LMFDB - Embedded newform 1503.1.f.b.1168.1

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			1168.1
Root			$-0.995472 + 0.0950560i$ of defining polynomial
Character	$\chi$	$=$	1503.1168
Dual form			1503.1.f.b.166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.981929 + 1.70075i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-1.42837 - 2.47401i) q^{4} +(1.42131 + 1.35522i) q^{6} +(-0.580057 + 1.00469i) q^{7} +3.64636 q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.981929 + 1.70075i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-1.42837 - 2.47401i) q^{4} +(1.42131 + 1.35522i) q^{6} +(-0.580057 + 1.00469i) q^{7} +3.64636 q^{8} +(-0.888835 - 0.458227i) q^{9} +(0.786053 - 1.36148i) q^{11} +(-2.74102 + 0.804835i) q^{12} +(-1.13915 - 1.97306i) q^{14} +(-2.15210 + 3.72755i) q^{16} +(1.65210 - 1.06174i) q^{18} +0.0951638 q^{19} +(0.839614 + 0.800570i) q^{21} +(1.54370 + 2.67376i) q^{22} +(0.859663 - 3.54358i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.654861 + 0.755750i) q^{27} +3.31414 q^{28} +(0.995472 - 1.72421i) q^{29} +(-0.981929 - 1.70075i) q^{31} +(-2.40324 - 4.16253i) q^{32} +(-1.13779 - 1.08488i) q^{33} +(0.135929 + 2.85350i) q^{36} +(-0.0934441 + 0.161850i) q^{38} +(-2.18601 + 0.641871i) q^{42} -4.49109 q^{44} +(0.888835 - 1.53951i) q^{47} +(3.11510 + 2.97024i) q^{48} +(-0.172932 - 0.299527i) q^{49} +(-0.981929 - 1.70075i) q^{50} +(-0.642315 - 1.85585i) q^{54} +(-2.11510 + 3.66346i) q^{56} +(0.0224357 - 0.0924813i) q^{57} +(1.95496 + 3.38610i) q^{58} +(0.959493 - 1.66189i) q^{61} +3.85674 q^{62} +(0.975950 - 0.627205i) q^{63} +5.13503 q^{64} +(2.96233 - 0.869819i) q^{66} +(-3.24102 - 1.67086i) q^{72} +(0.723734 + 0.690079i) q^{75} +(-0.135929 - 0.235436i) q^{76} +(0.911911 + 1.57948i) q^{77} +(0.580057 + 0.814576i) q^{81} +(0.781338 - 3.22072i) q^{84} +(-1.44091 - 1.37391i) q^{87} +(2.86624 - 4.96447i) q^{88} +0.471518 q^{89} +(-1.88431 + 0.553283i) q^{93} +(1.74555 + 3.02337i) q^{94} +(-4.61178 + 1.35414i) q^{96} +(0.142315 - 0.246497i) q^{97} +0.679228 q^{98} +(-1.32254 + 0.849945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$2$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$3$	0.235759	−	0.971812i	0.235759	−	0.971812i
$3$	0.235759	−	0.971812i	0.235759	−	0.971812i
$4$	−1.42837	−	2.47401i	−1.42837	−	2.47401i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	1.42131	+	1.35522i	1.42131	+	1.35522i
$7$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$7$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$8$	3.64636			3.64636
$9$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$10$		0			0
$11$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$11$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$12$	−2.74102	+	0.804835i	−2.74102	+	0.804835i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−1.13915	−	1.97306i	−1.13915	−	1.97306i
$15$		0			0
$16$	−2.15210	+	3.72755i	−2.15210	+	3.72755i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	1.65210	−	1.06174i	1.65210	−	1.06174i
$19$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$19$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$20$		0			0
$21$	0.839614	+	0.800570i	0.839614	+	0.800570i
$22$	1.54370	+	2.67376i	1.54370	+	2.67376i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	0.859663	−	3.54358i	0.859663	−	3.54358i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$28$	3.31414			3.31414
$29$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$29$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$30$		0			0
$31$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$31$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$32$	−2.40324	−	4.16253i	−2.40324	−	4.16253i
$33$	−1.13779	−	1.08488i	−1.13779	−	1.08488i
$34$		0			0
$35$		0			0
$36$	0.135929	+	2.85350i	0.135929	+	2.85350i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.0934441	+	0.161850i	−0.0934441	+	0.161850i
$39$		0			0
$40$		0			0
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	−2.18601	+	0.641871i	−2.18601	+	0.641871i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−4.49109			−4.49109
$45$		0			0
$46$		0			0
$47$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$47$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$48$	3.11510	+	2.97024i	3.11510	+	2.97024i
$49$	−0.172932	−	0.299527i	−0.172932	−	0.299527i
$50$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.642315	−	1.85585i	−0.642315	−	1.85585i
$55$		0			0
$56$	−2.11510	+	3.66346i	−2.11510	+	3.66346i
$57$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$58$	1.95496	+	3.38610i	1.95496	+	3.38610i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$61$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$62$	3.85674			3.85674
$63$	0.975950	−	0.627205i	0.975950	−	0.627205i
$64$	5.13503			5.13503
$65$		0			0
$66$	2.96233	−	0.869819i	2.96233	−	0.869819i
$67$		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			$\pi$
$72$	−3.24102	−	1.67086i	−3.24102	−	1.67086i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	0.723734	+	0.690079i	0.723734	+	0.690079i
$76$	−0.135929	−	0.235436i	−0.135929	−	0.235436i
$77$	0.911911	+	1.57948i	0.911911	+	1.57948i
$78$		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
$81$	0.580057	+	0.814576i	0.580057	+	0.814576i
$82$		0			0
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$	0.781338	−	3.22072i	0.781338	−	3.22072i
$85$		0			0
$86$		0			0
$87$	−1.44091	−	1.37391i	−1.44091	−	1.37391i
$88$	2.86624	−	4.96447i	2.86624	−	4.96447i
$89$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$89$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$94$	1.74555	+	3.02337i	1.74555	+	3.02337i
$95$		0			0
$96$	−4.61178	+	1.35414i	−4.61178	+	1.35414i
$97$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$97$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$98$	0.679228			0.679228
$99$	−1.32254	+	0.849945i	−1.32254	+	0.849945i
$100$	2.85674			2.85674
$101$		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
$107$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$107$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$108$	2.80511	+	0.540641i	2.80511	+	0.540641i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	−2.49668	−	4.32438i	−2.49668	−	4.32438i
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	0.135257	+	0.128968i	0.135257	+	0.128968i
$115$		0			0
$116$	−5.68760			−5.68760
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.735759	−	1.27437i	−0.735759	−	1.27437i
$122$	1.88431	+	3.26372i	1.88431	+	3.26372i
$123$		0			0
$124$	−2.80511	+	4.85859i	−2.80511	+	4.85859i
$125$		0			0
$126$	0.108406	+	2.27572i	0.108406	+	2.27572i
$127$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$127$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$128$	−2.63900	+	4.57088i	−2.63900	+	4.57088i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	−1.05882	+	4.36450i	−1.05882	+	4.36450i
$133$	−0.0552004	+	0.0956100i	−0.0552004	+	0.0956100i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$137$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$138$		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
$141$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$142$		0			0
$143$		0			0
$144$	3.62093	−	2.32703i	3.62093	−	2.32703i
$145$		0			0
$146$		0			0
$147$	−0.331854	+	0.0974412i	−0.331854	+	0.0974412i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	−1.88431	+	0.553283i	−1.88431	+	0.553283i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	0.347002			0.347002
$153$		0			0
$154$	−3.58173			−3.58173
$155$		0			0
$156$		0			0
$157$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$157$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−1.95496	+	0.186677i	−1.95496	+	0.186677i
$163$		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
$168$	3.06154	+	2.91917i	3.06154	+	2.91917i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		0			0
$171$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$172$		0			0
$173$	0.142315	−	0.246497i	0.142315	−	0.246497i	−0.786053	−	0.618159i	$-0.787879\pi$
$173$	0.142315	−	0.246497i	0.142315	−	0.246497i	0.928368	+	0.371662i	$0.121212\pi$
$174$	3.75155	−	1.10155i	3.75155	−	1.10155i
$175$	−0.580057	−	1.00469i	−0.580057	−	1.00469i
$176$	3.38333	+	5.86010i	3.38333	+	5.86010i
$177$		0			0
$178$	−0.462997	+	0.801934i	−0.462997	+	0.801934i
$179$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$179$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$180$		0			0
$181$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$181$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$182$		0			0
$183$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$184$		0			0
$185$		0			0
$186$	0.909260	−	3.74802i	0.909260	−	3.74802i
$187$		0			0
$188$	−5.07834			−5.07834
$189$	−0.379436	−	1.09631i	−0.379436	−	1.09631i
$190$		0			0
$191$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$191$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$192$	1.21063	−	4.99029i	1.21063	−	4.99029i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	0.279486	+	0.484084i	0.279486	+	0.484084i
$195$		0			0
$196$	−0.494021	+	0.855670i	−0.494021	+	0.855670i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.146904	−	3.08390i	−0.146904	−	3.08390i
$199$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$199$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$200$	−1.82318	+	3.15784i	−1.82318	+	3.15784i
$201$		0			0
$202$		0			0
$203$	1.15486	+	2.00028i	1.15486	+	2.00028i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.0748038	−	0.129564i	0.0748038	−	0.129564i
$210$		0			0
$211$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$211$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$212$		0			0
$213$		0			0
$214$	−1.13915	+	1.97306i	−1.13915	+	1.97306i
$215$		0			0
$216$	−2.38786	+	2.75574i	−2.38786	+	2.75574i
$217$	2.27830			2.27830
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$223$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$224$	5.57606			5.57606
$225$	0.841254	−	0.540641i	0.841254	−	0.540641i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	−0.260846	+	0.0765912i	−0.260846	+	0.0765912i
$229$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$229$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$230$		0			0
$231$	1.74994	−	0.513830i	1.74994	−	0.513830i
$232$	3.62985	−	6.28709i	3.62985	−	6.28709i
$233$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$233$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$239$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$240$		0			0
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	2.88985			2.88985
$243$	0.928368	−	0.371662i	0.928368	−	0.371662i
$244$	−5.48204			−5.48204
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−3.58047	−	6.20156i	−3.58047	−	6.20156i
$249$		0			0
$250$		0			0
$251$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$251$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$252$	−2.94572	−	1.51863i	−2.94572	−	1.51863i
$253$		0			0
$254$	1.54370	−	2.67376i	1.54370	−	2.67376i
$255$		0			0
$256$	−2.61510	−	4.52948i	−2.61510	−	4.52948i
$257$		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
$261$	−1.67489	+	1.07639i	−1.67489	+	1.07639i
$262$		0			0
$263$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$263$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$264$	−4.14879	−	3.95586i	−4.14879	−	3.95586i
$265$		0			0
$266$	−0.108406	−	0.187764i	−0.108406	−	0.187764i
$267$	0.111165	−	0.458227i	0.111165	−	0.458227i
$268$		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
$274$	−1.82318	−	3.15784i	−1.82318	−	3.15784i
$275$	0.786053	+	1.36148i	0.786053	+	1.36148i
$276$		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
$279$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$280$		0			0
$281$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$281$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$282$	3.34968	−	0.983554i	3.34968	−	0.983554i
$283$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$283$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.228701	+	4.80103i	0.228701	+	4.80103i
$289$	1.00000			1.00000
$290$		0			0
$291$	−0.205996	−	0.196417i	−0.205996	−	0.196417i
$292$		0			0
$293$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$293$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$294$	0.160134	−	0.660081i	0.160134	−	0.660081i
$295$		0			0
$296$		0			0
$297$	0.514186	+	1.48564i	0.514186	+	1.48564i
$298$		0			0
$299$		0			0
$300$	0.673501	−	2.77621i	0.673501	−	2.77621i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.204802	+	0.354728i	−0.204802	+	0.354728i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	2.60509	−	4.51215i	2.60509	−	4.51215i
$309$		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	$0.666667\pi$
$314$	−2.57211			−2.57211
$315$		0			0
$316$		0			0
$317$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$317$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$318$		0			0
$319$	−1.56499	−	2.71064i	−1.56499	−	2.71064i
$320$		0			0
$321$	0.273507	−	1.12741i	0.273507	−	1.12741i
$322$		0			0
$323$		0			0
$324$	1.18673	−	2.59858i	1.18673	−	2.59858i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.03115	+	1.78600i	1.03115	+	1.78600i
$330$		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
$334$	1.96386			1.96386
$335$		0			0
$336$	−4.79110	+	1.40679i	−4.79110	+	1.40679i
$337$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.841254	+	0.540641i	$0.181818\pi$
$337$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.0475819	+	0.998867i	$0.484848\pi$
$338$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$339$		0			0
$340$		0			0
$341$	−3.08739			−3.08739
$342$	0.157220	−	0.101039i	0.157220	−	0.101039i
$343$	−0.758872			−0.758872
$344$		0			0
$345$		0			0
$346$	0.279486	+	0.484084i	0.279486	+	0.484084i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−1.34090	+	5.52728i	−1.34090	+	5.52728i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	2.27830			2.27830
$351$		0			0
$352$	−7.55629			−7.55629
$353$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$353$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$354$		0			0
$355$		0			0
$356$	−0.673501	−	1.16654i	−0.673501	−	1.16654i
$357$		0			0
$358$	−0.0934441	+	0.161850i	−0.0934441	+	0.161850i
$359$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$359$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$360$		0			0
$361$	−0.990944			−0.990944
$362$	1.74555	−	3.02337i	1.74555	−	3.02337i
$363$	−1.41191	+	0.414574i	−1.41191	+	0.414574i
$364$		0			0
$365$		0			0
$366$	3.61596	−	1.06174i	3.61596	−	1.06174i
$367$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$367$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	4.06031	+	3.87150i	4.06031	+	3.87150i
$373$		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
$376$	3.24102	−	5.61361i	3.24102	−	5.61361i
$377$		0			0
$378$	2.23713	+	0.431171i	2.23713	+	0.431171i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	−0.370638	+	1.52779i	−0.370638	+	1.52779i
$382$	0.642315	+	1.11252i	0.642315	+	1.11252i
$383$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$383$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$384$	3.81987	+	3.64223i	3.81987	+	3.64223i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.813112			−0.813112
$389$		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
$392$	−0.630573	−	1.09218i	−0.630573	−	1.09218i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	3.99184	+	2.05794i	3.99184	+	2.05794i
$397$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$397$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$398$	0.279486	−	0.484084i	0.279486	−	0.484084i
$399$	0.0799009	+	0.0761853i	0.0799009	+	0.0761853i
$400$	−2.15210	−	3.72755i	−2.15210	−	3.72755i
$401$		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
$406$	−4.53596			−4.53596
$407$		0			0
$408$		0			0
$409$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$409$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$410$		0			0
$411$	1.34378	+	1.28129i	1.34378	+	1.28129i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	0.146904	+	0.254445i	0.146904	+	0.254445i
$419$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$419$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$420$		0			0
$421$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$421$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$422$	−2.57211			−2.57211
$423$	−1.49547	+	0.961081i	−1.49547	+	0.961081i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.11312	+	1.92798i	1.11312	+	1.92798i
$428$	−1.65707	−	2.87013i	−1.65707	−	2.87013i
$429$		0			0
$430$		0			0
$431$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$431$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$432$	−1.40777	−	4.06748i	−1.40777	−	4.06748i
$433$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$433$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$434$	−2.23713	+	3.87482i	−2.23713	+	3.87482i
$435$		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
$441$	0.0164569	+	0.345472i	0.0164569	+	0.345472i
$442$		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
$446$	−0.462997	−	0.801934i	−0.462997	−	0.801934i
$447$		0			0
$448$	−2.97861	+	5.15911i	−2.97861	+	5.15911i
$449$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$449$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$450$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	0.0818088	−	0.337221i	0.0818088	−	0.337221i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−3.90993			−3.90993
$459$		0			0
$460$		0			0
$461$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$461$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$462$	−0.844424	+	3.48076i	−0.844424	+	3.48076i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$	4.28471	+	7.42134i	4.28471	+	7.42134i
$465$		0			0
$466$	0.642315	−	1.11252i	0.642315	−	1.11252i
$467$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$467$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.25667	−	0.368991i	1.25667	−	0.368991i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i
$476$		0			0
$477$		0			0
$478$	0.925994			0.925994
$479$		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
$484$	−2.10187	+	3.64054i	−2.10187	+	3.64054i
$485$		0			0
$486$	−0.279486	+	1.94387i	−0.279486	+	1.94387i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	3.49866	−	6.05986i	3.49866	−	6.05986i
$489$		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
$496$	8.45284			8.45284
$497$		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
$501$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$502$	−0.815816	+	1.41303i	−0.815816	+	1.41303i
$503$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$503$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$504$	3.55867	−	2.28702i	3.55867	−	2.28702i
$505$		0			0
$506$		0			0
$507$	0.723734	+	0.690079i	0.723734	+	0.690079i
$508$	2.24555	+	3.88940i	2.24555	+	3.88940i
$509$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$509$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$510$		0			0
$511$		0			0
$512$	4.99337			4.99337
$513$	−0.0623191	+	0.0719200i	−0.0623191	+	0.0719200i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.39734	−	2.42027i	−1.39734	−	2.42027i
$518$		0			0
$519$	−0.205996	−	0.196417i	−0.205996	−	0.196417i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.186042	−	3.90550i	−0.186042	−	3.90550i
$523$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$523$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$524$		0			0
$525$	−1.11312	+	0.326842i	−1.11312	+	0.326842i
$526$	1.88431	+	3.26372i	1.88431	+	3.26372i
$527$		0			0
$528$	6.49257	−	1.90639i	6.49257	−	1.90639i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$	0.315386			0.315386
$533$		0			0
$534$	0.670173	+	0.639009i	0.670173	+	0.639009i
$535$		0			0
$536$		0			0
$537$	0.0224357	−	0.0924813i	0.0224357	−	0.0924813i
$538$		0			0
$539$	−0.543735			−0.543735
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−0.419102	+	1.72756i	−0.419102	+	1.72756i
$544$		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	$0.666667\pi$
$548$	5.30420			5.30420
$549$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$550$	−3.08739			−3.08739
$551$	0.0947329	−	0.164082i	0.0947329	−	0.164082i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$557$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$558$	−3.42800	−	1.76726i	−3.42800	−	1.76726i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.42131	−	2.46178i	−1.42131	−	2.46178i
$563$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$563$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$564$	−1.19726	+	4.93519i	−1.19726	+	4.93519i
$565$		0			0
$566$	−0.558972			−0.558972
$567$	−1.15486	+	0.110276i	−1.15486	+	0.110276i
$568$		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
$573$	−0.473420	−	0.451405i	−0.473420	−	0.451405i
$574$		0			0
$575$		0			0
$576$	−4.56420	−	2.35301i	−4.56420	−	2.35301i
$577$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$577$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$578$	−0.981929	+	1.70075i	−0.981929	+	1.70075i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	0.536330	−	0.157481i	0.536330	−	0.157481i
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.28463			−1.28463
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	0.715080	+	0.681827i	0.715080	+	0.681827i
$589$	−0.0934441	−	0.161850i	−0.0934441	−	0.161850i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	−3.03160	−	0.584293i	−3.03160	−	0.584293i
$595$		0			0
$596$		0			0
$597$	−0.0671040	+	0.276606i	−0.0671040	+	0.276606i
$598$		0			0
$599$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$599$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$600$	2.63900	+	2.51628i	2.63900	+	2.51628i
$601$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$601$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$602$		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	$0.333333\pi$
$608$	−0.228701	−	0.396123i	−0.228701	−	0.396123i
$609$	2.21616	−	0.650724i	2.21616	−	0.650724i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$613$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$614$		0			0
$615$		0			0
$616$	3.32516	+	5.75935i	3.32516	+	5.75935i
$617$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$617$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$618$		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
$622$	−1.96386			−1.96386
$623$	−0.273507	+	0.473728i	−0.273507	+	0.473728i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$	−0.108276	−	0.103241i	−0.108276	−	0.103241i
$628$	1.87076	−	3.24026i	1.87076	−	3.24026i
$629$		0			0
$630$		0			0
$631$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$631$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$632$		0			0
$633$	1.25667	−	0.368991i	1.25667	−	0.368991i
$634$	−1.42131	−	2.46178i	−1.42131	−	2.46178i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	6.14682			6.14682
$639$		0			0
$640$		0			0
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	1.64888	+	1.57221i	1.64888	+	1.57221i
$643$		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			$\pi$
$648$	2.11510	+	2.97024i	2.11510	+	2.97024i
$649$		0			0
$650$		0			0
$651$	0.537129	−	2.21408i	0.537129	−	2.21408i
$652$		0			0
$653$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$653$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−4.05006			−4.05006
$659$		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
$668$	−1.42837	+	2.47401i	−1.42837	+	2.47401i
$669$	0.341254	+	0.325385i	0.341254	+	0.325385i
$670$		0			0
$671$	−1.50842	−	2.61267i	−1.50842	−	2.61267i
$672$	1.31461	−	5.41888i	1.31461	−	5.41888i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$	−3.49109			−3.49109
$675$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$676$	2.85674			2.85674
$677$	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
$679$	0.165101	+	0.285964i	0.165101	+	0.285964i
$680$		0			0
$681$		0			0
$682$	3.03160	−	5.25088i	3.03160	−	5.25088i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.0129355	+	0.271550i	0.0129355	+	0.271550i
$685$		0			0
$686$	0.745158	−	1.29065i	0.745158	−	1.29065i
$687$	1.91030	−	0.560914i	1.91030	−	0.560914i
$688$		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	$0.666667\pi$
$692$	−0.813112			−0.813112
$693$	−0.0867810	−	1.82176i	−0.0867810	−	1.82176i
$694$		0			0
$695$		0			0
$696$	−5.25410	−	5.00977i	−5.25410	−	5.00977i
$697$		0			0
$698$		0			0
$699$	−0.154218	+	0.635697i	−0.154218	+	0.635697i
$700$	−1.65707	+	2.87013i	−1.65707	+	2.87013i
$701$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$701$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$702$		0			0
$703$		0			0
$704$	4.03641	−	6.99127i	4.03641	−	6.99127i
$705$		0			0
$706$	−0.815816	−	1.41303i	−0.815816	−	1.41303i
$707$		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
$712$	1.71933			1.71933
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.135929	−	0.235436i	−0.135929	−	0.235436i
$717$	−0.452418	+	0.132842i	−0.452418	+	0.132842i
$718$	1.28605	−	2.22751i	1.28605	−	2.22751i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.973036	−	1.68535i	0.973036	−	1.68535i
$723$		0			0
$724$	2.53917	+	4.39797i	2.53917	+	4.39797i
$725$	0.995472	+	1.72421i	0.995472	+	1.72421i
$726$	0.681308	−	2.80839i	0.681308	−	2.80839i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$730$		0			0
$731$		0			0
$732$	−1.29244	+	5.32751i	−1.29244	+	5.32751i
$733$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$733$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$734$	1.74555	+	3.02337i	1.74555	+	3.02337i
$735$		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	$0.666667\pi$
$744$	−6.87087	+	2.01747i	−6.87087	+	2.01747i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.672932	+	1.16555i	−0.672932	+	1.16555i
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	3.82573	+	6.62636i	3.82573	+	6.62636i
$753$	0.195876	−	0.807410i	0.195876	−	0.807410i
$754$		0			0
$755$		0			0
$756$	−2.17030	+	2.50466i	−2.17030	+	2.50466i
$757$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$757$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.723734	+	0.690079i	$0.242424\pi$
$761$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.235759	+	0.971812i	$0.424242\pi$
$762$	−2.23445	−	2.13054i	−2.23445	−	2.13054i
$763$		0			0
$764$	−1.86869			−1.86869
$765$		0			0
$766$	1.63163			1.63163
$767$		0			0
$768$	−5.01834	+	1.47352i	−5.01834	+	1.47352i
$769$		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
$775$	1.96386			1.96386
$776$	0.518932	−	0.898816i	0.518932	−	0.898816i
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.651174	+	1.88144i	0.651174	+	1.88144i
$784$	1.48867			1.48867
$785$		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
$789$	−1.38884	−	1.32425i	−1.38884	−	1.32425i
$790$		0			0
$791$		0			0
$792$	−4.82246	+	3.09921i	−4.82246	+	3.09921i
$793$		0			0
$794$	−1.42131	+	2.46178i	−1.42131	+	2.46178i
$795$		0			0
$796$	0.406556	+	0.704175i	0.406556	+	0.704175i
$797$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$797$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$798$	−0.208029	+	0.0610829i	−0.208029	+	0.0610829i
$799$		0			0
$800$	4.80648			4.80648
$801$	−0.419102	−	0.216062i	−0.419102	−	0.216062i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$809$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	3.29913	−	5.71426i	3.29913	−	5.71426i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−3.08739			−3.08739
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	−3.49866	+	1.02730i	−3.49866	+	1.02730i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	1.50842	−	0.442913i	1.50842	−	0.442913i
$826$		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
$836$	−0.427390			−0.427390
$837$	1.92837	+	0.371662i	1.92837	+	0.371662i
$838$	−1.28463			−1.28463
$839$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$839$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$840$		0			0
$841$	−1.48193	−	2.56678i	−1.48193	−	2.56678i
$842$	−0.815816	−	1.41303i	−0.815816	−	1.41303i
$843$	1.04758	+	0.998867i	1.04758	+	0.998867i
$844$	1.87076	−	3.24026i	1.87076	−	3.24026i
$845$		0			0
$846$	−0.166113	−	3.48714i	−0.166113	−	3.48714i
$847$	1.70713			1.70713
$848$		0			0
$849$	0.273100	−	0.0801894i	0.273100	−	0.0801894i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$853$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$854$	−4.37202			−4.37202
$855$		0			0
$856$	4.23020			4.23020
$857$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$857$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$858$		0			0
$859$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$859$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$860$		0			0
$861$		0			0
$862$	−1.42131	+	2.46178i	−1.42131	+	2.46178i
$863$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$863$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$864$	4.71962	+	0.909632i	4.71962	+	0.909632i
$865$		0			0
$866$	−1.65210	+	2.86152i	−1.65210	+	2.86152i
$867$	0.235759	−	0.971812i	0.235759	−	0.971812i
$868$	−3.25425	−	5.63652i	−3.25425	−	5.63652i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$877$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$878$		0			0
$879$	0.627639	−	0.184291i	0.627639	−	0.184291i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.603722	−	0.311240i	−0.603722	−	0.311240i
$883$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$883$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$884$		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
$889$	0.911911	−	1.57948i	0.911911	−	1.57948i
$890$		0			0
$891$	1.56499	−	0.149438i	1.56499	−	0.149438i
$892$	1.34700			1.34700
$893$	0.0845850	−	0.146505i	0.0845850	−	0.146505i
$894$		0			0
$895$		0			0
$896$	−3.06154	−	5.30274i	−3.06154	−	5.30274i
$897$		0			0
$898$	−1.65210	+	2.86152i	−1.65210	+	2.86152i
$899$	−3.90993			−3.90993
$900$	−2.53917	−	1.30903i	−2.53917	−	1.30903i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$907$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$911$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$912$	0.296445	+	0.282659i	0.296445	+	0.282659i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	2.84380	−	4.92561i	2.84380	−	4.92561i
$917$		0			0
$918$		0			0
$919$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$919$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$920$		0			0
$921$		0			0
$922$	−1.65210	−	2.86152i	−1.65210	−	2.86152i
$923$		0			0
$924$	−3.77078	−	3.59543i	−3.77078	−	3.59543i
$925$		0			0
$926$		0			0
$927$		0			0
$928$	−9.56943			−9.56943
$929$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$929$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$930$		0			0
$931$	−0.0164569	−	0.0285041i	−0.0164569	−	0.0285041i
$932$	0.934347	+	1.61834i	0.934347	+	1.61834i
$933$	0.959493	−	0.281733i	0.959493	−	0.281733i
$934$	1.95496	−	3.38610i	1.95496	−	3.38610i
$935$		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	$0.333333\pi$
$942$	−0.606397	+	2.49960i	−0.606397	+	2.49960i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$947$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$948$		0			0
$949$		0			0
$950$	−0.0934441	−	0.161850i	−0.0934441	−	0.161850i
$951$	1.04758	+	0.998867i	1.04758	+	0.998867i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$	−0.673501	+	1.16654i	−0.673501	+	1.16654i
$957$	−3.00319	+	0.881816i	−3.00319	+	0.881816i
$958$		0			0
$959$	−1.07701	−	1.86544i	−1.07701	−	1.86544i
$960$		0			0
$961$	−1.42837	+	2.47401i	−1.42837	+	2.47401i
$962$		0			0
$963$	−1.03115	−	0.531595i	−1.03115	−	0.531595i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$967$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$968$	−2.68285	−	4.64682i	−2.68285	−	4.64682i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−2.24555	−	1.76592i	−2.24555	−	1.76592i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	4.12985	+	7.15312i	4.12985	+	7.15312i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	0.370638	−	0.641964i	0.370638	−	0.641964i
$980$		0			0
$981$		0			0
$982$	3.92771			3.92771
$983$		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
$987$	1.97876	−	0.581017i	1.97876	−	0.581017i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−4.71962	+	8.17462i	−4.71962	+	8.17462i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$997$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$998$		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.1168.1	yes	20
9.4	even	3	inner	1503.1.f.b.166.1	✓	20
167.166	odd	2	CM	1503.1.f.b.1168.1	yes	20
1503.166	odd	6	inner	1503.1.f.b.166.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1503.1.f.b.166.1	✓	20	9.4	even	3	inner
1503.1.f.b.166.1	✓	20	1503.166	odd	6	inner
1503.1.f.b.1168.1	yes	20	1.1	even	1	trivial
1503.1.f.b.1168.1	yes	20	167.166	odd	2	CM

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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)

\(f(q)\)	\(=\)	\(q+(-0.981929 + 1.70075i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-1.42837 - 2.47401i) q^{4} +(1.42131 + 1.35522i) q^{6} +(-0.580057 + 1.00469i) q^{7} +3.64636 q^{8} +(-0.888835 - 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.981929 + 1.70075i) q^{2} +(0.235759 - 0.971812i) q^{3} +(-1.42837 - 2.47401i) q^{4} +(1.42131 + 1.35522i) q^{6} +(-0.580057 + 1.00469i) q^{7} +3.64636 q^{8} +(-0.888835 - 0.458227i) q^{9} +(0.786053 - 1.36148i) q^{11} +(-2.74102 + 0.804835i) q^{12} +(-1.13915 - 1.97306i) q^{14} +(-2.15210 + 3.72755i) q^{16} +(1.65210 - 1.06174i) q^{18} +0.0951638 q^{19} +(0.839614 + 0.800570i) q^{21} +(1.54370 + 2.67376i) q^{22} +(0.859663 - 3.54358i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.654861 + 0.755750i) q^{27} +3.31414 q^{28} +(0.995472 - 1.72421i) q^{29} +(-0.981929 - 1.70075i) q^{31} +(-2.40324 - 4.16253i) q^{32} +(-1.13779 - 1.08488i) q^{33} +(0.135929 + 2.85350i) q^{36} +(-0.0934441 + 0.161850i) q^{38} +(-2.18601 + 0.641871i) q^{42} -4.49109 q^{44} +(0.888835 - 1.53951i) q^{47} +(3.11510 + 2.97024i) q^{48} +(-0.172932 - 0.299527i) q^{49} +(-0.981929 - 1.70075i) q^{50} +(-0.642315 - 1.85585i) q^{54} +(-2.11510 + 3.66346i) q^{56} +(0.0224357 - 0.0924813i) q^{57} +(1.95496 + 3.38610i) q^{58} +(0.959493 - 1.66189i) q^{61} +3.85674 q^{62} +(0.975950 - 0.627205i) q^{63} +5.13503 q^{64} +(2.96233 - 0.869819i) q^{66} +(-3.24102 - 1.67086i) q^{72} +(0.723734 + 0.690079i) q^{75} +(-0.135929 - 0.235436i) q^{76} +(0.911911 + 1.57948i) q^{77} +(0.580057 + 0.814576i) q^{81} +(0.781338 - 3.22072i) q^{84} +(-1.44091 - 1.37391i) q^{87} +(2.86624 - 4.96447i) q^{88} +0.471518 q^{89} +(-1.88431 + 0.553283i) q^{93} +(1.74555 + 3.02337i) q^{94} +(-4.61178 + 1.35414i) q^{96} +(0.142315 - 0.246497i) q^{97} +0.679228 q^{98} +(-1.32254 + 0.849945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 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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