535 - 3.41147i) q^{47} +(5.63816 + 2.05212i) q^{49} +(-2.10537 - 11.9402i) q^{50} +(3.83022 + 3.21394i) q^{52} +10.3923 q^{53} -12.0000 q^{55} +(-1.32683 - 1.11334i) q^{56} +(-1.04189 - 5.90885i) q^{58} +(3.25519 + 1.18479i) q^{59} +(0.347296 - 1.96962i) q^{61} +(4.33013 - 7.50000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(16.2760 - 5.92396i) q^{65} +(6.12836 - 5.14230i) q^{67} +(5.63816 - 2.05212i) q^{70} +(5.19615 + 9.00000i) q^{71} +(-1.00000 + 1.73205i) q^{73} +(0.300767 - 1.70574i) q^{74} +(0.939693 + 0.342020i) q^{76} +(-0.601535 - 3.41147i) q^{77} +(-0.766044 - 0.642788i) q^{79} +17.3205 q^{80} +6.00000 q^{82} +(-5.30731 - 4.45336i) q^{83} +(-1.62760 - 0.592396i) q^{86} +(1.04189 - 5.90885i) q^{88} +(5.19615 - 9.00000i) q^{89} +(2.50000 + 4.33013i) q^{91} +(-6.51038 + 2.36959i) q^{92} +(-4.59627 + 3.85673i) q^{94} +(2.65366 - 2.22668i) q^{95} +(-15.9748 + 5.81434i) q^{97} +(-5.19615 - 9.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) $ 12 * q - 36 * q^10 + 6 * q^19 - 12 * q^28 + 6 * q^37 + 72 * q^46 - 144 * q^55 - 6 * q^64 - 12 * q^73 + 72 * q^82 + 30 * q^91

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.32683	−	1.11334i	−0.938209	−	0.787251i	0.0390637	−	0.999237i	$-0.487562\pi$
$2$	−1.32683	−	1.11334i	−0.938209	−	0.787251i	−0.977273	+	0.211986i	$0.932007\pi$
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	3.25519	+	1.18479i	1.45577	+	0.529855i	0.944195	−	0.329386i	$-0.106842\pi$
$5$	3.25519	+	1.18479i	1.45577	+	0.529855i	0.511570	+	0.859241i	$0.329064\pi$
$6$		0			0
$7$	−0.173648	+	0.984808i	−0.0656328	+	0.372222i	0.934246	+	0.356630i	$0.116074\pi$
$7$	−0.173648	+	0.984808i	−0.0656328	+	0.372222i	−0.999878	+	0.0155920i	$0.995037\pi$
$8$	−0.866025	+	1.50000i	−0.306186	+	0.530330i
$9$		0			0
$10$	−3.00000	−	5.19615i	−0.948683	−	1.64317i
$11$	−3.25519	+	1.18479i	−0.981477	+	0.357228i	−0.782414	−	0.622758i	$-0.786012\pi$
$11$	−3.25519	+	1.18479i	−0.981477	+	0.357228i	−0.199063	+	0.979987i	$0.563790\pi$
$12$		0			0
$13$	3.83022	−	3.21394i	1.06231	−	0.891386i	0.0679785	−	0.997687i	$-0.478345\pi$
$13$	3.83022	−	3.21394i	1.06231	−	0.891386i	0.994334	+	0.106301i	$0.0339006\pi$
$14$	1.32683	−	1.11334i	0.354610	−	0.297553i
$15$		0			0
$16$	4.69846	−	1.71010i	1.17462	−	0.427525i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$	−0.601535	+	3.41147i	−0.134507	+	0.762829i
$21$		0			0
$22$	5.63816	+	2.05212i	1.20206	+	0.437514i
$23$	1.20307	+	6.82295i	0.250857	+	1.42268i	0.806486	+	0.591253i	$0.201366\pi$
$23$	1.20307	+	6.82295i	0.250857	+	1.42268i	−0.555629	+	0.831430i	$0.687522\pi$
$24$		0			0
$25$	5.36231	+	4.49951i	1.07246	+	0.899903i
$26$	−8.66025			−1.69842
$27$		0			0
$28$	−1.00000			−0.188982
$29$	2.65366	+	2.22668i	0.492772	+	0.413484i	0.855018	−	0.518598i	$-0.173546\pi$
$29$	2.65366	+	2.22668i	0.492772	+	0.413484i	−0.362247	+	0.932082i	$0.617990\pi$
$30$		0			0
$31$	0.868241	+	4.92404i	0.155941	+	0.884383i	0.957921	+	0.287033i	$0.0926689\pi$
$31$	0.868241	+	4.92404i	0.155941	+	0.884383i	−0.801980	+	0.597351i	$0.796220\pi$
$32$	−4.88279	−	1.77719i	−0.863163	−	0.314166i
$33$		0			0
$34$		0			0
$35$	−1.73205	+	3.00000i	−0.292770	+	0.507093i
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−1.62760	+	0.592396i	−0.264031	+	0.0960994i
$39$		0			0
$40$	−4.59627	+	3.85673i	−0.726734	+	0.609802i
$41$	−2.65366	+	2.22668i	−0.414431	+	0.347749i	−0.826040	−	0.563611i	$-0.809412\pi$
$41$	−2.65366	+	2.22668i	−0.414431	+	0.347749i	0.411609	+	0.911361i	$0.364967\pi$
$42$		0			0
$43$	0.939693	−	0.342020i	0.143302	−	0.0521576i	−0.269374	−	0.963036i	$-0.586817\pi$
$43$	0.939693	−	0.342020i	0.143302	−	0.0521576i	0.412675	+	0.910878i	$0.364594\pi$
$44$	−1.73205	−	3.00000i	−0.261116	−	0.452267i
$45$		0			0
$46$	6.00000	−	10.3923i	0.884652	−	1.53226i
$47$	0.601535	−	3.41147i	0.0877429	−	0.497615i	−0.908988	−	0.416822i	$-0.863144\pi$
$47$	0.601535	−	3.41147i	0.0877429	−	0.497615i	0.996731	−	0.0807925i	$-0.0257451\pi$
$48$		0			0
$49$	5.63816	+	2.05212i	0.805451	+	0.293160i
$50$	−2.10537	−	11.9402i	−0.297745	−	1.68859i
$51$		0			0
$52$	3.83022	+	3.21394i	0.531156	+	0.445693i
$53$	10.3923			1.42749			0.713746	−	0.700404i	$-0.246997\pi$
$53$	10.3923			1.42749			0.713746	+	0.700404i	$0.246997\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$	−1.32683	−	1.11334i	−0.177305	−	0.148776i
$57$		0			0
$58$	−1.04189	−	5.90885i	−0.136807	−	0.775870i
$59$	3.25519	+	1.18479i	0.423790	+	0.154247i	0.545106	−	0.838367i	$-0.316489\pi$
$59$	3.25519	+	1.18479i	0.423790	+	0.154247i	−0.121316	+	0.992614i	$0.538712\pi$
$60$		0			0
$61$	0.347296	−	1.96962i	0.0444667	−	0.252183i	−0.954469	−	0.298311i	$-0.903577\pi$
$61$	0.347296	−	1.96962i	0.0444667	−	0.252183i	0.998936	+	0.0461272i	$0.0146880\pi$
$62$	4.33013	−	7.50000i	0.549927	−	0.952501i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	16.2760	−	5.92396i	2.01878	−	0.734777i
$66$		0			0
$67$	6.12836	−	5.14230i	0.748698	−	0.628232i	−0.186460	−	0.982462i	$-0.559702\pi$
$67$	6.12836	−	5.14230i	0.748698	−	0.628232i	0.935158	+	0.354230i	$0.115257\pi$
$68$		0			0
$69$		0			0
$70$	5.63816	−	2.05212i	0.673889	−	0.245275i
$71$	5.19615	+	9.00000i	0.616670	+	1.06810i	0.990089	+	0.140441i	$0.0448520\pi$
$71$	5.19615	+	9.00000i	0.616670	+	1.06810i	−0.373419	+	0.927663i	$0.621815\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	0.300767	−	1.70574i	0.0349635	−	0.198288i
$75$		0			0
$76$	0.939693	+	0.342020i	0.107790	+	0.0392324i
$77$	−0.601535	−	3.41147i	−0.0685513	−	0.388774i
$78$		0			0
$79$	−0.766044	−	0.642788i	−0.0861867	−	0.0723193i	0.598676	−	0.800991i	$-0.295694\pi$
$79$	−0.766044	−	0.642788i	−0.0861867	−	0.0723193i	−0.684863	+	0.728672i	$0.740138\pi$
$80$	17.3205			1.93649
$81$		0			0
$82$	6.00000			0.662589
$83$	−5.30731	−	4.45336i	−0.582553	−	0.488820i	0.303231	−	0.952917i	$-0.401935\pi$
$83$	−5.30731	−	4.45336i	−0.582553	−	0.488820i	−0.885784	+	0.464097i	$0.846379\pi$
$84$		0			0
$85$		0			0
$86$	−1.62760	−	0.592396i	−0.175508	−	0.0638797i
$87$		0			0
$88$	1.04189	−	5.90885i	0.111066	−	0.629885i
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	−0.447427	−	0.894321i	$-0.647659\pi$
$89$	5.19615	−	9.00000i	0.550791	−	0.953998i	0.998218	−	0.0596775i	$-0.0190072\pi$
$90$		0			0
$91$	2.50000	+	4.33013i	0.262071	+	0.453921i
$92$	−6.51038	+	2.36959i	−0.678754	+	0.247046i
$93$		0			0
$94$	−4.59627	+	3.85673i	−0.474069	+	0.397791i
$95$	2.65366	−	2.22668i	0.272259	−	0.228453i
$96$		0			0
$97$	−15.9748	+	5.81434i	−1.62199	+	0.590357i	−0.983760	−	0.179487i	$-0.942556\pi$
$97$	−15.9748	+	5.81434i	−1.62199	+	0.590357i	−0.638232	+	0.769844i	$0.720334\pi$
$98$	−5.19615	−	9.00000i	−0.524891	−	0.909137i
$99$		0			0
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	2.40614	−	13.6459i	0.239420	−	1.35782i	−0.593683	−	0.804699i	$-0.702327\pi$
$101$	2.40614	−	13.6459i	0.239420	−	1.35782i	0.833103	−	0.553118i	$-0.186562\pi$
$102$		0			0
$103$	−7.51754	−	2.73616i	−0.740725	−	0.269602i	−0.0560277	−	0.998429i	$-0.517844\pi$
$103$	−7.51754	−	2.73616i	−0.740725	−	0.269602i	−0.684698	+	0.728827i	$0.740066\pi$
$104$	1.50384	+	8.52869i	0.147463	+	0.836306i
$105$		0			0
$106$	−13.7888	−	11.5702i	−1.33929	−	1.12379i
$107$	−10.3923			−1.00466			−0.502331	−	0.864675i	$-0.667524\pi$
$107$	−10.3923			−1.00466			−0.502331	+	0.864675i	$0.667524\pi$
$108$		0			0
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$	15.9219	+	13.3601i	1.51810	+	1.27383i
$111$		0			0
$112$	0.868241	+	4.92404i	0.0820411	+	0.465278i
$113$	−16.2760	−	5.92396i	−1.53111	−	0.557280i	−0.567219	−	0.823567i	$-0.691981\pi$
$113$	−16.2760	−	5.92396i	−1.53111	−	0.557280i	−0.963894	+	0.266287i	$0.914203\pi$
$114$		0			0
$115$	−4.16756	+	23.6354i	−0.388627	+	2.20401i
$116$	−1.73205	+	3.00000i	−0.160817	+	0.278543i
$117$		0			0
$118$	−3.00000	−	5.19615i	−0.276172	−	0.478345i
$119$		0			0
$120$		0			0
$121$	0.766044	−	0.642788i	0.0696404	−	0.0584352i
$122$	−2.65366	+	2.22668i	−0.240251	+	0.201594i
$123$		0			0
$124$	−4.69846	+	1.71010i	−0.421934	+	0.153572i
$125$	3.46410	+	6.00000i	0.309839	+	0.536656i
$126$		0			0
$127$	−8.50000	+	14.7224i	−0.754253	+	1.30640i	0.191492	+	0.981494i	$0.438667\pi$
$127$	−8.50000	+	14.7224i	−0.754253	+	1.30640i	−0.945745	+	0.324910i	$0.894666\pi$
$128$	−2.10537	+	11.9402i	−0.186090	+	1.05537i
$129$		0			0
$130$	−28.1908	−	10.2606i	−2.47249	−	0.899915i
$131$	−0.601535	−	3.41147i	−0.0525564	−	0.298062i	0.947188	−	0.320679i	$-0.103911\pi$
$131$	−0.601535	−	3.41147i	−0.0525564	−	0.298062i	−0.999744	+	0.0226174i	$0.992800\pi$
$132$		0			0
$133$	0.766044	+	0.642788i	0.0664245	+	0.0557368i
$134$	−13.8564			−1.19701
$135$		0			0
$136$		0			0
$137$	−5.30731	−	4.45336i	−0.453434	−	0.380476i	0.387274	−	0.921965i	$-0.373417\pi$
$137$	−5.30731	−	4.45336i	−0.453434	−	0.380476i	−0.840708	+	0.541488i	$0.817861\pi$
$138$		0			0
$139$	−2.25743	−	12.8025i	−0.191472	−	1.08589i	−0.917353	−	0.398074i	$-0.869679\pi$
$139$	−2.25743	−	12.8025i	−0.191472	−	1.08589i	0.725881	−	0.687820i	$-0.241432\pi$
$140$	−3.25519	−	1.18479i	−0.275114	−	0.100133i
$141$		0			0
$142$	3.12567	−	17.7265i	0.262300	−	1.48758i
$143$	−8.66025	+	15.0000i	−0.724207	+	1.25436i
$144$		0			0
$145$	6.00000	+	10.3923i	0.498273	+	0.863034i
$146$	3.25519	−	1.18479i	0.269402	−	0.0980541i
$147$		0			0
$148$	−0.766044	+	0.642788i	−0.0629685	+	0.0528368i
$149$	5.30731	−	4.45336i	0.434792	−	0.364834i	−0.398964	−	0.916966i	$-0.630630\pi$
$149$	5.30731	−	4.45336i	0.434792	−	0.364834i	0.833756	+	0.552133i	$0.186186\pi$
$150$		0			0
$151$	15.0351	−	5.47232i	1.22354	−	0.445331i	0.352158	−	0.935941i	$-0.385448\pi$
$151$	15.0351	−	5.47232i	1.22354	−	0.445331i	0.871380	+	0.490609i	$0.163226\pi$
$152$	0.866025	+	1.50000i	0.0702439	+	0.121666i
$153$		0			0
$154$	−3.00000	+	5.19615i	−0.241747	+	0.418718i
$155$	−3.00767	+	17.0574i	−0.241582	+	1.37008i
$156$		0			0
$157$	12.2160	+	4.44626i	0.974943	+	0.354850i	0.779872	−	0.625939i	$-0.215284\pi$
$157$	12.2160	+	4.44626i	0.974943	+	0.354850i	0.195071	+	0.980789i	$0.437506\pi$
$158$	0.300767	+	1.70574i	0.0239278	+	0.135701i
$159$		0			0
$160$	−13.7888	−	11.5702i	−1.09010	−	0.914703i
$161$	−6.92820			−0.546019
$162$		0			0
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−2.65366	−	2.22668i	−0.207216	−	0.173875i
$165$		0			0
$166$	2.08378	+	11.8177i	0.161733	+	0.917231i
$167$	22.7863	+	8.29355i	1.76326	+	0.641774i	0.999991	−	0.00430705i	$-0.00137098\pi$
$167$	22.7863	+	8.29355i	1.76326	+	0.641774i	0.763269	+	0.646081i	$0.223593\pi$
$168$		0			0
$169$	2.08378	−	11.8177i	0.160291	−	0.909053i
$170$		0			0
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−13.0208	+	4.73917i	−0.989950	+	0.360312i	−0.785701	−	0.618606i	$-0.787698\pi$
$173$	−13.0208	+	4.73917i	−0.989950	+	0.360312i	−0.204249	+	0.978919i	$0.565475\pi$
$174$		0			0
$175$	−5.36231	+	4.49951i	−0.405353	+	0.340131i
$176$	−13.2683	+	11.1334i	−1.00013	+	0.839212i
$177$		0			0
$178$	−16.9145	+	6.15636i	−1.26779	+	0.461439i
$179$	−10.3923	−	18.0000i	−0.776757	−	1.34538i	−0.933801	−	0.357792i	$-0.883530\pi$
$179$	−10.3923	−	18.0000i	−0.776757	−	1.34538i	0.157044	−	0.987592i	$-0.449804\pi$
$180$		0			0
$181$	−8.50000	+	14.7224i	−0.631800	+	1.09431i	0.355383	+	0.934721i	$0.384350\pi$
$181$	−8.50000	+	14.7224i	−0.631800	+	1.09431i	−0.987184	+	0.159589i	$0.948983\pi$
$182$	1.50384	−	8.52869i	0.111472	−	0.632188i
$183$		0			0
$184$	−11.2763	−	4.10424i	−0.831301	−	0.302569i
$185$	0.601535	+	3.41147i	0.0442257	+	0.250817i
$186$		0			0
$187$		0			0
$188$	3.46410			0.252646
$189$		0			0
$190$	−6.00000			−0.435286
$191$	−5.30731	−	4.45336i	−0.384024	−	0.322234i	0.430256	−	0.902707i	$-0.358423\pi$
$191$	−5.30731	−	4.45336i	−0.384024	−	0.322234i	−0.814280	+	0.580473i	$0.802868\pi$
$192$		0			0
$193$	−1.73648	−	9.84808i	−0.124995	−	0.708880i	−0.981311	−	0.192428i	$-0.938364\pi$
$193$	−1.73648	−	9.84808i	−0.124995	−	0.708880i	0.856316	−	0.516452i	$-0.172747\pi$
$194$	27.6691	+	10.0707i	1.98653	+	0.723037i
$195$		0			0
$196$	−1.04189	+	5.90885i	−0.0744206	+	0.422060i
$197$	−5.19615	+	9.00000i	−0.370211	+	0.641223i	−0.989598	−	0.143862i	$-0.954048\pi$
$197$	−5.19615	+	9.00000i	−0.370211	+	0.641223i	0.619387	+	0.785086i	$0.287381\pi$
$198$		0			0
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	0.976923	+	0.213591i	$0.0685161\pi$
$199$	9.50000	+	16.4545i	0.673437	+	1.16643i	−0.303486	+	0.952836i	$0.598151\pi$
$200$	−11.3932	+	4.14677i	−0.805619	+	0.293221i
$201$		0			0
$202$	−18.3851	+	15.4269i	−1.29357	+	1.08543i
$203$	−2.65366	+	2.22668i	−0.186250	+	0.156282i
$204$		0			0
$205$	−11.2763	+	4.10424i	−0.787572	+	0.286653i
$206$	6.92820	+	12.0000i	0.482711	+	0.836080i
$207$		0			0
$208$	12.5000	−	21.6506i	0.866719	−	1.50120i
$209$	−0.601535	+	3.41147i	−0.0416090	+	0.235977i
$210$		0			0
$211$	−4.69846	−	1.71010i	−0.323456	−	0.117728i	0.175189	−	0.984535i	$-0.443946\pi$
$211$	−4.69846	−	1.71010i	−0.323456	−	0.117728i	−0.498644	+	0.866807i	$0.666169\pi$
$212$	1.80460	+	10.2344i	0.123941	+	0.702903i
$213$		0			0
$214$	13.7888	+	11.5702i	0.942583	+	0.790921i
$215$	3.46410			0.236250
$216$		0			0
$217$	−5.00000			−0.339422
$218$	−22.5561	−	18.9268i	−1.52769	−	1.28188i
$219$		0			0
$220$	−2.08378	−	11.8177i	−0.140488	−	0.796749i
$221$		0			0
$222$		0			0
$223$	−3.29932	+	18.7113i	−0.220938	+	1.25300i	0.649360	+	0.760481i	$0.275037\pi$
$223$	−3.29932	+	18.7113i	−0.220938	+	1.25300i	−0.870299	+	0.492524i	$0.836074\pi$
$224$	2.59808	−	4.50000i	0.173591	−	0.300669i
$225$		0			0
$226$	15.0000	+	25.9808i	0.997785	+	1.72821i
$227$	−13.0208	+	4.73917i	−0.864218	+	0.314550i	−0.735824	−	0.677173i	$-0.763205\pi$
$227$	−13.0208	+	4.73917i	−0.864218	+	0.314550i	−0.128395	+	0.991723i	$0.540982\pi$
$228$		0			0
$229$	3.83022	−	3.21394i	0.253108	−	0.212383i	−0.507401	−	0.861710i	$-0.669394\pi$
$229$	3.83022	−	3.21394i	0.253108	−	0.212383i	0.760509	+	0.649327i	$0.224949\pi$
$230$	31.8439	−	26.7202i	2.09972	−	1.76188i
$231$		0			0
$232$	−5.63816	+	2.05212i	−0.370163	+	0.134728i
$233$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$233$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	−0.601535	+	3.41147i	−0.0391566	+	0.222068i
$237$		0			0
$238$		0			0
$239$	1.20307	+	6.82295i	0.0778201	+	0.441340i	0.998676	+	0.0514372i	$0.0163802\pi$
$239$	1.20307	+	6.82295i	0.0778201	+	0.441340i	−0.920856	+	0.389903i	$0.872509\pi$
$240$		0			0
$241$	−14.5548	−	12.2130i	−0.937560	−	0.786706i	0.0395991	−	0.999216i	$-0.487392\pi$
$241$	−14.5548	−	12.2130i	−0.937560	−	0.786706i	−0.977159	+	0.212509i	$0.931836\pi$
$242$	−1.73205			−0.111340
$243$		0			0
$244$	2.00000			0.128037
$245$	15.9219	+	13.3601i	1.01722	+	0.853545i
$246$		0			0
$247$	−0.868241	−	4.92404i	−0.0552448	−	0.313309i
$248$	−8.13798	−	2.96198i	−0.516762	−	0.188086i
$249$		0			0
$250$	2.08378	−	11.8177i	0.131790	−	0.747417i
$251$	10.3923	−	18.0000i	0.655956	−	1.13615i	−0.325697	−	0.945474i	$-0.605599\pi$
$251$	10.3923	−	18.0000i	0.655956	−	1.13615i	0.981653	−	0.190676i	$-0.0610679\pi$
$252$		0			0
$253$	−12.0000	−	20.7846i	−0.754434	−	1.30672i
$254$	27.6691	−	10.0707i	1.73612	−	0.631894i
$255$		0			0
$256$	14.5548	−	12.2130i	0.909678	−	0.763310i
$257$	−2.65366	+	2.22668i	−0.165531	+	0.138897i	−0.721790	−	0.692112i	$-0.756680\pi$
$257$	−2.65366	+	2.22668i	−0.165531	+	0.138897i	0.556260	+	0.831009i	$0.312236\pi$
$258$		0			0
$259$	−0.939693	+	0.342020i	−0.0583897	+	0.0212521i
$260$	8.66025	+	15.0000i	0.537086	+	0.930261i
$261$		0			0
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	2.40614	−	13.6459i	0.148369	−	0.841442i	−0.816231	−	0.577725i	$-0.803940\pi$
$263$	2.40614	−	13.6459i	0.148369	−	0.841442i	0.964600	−	0.263717i	$-0.0849484\pi$
$264$		0			0
$265$	33.8289	+	12.3127i	2.07809	+	0.756365i
$266$	−0.300767	−	1.70574i	−0.0184412	−	0.104585i
$267$		0			0
$268$	6.12836	+	5.14230i	0.374349	+	0.314116i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$		0			0
$274$	2.08378	+	11.8177i	0.125886	+	0.713933i
$275$	−22.7863	−	8.29355i	−1.37407	−	0.500120i
$276$		0			0
$277$	2.95202	−	16.7417i	0.177370	−	1.00591i	−0.758003	−	0.652251i	$-0.773825\pi$
$277$	2.95202	−	16.7417i	0.177370	−	1.00591i	0.935373	−	0.353663i	$-0.115064\pi$
$278$	−11.2583	+	19.5000i	−0.675230	+	1.16953i
$279$		0			0
$280$	−3.00000	−	5.19615i	−0.179284	−	0.310530i
$281$	−13.0208	+	4.73917i	−0.776754	+	0.282715i	−0.699818	−	0.714321i	$-0.746736\pi$
$281$	−13.0208	+	4.73917i	−0.776754	+	0.282715i	−0.0769353	+	0.997036i	$0.524513\pi$
$282$		0			0
$283$	−9.95858	+	8.35624i	−0.591976	+	0.496727i	−0.888855	−	0.458188i	$-0.848499\pi$
$283$	−9.95858	+	8.35624i	−0.591976	+	0.496727i	0.296879	+	0.954915i	$0.404054\pi$
$284$	−7.96097	+	6.68004i	−0.472397	+	0.396388i
$285$		0			0
$286$	28.1908	−	10.2606i	1.66696	−	0.606722i
$287$	−1.73205	−	3.00000i	−0.102240	−	0.177084i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	3.60921	−	20.4688i	0.211940	−	1.20197i
$291$		0			0
$292$	−1.87939	−	0.684040i	−0.109983	−	0.0400304i
$293$	−2.40614	−	13.6459i	−0.140568	−	0.797202i	−0.970819	−	0.239812i	$-0.922914\pi$
$293$	−2.40614	−	13.6459i	−0.140568	−	0.797202i	0.830251	−	0.557390i	$-0.188197\pi$
$294$		0			0
$295$	9.19253	+	7.71345i	0.535210	+	0.449094i
$296$	−1.73205			−0.100673
$297$		0			0
$298$	−12.0000			−0.695141
$299$	26.5366	+	22.2668i	1.53465	+	1.28772i
$300$		0			0
$301$	0.173648	+	0.984808i	0.0100089	+	0.0567634i
$302$	−26.0415	−	9.47834i	−1.49852	−	0.545417i
$303$		0			0
$304$	0.868241	−	4.92404i	0.0497970	−	0.282413i
$305$	3.46410	−	6.00000i	0.198354	−	0.343559i
$306$		0			0
$307$	−10.0000	−	17.3205i	−0.570730	−	0.988534i	−0.996491	−	0.0836980i	$-0.973327\pi$
$307$	−10.0000	−	17.3205i	−0.570730	−	0.988534i	0.425761	−	0.904836i	$-0.360006\pi$
$308$	3.25519	−	1.18479i	0.185482	−	0.0675098i
$309$		0			0
$310$	22.9813	−	19.2836i	1.30525	−	1.09524i
$311$	−10.6146	+	8.90673i	−0.601900	+	0.505054i	−0.892056	−	0.451925i	$-0.850737\pi$
$311$	−10.6146	+	8.90673i	−0.601900	+	0.505054i	0.290156	+	0.956979i	$0.406293\pi$
$312$		0			0
$313$	0.939693	−	0.342020i	0.0531146	−	0.0193321i	−0.315326	−	0.948983i	$-0.602114\pi$
$313$	0.939693	−	0.342020i	0.0531146	−	0.0193321i	0.368441	+	0.929651i	$0.379892\pi$
$314$	−11.2583	−	19.5000i	−0.635344	−	1.10045i
$315$		0			0
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$	−4.81228	+	27.2918i	−0.270285	+	1.53286i	0.483268	+	0.875472i	$0.339450\pi$
$317$	−4.81228	+	27.2918i	−0.270285	+	1.53286i	−0.753553	+	0.657387i	$0.771662\pi$
$318$		0			0
$319$	−11.2763	−	4.10424i	−0.631352	−	0.229793i
$320$	−0.601535	−	3.41147i	−0.0336268	−	0.190707i
$321$		0			0
$322$	9.19253	+	7.71345i	0.512280	+	0.429854i
$323$		0			0
$324$		0			0
$325$	35.0000			1.94145
$326$	1.32683	+	1.11334i	0.0734862	+	0.0616622i
$327$		0			0
$328$	−1.04189	−	5.90885i	−0.0575287	−	0.326261i
$329$	3.25519	+	1.18479i	0.179464	+	0.0653197i
$330$		0			0
$331$	−3.29932	+	18.7113i	−0.181347	+	1.02847i	0.749213	+	0.662329i	$0.230432\pi$
$331$	−3.29932	+	18.7113i	−0.181347	+	1.02847i	−0.930560	+	0.366140i	$0.880679\pi$
$332$	3.46410	−	6.00000i	0.190117	−	0.329293i
$333$		0			0
$334$	−21.0000	−	36.3731i	−1.14907	−	1.99025i
$335$	26.0415	−	9.47834i	1.42280	−	0.517857i
$336$		0			0
$337$	3.83022	−	3.21394i	0.208645	−	0.175074i	−0.532476	−	0.846445i	$-0.678738\pi$
$337$	3.83022	−	3.21394i	0.208645	−	0.175074i	0.741122	+	0.671370i	$0.234294\pi$
$338$	−15.9219	+	13.3601i	−0.866039	+	0.726693i
$339$		0			0
$340$		0			0
$341$	−8.66025	−	15.0000i	−0.468979	−	0.812296i
$342$		0			0
$343$	−6.50000	+	11.2583i	−0.350967	+	0.607893i
$344$	−0.300767	+	1.70574i	−0.0162163	+	0.0919672i
$345$		0			0
$346$	22.5526	+	8.20848i	1.21244	+	0.441291i
$347$	−4.21074	−	23.8803i	−0.226045	−	1.28196i	−0.860678	−	0.509149i	$-0.829960\pi$
$347$	−4.21074	−	23.8803i	−0.226045	−	1.28196i	0.634634	−	0.772813i	$-0.281151\pi$
$348$		0			0
$349$	−0.766044	−	0.642788i	−0.0410054	−	0.0344076i	0.622055	−	0.782974i	$-0.286298\pi$
$349$	−0.766044	−	0.642788i	−0.0410054	−	0.0344076i	−0.663060	+	0.748566i	$0.730743\pi$
$350$	12.1244			0.648074
$351$		0			0
$352$	18.0000			0.959403
$353$	−13.2683	−	11.1334i	−0.706199	−	0.592572i	0.217331	−	0.976098i	$-0.430265\pi$
$353$	−13.2683	−	11.1334i	−0.706199	−	0.592572i	−0.923530	+	0.383527i	$0.874709\pi$
$354$		0			0
$355$	6.25133	+	35.4531i	0.331786	+	1.88165i
$356$	9.76557	+	3.55438i	0.517574	+	0.188382i
$357$		0			0
$358$	−6.25133	+	35.4531i	−0.330393	+	1.87375i
$359$	15.5885	−	27.0000i	0.822727	−	1.42501i	−0.0809166	−	0.996721i	$-0.525785\pi$
$359$	15.5885	−	27.0000i	0.822727	−	1.42501i	0.903644	−	0.428285i	$-0.140882\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	27.6691	−	10.0707i	1.45426	−	0.529306i
$363$		0			0
$364$	−3.83022	+	3.21394i	−0.200758	+	0.168456i
$365$	−5.30731	+	4.45336i	−0.277797	+	0.233100i
$366$		0			0
$367$	15.0351	−	5.47232i	0.784825	−	0.285653i	0.0816418	−	0.996662i	$-0.473984\pi$
$367$	15.0351	−	5.47232i	0.784825	−	0.285653i	0.703183	+	0.711009i	$0.251761\pi$
$368$	17.3205	+	30.0000i	0.902894	+	1.56386i
$369$		0			0
$370$	3.00000	−	5.19615i	0.155963	−	0.270135i
$371$	−1.80460	+	10.2344i	−0.0936904	+	0.531345i
$372$		0			0
$373$	−21.6129	−	7.86646i	−1.11908	−	0.407310i	−0.284761	−	0.958599i	$-0.591914\pi$
$373$	−21.6129	−	7.86646i	−1.11908	−	0.407310i	−0.834315	+	0.551289i	$0.814136\pi$
$374$		0			0
$375$		0			0
$376$	4.59627	+	3.85673i	0.237034	+	0.198895i
$377$	17.3205			0.892052
$378$		0			0
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$	2.65366	+	2.22668i	0.136130	+	0.114226i
$381$		0			0
$382$	2.08378	+	11.8177i	0.106615	+	0.604646i
$383$	−16.2760	−	5.92396i	−0.831662	−	0.302700i	−0.109121	−	0.994028i	$-0.534804\pi$
$383$	−16.2760	−	5.92396i	−0.831662	−	0.302700i	−0.722541	+	0.691328i	$0.757026\pi$
$384$		0			0
$385$	2.08378	−	11.8177i	0.106199	−	0.602285i
$386$	−8.66025	+	15.0000i	−0.440795	+	0.763480i
$387$		0			0
$388$	−8.50000	−	14.7224i	−0.431522	−	0.747418i
$389$	6.51038	−	2.36959i	0.330089	−	0.120143i	−0.171659	−	0.985156i	$-0.554913\pi$
$389$	6.51038	−	2.36959i	0.330089	−	0.120143i	0.501748	+	0.865014i	$0.332690\pi$
$390$		0			0
$391$		0			0
$392$	−7.96097	+	6.68004i	−0.402090	+	0.337393i
$393$		0			0
$394$	16.9145	−	6.15636i	0.852139	−	0.310153i
$395$	−1.73205	−	3.00000i	−0.0871489	−	0.150946i
$396$		0			0
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	0.500000	−	0.866025i	0.0250943	−	0.0434646i	0.878300	+	0.478110i	$0.158678\pi$
$398$	5.71458	−	32.4090i	0.286446	−	1.62452i
$399$		0			0
$400$	32.8892	+	11.9707i	1.64446	+	0.598535i
$401$	−0.601535	−	3.41147i	−0.0300392	−	0.170361i	0.966097	−	0.258178i	$-0.0831221\pi$
$401$	−0.601535	−	3.41147i	−0.0300392	−	0.170361i	−0.996137	+	0.0878170i	$0.972011\pi$
$402$		0			0
$403$	19.1511	+	16.0697i	0.953985	+	0.800488i
$404$	13.8564			0.689382
$405$		0			0
$406$	6.00000			0.297775
$407$	−2.65366	−	2.22668i	−0.131537	−	0.110373i
$408$		0			0
$409$	0.868241	+	4.92404i	0.0429317	+	0.243478i	0.998720	−	0.0505773i	$-0.0161061\pi$
$409$	0.868241	+	4.92404i	0.0429317	+	0.243478i	−0.955788	+	0.294055i	$0.904995\pi$
$410$	19.5311	+	7.10876i	0.964574	+	0.351076i
$411$		0			0
$412$	1.38919	−	7.87846i	0.0684403	−	0.388144i
$413$	−1.73205	+	3.00000i	−0.0852286	+	0.147620i
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	−24.4139	+	8.88594i	−1.19699	+	0.435669i
$417$		0			0
$418$	4.59627	−	3.85673i	0.224811	−	0.188639i
$419$	29.1902	−	24.4935i	1.42604	−	1.19659i	0.478025	−	0.878346i	$-0.341353\pi$
$419$	29.1902	−	24.4935i	1.42604	−	1.19659i	0.948010	−	0.318239i	$-0.103092\pi$
$420$		0			0
$421$	17.8542	−	6.49838i	0.870159	−	0.316712i	0.131927	−	0.991259i	$-0.457883\pi$
$421$	17.8542	−	6.49838i	0.870159	−	0.316712i	0.738231	+	0.674548i	$0.235661\pi$
$422$	4.33013	+	7.50000i	0.210787	+	0.365094i
$423$		0			0
$424$	−9.00000	+	15.5885i	−0.437079	+	0.757042i
$425$		0			0
$426$		0			0
$427$	1.87939	+	0.684040i	0.0909498	+	0.0331030i
$428$	−1.80460	−	10.2344i	−0.0872289	−	0.494699i
$429$		0			0
$430$	−4.59627	−	3.85673i	−0.221652	−	0.185988i
$431$	20.7846			1.00116			0.500580	−	0.865690i	$-0.333120\pi$
$431$	20.7846			1.00116			0.500580	+	0.865690i	$0.333120\pi$
$432$		0			0
$433$	−1.00000			−0.0480569			−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000			−0.0480569			−0.0240285	+	0.999711i	$0.507649\pi$
$434$	6.63414	+	5.56670i	0.318449	+	0.267210i
$435$		0			0
$436$	2.95202	+	16.7417i	0.141376	+	0.801784i
$437$	6.51038	+	2.36959i	0.311434	+	0.113353i
$438$		0			0
$439$	3.47296	−	19.6962i	0.165756	−	0.940046i	−0.782527	−	0.622617i	$-0.786069\pi$
$439$	3.47296	−	19.6962i	0.165756	−	0.940046i	0.948282	−	0.317429i	$-0.102820\pi$
$440$	10.3923	−	18.0000i	0.495434	−	0.858116i
$441$		0			0
$442$		0			0
$443$	−13.0208	+	4.73917i	−0.618635	+	0.225165i	−0.632277	−	0.774742i	$-0.717880\pi$
$443$	−13.0208	+	4.73917i	−0.618635	+	0.225165i	0.0136422	+	0.999907i	$0.495657\pi$
$444$		0			0
$445$	27.5776	−	23.1404i	1.30730	−	1.09696i
$446$	25.2097	−	21.1535i	1.19372	−	1.00165i
$447$		0			0
$448$	0.939693	−	0.342020i	0.0443963	−	0.0161589i
$449$	−5.19615	−	9.00000i	−0.245222	−	0.424736i	0.716972	−	0.697102i	$-0.245527\pi$
$449$	−5.19615	−	9.00000i	−0.245222	−	0.424736i	−0.962194	+	0.272365i	$0.912194\pi$
$450$		0			0
$451$	6.00000	−	10.3923i	0.282529	−	0.489355i
$452$	3.00767	−	17.0574i	0.141469	−	0.802311i
$453$		0			0
$454$	22.5526	+	8.20848i	1.05845	+	0.385243i
$455$	3.00767	+	17.0574i	0.141002	+	0.799662i
$456$		0			0
$457$	13.0228	+	10.9274i	0.609179	+	0.511162i	0.894381	−	0.447306i	$-0.147616\pi$
$457$	13.0228	+	10.9274i	0.609179	+	0.511162i	−0.285202	+	0.958467i	$0.592061\pi$
$458$	−8.66025			−0.404667
$459$		0			0
$460$	−24.0000			−1.11901
$461$	−21.2292	−	17.8135i	−0.988745	−	0.829655i	−0.00335908	−	0.999994i	$-0.501069\pi$
$461$	−21.2292	−	17.8135i	−0.988745	−	0.829655i	−0.985385	+	0.170339i	$0.945514\pi$
$462$		0			0
$463$	−5.38309	−	30.5290i	−0.250174	−	1.41880i	−0.808164	−	0.588957i	$-0.799539\pi$
$463$	−5.38309	−	30.5290i	−0.250174	−	1.41880i	0.557990	−	0.829847i	$-0.311573\pi$
$464$	16.2760	+	5.92396i	0.755592	+	0.275013i
$465$		0			0
$466$		0			0
$467$	−5.19615	+	9.00000i	−0.240449	+	0.416470i	−0.960842	−	0.277096i	$-0.910628\pi$
$467$	−5.19615	+	9.00000i	−0.240449	+	0.416470i	0.720393	+	0.693566i	$0.243961\pi$
$468$		0			0
$469$	4.00000	+	6.92820i	0.184703	+	0.319915i
$470$	−19.5311	+	7.10876i	−0.900905	+	0.327902i
$471$		0			0
$472$	−4.59627	+	3.85673i	−0.211560	+	0.177520i
$473$	−2.65366	+	2.22668i	−0.122015	+	0.102383i
$474$		0			0
$475$	6.57785	−	2.39414i	0.301812	−	0.109851i
$476$		0			0
$477$		0			0
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	2.40614	−	13.6459i	0.109939	−	0.623497i	−0.879193	−	0.476466i	$-0.841917\pi$
$479$	2.40614	−	13.6459i	0.109939	−	0.623497i	0.989132	−	0.147030i	$-0.0469715\pi$
$480$		0			0
$481$	4.69846	+	1.71010i	0.214231	+	0.0779739i
$482$	5.71458	+	32.4090i	0.260292	+	1.47619i
$483$		0			0
$484$	0.766044	+	0.642788i	0.0348202	+	0.0292176i
$485$	−58.8897			−2.67404
$486$		0			0
$487$	−19.0000			−0.860972			−0.430486	−	0.902597i	$-0.641658\pi$
$487$	−19.0000			−0.860972			−0.430486	+	0.902597i	$0.641658\pi$
$488$	2.65366	+	2.22668i	0.120125	+	0.100797i
$489$		0			0
$490$	−6.25133	−	35.4531i	−0.282407	−	1.60161i
$491$	−35.8071	−	13.0327i	−1.61595	−	0.588158i	−0.633347	−	0.773868i	$-0.718319\pi$
$491$	−35.8071	−	13.0327i	−1.61595	−	0.588158i	−0.982605	+	0.185710i	$0.940542\pi$
$492$		0			0
$493$		0			0
$494$	−4.33013	+	7.50000i	−0.194822	+	0.337441i
$495$		0			0
$496$	12.5000	+	21.6506i	0.561267	+	0.972142i
$497$	−9.76557	+	3.55438i	−0.438046	+	0.159436i
$498$		0			0
$499$	−21.4492	+	17.9981i	−0.960200	+	0.805704i	−0.980986	−	0.194080i	$-0.937828\pi$
$499$	−21.4492	+	17.9981i	−0.960200	+	0.805704i	0.0207856	+	0.999784i	$0.493383\pi$
$500$	−5.30731	+	4.45336i	−0.237350	+	0.199160i
$501$		0			0
$502$	−33.8289	+	12.3127i	−1.50986	+	0.549544i
$503$	20.7846	+	36.0000i	0.926740	+	1.60516i	0.788739	+	0.614729i	$0.210734\pi$
$503$	20.7846	+	36.0000i	0.926740	+	1.60516i	0.138001	+	0.990432i	$0.455932\pi$
$504$		0			0
$505$	24.0000	−	41.5692i	1.06799	−	1.84981i
$506$	−7.21842	+	40.9377i	−0.320898	+	1.81990i
$507$		0			0
$508$	−15.9748	−	5.81434i	−0.708766	−	0.257970i
$509$	4.81228	+	27.2918i	0.213301	+	1.20969i	0.883831	+	0.467806i	$0.154955\pi$
$509$	4.81228	+	27.2918i	0.213301	+	1.20969i	−0.670531	+	0.741882i	$0.733934\pi$
$510$		0			0
$511$	−1.53209	−	1.28558i	−0.0677756	−	0.0568705i
$512$	−8.66025			−0.382733
$513$		0			0
$514$	6.00000			0.264649
$515$	−21.2292	−	17.8135i	−0.935472	−	0.784955i
$516$		0			0
$517$	2.08378	+	11.8177i	0.0916445	+	0.519742i
$518$	1.62760	+	0.592396i	0.0715124	+	0.0260284i
$519$		0			0
$520$	−5.20945	+	29.5442i	−0.228449	+	1.29560i
$521$	−10.3923	+	18.0000i	−0.455295	+	0.788594i	−0.998705	−	0.0508731i	$-0.983800\pi$
$521$	−10.3923	+	18.0000i	−0.455295	+	0.788594i	0.543410	+	0.839467i	$0.317133\pi$
$522$		0			0
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	3.25519	−	1.18479i	0.142204	−	0.0517579i
$525$		0			0
$526$	−18.3851	+	15.4269i	−0.801627	+	0.672645i
$527$		0			0
$528$		0			0
$529$	−23.4923	+	8.55050i	−1.02141	+	0.371761i
$530$	−31.1769	−	54.0000i	−1.35424	−	2.34561i
$531$		0			0
$532$	−0.500000	+	0.866025i	−0.0216777	+	0.0375470i
$533$	−3.00767	+	17.0574i	−0.130277	+	0.738837i
$534$		0			0
$535$	−33.8289	−	12.3127i	−1.46255	−	0.532326i
$536$	2.40614	+	13.6459i	0.103929	+	0.589413i
$537$		0			0
$538$		0			0
$539$	−20.7846			−0.895257
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$	21.2292	+	17.8135i	0.911874	+	0.765153i
$543$		0			0
$544$		0			0
$545$	55.3382	+	20.1415i	2.37043	+	0.862766i
$546$		0			0
$547$	3.47296	−	19.6962i	0.148493	−	0.842147i	−0.816003	−	0.578048i	$-0.803815\pi$
$547$	3.47296	−	19.6962i	0.148493	−	0.842147i	0.964496	−	0.264098i	$-0.0850744\pi$
$548$	3.46410	−	6.00000i	0.147979	−	0.256307i
$549$		0			0
$550$	21.0000	+	36.3731i	0.895443	+	1.55095i
$551$	3.25519	−	1.18479i	0.138676	−	0.0504739i
$552$		0			0
$553$	0.766044	−	0.642788i	0.0325755	−	0.0273341i
$554$	−22.5561	+	18.9268i	−0.958316	+	0.804122i
$555$		0			0
$556$	12.2160	−	4.44626i	0.518074	−	0.188564i
$557$	5.19615	+	9.00000i	0.220168	+	0.381342i	0.954859	−	0.297060i	$-0.0960061\pi$
$557$	5.19615	+	9.00000i	0.220168	+	0.381342i	−0.734691	+	0.678402i	$0.762673\pi$
$558$		0			0
$559$	2.50000	−	4.33013i	0.105739	−	0.183145i
$560$	−3.00767	+	17.0574i	−0.127097	+	0.720805i
$561$		0			0
$562$	22.5526	+	8.20848i	0.951325	+	0.346254i
$563$	−6.01535	−	34.1147i	−0.253517	−	1.43776i	−0.799851	−	0.600198i	$-0.795088\pi$
$563$	−6.01535	−	34.1147i	−0.253517	−	1.43776i	0.546335	−	0.837567i	$-0.316023\pi$
$564$		0			0
$565$	−45.9627	−	38.5673i	−1.93366	−	1.62254i
$566$	22.5167			0.946446
$567$		0			0
$568$	−18.0000			−0.755263
$569$	18.5756	+	15.5868i	0.778729	+	0.653431i	0.942928	−	0.332996i	$-0.108059\pi$
$569$	18.5756	+	15.5868i	0.778729	+	0.653431i	−0.164199	+	0.986427i	$0.552504\pi$
$570$		0			0
$571$	7.11958	+	40.3771i	0.297945	+	1.68973i	0.654986	+	0.755641i	$0.272675\pi$
$571$	7.11958	+	40.3771i	0.297945	+	1.68973i	−0.357041	+	0.934089i	$0.616214\pi$
$572$	−16.2760	−	5.92396i	−0.680532	−	0.247693i
$573$		0			0
$574$	−1.04189	+	5.90885i	−0.0434876	+	0.246630i
$575$	−24.2487	+	42.0000i	−1.01124	+	1.75152i
$576$		0			0
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	0.965701	+	0.259656i	$0.0836092\pi$
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	−0.257982	+	0.966150i	$0.583058\pi$
$578$	−27.6691	+	10.0707i	−1.15088	+	0.418887i
$579$		0			0
$580$	−9.19253	+	7.71345i	−0.381699	+	0.320284i
$581$	5.30731	−	4.45336i	0.220184	−	0.184757i
$582$		0			0
$583$	−33.8289	+	12.3127i	−1.40105	+	0.509941i
$584$	−1.73205	−	3.00000i	−0.0716728	−	0.124141i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$	−1.20307	+	6.82295i	−0.0496560	+	0.281613i	−0.999518	−	0.0310575i	$-0.990113\pi$
$587$	−1.20307	+	6.82295i	−0.0496560	+	0.281613i	0.949862	+	0.312671i	$0.101224\pi$
$588$		0			0
$589$	4.69846	+	1.71010i	0.193597	+	0.0704635i
$590$	−3.60921	−	20.4688i	−0.148589	−	0.842689i
$591$		0			0
$592$	3.83022	+	3.21394i	0.157421	+	0.132092i
$593$	−20.7846			−0.853522			−0.426761	−	0.904365i	$-0.640345\pi$
$593$	−20.7846			−0.853522			−0.426761	+	0.904365i	$0.640345\pi$
$594$		0			0
$595$		0			0
$596$	5.30731	+	4.45336i	0.217396	+	0.182417i
$597$		0			0
$598$	−10.4189	−	59.0885i	−0.426060	−	2.41631i
$599$	22.7863	+	8.29355i	0.931024	+	0.338865i	0.762616	−	0.646852i	$-0.223915\pi$
$599$	22.7863	+	8.29355i	0.931024	+	0.338865i	0.168409	+	0.985717i	$0.446137\pi$
$600$		0			0
$601$	6.07769	−	34.4683i	0.247914	−	1.40599i	−0.565713	−	0.824602i	$-0.691399\pi$
$601$	6.07769	−	34.4683i	0.247914	−	1.40599i	0.813627	−	0.581388i	$-0.197490\pi$
$602$	0.866025	−	1.50000i	0.0352966	−	0.0611354i
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	3.25519	−	1.18479i	0.132342	−	0.0481687i
$606$		0			0
$607$	−9.95858	+	8.35624i	−0.404206	+	0.339169i	−0.822117	−	0.569319i	$-0.807207\pi$
$607$	−9.95858	+	8.35624i	−0.404206	+	0.339169i	0.417911	+	0.908488i	$0.362763\pi$
$608$	−3.98048	+	3.34002i	−0.161430	+	0.135456i
$609$		0			0
$610$	−11.2763	+	4.10424i	−0.456565	+	0.166176i
$611$	−8.66025	−	15.0000i	−0.350356	−	0.606835i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	−6.01535	+	34.1147i	−0.242760	+	1.37676i
$615$		0			0
$616$	5.63816	+	2.05212i	0.227168	+	0.0826823i
$617$	1.20307	+	6.82295i	0.0484338	+	0.274682i	0.999401	−	0.0346105i	$-0.0110191\pi$
$617$	1.20307	+	6.82295i	0.0484338	+	0.274682i	−0.950967	+	0.309292i	$0.899908\pi$
$618$		0			0
$619$	15.3209	+	12.8558i	0.615799	+	0.516716i	0.896480	−	0.443085i	$-0.146116\pi$
$619$	15.3209	+	12.8558i	0.615799	+	0.516716i	−0.280681	+	0.959801i	$0.590560\pi$
$620$	−17.3205			−0.695608
$621$		0			0
$622$	24.0000			0.962312
$623$	7.96097	+	6.68004i	0.318949	+	0.267630i
$624$		0			0
$625$	−1.91013	−	10.8329i	−0.0764052	−	0.433315i
$626$	−1.62760	−	0.592396i	−0.0650518	−	0.0236769i
$627$		0			0
$628$	−2.25743	+	12.8025i	−0.0900811	+	0.510875i
$629$		0			0
$630$		0			0
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	0.645748	−	0.763550i	$-0.276545\pi$
$631$	−8.50000	−	14.7224i	−0.338380	−	0.586091i	−0.984128	+	0.177459i	$0.943212\pi$
$632$	1.62760	−	0.592396i	0.0647423	−	0.0235643i
$633$		0			0
$634$	36.7701	−	30.8538i	1.46033	−	1.22536i
$635$	−45.1121	+	37.8536i	−1.79022	+	1.50217i
$636$		0			0
$637$	28.1908	−	10.2606i	1.11696	−	0.406540i
$638$	10.3923	+	18.0000i	0.411435	+	0.712627i
$639$		0			0
$640$	−21.0000	+	36.3731i	−0.830098	+	1.43777i
$641$	7.81995	−	44.3492i	0.308870	−	1.75169i	−0.295837	−	0.955238i	$-0.595599\pi$
$641$	7.81995	−	44.3492i	0.308870	−	1.75169i	0.604707	−	0.796448i	$-0.293290\pi$
$642$		0			0
$643$	−41.3465	−	15.0489i	−1.63055	−	0.593470i	−0.645196	−	0.764017i	$-0.723224\pi$
$643$	−41.3465	−	15.0489i	−1.63055	−	0.593470i	−0.985350	+	0.170547i	$0.945447\pi$
$644$	−1.20307	−	6.82295i	−0.0474076	−	0.268862i
$645$		0			0
$646$		0			0
$647$	20.7846			0.817127			0.408564	−	0.912730i	$-0.366030\pi$
$647$	20.7846			0.817127			0.408564	+	0.912730i	$0.366030\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	−46.4390	−	38.9669i	−1.82149	−	1.52841i
$651$		0			0
$652$	−0.173648	−	0.984808i	−0.00680059	−	0.0385680i
$653$	−16.2760	−	5.92396i	−0.636927	−	0.231823i	0.00331633	−	0.999995i	$-0.498944\pi$
$653$	−16.2760	−	5.92396i	−0.636927	−	0.231823i	−0.640244	+	0.768172i	$0.721167\pi$
$654$		0			0
$655$	2.08378	−	11.8177i	0.0814199	−	0.461755i
$656$	−8.66025	+	15.0000i	−0.338126	+	0.585652i
$657$		0			0
$658$	−3.00000	−	5.19615i	−0.116952	−	0.202567i
$659$	26.0415	−	9.47834i	1.01443	−	0.369224i	0.219300	−	0.975658i	$-0.429623\pi$
$659$	26.0415	−	9.47834i	1.01443	−	0.369224i	0.795134	+	0.606434i	$0.207400\pi$
$660$		0			0
$661$	−7.66044	+	6.42788i	−0.297957	+	0.250015i	−0.779493	−	0.626411i	$-0.784523\pi$
$661$	−7.66044	+	6.42788i	−0.297957	+	0.250015i	0.481536	+	0.876426i	$0.340079\pi$
$662$	25.2097	−	21.1535i	0.979804	−	0.822153i
$663$		0			0
$664$	11.2763	−	4.10424i	0.437606	−	0.159275i
$665$	1.73205	+	3.00000i	0.0671660	+	0.116335i
$666$		0			0
$667$	−12.0000	+	20.7846i	−0.464642	+	0.804783i
$668$	−4.21074	+	23.8803i	−0.162919	+	0.923957i
$669$		0			0
$670$	−45.1052	−	16.4170i	−1.74257	−	0.634243i
$671$	1.20307	+	6.82295i	0.0464440	+	0.263397i
$672$		0			0
$673$	−28.3436	−	23.7831i	−1.09257	−	0.916773i	−0.0956642	−	0.995414i	$-0.530497\pi$
$673$	−28.3436	−	23.7831i	−1.09257	−	0.916773i	−0.996903	+	0.0786409i	$0.974942\pi$
$674$	−8.66025			−0.333581
$675$		0			0
$676$	12.0000			0.461538
$677$	−13.2683	−	11.1334i	−0.509941	−	0.427892i	0.351167	−	0.936313i	$-0.385785\pi$
$677$	−13.2683	−	11.1334i	−0.509941	−	0.427892i	−0.861109	+	0.508421i	$0.830229\pi$
$678$		0			0
$679$	−2.95202	−	16.7417i	−0.113288	−	0.642489i
$680$		0			0
$681$		0			0
$682$	−5.20945	+	29.5442i	−0.199480	+	1.13131i
$683$	20.7846	−	36.0000i	0.795301	−	1.37750i	−0.127347	−	0.991858i	$-0.540646\pi$
$683$	20.7846	−	36.0000i	0.795301	−	1.37750i	0.922648	−	0.385643i	$-0.126021\pi$
$684$		0			0
$685$	−12.0000	−	20.7846i	−0.458496	−	0.794139i
$686$	21.1587	−	7.70115i	0.807844	−	0.294031i
$687$		0			0
$688$	3.83022	−	3.21394i	0.146026	−	0.122530i
$689$	39.8048	−	33.4002i	1.51644	−	1.27245i
$690$		0			0
$691$	−15.9748	+	5.81434i	−0.607709	+	0.221188i	−0.627501	−	0.778616i	$-0.715922\pi$
$691$	−15.9748	+	5.81434i	−0.607709	+	0.221188i	0.0197915	+	0.999804i	$0.493700\pi$
$692$	−6.92820	−	12.0000i	−0.263371	−	0.456172i
$693$		0			0
$694$	−21.0000	+	36.3731i	−0.797149	+	1.38070i
$695$	7.81995	−	44.3492i	0.296628	−	1.68226i
$696$		0			0
$697$		0			0
$698$	0.300767	+	1.70574i	0.0113842	+	0.0645631i
$699$		0			0
$700$	−5.36231	−	4.49951i	−0.202676	−	0.170066i
$701$	41.5692			1.57005			0.785024	−	0.619466i	$-0.212651\pi$
$701$	41.5692			1.57005			0.785024	+	0.619466i	$0.212651\pi$
$702$		0			0
$703$	1.00000			0.0377157
$704$	2.65366	+	2.22668i	0.100013	+	0.0839212i
$705$		0			0
$706$	5.20945	+	29.5442i	0.196060	+	1.11191i
$707$	13.0208	+	4.73917i	0.489696	+	0.178235i
$708$		0			0
$709$	−3.29932	+	18.7113i	−0.123908	+	0.702719i	0.858042	+	0.513580i	$0.171681\pi$
$709$	−3.29932	+	18.7113i	−0.123908	+	0.702719i	−0.981950	+	0.189140i	$0.939430\pi$
$710$	31.1769	−	54.0000i	1.17005	−	2.02658i
$711$		0			0
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$	−32.5519	+	11.8479i	−1.21908	+	0.443708i
$714$		0			0
$715$	−45.9627	+	38.5673i	−1.71891	+	1.44233i
$716$	15.9219	−	13.3601i	0.595031	−	0.499290i
$717$		0			0
$718$	−50.7434	+	18.4691i	−1.89373	+	0.689260i
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	0.946501	−	0.322700i	$-0.104591\pi$
$719$	5.19615	+	9.00000i	0.193784	+	0.335643i	−0.752717	+	0.658344i	$0.771257\pi$
$720$		0			0
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$	5.41381	−	30.7033i	0.201481	−	1.14266i
$723$		0			0
$724$	−15.9748	−	5.81434i	−0.593698	−	0.216088i
$725$	4.21074	+	23.8803i	0.156383	+	0.886893i
$726$		0			0
$727$	−12.2567	−	10.2846i	−0.454576	−	0.381435i	0.386555	−	0.922267i	$-0.373665\pi$
$727$	−12.2567	−	10.2846i	−0.454576	−	0.381435i	−0.841131	+	0.540832i	$0.818110\pi$
$728$	−8.66025			−0.320970
$729$		0			0
$730$	12.0000			0.444140
$731$		0			0
$732$		0			0
$733$	7.11958	+	40.3771i	0.262968	+	1.49136i	0.774761	+	0.632254i	$0.217870\pi$
$733$	7.11958	+	40.3771i	0.262968	+	1.49136i	−0.511793	+	0.859109i	$0.671019\pi$
$734$	−26.0415	−	9.47834i	−0.961210	−	0.349852i
$735$		0			0
$736$	6.25133	−	35.4531i	0.230427	−	1.30682i
$737$	−13.8564	+	24.0000i	−0.510407	+	0.884051i
$738$		0			0
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	0.986154	−	0.165831i	$-0.0530307\pi$
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	−0.636691	+	0.771119i	$0.719697\pi$
$740$	−3.25519	+	1.18479i	−0.119663	+	0.0435538i
$741$		0			0
$742$	13.7888	−	11.5702i	0.506203	−	0.424755i
$743$	5.30731	−	4.45336i	0.194706	−	0.163378i	−0.540223	−	0.841522i	$-0.681660\pi$
$743$	5.30731	−	4.45336i	0.194706	−	0.163378i	0.734929	+	0.678144i	$0.237215\pi$
$744$		0			0
$745$	22.5526	−	8.20848i	0.826264	−	0.300736i
$746$	19.9186	+	34.5000i	0.729271	+	1.26313i
$747$		0			0
$748$		0			0
$749$	1.80460	−	10.2344i	0.0659388	−	0.373958i
$750$		0			0
$751$	−4.69846	−	1.71010i	−0.171449	−	0.0624025i	0.254869	−	0.966976i	$-0.417968\pi$
$751$	−4.69846	−	1.71010i	−0.171449	−	0.0624025i	−0.426319	+	0.904573i	$0.640190\pi$
$752$	−3.00767	−	17.0574i	−0.109679	−	0.622018i
$753$		0			0
$754$	−22.9813	−	19.2836i	−0.836931	−	0.702268i
$755$	55.4256			2.01715
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	25.2097	+	21.1535i	0.915659	+	0.768329i
$759$		0			0
$760$	1.04189	+	5.90885i	0.0377933	+	0.214336i
$761$	−26.0415	−	9.47834i	−0.944005	−	0.343590i	−0.176259	−	0.984344i	$-0.556399\pi$
$761$	−26.0415	−	9.47834i	−0.944005	−	0.343590i	−0.767746	+	0.640754i	$0.778622\pi$
$762$		0			0
$763$	−2.95202	+	16.7417i	−0.106870	+	0.606091i
$764$	3.46410	−	6.00000i	0.125327	−	0.217072i
$765$		0			0
$766$	15.0000	+	25.9808i	0.541972	+	0.938723i
$767$	16.2760	−	5.92396i	0.587691	−	0.213902i
$768$		0			0
$769$	−9.95858	+	8.35624i	−0.359115	+	0.301334i	−0.804438	−	0.594037i	$-0.797533\pi$
$769$	−9.95858	+	8.35624i	−0.359115	+	0.301334i	0.445323	+	0.895370i	$0.353089\pi$
$770$	−15.9219	+	13.3601i	−0.573787	+	0.481464i
$771$		0			0
$772$	9.39693	−	3.42020i	0.338203	−	0.123096i
$773$	10.3923	+	18.0000i	0.373785	+	0.647415i	0.990144	−	0.140050i	$-0.0447264\pi$
$773$	10.3923	+	18.0000i	0.373785	+	0.647415i	−0.616359	+	0.787465i	$0.711393\pi$
$774$		0			0
$775$	−17.5000	+	30.3109i	−0.628619	+	1.08880i
$776$	5.11305	−	28.9975i	0.183548	−	1.04095i
$777$		0			0
$778$	−11.2763	−	4.10424i	−0.404275	−	0.147144i
$779$	0.601535	+	3.41147i	0.0215522	+	0.122229i
$780$		0			0
$781$	−27.5776	−	23.1404i	−0.986804	−	0.828027i
$782$		0			0
$783$		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.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32683 - 1.11334i) q^{2} +(0.173648 + 0.984808i) q^{4} +(3.25519 + 1.18479i) q^{5} +(-0.173648 + 0.984808i) q^{7} +(-0.866025 + 1.50000i) q^{8} +(-3.00000 - 5.19615i) q^{10} +(-3.25519 + 1.18479i) q^{11} +(3.83022 - 3.21394i) q^{13} +(1.32683 - 1.11334i) q^{14} +(4.69846 - 1.71010i) q^{16} +(0.500000 - 0.866025i) q^{19} +(-0.601535 + 3.41147i) q^{20} +(5.63816 + 2.05212i) q^{22} +(1.20307 + 6.82295i) q^{23} +(5.36231 + 4.49951i) q^{25} -8.66025 q^{26} -1.00000 q^{28} +(2.65366 + 2.22668i) q^{29} +(0.868241 + 4.92404i) q^{31} +(-4.88279 - 1.77719i) q^{32} +(-1.73205 + 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.62760 + 0.592396i) q^{38} +(-4.59627 + 3.85673i) q^{40} +(-2.65366 + 2.22668i) q^{41} +(0.939693 - 0.342020i) q^{43} +(-1.73205 - 3.00000i) q^{44} +(6.00000 - 10.3923i) q^{46} +(0.601535 - 3.41147i) q^{47} +(5.63816 + 2.05212i) q^{49} +(-2.10537 - 11.9402i) q^{50} +(3.83022 + 3.21394i) q^{52} +10.3923 q^{53} -12.0000 q^{55} +(-1.32683 - 1.11334i) q^{56} +(-1.04189 - 5.90885i) q^{58} +(3.25519 + 1.18479i) q^{59} +(0.347296 - 1.96962i) q^{61} +(4.33013 - 7.50000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(16.2760 - 5.92396i) q^{65} +(6.12836 - 5.14230i) q^{67} +(5.63816 - 2.05212i) q^{70} +(5.19615 + 9.00000i) q^{71} +(-1.00000 + 1.73205i) q^{73} +(0.300767 - 1.70574i) q^{74} +(0.939693 + 0.342020i) q^{76} +(-0.601535 - 3.41147i) q^{77} +(-0.766044 - 0.642788i) q^{79} +17.3205 q^{80} +6.00000 q^{82} +(-5.30731 - 4.45336i) q^{83} +(-1.62760 - 0.592396i) q^{86} +(1.04189 - 5.90885i) q^{88} +(5.19615 - 9.00000i) q^{89} +(2.50000 + 4.33013i) q^{91} +(-6.51038 + 2.36959i) q^{92} +(-4.59627 + 3.85673i) q^{94} +(2.65366 - 2.22668i) q^{95} +(-15.9748 + 5.81434i) q^{97} +(-5.19615 - 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) \) 12 * q - 36 * q^10 + 6 * q^19 - 12 * q^28 + 6 * q^37 + 72 * q^46 - 144 * q^55 - 6 * q^64 - 12 * q^73 + 72 * q^82 + 30 * q^91

Introduction

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