LMFDB - Embedded newform 729.2.e.n.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			568.1
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.n.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62760 - 0.592396i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.601535 - 3.41147i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(0.866025 + 1.50000i) q^{8} +(-3.00000 + 5.19615i) q^{10} +(-0.601535 - 3.41147i) q^{11} +(-4.69846 + 1.71010i) q^{13} +(1.62760 - 0.592396i) q^{14} +(-0.868241 - 4.92404i) q^{16} +(0.500000 + 0.866025i) q^{19} +(2.65366 - 2.22668i) q^{20} +(-1.04189 + 5.90885i) q^{22} +(-5.30731 - 4.45336i) q^{23} +(-6.57785 - 2.39414i) q^{25} +8.66025 q^{26} -1.00000 q^{28} +(3.25519 + 1.18479i) q^{29} +(3.83022 + 3.21394i) q^{31} +(-0.902302 + 5.11721i) q^{32} +(1.73205 + 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-0.300767 - 1.70574i) q^{38} +(5.63816 - 2.05212i) q^{40} +(-3.25519 + 1.18479i) q^{41} +(-0.173648 - 0.984808i) q^{43} +(1.73205 - 3.00000i) q^{44} +(6.00000 + 10.3923i) q^{46} +(-2.65366 + 2.22668i) q^{47} +(-1.04189 + 5.90885i) q^{49} +(9.28780 + 7.79339i) q^{50} +(-4.69846 - 1.71010i) q^{52} -10.3923 q^{53} -12.0000 q^{55} +(-1.62760 - 0.592396i) q^{56} +(-4.59627 - 3.85673i) q^{58} +(0.601535 - 3.41147i) q^{59} +(1.53209 - 1.28558i) q^{61} +(-4.33013 - 7.50000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(3.00767 + 17.0574i) q^{65} +(-7.51754 + 2.73616i) q^{67} +(-1.04189 - 5.90885i) q^{70} +(-5.19615 + 9.00000i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(-1.32683 + 1.11334i) q^{74} +(-0.173648 + 0.984808i) q^{76} +(2.65366 + 2.22668i) q^{77} +(0.939693 + 0.342020i) q^{79} -17.3205 q^{80} +6.00000 q^{82} +(-6.51038 - 2.36959i) q^{83} +(-0.300767 + 1.70574i) q^{86} +(4.59627 - 3.85673i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(2.50000 - 4.33013i) q^{91} +(-1.20307 - 6.82295i) q^{92} +(5.63816 - 2.05212i) q^{94} +(3.25519 - 1.18479i) q^{95} +(2.95202 + 16.7417i) q^{97} +(5.19615 - 9.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−1.62760	−	0.592396i	−1.15088	−	0.418887i	−0.305051	−	0.952336i	$-0.598674\pi$
$2$	−1.62760	−	0.592396i	−1.15088	−	0.418887i	−0.845833	+	0.533449i	$0.820896\pi$
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.601535	−	3.41147i	0.269015	−	1.52566i	−0.488340	−	0.872654i	$-0.662397\pi$
$5$	0.601535	−	3.41147i	0.269015	−	1.52566i	0.757354	−	0.653004i	$-0.226492\pi$
$6$		0			0
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i	−0.775974	−	0.630765i	$-0.782741\pi$
$7$	−0.766044	+	0.642788i	−0.289538	+	0.242951i	0.486436	+	0.873716i	$0.338297\pi$
$8$	0.866025	+	1.50000i	0.306186	+	0.530330i
$9$		0			0
$10$	−3.00000	+	5.19615i	−0.948683	+	1.64317i
$11$	−0.601535	−	3.41147i	−0.181370	−	1.02860i	−0.930532	−	0.366211i	$-0.880655\pi$
$11$	−0.601535	−	3.41147i	−0.181370	−	1.02860i	0.749162	−	0.662387i	$-0.230456\pi$
$12$		0			0
$13$	−4.69846	+	1.71010i	−1.30312	+	0.474297i	−0.898011	−	0.439972i	$-0.854988\pi$
$13$	−4.69846	+	1.71010i	−1.30312	+	0.474297i	−0.405108	+	0.914269i	$0.632766\pi$
$14$	1.62760	−	0.592396i	0.434993	−	0.158325i
$15$		0			0
$16$	−0.868241	−	4.92404i	−0.217060	−	1.23101i
$17$		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	$0.796740\pi$
$20$	2.65366	−	2.22668i	0.593375	−	0.497901i
$21$		0			0
$22$	−1.04189	+	5.90885i	−0.222131	+	1.25977i
$23$	−5.30731	−	4.45336i	−1.10665	−	0.928590i	−0.108797	−	0.994064i	$-0.534700\pi$
$23$	−5.30731	−	4.45336i	−1.10665	−	0.928590i	−0.997854	+	0.0654736i	$0.979144\pi$
$24$		0			0
$25$	−6.57785	−	2.39414i	−1.31557	−	0.478828i
$26$	8.66025			1.69842
$27$		0			0
$28$	−1.00000			−0.188982
$29$	3.25519	+	1.18479i	0.604474	+	0.220010i	0.626083	−	0.779756i	$-0.284657\pi$
$29$	3.25519	+	1.18479i	0.604474	+	0.220010i	−0.0216097	+	0.999766i	$0.506879\pi$
$30$		0			0
$31$	3.83022	+	3.21394i	0.687928	+	0.577240i	0.918311	−	0.395860i	$-0.129553\pi$
$31$	3.83022	+	3.21394i	0.687928	+	0.577240i	−0.230383	+	0.973100i	$0.573998\pi$
$32$	−0.902302	+	5.11721i	−0.159506	+	0.904604i
$33$		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	$0.140472\pi$
$38$	−0.300767	−	1.70574i	−0.0487909	−	0.276707i
$39$		0			0
$40$	5.63816	−	2.05212i	0.891471	−	0.324469i
$41$	−3.25519	+	1.18479i	−0.508375	+	0.185034i	−0.583457	−	0.812144i	$-0.698300\pi$
$41$	−3.25519	+	1.18479i	−0.508375	+	0.185034i	0.0750818	+	0.997177i	$0.476078\pi$
$42$		0			0
$43$	−0.173648	−	0.984808i	−0.0264811	−	0.150182i	0.968700	−	0.248234i	$-0.0798500\pi$
$43$	−0.173648	−	0.984808i	−0.0264811	−	0.150182i	−0.995181	+	0.0980518i	$0.968739\pi$
$44$	1.73205	−	3.00000i	0.261116	−	0.452267i
$45$		0			0
$46$	6.00000	+	10.3923i	0.884652	+	1.53226i
$47$	−2.65366	+	2.22668i	−0.387075	+	0.324795i	−0.815473	−	0.578796i	$-0.803523\pi$
$47$	−2.65366	+	2.22668i	−0.387075	+	0.324795i	0.428397	+	0.903591i	$0.359078\pi$
$48$		0			0
$49$	−1.04189	+	5.90885i	−0.148841	+	0.844121i
$50$	9.28780	+	7.79339i	1.31349	+	1.10215i
$51$		0			0
$52$	−4.69846	−	1.71010i	−0.651560	−	0.237148i
$53$	−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
$56$	−1.62760	−	0.592396i	−0.217497	−	0.0791623i
$57$		0			0
$58$	−4.59627	−	3.85673i	−0.603519	−	0.506413i
$59$	0.601535	−	3.41147i	0.0783132	−	0.444136i	−0.920287	−	0.391244i	$-0.872045\pi$
$59$	0.601535	−	3.41147i	0.0783132	−	0.444136i	0.998600	−	0.0528923i	$-0.0168440\pi$
$60$		0			0
$61$	1.53209	−	1.28558i	0.196164	−	0.164601i	−0.539415	−	0.842040i	$-0.681355\pi$
$61$	1.53209	−	1.28558i	0.196164	−	0.164601i	0.735579	+	0.677439i	$0.236910\pi$
$62$	−4.33013	−	7.50000i	−0.549927	−	0.952501i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	3.00767	+	17.0574i	0.373056	+	2.11571i
$66$		0			0
$67$	−7.51754	+	2.73616i	−0.918414	+	0.334275i	−0.757607	−	0.652711i	$-0.773632\pi$
$67$	−7.51754	+	2.73616i	−0.918414	+	0.334275i	−0.160807	+	0.986986i	$0.551410\pi$
$68$		0			0
$69$		0			0
$70$	−1.04189	−	5.90885i	−0.124530	−	0.706242i
$71$	−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	$0.870674\pi$
$74$	−1.32683	+	1.11334i	−0.154241	+	0.129423i
$75$		0			0
$76$	−0.173648	+	0.984808i	−0.0199188	+	0.112965i
$77$	2.65366	+	2.22668i	0.302412	+	0.253754i
$78$		0			0
$79$	0.939693	+	0.342020i	0.105724	+	0.0384803i	0.394340	−	0.918964i	$-0.370973\pi$
$79$	0.939693	+	0.342020i	0.105724	+	0.0384803i	−0.288617	+	0.957445i	$0.593195\pi$
$80$	−17.3205			−1.93649
$81$		0			0
$82$	6.00000			0.662589
$83$	−6.51038	−	2.36959i	−0.714607	−	0.260096i	−0.0409726	−	0.999160i	$-0.513046\pi$
$83$	−6.51038	−	2.36959i	−0.714607	−	0.260096i	−0.673635	+	0.739065i	$0.735268\pi$
$84$		0			0
$85$		0			0
$86$	−0.300767	+	1.70574i	−0.0324326	+	0.183934i
$87$		0			0
$88$	4.59627	−	3.85673i	0.489964	−	0.411128i
$89$	−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
$92$	−1.20307	−	6.82295i	−0.125429	−	0.711342i
$93$		0			0
$94$	5.63816	−	2.05212i	0.581531	−	0.211660i
$95$	3.25519	−	1.18479i	0.333976	−	0.121557i
$96$		0			0
$97$	2.95202	+	16.7417i	0.299732	+	1.69987i	0.647320	+	0.762218i	$0.275890\pi$
$97$	2.95202	+	16.7417i	0.299732	+	1.69987i	−0.347588	+	0.937647i	$0.612999\pi$
$98$	5.19615	−	9.00000i	0.524891	−	0.909137i
$99$		0			0
$100$	−3.50000	−	6.06218i	−0.350000	−	0.606218i
$101$	−10.6146	+	8.90673i	−1.05619	+	0.886252i	−0.993731	−	0.111795i	$-0.964340\pi$
$101$	−10.6146	+	8.90673i	−1.05619	+	0.886252i	−0.0624632	+	0.998047i	$0.519896\pi$
$102$		0			0
$103$	1.38919	−	7.87846i	0.136881	−	0.776288i	−0.836651	−	0.547736i	$-0.815490\pi$
$103$	1.38919	−	7.87846i	0.136881	−	0.776288i	0.973532	−	0.228552i	$-0.0733991\pi$
$104$	−6.63414	−	5.56670i	−0.650531	−	0.545860i
$105$		0			0
$106$	16.9145	+	6.15636i	1.64288	+	0.597959i
$107$	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	$0.197202\pi$
$110$	19.5311	+	7.10876i	1.86222	+	0.677793i
$111$		0			0
$112$	3.83022	+	3.21394i	0.361922	+	0.303689i
$113$	−3.00767	+	17.0574i	−0.282938	+	1.60462i	0.429620	+	0.903010i	$0.358647\pi$
$113$	−3.00767	+	17.0574i	−0.282938	+	1.60462i	−0.712558	+	0.701613i	$0.752464\pi$
$114$		0			0
$115$	−18.3851	+	15.4269i	−1.71442	+	1.43857i
$116$	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
$121$	−0.939693	+	0.342020i	−0.0854266	+	0.0310927i
$122$	−3.25519	+	1.18479i	−0.294711	+	0.107266i
$123$		0			0
$124$	0.868241	+	4.92404i	0.0779703	+	0.442192i
$125$	−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	$-0.438667\pi$
$128$	9.28780	−	7.79339i	0.820933	−	0.688844i
$129$		0			0
$130$	5.20945	−	29.5442i	0.456899	−	2.59120i
$131$	2.65366	+	2.22668i	0.231851	+	0.194546i	0.751310	−	0.659949i	$-0.229422\pi$
$131$	2.65366	+	2.22668i	0.231851	+	0.194546i	−0.519459	+	0.854495i	$0.673867\pi$
$132$		0			0
$133$	−0.939693	−	0.342020i	−0.0814817	−	0.0296569i
$134$	13.8564			1.19701
$135$		0			0
$136$		0			0
$137$	−6.51038	−	2.36959i	−0.556219	−	0.202447i	0.0485882	−	0.998819i	$-0.484528\pi$
$137$	−6.51038	−	2.36959i	−0.556219	−	0.202447i	−0.604808	+	0.796372i	$0.706750\pi$
$138$		0			0
$139$	−9.95858	−	8.35624i	−0.844676	−	0.708767i	0.113935	−	0.993488i	$-0.463655\pi$
$139$	−9.95858	−	8.35624i	−0.844676	−	0.708767i	−0.958610	+	0.284721i	$0.908099\pi$
$140$	−0.601535	+	3.41147i	−0.0508390	+	0.288322i
$141$		0			0
$142$	13.7888	−	11.5702i	1.15713	−	0.970948i
$143$	8.66025	+	15.0000i	0.724207	+	1.25436i
$144$		0			0
$145$	6.00000	−	10.3923i	0.498273	−	0.863034i
$146$	0.601535	+	3.41147i	0.0497834	+	0.282336i
$147$		0			0
$148$	0.939693	−	0.342020i	0.0772423	−	0.0281139i
$149$	6.51038	−	2.36959i	0.533351	−	0.194124i	−0.0612828	−	0.998120i	$-0.519519\pi$
$149$	6.51038	−	2.36959i	0.533351	−	0.194124i	0.594634	+	0.803996i	$0.297297\pi$
$150$		0			0
$151$	−2.77837	−	15.7569i	−0.226101	−	1.28228i	−0.860570	−	0.509332i	$-0.829892\pi$
$151$	−2.77837	−	15.7569i	−0.226101	−	1.28228i	0.634469	−	0.772948i	$-0.281219\pi$
$152$	−0.866025	+	1.50000i	−0.0702439	+	0.121666i
$153$		0			0
$154$	−3.00000	−	5.19615i	−0.241747	−	0.418718i
$155$	13.2683	−	11.1334i	1.06573	−	0.894257i
$156$		0			0
$157$	−2.25743	+	12.8025i	−0.180162	+	1.02175i	0.751853	+	0.659331i	$0.229160\pi$
$157$	−2.25743	+	12.8025i	−0.180162	+	1.02175i	−0.932015	+	0.362420i	$0.881951\pi$
$158$	−1.32683	−	1.11334i	−0.105557	−	0.0885726i
$159$		0			0
$160$	16.9145	+	6.15636i	1.33721	+	0.486703i
$161$	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	$0.512469\pi$
$164$	−3.25519	−	1.18479i	−0.254188	−	0.0925168i
$165$		0			0
$166$	9.19253	+	7.71345i	0.713479	+	0.598680i
$167$	4.21074	−	23.8803i	0.325837	−	1.84791i	−0.177888	−	0.984051i	$-0.556927\pi$
$167$	4.21074	−	23.8803i	0.325837	−	1.84791i	0.503725	−	0.863864i	$-0.331962\pi$
$168$		0			0
$169$	9.19253	−	7.71345i	0.707118	−	0.593342i
$170$		0			0
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−2.40614	−	13.6459i	−0.182935	−	1.03748i	−0.928579	−	0.371134i	$-0.878969\pi$
$173$	−2.40614	−	13.6459i	−0.182935	−	1.03748i	0.745644	−	0.666345i	$-0.232142\pi$
$174$		0			0
$175$	6.57785	−	2.39414i	0.497239	−	0.180980i
$176$	−16.2760	+	5.92396i	−1.22685	+	0.446535i
$177$		0			0
$178$	3.12567	+	17.7265i	0.234279	+	1.32866i
$179$	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	$-0.384350\pi$
$182$	−6.63414	+	5.56670i	−0.491755	+	0.412632i
$183$		0			0
$184$	2.08378	−	11.8177i	0.153618	−	0.871212i
$185$	−2.65366	−	2.22668i	−0.195101	−	0.163709i
$186$		0			0
$187$		0			0
$188$	−3.46410			−0.252646
$189$		0			0
$190$	−6.00000			−0.435286
$191$	−6.51038	−	2.36959i	−0.471075	−	0.171457i	0.0955644	−	0.995423i	$-0.469534\pi$
$191$	−6.51038	−	2.36959i	−0.471075	−	0.171457i	−0.566639	+	0.823966i	$0.691757\pi$
$192$		0			0
$193$	−7.66044	−	6.42788i	−0.551411	−	0.462689i	0.324008	−	0.946054i	$-0.394970\pi$
$193$	−7.66044	−	6.42788i	−0.551411	−	0.462689i	−0.875418	+	0.483366i	$0.839414\pi$
$194$	5.11305	−	28.9975i	0.367095	−	2.08190i
$195$		0			0
$196$	−4.59627	+	3.85673i	−0.328305	+	0.275480i
$197$	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	$-0.0685161\pi$
$200$	−2.10537	−	11.9402i	−0.148872	−	0.844297i
$201$		0			0
$202$	22.5526	−	8.20848i	1.58680	−	0.577547i
$203$	−3.25519	+	1.18479i	−0.228470	+	0.0831561i
$204$		0			0
$205$	2.08378	+	11.8177i	0.145537	+	0.825383i
$206$	−6.92820	+	12.0000i	−0.482711	+	0.836080i
$207$		0			0
$208$	12.5000	+	21.6506i	0.866719	+	1.50120i
$209$	2.65366	−	2.22668i	0.183557	−	0.154023i
$210$		0			0
$211$	0.868241	−	4.92404i	0.0597722	−	0.338985i	−0.940227	−	0.340549i	$-0.889387\pi$
$211$	0.868241	−	4.92404i	0.0597722	−	0.338985i	0.999999	+	0.00156464i	$0.000498040\pi$
$212$	−7.96097	−	6.68004i	−0.546761	−	0.458787i
$213$		0			0
$214$	−16.9145	−	6.15636i	−1.15625	−	0.420840i
$215$	−3.46410			−0.236250
$216$		0			0
$217$	−5.00000			−0.339422
$218$	−27.6691	−	10.0707i	−1.87399	−	0.682076i
$219$		0			0
$220$	−9.19253	−	7.71345i	−0.619760	−	0.520041i
$221$		0			0
$222$		0			0
$223$	−14.5548	+	12.2130i	−0.974664	+	0.817841i	−0.983276	−	0.182122i	$-0.941703\pi$
$223$	−14.5548	+	12.2130i	−0.974664	+	0.817841i	0.00861141	+	0.999963i	$0.497259\pi$
$224$	−2.59808	−	4.50000i	−0.173591	−	0.300669i
$225$		0			0
$226$	15.0000	−	25.9808i	0.997785	−	1.72821i
$227$	−2.40614	−	13.6459i	−0.159701	−	0.905710i	−0.954361	−	0.298655i	$-0.903462\pi$
$227$	−2.40614	−	13.6459i	−0.159701	−	0.905710i	0.794660	−	0.607055i	$-0.207649\pi$
$228$		0			0
$229$	−4.69846	+	1.71010i	−0.310483	+	0.113007i	−0.492562	−	0.870277i	$-0.663940\pi$
$229$	−4.69846	+	1.71010i	−0.310483	+	0.113007i	0.182079	+	0.983284i	$0.441717\pi$
$230$	39.0623	−	14.2175i	2.57569	−	0.937475i
$231$		0			0
$232$	1.04189	+	5.90885i	0.0684034	+	0.387935i
$233$		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
$236$	2.65366	−	2.22668i	0.172738	−	0.144945i
$237$		0			0
$238$		0			0
$239$	−5.30731	−	4.45336i	−0.343301	−	0.288064i	0.454792	−	0.890598i	$-0.349714\pi$
$239$	−5.30731	−	4.45336i	−0.343301	−	0.288064i	−0.798094	+	0.602533i	$0.794158\pi$
$240$		0			0
$241$	17.8542	+	6.49838i	1.15009	+	0.418598i	0.845547	−	0.533902i	$-0.179275\pi$
$241$	17.8542	+	6.49838i	1.15009	+	0.418598i	0.304541	+	0.952499i	$0.401497\pi$
$242$	1.73205			0.111340
$243$		0			0
$244$	2.00000			0.128037
$245$	19.5311	+	7.10876i	1.24780	+	0.454162i
$246$		0			0
$247$	−3.83022	−	3.21394i	−0.243711	−	0.204498i
$248$	−1.50384	+	8.52869i	−0.0954938	+	0.541572i
$249$		0			0
$250$	9.19253	−	7.71345i	0.581387	−	0.487841i
$251$	−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
$254$	5.11305	+	28.9975i	0.320821	+	1.81947i
$255$		0			0
$256$	−17.8542	+	6.49838i	−1.11588	+	0.406149i
$257$	−3.25519	+	1.18479i	−0.203053	+	0.0739053i	−0.441545	−	0.897239i	$-0.645569\pi$
$257$	−3.25519	+	1.18479i	−0.203053	+	0.0739053i	0.238491	+	0.971145i	$0.423347\pi$
$258$		0			0
$259$	0.173648	+	0.984808i	0.0107900	+	0.0611930i
$260$	−8.66025	+	15.0000i	−0.537086	+	0.930261i
$261$		0			0
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−10.6146	+	8.90673i	−0.654526	+	0.549212i	−0.908440	−	0.418014i	$-0.862726\pi$
$263$	−10.6146	+	8.90673i	−0.654526	+	0.549212i	0.253915	+	0.967227i	$0.418282\pi$
$264$		0			0
$265$	−6.25133	+	35.4531i	−0.384016	+	2.17787i
$266$	1.32683	+	1.11334i	0.0813530	+	0.0682633i
$267$		0			0
$268$	−7.51754	−	2.73616i	−0.459207	−	0.167138i
$269$		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
$274$	9.19253	+	7.71345i	0.555341	+	0.465987i
$275$	−4.21074	+	23.8803i	−0.253917	+	1.44004i
$276$		0			0
$277$	13.0228	−	10.9274i	0.782462	−	0.656563i	−0.161406	−	0.986888i	$-0.551603\pi$
$277$	13.0228	−	10.9274i	0.782462	−	0.656563i	0.943867	+	0.330325i	$0.107158\pi$
$278$	11.2583	+	19.5000i	0.675230	+	1.16953i
$279$		0			0
$280$	−3.00000	+	5.19615i	−0.179284	+	0.310530i
$281$	−2.40614	−	13.6459i	−0.143538	−	0.814046i	−0.968529	−	0.248900i	$-0.919931\pi$
$281$	−2.40614	−	13.6459i	−0.143538	−	0.814046i	0.824991	−	0.565146i	$-0.191180\pi$
$282$		0			0
$283$	12.2160	−	4.44626i	0.726166	−	0.264303i	0.0476250	−	0.998865i	$-0.484835\pi$
$283$	12.2160	−	4.44626i	0.726166	−	0.264303i	0.678541	+	0.734562i	$0.262613\pi$
$284$	−9.76557	+	3.55438i	−0.579480	+	0.210914i
$285$		0			0
$286$	−5.20945	−	29.5442i	−0.308041	−	1.74699i
$287$	1.73205	−	3.00000i	0.102240	−	0.177084i
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−15.9219	+	13.3601i	−0.934968	+	0.784531i
$291$		0			0
$292$	0.347296	−	1.96962i	0.0203240	−	0.115263i
$293$	10.6146	+	8.90673i	0.620113	+	0.520337i	0.897839	−	0.440324i	$-0.145136\pi$
$293$	10.6146	+	8.90673i	0.620113	+	0.520337i	−0.277726	+	0.960660i	$0.589581\pi$
$294$		0			0
$295$	−11.2763	−	4.10424i	−0.656532	−	0.238958i
$296$	1.73205			0.100673
$297$		0			0
$298$	−12.0000			−0.695141
$299$	32.5519	+	11.8479i	1.88253	+	0.685183i
$300$		0			0
$301$	0.766044	+	0.642788i	0.0441541	+	0.0370497i
$302$	−4.81228	+	27.2918i	−0.276916	+	1.57047i
$303$		0			0
$304$	3.83022	−	3.21394i	0.219678	−	0.184332i
$305$	−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	$0.973327\pi$
$308$	0.601535	+	3.41147i	0.0342756	+	0.194387i
$309$		0			0
$310$	−28.1908	+	10.2606i	−1.60113	+	0.582763i
$311$	−13.0208	+	4.73917i	−0.738340	+	0.268734i	−0.683691	−	0.729772i	$-0.739626\pi$
$311$	−13.0208	+	4.73917i	−0.738340	+	0.268734i	−0.0546491	+	0.998506i	$0.517404\pi$
$312$		0			0
$313$	−0.173648	−	0.984808i	−0.00981518	−	0.0556646i	0.979507	−	0.201411i	$-0.0645527\pi$
$313$	−0.173648	−	0.984808i	−0.00981518	−	0.0556646i	−0.989322	+	0.145747i	$0.953442\pi$
$314$	11.2583	−	19.5000i	0.635344	−	1.10045i
$315$		0			0
$316$	0.500000	+	0.866025i	0.0281272	+	0.0487177i
$317$	21.2292	−	17.8135i	1.19235	−	1.00050i	0.192538	−	0.981290i	$-0.438328\pi$
$317$	21.2292	−	17.8135i	1.19235	−	1.00050i	0.999815	−	0.0192136i	$-0.00611627\pi$
$318$		0			0
$319$	2.08378	−	11.8177i	0.116669	−	0.661664i
$320$	2.65366	+	2.22668i	0.148344	+	0.124475i
$321$		0			0
$322$	−11.2763	−	4.10424i	−0.628404	−	0.228720i
$323$		0			0
$324$		0			0
$325$	35.0000			1.94145
$326$	1.62760	+	0.592396i	0.0901442	+	0.0328098i
$327$		0			0
$328$	−4.59627	−	3.85673i	−0.253786	−	0.212952i
$329$	0.601535	−	3.41147i	0.0331637	−	0.188081i
$330$		0			0
$331$	−14.5548	+	12.2130i	−0.800007	+	0.671285i	−0.948200	−	0.317673i	$-0.897099\pi$
$331$	−14.5548	+	12.2130i	−0.800007	+	0.671285i	0.148194	+	0.988958i	$0.452654\pi$
$332$	−3.46410	−	6.00000i	−0.190117	−	0.329293i
$333$		0			0
$334$	−21.0000	+	36.3731i	−1.14907	+	1.99025i
$335$	4.81228	+	27.2918i	0.262923	+	1.49111i
$336$		0			0
$337$	−4.69846	+	1.71010i	−0.255942	+	0.0931551i	−0.466805	−	0.884361i	$-0.654595\pi$
$337$	−4.69846	+	1.71010i	−0.255942	+	0.0931551i	0.210863	+	0.977516i	$0.432373\pi$
$338$	−19.5311	+	7.10876i	−1.06235	+	0.386665i
$339$		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
$344$	1.32683	−	1.11334i	0.0715378	−	0.0600273i
$345$		0			0
$346$	−4.16756	+	23.6354i	−0.224049	+	1.27065i
$347$	18.5756	+	15.5868i	0.997190	+	0.836742i	0.986593	−	0.163202i	$-0.0521823\pi$
$347$	18.5756	+	15.5868i	0.997190	+	0.836742i	0.0105973	+	0.999944i	$0.496627\pi$
$348$		0			0
$349$	0.939693	+	0.342020i	0.0503006	+	0.0183079i	0.367048	−	0.930202i	$-0.380369\pi$
$349$	0.939693	+	0.342020i	0.0503006	+	0.0183079i	−0.316747	+	0.948510i	$0.602591\pi$
$350$	−12.1244			−0.648074
$351$		0			0
$352$	18.0000			0.959403
$353$	−16.2760	−	5.92396i	−0.866282	−	0.315301i	−0.129621	−	0.991564i	$-0.541376\pi$
$353$	−16.2760	−	5.92396i	−0.866282	−	0.315301i	−0.736660	+	0.676263i	$0.763598\pi$
$354$		0			0
$355$	27.5776	+	23.1404i	1.46367	+	1.22816i
$356$	1.80460	−	10.2344i	0.0956439	−	0.542423i
$357$		0			0
$358$	−27.5776	+	23.1404i	−1.45752	+	1.22301i
$359$	−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
$362$	5.11305	+	28.9975i	0.268736	+	1.52408i
$363$		0			0
$364$	4.69846	−	1.71010i	0.246266	−	0.0896336i
$365$	−6.51038	+	2.36959i	−0.340769	+	0.124030i
$366$		0			0
$367$	−2.77837	−	15.7569i	−0.145030	−	0.822505i	−0.967343	−	0.253470i	$-0.918428\pi$
$367$	−2.77837	−	15.7569i	−0.145030	−	0.822505i	0.822313	−	0.569035i	$-0.192683\pi$
$368$	−17.3205	+	30.0000i	−0.902894	+	1.56386i
$369$		0			0
$370$	3.00000	+	5.19615i	0.155963	+	0.270135i
$371$	7.96097	−	6.68004i	0.413313	−	0.346811i
$372$		0			0
$373$	3.99391	−	22.6506i	0.206797	−	1.17280i	−0.687791	−	0.725909i	$-0.741419\pi$
$373$	3.99391	−	22.6506i	0.206797	−	1.17280i	0.894587	−	0.446893i	$-0.147470\pi$
$374$		0			0
$375$		0			0
$376$	−5.63816	−	2.05212i	−0.290766	−	0.105830i
$377$	−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	$0.662267\pi$
$380$	3.25519	+	1.18479i	0.166988	+	0.0607786i
$381$		0			0
$382$	9.19253	+	7.71345i	0.470331	+	0.394655i
$383$	−3.00767	+	17.0574i	−0.153685	+	0.871591i	0.806293	+	0.591516i	$0.201470\pi$
$383$	−3.00767	+	17.0574i	−0.153685	+	0.871591i	−0.959978	+	0.280075i	$0.909641\pi$
$384$		0			0
$385$	9.19253	−	7.71345i	0.468495	−	0.393114i
$386$	8.66025	+	15.0000i	0.440795	+	0.763480i
$387$		0			0
$388$	−8.50000	+	14.7224i	−0.431522	+	0.747418i
$389$	1.20307	+	6.82295i	0.0609981	+	0.345937i	0.999998	+	0.00201979i	$0.000642918\pi$
$389$	1.20307	+	6.82295i	0.0609981	+	0.345937i	−0.939000	+	0.343917i	$0.888246\pi$
$390$		0			0
$391$		0			0
$392$	−9.76557	+	3.55438i	−0.493236	+	0.179523i
$393$		0			0
$394$	−3.12567	−	17.7265i	−0.157469	−	0.893050i
$395$	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	$0.825345\pi$
$398$	−25.2097	+	21.1535i	−1.26365	+	1.06033i
$399$		0			0
$400$	−6.07769	+	34.4683i	−0.303884	+	1.72341i
$401$	2.65366	+	2.22668i	0.132517	+	0.111195i	0.706637	−	0.707576i	$-0.250211\pi$
$401$	2.65366	+	2.22668i	0.132517	+	0.111195i	−0.574120	+	0.818771i	$0.694656\pi$
$402$		0			0
$403$	−23.4923	−	8.55050i	−1.17024	−	0.425931i
$404$	−13.8564			−0.689382
$405$		0			0
$406$	6.00000			0.297775
$407$	−3.25519	−	1.18479i	−0.161354	−	0.0587280i
$408$		0			0
$409$	3.83022	+	3.21394i	0.189392	+	0.158919i	0.732554	−	0.680709i	$-0.238328\pi$
$409$	3.83022	+	3.21394i	0.189392	+	0.158919i	−0.543161	+	0.839628i	$0.682773\pi$
$410$	3.60921	−	20.4688i	0.178246	−	1.01088i
$411$		0			0
$412$	6.12836	−	5.14230i	0.301922	−	0.253343i
$413$	1.73205	+	3.00000i	0.0852286	+	0.147620i
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$	−4.51151	−	25.5861i	−0.221195	−	1.25446i
$417$		0			0
$418$	−5.63816	+	2.05212i	−0.275771	+	0.100373i
$419$	35.8071	−	13.0327i	1.74929	−	0.636690i	0.749609	−	0.661881i	$-0.230242\pi$
$419$	35.8071	−	13.0327i	1.74929	−	0.636690i	0.999683	+	0.0251915i	$0.00801955\pi$
$420$		0			0
$421$	−3.29932	−	18.7113i	−0.160799	−	0.911935i	−0.953291	−	0.302053i	$-0.902328\pi$
$421$	−3.29932	−	18.7113i	−0.160799	−	0.911935i	0.792492	−	0.609882i	$-0.208783\pi$
$422$	−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
$427$	−0.347296	+	1.96962i	−0.0168068	+	0.0953164i
$428$	7.96097	+	6.68004i	0.384808	+	0.322892i
$429$		0			0
$430$	5.63816	+	2.05212i	0.271896	+	0.0989621i
$431$	−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	$0.507649\pi$
$434$	8.13798	+	2.96198i	0.390635	+	0.142180i
$435$		0			0
$436$	13.0228	+	10.9274i	0.623677	+	0.523327i
$437$	1.20307	−	6.82295i	0.0575506	−	0.326386i
$438$		0			0
$439$	15.3209	−	12.8558i	0.731226	−	0.613572i	−0.199239	−	0.979951i	$-0.563847\pi$
$439$	15.3209	−	12.8558i	0.731226	−	0.613572i	0.930466	+	0.366379i	$0.119403\pi$
$440$	−10.3923	−	18.0000i	−0.495434	−	0.858116i
$441$		0			0
$442$		0			0
$443$	−2.40614	−	13.6459i	−0.114319	−	0.648336i	−0.987085	−	0.160197i	$-0.948787\pi$
$443$	−2.40614	−	13.6459i	−0.114319	−	0.648336i	0.872766	−	0.488139i	$-0.162324\pi$
$444$		0			0
$445$	−33.8289	+	12.3127i	−1.60365	+	0.583679i
$446$	30.9243	−	11.2555i	1.46431	−	0.532965i
$447$		0			0
$448$	−0.173648	−	0.984808i	−0.00820411	−	0.0465278i
$449$	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
$452$	−13.2683	+	11.1334i	−0.624087	+	0.523671i
$453$		0			0
$454$	−4.16756	+	23.6354i	−0.195593	+	1.10926i
$455$	−13.2683	−	11.1334i	−0.622027	−	0.521942i
$456$		0			0
$457$	−15.9748	−	5.81434i	−0.747268	−	0.271983i	−0.0598126	−	0.998210i	$-0.519050\pi$
$457$	−15.9748	−	5.81434i	−0.747268	−	0.271983i	−0.687456	+	0.726226i	$0.741273\pi$
$458$	8.66025			0.404667
$459$		0			0
$460$	−24.0000			−1.11901
$461$	−26.0415	−	9.47834i	−1.21287	−	0.441450i	−0.345175	−	0.938538i	$-0.612180\pi$
$461$	−26.0415	−	9.47834i	−1.21287	−	0.441450i	−0.867700	+	0.497088i	$0.834403\pi$
$462$		0			0
$463$	−23.7474	−	19.9264i	−1.10363	−	0.926059i	−0.105970	−	0.994369i	$-0.533795\pi$
$463$	−23.7474	−	19.9264i	−1.10363	−	0.926059i	−0.997664	+	0.0683102i	$0.978239\pi$
$464$	3.00767	−	17.0574i	0.139628	−	0.791869i
$465$		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
$470$	−3.60921	−	20.4688i	−0.166480	−	0.944157i
$471$		0			0
$472$	5.63816	−	2.05212i	0.259517	−	0.0944565i
$473$	−3.25519	+	1.18479i	−0.149674	+	0.0544768i
$474$		0			0
$475$	−1.21554	−	6.89365i	−0.0557727	−	0.316303i
$476$		0			0
$477$		0			0
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−10.6146	+	8.90673i	−0.484995	+	0.406959i	−0.852228	−	0.523170i	$-0.824749\pi$
$479$	−10.6146	+	8.90673i	−0.484995	+	0.406959i	0.367234	+	0.930129i	$0.380305\pi$
$480$		0			0
$481$	−0.868241	+	4.92404i	−0.0395884	+	0.224517i
$482$	−25.2097	−	21.1535i	−1.14827	−	0.963514i
$483$		0			0
$484$	−0.939693	−	0.342020i	−0.0427133	−	0.0155464i
$485$	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	$0.641658\pi$
$488$	3.25519	+	1.18479i	0.147356	+	0.0536330i
$489$		0			0
$490$	−27.5776	−	23.1404i	−1.24583	−	1.04537i
$491$	−6.61688	+	37.5262i	−0.298616	+	1.69353i	0.353516	+	0.935429i	$0.384986\pi$
$491$	−6.61688	+	37.5262i	−0.298616	+	1.69353i	−0.652132	+	0.758106i	$0.726125\pi$
$492$		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
$497$	−1.80460	−	10.2344i	−0.0809476	−	0.459077i
$498$		0			0
$499$	26.3114	−	9.57656i	1.17786	−	0.428706i	0.322414	−	0.946599i	$-0.395506\pi$
$499$	26.3114	−	9.57656i	1.17786	−	0.428706i	0.855446	+	0.517893i	$0.173283\pi$
$500$	−6.51038	+	2.36959i	−0.291153	+	0.105971i
$501$		0			0
$502$	6.25133	+	35.4531i	0.279011	+	1.58235i
$503$	−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
$506$	31.8439	−	26.7202i	1.41563	−	1.18786i
$507$		0			0
$508$	2.95202	−	16.7417i	0.130975	−	0.742794i
$509$	−21.2292	−	17.8135i	−0.940970	−	0.789567i	0.0367840	−	0.999323i	$-0.488289\pi$
$509$	−21.2292	−	17.8135i	−0.940970	−	0.789567i	−0.977754	+	0.209756i	$0.932733\pi$
$510$		0			0
$511$	1.87939	+	0.684040i	0.0831391	+	0.0302602i
$512$	8.66025			0.382733
$513$		0			0
$514$	6.00000			0.264649
$515$	−26.0415	−	9.47834i	−1.14753	−	0.417666i
$516$		0			0
$517$	9.19253	+	7.71345i	0.404287	+	0.339237i
$518$	0.300767	−	1.70574i	0.0132150	−	0.0749458i
$519$		0			0
$520$	−22.9813	+	19.2836i	−1.00780	+	0.845643i
$521$	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	$0.310721\pi$
$524$	0.601535	+	3.41147i	0.0262782	+	0.149031i
$525$		0			0
$526$	22.5526	−	8.20848i	0.983341	−	0.357907i
$527$		0			0
$528$		0			0
$529$	4.34120	+	24.6202i	0.188748	+	1.07044i
$530$	31.1769	−	54.0000i	1.35424	−	2.34561i
$531$		0			0
$532$	−0.500000	−	0.866025i	−0.0216777	−	0.0375470i
$533$	13.2683	−	11.1334i	0.574713	−	0.482241i
$534$		0			0
$535$	6.25133	−	35.4531i	0.270269	−	1.53277i
$536$	−10.6146	−	8.90673i	−0.458482	−	0.384712i
$537$		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	$0.380917\pi$
$542$	26.0415	+	9.47834i	1.11858	+	0.407130i
$543$		0			0
$544$		0			0
$545$	10.2261	−	57.9951i	0.438038	−	2.48424i
$546$		0			0
$547$	15.3209	−	12.8558i	0.655074	−	0.549672i	−0.253532	−	0.967327i	$-0.581592\pi$
$547$	15.3209	−	12.8558i	0.655074	−	0.549672i	0.908606	+	0.417655i	$0.137148\pi$
$548$	−3.46410	−	6.00000i	−0.147979	−	0.256307i
$549$		0			0
$550$	21.0000	−	36.3731i	0.895443	−	1.55095i
$551$	0.601535	+	3.41147i	0.0256262	+	0.145334i
$552$		0			0
$553$	−0.939693	+	0.342020i	−0.0399598	+	0.0145442i
$554$	−27.6691	+	10.0707i	−1.17555	+	0.427865i
$555$		0			0
$556$	−2.25743	−	12.8025i	−0.0957362	−	0.542947i
$557$	−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
$560$	13.2683	−	11.1334i	0.560687	−	0.470472i
$561$		0			0
$562$	−4.16756	+	23.6354i	−0.175798	+	0.996999i
$563$	26.5366	+	22.2668i	1.11838	+	0.938434i	0.998522	−	0.0543563i	$-0.0173107\pi$
$563$	26.5366	+	22.2668i	1.11838	+	0.938434i	0.119861	+	0.992791i	$0.461755\pi$
$564$		0			0
$565$	56.3816	+	20.5212i	2.37199	+	0.863334i
$566$	−22.5167			−0.946446
$567$		0			0
$568$	−18.0000			−0.755263
$569$	22.7863	+	8.29355i	0.955253	+	0.347684i	0.772172	−	0.635414i	$-0.219171\pi$
$569$	22.7863	+	8.29355i	0.955253	+	0.347684i	0.183081	+	0.983098i	$0.441393\pi$
$570$		0			0
$571$	31.4078	+	26.3543i	1.31438	+	1.10289i	0.987465	+	0.157838i	$0.0504523\pi$
$571$	31.4078	+	26.3543i	1.31438	+	1.10289i	0.326911	+	0.945055i	$0.393992\pi$
$572$	−3.00767	+	17.0574i	−0.125757	+	0.713204i
$573$		0			0
$574$	−4.59627	+	3.85673i	−0.191844	+	0.160977i
$575$	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	$-0.0836092\pi$
$578$	−5.11305	−	28.9975i	−0.212675	−	1.20614i
$579$		0			0
$580$	11.2763	−	4.10424i	0.468223	−	0.170419i
$581$	6.51038	−	2.36959i	0.270096	−	0.0983070i
$582$		0			0
$583$	6.25133	+	35.4531i	0.258904	+	1.46832i
$584$	1.73205	−	3.00000i	0.0716728	−	0.124141i
$585$		0			0
$586$	−12.0000	−	20.7846i	−0.495715	−	0.858604i
$587$	5.30731	−	4.45336i	0.219056	−	0.183810i	−0.526655	−	0.850079i	$-0.676554\pi$
$587$	5.30731	−	4.45336i	0.219056	−	0.183810i	0.745712	+	0.666269i	$0.232110\pi$
$588$		0			0
$589$	−0.868241	+	4.92404i	−0.0357752	+	0.202891i
$590$	15.9219	+	13.3601i	0.655496	+	0.550026i
$591$		0			0
$592$	−4.69846	−	1.71010i	−0.193106	−	0.0702847i
$593$	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
$596$	6.51038	+	2.36959i	0.266676	+	0.0970620i
$597$		0			0
$598$	−45.9627	−	38.5673i	−1.87955	−	1.57713i
$599$	4.21074	−	23.8803i	0.172046	−	0.975723i	−0.769452	−	0.638705i	$-0.779470\pi$
$599$	4.21074	−	23.8803i	0.172046	−	0.975723i	0.941498	−	0.337018i	$-0.109418\pi$
$600$		0			0
$601$	26.8116	−	22.4976i	1.09367	−	0.917695i	0.0966832	−	0.995315i	$-0.469177\pi$
$601$	26.8116	−	22.4976i	1.09367	−	0.917695i	0.996983	+	0.0776203i	$0.0247322\pi$
$602$	−0.866025	−	1.50000i	−0.0352966	−	0.0611354i
$603$		0			0
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$	0.601535	+	3.41147i	0.0244559	+	0.138696i
$606$		0			0
$607$	12.2160	−	4.44626i	0.495832	−	0.180468i	−0.0819862	−	0.996633i	$-0.526126\pi$
$607$	12.2160	−	4.44626i	0.495832	−	0.180468i	0.577819	+	0.816165i	$0.303904\pi$
$608$	−4.88279	+	1.77719i	−0.198023	+	0.0720745i
$609$		0			0
$610$	2.08378	+	11.8177i	0.0843697	+	0.478484i
$611$	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	$0.846193\pi$
$614$	26.5366	−	22.2668i	1.07093	−	0.898616i
$615$		0			0
$616$	−1.04189	+	5.90885i	−0.0419789	+	0.238074i
$617$	−5.30731	−	4.45336i	−0.213664	−	0.179286i	0.529674	−	0.848201i	$-0.322314\pi$
$617$	−5.30731	−	4.45336i	−0.213664	−	0.179286i	−0.743338	+	0.668916i	$0.766759\pi$
$618$		0			0
$619$	−18.7939	−	6.84040i	−0.755389	−	0.274939i	−0.0645172	−	0.997917i	$-0.520551\pi$
$619$	−18.7939	−	6.84040i	−0.755389	−	0.274939i	−0.690871	+	0.722978i	$0.742773\pi$
$620$	17.3205			0.695608
$621$		0			0
$622$	24.0000			0.962312
$623$	9.76557	+	3.55438i	0.391249	+	0.142403i
$624$		0			0
$625$	−8.42649	−	7.07066i	−0.337060	−	0.282827i
$626$	−0.300767	+	1.70574i	−0.0120211	+	0.0681750i
$627$		0			0
$628$	−9.95858	+	8.35624i	−0.397391	+	0.333450i
$629$		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	$0.276545\pi$
$632$	0.300767	+	1.70574i	0.0119639	+	0.0678506i
$633$		0			0
$634$	−45.1052	+	16.4170i	−1.79136	+	0.652001i
$635$	−55.3382	+	20.1415i	−2.19603	+	0.799290i
$636$		0			0
$637$	−5.20945	−	29.5442i	−0.206406	−	1.17059i
$638$	−10.3923	+	18.0000i	−0.411435	+	0.712627i
$639$		0			0
$640$	−21.0000	−	36.3731i	−0.830098	−	1.43777i
$641$	−34.4975	+	28.9469i	−1.36257	+	1.14333i	−0.387391	+	0.921915i	$0.626624\pi$
$641$	−34.4975	+	28.9469i	−1.36257	+	1.14333i	−0.975179	+	0.221417i	$0.928932\pi$
$642$		0			0
$643$	7.64052	−	43.3315i	0.301313	−	1.70883i	−0.339060	−	0.940765i	$-0.610109\pi$
$643$	7.64052	−	43.3315i	0.301313	−	1.70883i	0.640373	−	0.768064i	$-0.278780\pi$
$644$	5.30731	+	4.45336i	0.209137	+	0.175487i
$645$		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
$650$	−56.9658	−	20.7339i	−2.23438	−	0.813249i
$651$		0			0
$652$	−0.766044	−	0.642788i	−0.0300006	−	0.0251735i
$653$	−3.00767	+	17.0574i	−0.117699	+	0.667506i	0.867679	+	0.497125i	$0.165611\pi$
$653$	−3.00767	+	17.0574i	−0.117699	+	0.667506i	−0.985378	+	0.170381i	$0.945500\pi$
$654$		0			0
$655$	9.19253	−	7.71345i	0.359182	−	0.301389i
$656$	8.66025	+	15.0000i	0.338126	+	0.585652i
$657$		0			0
$658$	−3.00000	+	5.19615i	−0.116952	+	0.202567i
$659$	4.81228	+	27.2918i	0.187460	+	1.06314i	0.922754	+	0.385389i	$0.125933\pi$
$659$	4.81228	+	27.2918i	0.187460	+	1.06314i	−0.735294	+	0.677748i	$0.762956\pi$
$660$		0			0
$661$	9.39693	−	3.42020i	0.365498	−	0.133030i	−0.152741	−	0.988266i	$-0.548810\pi$
$661$	9.39693	−	3.42020i	0.365498	−	0.133030i	0.518239	+	0.855236i	$0.326588\pi$
$662$	30.9243	−	11.2555i	1.20191	−	0.437459i
$663$		0			0
$664$	−2.08378	−	11.8177i	−0.0808663	−	0.458615i
$665$	−1.73205	+	3.00000i	−0.0671660	+	0.116335i
$666$		0			0
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	18.5756	−	15.5868i	0.718711	−	0.603070i
$669$		0			0
$670$	8.33511	−	47.2708i	0.322013	−	1.82623i
$671$	−5.30731	−	4.45336i	−0.204886	−	0.171920i
$672$		0			0
$673$	34.7686	+	12.6547i	1.34023	+	0.487805i	0.909886	−	0.414859i	$-0.136169\pi$
$673$	34.7686	+	12.6547i	1.34023	+	0.487805i	0.430346	+	0.902664i	$0.358391\pi$
$674$	8.66025			0.333581
$675$		0			0
$676$	12.0000			0.461538
$677$	−16.2760	−	5.92396i	−0.625536	−	0.227676i	0.00975136	−	0.999952i	$-0.496896\pi$
$677$	−16.2760	−	5.92396i	−0.625536	−	0.227676i	−0.635287	+	0.772276i	$0.719118\pi$
$678$		0			0
$679$	−13.0228	−	10.9274i	−0.499767	−	0.419355i
$680$		0			0
$681$		0			0
$682$	−22.9813	+	19.2836i	−0.880001	+	0.738408i
$683$	−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
$686$	3.90998	+	22.1746i	0.149284	+	0.846629i
$687$		0			0
$688$	−4.69846	+	1.71010i	−0.179127	+	0.0651970i
$689$	48.8279	−	17.7719i	1.86019	−	0.677055i
$690$		0			0
$691$	2.95202	+	16.7417i	0.112300	+	0.636885i	0.988052	+	0.154123i	$0.0492553\pi$
$691$	2.95202	+	16.7417i	0.112300	+	0.636885i	−0.875752	+	0.482762i	$0.839634\pi$
$692$	6.92820	−	12.0000i	0.263371	−	0.456172i
$693$		0			0
$694$	−21.0000	−	36.3731i	−0.797149	−	1.38070i
$695$	−34.4975	+	28.9469i	−1.30857	+	1.09802i
$696$		0			0
$697$		0			0
$698$	−1.32683	−	1.11334i	−0.0502212	−	0.0421406i
$699$		0			0
$700$	6.57785	+	2.39414i	0.248619	+	0.0904900i
$701$	−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
$704$	3.25519	+	1.18479i	0.122685	+	0.0446535i
$705$		0			0
$706$	22.9813	+	19.2836i	0.864914	+	0.725749i
$707$	2.40614	−	13.6459i	0.0904922	−	0.513207i
$708$		0			0
$709$	−14.5548	+	12.2130i	−0.546619	+	0.458668i	−0.873794	−	0.486296i	$-0.838348\pi$
$709$	−14.5548	+	12.2130i	−0.546619	+	0.458668i	0.327175	+	0.944964i	$0.393903\pi$
$710$	−31.1769	−	54.0000i	−1.17005	−	2.02658i
$711$		0			0
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$	−6.01535	−	34.1147i	−0.225277	−	1.27761i
$714$		0			0
$715$	56.3816	−	20.5212i	2.10855	−	0.767450i
$716$	19.5311	−	7.10876i	0.729913	−	0.265667i
$717$		0			0
$718$	9.37700	+	53.1796i	0.349947	+	1.98465i
$719$	−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
$722$	−23.8829	+	20.0401i	−0.888830	+	0.745817i
$723$		0			0
$724$	2.95202	−	16.7417i	0.109711	−	0.622202i
$725$	−18.5756	−	15.5868i	−0.689880	−	0.578878i
$726$		0			0
$727$	15.0351	+	5.47232i	0.557620	+	0.202957i	0.605429	−	0.795899i	$-0.293002\pi$
$727$	15.0351	+	5.47232i	0.557620	+	0.202957i	−0.0478087	+	0.998857i	$0.515224\pi$
$728$	8.66025			0.320970
$729$		0			0
$730$	12.0000			0.444140
$731$		0			0
$732$		0			0
$733$	31.4078	+	26.3543i	1.16007	+	0.973418i	0.999907	−	0.0136718i	$-0.00435201\pi$
$733$	31.4078	+	26.3543i	1.16007	+	0.973418i	0.160168	+	0.987090i	$0.448796\pi$
$734$	−4.81228	+	27.2918i	−0.177624	+	1.00736i
$735$		0			0
$736$	27.5776	−	23.1404i	1.01652	−	0.852965i
$737$	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	$0.0530307\pi$
$740$	−0.601535	−	3.41147i	−0.0221129	−	0.125408i
$741$		0			0
$742$	−16.9145	+	6.15636i	−0.620950	+	0.226007i
$743$	6.51038	−	2.36959i	0.238843	−	0.0869316i	−0.219826	−	0.975539i	$-0.570549\pi$
$743$	6.51038	−	2.36959i	0.238843	−	0.0869316i	0.458668	+	0.888608i	$0.348327\pi$
$744$		0			0
$745$	−4.16756	−	23.6354i	−0.152687	−	0.865934i
$746$	−19.9186	+	34.5000i	−0.729271	+	1.26313i
$747$		0			0
$748$		0			0
$749$	−7.96097	+	6.68004i	−0.290887	+	0.244084i
$750$		0			0
$751$	0.868241	−	4.92404i	0.0316826	−	0.179681i	−0.964860	−	0.262764i	$-0.915366\pi$
$751$	0.868241	−	4.92404i	0.0316826	−	0.179681i	0.996543	+	0.0830837i	$0.0264769\pi$
$752$	13.2683	+	11.1334i	0.483844	+	0.405994i
$753$		0			0
$754$	28.1908	+	10.2606i	1.02665	+	0.373669i
$755$	−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	$0.257361\pi$
$758$	30.9243	+	11.2555i	1.12322	+	0.408819i
$759$		0			0
$760$	4.59627	+	3.85673i	0.166724	+	0.139898i
$761$	−4.81228	+	27.2918i	−0.174445	+	0.989327i	0.764338	+	0.644816i	$0.223066\pi$
$761$	−4.81228	+	27.2918i	−0.174445	+	0.989327i	−0.938783	+	0.344510i	$0.888045\pi$
$762$		0			0
$763$	−13.0228	+	10.9274i	−0.471455	+	0.395598i
$764$	−3.46410	−	6.00000i	−0.125327	−	0.217072i
$765$		0			0
$766$	15.0000	−	25.9808i	0.541972	−	0.938723i
$767$	3.00767	+	17.0574i	0.108601	+	0.615906i
$768$		0			0
$769$	12.2160	−	4.44626i	0.440520	−	0.160336i	−0.112232	−	0.993682i	$-0.535800\pi$
$769$	12.2160	−	4.44626i	0.440520	−	0.160336i	0.552752	+	0.833346i	$0.313578\pi$
$770$	−19.5311	+	7.10876i	−0.703854	+	0.256182i
$771$		0			0
$772$	−1.73648	−	9.84808i	−0.0624973	−	0.354440i
$773$	−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
$776$	−22.5561	+	18.9268i	−0.809716	+	0.679432i
$777$		0			0
$778$	2.08378	−	11.8177i	0.0747071	−	0.423685i
$779$	−2.65366	−	2.22668i	−0.0950771	−	0.0797791i
$780$		0			0
$781$	33.8289	+	12.3127i	1.21049	+	0.440584i
$782$		0			0
$783$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.62760 - 0.592396i) q^{2} +(0.766044 + 0.642788i) q^{4} +(0.601535 - 3.41147i) q^{5} +(-0.766044 + 0.642788i) q^{7} +(0.866025 + 1.50000i) q^{8} +(-3.00000 + 5.19615i) q^{10} +(-0.601535 - 3.41147i) q^{11} +(-4.69846 + 1.71010i) q^{13} +(1.62760 - 0.592396i) q^{14} +(-0.868241 - 4.92404i) q^{16} +(0.500000 + 0.866025i) q^{19} +(2.65366 - 2.22668i) q^{20} +(-1.04189 + 5.90885i) q^{22} +(-5.30731 - 4.45336i) q^{23} +(-6.57785 - 2.39414i) q^{25} +8.66025 q^{26} -1.00000 q^{28} +(3.25519 + 1.18479i) q^{29} +(3.83022 + 3.21394i) q^{31} +(-0.902302 + 5.11721i) q^{32} +(1.73205 + 3.00000i) q^{35} +(0.500000 - 0.866025i) q^{37} +(-0.300767 - 1.70574i) q^{38} +(5.63816 - 2.05212i) q^{40} +(-3.25519 + 1.18479i) q^{41} +(-0.173648 - 0.984808i) q^{43} +(1.73205 - 3.00000i) q^{44} +(6.00000 + 10.3923i) q^{46} +(-2.65366 + 2.22668i) q^{47} +(-1.04189 + 5.90885i) q^{49} +(9.28780 + 7.79339i) q^{50} +(-4.69846 - 1.71010i) q^{52} -10.3923 q^{53} -12.0000 q^{55} +(-1.62760 - 0.592396i) q^{56} +(-4.59627 - 3.85673i) q^{58} +(0.601535 - 3.41147i) q^{59} +(1.53209 - 1.28558i) q^{61} +(-4.33013 - 7.50000i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(3.00767 + 17.0574i) q^{65} +(-7.51754 + 2.73616i) q^{67} +(-1.04189 - 5.90885i) q^{70} +(-5.19615 + 9.00000i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(-1.32683 + 1.11334i) q^{74} +(-0.173648 + 0.984808i) q^{76} +(2.65366 + 2.22668i) q^{77} +(0.939693 + 0.342020i) q^{79} -17.3205 q^{80} +6.00000 q^{82} +(-6.51038 - 2.36959i) q^{83} +(-0.300767 + 1.70574i) q^{86} +(4.59627 - 3.85673i) q^{88} +(-5.19615 - 9.00000i) q^{89} +(2.50000 - 4.33013i) q^{91} +(-1.20307 - 6.82295i) q^{92} +(5.63816 - 2.05212i) q^{94} +(3.25519 - 1.18479i) q^{95} +(2.95202 + 16.7417i) q^{97} +(5.19615 - 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 36 q^{10} + 6 q^{19} - 12 q^{28} + 6 q^{37} + 72 q^{46} - 144 q^{55} - 6 q^{64} - 12 q^{73} + 72 q^{82} + 30 q^{91}+O(q^{100}) \) 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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