LMFDB - Embedded newform 3971.1.bc.a.1560.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3971,1,Mod(262,3971)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3971, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([54, 55]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3971.262");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3971 = 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3971.bc (of order $90$, degree $24$, 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:	$1.98178716517$
Analytic rank:	$0$
Dimension:	$24$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.5285401.1

Embedding invariants

Embedding label			1560.1
Root			$0.0348995 - 0.999391i$ of defining polynomial
Character	$\chi$	$=$	3971.1560
Dual form			3971.1.bc.a.3943.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.559193 + 0.829038i) q^{4} +(0.996161 + 1.27503i) q^{5} +(0.169131 - 1.60917i) q^{7} +(0.990268 + 0.139173i) q^{9} +(-0.104528 - 0.994522i) q^{11} +(-0.374607 + 0.927184i) q^{16} +(0.612019 - 0.0860137i) q^{17} +(-0.500000 + 1.53884i) q^{20} +(-0.580762 - 0.211380i) q^{23} +(-0.391438 + 1.56997i) q^{25} +(1.42864 - 0.759621i) q^{28} +(2.22022 - 1.38735i) q^{35} +(0.438371 + 0.898794i) q^{36} +(-0.580762 + 0.211380i) q^{43} +(0.766044 - 0.642788i) q^{44} +(0.809017 + 1.40126i) q^{45} +(-0.444576 - 0.429322i) q^{47} +(-1.58268 - 0.336408i) q^{49} +(1.16392 - 1.12398i) q^{55} +(0.0215691 - 0.617657i) q^{61} +(0.391438 - 1.56997i) q^{63} +(-0.978148 + 0.207912i) q^{64} +(0.413545 + 0.459289i) q^{68} +(-0.483844 - 1.94059i) q^{73} -1.61803 q^{77} +(-1.55535 + 0.445991i) q^{80} +(0.961262 + 0.275637i) q^{81} +(-1.08268 + 1.20243i) q^{83} +(0.719340 + 0.694658i) q^{85} +(-0.149516 - 0.599676i) q^{92} +(0.0348995 - 0.999391i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{7} + 3 q^{11} - 12 q^{20} + 6 q^{45} - 6 q^{49} + 3 q^{64} - 9 q^{68} - 12 q^{77} + 6 q^{83}+O(q^{100}) $ 24 * q - 9 * q^7 + 3 * q^11 - 12 * q^20 + 6 * q^45 - 6 * q^49 + 3 * q^64 - 9 * q^68 - 12 * q^77 + 6 * q^83

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3971\mathbb{Z}\right)^\times$.

$n$	$1806$	$2168$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{18}\right)$

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			0		−0.882948	−	0.469472i	$-0.844444\pi$
$2$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$3$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$3$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$4$	0.559193	+	0.829038i	0.559193	+	0.829038i
$5$	0.996161	+	1.27503i	0.996161	+	1.27503i	0.961262	+	0.275637i	$0.0888889\pi$
$5$	0.996161	+	1.27503i	0.996161	+	1.27503i	0.0348995	+	0.999391i	$0.488889\pi$
$6$		0			0
$7$	0.169131	−	1.60917i	0.169131	−	1.60917i	−0.500000	−	0.866025i	$-0.666667\pi$
$7$	0.169131	−	1.60917i	0.169131	−	1.60917i	0.669131	−	0.743145i	$-0.266667\pi$
$8$		0			0
$9$	0.990268	+	0.139173i	0.990268	+	0.139173i
$10$		0			0
$11$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$11$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$12$		0			0
$13$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$13$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$14$		0			0
$15$		0			0
$16$	−0.374607	+	0.927184i	−0.374607	+	0.927184i
$17$	0.612019	−	0.0860137i	0.612019	−	0.0860137i	0.173648	−	0.984808i	$-0.444444\pi$
$17$	0.612019	−	0.0860137i	0.612019	−	0.0860137i	0.438371	+	0.898794i	$0.355556\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$21$		0			0
$22$		0			0
$23$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$23$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$24$		0			0
$25$	−0.391438	+	1.56997i	−0.391438	+	1.56997i
$26$		0			0
$27$		0			0
$28$	1.42864	−	0.759621i	1.42864	−	0.759621i
$29$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$29$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$30$		0			0
$31$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$31$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.22022	−	1.38735i	2.22022	−	1.38735i
$36$	0.438371	+	0.898794i	0.438371	+	0.898794i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$41$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$42$		0			0
$43$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	−0.615661	−	0.788011i	$-0.711111\pi$
$43$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	0.0348995	+	0.999391i	$0.488889\pi$
$44$	0.766044	−	0.642788i	0.766044	−	0.642788i
$45$	0.809017	+	1.40126i	0.809017	+	1.40126i
$46$		0			0
$47$	−0.444576	−	0.429322i	−0.444576	−	0.429322i	0.438371	−	0.898794i	$-0.355556\pi$
$47$	−0.444576	−	0.429322i	−0.444576	−	0.429322i	−0.882948	+	0.469472i	$0.844444\pi$
$48$		0			0
$49$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$53$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$54$		0			0
$55$	1.16392	−	1.12398i	1.16392	−	1.12398i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.719340	−	0.694658i	$-0.244444\pi$
$59$		0			0		−0.719340	+	0.694658i	$0.755556\pi$
$60$		0			0
$61$	0.0215691	−	0.617657i	0.0215691	−	0.617657i	−0.939693	−	0.342020i	$-0.888889\pi$
$61$	0.0215691	−	0.617657i	0.0215691	−	0.617657i	0.961262	−	0.275637i	$-0.0888889\pi$
$62$		0			0
$63$	0.391438	−	1.56997i	0.391438	−	1.56997i
$64$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$65$		0			0
$66$		0			0
$67$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$67$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$68$	0.413545	+	0.459289i	0.413545	+	0.459289i
$69$		0			0
$70$		0			0
$71$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$71$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$72$		0			0
$73$	−0.483844	−	1.94059i	−0.483844	−	1.94059i	−0.241922	−	0.970296i	$-0.577778\pi$
$73$	−0.483844	−	1.94059i	−0.483844	−	1.94059i	−0.241922	−	0.970296i	$-0.577778\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.61803			−1.61803
$78$		0			0
$79$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$79$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$80$	−1.55535	+	0.445991i	−1.55535	+	0.445991i
$81$	0.961262	+	0.275637i	0.961262	+	0.275637i
$82$		0			0
$83$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.104528	+	0.994522i	$0.533333\pi$
$83$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.978148	+	0.207912i	$0.933333\pi$
$84$		0			0
$85$	0.719340	+	0.694658i	0.719340	+	0.694658i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$89$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$90$		0			0
$91$		0			0
$92$	−0.149516	−	0.599676i	−0.149516	−	0.599676i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$97$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$98$		0			0
$99$	0.0348995	−	0.999391i	0.0348995	−	0.999391i
$100$	−1.52045	+	0.553400i	−1.52045	+	0.553400i
$101$	0.606126	+	1.50021i	0.606126	+	1.50021i	0.848048	+	0.529919i	$0.177778\pi$
$101$	0.606126	+	1.50021i	0.606126	+	1.50021i	−0.241922	+	0.970296i	$0.577778\pi$
$102$		0			0
$103$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$103$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$107$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$108$		0			0
$109$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$109$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$110$		0			0
$111$		0			0
$112$	1.42864	+	0.759621i	1.42864	+	0.759621i
$113$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$113$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$120$		0			0
$121$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$126$		0			0
$127$		0			0		−0.848048	−	0.529919i	$-0.822222\pi$
$127$		0			0		0.848048	+	0.529919i	$0.177778\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	0.438371	+	0.898794i	$0.355556\pi$
$131$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	−0.719340	+	0.694658i	$0.755556\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.0564686	+	1.61705i	−0.0564686	+	1.61705i	0.559193	+	0.829038i	$0.311111\pi$
$137$	−0.0564686	+	1.61705i	−0.0564686	+	1.61705i	−0.615661	+	0.788011i	$0.711111\pi$
$138$		0			0
$139$	−0.616528	+	0.0431119i	−0.616528	+	0.0431119i	−0.374607	−	0.927184i	$-0.622222\pi$
$139$	−0.616528	+	0.0431119i	−0.616528	+	0.0431119i	−0.241922	+	0.970296i	$0.577778\pi$
$140$	2.39169	+	1.06485i	2.39169	+	1.06485i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.749213	+	1.85437i	−0.749213	+	1.85437i	−0.374607	+	0.927184i	$0.622222\pi$
$149$	−0.749213	+	1.85437i	−0.749213	+	1.85437i	−0.374607	+	0.927184i	$0.622222\pi$
$150$		0			0
$151$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$151$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$152$		0			0
$153$	0.618034			0.618034
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.904793	+	1.34141i	−0.904793	+	1.34141i	0.0348995	+	0.999391i	$0.488889\pi$
$157$	−0.904793	+	1.34141i	−0.904793	+	1.34141i	−0.939693	+	0.342020i	$0.888889\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$162$		0			0
$163$	−1.08268	−	1.20243i	−1.08268	−	1.20243i	−0.978148	−	0.207912i	$-0.933333\pi$
$163$	−1.08268	−	1.20243i	−1.08268	−	1.20243i	−0.104528	−	0.994522i	$-0.533333\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.615661	−	0.788011i	$-0.288889\pi$
$167$		0			0		−0.615661	+	0.788011i	$0.711111\pi$
$168$		0			0
$169$	−0.719340	+	0.694658i	−0.719340	+	0.694658i
$170$		0			0
$171$		0			0
$172$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$173$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$173$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$174$		0			0
$175$	2.46015	+	0.895420i	2.46015	+	0.895420i
$176$	0.961262	+	0.275637i	0.961262	+	0.275637i
$177$		0			0
$178$		0			0
$179$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$179$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$180$	−0.709299	+	1.45428i	−0.709299	+	1.45428i
$181$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$181$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.149516	−	0.599676i	−0.149516	−	0.599676i
$188$	0.107320	−	0.608645i	0.107320	−	0.608645i
$189$		0			0
$190$		0			0
$191$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$191$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$192$		0			0
$193$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$193$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$194$		0			0
$195$		0			0
$196$	−0.606126	−	1.50021i	−0.606126	−	1.50021i
$197$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$197$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$198$		0			0
$199$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$199$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.545692	−	0.290149i	−0.545692	−	0.290149i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.882948	−	0.469472i	$-0.844444\pi$
$211$		0			0		0.882948	+	0.469472i	$0.155556\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.848048	−	0.529919i	−0.848048	−	0.529919i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	1.58268	+	0.336408i	1.58268	+	0.336408i
$221$		0			0
$222$		0			0
$223$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$223$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$224$		0			0
$225$	−0.606126	+	1.50021i	−0.606126	+	1.50021i
$226$		0			0
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$		0			0
$229$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$229$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0564686	−	1.61705i	−0.0564686	−	1.61705i	−0.615661	−	0.788011i	$-0.711111\pi$
$233$	−0.0564686	−	1.61705i	−0.0564686	−	1.61705i	0.559193	−	0.829038i	$-0.311111\pi$
$234$		0			0
$235$	0.104528	−	0.994522i	0.104528	−	0.994522i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$239$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$240$		0			0
$241$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$241$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$242$		0			0
$243$		0			0
$244$	0.524123	−	0.327508i	0.524123	−	0.327508i
$245$	−1.14767	−	2.35307i	−1.14767	−	2.35307i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.380500	+	0.487017i	−0.380500	+	0.487017i	−0.939693	−	0.342020i	$-0.888889\pi$
$251$	−0.380500	+	0.487017i	−0.380500	+	0.487017i	0.559193	+	0.829038i	$0.311111\pi$
$252$	1.52045	−	0.553400i	1.52045	−	0.553400i
$253$	−0.149516	+	0.599676i	−0.149516	+	0.599676i
$254$		0			0
$255$		0			0
$256$	−0.719340	−	0.694658i	−0.719340	−	0.694658i
$257$		0			0		0.438371	−	0.898794i	$-0.355556\pi$
$257$		0			0		−0.438371	+	0.898794i	$0.644444\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$263$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.374607	−	0.927184i	$-0.377778\pi$
$269$		0			0		−0.374607	+	0.927184i	$0.622222\pi$
$270$		0			0
$271$	0.594092	+	0.170353i	0.594092	+	0.170353i	0.559193	−	0.829038i	$-0.311111\pi$
$271$	0.594092	+	0.170353i	0.594092	+	0.170353i	0.0348995	+	0.999391i	$0.488889\pi$
$272$	−0.149516	+	0.599676i	−0.149516	+	0.599676i
$273$		0			0
$274$		0			0
$275$	1.60229	+	0.225187i	1.60229	+	0.225187i
$276$		0			0
$277$	1.33826	+	1.48629i	1.33826	+	1.48629i	0.669131	+	0.743145i	$0.266667\pi$
$277$	1.33826	+	1.48629i	1.33826	+	1.48629i	0.669131	+	0.743145i	$0.266667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.0348995	−	0.999391i	$-0.488889\pi$
$281$		0			0		−0.0348995	+	0.999391i	$0.511111\pi$
$282$		0			0
$283$	−0.709299	−	1.45428i	−0.709299	−	1.45428i	−0.882948	−	0.469472i	$-0.844444\pi$
$283$	−0.709299	−	1.45428i	−0.709299	−	1.45428i	0.173648	−	0.984808i	$-0.444444\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.594092	+	0.170353i	−0.594092	+	0.170353i
$290$		0			0
$291$		0			0
$292$	1.33826	−	1.48629i	1.33826	−	1.48629i
$293$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$293$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	0.241922	+	0.970296i	0.241922	+	0.970296i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.809017	−	0.587785i	0.809017	−	0.587785i
$306$		0			0
$307$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$307$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$308$	−0.904793	−	1.34141i	−0.904793	−	1.34141i
$309$		0			0
$310$		0			0
$311$	0.564602	+	0.251377i	0.564602	+	0.251377i	0.669131	−	0.743145i	$-0.266667\pi$
$311$	0.564602	+	0.251377i	0.564602	+	0.251377i	−0.104528	+	0.994522i	$0.533333\pi$
$312$		0			0
$313$	−0.545692	+	0.290149i	−0.545692	+	0.290149i	−0.719340	−	0.694658i	$-0.755556\pi$
$313$	−0.545692	+	0.290149i	−0.545692	+	0.290149i	0.173648	+	0.984808i	$0.444444\pi$
$314$		0			0
$315$	2.39169	−	1.06485i	2.39169	−	1.06485i
$316$		0			0
$317$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$317$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$318$		0			0
$319$		0			0
$320$	−1.23949	−	1.04005i	−1.23949	−	1.04005i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.309017	+	0.951057i	0.309017	+	0.951057i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−1.60229	−	0.225187i	−1.60229	−	0.225187i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$337$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$338$		0			0
$339$		0			0
$340$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$341$		0			0
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.380500	−	0.487017i	−0.380500	−	0.487017i	0.559193	−	0.829038i	$-0.311111\pi$
$347$	−0.380500	−	0.487017i	−0.380500	−	0.487017i	−0.939693	+	0.342020i	$0.888889\pi$
$348$		0			0
$349$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.978148	+	0.207912i	$0.933333\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$353$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.444576	+	0.429322i	−0.444576	+	0.429322i	−0.882948	−	0.469472i	$-0.844444\pi$
$359$	−0.444576	+	0.429322i	−0.444576	+	0.429322i	0.438371	+	0.898794i	$0.355556\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.99232	−	2.55006i	1.99232	−	2.55006i
$366$		0			0
$367$	1.61409	−	0.112868i	1.61409	−	0.112868i	0.766044	−	0.642788i	$-0.222222\pi$
$367$	1.61409	−	0.112868i	1.61409	−	0.112868i	0.848048	+	0.529919i	$0.177778\pi$
$368$	0.413545	−	0.459289i	0.413545	−	0.459289i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$379$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.848048	−	0.529919i	$-0.177778\pi$
$383$		0			0		−0.848048	+	0.529919i	$0.822222\pi$
$384$		0			0
$385$	−1.61182	−	2.06304i	−1.61182	−	2.06304i
$386$		0			0
$387$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$388$		0			0
$389$	0.270928	−	0.555485i	0.270928	−	0.555485i	−0.719340	−	0.694658i	$-0.755556\pi$
$389$	0.270928	−	0.555485i	0.270928	−	0.555485i	0.990268	+	0.139173i	$0.0444444\pi$
$390$		0			0
$391$	−0.373619	−	0.0794152i	−0.373619	−	0.0794152i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	0.848048	−	0.529919i	0.848048	−	0.529919i
$397$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$397$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$398$		0			0
$399$		0			0
$400$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$401$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$401$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$402$		0			0
$403$		0			0
$404$	−0.904793	+	1.34141i	−0.904793	+	1.34141i
$405$	0.606126	+	1.50021i	0.606126	+	1.50021i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$409$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.61166	−	0.182625i	−2.61166	−	0.182625i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$419$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$421$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$422$		0			0
$423$	−0.380500	−	0.487017i	−0.380500	−	0.487017i
$424$		0			0
$425$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$426$		0			0
$427$	−0.990268	−	0.139173i	−0.990268	−	0.139173i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.374607	−	0.927184i	$-0.622222\pi$
$431$		0			0		0.374607	+	0.927184i	$0.377778\pi$
$432$		0			0
$433$		0			0		−0.559193	−	0.829038i	$-0.688889\pi$
$433$		0			0		0.559193	+	0.829038i	$0.311111\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$439$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$440$		0			0
$441$	−1.52045	−	0.553400i	−1.52045	−	0.553400i
$442$		0			0
$443$	0.391438	−	1.56997i	0.391438	−	1.56997i	−0.374607	−	0.927184i	$-0.622222\pi$
$443$	0.391438	−	1.56997i	0.391438	−	1.56997i	0.766044	−	0.642788i	$-0.222222\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.169131	+	1.60917i	0.169131	+	1.60917i
$449$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$449$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$458$		0			0
$459$		0			0
$460$	0.615661	−	0.788011i	0.615661	−	0.788011i
$461$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.559193	−	0.829038i	$-0.311111\pi$
$461$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.961262	+	0.275637i	$0.0888889\pi$
$462$		0			0
$463$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$463$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.913545	−	0.406737i	$-0.133333\pi$
$467$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.669131	+	0.743145i	$0.266667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.270928	+	0.555485i	0.270928	+	0.555485i
$474$		0			0
$475$		0			0
$476$	0.809017	−	0.587785i	0.809017	−	0.587785i
$477$		0			0
$478$		0			0
$479$	0.0215691	−	0.617657i	0.0215691	−	0.617657i	−0.939693	−	0.342020i	$-0.888889\pi$
$479$	0.0215691	−	0.617657i	0.0215691	−	0.617657i	0.961262	−	0.275637i	$-0.0888889\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.719340	−	0.694658i	−0.719340	−	0.694658i
$485$		0			0
$486$		0			0
$487$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$487$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.391438	+	1.56997i	0.391438	+	1.56997i	0.766044	+	0.642788i	$0.222222\pi$
$491$	0.391438	+	1.56997i	0.391438	+	1.56997i	−0.374607	+	0.927184i	$0.622222\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	1.30902	−	0.951057i	1.30902	−	0.951057i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.55535	−	0.445991i	−1.55535	−	0.445991i	−0.615661	−	0.788011i	$-0.711111\pi$
$499$	−1.55535	−	0.445991i	−1.55535	−	0.445991i	−0.939693	+	0.342020i	$0.888889\pi$
$500$	−0.848048	−	0.529919i	−0.848048	−	0.529919i
$501$		0			0
$502$		0			0
$503$	−1.43868	−	1.38932i	−1.43868	−	1.38932i	−0.719340	−	0.694658i	$-0.755556\pi$
$503$	−1.43868	−	1.38932i	−1.43868	−	1.38932i	−0.719340	−	0.694658i	$-0.755556\pi$
$504$		0			0
$505$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$509$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$510$		0			0
$511$	−3.20457	+	0.450374i	−3.20457	+	0.450374i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.380500	+	0.487017i	−0.380500	+	0.487017i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$521$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$522$		0			0
$523$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$523$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$524$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.473442	−	0.397265i	−0.473442	−	0.397265i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$540$		0			0
$541$	0.612019	+	0.0860137i	0.612019	+	0.0860137i	0.438371	−	0.898794i	$-0.355556\pi$
$541$	0.612019	+	0.0860137i	0.612019	+	0.0860137i	0.173648	+	0.984808i	$0.444444\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.961262	−	0.275637i	$-0.0888889\pi$
$547$		0			0		−0.961262	+	0.275637i	$0.911111\pi$
$548$	−1.37217	+	0.857427i	−1.37217	+	0.857427i
$549$	0.107320	−	0.608645i	0.107320	−	0.608645i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.380500	−	0.487017i	−0.380500	−	0.487017i
$557$	1.61409	−	0.112868i	1.61409	−	0.112868i	0.766044	−	0.642788i	$-0.222222\pi$
$557$	1.61409	−	0.112868i	1.61409	−	0.112868i	0.848048	+	0.529919i	$0.177778\pi$
$558$		0			0
$559$		0			0
$560$	0.454617	+	2.57826i	0.454617	+	2.57826i
$561$		0			0
$562$		0			0
$563$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$563$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.606126	−	1.50021i	0.606126	−	1.50021i
$568$		0			0
$569$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$569$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$570$		0			0
$571$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$571$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.559193	−	0.829038i	0.559193	−	0.829038i
$576$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$577$	1.33826	−	1.48629i	1.33826	−	1.48629i	0.669131	−	0.743145i	$-0.266667\pi$
$577$	1.33826	−	1.48629i	1.33826	−	1.48629i	0.669131	−	0.743145i	$-0.266667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.75181	+	1.94558i	1.75181	+	1.94558i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.43868	+	1.38932i	−1.43868	+	1.38932i	−0.719340	+	0.694658i	$0.755556\pi$
$587$	−1.43868	+	1.38932i	−1.43868	+	1.38932i	−0.719340	+	0.694658i	$0.755556\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$593$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$594$		0			0
$595$	1.23949	−	1.04005i	1.23949	−	1.04005i
$596$	−1.95630	+	0.415823i	−1.95630	+	0.415823i
$597$		0			0
$598$		0			0
$599$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$599$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$600$		0			0
$601$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$601$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.23949	−	1.04005i	−1.23949	−	1.04005i
$606$		0			0
$607$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$607$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.345600	+	0.512373i	0.345600	+	0.512373i
$613$	0.345600	−	0.512373i	0.345600	−	0.512373i	−0.615661	−	0.788011i	$-0.711111\pi$
$613$	0.345600	−	0.512373i	0.345600	−	0.512373i	0.961262	+	0.275637i	$0.0888889\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$617$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$618$		0			0
$619$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$619$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$	−1.61803			−1.61803
$629$		0			0
$630$		0			0
$631$	1.11839	+	1.65808i	1.11839	+	1.65808i	0.559193	+	0.829038i	$0.311111\pi$
$631$	1.11839	+	1.65808i	1.11839	+	1.65808i	0.559193	+	0.829038i	$0.311111\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.559193	−	0.829038i	$-0.311111\pi$
$641$		0			0		−0.559193	+	0.829038i	$0.688889\pi$
$642$		0			0
$643$	−0.231520	+	0.573031i	−0.231520	+	0.573031i	−0.997564	−	0.0697565i	$-0.977778\pi$
$643$	−0.231520	+	0.573031i	−0.231520	+	0.573031i	0.766044	+	0.642788i	$0.222222\pi$
$644$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$645$		0			0
$646$		0			0
$647$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$647$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.391438	−	1.56997i	0.391438	−	1.56997i
$653$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	0.913545	+	0.406737i	$0.133333\pi$
$653$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	−0.978148	+	0.207912i	$0.933333\pi$
$654$		0			0
$655$	−2.31159	+	1.22909i	−2.31159	+	1.22909i
$656$		0			0
$657$	−0.209057	−	1.98904i	−0.209057	−	1.98904i
$658$		0			0
$659$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$659$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$660$		0			0
$661$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$661$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.616528	+	0.0431119i	−0.616528	+	0.0431119i
$672$		0			0
$673$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$673$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$674$		0			0
$675$		0			0
$676$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$677$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$677$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$686$		0			0
$687$		0			0
$688$	0.0215691	−	0.617657i	0.0215691	−	0.617657i
$689$		0			0
$690$		0			0
$691$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.669131	−	0.743145i	$-0.266667\pi$
$691$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$692$		0			0
$693$	−1.60229	−	0.225187i	−1.60229	−	0.225187i
$694$		0			0
$695$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.633360	+	2.54027i	0.633360	+	2.54027i
$701$	0.270928	+	0.555485i	0.270928	+	0.555485i	0.990268	−	0.139173i	$-0.0444444\pi$
$701$	0.270928	+	0.555485i	0.270928	+	0.555485i	−0.719340	+	0.694658i	$0.755556\pi$
$702$		0			0
$703$		0			0
$704$	0.309017	+	0.951057i	0.309017	+	0.951057i
$705$		0			0
$706$		0			0
$707$	2.51662	−	0.721628i	2.51662	−	0.721628i
$708$		0			0
$709$	−1.37217	−	0.857427i	−1.37217	−	0.857427i	−0.374607	−	0.927184i	$-0.622222\pi$
$709$	−1.37217	−	0.857427i	−1.37217	−	0.857427i	−0.997564	+	0.0697565i	$0.977778\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.391438	+	1.56997i	0.391438	+	1.56997i	0.766044	+	0.642788i	$0.222222\pi$
$719$	0.391438	+	1.56997i	0.391438	+	1.56997i	−0.374607	+	0.927184i	$0.622222\pi$
$720$	−1.60229	+	0.225187i	−1.60229	+	0.225187i
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	−0.615661	−	0.788011i	$-0.711111\pi$
$727$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	0.0348995	+	0.999391i	$0.488889\pi$
$728$		0			0
$729$	0.913545	+	0.406737i	0.913545	+	0.406737i
$730$		0			0
$731$	−0.337256	+	0.179322i	−0.337256	+	0.179322i
$732$		0			0
$733$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.978148	−	0.207912i	$-0.933333\pi$
$733$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.500000	+	0.866025i	$0.666667\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	1.42864	+	0.759621i	1.42864	+	0.759621i	0.990268	−	0.139173i	$-0.0444444\pi$
$739$	1.42864	+	0.759621i	1.42864	+	0.759621i	0.438371	+	0.898794i	$0.355556\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.990268	−	0.139173i	$-0.0444444\pi$
$743$		0			0		−0.990268	+	0.139173i	$0.955556\pi$
$744$		0			0
$745$	−3.11071	+	0.891981i	−3.11071	+	0.891981i
$746$		0			0
$747$	−1.23949	+	1.04005i	−1.23949	+	1.04005i
$748$	0.413545	−	0.459289i	0.413545	−	0.459289i
$749$		0			0
$750$		0			0
$751$		0			0		−0.719340	−	0.694658i	$-0.755556\pi$
$751$		0			0		0.719340	+	0.694658i	$0.244444\pi$
$752$	0.564602	−	0.251377i	0.564602	−	0.251377i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.69610	−	1.05984i	1.69610	−	1.05984i	0.848048	−	0.529919i	$-0.177778\pi$
$757$	1.69610	−	1.05984i	1.69610	−	1.05984i	0.848048	−	0.529919i	$-0.177778\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$761$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$762$		0			0
$763$		0			0
$764$	−0.0564686	+	1.61705i	−0.0564686	+	1.61705i
$765$	0.615661	+	0.788011i	0.615661	+	0.788011i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$769$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$773$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.904793	−	1.34141i	0.904793	−	1.34141i
$785$	−2.61166	+	0.182625i	−2.61166	+	0.182625i
$786$		0			0
$787$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$787$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$788$	0.876742	−	1.79759i	0.876742	−	1.79759i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.16392	−	1.12398i	1.16392	−	1.12398i
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$804$		0			0
$805$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.913545	−	0.406737i	$-0.133333\pi$
$809$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.669131	+	0.743145i	$0.266667\pi$
$810$		0			0
$811$		0			0		0.241922	−	0.970296i	$-0.422222\pi$
$811$		0			0		−0.241922	+	0.970296i	$0.577778\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.454617	−	2.57826i	0.454617	−	2.57826i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.345600	+	0.512373i	0.345600	+	0.512373i	0.961262	−	0.275637i	$-0.0888889\pi$
$821$	0.345600	+	0.512373i	0.345600	+	0.512373i	−0.615661	+	0.788011i	$0.711111\pi$
$822$		0			0
$823$	0.606126	+	1.50021i	0.606126	+	1.50021i	0.848048	+	0.529919i	$0.177778\pi$
$823$	0.606126	+	1.50021i	0.606126	+	1.50021i	−0.241922	+	0.970296i	$0.577778\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.990268	−	0.139173i	$-0.955556\pi$
$827$		0			0		0.990268	+	0.139173i	$0.0444444\pi$
$828$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$829$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$829$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.997564	−	0.0697565i	−0.997564	−	0.0697565i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$839$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$840$		0			0
$841$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.60229	−	0.225187i	−1.60229	−	0.225187i
$846$		0			0
$847$	0.169131	+	1.60917i	0.169131	+	1.60917i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.612019	−	0.0860137i	0.612019	−	0.0860137i	0.173648	−	0.984808i	$-0.444444\pi$
$853$	0.612019	−	0.0860137i	0.612019	−	0.0860137i	0.438371	+	0.898794i	$0.355556\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$857$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$858$		0			0
$859$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$859$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$860$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$861$		0			0
$862$		0			0
$863$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$863$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.500000	+	1.53884i	0.500000	+	1.53884i
$876$		0			0
$877$		0			0		−0.997564	−	0.0697565i	$-0.977778\pi$
$877$		0			0		0.997564	+	0.0697565i	$0.0222222\pi$
$878$		0			0
$879$		0			0
$880$	0.606126	+	1.50021i	0.606126	+	1.50021i
$881$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$882$		0			0
$883$	1.16392	+	1.12398i	1.16392	+	1.12398i	0.990268	+	0.139173i	$0.0444444\pi$
$883$	1.16392	+	1.12398i	1.16392	+	1.12398i	0.173648	+	0.984808i	$0.444444\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.997564	−	0.0697565i	$-0.0222222\pi$
$887$		0			0		−0.997564	+	0.0697565i	$0.977778\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.173648	−	0.984808i	0.173648	−	0.984808i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.615661	−	0.788011i	$-0.711111\pi$
$907$		0			0		0.615661	+	0.788011i	$0.288889\pi$
$908$		0			0
$909$	0.391438	+	1.56997i	0.391438	+	1.56997i
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$	1.30902	+	0.951057i	1.30902	+	0.951057i
$914$		0			0
$915$		0			0
$916$	0.594092	−	0.170353i	0.594092	−	0.170353i
$917$	2.51662	+	0.721628i	2.51662	+	0.721628i
$918$		0			0
$919$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.104528	+	0.994522i	$0.533333\pi$
$919$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.978148	+	0.207912i	$0.933333\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.612019	−	0.0860137i	0.612019	−	0.0860137i	0.173648	−	0.984808i	$-0.444444\pi$
$929$	0.612019	−	0.0860137i	0.612019	−	0.0860137i	0.438371	+	0.898794i	$0.355556\pi$
$930$		0			0
$931$		0			0
$932$	1.30902	−	0.951057i	1.30902	−	0.951057i
$933$		0			0
$934$		0			0
$935$	0.615661	−	0.788011i	0.615661	−	0.788011i
$936$		0			0
$937$	−0.231520	−	0.573031i	−0.231520	−	0.573031i	0.766044	−	0.642788i	$-0.222222\pi$
$937$	−0.231520	−	0.573031i	−0.231520	−	0.573031i	−0.997564	+	0.0697565i	$0.977778\pi$
$938$		0			0
$939$		0			0
$940$	0.882948	−	0.469472i	0.882948	−	0.469472i
$941$		0			0		0.882948	−	0.469472i	$-0.155556\pi$
$941$		0			0		−0.882948	+	0.469472i	$0.844444\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.997564	−	0.0697565i	$-0.977778\pi$
$947$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.241922	−	0.970296i	$-0.577778\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.241922	−	0.970296i	$-0.577778\pi$
$953$		0			0		0.241922	+	0.970296i	$0.422222\pi$
$954$		0			0
$955$	0.0913681	+	2.61644i	0.0913681	+	2.61644i
$956$	0.473442	−	0.397265i	0.473442	−	0.397265i
$957$		0			0
$958$		0			0
$959$	2.59256	+	0.364360i	2.59256	+	0.364360i
$960$		0			0
$961$	0.913545	−	0.406737i	0.913545	−	0.406737i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$967$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.438371	−	0.898794i	$-0.644444\pi$
$971$		0			0		0.438371	+	0.898794i	$0.355556\pi$
$972$		0			0
$973$	−0.0348995	+	0.999391i	−0.0348995	+	0.999391i
$974$		0			0
$975$		0			0
$976$	0.564602	+	0.251377i	0.564602	+	0.251377i
$977$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$977$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$978$		0			0
$979$		0			0
$980$	1.30902	−	2.26728i	1.30902	−	2.26728i
$981$		0			0
$982$		0			0
$983$		0			0		−0.961262	−	0.275637i	$-0.911111\pi$
$983$		0			0		0.961262	+	0.275637i	$0.0888889\pi$
$984$		0			0
$985$	1.21225	−	3.00043i	1.21225	−	3.00043i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.381966			0.381966
$990$		0			0
$991$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$991$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.75181	−	1.94558i	1.75181	−	1.94558i
$996$		0			0
$997$	−0.709299	+	1.45428i	−0.709299	+	1.45428i	0.173648	+	0.984808i	$0.444444\pi$
$997$	−0.709299	+	1.45428i	−0.709299	+	1.45428i	−0.882948	+	0.469472i	$0.844444\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3971.1.bc.a.1560.1		24
11.5	even	5	inner	3971.1.bc.a.2282.1		24
19.2	odd	18		3971.1.s.a.3903.1		8
19.3	odd	18		209.1.m.a.75.1	✓	4
19.4	even	9	inner	3971.1.bc.a.1571.1		24
19.5	even	9		3971.1.s.a.2957.1		8
19.6	even	9	inner	3971.1.bc.a.262.1		24
19.7	even	3	inner	3971.1.bc.a.2473.1		24
19.8	odd	6	inner	3971.1.bc.a.1021.1		24
19.9	even	9	inner	3971.1.bc.a.3221.1		24
19.10	odd	18	inner	3971.1.bc.a.3221.1		24
19.11	even	3	inner	3971.1.bc.a.1021.1		24
19.12	odd	6	inner	3971.1.bc.a.2473.1		24
19.13	odd	18	inner	3971.1.bc.a.262.1		24
19.14	odd	18		3971.1.s.a.2957.1		8
19.15	odd	18	inner	3971.1.bc.a.1571.1		24
19.16	even	9		209.1.m.a.75.1	✓	4
19.17	even	9		3971.1.s.a.3903.1		8
19.18	odd	2	CM	3971.1.bc.a.1560.1		24
57.35	odd	18		1881.1.bv.a.1747.1		4
57.41	even	18		1881.1.bv.a.1747.1		4
76.3	even	18		3344.1.bx.a.1329.1		4
76.35	odd	18		3344.1.bx.a.1329.1		4
209.3	odd	90		2299.1.m.b.1291.1		4
209.5	even	45		3971.1.s.a.3679.1		8
209.16	even	45		209.1.m.a.170.1	yes	4
209.27	odd	30	inner	3971.1.bc.a.1743.1		24
209.35	odd	90		2299.1.m.c.1576.1		4
209.41	even	90		2299.1.m.c.1291.1		4
209.49	even	15	inner	3971.1.bc.a.1743.1		24
209.54	odd	18		2299.1.m.a.493.1		4
209.60	odd	90		209.1.m.a.170.1	yes	4
209.71	odd	90		3971.1.s.a.3679.1		8
209.73	odd	90		2299.1.b.b.1937.1		2
209.79	even	90		2299.1.m.c.1576.1		4
209.82	even	45	inner	3971.1.bc.a.984.1		24
209.92	even	45		2299.1.b.a.1937.1		2
209.93	even	45		3971.1.s.a.654.1		8
209.98	even	18		2299.1.m.a.493.1		4
209.104	even	45	inner	3971.1.bc.a.3943.1		24
209.117	even	90		2299.1.b.b.1937.1		2
209.126	odd	30	inner	3971.1.bc.a.3195.1		24
209.130	even	45		2299.1.m.b.1576.1		4
209.136	odd	90		2299.1.b.a.1937.1		2
209.137	even	45	inner	3971.1.bc.a.2293.1		24
209.148	odd	90	inner	3971.1.bc.a.2293.1		24
209.149	odd	90		2299.1.m.a.1842.1		4
209.159	even	15	inner	3971.1.bc.a.3195.1		24
209.168	even	45		2299.1.m.b.1291.1		4
209.170	odd	10	inner	3971.1.bc.a.2282.1		24
209.174	odd	90		2299.1.m.b.1576.1		4
209.181	odd	90	inner	3971.1.bc.a.3943.1		24
209.192	odd	90		3971.1.s.a.654.1		8
209.193	even	90		2299.1.m.a.1842.1		4
209.203	odd	90	inner	3971.1.bc.a.984.1		24
209.206	odd	90		2299.1.m.c.1291.1		4
627.269	even	90		1881.1.bv.a.379.1		4
627.434	odd	90		1881.1.bv.a.379.1		4
836.643	odd	90		3344.1.bx.a.1633.1		4
836.687	even	90		3344.1.bx.a.1633.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.1.m.a.75.1	✓	4	19.3	odd	18
209.1.m.a.75.1	✓	4	19.16	even	9
209.1.m.a.170.1	yes	4	209.16	even	45
209.1.m.a.170.1	yes	4	209.60	odd	90
1881.1.bv.a.379.1		4	627.269	even	90
1881.1.bv.a.379.1		4	627.434	odd	90
1881.1.bv.a.1747.1		4	57.35	odd	18
1881.1.bv.a.1747.1		4	57.41	even	18
2299.1.b.a.1937.1		2	209.92	even	45
2299.1.b.a.1937.1		2	209.136	odd	90
2299.1.b.b.1937.1		2	209.73	odd	90
2299.1.b.b.1937.1		2	209.117	even	90
2299.1.m.a.493.1		4	209.54	odd	18
2299.1.m.a.493.1		4	209.98	even	18
2299.1.m.a.1842.1		4	209.149	odd	90
2299.1.m.a.1842.1		4	209.193	even	90
2299.1.m.b.1291.1		4	209.3	odd	90
2299.1.m.b.1291.1		4	209.168	even	45
2299.1.m.b.1576.1		4	209.130	even	45
2299.1.m.b.1576.1		4	209.174	odd	90
2299.1.m.c.1291.1		4	209.41	even	90
2299.1.m.c.1291.1		4	209.206	odd	90
2299.1.m.c.1576.1		4	209.35	odd	90
2299.1.m.c.1576.1		4	209.79	even	90
3344.1.bx.a.1329.1		4	76.3	even	18
3344.1.bx.a.1329.1		4	76.35	odd	18
3344.1.bx.a.1633.1		4	836.643	odd	90
3344.1.bx.a.1633.1		4	836.687	even	90
3971.1.s.a.654.1		8	209.93	even	45
3971.1.s.a.654.1		8	209.192	odd	90
3971.1.s.a.2957.1		8	19.5	even	9
3971.1.s.a.2957.1		8	19.14	odd	18
3971.1.s.a.3679.1		8	209.5	even	45
3971.1.s.a.3679.1		8	209.71	odd	90
3971.1.s.a.3903.1		8	19.2	odd	18
3971.1.s.a.3903.1		8	19.17	even	9
3971.1.bc.a.262.1		24	19.6	even	9	inner
3971.1.bc.a.262.1		24	19.13	odd	18	inner
3971.1.bc.a.984.1		24	209.82	even	45	inner
3971.1.bc.a.984.1		24	209.203	odd	90	inner
3971.1.bc.a.1021.1		24	19.8	odd	6	inner
3971.1.bc.a.1021.1		24	19.11	even	3	inner
3971.1.bc.a.1560.1		24	1.1	even	1	trivial
3971.1.bc.a.1560.1		24	19.18	odd	2	CM
3971.1.bc.a.1571.1		24	19.4	even	9	inner
3971.1.bc.a.1571.1		24	19.15	odd	18	inner
3971.1.bc.a.1743.1		24	209.27	odd	30	inner
3971.1.bc.a.1743.1		24	209.49	even	15	inner
3971.1.bc.a.2282.1		24	11.5	even	5	inner
3971.1.bc.a.2282.1		24	209.170	odd	10	inner
3971.1.bc.a.2293.1		24	209.137	even	45	inner
3971.1.bc.a.2293.1		24	209.148	odd	90	inner
3971.1.bc.a.2473.1		24	19.7	even	3	inner
3971.1.bc.a.2473.1		24	19.12	odd	6	inner
3971.1.bc.a.3195.1		24	209.126	odd	30	inner
3971.1.bc.a.3195.1		24	209.159	even	15	inner
3971.1.bc.a.3221.1		24	19.9	even	9	inner
3971.1.bc.a.3221.1		24	19.10	odd	18	inner
3971.1.bc.a.3943.1		24	209.104	even	45	inner
3971.1.bc.a.3943.1		24	209.181	odd	90	inner

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:	\( N \)	\(=\)	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3971.bc (of order \(90\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.559193 + 0.829038i) q^{4} +(0.996161 + 1.27503i) q^{5} +(0.169131 - 1.60917i) q^{7} +(0.990268 + 0.139173i) q^{9} +(-0.104528 - 0.994522i) q^{11} +(-0.374607 + 0.927184i) q^{16} +(0.612019 - 0.0860137i) q^{17} +(-0.500000 + 1.53884i) q^{20} +(-0.580762 - 0.211380i) q^{23} +(-0.391438 + 1.56997i) q^{25} +(1.42864 - 0.759621i) q^{28} +(2.22022 - 1.38735i) q^{35} +(0.438371 + 0.898794i) q^{36} +(-0.580762 + 0.211380i) q^{43} +(0.766044 - 0.642788i) q^{44} +(0.809017 + 1.40126i) q^{45} +(-0.444576 - 0.429322i) q^{47} +(-1.58268 - 0.336408i) q^{49} +(1.16392 - 1.12398i) q^{55} +(0.0215691 - 0.617657i) q^{61} +(0.391438 - 1.56997i) q^{63} +(-0.978148 + 0.207912i) q^{64} +(0.413545 + 0.459289i) q^{68} +(-0.483844 - 1.94059i) q^{73} -1.61803 q^{77} +(-1.55535 + 0.445991i) q^{80} +(0.961262 + 0.275637i) q^{81} +(-1.08268 + 1.20243i) q^{83} +(0.719340 + 0.694658i) q^{85} +(-0.149516 - 0.599676i) q^{92} +(0.0348995 - 0.999391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{7} + 3 q^{11} - 12 q^{20} + 6 q^{45} - 6 q^{49} + 3 q^{64} - 9 q^{68} - 12 q^{77} + 6 q^{83}+O(q^{100}) \) 24 * q - 9 * q^7 + 3 * q^11 - 12 * q^20 + 6 * q^45 - 6 * q^49 + 3 * q^64 - 9 * q^68 - 12 * q^77 + 6 * q^83

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