LMFDB - Embedded newform 729.2.e.n.82.2

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			82.2
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	729.82
Dual form			729.2.e.n.649.2

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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	0.884896	+	0.465788i	$0.154229\pi$
$2$	0.300767	+	1.70574i	0.212675	+	1.20614i	−0.672222	+	0.740350i	$0.734660\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	2.65366	+	2.22668i	1.18675	+	0.995802i	0.999910	+	0.0134121i	$0.00426933\pi$
$5$	2.65366	+	2.22668i	1.18675	+	0.995802i	0.186841	+	0.982390i	$0.440175\pi$
$6$		0			0
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i	0.513442	−	0.858124i	$-0.328370\pi$
$7$	0.939693	+	0.342020i	0.355170	+	0.129271i	−0.158272	+	0.987396i	$0.550592\pi$
$8$	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	−0.948225	−	0.317600i	$-0.897123\pi$
$11$	−2.65366	+	2.22668i	−0.800107	+	0.671370i	0.148117	+	0.988970i	$0.452679\pi$
$12$		0			0
$13$	0.868241	−	4.92404i	0.240807	−	1.36568i	−0.589226	−	0.807968i	$-0.700567\pi$
$13$	0.868241	−	4.92404i	0.240807	−	1.36568i	0.830033	−	0.557714i	$-0.188322\pi$
$14$	−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	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−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	0.442225	−	0.896904i	$-0.354189\pi$
$23$	6.51038	−	2.36959i	1.35751	−	0.494093i	0.915283	+	0.402811i	$0.131967\pi$
$24$		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	−0.988330	−	0.152326i	$-0.951324\pi$
$29$	−0.601535	−	3.41147i	−0.111702	−	0.633495i	0.876628	−	0.481169i	$-0.159788\pi$
$30$		0			0
$31$	−4.69846	+	1.71010i	−0.843869	+	0.307143i	−0.727538	−	0.686067i	$-0.759336\pi$
$31$	−4.69846	+	1.71010i	−0.843869	+	0.307143i	−0.116331	+	0.993211i	$0.537113\pi$
$32$	−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	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−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	−0.901122	−	0.433566i	$-0.857255\pi$
$41$	0.601535	−	3.41147i	0.0939440	−	0.532783i	0.995066	−	0.0992168i	$-0.0316337\pi$
$42$		0			0
$43$	−0.766044	+	0.642788i	−0.116821	+	0.0980242i	−0.699327	−	0.714802i	$-0.746517\pi$
$43$	−0.766044	+	0.642788i	−0.116821	+	0.0980242i	0.582506	+	0.812826i	$0.302072\pi$
$44$	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	0.568334	−	0.822798i	$-0.307588\pi$
$47$	3.25519	+	1.18479i	0.474818	+	0.172820i	−0.0935154	+	0.995618i	$0.529810\pi$
$48$		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	0.798971	−	0.601370i	$-0.205378\pi$
$59$	2.65366	+	2.22668i	0.345477	+	0.289889i	−0.453494	+	0.891259i	$0.649823\pi$
$60$		0			0
$61$	−1.87939	−	0.684040i	−0.240631	−	0.0875824i	0.218890	−	0.975750i	$-0.429756\pi$
$61$	−1.87939	−	0.684040i	−0.240631	−	0.0875824i	−0.459520	+	0.888167i	$0.651979\pi$
$62$	−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	−0.774352	−	0.632756i	$-0.781924\pi$
$67$	1.38919	−	7.87846i	0.169716	−	0.962507i	0.944068	−	0.329752i	$-0.106965\pi$
$68$		0			0
$69$		0			0
$70$	−4.59627	+	3.85673i	−0.549359	+	0.460967i
$71$	−5.19615	+	9.00000i	−0.616670	+	1.06810i	0.373419	+	0.927663i	$0.378185\pi$
$71$	−5.19615	+	9.00000i	−0.616670	+	1.06810i	−0.990089	+	0.140441i	$0.955148\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	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	0.973480	−	0.228773i	$-0.0734713\pi$
$79$	−0.173648	−	0.984808i	−0.0195369	−	0.110800i	−0.993017	+	0.117973i	$0.962360\pi$
$80$	−17.3205			−1.93649
$81$		0			0
$82$	6.00000			0.662589
$83$	1.20307	+	6.82295i	0.132054	+	0.748916i	0.976866	+	0.213852i	$0.0686012\pi$
$83$	1.20307	+	6.82295i	0.132054	+	0.748916i	−0.844812	+	0.535063i	$0.820288\pi$
$84$		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	−0.998218	−	0.0596775i	$-0.980993\pi$
$89$	−5.19615	−	9.00000i	−0.550791	−	0.953998i	0.447427	−	0.894321i	$-0.352341\pi$
$90$		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	0.336440	−	0.941705i	$-0.390777\pi$
$97$	13.0228	−	10.9274i	1.32226	−	1.10951i	0.985820	−	0.167803i	$-0.0536674\pi$
$98$	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	0.895566	−	0.444929i	$-0.146771\pi$
$101$	13.0208	+	4.73917i	1.29561	+	0.471565i	0.400048	+	0.916494i	$0.368993\pi$
$102$		0			0
$103$	6.12836	+	5.14230i	0.603845	+	0.506686i	0.892679	−	0.450693i	$-0.148823\pi$
$103$	6.12836	+	5.14230i	0.603845	+	0.506686i	−0.288834	+	0.957379i	$0.593268\pi$
$104$	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	−0.996839	−	0.0794428i	$-0.974686\pi$
$113$	−13.2683	−	11.1334i	−1.24817	−	1.04734i	−0.251335	−	0.967900i	$-0.580870\pi$
$114$		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	−0.945745	−	0.324910i	$-0.894666\pi$
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	0.191492	−	0.981494i	$-0.438667\pi$
$128$	−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	−0.480285	−	0.877113i	$-0.659467\pi$
$131$	−3.25519	+	1.18479i	−0.284407	+	0.103516i	0.195878	+	0.980628i	$0.437244\pi$
$132$		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	0.992082	+	0.125593i	$0.0400833\pi$
$137$	1.20307	+	6.82295i	0.102785	+	0.582924i	−0.889297	+	0.457331i	$0.848806\pi$
$138$		0			0
$139$	12.2160	−	4.44626i	1.03615	−	0.377127i	0.232729	−	0.972542i	$-0.425234\pi$
$139$	12.2160	−	4.44626i	1.03615	−	0.377127i	0.803419	+	0.595415i	$0.203012\pi$
$140$	−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	0.895039	+	0.445988i	$0.147148\pi$
$149$	−1.20307	+	6.82295i	−0.0985593	+	0.558958i	−0.993598	+	0.112970i	$0.963964\pi$
$150$		0			0
$151$	−12.2567	+	10.2846i	−0.997437	+	0.836949i	−0.986627	−	0.162993i	$-0.947885\pi$
$151$	−12.2567	+	10.2846i	−0.997437	+	0.836949i	−0.0108097	+	0.999942i	$0.503441\pi$
$152$	−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	0.152143	−	0.988359i	$-0.451383\pi$
$157$	−9.95858	−	8.35624i	−0.794781	−	0.666900i	−0.946924	+	0.321458i	$0.895827\pi$
$158$	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	0.941157	+	0.337970i	$0.109740\pi$
$167$	18.5756	+	15.5868i	1.43742	+	1.20614i	0.496265	+	0.868171i	$0.334704\pi$
$168$		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	−0.949893	−	0.312574i	$-0.898809\pi$
$173$	−10.6146	+	8.90673i	−0.807015	+	0.677166i	0.142878	+	0.989740i	$0.454364\pi$
$174$		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	−0.157044	−	0.987592i	$-0.550196\pi$
$179$	10.3923	−	18.0000i	0.776757	−	1.34538i	0.933801	−	0.357792i	$-0.116470\pi$
$180$		0			0
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	−0.987184	−	0.159589i	$-0.948983\pi$
$181$	−8.50000	−	14.7224i	−0.631800	−	1.09431i	0.355383	−	0.934721i	$-0.384350\pi$
$182$	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	0.996895	+	0.0787408i	$0.0250900\pi$
$191$	1.20307	+	6.82295i	0.0870511	+	0.493691i	−0.909844	+	0.414950i	$0.863799\pi$
$192$		0			0
$193$	9.39693	−	3.42020i	0.676406	−	0.246191i	0.0191021	−	0.999818i	$-0.493919\pi$
$193$	9.39693	−	3.42020i	0.676406	−	0.246191i	0.657303	+	0.753626i	$0.271697\pi$
$194$	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	0.989598	−	0.143862i	$-0.0459522\pi$
$197$	5.19615	+	9.00000i	0.370211	+	0.641223i	−0.619387	+	0.785086i	$0.712619\pi$
$198$		0			0
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	−0.303486	−	0.952836i	$-0.598151\pi$
$199$	9.50000	−	16.4545i	0.673437	−	1.16643i	0.976923	−	0.213591i	$-0.0685161\pi$
$200$	−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	0.765038	−	0.643985i	$-0.222720\pi$
$211$	3.83022	+	3.21394i	0.263683	+	0.221257i	−0.501354	+	0.865242i	$0.667165\pi$
$212$	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	0.861688	−	0.507439i	$-0.169408\pi$
$223$	17.8542	+	6.49838i	1.19560	+	0.435164i	0.333915	+	0.942603i	$0.391630\pi$
$224$	−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	−0.923055	−	0.384668i	$-0.874316\pi$
$227$	−10.6146	+	8.90673i	−0.704517	+	0.591160i	0.218538	+	0.975829i	$0.429871\pi$
$228$		0			0
$229$	0.868241	−	4.92404i	0.0573750	−	0.325390i	−0.942588	−	0.333957i	$-0.891616\pi$
$229$	0.868241	−	4.92404i	0.0573750	−	0.325390i	0.999963	+	0.00856731i	$0.00272709\pi$
$230$	−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	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$		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	−0.122763	−	0.992436i	$-0.539175\pi$
$239$	6.51038	−	2.36959i	0.421122	−	0.153276i	0.543884	+	0.839160i	$0.316953\pi$
$240$		0			0
$241$	−3.29932	−	18.7113i	−0.212528	−	1.20530i	−0.885146	−	0.465314i	$-0.845941\pi$
$241$	−3.29932	−	18.7113i	−0.212528	−	1.20530i	0.672618	−	0.739990i	$-0.265170\pi$
$242$	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	−0.981653	−	0.190676i	$-0.938932\pi$
$251$	−10.3923	−	18.0000i	−0.655956	−	1.13615i	0.325697	−	0.945474i	$-0.394401\pi$
$252$		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	−0.960282	−	0.279033i	$-0.909986\pi$
$257$	0.601535	−	3.41147i	0.0375227	−	0.212802i	0.997804	+	0.0662307i	$0.0210973\pi$
$258$		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	0.710685	−	0.703510i	$-0.248385\pi$
$263$	13.0208	+	4.73917i	0.802895	+	0.292230i	0.0922092	+	0.995740i	$0.470607\pi$
$264$		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	−0.185864	−	0.982576i	$-0.559508\pi$
$277$	−15.9748	−	5.81434i	−0.959831	−	0.349350i	−0.773967	+	0.633226i	$0.781731\pi$
$278$	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	−0.901926	−	0.431890i	$-0.857847\pi$
$281$	−10.6146	+	8.90673i	−0.633215	+	0.531331i	0.268711	+	0.963221i	$0.413402\pi$
$282$		0			0
$283$	−2.25743	+	12.8025i	−0.134190	+	0.761030i	0.841230	+	0.540677i	$0.181832\pi$
$283$	−2.25743	+	12.8025i	−0.134190	+	0.761030i	−0.975420	+	0.220353i	$0.929279\pi$
$284$	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	−0.693093	−	0.720848i	$-0.743753\pi$
$293$	−13.0208	+	4.73917i	−0.760681	+	0.276865i	−0.0675880	+	0.997713i	$0.521530\pi$
$294$		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	0.425761	+	0.904836i	$0.360006\pi$
$307$	−10.0000	+	17.3205i	−0.570730	+	0.988534i	−0.996491	+	0.0836980i	$0.973327\pi$
$308$	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	−0.837407	−	0.546580i	$-0.815929\pi$
$311$	2.40614	−	13.6459i	0.136440	−	0.773788i	0.973846	−	0.227208i	$-0.0729596\pi$
$312$		0			0
$313$	−0.766044	+	0.642788i	−0.0432994	+	0.0363325i	−0.664181	−	0.747572i	$-0.731219\pi$
$313$	−0.766044	+	0.642788i	−0.0432994	+	0.0363325i	0.620881	+	0.783905i	$0.286775\pi$
$314$	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	−0.516547	−	0.856259i	$-0.672783\pi$
$317$	−26.0415	−	9.47834i	−1.46264	−	0.532357i	−0.946091	+	0.323902i	$0.895005\pi$
$318$		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	0.782366	−	0.622819i	$-0.214013\pi$
$331$	17.8542	+	6.49838i	0.981353	+	0.357183i	0.198987	+	0.980002i	$0.436235\pi$
$332$	−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	−0.951985	−	0.306145i	$-0.900961\pi$
$337$	0.868241	−	4.92404i	0.0472961	−	0.268229i	0.999281	+	0.0379157i	$0.0120718\pi$
$338$	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	−0.871275	−	0.490794i	$-0.836707\pi$
$347$	−22.7863	+	8.29355i	−1.22323	+	0.445221i	−0.351959	+	0.936015i	$0.614484\pi$
$348$		0			0
$349$	−0.173648	−	0.984808i	−0.00929517	−	0.0527156i	0.979807	−	0.199944i	$-0.0640759\pi$
$349$	−0.173648	−	0.984808i	−0.00929517	−	0.0527156i	−0.989103	+	0.147228i	$0.952965\pi$
$350$	−12.1244			−0.648074
$351$		0			0
$352$	18.0000			0.959403
$353$	3.00767	+	17.0574i	0.160082	+	0.907872i	0.953991	+	0.299835i	$0.0969317\pi$
$353$	3.00767	+	17.0574i	0.160082	+	0.907872i	−0.793909	+	0.608037i	$0.791957\pi$
$354$		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	−0.903644	−	0.428285i	$-0.859118\pi$
$359$	−15.5885	−	27.0000i	−0.822727	−	1.42501i	0.0809166	−	0.996721i	$-0.474215\pi$
$360$		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	−0.903955	−	0.427627i	$-0.859350\pi$
$367$	−12.2567	+	10.2846i	−0.639795	+	0.536852i	0.264160	+	0.964479i	$0.414905\pi$
$368$	−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	0.972551	−	0.232689i	$-0.0747526\pi$
$373$	17.6190	+	14.7841i	0.912278	+	0.765492i	−0.0602727	+	0.998182i	$0.519197\pi$
$374$		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	0.237437	−	0.971403i	$-0.423693\pi$
$383$	−13.2683	−	11.1334i	−0.677977	−	0.568891i	−0.915415	+	0.402512i	$0.868137\pi$
$384$		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	−0.498250	−	0.867034i	$-0.666024\pi$
$389$	5.30731	−	4.45336i	0.269091	−	0.225794i	0.767341	+	0.641239i	$0.221579\pi$
$390$		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	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	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	−0.422017	−	0.906588i	$-0.638678\pi$
$401$	−3.25519	+	1.18479i	−0.162556	+	0.0591657i	0.259460	+	0.965754i	$0.416455\pi$
$402$		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	−0.455559	−	0.890206i	$-0.650561\pi$
$409$	−4.69846	+	1.71010i	−0.232324	+	0.0845590i	0.223235	+	0.974765i	$0.428338\pi$
$410$	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	0.198402	+	0.980121i	$0.436425\pi$
$419$	−6.61688	+	37.5262i	−0.323256	+	1.83328i	−0.521658	+	0.853155i	$0.674686\pi$
$420$		0			0
$421$	−14.5548	+	12.2130i	−0.709360	+	0.595223i	−0.924419	−	0.381377i	$-0.875450\pi$
$421$	−14.5548	+	12.2130i	−0.709360	+	0.595223i	0.215060	+	0.976601i	$0.431005\pi$
$422$	−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	−0.147939	−	0.988996i	$-0.547264\pi$
$439$	−18.7939	−	6.84040i	−0.896982	−	0.326475i	−0.749043	+	0.662522i	$0.769486\pi$
$440$	−10.3923	−	18.0000i	−0.495434	−	0.858116i
$441$		0			0
$442$		0			0
$443$	−10.6146	+	8.90673i	−0.504316	+	0.423171i	−0.859124	−	0.511768i	$-0.828991\pi$
$443$	−10.6146	+	8.90673i	−0.504316	+	0.423171i	0.354808	+	0.934939i	$0.384546\pi$
$444$		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	−0.716972	−	0.697102i	$-0.754473\pi$
$449$	5.19615	−	9.00000i	0.245222	−	0.424736i	0.962194	+	0.272365i	$0.0878059\pi$
$450$		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	0.972658	+	0.232241i	$0.0746059\pi$
$457$	2.95202	+	16.7417i	0.138090	+	0.783145i	−0.834569	+	0.550904i	$0.814283\pi$
$458$	8.66025			0.404667
$459$		0			0
$460$	−24.0000			−1.11901
$461$	4.81228	+	27.2918i	0.224130	+	1.27111i	0.864341	+	0.502906i	$0.167736\pi$
$461$	4.81228	+	27.2918i	0.224130	+	1.27111i	−0.640211	+	0.768199i	$0.721153\pi$
$462$		0			0
$463$	29.1305	−	10.6026i	1.35381	−	0.492746i	0.439674	−	0.898158i	$-0.355094\pi$
$463$	29.1305	−	10.6026i	1.35381	−	0.492746i	0.914134	+	0.405412i	$0.132872\pi$
$464$	13.2683	+	11.1334i	0.615964	+	0.516855i
$465$		0			0
$466$		0			0
$467$	5.19615	+	9.00000i	0.240449	+	0.416470i	0.960842	−	0.277096i	$-0.0893719\pi$
$467$	5.19615	+	9.00000i	0.240449	+	0.416470i	−0.720393	+	0.693566i	$0.756039\pi$
$468$		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	0.621898	−	0.783098i	$-0.286362\pi$
$479$	13.0208	+	4.73917i	0.594934	+	0.216538i	−0.0269642	+	0.999636i	$0.508584\pi$
$480$		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	−0.986863	−	0.161561i	$-0.948347\pi$
$491$	−29.1902	−	24.4935i	−1.31734	−	1.10538i	−0.330473	−	0.943815i	$-0.607208\pi$
$492$		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	0.658571	+	0.752518i	$0.271161\pi$
$499$	−4.86215	+	27.5746i	−0.217660	+	1.23441i	−0.876231	+	0.481891i	$0.839950\pi$
$500$	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	−0.138001	+	0.990432i	$0.544068\pi$
$503$	−20.7846	+	36.0000i	−0.926740	+	1.60516i	−0.788739	+	0.614729i	$0.789266\pi$
$504$		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	0.307223	−	0.951638i	$-0.400600\pi$
$509$	26.0415	−	9.47834i	1.15427	−	0.420120i	0.847047	+	0.531517i	$0.178378\pi$
$510$		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	0.998705	−	0.0508731i	$-0.0162004\pi$
$521$	10.3923	+	18.0000i	0.455295	+	0.788594i	−0.543410	+	0.839467i	$0.682867\pi$
$522$		0			0
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	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	−0.0926033	−	0.995703i	$-0.529519\pi$
$547$	−18.7939	−	6.84040i	−0.803567	−	0.292475i	−0.710964	+	0.703229i	$0.751741\pi$
$548$	−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	−0.954859	−	0.297060i	$-0.903994\pi$
$557$	−5.19615	+	9.00000i	−0.220168	+	0.381342i	0.734691	+	0.678402i	$0.237327\pi$
$558$		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	−0.919712	−	0.392593i	$-0.871578\pi$
$563$	−32.5519	+	11.8479i	−1.37190	+	0.499331i	−0.452187	+	0.891923i	$0.649356\pi$
$564$		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	−0.936371	−	0.351013i	$-0.885837\pi$
$569$	−4.21074	−	23.8803i	−0.176524	−	1.00112i	0.759847	−	0.650102i	$-0.225274\pi$
$570$		0			0
$571$	−38.5274	+	14.0228i	−1.61232	+	0.586837i	−0.981897	−	0.189414i	$-0.939341\pi$
$571$	−38.5274	+	14.0228i	−1.61232	+	0.586837i	−0.630424	+	0.776251i	$0.717119\pi$
$572$	−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	−0.257982	−	0.966150i	$-0.583058\pi$
$577$	17.0000	−	29.4449i	0.707719	−	1.22581i	0.965701	−	0.259656i	$-0.0836092\pi$
$578$	−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	0.204150	−	0.978940i	$-0.434557\pi$
$587$	−6.51038	−	2.36959i	−0.268712	−	0.0978032i	−0.472862	+	0.881136i	$0.656779\pi$
$588$		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	0.937861	−	0.347012i	$-0.112804\pi$
$599$	18.5756	+	15.5868i	0.758978	+	0.636858i	−0.178883	+	0.983870i	$0.557248\pi$
$600$		0			0
$601$	−32.8892	−	11.9707i	−1.34158	−	0.488295i	−0.431270	−	0.902223i	$-0.641934\pi$
$601$	−32.8892	−	11.9707i	−1.34158	−	0.488295i	−0.910310	+	0.413928i	$0.864157\pi$
$602$	−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	0.904103	+	0.427315i	$0.140540\pi$
$607$	−2.25743	+	12.8025i	−0.0916261	+	0.519637i	−0.995729	+	0.0923229i	$0.970571\pi$
$608$	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	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−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	−0.207629	−	0.978208i	$-0.566575\pi$
$617$	6.51038	−	2.36959i	0.262098	−	0.0953959i	0.469727	+	0.882812i	$0.344352\pi$
$618$		0			0
$619$	3.47296	+	19.6962i	0.139590	+	0.791655i	0.971553	+	0.236823i	$0.0761063\pi$
$619$	3.47296	+	19.6962i	0.139590	+	0.791655i	−0.831963	+	0.554832i	$0.812783\pi$
$620$	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	−0.984128	−	0.177459i	$-0.943212\pi$
$631$	−8.50000	+	14.7224i	−0.338380	+	0.586091i	0.645748	+	0.763550i	$0.276545\pi$
$632$	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	0.992098	−	0.125467i	$-0.0400430\pi$
$641$	42.3175	+	15.4023i	1.67144	+	0.608354i	0.679342	+	0.733822i	$0.262265\pi$
$642$		0			0
$643$	33.7060	+	28.2827i	1.32923	+	1.11536i	0.984256	+	0.176748i	$0.0565577\pi$
$643$	33.7060	+	28.2827i	1.32923	+	1.11536i	0.344977	+	0.938611i	$0.387887\pi$
$644$	−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	0.345135	−	0.938553i	$-0.387833\pi$
$653$	−13.2683	−	11.1334i	−0.519228	−	0.435684i	−0.864362	+	0.502869i	$0.832278\pi$
$654$		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	−0.127620	−	0.991823i	$-0.540734\pi$
$659$	21.2292	−	17.8135i	0.826974	−	0.693914i	0.954594	+	0.297910i	$0.0962894\pi$
$660$		0			0
$661$	−1.73648	+	9.84808i	−0.0675413	+	0.383046i	0.932234	+	0.361856i	$0.117857\pi$
$661$	−1.73648	+	9.84808i	−0.0675413	+	0.383046i	−0.999775	+	0.0211902i	$0.993254\pi$
$662$	−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	−0.814221	−	0.580554i	$-0.802836\pi$
$673$	−6.42498	−	36.4379i	−0.247665	−	1.40458i	0.566557	−	0.824023i	$-0.308275\pi$
$674$	8.66025			0.333581
$675$		0			0
$676$	12.0000			0.461538
$677$	3.00767	+	17.0574i	0.115594	+	0.655568i	0.986454	+	0.164037i	$0.0524516\pi$
$677$	3.00767	+	17.0574i	0.115594	+	0.655568i	−0.870860	+	0.491531i	$0.836437\pi$
$678$		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	−0.922648	−	0.385643i	$-0.873979\pi$
$683$	−20.7846	−	36.0000i	−0.795301	−	1.37750i	0.127347	−	0.991858i	$-0.459354\pi$
$684$		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	−0.360551	−	0.932739i	$-0.617411\pi$
$691$	13.0228	−	10.9274i	0.495409	−	0.415697i	0.855960	+	0.517042i	$0.172967\pi$
$692$	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	0.654775	−	0.755824i	$-0.272763\pi$
$709$	17.8542	+	6.49838i	0.670527	+	0.244052i	0.0157523	+	0.999876i	$0.494986\pi$
$710$	−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	−0.946501	−	0.322700i	$-0.895409\pi$
$719$	−5.19615	+	9.00000i	−0.193784	+	0.335643i	0.752717	+	0.658344i	$0.228743\pi$
$720$		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	−0.991984	−	0.126367i	$-0.959668\pi$
$727$	−2.77837	−	15.7569i	−0.103044	−	0.584392i	0.888939	−	0.458025i	$-0.151443\pi$
$728$	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	−0.934929	−	0.354835i	$-0.884537\pi$
$733$	−38.5274	+	14.0228i	−1.42304	+	0.517945i	−0.488113	+	0.872780i	$0.662315\pi$
$734$	−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	−0.636691	−	0.771119i	$-0.719697\pi$
$739$	9.50000	−	16.4545i	0.349463	−	0.605288i	0.986154	+	0.165831i	$0.0530307\pi$
$740$	−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	−0.998891	−	0.0470853i	$-0.985007\pi$
$743$	−1.20307	+	6.82295i	−0.0441364	+	0.250310i	0.954755	+	0.297395i	$0.0961178\pi$
$744$		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	0.709991	−	0.704211i	$-0.248699\pi$
$751$	3.83022	+	3.21394i	0.139767	+	0.117278i	−0.570224	+	0.821489i	$0.693144\pi$
$752$	−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	0.171037	−	0.985265i	$-0.445288\pi$
$761$	−21.2292	−	17.8135i	−0.769560	−	0.645737i	−0.940596	+	0.339528i	$0.889733\pi$
$762$		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	0.916670	+	0.399646i	$0.130867\pi$
$769$	−2.25743	+	12.8025i	−0.0814049	+	0.461670i	−0.998075	+	0.0620244i	$0.980244\pi$
$770$	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	−0.990144	−	0.140050i	$-0.955274\pi$
$773$	−10.3923	+	18.0000i	−0.373785	+	0.647415i	0.616359	+	0.787465i	$0.288607\pi$
$774$		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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