LMFDB - Embedded newform 1503.1.f.b.1168.7

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			1168.7
Root			$0.580057 - 0.814576i$ of defining polynomial
Character	$\chi$	$=$	1503.1168
Dual form			1503.1.f.b.166.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.566498i) q^{2} +(0.723734 - 0.690079i) q^{3} +(0.286053 + 0.495458i) q^{4} +(-0.154218 - 0.635697i) q^{6} +(0.995472 - 1.72421i) q^{7} +1.02837 q^{8} +(0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.566498i) q^{2} +(0.723734 - 0.690079i) q^{3} +(0.286053 + 0.495458i) q^{4} +(-0.154218 - 0.635697i) q^{6} +(0.995472 - 1.72421i) q^{7} +1.02837 q^{8} +(0.0475819 - 0.998867i) q^{9} +(-0.928368 + 1.60798i) q^{11} +(0.548932 + 0.161181i) q^{12} +(-0.651174 - 1.12787i) q^{14} +(0.0502942 - 0.0871120i) q^{16} +(-0.550294 - 0.353653i) q^{18} -1.77767 q^{19} +(-0.469383 - 1.93482i) q^{21} +(0.607279 + 1.05184i) q^{22} +(0.744267 - 0.709657i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.654861 - 0.755750i) q^{27} +1.13903 q^{28} +(-0.580057 + 1.00469i) q^{29} +(0.327068 + 0.566498i) q^{31} +(0.481286 + 0.833612i) q^{32} +(0.437742 + 1.80440i) q^{33} +(0.508508 - 0.262154i) q^{36} +(-0.581419 + 1.00705i) q^{38} +(-1.24959 - 0.366914i) q^{42} -1.06225 q^{44} +(-0.0475819 + 0.0824143i) q^{47} +(-0.0237146 - 0.0977529i) q^{48} +(-1.48193 - 2.56678i) q^{49} +(0.327068 + 0.566498i) q^{50} +(-0.642315 + 0.123796i) q^{54} +(1.02371 - 1.77313i) q^{56} +(-1.28656 + 1.22673i) q^{57} +(0.379436 + 0.657203i) q^{58} +(0.959493 - 1.66189i) q^{61} +0.427894 q^{62} +(-1.67489 - 1.07639i) q^{63} +0.730242 q^{64} +(1.16536 + 0.342180i) q^{66} +(0.0489319 - 1.02721i) q^{72} +(0.235759 + 0.971812i) q^{75} +(-0.508508 - 0.880762i) q^{76} +(1.84833 + 3.20140i) q^{77} +(-0.995472 - 0.0950560i) q^{81} +(0.824356 - 0.786022i) q^{84} +(0.273507 + 1.12741i) q^{87} +(-0.954707 + 1.65360i) q^{88} +1.44747 q^{89} +(0.627639 + 0.184291i) q^{93} +(0.0311250 + 0.0539102i) q^{94} +(0.923582 + 0.271188i) q^{96} +(0.142315 - 0.246497i) q^{97} -1.93877 q^{98} +(1.56199 + 1.00383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.327068	−	0.566498i	0.327068	−	0.566498i	−0.654861	−	0.755750i	$-0.727273\pi$
$2$	0.327068	−	0.566498i	0.327068	−	0.566498i	0.981929	+	0.189251i	$0.0606061\pi$
$3$	0.723734	−	0.690079i	0.723734	−	0.690079i
$3$	0.723734	−	0.690079i	0.723734	−	0.690079i
$4$	0.286053	+	0.495458i	0.286053	+	0.495458i
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$	−0.154218	−	0.635697i	−0.154218	−	0.635697i
$7$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.415415	−	0.909632i	$-0.363636\pi$
$7$	0.995472	−	1.72421i	0.995472	−	1.72421i	0.580057	−	0.814576i	$-0.303030\pi$
$8$	1.02837			1.02837
$9$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$10$		0			0
$11$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.142315	+	0.989821i	$0.545455\pi$
$11$	−0.928368	+	1.60798i	−0.928368	+	1.60798i	−0.786053	+	0.618159i	$0.787879\pi$
$12$	0.548932	+	0.161181i	0.548932	+	0.161181i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−0.651174	−	1.12787i	−0.651174	−	1.12787i
$15$		0			0
$16$	0.0502942	−	0.0871120i	0.0502942	−	0.0871120i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−0.550294	−	0.353653i	−0.550294	−	0.353653i
$19$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$19$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$20$		0			0
$21$	−0.469383	−	1.93482i	−0.469383	−	1.93482i
$22$	0.607279	+	1.05184i	0.607279	+	1.05184i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	0.744267	−	0.709657i	0.744267	−	0.709657i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$28$	1.13903			1.13903
$29$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$29$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$30$		0			0
$31$	0.327068	+	0.566498i	0.327068	+	0.566498i	0.981929	−	0.189251i	$-0.0606061\pi$
$31$	0.327068	+	0.566498i	0.327068	+	0.566498i	−0.654861	+	0.755750i	$0.727273\pi$
$32$	0.481286	+	0.833612i	0.481286	+	0.833612i
$33$	0.437742	+	1.80440i	0.437742	+	1.80440i
$34$		0			0
$35$		0			0
$36$	0.508508	−	0.262154i	0.508508	−	0.262154i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.581419	+	1.00705i	−0.581419	+	1.00705i
$39$		0			0
$40$		0			0
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	−1.24959	−	0.366914i	−1.24959	−	0.366914i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−1.06225			−1.06225
$45$		0			0
$46$		0			0
$47$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$47$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$48$	−0.0237146	−	0.0977529i	−0.0237146	−	0.0977529i
$49$	−1.48193	−	2.56678i	−1.48193	−	2.56678i
$50$	0.327068	+	0.566498i	0.327068	+	0.566498i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.642315	+	0.123796i	−0.642315	+	0.123796i
$55$		0			0
$56$	1.02371	−	1.77313i	1.02371	−	1.77313i
$57$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$58$	0.379436	+	0.657203i	0.379436	+	0.657203i
$59$		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	$-0.242424\pi$
$62$	0.427894			0.427894
$63$	−1.67489	−	1.07639i	−1.67489	−	1.07639i
$64$	0.730242			0.730242
$65$		0			0
$66$	1.16536	+	0.342180i	1.16536	+	0.342180i
$67$		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			$\pi$
$72$	0.0489319	−	1.02721i	0.0489319	−	1.02721i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	0.235759	+	0.971812i	0.235759	+	0.971812i
$76$	−0.508508	−	0.880762i	−0.508508	−	0.880762i
$77$	1.84833	+	3.20140i	1.84833	+	3.20140i
$78$		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
$81$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$82$		0			0
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$	0.824356	−	0.786022i	0.824356	−	0.786022i
$85$		0			0
$86$		0			0
$87$	0.273507	+	1.12741i	0.273507	+	1.12741i
$88$	−0.954707	+	1.65360i	−0.954707	+	1.65360i
$89$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$89$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.627639	+	0.184291i	0.627639	+	0.184291i
$94$	0.0311250	+	0.0539102i	0.0311250	+	0.0539102i
$95$		0			0
$96$	0.923582	+	0.271188i	0.923582	+	0.271188i
$97$	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	$0.121212\pi$
$98$	−1.93877			−1.93877
$99$	1.56199	+	1.00383i	1.56199	+	1.00383i
$100$	−0.572106			−0.572106
$101$		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
$107$	−1.99094			−1.99094			−0.995472	−	0.0950560i	$-0.969697\pi$
$107$	−1.99094			−1.99094			−0.995472	+	0.0950560i	$0.969697\pi$
$108$	0.187118	−	0.540641i	0.187118	−	0.540641i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	−0.100133	−	0.173435i	−0.100133	−	0.173435i
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	0.274150	+	1.13006i	0.274150	+	1.13006i
$115$		0			0
$116$	−0.663708			−0.663708
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.22373	−	2.11957i	−1.22373	−	2.11957i
$122$	−0.627639	−	1.08710i	−0.627639	−	1.08710i
$123$		0			0
$124$	−0.187118	+	0.324097i	−0.187118	+	0.324097i
$125$		0			0
$126$	−1.15757	+	0.596770i	−1.15757	+	0.596770i
$127$	1.85674			1.85674			0.928368	−	0.371662i	$-0.121212\pi$
$127$	1.85674			1.85674			0.928368	+	0.371662i	$0.121212\pi$
$128$	−0.242448	+	0.419932i	−0.242448	+	0.419932i
$129$		0			0
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	−0.768787	+	0.733036i	−0.768787	+	0.733036i
$133$	−1.76962	+	3.06507i	−1.76962	+	3.06507i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$137$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$138$		0			0
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$	0.0224357	+	0.0924813i	0.0224357	+	0.0924813i
$142$		0			0
$143$		0			0
$144$	−0.0846203	−	0.0543822i	−0.0846203	−	0.0543822i
$145$		0			0
$146$		0			0
$147$	−2.84380	−	0.835015i	−2.84380	−	0.835015i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	0.627639	+	0.184291i	0.627639	+	0.184291i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	−1.82811			−1.82811
$153$		0			0
$154$	2.41812			2.41812
$155$		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
$162$	−0.379436	+	0.532843i	−0.379436	+	0.532843i
$163$		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
$168$	−0.482700	−	1.98972i	−0.482700	−	1.98972i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		0			0
$171$	−0.0845850	+	1.77566i	−0.0845850	+	1.77566i
$172$		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	$0.121212\pi$
$174$	0.728132	+	0.213799i	0.728132	+	0.213799i
$175$	0.995472	+	1.72421i	0.995472	+	1.72421i
$176$	0.0933830	+	0.161744i	0.0933830	+	0.161744i
$177$		0			0
$178$	0.473420	−	0.819988i	0.473420	−	0.819988i
$179$	−1.77767			−1.77767			−0.888835	−	0.458227i	$-0.848485\pi$
$179$	−1.77767			−1.77767			−0.888835	+	0.458227i	$0.848485\pi$
$180$		0			0
$181$	0.0951638			0.0951638			0.0475819	−	0.998867i	$-0.484848\pi$
$181$	0.0951638			0.0951638			0.0475819	+	0.998867i	$0.484848\pi$
$182$		0			0
$183$	−0.452418	−	1.86489i	−0.452418	−	1.86489i
$184$		0			0
$185$		0			0
$186$	0.309681	−	0.295281i	0.309681	−	0.295281i
$187$		0			0
$188$	−0.0544438			−0.0544438
$189$	−1.95496	+	0.376789i	−1.95496	+	0.376789i
$190$		0			0
$191$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$191$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$192$	0.528501	−	0.503924i	0.528501	−	0.503924i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	−0.0930932	−	0.161242i	−0.0930932	−	0.161242i
$195$		0			0
$196$	0.847821	−	1.46847i	0.847821	−	1.46847i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	1.07954	−	0.556543i	1.07954	−	0.556543i
$199$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$199$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$200$	−0.514186	+	0.890596i	−0.514186	+	0.890596i
$201$		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
$209$	1.65033	−	2.85846i	1.65033	−	2.85846i
$210$		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
$214$	−0.651174	+	1.12787i	−0.651174	+	1.12787i
$215$		0			0
$216$	−0.673440	−	0.777191i	−0.673440	−	0.777191i
$217$	1.30235			1.30235
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$223$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$224$	1.91643			1.91643
$225$	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	$0.666667\pi$
$228$	−0.975820	−	0.286527i	−0.975820	−	0.286527i
$229$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$229$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$230$		0			0
$231$	3.54692	+	1.04147i	3.54692	+	1.04147i
$232$	−0.596514	+	1.03319i	−0.596514	+	1.03319i
$233$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$233$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	−0.959493	−	0.281733i	$-0.909091\pi$
$239$	−0.723734	−	1.25354i	−0.723734	−	1.25354i	0.235759	−	0.971812i	$-0.424242\pi$
$240$		0			0
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−1.60098			−1.60098
$243$	−0.786053	+	0.618159i	−0.786053	+	0.618159i
$244$	1.09786			1.09786
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.336347	+	0.582571i	0.336347	+	0.582571i
$249$		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	$0.363636\pi$
$252$	0.0541973	−	1.13774i	0.0541973	−	1.13774i
$253$		0			0
$254$	0.607279	−	1.05184i	0.607279	−	1.05184i
$255$		0			0
$256$	0.523715	+	0.907100i	0.523715	+	0.907100i
$257$		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
$261$	0.975950	+	0.627205i	0.975950	+	0.627205i
$262$		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	$-0.242424\pi$
$264$	0.450161	+	1.85559i	0.450161	+	1.85559i
$265$		0			0
$266$	1.15757	+	2.00498i	1.15757	+	2.00498i
$267$	1.04758	−	0.998867i	1.04758	−	0.998867i
$268$		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
$274$	−0.514186	−	0.890596i	−0.514186	−	0.890596i
$275$	−0.928368	−	1.60798i	−0.928368	−	1.60798i
$276$		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
$279$	0.581419	−	0.299742i	0.581419	−	0.299742i
$280$		0			0
$281$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$281$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$282$	0.0597285	+	0.0175379i	0.0597285	+	0.0175379i
$283$	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
$288$	0.855569	−	0.441076i	0.855569	−	0.441076i
$289$	1.00000			1.00000
$290$		0			0
$291$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i
$292$		0			0
$293$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$293$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$294$	−1.40315	+	1.33790i	−1.40315	+	1.33790i
$295$		0			0
$296$		0			0
$297$	1.82318	−	0.351390i	1.82318	−	0.351390i
$298$		0			0
$299$		0			0
$300$	−0.414053	+	0.394798i	−0.414053	+	0.394798i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.0894065	+	0.154857i	−0.0894065	+	0.154857i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−1.05744	+	1.83154i	−1.05744	+	1.83154i
$309$		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	$0.666667\pi$
$314$	0.856736			0.856736
$315$		0			0
$316$		0			0
$317$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$317$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$318$		0			0
$319$	−1.07701	−	1.86544i	−1.07701	−	1.86544i
$320$		0			0
$321$	−1.44091	+	1.37391i	−1.44091	+	1.37391i
$322$		0			0
$323$		0			0
$324$	−0.237662	−	0.520406i	−0.237662	−	0.520406i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.0947329	+	0.164082i	0.0947329	+	0.164082i
$330$		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
$334$	−0.654136			−0.654136
$335$		0			0
$336$	−0.192154	−	0.0564214i	−0.192154	−	0.0564214i
$337$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$337$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$338$	0.327068	+	0.566498i	0.327068	+	0.566498i
$339$		0			0
$340$		0			0
$341$	−1.21456			−1.21456
$342$	0.978242	+	0.628678i	0.978242	+	0.628678i
$343$	−3.90993			−3.90993
$344$		0			0
$345$		0			0
$346$	−0.0930932	−	0.161242i	−0.0930932	−	0.161242i
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−0.480348	+	0.458011i	−0.480348	+	0.458011i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	1.30235			1.30235
$351$		0			0
$352$	−1.78724			−1.78724
$353$	−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
$356$	0.414053	+	0.717160i	0.414053	+	0.717160i
$357$		0			0
$358$	−0.581419	+	1.00705i	−0.581419	+	1.00705i
$359$	−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
$361$	2.16011			2.16011
$362$	0.0311250	−	0.0539102i	0.0311250	−	0.0539102i
$363$	−2.34833	−	0.689531i	−2.34833	−	0.689531i
$364$		0			0
$365$		0			0
$366$	−1.20443	−	0.353653i	−1.20443	−	0.353653i
$367$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	−0.888835	−	0.458227i	$-0.848485\pi$
$367$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i	0.841254	+	0.540641i	$0.181818\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.0882293	+	0.363686i	0.0882293	+	0.363686i
$373$		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
$376$	−0.0489319	+	0.0847525i	−0.0489319	+	0.0847525i
$377$		0			0
$378$	−0.425956	+	1.23072i	−0.425956	+	1.23072i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	1.34378	−	1.28129i	1.34378	−	1.28129i
$382$	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	$0.969697\pi$
$384$	0.114318	+	0.471227i	0.114318	+	0.471227i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.162838			0.162838
$389$		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
$392$	−1.52397	−	2.63960i	−1.52397	−	2.63960i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−0.0505439	+	1.06105i	−0.0505439	+	1.06105i
$397$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$397$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$398$	−0.0930932	+	0.161242i	−0.0930932	+	0.161242i
$399$	0.834408	+	3.43948i	0.834408	+	3.43948i
$400$	0.0502942	+	0.0871120i	0.0502942	+	0.0871120i
$401$		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
$406$	1.51087			1.51087
$407$		0			0
$408$		0			0
$409$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.786053	−	0.618159i	$-0.787879\pi$
$409$	−0.928368	−	1.60798i	−0.928368	−	1.60798i	−0.142315	−	0.989821i	$-0.545455\pi$
$410$		0			0
$411$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$	−1.07954	−	1.86982i	−1.07954	−	1.86982i
$419$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$419$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$420$		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	$0.303030\pi$
$422$	0.856736			0.856736
$423$	0.0800569	+	0.0514495i	0.0800569	+	0.0514495i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.91030	−	3.30873i	−1.91030	−	3.30873i
$428$	−0.569516	−	0.986430i	−0.569516	−	0.986430i
$429$		0			0
$430$		0			0
$431$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$431$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$432$	−0.0987706	+	0.0190365i	−0.0987706	+	0.0190365i
$433$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$433$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$434$	0.425956	−	0.737778i	0.425956	−	0.737778i
$435$		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
$441$	−2.63438	+	1.35812i	−2.63438	+	1.35812i
$442$		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
$446$	0.473420	+	0.819988i	0.473420	+	0.819988i
$447$		0			0
$448$	0.726935	−	1.25909i	0.726935	−	1.25909i
$449$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$449$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$450$	0.581419	−	0.299742i	0.581419	−	0.299742i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−1.32306	+	1.26154i	−1.32306	+	1.26154i
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−0.758872			−0.758872
$459$		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	$0.848485\pi$
$462$	1.75007	−	1.66869i	1.75007	−	1.66869i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$	0.0583469	+	0.101060i	0.0583469	+	0.101060i
$465$		0			0
$466$	0.642315	−	1.11252i	0.642315	−	1.11252i
$467$	1.16011			1.16011			0.580057	−	0.814576i	$-0.303030\pi$
$467$	1.16011			1.16011			0.580057	+	0.814576i	$0.303030\pi$
$468$		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
$475$	0.888835	−	1.53951i	0.888835	−	1.53951i
$476$		0			0
$477$		0			0
$478$	−0.946841			−0.946841
$479$		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
$484$	0.700106	−	1.21262i	0.700106	−	1.21262i
$485$		0			0
$486$	0.0930932	+	0.647478i	0.0930932	+	0.647478i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	0.986715	−	1.70904i	0.986715	−	1.70904i
$489$		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
$496$	0.0657984			0.0657984
$497$		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
$502$	0.271738	−	0.470664i	0.271738	−	0.470664i
$503$	0.471518			0.471518			0.235759	−	0.971812i	$-0.424242\pi$
$503$	0.471518			0.471518			0.235759	+	0.971812i	$0.424242\pi$
$504$	−1.72241	−	1.10692i	−1.72241	−	1.10692i
$505$		0			0
$506$		0			0
$507$	0.235759	+	0.971812i	0.235759	+	0.971812i
$508$	0.531125	+	0.919936i	0.531125	+	0.919936i
$509$	0.786053	+	1.36148i	0.786053	+	1.36148i	0.928368	+	0.371662i	$0.121212\pi$
$509$	0.786053	+	1.36148i	0.786053	+	1.36148i	−0.142315	+	0.989821i	$0.545455\pi$
$510$		0			0
$511$		0			0
$512$	0.200266			0.200266
$513$	1.16413	+	1.34347i	1.16413	+	1.34347i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.0883470	−	0.153022i	−0.0883470	−	0.153022i
$518$		0			0
$519$	−0.0671040	−	0.276606i	−0.0671040	−	0.276606i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	0.674512	−	0.347735i	0.674512	−	0.347735i
$523$	1.96386			1.96386			0.981929	−	0.189251i	$-0.0606061\pi$
$523$	1.96386			1.96386			0.981929	+	0.189251i	$0.0606061\pi$
$524$		0			0
$525$	1.91030	+	0.560914i	1.91030	+	0.560914i
$526$	−0.627639	−	1.08710i	−0.627639	−	1.08710i
$527$		0			0
$528$	0.179201	+	0.0526180i	0.179201	+	0.0526180i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$	−2.02482			−2.02482
$533$		0			0
$534$	−0.223226	−	0.920151i	−0.223226	−	0.920151i
$535$		0			0
$536$		0			0
$537$	−1.28656	+	1.22673i	−1.28656	+	1.22673i
$538$		0			0
$539$	5.50310			5.50310
$540$		0			0
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	0.0688733	−	0.0656706i	0.0688733	−	0.0656706i
$544$		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	$0.666667\pi$
$548$	0.899412			0.899412
$549$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$550$	−1.21456			−1.21456
$551$	1.03115	−	1.78600i	1.03115	−	1.78600i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.57211			−1.57211			−0.786053	−	0.618159i	$-0.787879\pi$
$557$	−1.57211			−1.57211			−0.786053	+	0.618159i	$0.787879\pi$
$558$	0.0203600	−	0.427409i	0.0203600	−	0.427409i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.154218	+	0.267114i	0.154218	+	0.267114i
$563$	−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	$-0.484848\pi$
$564$	−0.0394028	+	0.0375705i	−0.0394028	+	0.0375705i
$565$		0			0
$566$	0.186186			0.186186
$567$	−1.15486	+	1.62177i	−1.15486	+	1.62177i
$568$		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
$573$	0.462997	+	1.90850i	0.462997	+	1.90850i
$574$		0			0
$575$		0			0
$576$	0.0347463	−	0.729415i	0.0347463	−	0.729415i
$577$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$577$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$578$	0.327068	−	0.566498i	0.327068	−	0.566498i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	−0.178645	−	0.0524548i	−0.178645	−	0.0524548i
$583$		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	$0.666667\pi$
$588$	−0.399763	−	1.64784i	−0.399763	−	1.64784i
$589$	−0.581419	−	1.00705i	−0.581419	−	1.00705i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	0.397243	−	1.14776i	0.397243	−	1.14776i
$595$		0			0
$596$		0			0
$597$	−0.205996	+	0.196417i	−0.205996	+	0.196417i
$598$		0			0
$599$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$599$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$600$	0.242448	+	0.999383i	0.242448	+	0.999383i
$601$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$601$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$602$		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	$0.333333\pi$
$608$	−0.855569	−	1.48189i	−0.855569	−	1.48189i
$609$	2.21616	+	0.650724i	2.21616	+	0.650724i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$613$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$614$		0			0
$615$		0			0
$616$	1.90077	+	3.29223i	1.90077	+	3.29223i
$617$	−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
$622$	0.654136			0.654136
$623$	1.44091	−	2.49574i	1.44091	−	2.49574i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$	−0.778161	−	3.20762i	−0.778161	−	3.20762i
$628$	−0.374650	+	0.648913i	−0.374650	+	0.648913i
$629$		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
$634$	0.154218	+	0.267114i	0.154218	+	0.267114i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.40903			−1.40903
$639$		0			0
$640$		0			0
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	0.307040	+	1.26564i	0.307040	+	1.26564i
$643$		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			$\pi$
$648$	−1.02371	−	0.0977529i	−1.02371	−	0.0977529i
$649$		0			0
$650$		0			0
$651$	0.942554	−	0.898723i	0.942554	−	0.898723i
$652$		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
$658$	0.123936			0.123936
$659$		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
$668$	0.286053	−	0.495458i	0.286053	−	0.495458i
$669$	0.341254	+	1.40667i	0.341254	+	1.40667i
$670$		0			0
$671$	1.78153	+	3.08569i	1.78153	+	3.08569i
$672$	1.38698	−	1.32249i	1.38698	−	1.32249i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$	−0.0622501			−0.0622501
$675$	0.981929	−	0.189251i	0.981929	−	0.189251i
$676$	−0.572106			−0.572106
$677$	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
$679$	−0.283341	−	0.490761i	−0.283341	−	0.490761i
$680$		0			0
$681$		0			0
$682$	−0.397243	+	0.688045i	−0.397243	+	0.688045i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.903960	+	0.466024i	−0.903960	+	0.466024i
$685$		0			0
$686$	−1.27881	+	2.21497i	−1.27881	+	2.21497i
$687$	−1.11312	−	0.326842i	−1.11312	−	0.326842i
$688$		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	$0.666667\pi$
$692$	0.162838			0.162838
$693$	3.28572	−	1.69391i	3.28572	−	1.69391i
$694$		0			0
$695$		0			0
$696$	0.281267	+	1.15940i	0.281267	+	1.15940i
$697$		0			0
$698$		0			0
$699$	1.42131	−	1.35522i	1.42131	−	1.35522i
$700$	−0.569516	+	0.986430i	−0.569516	+	0.986430i
$701$	1.44747			1.44747			0.723734	−	0.690079i	$-0.242424\pi$
$701$	1.44747			1.44747			0.723734	+	0.690079i	$0.242424\pi$
$702$		0			0
$703$		0			0
$704$	−0.677933	+	1.17421i	−0.677933	+	1.17421i
$705$		0			0
$706$	0.271738	+	0.470664i	0.271738	+	0.470664i
$707$		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
$712$	1.48853			1.48853
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.508508	−	0.880762i	−0.508508	−	0.880762i
$717$	−1.38884	−	0.407799i	−1.38884	−	0.407799i
$718$	−0.428368	+	0.741955i	−0.428368	+	0.741955i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	0.706504	−	1.22370i	0.706504	−	1.22370i
$723$		0			0
$724$	0.0272219	+	0.0471497i	0.0272219	+	0.0471497i
$725$	−0.580057	−	1.00469i	−0.580057	−	1.00469i
$726$	−1.15868	+	1.10480i	−1.15868	+	1.10480i
$727$		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
$732$	0.794561	−	0.757613i	0.794561	−	0.757613i
$733$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.841254	+	0.540641i	$0.181818\pi$
$733$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.0475819	+	0.998867i	$0.484848\pi$
$734$	0.0311250	+	0.0539102i	0.0311250	+	0.0539102i
$735$		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	$0.666667\pi$
$744$	0.645446	+	0.189520i	0.645446	+	0.189520i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.98193	+	3.43280i	−1.98193	+	3.43280i
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	0.00478618	+	0.00828992i	0.00478618	+	0.00828992i
$753$	0.601300	−	0.573338i	0.601300	−	0.573338i
$754$		0			0
$755$		0			0
$756$	−0.745907	−	0.860822i	−0.745907	−	0.860822i
$757$	−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	$0.424242\pi$
$762$	−0.286343	−	1.18032i	−0.286343	−	1.18032i
$763$		0			0
$764$	−1.12353			−1.12353
$765$		0			0
$766$	−0.543476			−0.543476
$767$		0			0
$768$	1.00500	+	0.295095i	1.00500	+	0.295095i
$769$		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
$775$	−0.654136			−0.654136
$776$	0.146352	−	0.253490i	0.146352	−	0.253490i
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.13915	−	0.219553i	1.13915	−	0.219553i
$784$	−0.298129			−0.298129
$785$		0			0
$786$		0			0
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	−0.452418	−	1.86489i	−0.452418	−	1.86489i
$790$		0			0
$791$		0			0
$792$	1.60630	+	1.03231i	1.60630	+	1.03231i
$793$		0			0
$794$	0.154218	−	0.267114i	0.154218	−	0.267114i
$795$		0			0
$796$	−0.0814192	−	0.141022i	−0.0814192	−	0.141022i
$797$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$797$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$798$	2.22137	+	0.652252i	2.22137	+	0.652252i
$799$		0			0
$800$	−0.962573			−0.962573
$801$	0.0688733	−	1.44583i	0.0688733	−	1.44583i
$802$		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			$\pi$
$812$	−0.660703	+	1.14437i	−0.660703	+	1.14437i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−1.21456			−1.21456
$819$		0			0
$820$		0			0
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	−0.986715	−	0.289726i	−0.986715	−	0.289726i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	−1.78153	−	0.523103i	−1.78153	−	0.523103i
$826$		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
$836$	1.88833			1.88833
$837$	0.213947	−	0.618159i	0.213947	−	0.618159i
$838$	−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
$841$	−0.172932	−	0.299527i	−0.172932	−	0.299527i
$842$	0.271738	+	0.470664i	0.271738	+	0.470664i
$843$	0.111165	+	0.458227i	0.111165	+	0.458227i
$844$	−0.374650	+	0.648913i	−0.374650	+	0.648913i
$845$		0			0
$846$	0.0553301	−	0.0285246i	0.0553301	−	0.0285246i
$847$	−4.87277			−4.87277
$848$		0			0
$849$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.786053	−	1.36148i	0.786053	−	1.36148i	−0.142315	−	0.989821i	$-0.545455\pi$
$853$	0.786053	−	1.36148i	0.786053	−	1.36148i	0.928368	−	0.371662i	$-0.121212\pi$
$854$	−2.49919			−2.49919
$855$		0			0
$856$	−2.04743			−2.04743
$857$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.0475819	−	0.998867i	$-0.484848\pi$
$857$	0.888835	−	1.53951i	0.888835	−	1.53951i	0.841254	−	0.540641i	$-0.181818\pi$
$858$		0			0
$859$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	−0.995472	−	0.0950560i	$-0.969697\pi$
$859$	−0.580057	−	1.00469i	−0.580057	−	1.00469i	0.415415	−	0.909632i	$-0.363636\pi$
$860$		0			0
$861$		0			0
$862$	0.154218	−	0.267114i	0.154218	−	0.267114i
$863$	−0.284630			−0.284630			−0.142315	−	0.989821i	$-0.545455\pi$
$863$	−0.284630			−0.284630			−0.142315	+	0.989821i	$0.545455\pi$
$864$	0.314827	−	0.909632i	0.314827	−	0.909632i
$865$		0			0
$866$	0.550294	−	0.953137i	0.550294	−	0.953137i
$867$	0.723734	−	0.690079i	0.723734	−	0.690079i
$868$	0.372541	+	0.645259i	0.372541	+	0.645259i
$869$		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
$877$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.841254	+	0.540641i	$0.181818\pi$
$877$	0.888835	+	1.53951i	0.888835	+	1.53951i	0.0475819	+	0.998867i	$0.484848\pi$
$878$		0			0
$879$	−1.88431	−	0.553283i	−1.88431	−	0.553283i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.0922502	+	1.93657i	−0.0922502	+	1.93657i
$883$	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
$889$	1.84833	−	3.20140i	1.84833	−	3.20140i
$890$		0			0
$891$	1.07701	−	1.51245i	1.07701	−	1.51245i
$892$	−0.828105			−0.828105
$893$	0.0845850	−	0.146505i	0.0845850	−	0.146505i
$894$		0			0
$895$		0			0
$896$	0.482700	+	0.836060i	0.482700	+	0.836060i
$897$		0			0
$898$	0.550294	−	0.953137i	0.550294	−	0.953137i
$899$	−0.758872			−0.758872
$900$	−0.0272219	+	0.571458i	−0.0272219	+	0.571458i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	−0.959493	−	0.281733i	$-0.909091\pi$
$907$	−0.235759	+	0.408346i	−0.235759	+	0.408346i	0.723734	+	0.690079i	$0.242424\pi$
$908$		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	$0.848485\pi$
$912$	0.0421567	+	0.173772i	0.0421567	+	0.173772i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.331854	−	0.574788i	0.331854	−	0.574788i
$917$		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
$922$	0.550294	+	0.953137i	0.550294	+	0.953137i
$923$		0			0
$924$	0.498602	+	2.05527i	0.498602	+	2.05527i
$925$		0			0
$926$		0			0
$927$		0			0
$928$	−1.11669			−1.11669
$929$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.327068	+	0.945001i	$0.606061\pi$
$929$	−0.981929	+	1.70075i	−0.981929	+	1.70075i	−0.654861	+	0.755750i	$0.727273\pi$
$930$		0			0
$931$	2.63438	+	4.56288i	2.63438	+	4.56288i
$932$	0.561767	+	0.973010i	0.561767	+	0.973010i
$933$	0.959493	+	0.281733i	0.959493	+	0.281733i
$934$	0.379436	−	0.657203i	0.379436	−	0.657203i
$935$		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	$0.333333\pi$
$942$	0.620049	−	0.591215i	0.620049	−	0.591215i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	0.235759	+	0.971812i	$0.424242\pi$
$947$	−0.723734	+	1.25354i	−0.723734	+	1.25354i	−0.959493	+	0.281733i	$0.909091\pi$
$948$		0			0
$949$		0			0
$950$	−0.581419	−	1.00705i	−0.581419	−	1.00705i
$951$	0.111165	+	0.458227i	0.111165	+	0.458227i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$	0.414053	−	0.717160i	0.414053	−	0.717160i
$957$	−2.06677	−	0.606859i	−2.06677	−	0.606859i
$958$		0			0
$959$	−1.56499	−	2.71064i	−1.56499	−	2.71064i
$960$		0			0
$961$	0.286053	−	0.495458i	0.286053	−	0.495458i
$962$		0			0
$963$	−0.0947329	+	1.98869i	−0.0947329	+	1.98869i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$967$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$968$	−1.25845	−	2.17970i	−1.25845	−	2.17970i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−0.531125	−	0.212630i	−0.531125	−	0.212630i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.0965138	−	0.167167i	−0.0965138	−	0.167167i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$	−1.34378	+	2.32750i	−1.34378	+	2.32750i
$980$		0			0
$981$		0			0
$982$	−1.30827			−1.30827
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.181791	+	0.0533787i	0.181791	+	0.0533787i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−0.314827	+	0.545296i	−0.314827	+	0.545296i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	0.415415	+	0.909632i	$0.363636\pi$
$997$	−0.580057	+	1.00469i	−0.580057	+	1.00469i	−0.995472	+	0.0950560i	$0.969697\pi$
$998$		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.1168.7	yes	20
9.4	even	3	inner	1503.1.f.b.166.7	✓	20
167.166	odd	2	CM	1503.1.f.b.1168.7	yes	20
1503.166	odd	6	inner	1503.1.f.b.166.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1503.1.f.b.166.7	✓	20	9.4	even	3	inner
1503.1.f.b.166.7	✓	20	1503.166	odd	6	inner
1503.1.f.b.1168.7	yes	20	1.1	even	1	trivial
1503.1.f.b.1168.7	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)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.566498i) q^{2} +(0.723734 - 0.690079i) q^{3} +(0.286053 + 0.495458i) q^{4} +(-0.154218 - 0.635697i) q^{6} +(0.995472 - 1.72421i) q^{7} +1.02837 q^{8} +(0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.566498i) q^{2} +(0.723734 - 0.690079i) q^{3} +(0.286053 + 0.495458i) q^{4} +(-0.154218 - 0.635697i) q^{6} +(0.995472 - 1.72421i) q^{7} +1.02837 q^{8} +(0.0475819 - 0.998867i) q^{9} +(-0.928368 + 1.60798i) q^{11} +(0.548932 + 0.161181i) q^{12} +(-0.651174 - 1.12787i) q^{14} +(0.0502942 - 0.0871120i) q^{16} +(-0.550294 - 0.353653i) q^{18} -1.77767 q^{19} +(-0.469383 - 1.93482i) q^{21} +(0.607279 + 1.05184i) q^{22} +(0.744267 - 0.709657i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.654861 - 0.755750i) q^{27} +1.13903 q^{28} +(-0.580057 + 1.00469i) q^{29} +(0.327068 + 0.566498i) q^{31} +(0.481286 + 0.833612i) q^{32} +(0.437742 + 1.80440i) q^{33} +(0.508508 - 0.262154i) q^{36} +(-0.581419 + 1.00705i) q^{38} +(-1.24959 - 0.366914i) q^{42} -1.06225 q^{44} +(-0.0475819 + 0.0824143i) q^{47} +(-0.0237146 - 0.0977529i) q^{48} +(-1.48193 - 2.56678i) q^{49} +(0.327068 + 0.566498i) q^{50} +(-0.642315 + 0.123796i) q^{54} +(1.02371 - 1.77313i) q^{56} +(-1.28656 + 1.22673i) q^{57} +(0.379436 + 0.657203i) q^{58} +(0.959493 - 1.66189i) q^{61} +0.427894 q^{62} +(-1.67489 - 1.07639i) q^{63} +0.730242 q^{64} +(1.16536 + 0.342180i) q^{66} +(0.0489319 - 1.02721i) q^{72} +(0.235759 + 0.971812i) q^{75} +(-0.508508 - 0.880762i) q^{76} +(1.84833 + 3.20140i) q^{77} +(-0.995472 - 0.0950560i) q^{81} +(0.824356 - 0.786022i) q^{84} +(0.273507 + 1.12741i) q^{87} +(-0.954707 + 1.65360i) q^{88} +1.44747 q^{89} +(0.627639 + 0.184291i) q^{93} +(0.0311250 + 0.0539102i) q^{94} +(0.923582 + 0.271188i) q^{96} +(0.142315 - 0.246497i) q^{97} -1.93877 q^{98} +(1.56199 + 1.00383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{3} - 11 q^{4} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 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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