LMFDB - Embedded newform 1503.1.f.b.1168.8

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			1168.8
Root			$-0.327068 + 0.945001i$ of defining polynomial
Character	$\chi$	$=$	1503.1168
Dual form			1503.1.f.b.166.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.786053 - 1.36148i) q^{2} +(0.0475819 + 0.998867i) q^{3} +(-0.735759 - 1.27437i) q^{4} +(1.39734 + 0.720381i) q^{6} +(-0.981929 + 1.70075i) q^{7} -0.741276 q^{8} +(-0.995472 + 0.0950560i) q^{9} +O(q^{10})$	\(q+(0.786053 - 1.36148i) q^{2} +(0.0475819 + 0.998867i) q^{3} +(-0.735759 - 1.27437i) q^{4} +(1.39734 + 0.720381i) q^{6} +(-0.981929 + 1.70075i) q^{7} -0.741276 q^{8} +(-0.995472 + 0.0950560i) q^{9} +(-0.723734 + 1.25354i) q^{11} +(1.23792 - 0.795563i) q^{12} +(1.54370 + 2.67376i) q^{14} +(0.153077 - 0.265136i) q^{16} +(-0.653077 + 1.43004i) q^{18} +1.16011 q^{19} +(-1.74555 - 0.899892i) q^{21} +(1.13779 + 1.97070i) q^{22} +(-0.0352713 - 0.740437i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.142315 - 0.989821i) q^{27} +2.88985 q^{28} +(0.327068 - 0.566498i) q^{29} +(0.786053 + 1.36148i) q^{31} +(-0.611291 - 1.05879i) q^{32} +(-1.28656 - 0.663268i) q^{33} +(0.853564 + 1.19866i) q^{36} +(0.911911 - 1.57948i) q^{38} +(-2.59728 + 1.66917i) q^{42} +2.12998 q^{44} +(0.995472 - 1.72421i) q^{47} +(0.272120 + 0.140287i) q^{48} +(-1.42837 - 2.47401i) q^{49} +(0.786053 + 1.36148i) q^{50} +(-1.45949 - 0.584293i) q^{54} +(0.727880 - 1.26073i) q^{56} +(0.0552004 + 1.15880i) q^{57} +(-0.514186 - 0.890596i) q^{58} +(-0.841254 + 1.45709i) q^{61} +2.47152 q^{62} +(0.815816 - 1.78639i) q^{63} -1.61587 q^{64} +(-1.91433 + 1.23027i) q^{66} +(0.737920 - 0.0704628i) q^{72} +(-0.888835 - 0.458227i) q^{75} +(-0.853564 - 1.47842i) q^{76} +(-1.42131 - 2.46178i) q^{77} +(0.981929 - 0.189251i) q^{81} +(0.137505 + 2.88658i) q^{84} +(0.581419 + 0.299742i) q^{87} +(0.536487 - 0.929222i) q^{88} +0.0951638 q^{89} +(-1.32254 + 0.849945i) q^{93} +(-1.56499 - 2.71064i) q^{94} +(1.02850 - 0.660977i) q^{96} +(0.959493 - 1.66189i) q^{97} -4.49109 q^{98} +(0.601300 - 1.31666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$2$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$3$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$3$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$4$	−0.735759	−	1.27437i	−0.735759	−	1.27437i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	1.39734	+	0.720381i	1.39734	+	0.720381i
$7$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$7$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$8$	−0.741276			−0.741276
$9$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$10$		0			0
$11$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$11$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$12$	1.23792	−	0.795563i	1.23792	−	0.795563i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	1.54370	+	2.67376i	1.54370	+	2.67376i
$15$		0			0
$16$	0.153077	−	0.265136i	0.153077	−	0.265136i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−0.653077	+	1.43004i	−0.653077	+	1.43004i
$19$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$19$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$20$		0			0
$21$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$22$	1.13779	+	1.97070i	1.13779	+	1.97070i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.0352713	−	0.740437i	−0.0352713	−	0.740437i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$28$	2.88985			2.88985
$29$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$29$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$30$		0			0
$31$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$31$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$32$	−0.611291	−	1.05879i	−0.611291	−	1.05879i
$33$	−1.28656	−	0.663268i	−1.28656	−	0.663268i
$34$		0			0
$35$		0			0
$36$	0.853564	+	1.19866i	0.853564	+	1.19866i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.911911	−	1.57948i	0.911911	−	1.57948i
$39$		0			0
$40$		0			0
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	−2.59728	+	1.66917i	−2.59728	+	1.66917i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	2.12998			2.12998
$45$		0			0
$46$		0			0
$47$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$47$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$48$	0.272120	+	0.140287i	0.272120	+	0.140287i
$49$	−1.42837	−	2.47401i	−1.42837	−	2.47401i
$50$	0.786053	+	1.36148i	0.786053	+	1.36148i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−1.45949	−	0.584293i	−1.45949	−	0.584293i
$55$		0			0
$56$	0.727880	−	1.26073i	0.727880	−	1.26073i
$57$	0.0552004	+	1.15880i	0.0552004	+	1.15880i
$58$	−0.514186	−	0.890596i	−0.514186	−	0.890596i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$61$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$62$	2.47152			2.47152
$63$	0.815816	−	1.78639i	0.815816	−	1.78639i
$64$	−1.61587			−1.61587
$65$		0			0
$66$	−1.91433	+	1.23027i	−1.91433	+	1.23027i
$67$		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			$\pi$
$72$	0.737920	−	0.0704628i	0.737920	−	0.0704628i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$76$	−0.853564	−	1.47842i	−0.853564	−	1.47842i
$77$	−1.42131	−	2.46178i	−1.42131	−	2.46178i
$78$		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
$81$	0.981929	−	0.189251i	0.981929	−	0.189251i
$82$		0			0
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$	0.137505	+	2.88658i	0.137505	+	2.88658i
$85$		0			0
$86$		0			0
$87$	0.581419	+	0.299742i	0.581419	+	0.299742i
$88$	0.536487	−	0.929222i	0.536487	−	0.929222i
$89$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$89$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.32254	+	0.849945i	−1.32254	+	0.849945i
$94$	−1.56499	−	2.71064i	−1.56499	−	2.71064i
$95$		0			0
$96$	1.02850	−	0.660977i	1.02850	−	0.660977i
$97$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$97$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$98$	−4.49109			−4.49109
$99$	0.601300	−	1.31666i	0.601300	−	1.31666i
$100$	1.47152			1.47152
$101$		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
$107$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$107$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$108$	−1.15669	+	0.909632i	−1.15669	+	0.909632i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	0.300620	+	0.520690i	0.300620	+	0.520690i
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	1.62108	+	0.835724i	1.62108	+	0.835724i
$115$		0			0
$116$	−0.962573			−0.962573
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.547582	−	0.948440i	−0.547582	−	0.948440i
$122$	1.32254	+	2.29071i	1.32254	+	2.29071i
$123$		0			0
$124$	1.15669	−	2.00345i	1.15669	−	2.00345i
$125$		0			0
$126$	−1.79086	−	2.51492i	−1.79086	−	2.51492i
$127$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$127$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$128$	−0.658873	+	1.14120i	−0.658873	+	1.14120i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	0.101348	+	2.12756i	0.101348	+	2.12756i
$133$	−1.13915	+	1.97306i	−1.13915	+	1.97306i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$137$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$138$		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
$141$	1.76962	+	0.912303i	1.76962	+	0.912303i
$142$		0			0
$143$		0			0
$144$	−0.127181	+	0.278487i	−0.127181	+	0.278487i
$145$		0			0
$146$		0			0
$147$	2.40324	−	1.54447i	2.40324	−	1.54447i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	−1.32254	+	0.849945i	−1.32254	+	0.849945i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	−0.859965			−0.859965
$153$		0			0
$154$	−4.46890			−4.46890
$155$		0			0
$156$		0			0
$157$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$157$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.514186	−	1.48564i	0.514186	−	1.48564i
$163$		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
$168$	1.29393	+	0.667068i	1.29393	+	0.667068i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		0			0
$171$	−1.15486	+	0.110276i	−1.15486	+	0.110276i
$172$		0			0
$173$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.235759	−	0.971812i	$-0.424242\pi$
$173$	0.959493	−	1.66189i	0.959493	−	1.66189i	0.723734	−	0.690079i	$-0.242424\pi$
$174$	0.865121	−	0.555979i	0.865121	−	0.555979i
$175$	−0.981929	−	1.70075i	−0.981929	−	1.70075i
$176$	0.221573	+	0.383776i	0.221573	+	0.383776i
$177$		0			0
$178$	0.0748038	−	0.129564i	0.0748038	−	0.129564i
$179$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$179$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$180$		0			0
$181$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$181$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$182$		0			0
$183$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$184$		0			0
$185$		0			0
$186$	0.117600	+	2.46872i	0.117600	+	2.46872i
$187$		0			0
$188$	−2.92971			−2.92971
$189$	1.82318	+	0.729892i	1.82318	+	0.729892i
$190$		0			0
$191$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$191$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$192$	−0.0768864	−	1.61404i	−0.0768864	−	1.61404i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	−1.50842	−	2.61267i	−1.50842	−	2.61267i
$195$		0			0
$196$	−2.10187	+	3.64054i	−2.10187	+	3.64054i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−1.31996	−	1.85363i	−1.31996	−	1.85363i
$199$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$199$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$200$	0.370638	−	0.641964i	0.370638	−	0.641964i
$201$		0			0
$202$		0			0
$203$	0.642315	+	1.11252i	0.642315	+	1.11252i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.839614	+	1.45425i	−0.839614	+	1.45425i
$210$		0			0
$211$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$211$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$212$		0			0
$213$		0			0
$214$	1.54370	−	2.67376i	1.54370	−	2.67376i
$215$		0			0
$216$	0.105495	+	0.733731i	0.105495	+	0.733731i
$217$	−3.08739			−3.08739
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$223$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$224$	2.40098			2.40098
$225$	0.415415	−	0.909632i	0.415415	−	0.909632i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	1.43613	−	0.922943i	1.43613	−	0.922943i
$229$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$229$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$230$		0			0
$231$	2.39136	−	1.53684i	2.39136	−	1.53684i
$232$	−0.242448	+	0.419932i	−0.242448	+	0.419932i
$233$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$233$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$239$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$240$		0			0
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−1.72171			−1.72171
$243$	0.235759	+	0.971812i	0.235759	+	0.971812i
$244$	2.47584			2.47584
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.582682	−	1.00924i	−0.582682	−	1.00924i
$249$		0			0
$250$		0			0
$251$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$251$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$252$	−2.87677	+	0.274698i	−2.87677	+	0.274698i
$253$		0			0
$254$	1.13779	−	1.97070i	1.13779	−	1.97070i
$255$		0			0
$256$	0.227880	+	0.394700i	0.227880	+	0.394700i
$257$		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
$261$	−0.271738	+	0.595023i	−0.271738	+	0.595023i
$262$		0			0
$263$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$263$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$264$	0.953697	+	0.491665i	0.953697	+	0.491665i
$265$		0			0
$266$	1.79086	+	3.10187i	1.79086	+	3.10187i
$267$	0.00452808	+	0.0950560i	0.00452808	+	0.0950560i
$268$		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
$274$	0.370638	+	0.641964i	0.370638	+	0.641964i
$275$	−0.723734	−	1.25354i	−0.723734	−	1.25354i
$276$		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
$279$	−0.911911	−	1.28060i	−0.911911	−	1.28060i
$280$		0			0
$281$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$281$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$282$	2.63310	−	1.69219i	2.63310	−	1.69219i
$283$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.723734	+	0.690079i	$0.242424\pi$
$283$	0.959493	+	1.66189i	0.959493	+	1.66189i	0.235759	+	0.971812i	$0.424242\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.709167	+	0.995885i	0.709167	+	0.995885i
$289$	1.00000			1.00000
$290$		0			0
$291$	1.70566	+	0.879330i	1.70566	+	0.879330i
$292$		0			0
$293$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$293$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$294$	−0.213695	−	4.48601i	−0.213695	−	4.48601i
$295$		0			0
$296$		0			0
$297$	1.34378	+	0.537970i	1.34378	+	0.537970i
$298$		0			0
$299$		0			0
$300$	0.0700176	+	1.46985i	0.0700176	+	1.46985i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.177586	−	0.307588i	0.177586	−	0.307588i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−2.09148	+	3.62256i	−2.09148	+	3.62256i
$309$		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	$0.666667\pi$
$314$	0.447468			0.447468
$315$		0			0
$316$		0			0
$317$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$317$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$318$		0			0
$319$	0.473420	+	0.819988i	0.473420	+	0.819988i
$320$		0			0
$321$	0.0934441	+	1.96163i	0.0934441	+	1.96163i
$322$		0			0
$323$		0			0
$324$	−0.963639	−	1.11210i	−0.963639	−	1.11210i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.95496	+	3.38610i	1.95496	+	3.38610i
$330$		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
$334$	−1.57211			−1.57211
$335$		0			0
$336$	−0.505796	+	0.325055i	−0.505796	+	0.325055i
$337$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.580057	+	0.814576i	$0.303030\pi$
$337$	0.995472	+	1.72421i	0.995472	+	1.72421i	0.415415	+	0.909632i	$0.363636\pi$
$338$	0.786053	+	1.36148i	0.786053	+	1.36148i
$339$		0			0
$340$		0			0
$341$	−2.27557			−2.27557
$342$	−0.757643	+	1.65901i	−0.757643	+	1.65901i
$343$	3.64636			3.64636
$344$		0			0
$345$		0			0
$346$	−1.50842	−	2.61267i	−1.50842	−	2.61267i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−0.0458011	−	0.961482i	−0.0458011	−	0.961482i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	−3.08739			−3.08739
$351$		0			0
$352$	1.76965			1.76965
$353$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$353$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$354$		0			0
$355$		0			0
$356$	−0.0700176	−	0.121274i	−0.0700176	−	0.121274i
$357$		0			0
$358$	0.911911	−	1.57948i	0.911911	−	1.57948i
$359$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$359$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$360$		0			0
$361$	0.345864			0.345864
$362$	−1.56499	+	2.71064i	−1.56499	+	2.71064i
$363$	0.921310	−	0.592090i	0.921310	−	0.592090i
$364$		0			0
$365$		0			0
$366$	−2.22518	+	1.43004i	−2.22518	+	1.43004i
$367$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$367$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	2.05622	+	1.06005i	2.05622	+	1.06005i
$373$		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
$376$	−0.737920	+	1.27811i	−0.737920	+	1.27811i
$377$		0			0
$378$	2.42685	−	1.90850i	2.42685	−	1.90850i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.0688733	+	1.44583i	0.0688733	+	1.44583i
$382$	1.45949	+	2.52792i	1.45949	+	2.52792i
$383$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$383$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$384$	−1.17126	−	0.603826i	−1.17126	−	0.603826i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−2.82382			−2.82382
$389$		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
$392$	1.05882	+	1.83392i	1.05882	+	1.83392i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−2.12033	+	0.202467i	−2.12033	+	0.202467i
$397$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$397$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$398$	−1.50842	+	2.61267i	−1.50842	+	2.61267i
$399$	−2.02503	−	1.04398i	−2.02503	−	1.04398i
$400$	0.153077	+	0.265136i	0.153077	+	0.265136i
$401$		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
$406$	2.01957			2.01957
$407$		0			0
$408$		0			0
$409$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$409$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$410$		0			0
$411$	−0.419102	−	0.216062i	−0.419102	−	0.216062i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	1.31996	+	2.28624i	1.31996	+	2.28624i
$419$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$419$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$420$		0			0
$421$	0.654861	−	1.13425i	0.654861	−	1.13425i	−0.327068	−	0.945001i	$-0.606061\pi$
$421$	0.654861	−	1.13425i	0.654861	−	1.13425i	0.981929	−	0.189251i	$-0.0606061\pi$
$422$	0.447468			0.447468
$423$	−0.827068	+	1.81103i	−0.827068	+	1.81103i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.65210	−	2.86152i	−1.65210	−	2.86152i
$428$	−1.44493	−	2.50268i	−1.44493	−	2.50268i
$429$		0			0
$430$		0			0
$431$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$431$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$432$	−0.284223	−	0.113786i	−0.284223	−	0.113786i
$433$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$433$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$434$	−2.42685	+	4.20343i	−2.42685	+	4.20343i
$435$		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
$441$	1.65707	+	2.32703i	1.65707	+	2.32703i
$442$		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
$446$	0.0748038	+	0.129564i	0.0748038	+	0.129564i
$447$		0			0
$448$	1.58667	−	2.74820i	1.58667	−	2.74820i
$449$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$449$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$450$	−0.911911	−	1.28060i	−0.911911	−	1.28060i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.0409188	−	0.858991i	−0.0409188	−	0.858991i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	1.02837			1.02837
$459$		0			0
$460$		0			0
$461$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$461$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$462$	−0.212639	−	4.46384i	−0.212639	−	4.46384i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$	−0.100133	−	0.173435i	−0.100133	−	0.173435i
$465$		0			0
$466$	1.45949	−	2.52792i	1.45949	−	2.52792i
$467$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$467$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.580057	+	1.00469i	−0.580057	+	1.00469i
$476$		0			0
$477$		0			0
$478$	−0.149608			−0.149608
$479$		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
$484$	−0.805777	+	1.39565i	−0.805777	+	1.39565i
$485$		0			0
$486$	1.50842	+	0.442913i	1.50842	+	0.442913i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	0.623601	−	1.08011i	0.623601	−	1.08011i
$489$		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
$496$	0.481305			0.481305
$497$		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
$501$	0.841254	−	0.540641i	0.841254	−	0.540641i
$502$	−1.02951	+	1.78316i	−1.02951	+	1.78316i
$503$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$503$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$504$	−0.604745	+	1.32421i	−0.604745	+	1.32421i
$505$		0			0
$506$		0			0
$507$	−0.888835	−	0.458227i	−0.888835	−	0.458227i
$508$	−1.06499	−	1.84461i	−1.06499	−	1.84461i
$509$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	0.723734	−	0.690079i	$-0.242424\pi$
$509$	−0.235759	−	0.408346i	−0.235759	−	0.408346i	−0.959493	+	0.281733i	$0.909091\pi$
$510$		0			0
$511$		0			0
$512$	−0.601241			−0.601241
$513$	−0.165101	−	1.14831i	−0.165101	−	1.14831i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.44091	+	2.49574i	1.44091	+	2.49574i
$518$		0			0
$519$	1.70566	+	0.879330i	1.70566	+	0.879330i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	0.596514	+	0.837686i	0.596514	+	0.837686i
$523$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$523$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$524$		0			0
$525$	1.65210	−	1.06174i	1.65210	−	1.06174i
$526$	1.32254	+	2.29071i	1.32254	+	2.29071i
$527$		0			0
$528$	−0.372799	+	0.239583i	−0.372799	+	0.239583i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$	3.35256			3.35256
$533$		0			0
$534$	0.132977	+	0.0685542i	0.132977	+	0.0685542i
$535$		0			0
$536$		0			0
$537$	0.0552004	+	1.15880i	0.0552004	+	1.15880i
$538$		0			0
$539$	4.13503			4.13503
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−0.0947329	−	1.98869i	−0.0947329	−	1.98869i
$544$		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	$0.666667\pi$
$548$	0.693847			0.693847
$549$	0.698939	−	1.53046i	0.698939	−	1.53046i
$550$	−2.27557			−2.27557
$551$	0.379436	−	0.657203i	0.379436	−	0.657203i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$557$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$558$	−2.46033	+	0.234933i	−2.46033	+	0.234933i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.39734	−	2.42027i	−1.39734	−	2.42027i
$563$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	0.580057	−	0.814576i	$-0.303030\pi$
$563$	−0.415415	−	0.719520i	−0.415415	−	0.719520i	−0.995472	+	0.0950560i	$0.969697\pi$
$564$	−0.139401	−	2.92639i	−0.139401	−	2.92639i
$565$		0			0
$566$	3.01685			3.01685
$567$	−0.642315	+	1.85585i	−0.642315	+	1.85585i
$568$		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
$573$	−1.65033	−	0.850806i	−1.65033	−	0.850806i
$574$		0			0
$575$		0			0
$576$	1.60856	−	0.153599i	1.60856	−	0.153599i
$577$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$577$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$578$	0.786053	−	1.36148i	0.786053	−	1.36148i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	2.53794	−	1.63103i	2.53794	−	1.63103i
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−2.91899			−2.91899
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	−3.73643	−	1.92626i	−3.73643	−	1.92626i
$589$	0.911911	+	1.57948i	0.911911	+	1.57948i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	1.78872	−	1.40667i	1.78872	−	1.40667i
$595$		0			0
$596$		0			0
$597$	−0.0913090	−	1.91681i	−0.0913090	−	1.91681i
$598$		0			0
$599$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$599$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$600$	0.658873	+	0.339672i	0.658873	+	0.339672i
$601$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$601$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$602$		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	$0.333333\pi$
$608$	−0.709167	−	1.22831i	−0.709167	−	1.22831i
$609$	−1.08070	+	0.694523i	−1.08070	+	0.694523i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$613$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$614$		0			0
$615$		0			0
$616$	1.05358	+	1.82486i	1.05358	+	1.82486i
$617$	0.654861	+	1.13425i	0.654861	+	1.13425i	0.981929	+	0.189251i	$0.0606061\pi$
$617$	0.654861	+	1.13425i	0.654861	+	1.13425i	−0.327068	+	0.945001i	$0.606061\pi$
$618$		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
$622$	1.57211			1.57211
$623$	−0.0934441	+	0.161850i	−0.0934441	+	0.161850i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$	−1.49256	−	0.769467i	−1.49256	−	0.769467i
$628$	0.209419	−	0.362724i	0.209419	−	0.362724i
$629$		0			0
$630$		0			0
$631$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$631$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$632$		0			0
$633$	−0.239446	+	0.153882i	−0.239446	+	0.153882i
$634$	−1.39734	−	2.42027i	−1.39734	−	2.42027i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	1.48853			1.48853
$639$		0			0
$640$		0			0
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	2.74418	+	1.41473i	2.74418	+	1.41473i
$643$		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			$\pi$
$648$	−0.727880	+	0.140287i	−0.727880	+	0.140287i
$649$		0			0
$650$		0			0
$651$	−0.146904	−	3.08390i	−0.146904	−	3.08390i
$652$		0			0
$653$	0.142315	+	0.246497i	0.142315	+	0.246497i	0.928368	−	0.371662i	$-0.121212\pi$
$653$	0.142315	+	0.246497i	0.142315	+	0.246497i	−0.786053	+	0.618159i	$0.787879\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	6.14682			6.14682
$659$		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
$668$	−0.735759	+	1.27437i	−0.735759	+	1.27437i
$669$	−0.0845850	−	0.0436066i	−0.0845850	−	0.0436066i
$670$		0			0
$671$	−1.21769	−	2.10910i	−1.21769	−	2.10910i
$672$	0.114243	+	2.39826i	0.114243	+	2.39826i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$	3.12998			3.12998
$675$	0.928368	+	0.371662i	0.928368	+	0.371662i
$676$	1.47152			1.47152
$677$	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
$679$	1.88431	+	3.26372i	1.88431	+	3.26372i
$680$		0			0
$681$		0			0
$682$	−1.78872	+	3.09816i	−1.78872	+	3.09816i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.990232	+	1.39059i	0.990232	+	1.39059i
$685$		0			0
$686$	2.86624	−	4.96447i	2.86624	−	4.96447i
$687$	−0.550294	+	0.353653i	−0.550294	+	0.353653i
$688$		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	$0.666667\pi$
$692$	−2.82382			−2.82382
$693$	1.64888	+	2.31553i	1.64888	+	2.31553i
$694$		0			0
$695$		0			0
$696$	−0.430992	−	0.222192i	−0.430992	−	0.222192i
$697$		0			0
$698$		0			0
$699$	0.0883470	+	1.85463i	0.0883470	+	1.85463i
$700$	−1.44493	+	2.50268i	−1.44493	+	2.50268i
$701$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$701$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$702$		0			0
$703$		0			0
$704$	1.16946	−	2.02557i	1.16946	−	2.02557i
$705$		0			0
$706$	−1.02951	−	1.78316i	−1.02951	−	1.78316i
$707$		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
$712$	−0.0705427			−0.0705427
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.853564	−	1.47842i	−0.853564	−	1.47842i
$717$	0.0800569	−	0.0514495i	0.0800569	−	0.0514495i
$718$	−0.223734	+	0.387519i	−0.223734	+	0.387519i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.271868	−	0.470888i	0.271868	−	0.470888i
$723$		0			0
$724$	1.46485	+	2.53720i	1.46485	+	2.53720i
$725$	0.327068	+	0.566498i	0.327068	+	0.566498i
$726$	−0.0819224	−	1.71976i	−0.0819224	−	1.71976i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$730$		0			0
$731$		0			0
$732$	0.117805	+	2.47303i	0.117805	+	2.47303i
$733$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$733$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$734$	−1.56499	−	2.71064i	−1.56499	−	2.71064i
$735$		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	$0.666667\pi$
$744$	0.980367	−	0.630044i	0.980367	−	0.630044i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.92837	+	3.34003i	−1.92837	+	3.34003i
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−0.304767	−	0.527871i	−0.304767	−	0.527871i
$753$	−0.0623191	−	1.30824i	−0.0623191	−	1.30824i
$754$		0			0
$755$		0			0
$756$	−0.411269	−	2.86044i	−0.411269	−	2.86044i
$757$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	−0.888835	−	0.458227i	$-0.848485\pi$
$761$	−0.841254	−	1.45709i	−0.841254	−	1.45709i	0.0475819	−	0.998867i	$-0.484848\pi$
$762$	2.02261	+	1.04273i	2.02261	+	1.04273i
$763$		0			0
$764$	2.73222			2.73222
$765$		0			0
$766$	2.05902			2.05902
$767$		0			0
$768$	−0.383410	+	0.246403i	−0.383410	+	0.246403i
$769$		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
$775$	−1.57211			−1.57211
$776$	−0.711249	+	1.23192i	−0.711249	+	1.23192i
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.607279	−	0.243118i	−0.607279	−	0.243118i
$784$	−0.874598			−0.874598
$785$		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
$789$	−1.49547	−	0.770969i	−1.49547	−	0.770969i
$790$		0			0
$791$		0			0
$792$	−0.445729	+	0.976011i	−0.445729	+	0.976011i
$793$		0			0
$794$	−1.39734	+	2.42027i	−1.39734	+	2.42027i
$795$		0			0
$796$	1.41191	+	2.44550i	1.41191	+	2.44550i
$797$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$797$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$798$	−3.01314	+	1.93643i	−3.01314	+	1.93643i
$799$		0			0
$800$	1.22258			1.22258
$801$	−0.0947329	+	0.00904590i	−0.0947329	+	0.00904590i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$809$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.945178	−	1.63710i	0.945178	−	1.63710i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−2.27557			−2.27557
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	−0.623601	+	0.400764i	−0.623601	+	0.400764i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	1.21769	−	0.782560i	1.21769	−	0.782560i
$826$		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
$836$	2.47101			2.47101
$837$	1.23576	−	0.971812i	1.23576	−	0.971812i
$838$	−2.91899			−2.91899
$839$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	0.0475819	+	0.998867i	$0.484848\pi$
$839$	−0.841254	+	1.45709i	−0.841254	+	1.45709i	−0.888835	+	0.458227i	$0.848485\pi$
$840$		0			0
$841$	0.286053	+	0.495458i	0.286053	+	0.495458i
$842$	−1.02951	−	1.78316i	−1.02951	−	1.78316i
$843$	1.58006	+	0.814576i	1.58006	+	0.814576i
$844$	0.209419	−	0.362724i	0.209419	−	0.362724i
$845$		0			0
$846$	1.81556	+	2.54960i	1.81556	+	2.54960i
$847$	2.15075			2.15075
$848$		0			0
$849$	−1.61435	+	1.03748i	−1.61435	+	1.03748i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$853$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$854$	−5.19456			−5.19456
$855$		0			0
$856$	−1.45576			−1.45576
$857$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$857$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$858$		0			0
$859$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$859$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$860$		0			0
$861$		0			0
$862$	−1.39734	+	2.42027i	−1.39734	+	2.42027i
$863$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$863$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$864$	−0.961014	+	0.755750i	−0.961014	+	0.755750i
$865$		0			0
$866$	0.653077	−	1.13116i	0.653077	−	1.13116i
$867$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$868$	2.27158	+	3.93449i	2.27158	+	3.93449i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$877$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$878$		0			0
$879$	1.56199	−	1.00383i	1.56199	−	1.00383i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	4.47076	−	0.426905i	4.47076	−	0.426905i
$883$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$883$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$884$		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
$889$	−1.42131	+	2.46178i	−1.42131	+	2.46178i
$890$		0			0
$891$	−0.473420	+	1.36786i	−0.473420	+	1.36786i
$892$	0.140035			0.140035
$893$	1.15486	−	2.00028i	1.15486	−	2.00028i
$894$		0			0
$895$		0			0
$896$	−1.29393	−	2.24116i	−1.29393	−	2.24116i
$897$		0			0
$898$	0.653077	−	1.13116i	0.653077	−	1.13116i
$899$	1.02837			1.02837
$900$	−1.46485	+	0.139877i	−1.46485	+	0.139877i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$907$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	−0.995472	−	0.0950560i	$-0.969697\pi$
$911$	−0.415415	+	0.719520i	−0.415415	+	0.719520i	0.580057	+	0.814576i	$0.303030\pi$
$912$	0.315690	+	0.162749i	0.315690	+	0.162749i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.481286	−	0.833612i	0.481286	−	0.833612i
$917$		0			0
$918$		0			0
$919$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$919$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$920$		0			0
$921$		0			0
$922$	0.653077	+	1.13116i	0.653077	+	1.13116i
$923$		0			0
$924$	−3.71797	−	1.91675i	−3.71797	−	1.91675i
$925$		0			0
$926$		0			0
$927$		0			0
$928$	−0.799734			−0.799734
$929$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$929$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$930$		0			0
$931$	−1.65707	−	2.87013i	−1.65707	−	2.87013i
$932$	−1.36611	−	2.36617i	−1.36611	−	2.36617i
$933$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$934$	−0.514186	+	0.890596i	−0.514186	+	0.890596i
$935$		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	$0.333333\pi$
$942$	0.0212914	+	0.446961i	0.0212914	+	0.446961i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$947$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$948$		0			0
$949$		0			0
$950$	0.911911	+	1.57948i	0.911911	+	1.57948i
$951$	1.58006	+	0.814576i	1.58006	+	0.814576i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$	−0.0700176	+	0.121274i	−0.0700176	+	0.121274i
$957$	−0.796533	+	0.511901i	−0.796533	+	0.511901i
$958$		0			0
$959$	−0.462997	−	0.801934i	−0.462997	−	0.801934i
$960$		0			0
$961$	−0.735759	+	1.27437i	−0.735759	+	1.27437i
$962$		0			0
$963$	−1.95496	+	0.186677i	−1.95496	+	0.186677i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$967$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$968$	0.405909	+	0.703056i	0.405909	+	0.703056i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	1.06499	−	1.01546i	1.06499	−	1.01546i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.257552	+	0.446094i	0.257552	+	0.446094i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	−0.0688733	+	0.119292i	−0.0688733	+	0.119292i
$980$		0			0
$981$		0			0
$982$	−3.14421			−3.14421
$983$		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
$987$	−3.28924	+	2.11387i	−3.28924	+	2.11387i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	0.961014	−	1.66452i	0.961014	−	1.66452i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$997$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$998$		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.1168.8	yes	20
9.4	even	3	inner	1503.1.f.b.166.8	✓	20
167.166	odd	2	CM	1503.1.f.b.1168.8	yes	20
1503.166	odd	6	inner	1503.1.f.b.166.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1503.1.f.b.166.8	✓	20	9.4	even	3	inner
1503.1.f.b.166.8	✓	20	1503.166	odd	6	inner
1503.1.f.b.1168.8	yes	20	1.1	even	1	trivial
1503.1.f.b.1168.8	yes	20	167.166	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.786053 - 1.36148i) q^{2} +(0.0475819 + 0.998867i) q^{3} +(-0.735759 - 1.27437i) q^{4} +(1.39734 + 0.720381i) q^{6} +(-0.981929 + 1.70075i) q^{7} -0.741276 q^{8} +(-0.995472 + 0.0950560i) q^{9} +O(q^{10})\)	\(q+(0.786053 - 1.36148i) q^{2} +(0.0475819 + 0.998867i) q^{3} +(-0.735759 - 1.27437i) q^{4} +(1.39734 + 0.720381i) q^{6} +(-0.981929 + 1.70075i) q^{7} -0.741276 q^{8} +(-0.995472 + 0.0950560i) q^{9} +(-0.723734 + 1.25354i) q^{11} +(1.23792 - 0.795563i) q^{12} +(1.54370 + 2.67376i) q^{14} +(0.153077 - 0.265136i) q^{16} +(-0.653077 + 1.43004i) q^{18} +1.16011 q^{19} +(-1.74555 - 0.899892i) q^{21} +(1.13779 + 1.97070i) q^{22} +(-0.0352713 - 0.740437i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.142315 - 0.989821i) q^{27} +2.88985 q^{28} +(0.327068 - 0.566498i) q^{29} +(0.786053 + 1.36148i) q^{31} +(-0.611291 - 1.05879i) q^{32} +(-1.28656 - 0.663268i) q^{33} +(0.853564 + 1.19866i) q^{36} +(0.911911 - 1.57948i) q^{38} +(-2.59728 + 1.66917i) q^{42} +2.12998 q^{44} +(0.995472 - 1.72421i) q^{47} +(0.272120 + 0.140287i) q^{48} +(-1.42837 - 2.47401i) q^{49} +(0.786053 + 1.36148i) q^{50} +(-1.45949 - 0.584293i) q^{54} +(0.727880 - 1.26073i) q^{56} +(0.0552004 + 1.15880i) q^{57} +(-0.514186 - 0.890596i) q^{58} +(-0.841254 + 1.45709i) q^{61} +2.47152 q^{62} +(0.815816 - 1.78639i) q^{63} -1.61587 q^{64} +(-1.91433 + 1.23027i) q^{66} +(0.737920 - 0.0704628i) q^{72} +(-0.888835 - 0.458227i) q^{75} +(-0.853564 - 1.47842i) q^{76} +(-1.42131 - 2.46178i) q^{77} +(0.981929 - 0.189251i) q^{81} +(0.137505 + 2.88658i) q^{84} +(0.581419 + 0.299742i) q^{87} +(0.536487 - 0.929222i) q^{88} +0.0951638 q^{89} +(-1.32254 + 0.849945i) q^{93} +(-1.56499 - 2.71064i) q^{94} +(1.02850 - 0.660977i) q^{96} +(0.959493 - 1.66189i) q^{97} -4.49109 q^{98} +(0.601300 - 1.31666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 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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