LMFDB - Embedded newform 1503.1.f.b.1168.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1503,1,Mod(166,1503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1503, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1503.166");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1503 = 3^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1503.f (of order $6$, degree $2$, 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:	$0.750094713987$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{33}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{33} + \cdots)$

Embedding invariants

Embedding label			1168.10
Root			$0.0475819 - 0.998867i$ of defining polynomial
Character	$\chi$	$=$	1503.1168
Dual form			1503.1.f.b.166.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.995472 - 1.72421i) q^{2} +(-0.786053 - 0.618159i) q^{3} +(-1.48193 - 2.56678i) q^{4} +(-1.84833 + 0.739959i) q^{6} +(0.888835 - 1.53951i) q^{7} -3.90993 q^{8} +(0.235759 + 0.971812i) q^{9} +O(q^{10})$	\(q+(0.995472 - 1.72421i) q^{2} +(-0.786053 - 0.618159i) q^{3} +(-1.48193 - 2.56678i) q^{4} +(-1.84833 + 0.739959i) q^{6} +(0.888835 - 1.53951i) q^{7} -3.90993 q^{8} +(0.235759 + 0.971812i) q^{9} +(0.327068 - 0.566498i) q^{11} +(-0.421801 + 2.93369i) q^{12} +(-1.76962 - 3.06507i) q^{14} +(-2.41030 + 4.17476i) q^{16} +(1.91030 + 0.560914i) q^{18} +1.44747 q^{19} +(-1.65033 + 0.660694i) q^{21} +(-0.651174 - 1.12787i) q^{22} +(3.07341 + 2.41696i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.415415 - 0.909632i) q^{27} -5.26876 q^{28} +(-0.0475819 + 0.0824143i) q^{29} +(0.995472 + 1.72421i) q^{31} +(2.84380 + 4.92561i) q^{32} +(-0.607279 + 0.243118i) q^{33} +(2.14504 - 2.04530i) q^{36} +(1.44091 - 2.49574i) q^{38} +(-0.503687 + 3.50322i) q^{42} -1.93877 q^{44} +(-0.235759 + 0.408346i) q^{47} +(4.47528 - 1.79163i) q^{48} +(-1.08006 - 1.87071i) q^{49} +(0.995472 + 1.72421i) q^{50} +(-1.15486 - 1.62177i) q^{54} +(-3.47528 + 6.01937i) q^{56} +(-1.13779 - 0.894765i) q^{57} +(0.0947329 + 0.164082i) q^{58} +(0.142315 - 0.246497i) q^{61} +3.96386 q^{62} +(1.70566 + 0.500828i) q^{63} +6.50310 q^{64} +(-0.185343 + 1.28909i) q^{66} +(-0.921801 - 3.79972i) q^{72} +(0.928368 - 0.371662i) q^{75} +(-2.14504 - 3.71533i) q^{76} +(-0.581419 - 1.00705i) q^{77} +(-0.888835 + 0.458227i) q^{81} +(4.14153 + 3.25693i) q^{84} +(0.0883470 - 0.0353688i) q^{87} +(-1.27881 + 2.21497i) q^{88} -1.57211 q^{89} +(0.283341 - 1.97068i) q^{93} +(0.469383 + 0.812995i) q^{94} +(0.809430 - 5.62971i) q^{96} +(0.654861 - 1.13425i) q^{97} -4.30067 q^{98} +(0.627639 + 0.184291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 20 * q - q^2 + q^3 - 11 * q^4 - q^6 - q^7 - 2 * q^8 + q^9	$ 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9} - q^{11} + q^{14} - 12 q^{16} + 2 q^{18} + 2 q^{19} - q^{21} + q^{22} + q^{24} - 10 q^{25} - 2 q^{27} - q^{29} - q^{31} - q^{33} + q^{38} - 13 q^{42} - 22 q^{44} - q^{47} + 21 q^{48} - 11 q^{49} - q^{50} - 12 q^{54} - q^{56} - q^{57} + q^{58} + 2 q^{61} + 42 q^{62} + 2 q^{63} + 20 q^{64} - 2 q^{66} - 10 q^{72} + q^{75} + q^{77} + q^{81} + 22 q^{84} - q^{87} - q^{88} + 2 q^{89} + 2 q^{93} + q^{94} + 2 q^{97} - 22 q^{98} + 2 q^{99}+O(q^{100}) $ 20 * q - q^2 + q^3 - 11 * q^4 - q^6 - q^7 - 2 * q^8 + q^9 - q^11 + q^14 - 12 * q^16 + 2 * q^18 + 2 * q^19 - q^21 + q^22 + q^24 - 10 * q^25 - 2 * q^27 - q^29 - q^31 - q^33 + q^38 - 13 * q^42 - 22 * q^44 - q^47 + 21 * q^48 - 11 * q^49 - q^50 - 12 * q^54 - q^56 - q^57 + q^58 + 2 * q^61 + 42 * q^62 + 2 * q^63 + 20 * q^64 - 2 * q^66 - 10 * q^72 + q^75 + q^77 + q^81 + 22 * q^84 - q^87 - q^88 + 2 * q^89 + 2 * q^93 + q^94 + 2 * q^97 - 22 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1503\mathbb{Z}\right)^\times$.

$n$	$172$	$335$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$2$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$3$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$3$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$4$	−1.48193	−	2.56678i	−1.48193	−	2.56678i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	−1.84833	+	0.739959i	−1.84833	+	0.739959i
$7$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$7$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$8$	−3.90993			−3.90993
$9$	0.235759	+	0.971812i	0.235759	+	0.971812i
$10$		0			0
$11$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$11$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$12$	−0.421801	+	2.93369i	−0.421801	+	2.93369i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−1.76962	−	3.06507i	−1.76962	−	3.06507i
$15$		0			0
$16$	−2.41030	+	4.17476i	−2.41030	+	4.17476i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	1.91030	+	0.560914i	1.91030	+	0.560914i
$19$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$19$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$20$		0			0
$21$	−1.65033	+	0.660694i	−1.65033	+	0.660694i
$22$	−0.651174	−	1.12787i	−0.651174	−	1.12787i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	3.07341	+	2.41696i	3.07341	+	2.41696i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	0.415415	−	0.909632i	0.415415	−	0.909632i
$28$	−5.26876			−5.26876
$29$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$29$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$30$		0			0
$31$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$31$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$32$	2.84380	+	4.92561i	2.84380	+	4.92561i
$33$	−0.607279	+	0.243118i	−0.607279	+	0.243118i
$34$		0			0
$35$		0			0
$36$	2.14504	−	2.04530i	2.14504	−	2.04530i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.44091	−	2.49574i	1.44091	−	2.49574i
$39$		0			0
$40$		0			0
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	−0.503687	+	3.50322i	−0.503687	+	3.50322i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−1.93877			−1.93877
$45$		0			0
$46$		0			0
$47$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$47$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$48$	4.47528	−	1.79163i	4.47528	−	1.79163i
$49$	−1.08006	−	1.87071i	−1.08006	−	1.87071i
$50$	0.995472	+	1.72421i	0.995472	+	1.72421i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−1.15486	−	1.62177i	−1.15486	−	1.62177i
$55$		0			0
$56$	−3.47528	+	6.01937i	−3.47528	+	6.01937i
$57$	−1.13779	−	0.894765i	−1.13779	−	0.894765i
$58$	0.0947329	+	0.164082i	0.0947329	+	0.164082i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$61$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$62$	3.96386			3.96386
$63$	1.70566	+	0.500828i	1.70566	+	0.500828i
$64$	6.50310			6.50310
$65$		0			0
$66$	−0.185343	+	1.28909i	−0.185343	+	1.28909i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−0.921801	−	3.79972i	−0.921801	−	3.79972i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	0.928368	−	0.371662i	0.928368	−	0.371662i
$76$	−2.14504	−	3.71533i	−2.14504	−	3.71533i
$77$	−0.581419	−	1.00705i	−0.581419	−	1.00705i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$82$		0			0
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$	4.14153	+	3.25693i	4.14153	+	3.25693i
$85$		0			0
$86$		0			0
$87$	0.0883470	−	0.0353688i	0.0883470	−	0.0353688i
$88$	−1.27881	+	2.21497i	−1.27881	+	2.21497i
$89$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$89$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.283341	−	1.97068i	0.283341	−	1.97068i
$94$	0.469383	+	0.812995i	0.469383	+	0.812995i
$95$		0			0
$96$	0.809430	−	5.62971i	0.809430	−	5.62971i
$97$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$97$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$98$	−4.30067			−4.30067
$99$	0.627639	+	0.184291i	0.627639	+	0.184291i
$100$	2.96386			2.96386
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$107$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$108$	−2.95044	+	0.281733i	−2.95044	+	0.281733i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	4.28471	+	7.42134i	4.28471	+	7.42134i
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	−2.67540	+	1.07107i	−2.67540	+	1.07107i
$115$		0			0
$116$	0.282052			0.282052
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.286053	+	0.495458i	0.286053	+	0.495458i
$122$	−0.283341	−	0.490761i	−0.283341	−	0.490761i
$123$		0			0
$124$	2.95044	−	5.11031i	2.95044	−	5.11031i
$125$		0			0
$126$	2.56147	−	2.44236i	2.56147	−	2.44236i
$127$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$127$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$128$	3.62985	−	6.28709i	3.62985	−	6.28709i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	1.52397	+	1.19847i	1.52397	+	1.19847i
$133$	1.28656	−	2.22839i	1.28656	−	2.22839i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$137$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$138$		0			0
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$	0.437742	−	0.175245i	0.437742	−	0.175245i
$142$		0			0
$143$		0			0
$144$	−4.62533	−	1.35812i	−4.62533	−	1.35812i
$145$		0			0
$146$		0			0
$147$	−0.307416	+	2.13813i	−0.307416	+	2.13813i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	0.283341	−	1.97068i	0.283341	−	1.97068i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	−5.65950			−5.65950
$153$		0			0
$154$	−2.31515			−2.31515
$155$		0			0
$156$		0			0
$157$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$157$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$167$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$168$	6.45268	−	2.58327i	6.45268	−	2.58327i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		0			0
$171$	0.341254	+	1.40667i	0.341254	+	1.40667i
$172$		0			0
$173$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$173$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$174$	0.0269638	−	0.187537i	0.0269638	−	0.187537i
$175$	0.888835	+	1.53951i	0.888835	+	1.53951i
$176$	1.57666	+	2.73086i	1.57666	+	2.73086i
$177$		0			0
$178$	−1.56499	+	2.71064i	−1.56499	+	2.71064i
$179$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$179$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$180$		0			0
$181$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$181$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$182$		0			0
$183$	−0.264241	+	0.105786i	−0.264241	+	0.105786i
$184$		0			0
$185$		0			0
$186$	−3.11580	−	2.45029i	−3.11580	−	2.45029i
$187$		0			0
$188$	1.39751			1.39751
$189$	−1.03115	−	1.44805i	−1.03115	−	1.44805i
$190$		0			0
$191$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$191$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$192$	−5.11178	−	4.01995i	−5.11178	−	4.01995i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	−1.30379	−	2.25823i	−1.30379	−	2.25823i
$195$		0			0
$196$	−3.20113	+	5.54453i	−3.20113	+	5.54453i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.942554	−	0.898723i	0.942554	−	0.898723i
$199$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$199$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$200$	1.95496	−	3.38610i	1.95496	−	3.38610i
$201$		0			0
$202$		0			0
$203$	0.0845850	+	0.146505i	0.0845850	+	0.146505i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.473420	−	0.819988i	0.473420	−	0.819988i
$210$		0			0
$211$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$211$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$212$		0			0
$213$		0			0
$214$	−1.76962	+	3.06507i	−1.76962	+	3.06507i
$215$		0			0
$216$	−1.62424	+	3.55660i	−1.62424	+	3.55660i
$217$	3.53924			3.53924
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$223$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$224$	10.1107			10.1107
$225$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	−0.610543	+	4.24642i	−0.610543	+	4.24642i
$229$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$229$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$230$		0			0
$231$	−0.165489	+	1.15100i	−0.165489	+	1.15100i
$232$	0.186042	−	0.322234i	0.186042	−	0.322234i
$233$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$233$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$239$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$240$		0			0
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	1.13903			1.13903
$243$	0.981929	+	0.189251i	0.981929	+	0.189251i
$244$	−0.843602			−0.843602
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−3.89223	−	6.74153i	−3.89223	−	6.74153i
$249$		0			0
$250$		0			0
$251$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$251$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$252$	−1.24216	−	5.12024i	−1.24216	−	5.12024i
$253$		0			0
$254$	−0.651174	+	1.12787i	−0.651174	+	1.12787i
$255$		0			0
$256$	−3.97528	−	6.88539i	−3.97528	−	6.88539i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.0913090	−	0.0268107i	−0.0913090	−	0.0268107i
$262$		0			0
$263$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$263$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$264$	2.37442	−	0.950573i	2.37442	−	0.950573i
$265$		0			0
$266$	−2.56147	−	4.43660i	−2.56147	−	4.43660i
$267$	1.23576	+	0.971812i	1.23576	+	0.971812i
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$	1.95496	+	3.38610i	1.95496	+	3.38610i
$275$	0.327068	+	0.566498i	0.327068	+	0.566498i
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$	−1.44091	+	1.37391i	−1.44091	+	1.37391i
$280$		0			0
$281$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$281$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$282$	0.133600	−	0.929210i	0.133600	−	0.929210i
$283$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$283$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.11631	+	3.92489i	−4.11631	+	3.92489i
$289$	1.00000			1.00000
$290$		0			0
$291$	−1.21590	+	0.486774i	−1.21590	+	0.486774i
$292$		0			0
$293$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$293$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$294$	3.38055	+	2.65849i	3.38055	+	2.65849i
$295$		0			0
$296$		0			0
$297$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$298$		0			0
$299$		0			0
$300$	−2.32975	−	1.83214i	−2.32975	−	1.83214i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−3.48883	+	6.04283i	−3.48883	+	6.04283i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−1.72324	+	2.98475i	−1.72324	+	2.98475i
$309$		0			0
$310$		0			0
$311$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$311$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	−1.65414			−1.65414
$315$		0			0
$316$		0			0
$317$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$317$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$318$		0			0
$319$	0.0311250	+	0.0539102i	0.0311250	+	0.0539102i
$320$		0			0
$321$	1.39734	+	1.09888i	1.39734	+	1.09888i
$322$		0			0
$323$		0			0
$324$	2.49336	+	1.60238i	2.49336	+	1.60238i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.419102	+	0.725906i	0.419102	+	0.725906i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$		0			0
$334$	−1.99094			−1.99094
$335$		0			0
$336$	1.21956	−	8.48220i	1.21956	−	8.48220i
$337$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$337$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$338$	0.995472	+	1.72421i	0.995472	+	1.72421i
$339$		0			0
$340$		0			0
$341$	1.30235			1.30235
$342$	2.76509	+	0.811905i	2.76509	+	0.811905i
$343$	−2.06230			−2.06230
$344$		0			0
$345$		0			0
$346$	−1.30379	−	2.25823i	−1.30379	−	2.25823i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−0.221708	−	0.174353i	−0.221708	−	0.174353i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	3.53924			3.53924
$351$		0			0
$352$	3.72046			3.72046
$353$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$353$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$354$		0			0
$355$		0			0
$356$	2.32975	+	4.03524i	2.32975	+	4.03524i
$357$		0			0
$358$	1.44091	−	2.49574i	1.44091	−	2.49574i
$359$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$359$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$360$		0			0
$361$	1.09516			1.09516
$362$	0.469383	−	0.812995i	0.469383	−	0.812995i
$363$	0.0814192	−	0.566283i	0.0814192	−	0.566283i
$364$		0			0
$365$		0			0
$366$	−0.0806472	+	0.560914i	−0.0806472	+	0.560914i
$367$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$367$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−5.47818	+	2.19313i	−5.47818	+	2.19313i
$373$		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
$376$	0.921801	−	1.59661i	0.921801	−	1.59661i
$377$		0			0
$378$	−3.52322	+	0.336426i	−3.52322	+	0.336426i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.514186	+	0.404360i	0.514186	+	0.404360i
$382$	1.15486	+	2.00028i	1.15486	+	2.00028i
$383$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$383$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$384$	−6.73968	+	2.69816i	−6.73968	+	2.69816i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−3.88183			−3.88183
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	4.22295	+	7.31436i	4.22295	+	7.31436i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−0.457081	−	1.88411i	−0.457081	−	1.88411i
$397$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$397$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$398$	−1.30379	+	2.25823i	−1.30379	+	2.25823i
$399$	−2.38880	+	0.956333i	−2.38880	+	0.956333i
$400$	−2.41030	−	4.17476i	−2.41030	−	4.17476i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.336808			0.336808
$407$		0			0
$408$		0			0
$409$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$409$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$410$		0			0
$411$	1.82318	−	0.729892i	1.82318	−	0.729892i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	−0.942554	−	1.63255i	−0.942554	−	1.63255i
$419$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$419$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$420$		0			0
$421$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$421$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$422$	−1.65414			−1.65414
$423$	−0.452418	−	0.132842i	−0.452418	−	0.132842i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.252989	−	0.438190i	−0.252989	−	0.438190i
$428$	2.63438	+	4.56288i	2.63438	+	4.56288i
$429$		0			0
$430$		0			0
$431$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$431$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$432$	2.79622	+	3.92674i	2.79622	+	3.92674i
$433$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$433$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$434$	3.52322	−	6.10239i	3.52322	−	6.10239i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	1.56335	−	1.49065i	1.56335	−	1.49065i
$442$		0			0
$443$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$443$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$		0			0
$446$	−1.56499	−	2.71064i	−1.56499	−	2.71064i
$447$		0			0
$448$	5.78019	−	10.0116i	5.78019	−	10.0116i
$449$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$449$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$450$	−1.44091	+	1.37391i	−1.44091	+	1.37391i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	4.44867	+	3.49847i	4.44867	+	3.49847i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−0.189466			−0.189466
$459$		0			0
$460$		0			0
$461$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$461$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$462$	1.81983	+	1.43113i	1.81983	+	1.43113i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$	−0.229373	−	0.397286i	−0.229373	−	0.397286i
$465$		0			0
$466$	1.15486	−	2.00028i	1.15486	−	2.00028i
$467$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$467$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.723734	+	1.25354i	−0.723734	+	1.25354i
$476$		0			0
$477$		0			0
$478$	3.12998			3.12998
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.847821	−	1.46847i	0.847821	−	1.46847i
$485$		0			0
$486$	1.30379	−	1.50465i	1.30379	−	1.50465i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	−0.556441	+	0.963784i	−0.556441	+	0.963784i
$489$		0			0
$490$		0			0
$491$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−9.59753			−9.59753
$497$		0			0
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$502$	1.67489	−	2.90099i	1.67489	−	2.90099i
$503$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$503$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$504$	−6.66902	−	1.95820i	−6.66902	−	1.95820i
$505$		0			0
$506$		0			0
$507$	0.928368	−	0.371662i	0.928368	−	0.371662i
$508$	0.969383	+	1.67902i	0.969383	+	1.67902i
$509$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$509$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$510$		0			0
$511$		0			0
$512$	−8.56943			−8.56943
$513$	0.601300	−	1.31666i	0.601300	−	1.31666i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.154218	+	0.267114i	0.154218	+	0.267114i
$518$		0			0
$519$	−1.21590	+	0.486774i	−1.21590	+	0.486774i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.137123	+	0.130746i	−0.137123	+	0.130746i
$523$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$523$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$524$		0			0
$525$	0.252989	−	1.75958i	0.252989	−	1.75958i
$526$	−0.283341	−	0.490761i	−0.283341	−	0.490761i
$527$		0			0
$528$	0.448765	−	3.12123i	0.448765	−	3.12123i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$	−7.62637			−7.62637
$533$		0			0
$534$	2.90577	−	1.16329i	2.90577	−	1.16329i
$535$		0			0
$536$		0			0
$537$	−1.13779	−	0.894765i	−1.13779	−	0.894765i
$538$		0			0
$539$	−1.41301			−1.41301
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−0.370638	−	0.291473i	−0.370638	−	0.291473i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$547$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$548$	5.82059			5.82059
$549$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$550$	1.30235			1.30235
$551$	−0.0688733	+	0.119292i	−0.0688733	+	0.119292i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$557$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$558$	0.934515	+	3.85212i	0.934515	+	3.85212i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.84833	+	3.20140i	1.84833	+	3.20140i
$563$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.723734	+	0.690079i	$0.242424\pi$
$563$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.235759	+	0.971812i	$0.424242\pi$
$564$	−1.09852	−	0.863884i	−1.09852	−	0.863884i
$565$		0			0
$566$	2.60758			2.60758
$567$	−0.0845850	+	1.77566i	−0.0845850	+	1.77566i
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$	1.07701	−	0.431171i	1.07701	−	0.431171i
$574$		0			0
$575$		0			0
$576$	1.53316	+	6.31979i	1.53316	+	6.31979i
$577$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$577$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$578$	0.995472	−	1.72421i	0.995472	−	1.72421i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	−0.371098	+	2.58104i	−0.371098	+	2.58104i
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−2.30972			−2.30972
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	5.94366	−	2.37948i	5.94366	−	2.37948i
$589$	1.44091	+	2.49574i	1.44091	+	2.49574i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−1.29645	+	0.123796i	−1.29645	+	0.123796i
$595$		0			0
$596$		0			0
$597$	1.02951	+	0.809616i	1.02951	+	0.809616i
$598$		0			0
$599$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$599$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$600$	−3.62985	+	1.45317i	−3.62985	+	1.45317i
$601$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$601$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	4.11631	+	7.12966i	4.11631	+	7.12966i
$609$	0.0240754	−	0.167448i	0.0240754	−	0.167448i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$613$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$614$		0			0
$615$		0			0
$616$	2.27331	+	3.93749i	2.27331	+	3.93749i
$617$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$617$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$		0			0
$622$	1.99094			1.99094
$623$	−1.39734	+	2.42027i	−1.39734	+	2.42027i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$	−0.879017	+	0.351905i	−0.879017	+	0.351905i
$628$	−1.23123	+	2.13255i	−1.23123	+	2.13255i
$629$		0			0
$630$		0			0
$631$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$631$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$632$		0			0
$633$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$634$	1.84833	+	3.20140i	1.84833	+	3.20140i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.123936			0.123936
$639$		0			0
$640$		0			0
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	3.28572	−	1.31540i	3.28572	−	1.31540i
$643$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	3.47528	−	1.79163i	3.47528	−	1.79163i
$649$		0			0
$650$		0			0
$651$	−2.78203	−	2.18781i	−2.78203	−	2.18781i
$652$		0			0
$653$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$653$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	1.66882			1.66882
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.48193	+	2.56678i	−1.48193	+	2.56678i
$669$	−1.45949	+	0.584293i	−1.45949	+	0.584293i
$670$		0			0
$671$	−0.0930932	−	0.161242i	−0.0930932	−	0.161242i
$672$	−7.94753	−	6.25001i	−7.94753	−	6.25001i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$	−0.938766			−0.938766
$675$	0.580057	+	0.814576i	0.580057	+	0.814576i
$676$	2.96386			2.96386
$677$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$677$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$678$		0			0
$679$	−1.16413	−	2.01633i	−1.16413	−	2.01633i
$680$		0			0
$681$		0			0
$682$	1.29645	−	2.24552i	1.29645	−	2.24552i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	3.10488	−	2.96050i	3.10488	−	2.96050i
$685$		0			0
$686$	−2.05296	+	3.55584i	−2.05296	+	3.55584i
$687$	−0.0135432	+	0.0941952i	−0.0135432	+	0.0941952i
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$	−3.88183			−3.88183
$693$	0.841586	−	0.802450i	0.841586	−	0.802450i
$694$		0			0
$695$		0			0
$696$	−0.345431	+	0.138290i	−0.345431	+	0.138290i
$697$		0			0
$698$		0			0
$699$	−0.911911	−	0.717135i	−0.911911	−	0.717135i
$700$	2.63438	−	4.56288i	2.63438	−	4.56288i
$701$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$701$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$702$		0			0
$703$		0			0
$704$	2.12696	−	3.68400i	2.12696	−	3.68400i
$705$		0			0
$706$	1.67489	+	2.90099i	1.67489	+	2.90099i
$707$		0			0
$708$		0			0
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	6.14682			6.14682
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−2.14504	−	3.71533i	−2.14504	−	3.71533i
$717$	0.223734	−	1.55610i	0.223734	−	1.55610i
$718$	0.827068	−	1.43252i	0.827068	−	1.43252i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	1.09020	−	1.88829i	1.09020	−	1.88829i
$723$		0			0
$724$	−0.698756	−	1.21028i	−0.698756	−	1.21028i
$725$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i
$726$	−0.895339	−	0.704102i	−0.895339	−	0.704102i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$730$		0			0
$731$		0			0
$732$	0.663116	+	0.521480i	0.663116	+	0.521480i
$733$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$733$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$734$	0.469383	+	0.812995i	0.469383	+	0.812995i
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$743$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$744$	−1.10784	+	7.70522i	−1.10784	+	7.70522i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.58006	+	2.73674i	−1.58006	+	2.73674i
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−1.13650	−	1.96847i	−1.13650	−	1.96847i
$753$	−1.32254	−	1.04006i	−1.32254	−	1.04006i
$754$		0			0
$755$		0			0
$756$	−2.18872	+	4.79264i	−2.18872	+	4.79264i
$757$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$757$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$761$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$762$	1.20906	−	0.484034i	1.20906	−	0.484034i
$763$		0			0
$764$	3.43841			3.43841
$765$		0			0
$766$	−3.34978			−3.34978
$767$		0			0
$768$	−1.13148	+	7.86964i	−1.13148	+	7.86964i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	−1.99094			−1.99094
$776$	−2.56046	+	4.43485i	−2.56046	+	4.43485i
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.0552004	+	0.0775182i	0.0552004	+	0.0775182i
$784$	10.4130			10.4130
$785$		0			0
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	−0.264241	+	0.105786i	−0.264241	+	0.105786i
$790$		0			0
$791$		0			0
$792$	−2.45402	−	0.720566i	−2.45402	−	0.720566i
$793$		0			0
$794$	1.84833	−	3.20140i	1.84833	−	3.20140i
$795$		0			0
$796$	1.94091	+	3.36176i	1.94091	+	3.36176i
$797$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$797$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$798$	−0.729071	+	5.07080i	−0.729071	+	5.07080i
$799$		0			0
$800$	−5.68760			−5.68760
$801$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$809$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.250698	−	0.434221i	0.250698	−	0.434221i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.30235			1.30235
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	0.556441	−	3.87013i	0.556441	−	3.87013i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	0.0930932	−	0.647478i	0.0930932	−	0.647478i
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−2.80630			−2.80630
$837$	1.98193	−	0.189251i	1.98193	−	0.189251i
$838$	−2.30972			−2.30972
$839$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$839$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$840$		0			0
$841$	0.495472	+	0.858183i	0.495472	+	0.858183i
$842$	1.67489	+	2.90099i	1.67489	+	2.90099i
$843$	1.72373	−	0.690079i	1.72373	−	0.690079i
$844$	−1.23123	+	2.13255i	−1.23123	+	2.13255i
$845$		0			0
$846$	−0.679417	+	0.647822i	−0.679417	+	0.647822i
$847$	1.01702			1.01702
$848$		0			0
$849$	0.186393	−	1.29639i	0.186393	−	1.29639i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$853$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$854$	−1.00737			−1.00737
$855$		0			0
$856$	6.95057			6.95057
$857$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$857$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$859$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$860$		0			0
$861$		0			0
$862$	1.84833	−	3.20140i	1.84833	−	3.20140i
$863$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$863$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$864$	5.66185	−	0.540641i	5.66185	−	0.540641i
$865$		0			0
$866$	−1.91030	+	3.30873i	−1.91030	+	3.30873i
$867$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$868$	−5.24491	−	9.08444i	−5.24491	−	9.08444i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.25667	+	0.368991i	1.25667	+	0.368991i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$877$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$878$		0			0
$879$	−0.165101	+	1.14831i	−0.165101	+	1.14831i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−1.01392	−	4.17944i	−1.01392	−	4.17944i
$883$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$883$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	−0.581419	+	1.00705i	−0.581419	+	1.00705i
$890$		0			0
$891$	−0.0311250	+	0.653395i	−0.0311250	+	0.653395i
$892$	−4.65950			−4.65950
$893$	−0.341254	+	0.591068i	−0.341254	+	0.591068i
$894$		0			0
$895$		0			0
$896$	−6.45268	−	11.1764i	−6.45268	−	11.1764i
$897$		0			0
$898$	−1.91030	+	3.30873i	−1.91030	+	3.30873i
$899$	−0.189466			−0.189466
$900$	0.698756	+	2.88031i	0.698756	+	2.88031i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$907$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$911$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$912$	6.47783	−	2.59333i	6.47783	−	2.59333i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.141026	+	0.244264i	−0.141026	+	0.244264i
$917$		0			0
$918$		0			0
$919$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$919$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$920$		0			0
$921$		0			0
$922$	−1.91030	−	3.30873i	−1.91030	−	3.30873i
$923$		0			0
$924$	3.19961	−	1.28093i	3.19961	−	1.28093i
$925$		0			0
$926$		0			0
$927$		0			0
$928$	−0.541254			−0.541254
$929$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$929$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$930$		0			0
$931$	−1.56335	−	2.70780i	−1.56335	−	2.70780i
$932$	−1.71921	−	2.97775i	−1.71921	−	2.97775i
$933$	0.142315	−	0.989821i	0.142315	−	0.989821i
$934$	0.0947329	−	0.164082i	0.0947329	−	0.164082i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$	1.30024	+	1.02252i	1.30024	+	1.02252i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$947$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$948$		0			0
$949$		0			0
$950$	1.44091	+	2.49574i	1.44091	+	2.49574i
$951$	1.72373	−	0.690079i	1.72373	−	0.690079i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$	2.32975	−	4.03524i	2.32975	−	4.03524i
$957$	0.00885911	−	0.0616165i	0.00885911	−	0.0616165i
$958$		0			0
$959$	1.74555	+	3.02337i	1.74555	+	3.02337i
$960$		0			0
$961$	−1.48193	+	2.56678i	−1.48193	+	2.56678i
$962$		0			0
$963$	−0.419102	−	1.72756i	−0.419102	−	1.72756i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$967$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$968$	−1.11845	−	1.93721i	−1.11845	−	1.93721i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−0.969383	−	2.80085i	−0.969383	−	2.80085i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.686042	+	1.18826i	0.686042	+	1.18826i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	−0.514186	+	0.890596i	−0.514186	+	0.890596i
$980$		0			0
$981$		0			0
$982$	−3.98189			−3.98189
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.119289	−	0.829672i	0.119289	−	0.829672i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−5.66185	+	9.80661i	−5.66185	+	9.80661i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$997$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1503.1.f.b.1168.10	yes	20
9.4	even	3	inner	1503.1.f.b.166.10	✓	20
167.166	odd	2	CM	1503.1.f.b.1168.10	yes	20
1503.166	odd	6	inner	1503.1.f.b.166.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1503.1.f.b.166.10	✓	20	9.4	even	3	inner
1503.1.f.b.166.10	✓	20	1503.166	odd	6	inner
1503.1.f.b.1168.10	yes	20	1.1	even	1	trivial
1503.1.f.b.1168.10	yes	20	167.166	odd	2	CM

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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:	\( N \)	\(=\)	\( 1503 = 3^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1503.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.995472 - 1.72421i) q^{2} +(-0.786053 - 0.618159i) q^{3} +(-1.48193 - 2.56678i) q^{4} +(-1.84833 + 0.739959i) q^{6} +(0.888835 - 1.53951i) q^{7} -3.90993 q^{8} +(0.235759 + 0.971812i) q^{9} +O(q^{10})\)	\(q+(0.995472 - 1.72421i) q^{2} +(-0.786053 - 0.618159i) q^{3} +(-1.48193 - 2.56678i) q^{4} +(-1.84833 + 0.739959i) q^{6} +(0.888835 - 1.53951i) q^{7} -3.90993 q^{8} +(0.235759 + 0.971812i) q^{9} +(0.327068 - 0.566498i) q^{11} +(-0.421801 + 2.93369i) q^{12} +(-1.76962 - 3.06507i) q^{14} +(-2.41030 + 4.17476i) q^{16} +(1.91030 + 0.560914i) q^{18} +1.44747 q^{19} +(-1.65033 + 0.660694i) q^{21} +(-0.651174 - 1.12787i) q^{22} +(3.07341 + 2.41696i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.415415 - 0.909632i) q^{27} -5.26876 q^{28} +(-0.0475819 + 0.0824143i) q^{29} +(0.995472 + 1.72421i) q^{31} +(2.84380 + 4.92561i) q^{32} +(-0.607279 + 0.243118i) q^{33} +(2.14504 - 2.04530i) q^{36} +(1.44091 - 2.49574i) q^{38} +(-0.503687 + 3.50322i) q^{42} -1.93877 q^{44} +(-0.235759 + 0.408346i) q^{47} +(4.47528 - 1.79163i) q^{48} +(-1.08006 - 1.87071i) q^{49} +(0.995472 + 1.72421i) q^{50} +(-1.15486 - 1.62177i) q^{54} +(-3.47528 + 6.01937i) q^{56} +(-1.13779 - 0.894765i) q^{57} +(0.0947329 + 0.164082i) q^{58} +(0.142315 - 0.246497i) q^{61} +3.96386 q^{62} +(1.70566 + 0.500828i) q^{63} +6.50310 q^{64} +(-0.185343 + 1.28909i) q^{66} +(-0.921801 - 3.79972i) q^{72} +(0.928368 - 0.371662i) q^{75} +(-2.14504 - 3.71533i) q^{76} +(-0.581419 - 1.00705i) q^{77} +(-0.888835 + 0.458227i) q^{81} +(4.14153 + 3.25693i) q^{84} +(0.0883470 - 0.0353688i) q^{87} +(-1.27881 + 2.21497i) q^{88} -1.57211 q^{89} +(0.283341 - 1.97068i) q^{93} +(0.469383 + 0.812995i) q^{94} +(0.809430 - 5.62971i) q^{96} +(0.654861 - 1.13425i) q^{97} -4.30067 q^{98} +(0.627639 + 0.184291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 20 * q - q^2 + q^3 - 11 * q^4 - q^6 - q^7 - 2 * q^8 + q^9	\( 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9} - q^{11} + q^{14} - 12 q^{16} + 2 q^{18} + 2 q^{19} - q^{21} + q^{22} + q^{24} - 10 q^{25} - 2 q^{27} - q^{29} - q^{31} - q^{33} + q^{38} - 13 q^{42} - 22 q^{44} - q^{47} + 21 q^{48} - 11 q^{49} - q^{50} - 12 q^{54} - q^{56} - q^{57} + q^{58} + 2 q^{61} + 42 q^{62} + 2 q^{63} + 20 q^{64} - 2 q^{66} - 10 q^{72} + q^{75} + q^{77} + q^{81} + 22 q^{84} - q^{87} - q^{88} + 2 q^{89} + 2 q^{93} + q^{94} + 2 q^{97} - 22 q^{98} + 2 q^{99}+O(q^{100}) \) 20 * q - q^2 + q^3 - 11 * q^4 - q^6 - q^7 - 2 * q^8 + q^9 - q^11 + q^14 - 12 * q^16 + 2 * q^18 + 2 * q^19 - q^21 + q^22 + q^24 - 10 * q^25 - 2 * q^27 - q^29 - q^31 - q^33 + q^38 - 13 * q^42 - 22 * q^44 - q^47 + 21 * q^48 - 11 * q^49 - q^50 - 12 * q^54 - q^56 - q^57 + q^58 + 2 * q^61 + 42 * q^62 + 2 * q^63 + 20 * q^64 - 2 * q^66 - 10 * q^72 + q^75 + q^77 + q^81 + 22 * q^84 - q^87 - q^88 + 2 * q^89 + 2 * q^93 + q^94 + 2 * q^97 - 22 * q^98 + 2 * q^99

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