LMFDB - Embedded newform 729.2.e.n.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			649.2
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.649
Dual form			729.2.e.n.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.300767 - 1.70574i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(2.65366 - 2.22668i) q^{5} +(0.939693 - 0.342020i) q^{7} +(0.866025 - 1.50000i) q^{8} +(-3.00000 - 5.19615i) q^{10} +(-2.65366 - 2.22668i) q^{11} +(0.868241 + 4.92404i) q^{13} +(-0.300767 - 1.70574i) q^{14} +(-3.83022 - 3.21394i) q^{16} +(0.500000 - 0.866025i) q^{19} +(-3.25519 + 1.18479i) q^{20} +(-4.59627 + 3.85673i) q^{22} +(6.51038 + 2.36959i) q^{23} +(1.21554 - 6.89365i) q^{25} +8.66025 q^{26} -1.00000 q^{28} +(-0.601535 + 3.41147i) q^{29} +(-4.69846 - 1.71010i) q^{31} +(-3.98048 + 3.34002i) q^{32} +(1.73205 - 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.32683 - 1.11334i) q^{38} +(-1.04189 - 5.90885i) q^{40} +(0.601535 + 3.41147i) q^{41} +(-0.766044 - 0.642788i) q^{43} +(1.73205 + 3.00000i) q^{44} +(6.00000 - 10.3923i) q^{46} +(3.25519 - 1.18479i) q^{47} +(-4.59627 + 3.85673i) q^{49} +(-11.3932 - 4.14677i) q^{50} +(0.868241 - 4.92404i) q^{52} -10.3923 q^{53} -12.0000 q^{55} +(0.300767 - 1.70574i) q^{56} +(5.63816 + 2.05212i) q^{58} +(2.65366 - 2.22668i) q^{59} +(-1.87939 + 0.684040i) q^{61} +(-4.33013 + 7.50000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(13.2683 + 11.1334i) q^{65} +(1.38919 + 7.87846i) q^{67} +(-4.59627 - 3.85673i) q^{70} +(-5.19615 - 9.00000i) q^{71} +(-1.00000 + 1.73205i) q^{73} +(1.62760 - 0.592396i) q^{74} +(-0.766044 + 0.642788i) q^{76} +(-3.25519 - 1.18479i) q^{77} +(-0.173648 + 0.984808i) q^{79} -17.3205 q^{80} +6.00000 q^{82} +(1.20307 - 6.82295i) q^{83} +(-1.32683 + 1.11334i) q^{86} +(-5.63816 + 2.05212i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(2.50000 + 4.33013i) q^{91} +(-5.30731 - 4.45336i) q^{92} +(-1.04189 - 5.90885i) q^{94} +(-0.601535 - 3.41147i) q^{95} +(13.0228 + 10.9274i) q^{97} +(5.19615 + 9.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	0.300767	−	1.70574i	0.212675	−	1.20614i	−0.672222	−	0.740350i	$-0.734660\pi$
$2$	0.300767	−	1.70574i	0.212675	−	1.20614i	0.884896	−	0.465788i	$-0.154229\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	2.65366	−	2.22668i	1.18675	−	0.995802i	0.186841	−	0.982390i	$-0.440175\pi$
$5$	2.65366	−	2.22668i	1.18675	−	0.995802i	0.999910	−	0.0134121i	$-0.00426933\pi$
$6$		0			0
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i	−0.158272	−	0.987396i	$-0.550592\pi$
$7$	0.939693	−	0.342020i	0.355170	−	0.129271i	0.513442	+	0.858124i	$0.328370\pi$
$8$	0.866025	−	1.50000i	0.306186	−	0.530330i
$9$		0			0
$10$	−3.00000	−	5.19615i	−0.948683	−	1.64317i
$11$	−2.65366	−	2.22668i	−0.800107	−	0.671370i	0.148117	−	0.988970i	$-0.452679\pi$
$11$	−2.65366	−	2.22668i	−0.800107	−	0.671370i	−0.948225	+	0.317600i	$0.897123\pi$
$12$		0			0
$13$	0.868241	+	4.92404i	0.240807	+	1.36568i	0.830033	+	0.557714i	$0.188322\pi$
$13$	0.868241	+	4.92404i	0.240807	+	1.36568i	−0.589226	+	0.807968i	$0.700567\pi$
$14$	−0.300767	−	1.70574i	−0.0803835	−	0.455877i
$15$		0			0
$16$	−3.83022	−	3.21394i	−0.957556	−	0.803485i
$17$		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	$0.130073\pi$
$20$	−3.25519	+	1.18479i	−0.727883	+	0.264928i
$21$		0			0
$22$	−4.59627	+	3.85673i	−0.979927	+	0.822257i
$23$	6.51038	+	2.36959i	1.35751	+	0.494093i	0.915283	−	0.402811i	$-0.131967\pi$
$23$	6.51038	+	2.36959i	1.35751	+	0.494093i	0.442225	+	0.896904i	$0.354189\pi$
$24$		0			0
$25$	1.21554	−	6.89365i	0.243107	−	1.37873i
$26$	8.66025			1.69842
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−0.601535	+	3.41147i	−0.111702	+	0.633495i	0.876628	+	0.481169i	$0.159788\pi$
$29$	−0.601535	+	3.41147i	−0.111702	+	0.633495i	−0.988330	+	0.152326i	$0.951324\pi$
$30$		0			0
$31$	−4.69846	−	1.71010i	−0.843869	−	0.307143i	−0.116331	−	0.993211i	$-0.537113\pi$
$31$	−4.69846	−	1.71010i	−0.843869	−	0.307143i	−0.727538	+	0.686067i	$0.759336\pi$
$32$	−3.98048	+	3.34002i	−0.703657	+	0.590438i
$33$		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	$0.807139\pi$
$38$	−1.32683	−	1.11334i	−0.215240	−	0.180608i
$39$		0			0
$40$	−1.04189	−	5.90885i	−0.164737	−	0.934271i
$41$	0.601535	+	3.41147i	0.0939440	+	0.532783i	0.995066	+	0.0992168i	$0.0316337\pi$
$41$	0.601535	+	3.41147i	0.0939440	+	0.532783i	−0.901122	+	0.433566i	$0.857255\pi$
$42$		0			0
$43$	−0.766044	−	0.642788i	−0.116821	−	0.0980242i	0.582506	−	0.812826i	$-0.302072\pi$
$43$	−0.766044	−	0.642788i	−0.116821	−	0.0980242i	−0.699327	+	0.714802i	$0.746517\pi$
$44$	1.73205	+	3.00000i	0.261116	+	0.452267i
$45$		0			0
$46$	6.00000	−	10.3923i	0.884652	−	1.53226i
$47$	3.25519	−	1.18479i	0.474818	−	0.172820i	−0.0935154	−	0.995618i	$-0.529810\pi$
$47$	3.25519	−	1.18479i	0.474818	−	0.172820i	0.568334	+	0.822798i	$0.307588\pi$
$48$		0			0
$49$	−4.59627	+	3.85673i	−0.656610	+	0.550961i
$50$	−11.3932	−	4.14677i	−1.61124	−	0.586442i
$51$		0			0
$52$	0.868241	−	4.92404i	0.120403	−	0.682841i
$53$	−10.3923			−1.42749			−0.713746	−	0.700404i	$-0.753003\pi$
$53$	−10.3923			−1.42749			−0.713746	+	0.700404i	$0.753003\pi$
$54$		0			0
$55$	−12.0000			−1.61808
$56$	0.300767	−	1.70574i	0.0401917	−	0.227939i
$57$		0			0
$58$	5.63816	+	2.05212i	0.740326	+	0.269457i
$59$	2.65366	−	2.22668i	0.345477	−	0.289889i	−0.453494	−	0.891259i	$-0.649823\pi$
$59$	2.65366	−	2.22668i	0.345477	−	0.289889i	0.798971	+	0.601370i	$0.205378\pi$
$60$		0			0
$61$	−1.87939	+	0.684040i	−0.240631	+	0.0875824i	−0.459520	−	0.888167i	$-0.651979\pi$
$61$	−1.87939	+	0.684040i	−0.240631	+	0.0875824i	0.218890	+	0.975750i	$0.429756\pi$
$62$	−4.33013	+	7.50000i	−0.549927	+	0.952501i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	13.2683	+	11.1334i	1.64573	+	1.38093i
$66$		0			0
$67$	1.38919	+	7.87846i	0.169716	+	0.962507i	0.944068	+	0.329752i	$0.106965\pi$
$67$	1.38919	+	7.87846i	0.169716	+	0.962507i	−0.774352	+	0.632756i	$0.781924\pi$
$68$		0			0
$69$		0			0
$70$	−4.59627	−	3.85673i	−0.549359	−	0.460967i
$71$	−5.19615	−	9.00000i	−0.616670	−	1.06810i	−0.990089	−	0.140441i	$-0.955148\pi$
$71$	−5.19615	−	9.00000i	−0.616670	−	1.06810i	0.373419	−	0.927663i	$-0.378185\pi$
$72$		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	$0.204008\pi$
$74$	1.62760	−	0.592396i	0.189204	−	0.0688647i
$75$		0			0
$76$	−0.766044	+	0.642788i	−0.0878713	+	0.0737328i
$77$	−3.25519	−	1.18479i	−0.370963	−	0.135020i
$78$		0			0
$79$	−0.173648	+	0.984808i	−0.0195369	+	0.110800i	−0.993017	−	0.117973i	$-0.962360\pi$
$79$	−0.173648	+	0.984808i	−0.0195369	+	0.110800i	0.973480	+	0.228773i	$0.0734713\pi$
$80$	−17.3205			−1.93649
$81$		0			0
$82$	6.00000			0.662589
$83$	1.20307	−	6.82295i	0.132054	−	0.748916i	−0.844812	−	0.535063i	$-0.820288\pi$
$83$	1.20307	−	6.82295i	0.132054	−	0.748916i	0.976866	−	0.213852i	$-0.0686012\pi$
$84$		0			0
$85$		0			0
$86$	−1.32683	+	1.11334i	−0.143076	+	0.120055i
$87$		0			0
$88$	−5.63816	+	2.05212i	−0.601029	+	0.218757i
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$	2.50000	+	4.33013i	0.262071	+	0.453921i
$92$	−5.30731	−	4.45336i	−0.553325	−	0.464295i
$93$		0			0
$94$	−1.04189	−	5.90885i	−0.107463	−	0.609451i
$95$	−0.601535	−	3.41147i	−0.0617162	−	0.350010i
$96$		0			0
$97$	13.0228	+	10.9274i	1.32226	+	1.10951i	0.985820	+	0.167803i	$0.0536674\pi$
$97$	13.0228	+	10.9274i	1.32226	+	1.10951i	0.336440	+	0.941705i	$0.390777\pi$
$98$	5.19615	+	9.00000i	0.524891	+	0.909137i
$99$		0			0
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	13.0208	−	4.73917i	1.29561	−	0.471565i	0.400048	−	0.916494i	$-0.368993\pi$
$101$	13.0208	−	4.73917i	1.29561	−	0.471565i	0.895566	+	0.444929i	$0.146771\pi$
$102$		0			0
$103$	6.12836	−	5.14230i	0.603845	−	0.506686i	−0.288834	−	0.957379i	$-0.593268\pi$
$103$	6.12836	−	5.14230i	0.603845	−	0.506686i	0.892679	+	0.450693i	$0.148823\pi$
$104$	8.13798	+	2.96198i	0.797994	+	0.290446i
$105$		0			0
$106$	−3.12567	+	17.7265i	−0.303592	+	1.72175i
$107$	10.3923			1.00466			0.502331	−	0.864675i	$-0.332476\pi$
$107$	10.3923			1.00466			0.502331	+	0.864675i	$0.332476\pi$
$108$		0			0
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$	−3.60921	+	20.4688i	−0.344125	+	1.95163i
$111$		0			0
$112$	−4.69846	−	1.71010i	−0.443963	−	0.161589i
$113$	−13.2683	+	11.1334i	−1.24817	+	1.04734i	−0.251335	+	0.967900i	$0.580870\pi$
$113$	−13.2683	+	11.1334i	−1.24817	+	1.04734i	−0.996839	+	0.0794428i	$0.974686\pi$
$114$		0			0
$115$	22.5526	−	8.20848i	2.10304	−	0.765445i
$116$	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
$121$	0.173648	+	0.984808i	0.0157862	+	0.0895280i
$122$	0.601535	+	3.41147i	0.0544604	+	0.308860i
$123$		0			0
$124$	3.83022	+	3.21394i	0.343964	+	0.288620i
$125$	−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	$0.894666\pi$
$128$	−11.3932	+	4.14677i	−1.00702	+	0.366526i
$129$		0			0
$130$	22.9813	−	19.2836i	2.01560	−	1.69129i
$131$	−3.25519	−	1.18479i	−0.284407	−	0.103516i	0.195878	−	0.980628i	$-0.437244\pi$
$131$	−3.25519	−	1.18479i	−0.284407	−	0.103516i	−0.480285	+	0.877113i	$0.659467\pi$
$132$		0			0
$133$	0.173648	−	0.984808i	0.0150572	−	0.0853937i
$134$	13.8564			1.19701
$135$		0			0
$136$		0			0
$137$	1.20307	−	6.82295i	0.102785	−	0.582924i	−0.889297	−	0.457331i	$-0.848806\pi$
$137$	1.20307	−	6.82295i	0.102785	−	0.582924i	0.992082	−	0.125593i	$-0.0400833\pi$
$138$		0			0
$139$	12.2160	+	4.44626i	1.03615	+	0.377127i	0.803419	−	0.595415i	$-0.203012\pi$
$139$	12.2160	+	4.44626i	1.03615	+	0.377127i	0.232729	+	0.972542i	$0.425234\pi$
$140$	−2.65366	+	2.22668i	−0.224275	+	0.188189i
$141$		0			0
$142$	−16.9145	+	6.15636i	−1.41943	+	0.516630i
$143$	8.66025	−	15.0000i	0.724207	−	1.25436i
$144$		0			0
$145$	6.00000	+	10.3923i	0.498273	+	0.863034i
$146$	2.65366	+	2.22668i	0.219618	+	0.184281i
$147$		0			0
$148$	−0.173648	−	0.984808i	−0.0142738	−	0.0809507i
$149$	−1.20307	−	6.82295i	−0.0985593	−	0.558958i	−0.993598	−	0.112970i	$-0.963964\pi$
$149$	−1.20307	−	6.82295i	−0.0985593	−	0.558958i	0.895039	−	0.445988i	$-0.147148\pi$
$150$		0			0
$151$	−12.2567	−	10.2846i	−0.997437	−	0.836949i	−0.0108097	−	0.999942i	$-0.503441\pi$
$151$	−12.2567	−	10.2846i	−0.997437	−	0.836949i	−0.986627	+	0.162993i	$0.947885\pi$
$152$	−0.866025	−	1.50000i	−0.0702439	−	0.121666i
$153$		0			0
$154$	−3.00000	+	5.19615i	−0.241747	+	0.418718i
$155$	−16.2760	+	5.92396i	−1.30732	+	0.475824i
$156$		0			0
$157$	−9.95858	+	8.35624i	−0.794781	+	0.666900i	−0.946924	−	0.321458i	$-0.895827\pi$
$157$	−9.95858	+	8.35624i	−0.794781	+	0.666900i	0.152143	+	0.988359i	$0.451383\pi$
$158$	1.62760	+	0.592396i	0.129485	+	0.0471285i
$159$		0			0
$160$	−3.12567	+	17.7265i	−0.247106	+	1.40141i
$161$	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	$0.512469\pi$
$164$	0.601535	−	3.41147i	0.0469720	−	0.266391i
$165$		0			0
$166$	−11.2763	−	4.10424i	−0.875212	−	0.318551i
$167$	18.5756	−	15.5868i	1.43742	−	1.20614i	0.496265	−	0.868171i	$-0.334704\pi$
$167$	18.5756	−	15.5868i	1.43742	−	1.20614i	0.941157	−	0.337970i	$-0.109740\pi$
$168$		0			0
$169$	−11.2763	+	4.10424i	−0.867409	+	0.315711i
$170$		0			0
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−10.6146	−	8.90673i	−0.807015	−	0.677166i	0.142878	−	0.989740i	$-0.454364\pi$
$173$	−10.6146	−	8.90673i	−0.807015	−	0.677166i	−0.949893	+	0.312574i	$0.898809\pi$
$174$		0			0
$175$	−1.21554	−	6.89365i	−0.0918860	−	0.521111i
$176$	3.00767	+	17.0574i	0.226712	+	1.28575i
$177$		0			0
$178$	13.7888	+	11.5702i	1.03351	+	0.867221i
$179$	10.3923	+	18.0000i	0.776757	+	1.34538i	0.933801	+	0.357792i	$0.116470\pi$
$179$	10.3923	+	18.0000i	0.776757	+	1.34538i	−0.157044	+	0.987592i	$0.550196\pi$
$180$		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	$0.948983\pi$
$182$	8.13798	−	2.96198i	0.603227	−	0.219557i
$183$		0			0
$184$	9.19253	−	7.71345i	0.677683	−	0.568643i
$185$	3.25519	+	1.18479i	0.239326	+	0.0871077i
$186$		0			0
$187$		0			0
$188$	−3.46410			−0.252646
$189$		0			0
$190$	−6.00000			−0.435286
$191$	1.20307	−	6.82295i	0.0870511	−	0.493691i	−0.909844	−	0.414950i	$-0.863799\pi$
$191$	1.20307	−	6.82295i	0.0870511	−	0.493691i	0.996895	−	0.0787408i	$-0.0250900\pi$
$192$		0			0
$193$	9.39693	+	3.42020i	0.676406	+	0.246191i	0.657303	−	0.753626i	$-0.271697\pi$
$193$	9.39693	+	3.42020i	0.676406	+	0.246191i	0.0191021	+	0.999818i	$0.493919\pi$
$194$	22.5561	−	18.9268i	1.61943	−	1.35886i
$195$		0			0
$196$	5.63816	−	2.05212i	0.402725	−	0.146580i
$197$	5.19615	−	9.00000i	0.370211	−	0.641223i	−0.619387	−	0.785086i	$-0.712619\pi$
$197$	5.19615	−	9.00000i	0.370211	−	0.641223i	0.989598	+	0.143862i	$0.0459522\pi$
$198$		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	$0.598151\pi$
$200$	−9.28780	−	7.79339i	−0.656746	−	0.551076i
$201$		0			0
$202$	−4.16756	−	23.6354i	−0.293228	−	1.66298i
$203$	0.601535	+	3.41147i	0.0422195	+	0.239439i
$204$		0			0
$205$	9.19253	+	7.71345i	0.642034	+	0.538731i
$206$	−6.92820	−	12.0000i	−0.482711	−	0.836080i
$207$		0			0
$208$	12.5000	−	21.6506i	0.866719	−	1.50120i
$209$	−3.25519	+	1.18479i	−0.225166	+	0.0819538i
$210$		0			0
$211$	3.83022	−	3.21394i	0.263683	−	0.221257i	−0.501354	−	0.865242i	$-0.667165\pi$
$211$	3.83022	−	3.21394i	0.263683	−	0.221257i	0.765038	+	0.643985i	$0.222720\pi$
$212$	9.76557	+	3.55438i	0.670702	+	0.244116i
$213$		0			0
$214$	3.12567	−	17.7265i	0.213666	−	1.21176i
$215$	−3.46410			−0.236250
$216$		0			0
$217$	−5.00000			−0.339422
$218$	5.11305	−	28.9975i	0.346299	−	1.96396i
$219$		0			0
$220$	11.2763	+	4.10424i	0.760249	+	0.276708i
$221$		0			0
$222$		0			0
$223$	17.8542	−	6.49838i	1.19560	−	0.435164i	0.333915	−	0.942603i	$-0.391630\pi$
$223$	17.8542	−	6.49838i	1.19560	−	0.435164i	0.861688	+	0.507439i	$0.169408\pi$
$224$	−2.59808	+	4.50000i	−0.173591	+	0.300669i
$225$		0			0
$226$	15.0000	+	25.9808i	0.997785	+	1.72821i
$227$	−10.6146	−	8.90673i	−0.704517	−	0.591160i	0.218538	−	0.975829i	$-0.429871\pi$
$227$	−10.6146	−	8.90673i	−0.704517	−	0.591160i	−0.923055	+	0.384668i	$0.874316\pi$
$228$		0			0
$229$	0.868241	+	4.92404i	0.0573750	+	0.325390i	0.999963	−	0.00856731i	$-0.00272709\pi$
$229$	0.868241	+	4.92404i	0.0573750	+	0.325390i	−0.942588	+	0.333957i	$0.891616\pi$
$230$	−7.21842	−	40.9377i	−0.475968	−	2.69935i
$231$		0			0
$232$	4.59627	+	3.85673i	0.301760	+	0.253206i
$233$		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
$236$	−3.25519	+	1.18479i	−0.211895	+	0.0771234i
$237$		0			0
$238$		0			0
$239$	6.51038	+	2.36959i	0.421122	+	0.153276i	0.543884	−	0.839160i	$-0.316953\pi$
$239$	6.51038	+	2.36959i	0.421122	+	0.153276i	−0.122763	+	0.992436i	$0.539175\pi$
$240$		0			0
$241$	−3.29932	+	18.7113i	−0.212528	+	1.20530i	0.672618	+	0.739990i	$0.265170\pi$
$241$	−3.29932	+	18.7113i	−0.212528	+	1.20530i	−0.885146	+	0.465314i	$0.845941\pi$
$242$	1.73205			0.111340
$243$		0			0
$244$	2.00000			0.128037
$245$	−3.60921	+	20.4688i	−0.230584	+	1.30771i
$246$		0			0
$247$	4.69846	+	1.71010i	0.298956	+	0.108811i
$248$	−6.63414	+	5.56670i	−0.421268	+	0.353486i
$249$		0			0
$250$	−11.2763	+	4.10424i	−0.713177	+	0.259575i
$251$	−10.3923	+	18.0000i	−0.655956	+	1.13615i	0.325697	+	0.945474i	$0.394401\pi$
$251$	−10.3923	+	18.0000i	−0.655956	+	1.13615i	−0.981653	+	0.190676i	$0.938932\pi$
$252$		0			0
$253$	−12.0000	−	20.7846i	−0.754434	−	1.30672i
$254$	22.5561	+	18.9268i	1.41529	+	1.18757i
$255$		0			0
$256$	3.29932	+	18.7113i	0.206207	+	1.16946i
$257$	0.601535	+	3.41147i	0.0375227	+	0.212802i	0.997804	−	0.0662307i	$-0.0210973\pi$
$257$	0.601535	+	3.41147i	0.0375227	+	0.212802i	−0.960282	+	0.279033i	$0.909986\pi$
$258$		0			0
$259$	0.766044	+	0.642788i	0.0475997	+	0.0399409i
$260$	−8.66025	−	15.0000i	−0.537086	−	0.930261i
$261$		0			0
$262$	−3.00000	+	5.19615i	−0.185341	+	0.321019i
$263$	13.0208	−	4.73917i	0.802895	−	0.292230i	0.0922092	−	0.995740i	$-0.470607\pi$
$263$	13.0208	−	4.73917i	0.802895	−	0.292230i	0.710685	+	0.703510i	$0.248385\pi$
$264$		0			0
$265$	−27.5776	+	23.1404i	−1.69408	+	1.42150i
$266$	−1.62760	−	0.592396i	−0.0997943	−	0.0363221i
$267$		0			0
$268$	1.38919	−	7.87846i	0.0848580	−	0.481254i
$269$		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
$274$	−11.2763	−	4.10424i	−0.681227	−	0.247946i
$275$	−18.5756	+	15.5868i	−1.12015	+	0.939918i
$276$		0			0
$277$	−15.9748	+	5.81434i	−0.959831	+	0.349350i	−0.773967	−	0.633226i	$-0.781731\pi$
$277$	−15.9748	+	5.81434i	−0.959831	+	0.349350i	−0.185864	+	0.982576i	$0.559508\pi$
$278$	11.2583	−	19.5000i	0.675230	−	1.16953i
$279$		0			0
$280$	−3.00000	−	5.19615i	−0.179284	−	0.310530i
$281$	−10.6146	−	8.90673i	−0.633215	−	0.531331i	0.268711	−	0.963221i	$-0.413402\pi$
$281$	−10.6146	−	8.90673i	−0.633215	−	0.531331i	−0.901926	+	0.431890i	$0.857847\pi$
$282$		0			0
$283$	−2.25743	−	12.8025i	−0.134190	−	0.761030i	−0.975420	−	0.220353i	$-0.929279\pi$
$283$	−2.25743	−	12.8025i	−0.134190	−	0.761030i	0.841230	−	0.540677i	$-0.181832\pi$
$284$	1.80460	+	10.2344i	0.107084	+	0.607301i
$285$		0			0
$286$	−22.9813	−	19.2836i	−1.35891	−	1.14026i
$287$	1.73205	+	3.00000i	0.102240	+	0.177084i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	19.5311	−	7.10876i	1.14691	−	0.417440i
$291$		0			0
$292$	1.53209	−	1.28558i	0.0896587	−	0.0752326i
$293$	−13.0208	−	4.73917i	−0.760681	−	0.276865i	−0.0675880	−	0.997713i	$-0.521530\pi$
$293$	−13.0208	−	4.73917i	−0.760681	−	0.276865i	−0.693093	+	0.720848i	$0.743753\pi$
$294$		0			0
$295$	2.08378	−	11.8177i	0.121322	−	0.688053i
$296$	1.73205			0.100673
$297$		0			0
$298$	−12.0000			−0.695141
$299$	−6.01535	+	34.1147i	−0.347877	+	1.97291i
$300$		0			0
$301$	−0.939693	−	0.342020i	−0.0541630	−	0.0197137i
$302$	−21.2292	+	17.8135i	−1.22161	+	1.02505i
$303$		0			0
$304$	−4.69846	+	1.71010i	−0.269475	+	0.0980810i
$305$	−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	$-0.360006\pi$
$308$	2.65366	+	2.22668i	0.151206	+	0.126877i
$309$		0			0
$310$	5.20945	+	29.5442i	0.295877	+	1.67800i
$311$	2.40614	+	13.6459i	0.136440	+	0.773788i	0.973846	+	0.227208i	$0.0729596\pi$
$311$	2.40614	+	13.6459i	0.136440	+	0.773788i	−0.837407	+	0.546580i	$0.815929\pi$
$312$		0			0
$313$	−0.766044	−	0.642788i	−0.0432994	−	0.0363325i	0.620881	−	0.783905i	$-0.286775\pi$
$313$	−0.766044	−	0.642788i	−0.0432994	−	0.0363325i	−0.664181	+	0.747572i	$0.731219\pi$
$314$	11.2583	+	19.5000i	0.635344	+	1.10045i
$315$		0			0
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$	−26.0415	+	9.47834i	−1.46264	+	0.532357i	−0.946091	−	0.323902i	$-0.895005\pi$
$317$	−26.0415	+	9.47834i	−1.46264	+	0.532357i	−0.516547	+	0.856259i	$0.672783\pi$
$318$		0			0
$319$	9.19253	−	7.71345i	0.514683	−	0.431870i
$320$	−3.25519	−	1.18479i	−0.181971	−	0.0662319i
$321$		0			0
$322$	2.08378	−	11.8177i	0.116124	−	0.658574i
$323$		0			0
$324$		0			0
$325$	35.0000			1.94145
$326$	−0.300767	+	1.70574i	−0.0166580	+	0.0944720i
$327$		0			0
$328$	5.63816	+	2.05212i	0.311315	+	0.113309i
$329$	2.65366	−	2.22668i	0.146301	−	0.122761i
$330$		0			0
$331$	17.8542	−	6.49838i	0.981353	−	0.357183i	0.198987	−	0.980002i	$-0.436235\pi$
$331$	17.8542	−	6.49838i	0.981353	−	0.357183i	0.782366	+	0.622819i	$0.214013\pi$
$332$	−3.46410	+	6.00000i	−0.190117	+	0.329293i
$333$		0			0
$334$	−21.0000	−	36.3731i	−1.14907	−	1.99025i
$335$	21.2292	+	17.8135i	1.15988	+	0.973253i
$336$		0			0
$337$	0.868241	+	4.92404i	0.0472961	+	0.268229i	0.999281	−	0.0379157i	$-0.0120718\pi$
$337$	0.868241	+	4.92404i	0.0472961	+	0.268229i	−0.951985	+	0.306145i	$0.900961\pi$
$338$	3.60921	+	20.4688i	0.196315	+	1.11336i
$339$		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
$344$	−1.62760	+	0.592396i	−0.0877541	+	0.0319399i
$345$		0			0
$346$	−18.3851	+	15.4269i	−0.988387	+	0.829355i
$347$	−22.7863	−	8.29355i	−1.22323	−	0.445221i	−0.351959	−	0.936015i	$-0.614484\pi$
$347$	−22.7863	−	8.29355i	−1.22323	−	0.445221i	−0.871275	+	0.490794i	$0.836707\pi$
$348$		0			0
$349$	−0.173648	+	0.984808i	−0.00929517	+	0.0527156i	−0.989103	−	0.147228i	$-0.952965\pi$
$349$	−0.173648	+	0.984808i	−0.00929517	+	0.0527156i	0.979807	+	0.199944i	$0.0640759\pi$
$350$	−12.1244			−0.648074
$351$		0			0
$352$	18.0000			0.959403
$353$	3.00767	−	17.0574i	0.160082	−	0.907872i	−0.793909	−	0.608037i	$-0.791957\pi$
$353$	3.00767	−	17.0574i	0.160082	−	0.907872i	0.953991	−	0.299835i	$-0.0969317\pi$
$354$		0			0
$355$	−33.8289	−	12.3127i	−1.79545	−	0.653492i
$356$	7.96097	−	6.68004i	0.421930	−	0.354042i
$357$		0			0
$358$	33.8289	−	12.3127i	1.78791	−	0.650748i
$359$	−15.5885	+	27.0000i	−0.822727	+	1.42501i	0.0809166	+	0.996721i	$0.474215\pi$
$359$	−15.5885	+	27.0000i	−0.822727	+	1.42501i	−0.903644	+	0.428285i	$0.859118\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	22.5561	+	18.9268i	1.18552	+	0.994770i
$363$		0			0
$364$	−0.868241	−	4.92404i	−0.0455082	−	0.258090i
$365$	1.20307	+	6.82295i	0.0629716	+	0.357129i
$366$		0			0
$367$	−12.2567	−	10.2846i	−0.639795	−	0.536852i	0.264160	−	0.964479i	$-0.414905\pi$
$367$	−12.2567	−	10.2846i	−0.639795	−	0.536852i	−0.903955	+	0.427627i	$0.859350\pi$
$368$	−17.3205	−	30.0000i	−0.902894	−	1.56386i
$369$		0			0
$370$	3.00000	−	5.19615i	0.155963	−	0.270135i
$371$	−9.76557	+	3.55438i	−0.507003	+	0.184534i
$372$		0			0
$373$	17.6190	−	14.7841i	0.912278	−	0.765492i	−0.0602727	−	0.998182i	$-0.519197\pi$
$373$	17.6190	−	14.7841i	0.912278	−	0.765492i	0.972551	+	0.232689i	$0.0747526\pi$
$374$		0			0
$375$		0			0
$376$	1.04189	−	5.90885i	0.0537313	−	0.304725i
$377$	−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	$0.662267\pi$
$380$	−0.601535	+	3.41147i	−0.0308581	+	0.175005i
$381$		0			0
$382$	−11.2763	−	4.10424i	−0.576946	−	0.209991i
$383$	−13.2683	+	11.1334i	−0.677977	+	0.568891i	−0.915415	−	0.402512i	$-0.868137\pi$
$383$	−13.2683	+	11.1334i	−0.677977	+	0.568891i	0.237437	+	0.971403i	$0.423693\pi$
$384$		0			0
$385$	−11.2763	+	4.10424i	−0.574694	+	0.209172i
$386$	8.66025	−	15.0000i	0.440795	−	0.763480i
$387$		0			0
$388$	−8.50000	−	14.7224i	−0.431522	−	0.747418i
$389$	5.30731	+	4.45336i	0.269091	+	0.225794i	0.767341	−	0.641239i	$-0.221579\pi$
$389$	5.30731	+	4.45336i	0.269091	+	0.225794i	−0.498250	+	0.867034i	$0.666024\pi$
$390$		0			0
$391$		0			0
$392$	1.80460	+	10.2344i	0.0911463	+	0.516916i
$393$		0			0
$394$	−13.7888	−	11.5702i	−0.694670	−	0.582897i
$395$	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	$0.158678\pi$
$398$	30.9243	−	11.2555i	1.55010	−	0.564189i
$399$		0			0
$400$	−26.8116	+	22.4976i	−1.34058	+	1.12488i
$401$	−3.25519	−	1.18479i	−0.162556	−	0.0591657i	0.259460	−	0.965754i	$-0.416455\pi$
$401$	−3.25519	−	1.18479i	−0.162556	−	0.0591657i	−0.422017	+	0.906588i	$0.638678\pi$
$402$		0			0
$403$	4.34120	−	24.6202i	0.216251	−	1.22642i
$404$	−13.8564			−0.689382
$405$		0			0
$406$	6.00000			0.297775
$407$	0.601535	−	3.41147i	0.0298170	−	0.169100i
$408$		0			0
$409$	−4.69846	−	1.71010i	−0.232324	−	0.0845590i	0.223235	−	0.974765i	$-0.428338\pi$
$409$	−4.69846	−	1.71010i	−0.232324	−	0.0845590i	−0.455559	+	0.890206i	$0.650561\pi$
$410$	15.9219	−	13.3601i	0.786328	−	0.659808i
$411$		0			0
$412$	−7.51754	+	2.73616i	−0.370363	+	0.134801i
$413$	1.73205	−	3.00000i	0.0852286	−	0.147620i
$414$		0			0
$415$	−12.0000	−	20.7846i	−0.589057	−	1.02028i
$416$	−19.9024	−	16.7001i	−0.975796	−	0.818790i
$417$		0			0
$418$	1.04189	+	5.90885i	0.0509605	+	0.289011i
$419$	−6.61688	−	37.5262i	−0.323256	−	1.83328i	−0.521658	−	0.853155i	$-0.674686\pi$
$419$	−6.61688	−	37.5262i	−0.323256	−	1.83328i	0.198402	−	0.980121i	$-0.436425\pi$
$420$		0			0
$421$	−14.5548	−	12.2130i	−0.709360	−	0.595223i	0.215060	−	0.976601i	$-0.431005\pi$
$421$	−14.5548	−	12.2130i	−0.709360	−	0.595223i	−0.924419	+	0.381377i	$0.875450\pi$
$422$	−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
$427$	−1.53209	+	1.28558i	−0.0741430	+	0.0622133i
$428$	−9.76557	−	3.55438i	−0.472037	−	0.171807i
$429$		0			0
$430$	−1.04189	+	5.90885i	−0.0502444	+	0.284950i
$431$	−20.7846			−1.00116			−0.500580	−	0.865690i	$-0.666880\pi$
$431$	−20.7846			−1.00116			−0.500580	+	0.865690i	$0.666880\pi$
$432$		0			0
$433$	−1.00000			−0.0480569			−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000			−0.0480569			−0.0240285	+	0.999711i	$0.507649\pi$
$434$	−1.50384	+	8.52869i	−0.0721865	+	0.409390i
$435$		0			0
$436$	−15.9748	−	5.81434i	−0.765053	−	0.278457i
$437$	5.30731	−	4.45336i	0.253883	−	0.213033i
$438$		0			0
$439$	−18.7939	+	6.84040i	−0.896982	+	0.326475i	−0.749043	−	0.662522i	$-0.769486\pi$
$439$	−18.7939	+	6.84040i	−0.896982	+	0.326475i	−0.147939	+	0.988996i	$0.547264\pi$
$440$	−10.3923	+	18.0000i	−0.495434	+	0.858116i
$441$		0			0
$442$		0			0
$443$	−10.6146	−	8.90673i	−0.504316	−	0.423171i	0.354808	−	0.934939i	$-0.384546\pi$
$443$	−10.6146	−	8.90673i	−0.504316	−	0.423171i	−0.859124	+	0.511768i	$0.828991\pi$
$444$		0			0
$445$	6.25133	+	35.4531i	0.296342	+	1.68064i
$446$	−5.71458	−	32.4090i	−0.270593	−	1.53461i
$447$		0			0
$448$	−0.766044	−	0.642788i	−0.0361922	−	0.0303689i
$449$	5.19615	+	9.00000i	0.245222	+	0.424736i	0.962194	−	0.272365i	$-0.0878059\pi$
$449$	5.19615	+	9.00000i	0.245222	+	0.424736i	−0.716972	+	0.697102i	$0.754473\pi$
$450$		0			0
$451$	6.00000	−	10.3923i	0.282529	−	0.489355i
$452$	16.2760	−	5.92396i	0.765556	−	0.278640i
$453$		0			0
$454$	−18.3851	+	15.4269i	−0.862854	+	0.724020i
$455$	16.2760	+	5.92396i	0.763028	+	0.277720i
$456$		0			0
$457$	2.95202	−	16.7417i	0.138090	−	0.783145i	−0.834569	−	0.550904i	$-0.814283\pi$
$457$	2.95202	−	16.7417i	0.138090	−	0.783145i	0.972658	−	0.232241i	$-0.0746059\pi$
$458$	8.66025			0.404667
$459$		0			0
$460$	−24.0000			−1.11901
$461$	4.81228	−	27.2918i	0.224130	−	1.27111i	−0.640211	−	0.768199i	$-0.721153\pi$
$461$	4.81228	−	27.2918i	0.224130	−	1.27111i	0.864341	−	0.502906i	$-0.167736\pi$
$462$		0			0
$463$	29.1305	+	10.6026i	1.35381	+	0.492746i	0.914134	−	0.405412i	$-0.132872\pi$
$463$	29.1305	+	10.6026i	1.35381	+	0.492746i	0.439674	+	0.898158i	$0.355094\pi$
$464$	13.2683	−	11.1334i	0.615964	−	0.516855i
$465$		0			0
$466$		0			0
$467$	5.19615	−	9.00000i	0.240449	−	0.416470i	−0.720393	−	0.693566i	$-0.756039\pi$
$467$	5.19615	−	9.00000i	0.240449	−	0.416470i	0.960842	+	0.277096i	$0.0893719\pi$
$468$		0			0
$469$	4.00000	+	6.92820i	0.184703	+	0.319915i
$470$	−15.9219	−	13.3601i	−0.734424	−	0.616255i
$471$		0			0
$472$	−1.04189	−	5.90885i	−0.0479568	−	0.271977i
$473$	0.601535	+	3.41147i	0.0276586	+	0.156860i
$474$		0			0
$475$	−5.36231	−	4.49951i	−0.246040	−	0.206452i
$476$		0			0
$477$		0			0
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	13.0208	−	4.73917i	0.594934	−	0.216538i	−0.0269642	−	0.999636i	$-0.508584\pi$
$479$	13.0208	−	4.73917i	0.594934	−	0.216538i	0.621898	+	0.783098i	$0.286362\pi$
$480$		0			0
$481$	−3.83022	+	3.21394i	−0.174643	+	0.146543i
$482$	30.9243	+	11.2555i	1.40856	+	0.512675i
$483$		0			0
$484$	0.173648	−	0.984808i	0.00789310	−	0.0447640i
$485$	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	$0.641658\pi$
$488$	−0.601535	+	3.41147i	−0.0272302	+	0.154430i
$489$		0			0
$490$	33.8289	+	12.3127i	1.52824	+	0.556232i
$491$	−29.1902	+	24.4935i	−1.31734	+	1.10538i	−0.330473	+	0.943815i	$0.607208\pi$
$491$	−29.1902	+	24.4935i	−1.31734	+	1.10538i	−0.986863	+	0.161561i	$0.948347\pi$
$492$		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
$497$	−7.96097	−	6.68004i	−0.357098	−	0.299641i
$498$		0			0
$499$	−4.86215	−	27.5746i	−0.217660	−	1.23441i	−0.876231	−	0.481891i	$-0.839950\pi$
$499$	−4.86215	−	27.5746i	−0.217660	−	1.23441i	0.658571	−	0.752518i	$-0.271161\pi$
$500$	1.20307	+	6.82295i	0.0538029	+	0.305132i
$501$		0			0
$502$	27.5776	+	23.1404i	1.23085	+	1.03280i
$503$	−20.7846	−	36.0000i	−0.926740	−	1.60516i	−0.788739	−	0.614729i	$-0.789266\pi$
$503$	−20.7846	−	36.0000i	−0.926740	−	1.60516i	−0.138001	−	0.990432i	$-0.544068\pi$
$504$		0			0
$505$	24.0000	−	41.5692i	1.06799	−	1.84981i
$506$	−39.0623	+	14.2175i	−1.73653	+	0.632045i
$507$		0			0
$508$	13.0228	−	10.9274i	0.577791	−	0.484825i
$509$	26.0415	+	9.47834i	1.15427	+	0.420120i	0.847047	−	0.531517i	$-0.178378\pi$
$509$	26.0415	+	9.47834i	1.15427	+	0.420120i	0.307223	+	0.951638i	$0.400600\pi$
$510$		0			0
$511$	−0.347296	+	1.96962i	−0.0153635	+	0.0871307i
$512$	8.66025			0.382733
$513$		0			0
$514$	6.00000			0.264649
$515$	4.81228	−	27.2918i	0.212054	−	1.20262i
$516$		0			0
$517$	−11.2763	−	4.10424i	−0.495932	−	0.180504i
$518$	1.32683	−	1.11334i	0.0582975	−	0.0489174i
$519$		0			0
$520$	28.1908	−	10.2606i	1.23625	−	0.449957i
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	−0.543410	−	0.839467i	$-0.682867\pi$
$521$	10.3923	−	18.0000i	0.455295	−	0.788594i	0.998705	+	0.0508731i	$0.0162004\pi$
$522$		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	$0.977388\pi$
$524$	2.65366	+	2.22668i	0.115925	+	0.0972730i
$525$		0			0
$526$	−4.16756	−	23.6354i	−0.181714	−	1.03055i
$527$		0			0
$528$		0			0
$529$	19.1511	+	16.0697i	0.832657	+	0.698682i
$530$	31.1769	+	54.0000i	1.35424	+	2.34561i
$531$		0			0
$532$	−0.500000	+	0.866025i	−0.0216777	+	0.0375470i
$533$	−16.2760	+	5.92396i	−0.704990	+	0.256595i
$534$		0			0
$535$	27.5776	−	23.1404i	1.19228	−	1.00044i
$536$	13.0208	+	4.73917i	0.562411	+	0.204701i
$537$		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	$0.380917\pi$
$542$	−4.81228	+	27.2918i	−0.206705	+	1.17228i
$543$		0			0
$544$		0			0
$545$	45.1121	−	37.8536i	1.93239	−	1.62147i
$546$		0			0
$547$	−18.7939	+	6.84040i	−0.803567	+	0.292475i	−0.710964	−	0.703229i	$-0.751741\pi$
$547$	−18.7939	+	6.84040i	−0.803567	+	0.292475i	−0.0926033	+	0.995703i	$0.529519\pi$
$548$	−3.46410	+	6.00000i	−0.147979	+	0.256307i
$549$		0			0
$550$	21.0000	+	36.3731i	0.895443	+	1.55095i
$551$	2.65366	+	2.22668i	0.113050	+	0.0948598i
$552$		0			0
$553$	0.173648	+	0.984808i	0.00738427	+	0.0418783i
$554$	5.11305	+	28.9975i	0.217233	+	1.23199i
$555$		0			0
$556$	−9.95858	−	8.35624i	−0.422338	−	0.354383i
$557$	−5.19615	−	9.00000i	−0.220168	−	0.381342i	0.734691	−	0.678402i	$-0.237327\pi$
$557$	−5.19615	−	9.00000i	−0.220168	−	0.381342i	−0.954859	+	0.297060i	$0.903994\pi$
$558$		0			0
$559$	2.50000	−	4.33013i	0.105739	−	0.183145i
$560$	−16.2760	+	5.92396i	−0.687785	+	0.250333i
$561$		0			0
$562$	−18.3851	+	15.4269i	−0.775527	+	0.650745i
$563$	−32.5519	−	11.8479i	−1.37190	−	0.499331i	−0.452187	−	0.891923i	$-0.649356\pi$
$563$	−32.5519	−	11.8479i	−1.37190	−	0.499331i	−0.919712	+	0.392593i	$0.871578\pi$
$564$		0			0
$565$	−10.4189	+	59.0885i	−0.438326	+	2.48587i
$566$	−22.5167			−0.946446
$567$		0			0
$568$	−18.0000			−0.755263
$569$	−4.21074	+	23.8803i	−0.176524	+	1.00112i	0.759847	+	0.650102i	$0.225274\pi$
$569$	−4.21074	+	23.8803i	−0.176524	+	1.00112i	−0.936371	+	0.351013i	$0.885837\pi$
$570$		0			0
$571$	−38.5274	−	14.0228i	−1.61232	−	0.586837i	−0.630424	−	0.776251i	$-0.717119\pi$
$571$	−38.5274	−	14.0228i	−1.61232	−	0.586837i	−0.981897	+	0.189414i	$0.939341\pi$
$572$	−13.2683	+	11.1334i	−0.554775	+	0.465511i
$573$		0			0
$574$	5.63816	−	2.05212i	0.235332	−	0.0856539i
$575$	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	$0.583058\pi$
$578$	−22.5561	−	18.9268i	−0.938209	−	0.787251i
$579$		0			0
$580$	−2.08378	−	11.8177i	−0.0865242	−	0.490703i
$581$	−1.20307	−	6.82295i	−0.0499117	−	0.283064i
$582$		0			0
$583$	27.5776	+	23.1404i	1.14215	+	0.958376i
$584$	1.73205	+	3.00000i	0.0716728	+	0.124141i
$585$		0			0
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$	−6.51038	+	2.36959i	−0.268712	+	0.0978032i	−0.472862	−	0.881136i	$-0.656779\pi$
$587$	−6.51038	+	2.36959i	−0.268712	+	0.0978032i	0.204150	+	0.978940i	$0.434557\pi$
$588$		0			0
$589$	−3.83022	+	3.21394i	−0.157822	+	0.132428i
$590$	−19.5311	−	7.10876i	−0.804084	−	0.292663i
$591$		0			0
$592$	0.868241	−	4.92404i	0.0356845	−	0.202377i
$593$	20.7846			0.853522			0.426761	−	0.904365i	$-0.359655\pi$
$593$	20.7846			0.853522			0.426761	+	0.904365i	$0.359655\pi$
$594$		0			0
$595$		0			0
$596$	−1.20307	+	6.82295i	−0.0492797	+	0.279479i
$597$		0			0
$598$	56.3816	+	20.5212i	2.30561	+	0.839175i
$599$	18.5756	−	15.5868i	0.758978	−	0.636858i	−0.178883	−	0.983870i	$-0.557248\pi$
$599$	18.5756	−	15.5868i	0.758978	−	0.636858i	0.937861	+	0.347012i	$0.112804\pi$
$600$		0			0
$601$	−32.8892	+	11.9707i	−1.34158	+	0.488295i	−0.910310	−	0.413928i	$-0.864157\pi$
$601$	−32.8892	+	11.9707i	−1.34158	+	0.488295i	−0.431270	+	0.902223i	$0.641934\pi$
$602$	−0.866025	+	1.50000i	−0.0352966	+	0.0611354i
$603$		0			0
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	2.65366	+	2.22668i	0.107886	+	0.0905275i
$606$		0			0
$607$	−2.25743	−	12.8025i	−0.0916261	−	0.519637i	−0.995729	−	0.0923229i	$-0.970571\pi$
$607$	−2.25743	−	12.8025i	−0.0916261	−	0.519637i	0.904103	−	0.427315i	$-0.140540\pi$
$608$	0.902302	+	5.11721i	0.0365932	+	0.207530i
$609$		0			0
$610$	9.19253	+	7.71345i	0.372195	+	0.312309i
$611$	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	$0.179527\pi$
$614$	−32.5519	+	11.8479i	−1.31369	+	0.478143i
$615$		0			0
$616$	−4.59627	+	3.85673i	−0.185189	+	0.155392i
$617$	6.51038	+	2.36959i	0.262098	+	0.0953959i	0.469727	−	0.882812i	$-0.344352\pi$
$617$	6.51038	+	2.36959i	0.262098	+	0.0953959i	−0.207629	+	0.978208i	$0.566575\pi$
$618$		0			0
$619$	3.47296	−	19.6962i	0.139590	−	0.791655i	−0.831963	−	0.554832i	$-0.812783\pi$
$619$	3.47296	−	19.6962i	0.139590	−	0.791655i	0.971553	−	0.236823i	$-0.0761063\pi$
$620$	17.3205			0.695608
$621$		0			0
$622$	24.0000			0.962312
$623$	−1.80460	+	10.2344i	−0.0723000	+	0.410033i
$624$		0			0
$625$	10.3366	+	3.76222i	0.413465	+	0.150489i
$626$	−1.32683	+	1.11334i	−0.0530307	+	0.0444980i
$627$		0			0
$628$	12.2160	−	4.44626i	0.487472	−	0.177425i
$629$		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	$0.943212\pi$
$632$	1.32683	+	1.11334i	0.0527784	+	0.0442863i
$633$		0			0
$634$	8.33511	+	47.2708i	0.331030	+	1.87736i
$635$	10.2261	+	57.9951i	0.405810	+	2.30146i
$636$		0			0
$637$	−22.9813	−	19.2836i	−0.910554	−	0.764045i
$638$	−10.3923	−	18.0000i	−0.411435	−	0.712627i
$639$		0			0
$640$	−21.0000	+	36.3731i	−0.830098	+	1.43777i
$641$	42.3175	−	15.4023i	1.67144	−	0.608354i	0.679342	−	0.733822i	$-0.262265\pi$
$641$	42.3175	−	15.4023i	1.67144	−	0.608354i	0.992098	+	0.125467i	$0.0400430\pi$
$642$		0			0
$643$	33.7060	−	28.2827i	1.32923	−	1.11536i	0.344977	−	0.938611i	$-0.387887\pi$
$643$	33.7060	−	28.2827i	1.32923	−	1.11536i	0.984256	−	0.176748i	$-0.0565577\pi$
$644$	−6.51038	−	2.36959i	−0.256545	−	0.0933747i
$645$		0			0
$646$		0			0
$647$	−20.7846			−0.817127			−0.408564	−	0.912730i	$-0.633970\pi$
$647$	−20.7846			−0.817127			−0.408564	+	0.912730i	$0.633970\pi$
$648$		0			0
$649$	−12.0000			−0.471041
$650$	10.5269	−	59.7008i	0.412897	−	2.34166i
$651$		0			0
$652$	0.939693	+	0.342020i	0.0368012	+	0.0133945i
$653$	−13.2683	+	11.1334i	−0.519228	+	0.435684i	−0.864362	−	0.502869i	$-0.832278\pi$
$653$	−13.2683	+	11.1334i	−0.519228	+	0.435684i	0.345135	+	0.938553i	$0.387833\pi$
$654$		0			0
$655$	−11.2763	+	4.10424i	−0.440602	+	0.160366i
$656$	8.66025	−	15.0000i	0.338126	−	0.585652i
$657$		0			0
$658$	−3.00000	−	5.19615i	−0.116952	−	0.202567i
$659$	21.2292	+	17.8135i	0.826974	+	0.693914i	0.954594	−	0.297910i	$-0.0962894\pi$
$659$	21.2292	+	17.8135i	0.826974	+	0.693914i	−0.127620	+	0.991823i	$0.540734\pi$
$660$		0			0
$661$	−1.73648	−	9.84808i	−0.0675413	−	0.383046i	−0.999775	−	0.0211902i	$-0.993254\pi$
$661$	−1.73648	−	9.84808i	−0.0675413	−	0.383046i	0.932234	−	0.361856i	$-0.117857\pi$
$662$	−5.71458	−	32.4090i	−0.222104	−	1.25961i
$663$		0			0
$664$	−9.19253	−	7.71345i	−0.356739	−	0.299340i
$665$	−1.73205	−	3.00000i	−0.0671660	−	0.116335i
$666$		0			0
$667$	−12.0000	+	20.7846i	−0.464642	+	0.804783i
$668$	−22.7863	+	8.29355i	−0.881630	+	0.320887i
$669$		0			0
$670$	36.7701	−	30.8538i	1.42055	−	1.19199i
$671$	6.51038	+	2.36959i	0.251330	+	0.0914768i
$672$		0			0
$673$	−6.42498	+	36.4379i	−0.247665	+	1.40458i	0.566557	+	0.824023i	$0.308275\pi$
$673$	−6.42498	+	36.4379i	−0.247665	+	1.40458i	−0.814221	+	0.580554i	$0.802836\pi$
$674$	8.66025			0.333581
$675$		0			0
$676$	12.0000			0.461538
$677$	3.00767	−	17.0574i	0.115594	−	0.655568i	−0.870860	−	0.491531i	$-0.836437\pi$
$677$	3.00767	−	17.0574i	0.115594	−	0.655568i	0.986454	−	0.164037i	$-0.0524516\pi$
$678$		0			0
$679$	15.9748	+	5.81434i	0.613056	+	0.223134i
$680$		0			0
$681$		0			0
$682$	28.1908	−	10.2606i	1.07948	−	0.392899i
$683$	−20.7846	+	36.0000i	−0.795301	+	1.37750i	0.127347	+	0.991858i	$0.459354\pi$
$683$	−20.7846	+	36.0000i	−0.795301	+	1.37750i	−0.922648	+	0.385643i	$0.873979\pi$
$684$		0			0
$685$	−12.0000	−	20.7846i	−0.458496	−	0.794139i
$686$	17.2488	+	14.4734i	0.658561	+	0.552598i
$687$		0			0
$688$	0.868241	+	4.92404i	0.0331014	+	0.187727i
$689$	−9.02302	−	51.1721i	−0.343750	−	1.94950i
$690$		0			0
$691$	13.0228	+	10.9274i	0.495409	+	0.415697i	0.855960	−	0.517042i	$-0.172967\pi$
$691$	13.0228	+	10.9274i	0.495409	+	0.415697i	−0.360551	+	0.932739i	$0.617411\pi$
$692$	6.92820	+	12.0000i	0.263371	+	0.456172i
$693$		0			0
$694$	−21.0000	+	36.3731i	−0.797149	+	1.38070i
$695$	42.3175	−	15.4023i	1.60519	−	0.584243i
$696$		0			0
$697$		0			0
$698$	1.62760	+	0.592396i	0.0616054	+	0.0224225i
$699$		0			0
$700$	−1.21554	+	6.89365i	−0.0459430	+	0.260556i
$701$	−41.5692			−1.57005			−0.785024	−	0.619466i	$-0.787349\pi$
$701$	−41.5692			−1.57005			−0.785024	+	0.619466i	$0.787349\pi$
$702$		0			0
$703$	1.00000			0.0377157
$704$	−0.601535	+	3.41147i	−0.0226712	+	0.128575i
$705$		0			0
$706$	−28.1908	−	10.2606i	−1.06097	−	0.386163i
$707$	10.6146	−	8.90673i	0.399204	−	0.334972i
$708$		0			0
$709$	17.8542	−	6.49838i	0.670527	−	0.244052i	0.0157523	−	0.999876i	$-0.494986\pi$
$709$	17.8542	−	6.49838i	0.670527	−	0.244052i	0.654775	+	0.755824i	$0.272763\pi$
$710$	−31.1769	+	54.0000i	−1.17005	+	2.02658i
$711$		0			0
$712$	9.00000	+	15.5885i	0.337289	+	0.584202i
$713$	−26.5366	−	22.2668i	−0.993802	−	0.833899i
$714$		0			0
$715$	−10.4189	−	59.0885i	−0.389644	−	2.20978i
$716$	−3.60921	−	20.4688i	−0.134882	−	0.764957i
$717$		0			0
$718$	41.3664	+	34.7105i	1.54378	+	1.29539i
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	0.752717	−	0.658344i	$-0.228743\pi$
$719$	−5.19615	−	9.00000i	−0.193784	−	0.335643i	−0.946501	+	0.322700i	$0.895409\pi$
$720$		0			0
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$	29.2967	−	10.6631i	1.09031	−	0.396841i
$723$		0			0
$724$	13.0228	−	10.9274i	0.483987	−	0.406113i
$725$	22.7863	+	8.29355i	0.846263	+	0.308015i
$726$		0			0
$727$	−2.77837	+	15.7569i	−0.103044	+	0.584392i	0.888939	+	0.458025i	$0.151443\pi$
$727$	−2.77837	+	15.7569i	−0.103044	+	0.584392i	−0.991984	+	0.126367i	$0.959668\pi$
$728$	8.66025			0.320970
$729$		0			0
$730$	12.0000			0.444140
$731$		0			0
$732$		0			0
$733$	−38.5274	−	14.0228i	−1.42304	−	0.517945i	−0.488113	−	0.872780i	$-0.662315\pi$
$733$	−38.5274	−	14.0228i	−1.42304	−	0.517945i	−0.934929	+	0.354835i	$0.884537\pi$
$734$	−21.2292	+	17.8135i	−0.783586	+	0.657507i
$735$		0			0
$736$	−33.8289	+	12.3127i	−1.24695	+	0.453853i
$737$	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	$0.719697\pi$
$740$	−2.65366	−	2.22668i	−0.0975503	−	0.0818544i
$741$		0			0
$742$	3.12567	+	17.7265i	0.114747	+	0.650762i
$743$	−1.20307	−	6.82295i	−0.0441364	−	0.250310i	0.954755	−	0.297395i	$-0.0961178\pi$
$743$	−1.20307	−	6.82295i	−0.0441364	−	0.250310i	−0.998891	+	0.0470853i	$0.985007\pi$
$744$		0			0
$745$	−18.3851	−	15.4269i	−0.673577	−	0.565198i
$746$	−19.9186	−	34.5000i	−0.729271	−	1.26313i
$747$		0			0
$748$		0			0
$749$	9.76557	−	3.55438i	0.356826	−	0.129874i
$750$		0			0
$751$	3.83022	−	3.21394i	0.139767	−	0.117278i	−0.570224	−	0.821489i	$-0.693144\pi$
$751$	3.83022	−	3.21394i	0.139767	−	0.117278i	0.709991	+	0.704211i	$0.248699\pi$
$752$	−16.2760	−	5.92396i	−0.593523	−	0.216025i
$753$		0			0
$754$	−5.20945	+	29.5442i	−0.189717	+	1.07594i
$755$	−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	$0.257361\pi$
$758$	−5.71458	+	32.4090i	−0.207563	+	1.17715i
$759$		0			0
$760$	−5.63816	−	2.05212i	−0.204517	−	0.0744382i
$761$	−21.2292	+	17.8135i	−0.769560	+	0.645737i	−0.940596	−	0.339528i	$-0.889733\pi$
$761$	−21.2292	+	17.8135i	−0.769560	+	0.645737i	0.171037	+	0.985265i	$0.445288\pi$
$762$		0			0
$763$	15.9748	−	5.81434i	0.578326	−	0.210493i
$764$	−3.46410	+	6.00000i	−0.125327	+	0.217072i
$765$		0			0
$766$	15.0000	+	25.9808i	0.541972	+	0.938723i
$767$	13.2683	+	11.1334i	0.479090	+	0.402004i
$768$		0			0
$769$	−2.25743	−	12.8025i	−0.0814049	−	0.461670i	−0.998075	−	0.0620244i	$-0.980244\pi$
$769$	−2.25743	−	12.8025i	−0.0814049	−	0.461670i	0.916670	−	0.399646i	$-0.130867\pi$
$770$	3.60921	+	20.4688i	0.130067	+	0.737646i
$771$		0			0
$772$	−7.66044	−	6.42788i	−0.275705	−	0.231344i
$773$	−10.3923	−	18.0000i	−0.373785	−	0.647415i	0.616359	−	0.787465i	$-0.288607\pi$
$773$	−10.3923	−	18.0000i	−0.373785	−	0.647415i	−0.990144	+	0.140050i	$0.955274\pi$
$774$		0			0
$775$	−17.5000	+	30.3109i	−0.628619	+	1.08880i
$776$	27.6691	−	10.0707i	0.993264	−	0.361518i
$777$		0			0
$778$	9.19253	−	7.71345i	0.329568	−	0.276541i
$779$	3.25519	+	1.18479i	0.116629	+	0.0424496i
$780$		0			0
$781$	−6.25133	+	35.4531i	−0.223690	+	1.26861i
$782$		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)

\(f(q)\)	\(=\)	\(q+(0.300767 - 1.70574i) q^{2} +(-0.939693 - 0.342020i) q^{4} +(2.65366 - 2.22668i) q^{5} +(0.939693 - 0.342020i) q^{7} +(0.866025 - 1.50000i) q^{8} +(-3.00000 - 5.19615i) q^{10} +(-2.65366 - 2.22668i) q^{11} +(0.868241 + 4.92404i) q^{13} +(-0.300767 - 1.70574i) q^{14} +(-3.83022 - 3.21394i) q^{16} +(0.500000 - 0.866025i) q^{19} +(-3.25519 + 1.18479i) q^{20} +(-4.59627 + 3.85673i) q^{22} +(6.51038 + 2.36959i) q^{23} +(1.21554 - 6.89365i) q^{25} +8.66025 q^{26} -1.00000 q^{28} +(-0.601535 + 3.41147i) q^{29} +(-4.69846 - 1.71010i) q^{31} +(-3.98048 + 3.34002i) q^{32} +(1.73205 - 3.00000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.32683 - 1.11334i) q^{38} +(-1.04189 - 5.90885i) q^{40} +(0.601535 + 3.41147i) q^{41} +(-0.766044 - 0.642788i) q^{43} +(1.73205 + 3.00000i) q^{44} +(6.00000 - 10.3923i) q^{46} +(3.25519 - 1.18479i) q^{47} +(-4.59627 + 3.85673i) q^{49} +(-11.3932 - 4.14677i) q^{50} +(0.868241 - 4.92404i) q^{52} -10.3923 q^{53} -12.0000 q^{55} +(0.300767 - 1.70574i) q^{56} +(5.63816 + 2.05212i) q^{58} +(2.65366 - 2.22668i) q^{59} +(-1.87939 + 0.684040i) q^{61} +(-4.33013 + 7.50000i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(13.2683 + 11.1334i) q^{65} +(1.38919 + 7.87846i) q^{67} +(-4.59627 - 3.85673i) q^{70} +(-5.19615 - 9.00000i) q^{71} +(-1.00000 + 1.73205i) q^{73} +(1.62760 - 0.592396i) q^{74} +(-0.766044 + 0.642788i) q^{76} +(-3.25519 - 1.18479i) q^{77} +(-0.173648 + 0.984808i) q^{79} -17.3205 q^{80} +6.00000 q^{82} +(1.20307 - 6.82295i) q^{83} +(-1.32683 + 1.11334i) q^{86} +(-5.63816 + 2.05212i) q^{88} +(-5.19615 + 9.00000i) q^{89} +(2.50000 + 4.33013i) q^{91} +(-5.30731 - 4.45336i) q^{92} +(-1.04189 - 5.90885i) q^{94} +(-0.601535 - 3.41147i) q^{95} +(13.0228 + 10.9274i) q^{97} +(5.19615 + 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) \) 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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