LMFDB - Embedded newform 943.1.n.b.390.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [943,1,Mod(367,943)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(943, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("943.367");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 943 = 23 \cdot 41 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	943.n (of order $20$, degree $8$, 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:	$0.470618306913$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{60}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{60} - \cdots)$

Embedding invariants

Embedding label			390.1
Root			$0.406737 - 0.913545i$ of defining polynomial
Character	$\chi$	$=$	943.390
Dual form			943.1.n.b.781.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86055 - 0.604528i) q^{2} +(-0.506809 - 0.506809i) q^{3} +(2.28716 + 1.66172i) q^{4} +(0.636561 + 1.24932i) q^{6} +(-2.10094 - 2.89169i) q^{8} -0.486290i q^{9} +O(q^{10})$	\(q+(-1.86055 - 0.604528i) q^{2} +(-0.506809 - 0.506809i) q^{3} +(2.28716 + 1.66172i) q^{4} +(0.636561 + 1.24932i) q^{6} +(-2.10094 - 2.89169i) q^{8} -0.486290i q^{9} +(-0.316980 - 2.00133i) q^{12} +(-1.38488 + 0.705634i) q^{13} +(1.28716 + 3.96149i) q^{16} +(-0.293976 + 0.904765i) q^{18} +(0.309017 - 0.951057i) q^{23} +(-0.400762 + 2.53031i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(3.00322 - 0.475663i) q^{26} +(-0.753265 + 0.753265i) q^{27} +(-0.292088 - 1.84417i) q^{29} +(0.658114 - 0.478148i) q^{31} -4.57433i q^{32} +(0.808078 - 1.11222i) q^{36} +(1.05949 + 0.344250i) q^{39} +(-0.978148 + 0.207912i) q^{41} +(-1.14988 + 1.58268i) q^{46} +(0.0475201 + 0.0932634i) q^{47} +(1.35537 - 2.66006i) q^{48} +(-0.587785 - 0.809017i) q^{49} +1.95630i q^{50} +(-4.34003 - 0.687393i) q^{52} +(1.85685 - 0.946115i) q^{54} +(-0.571411 + 3.60775i) q^{58} +(-0.500000 + 1.53884i) q^{59} +(-1.51351 + 0.491768i) q^{62} +(-1.47815 + 4.54927i) q^{64} +(-0.638616 + 0.325391i) q^{69} +(-1.07587 - 0.170401i) q^{71} +(-1.40620 + 1.02166i) q^{72} -1.98904i q^{73} +(-0.325391 + 0.638616i) q^{75} +(-1.76313 - 1.28099i) q^{78} +0.277233 q^{81} +(1.94558 + 0.204489i) q^{82} +(-0.786610 + 1.08268i) q^{87} +(2.28716 - 1.66172i) q^{92} +(-0.575867 - 0.0912084i) q^{93} +(-0.0320330 - 0.202248i) q^{94} +(-2.31831 + 2.31831i) q^{96} +(0.604528 + 1.86055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6	$ 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6} + 2 q^{13} - 6 q^{16} + 6 q^{18} - 4 q^{23} - 22 q^{24} + 4 q^{25} + 12 q^{26} + 6 q^{27} - 8 q^{29} - 10 q^{36} + 2 q^{41} + 2 q^{47} - 18 q^{48} - 6 q^{54} + 2 q^{58} - 8 q^{59} - 10 q^{62} - 6 q^{64} - 2 q^{69} - 2 q^{71} + 16 q^{72} + 2 q^{75} - 2 q^{78} - 12 q^{81} + 10 q^{92} + 6 q^{93} + 18 q^{94} - 10 q^{96} + 6 q^{98}+O(q^{100}) $ 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6 + 2 * q^13 - 6 * q^16 + 6 * q^18 - 4 * q^23 - 22 * q^24 + 4 * q^25 + 12 * q^26 + 6 * q^27 - 8 * q^29 - 10 * q^36 + 2 * q^41 + 2 * q^47 - 18 * q^48 - 6 * q^54 + 2 * q^58 - 8 * q^59 - 10 * q^62 - 6 * q^64 - 2 * q^69 - 2 * q^71 + 16 * q^72 + 2 * q^75 - 2 * q^78 - 12 * q^81 + 10 * q^92 + 6 * q^93 + 18 * q^94 - 10 * q^96 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/943\mathbb{Z}\right)^\times$.

$n$	$47$	$534$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	−1.86055	−	0.604528i	−1.86055	−	0.604528i	−0.994522	−	0.104528i	$-0.966667\pi$
$2$	−1.86055	−	0.604528i	−1.86055	−	0.604528i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−0.506809	−	0.506809i	−0.506809	−	0.506809i	0.406737	−	0.913545i	$-0.366667\pi$
$3$	−0.506809	−	0.506809i	−0.506809	−	0.506809i	−0.913545	+	0.406737i	$0.866667\pi$
$4$	2.28716	+	1.66172i	2.28716	+	1.66172i
$5$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$5$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$6$	0.636561	+	1.24932i	0.636561	+	1.24932i
$7$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$7$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$8$	−2.10094	−	2.89169i	−2.10094	−	2.89169i
$9$		−	0.486290i		−	0.486290i
$10$		0			0
$11$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$11$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$12$	−0.316980	−	2.00133i	−0.316980	−	2.00133i
$13$	−1.38488	+	0.705634i	−1.38488	+	0.705634i	−0.978148	−	0.207912i	$-0.933333\pi$
$13$	−1.38488	+	0.705634i	−1.38488	+	0.705634i	−0.406737	+	0.913545i	$0.633333\pi$
$14$		0			0
$15$		0			0
$16$	1.28716	+	3.96149i	1.28716	+	3.96149i
$17$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$17$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$18$	−0.293976	+	0.904765i	−0.293976	+	0.904765i
$19$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$19$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.309017	−	0.951057i	0.309017	−	0.951057i
$23$	0.309017	−	0.951057i	0.309017	−	0.951057i
$24$	−0.400762	+	2.53031i	−0.400762	+	2.53031i
$25$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$26$	3.00322	−	0.475663i	3.00322	−	0.475663i
$27$	−0.753265	+	0.753265i	−0.753265	+	0.753265i
$28$		0			0
$29$	−0.292088	−	1.84417i	−0.292088	−	1.84417i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−0.292088	−	1.84417i	−0.292088	−	1.84417i	0.207912	−	0.978148i	$-0.433333\pi$
$30$		0			0
$31$	0.658114	−	0.478148i	0.658114	−	0.478148i	−0.207912	−	0.978148i	$-0.566667\pi$
$31$	0.658114	−	0.478148i	0.658114	−	0.478148i	0.866025	+	0.500000i	$0.166667\pi$
$32$		−	4.57433i		−	4.57433i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.808078	−	1.11222i	0.808078	−	1.11222i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$		0			0
$39$	1.05949	+	0.344250i	1.05949	+	0.344250i
$40$		0			0
$41$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$41$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$42$		0			0
$43$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$43$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$44$		0			0
$45$		0			0
$46$	−1.14988	+	1.58268i	−1.14988	+	1.58268i
$47$	0.0475201	+	0.0932634i	0.0475201	+	0.0932634i	0.913545	−	0.406737i	$-0.133333\pi$
$47$	0.0475201	+	0.0932634i	0.0475201	+	0.0932634i	−0.866025	+	0.500000i	$0.833333\pi$
$48$	1.35537	−	2.66006i	1.35537	−	2.66006i
$49$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$50$			1.95630i			1.95630i
$51$		0			0
$52$	−4.34003	−	0.687393i	−4.34003	−	0.687393i
$53$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$53$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$54$	1.85685	−	0.946115i	1.85685	−	0.946115i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.571411	+	3.60775i	−0.571411	+	3.60775i
$59$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$59$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$60$		0			0
$61$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$61$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$62$	−1.51351	+	0.491768i	−1.51351	+	0.491768i
$63$		0			0
$64$	−1.47815	+	4.54927i	−1.47815	+	4.54927i
$65$		0			0
$66$		0			0
$67$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$67$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$68$		0			0
$69$	−0.638616	+	0.325391i	−0.638616	+	0.325391i
$70$		0			0
$71$	−1.07587	−	0.170401i	−1.07587	−	0.170401i	−0.406737	−	0.913545i	$-0.633333\pi$
$71$	−1.07587	−	0.170401i	−1.07587	−	0.170401i	−0.669131	+	0.743145i	$0.733333\pi$
$72$	−1.40620	+	1.02166i	−1.40620	+	1.02166i
$73$		−	1.98904i		−	1.98904i	−0.104528	−	0.994522i	$-0.533333\pi$
$73$		−	1.98904i		−	1.98904i	0.104528	−	0.994522i	$-0.466667\pi$
$74$		0			0
$75$	−0.325391	+	0.638616i	−0.325391	+	0.638616i
$76$		0			0
$77$		0			0
$78$	−1.76313	−	1.28099i	−1.76313	−	1.28099i
$79$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$79$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$80$		0			0
$81$	0.277233			0.277233
$82$	1.94558	+	0.204489i	1.94558	+	0.204489i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.786610	+	1.08268i	−0.786610	+	1.08268i
$88$		0			0
$89$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$89$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$90$		0			0
$91$		0			0
$92$	2.28716	−	1.66172i	2.28716	−	1.66172i
$93$	−0.575867	−	0.0912084i	−0.575867	−	0.0912084i
$94$	−0.0320330	−	0.202248i	−0.0320330	−	0.202248i
$95$		0			0
$96$	−2.31831	+	2.31831i	−2.31831	+	2.31831i
$97$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$97$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$98$	0.604528	+	1.86055i	0.604528	+	1.86055i
$99$		0			0
$100$	0.873619	−	2.68872i	0.873619	−	2.68872i
$101$	−1.76007	−	0.896802i	−1.76007	−	0.896802i	−0.951057	−	0.309017i	$-0.900000\pi$
$101$	−1.76007	−	0.896802i	−1.76007	−	0.896802i	−0.809017	−	0.587785i	$-0.800000\pi$
$102$		0			0
$103$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$103$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$104$	4.95003	+	2.52217i	4.95003	+	2.52217i
$105$		0			0
$106$		0			0
$107$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$107$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$108$	−2.97456	+	0.471124i	−2.97456	+	0.471124i
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$113$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$		0			0
$116$	2.39645	−	4.70330i	2.39645	−	4.70330i
$117$	0.343142	+	0.673455i	0.343142	+	0.673455i
$118$	1.86055	−	2.56082i	1.86055	−	2.56082i
$119$		0			0
$120$		0			0
$121$	0.951057	+	0.309017i	0.951057	+	0.309017i
$122$		0			0
$123$	0.601105	+	0.390362i	0.601105	+	0.390362i
$124$	2.29976			2.29976
$125$		0			0
$126$		0			0
$127$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$127$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$128$	2.81160	−	3.86984i	2.81160	−	3.86984i
$129$		0			0
$130$		0			0
$131$	0.122881	+	0.169131i	0.122881	+	0.169131i	0.866025	−	0.500000i	$-0.166667\pi$
$131$	0.122881	+	0.169131i	0.122881	+	0.169131i	−0.743145	+	0.669131i	$0.766667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$137$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$138$	1.38488	−	0.219344i	1.38488	−	0.219344i
$139$	−0.128496	−	0.395472i	−0.128496	−	0.395472i	0.866025	−	0.500000i	$-0.166667\pi$
$139$	−0.128496	−	0.395472i	−0.128496	−	0.395472i	−0.994522	+	0.104528i	$0.966667\pi$
$140$		0			0
$141$	0.0231831	−	0.0713503i	0.0231831	−	0.0713503i
$142$	1.89869	+	0.967431i	1.89869	+	0.967431i
$143$		0			0
$144$	1.92643	−	0.625935i	1.92643	−	0.625935i
$145$		0			0
$146$	−1.20243	+	3.70071i	−1.20243	+	3.70071i
$147$	−0.112122	+	0.707912i	−0.112122	+	0.707912i
$148$		0			0
$149$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$149$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$150$	0.991468	−	0.991468i	0.991468	−	0.991468i
$151$	−1.12146	+	0.571411i	−1.12146	+	0.571411i	−0.913545	−	0.406737i	$-0.866667\pi$
$151$	−1.12146	+	0.571411i	−1.12146	+	0.571411i	−0.207912	+	0.978148i	$0.566667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	1.85119	+	2.54794i	1.85119	+	2.54794i
$157$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$157$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.515805	−	0.167595i	−0.515805	−	0.167595i
$163$	1.98904			1.98904			0.994522	−	0.104528i	$-0.0333333\pi$
$163$	1.98904			1.98904			0.994522	+	0.104528i	$0.0333333\pi$
$164$	−2.58268	−	1.14988i	−2.58268	−	1.14988i
$165$		0			0
$166$		0			0
$167$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$167$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$168$		0			0
$169$	0.832200	−	1.14543i	0.832200	−	1.14543i
$170$		0			0
$171$		0			0
$172$		0			0
$173$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$173$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$174$	2.11803	−	1.53884i	2.11803	−	1.53884i
$175$		0			0
$176$		0			0
$177$	1.03330	−	0.526494i	1.03330	−	0.526494i
$178$		0			0
$179$	1.90807	−	0.302208i	1.90807	−	0.302208i	0.913545	−	0.406737i	$-0.133333\pi$
$179$	1.90807	−	0.302208i	1.90807	−	0.302208i	0.994522	+	0.104528i	$0.0333333\pi$
$180$		0			0
$181$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$181$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$182$		0			0
$183$		0			0
$184$	−3.39939	+	1.10453i	−3.39939	+	1.10453i
$185$		0			0
$186$	1.01629	+	0.517826i	1.01629	+	0.517826i
$187$		0			0
$188$	−0.0462916	+	0.292274i	−0.0462916	+	0.292274i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	3.05475	−	1.55647i	3.05475	−	1.55647i
$193$	−0.243145	−	1.53516i	−0.243145	−	1.53516i	−0.743145	−	0.669131i	$-0.766667\pi$
$193$	−0.243145	−	1.53516i	−0.243145	−	1.53516i	0.500000	−	0.866025i	$-0.333333\pi$
$194$		0			0
$195$		0			0
$196$		−	2.82709i		−	2.82709i
$197$	0.873619	+	1.20243i	0.873619	+	1.20243i	0.978148	+	0.207912i	$0.0666667\pi$
$197$	0.873619	+	1.20243i	0.873619	+	1.20243i	−0.104528	+	0.994522i	$0.533333\pi$
$198$		0			0
$199$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$199$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$200$	−2.10094	+	2.89169i	−2.10094	+	2.89169i
$201$		0			0
$202$	2.73256	+	2.73256i	2.73256	+	2.73256i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.462489	−	0.150272i	−0.462489	−	0.150272i
$208$	−4.57793	−	4.57793i	−4.57793	−	4.57793i
$209$		0			0
$210$		0			0
$211$	−0.412215	−	0.809017i	−0.412215	−	0.809017i	0.587785	−	0.809017i	$-0.300000\pi$
$211$	−0.412215	−	0.809017i	−0.412215	−	0.809017i	−1.00000			$\pi$
$212$		0			0
$213$	0.458898	+	0.631620i	0.458898	+	0.631620i
$214$		0			0
$215$		0			0
$216$	3.76077	+	0.595648i	3.76077	+	0.595648i
$217$		0			0
$218$		0			0
$219$	−1.00806	+	1.00806i	−1.00806	+	1.00806i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$223$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$224$		0			0
$225$	−0.462489	+	0.150272i	−0.462489	+	0.150272i
$226$		0			0
$227$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$227$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$228$		0			0
$229$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$229$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$230$		0			0
$231$		0			0
$232$	−4.71912	+	4.71912i	−4.71912	+	4.71912i
$233$	1.72129	−	0.877042i	1.72129	−	0.877042i	0.743145	−	0.669131i	$-0.233333\pi$
$233$	1.72129	−	0.877042i	1.72129	−	0.877042i	0.978148	−	0.207912i	$-0.0666667\pi$
$234$	−0.231310	−	1.46043i	−0.231310	−	1.46043i
$235$		0			0
$236$	−3.70071	+	2.68872i	−3.70071	+	2.68872i
$237$		0			0
$238$		0			0
$239$	−0.847673	+	1.66365i	−0.847673	+	1.66365i	−0.104528	+	0.994522i	$0.533333\pi$
$239$	−0.847673	+	1.66365i	−0.847673	+	1.66365i	−0.743145	+	0.669131i	$0.766667\pi$
$240$		0			0
$241$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$241$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$242$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$243$	0.612761	+	0.612761i	0.612761	+	0.612761i
$244$		0			0
$245$		0			0
$246$	−0.882400	−	1.08967i	−0.882400	−	1.08967i
$247$		0			0
$248$	−2.76531	−	0.898504i	−2.76531	−	0.898504i
$249$		0			0
$250$		0			0
$251$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$251$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$252$		0			0
$253$		0			0
$254$	1.14988	+	1.58268i	1.14988	+	1.58268i
$255$		0			0
$256$	−3.70071	+	2.68872i	−3.70071	+	2.68872i
$257$	1.24314	+	0.196895i	1.24314	+	0.196895i	0.743145	−	0.669131i	$-0.233333\pi$
$257$	1.24314	+	0.196895i	1.24314	+	0.196895i	0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.896802	+	0.142040i	−0.896802	+	0.142040i
$262$	−0.126381	−	0.388960i	−0.126381	−	0.388960i
$263$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$263$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.614648	−	1.89169i	0.614648	−	1.89169i	0.207912	−	0.978148i	$-0.433333\pi$
$269$	0.614648	−	1.89169i	0.614648	−	1.89169i	0.406737	−	0.913545i	$-0.366667\pi$
$270$		0			0
$271$	0.587785	+	1.80902i	0.587785	+	1.80902i	0.587785	+	0.809017i	$0.300000\pi$
$271$	0.587785	+	1.80902i	0.587785	+	1.80902i			1.00000i	$0.5\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−2.00133	−	0.316980i	−2.00133	−	0.316980i
$277$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	0.207912	+	0.978148i	$0.433333\pi$
$278$			0.813473i			0.813473i
$279$	−0.232518	−	0.320034i	−0.232518	−	0.320034i
$280$		0			0
$281$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$281$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$282$	−0.0862665	+	0.118736i	−0.0862665	+	0.118736i
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$	−2.17753	−	2.17753i	−2.17753	−	2.17753i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.22445			−2.22445
$289$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$290$		0			0
$291$		0			0
$292$	3.30524	−	4.54927i	3.30524	−	4.54927i
$293$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$293$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$294$	0.636561	−	1.24932i	0.636561	−	1.24932i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.243145	+	1.53516i	0.243145	+	1.53516i
$300$	−1.80543	+	0.919911i	−1.80543	+	0.919911i
$301$		0			0
$302$	2.43196	−	0.385184i	2.43196	−	0.385184i
$303$	0.437513	+	1.34653i	0.437513	+	1.34653i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.80902	−	0.587785i	1.80902	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$307$	1.80902	−	0.587785i	1.80902	−	0.587785i	1.00000			$0$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.262394	−	1.65669i	0.262394	−	1.65669i	−0.406737	−	0.913545i	$-0.633333\pi$
$311$	0.262394	−	1.65669i	0.262394	−	1.65669i	0.669131	−	0.743145i	$-0.266667\pi$
$312$	−1.23046	−	3.78698i	−1.23046	−	3.78698i
$313$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$313$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.896802	−	0.142040i	−0.896802	−	0.142040i	−0.309017	−	0.951057i	$-0.600000\pi$
$317$	−0.896802	−	0.142040i	−0.896802	−	0.142040i	−0.587785	+	0.809017i	$0.700000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.634077	+	0.460684i	0.634077	+	0.460684i
$325$	1.09905	+	1.09905i	1.09905	+	1.09905i
$326$	−3.70071	−	1.20243i	−3.70071	−	1.20243i
$327$		0			0
$328$	2.65624	+	2.39169i	2.65624	+	2.39169i
$329$		0			0
$330$		0			0
$331$	1.41228	+	1.41228i	1.41228	+	1.41228i	0.743145	+	0.669131i	$0.233333\pi$
$331$	1.41228	+	1.41228i	1.41228	+	1.41228i	0.669131	+	0.743145i	$0.266667\pi$
$332$		0			0
$333$		0			0
$334$	−1.75441	−	3.44322i	−1.75441	−	3.44322i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−2.24079	+	1.62803i	−2.24079	+	1.62803i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.373619	−	1.14988i	0.373619	−	1.14988i
$347$	0.278768	+	0.142040i	0.278768	+	0.142040i	0.587785	−	0.809017i	$-0.300000\pi$
$347$	0.278768	+	0.142040i	0.278768	+	0.142040i	−0.309017	+	0.951057i	$0.600000\pi$
$348$	−3.59821	+	1.16913i	−3.59821	+	1.16913i
$349$	0.198825	−	0.0646021i	0.198825	−	0.0646021i	−0.207912	−	0.978148i	$-0.566667\pi$
$349$	0.198825	−	0.0646021i	0.198825	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$350$		0			0
$351$	0.511655	−	1.57471i	0.511655	−	1.57471i
$352$		0			0
$353$	0.128496	+	0.395472i	0.128496	+	0.395472i	0.994522	−	0.104528i	$-0.0333333\pi$
$353$	0.128496	+	0.395472i	0.128496	+	0.395472i	−0.866025	+	0.500000i	$0.833333\pi$
$354$	−2.24079	+	0.354906i	−2.24079	+	0.354906i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−3.73274	−	0.591208i	−3.73274	−	0.591208i
$359$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$359$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$360$		0			0
$361$	0.587785	+	0.809017i	0.587785	+	0.809017i
$362$		0			0
$363$	−0.325391	−	0.638616i	−0.325391	−	0.638616i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$367$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$368$	4.16535			4.16535
$369$	0.101105	+	0.475663i	0.101105	+	0.475663i
$370$		0			0
$371$		0			0
$372$	−1.16554	−	1.16554i	−1.16554	−	1.16554i
$373$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$373$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$374$		0			0
$375$		0			0
$376$	0.169852	−	0.333354i	0.169852	−	0.333354i
$377$	1.70582	+	2.34786i	1.70582	+	2.34786i
$378$		0			0
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	0.112122	+	0.707912i	0.112122	+	0.707912i
$382$		0			0
$383$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$383$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$384$	−3.38621	+	0.536324i	−3.38621	+	0.536324i
$385$		0			0
$386$	−0.475663	+	3.00322i	−0.475663	+	3.00322i
$387$		0			0
$388$		0			0
$389$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$389$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$390$		0			0
$391$		0			0
$392$	−1.10453	+	3.39939i	−1.10453	+	3.39939i
$393$	0.0234399	−	0.147994i	0.0234399	−	0.147994i
$394$	−0.898504	−	2.76531i	−0.898504	−	2.76531i
$395$		0			0
$396$		0			0
$397$	−1.72129	+	0.877042i	−1.72129	+	0.877042i	−0.743145	+	0.669131i	$0.766667\pi$
$397$	−1.72129	+	0.877042i	−1.72129	+	0.877042i	−0.978148	+	0.207912i	$0.933333\pi$
$398$		0			0
$399$		0			0
$400$	3.36984	−	2.44833i	3.36984	−	2.44833i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	−0.574014	+	1.12657i	−0.574014	+	1.12657i
$404$	−2.53534	−	4.97589i	−2.53534	−	4.97589i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$409$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.769639	+	0.559175i	0.769639	+	0.559175i
$415$		0			0
$416$	3.22780	+	6.33492i	3.22780	+	6.33492i
$417$	−0.135305	+	0.265552i	−0.135305	+	0.265552i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$421$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$422$	0.277871	+	1.75441i	0.277871	+	1.75441i
$423$	0.0453530	−	0.0231085i	0.0453530	−	0.0231085i
$424$		0			0
$425$		0			0
$426$	−0.471970	−	1.45258i	−0.471970	−	1.45258i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$431$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$432$	−3.95362	−	2.01447i	−3.95362	−	2.01447i
$433$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$433$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	2.48496	−	1.26615i	2.48496	−	1.26615i
$439$	0.262394	+	1.65669i	0.262394	+	1.65669i	0.669131	+	0.743145i	$0.266667\pi$
$439$	0.262394	+	1.65669i	0.262394	+	1.65669i	−0.406737	+	0.913545i	$0.633333\pi$
$440$		0			0
$441$	−0.393417	+	0.285834i	−0.393417	+	0.285834i
$442$		0			0
$443$	−1.14988	−	1.58268i	−1.14988	−	1.58268i	−0.743145	−	0.669131i	$-0.766667\pi$
$443$	−1.14988	−	1.58268i	−1.14988	−	1.58268i	−0.406737	−	0.913545i	$-0.633333\pi$
$444$		0			0
$445$		0			0
$446$	−1.35177	+	1.86055i	−1.35177	+	1.86055i
$447$		0			0
$448$		0			0
$449$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$449$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$450$	0.951326			0.951326
$451$		0			0
$452$		0			0
$453$	0.857960	+	0.278768i	0.857960	+	0.278768i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$457$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.08268	−	0.786610i	1.08268	−	0.786610i	0.104528	−	0.994522i	$-0.466667\pi$
$461$	1.08268	−	0.786610i	1.08268	−	0.786610i	0.978148	+	0.207912i	$0.0666667\pi$
$462$		0			0
$463$	−0.309017	−	1.95106i	−0.309017	−	1.95106i	−0.309017	−	0.951057i	$-0.600000\pi$
$463$	−0.309017	−	1.95106i	−0.309017	−	1.95106i		−	1.00000i	$-0.5\pi$
$464$	6.92970	−	3.53086i	6.92970	−	3.53086i
$465$		0			0
$466$	−3.73274	+	0.591208i	−3.73274	+	0.591208i
$467$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$	−0.334272	+	2.11051i	−0.334272	+	2.11051i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	5.50033	−	1.78716i	5.50033	−	1.78716i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	2.58286	−	2.58286i	2.58286	−	2.58286i
$479$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$479$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.66172	+	2.28716i	1.66172	+	2.28716i
$485$		0			0
$486$	−0.769639	−	1.51050i	−0.769639	−	1.51050i
$487$	−0.122881	+	0.169131i	−0.122881	+	0.169131i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$	−0.122881	+	0.169131i	−0.122881	+	0.169131i	0.743145	+	0.669131i	$0.233333\pi$
$488$		0			0
$489$	−1.00806	−	1.00806i	−1.00806	−	1.00806i
$490$		0			0
$491$	0.813473			0.813473			0.406737	−	0.913545i	$-0.366667\pi$
$491$	0.813473			0.813473			0.406737	+	0.913545i	$0.366667\pi$
$492$	0.726153	+	1.89169i	0.726153	+	1.89169i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.74128	+	1.99165i	2.74128	+	1.99165i
$497$		0			0
$498$		0			0
$499$	0.906737	−	1.77957i	0.906737	−	1.77957i	0.406737	−	0.913545i	$-0.366667\pi$
$499$	0.906737	−	1.77957i	0.906737	−	1.77957i	0.500000	−	0.866025i	$-0.333333\pi$
$500$		0			0
$501$		−	1.41582i		−	1.41582i
$502$		0			0
$503$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$503$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.00228	+	0.158745i	−1.00228	+	0.158745i
$508$	−0.873619	−	2.68872i	−0.873619	−	2.68872i
$509$	−0.0809764	+	0.511265i	−0.0809764	+	0.511265i	0.913545	+	0.406737i	$0.133333\pi$
$509$	−0.0809764	+	0.511265i	−0.0809764	+	0.511265i	−0.994522	+	0.104528i	$0.966667\pi$
$510$		0			0
$511$		0			0
$512$	3.96149	−	1.28716i	3.96149	−	1.28716i
$513$		0			0
$514$	−2.19390	−	1.11785i	−2.19390	−	1.11785i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.313225	−	0.313225i	0.313225	−	0.313225i
$520$		0			0
$521$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$521$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$522$	1.75441	+	0.277871i	1.75441	+	0.277871i
$523$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$523$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$524$			0.591023i			0.591023i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$530$		0			0
$531$	0.748323	+	0.243145i	0.748323	+	0.243145i
$532$		0			0
$533$	1.20791	−	0.978148i	1.20791	−	0.978148i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.12019	−	0.813864i	−1.12019	−	0.813864i
$538$	−2.28716	+	3.14801i	−2.28716	+	3.14801i
$539$		0			0
$540$		0			0
$541$	1.01807	+	1.40126i	1.01807	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$541$	1.01807	+	1.40126i	1.01807	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$542$		−	3.72109i		−	3.72109i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.889993	+	0.889993i	−0.889993	+	0.889993i	−0.994522	−	0.104528i	$-0.966667\pi$
$547$	−0.889993	+	0.889993i	−0.889993	+	0.889993i	0.104528	+	0.994522i	$0.466667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	2.28263	+	1.16306i	2.28263	+	1.16306i
$553$		0			0
$554$	1.51351	−	0.491768i	1.51351	−	0.491768i
$555$		0			0
$556$	0.363271	−	1.11803i	0.363271	−	1.11803i
$557$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$557$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$558$	0.239142	+	0.736002i	0.239142	+	0.736002i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$563$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$564$	0.171588	−	0.124666i	0.171588	−	0.124666i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	1.76758	+	3.46908i	1.76758	+	3.46908i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$571$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.00000			−1.00000
$576$	2.21226	+	0.718808i	2.21226	+	0.718808i
$577$	0.770236	+	0.770236i	0.770236	+	0.770236i	0.978148	−	0.207912i	$-0.0666667\pi$
$577$	0.770236	+	0.770236i	0.770236	+	0.770236i	−0.207912	+	0.978148i	$0.566667\pi$
$578$	1.58268	+	1.14988i	1.58268	+	1.14988i
$579$	−0.654803	+	0.901259i	−0.654803	+	0.901259i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−5.75170	+	4.17886i	−5.75170	+	4.17886i
$585$		0			0
$586$		0			0
$587$	−1.49452	+	0.761497i	−1.49452	+	0.761497i	−0.994522	−	0.104528i	$-0.966667\pi$
$587$	−1.49452	+	0.761497i	−1.49452	+	0.761497i	−0.500000	+	0.866025i	$0.666667\pi$
$588$	−1.43279	+	1.43279i	−1.43279	+	1.43279i
$589$		0			0
$590$		0			0
$591$	0.166646	−	1.05216i	0.166646	−	1.05216i
$592$		0			0
$593$	−0.809017	−	0.412215i	−0.809017	−	0.412215i		−	1.00000i	$-0.5\pi$
$593$	−0.809017	−	0.412215i	−0.809017	−	0.412215i	−0.809017	+	0.587785i	$0.800000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.475663	−	3.00322i	0.475663	−	3.00322i
$599$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$599$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$600$	2.53031	−	0.400762i	2.53031	−	0.400762i
$601$	1.32028	−	1.32028i	1.32028	−	1.32028i	0.406737	−	0.913545i	$-0.366667\pi$
$601$	1.32028	−	1.32028i	1.32028	−	1.32028i	0.913545	−	0.406737i	$-0.133333\pi$
$602$		0			0
$603$		0			0
$604$	−3.51448	−	0.556639i	−3.51448	−	0.556639i
$605$		0			0
$606$		−	2.76977i		−	2.76977i
$607$	−0.690983	−	0.951057i	−0.690983	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$607$	−0.690983	−	0.951057i	−0.690983	−	0.951057i	−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.131620	−	0.0956272i	−0.131620	−	0.0956272i
$612$		0			0
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$	−3.72109			−3.72109
$615$		0			0
$616$		0			0
$617$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$617$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$618$		0			0
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$	0.483626	+	0.949169i	0.483626	+	0.949169i
$622$	−1.48971	+	2.92373i	−1.48971	+	2.92373i
$623$		0			0
$624$			4.64027i			4.64027i
$625$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$631$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$632$		0			0
$633$	−0.201103	+	0.618931i	−0.201103	+	0.618931i
$634$	1.58268	+	0.806414i	1.58268	+	0.806414i
$635$		0			0
$636$		0			0
$637$	1.38488	+	0.705634i	1.38488	+	0.705634i
$638$		0			0
$639$	−0.0828641	+	0.523183i	−0.0828641	+	0.523183i
$640$		0			0
$641$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$641$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$642$		0			0
$643$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$643$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$647$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$648$	−0.582449	−	0.801672i	−0.582449	−	0.801672i
$649$		0			0
$650$	−1.38043	−	2.70924i	−1.38043	−	2.70924i
$651$		0			0
$652$	4.54927	+	3.30524i	4.54927	+	3.30524i
$653$	1.18606	+	1.18606i	1.18606	+	1.18606i	0.978148	+	0.207912i	$0.0666667\pi$
$653$	1.18606	+	1.18606i	1.18606	+	1.18606i	0.207912	+	0.978148i	$0.433333\pi$
$654$		0			0
$655$		0			0
$656$	−2.08268	−	3.60730i	−2.08268	−	3.60730i
$657$	−0.967251			−0.967251
$658$		0			0
$659$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$659$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$660$		0			0
$661$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$661$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$662$	−1.77384	−	3.48137i	−1.77384	−	3.48137i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.84417	−	0.292088i	−1.84417	−	0.292088i
$668$	0.873619	+	5.51581i	0.873619	+	5.51581i
$669$	−0.750739	+	0.382520i	−0.750739	+	0.382520i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.196895	−	1.24314i	0.196895	−	1.24314i	−0.669131	−	0.743145i	$-0.733333\pi$
$673$	0.196895	−	1.24314i	0.196895	−	1.24314i	0.866025	−	0.500000i	$-0.166667\pi$
$674$		0			0
$675$	0.949169	+	0.483626i	0.949169	+	0.483626i
$676$	3.80676	−	1.23689i	3.80676	−	1.23689i
$677$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$677$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.506809	+	0.506809i	−0.506809	+	0.506809i	−0.913545	−	0.406737i	$-0.866667\pi$
$683$	−0.506809	+	0.506809i	−0.506809	+	0.506809i	0.406737	+	0.913545i	$0.366667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.642040	+	1.26007i	0.642040	+	1.26007i	0.951057	+	0.309017i	$0.100000\pi$
$691$	0.642040	+	1.26007i	0.642040	+	1.26007i	−0.309017	+	0.951057i	$0.600000\pi$
$692$	−1.02700	+	1.41355i	−1.02700	+	1.41355i
$693$		0			0
$694$	−0.432795	−	0.432795i	−0.432795	−	0.432795i
$695$		0			0
$696$	4.78339			4.78339
$697$		0			0
$698$	−0.408977			−0.408977
$699$	−1.31686	−	0.427873i	−1.31686	−	0.427873i
$700$		0			0
$701$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$701$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$702$	−1.90392	+	2.62052i	−1.90392	+	2.62052i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		−	0.813473i		−	0.813473i
$707$		0			0
$708$	3.23822	+	0.512884i	3.23822	+	0.512884i
$709$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$709$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.251377	−	0.773659i	−0.251377	−	0.773659i
$714$		0			0
$715$		0			0
$716$	4.86625	+	2.47948i	4.86625	+	2.47948i
$717$	1.27276	−	0.413545i	1.27276	−	0.413545i
$718$		0			0
$719$	0.809017	+	0.412215i	0.809017	+	0.412215i	0.809017	−	0.587785i	$-0.200000\pi$
$719$	0.809017	+	0.412215i	0.809017	+	0.412215i			1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$723$		0			0
$724$		0			0
$725$	−1.66365	+	0.847673i	−1.66365	+	0.847673i
$726$	0.219344	+	1.38488i	0.219344	+	1.38488i
$727$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$727$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$728$		0			0
$729$		−	0.898338i		−	0.898338i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$		0			0
$735$		0			0
$736$	−4.35045	−	1.41355i	−4.35045	−	1.41355i
$737$		0			0
$738$	0.0994407	−	0.946115i	0.0994407	−	0.946115i
$739$	−1.82709			−1.82709			−0.913545	−	0.406737i	$-0.866667\pi$
$739$	−1.82709			−1.82709			−0.913545	+	0.406737i	$0.866667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$743$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$744$	0.946115	+	1.85685i	0.946115	+	1.85685i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$751$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$752$	−0.308295	+	0.308295i	−0.308295	+	0.308295i
$753$		0			0
$754$	−1.75441	−	5.39952i	−1.75441	−	5.39952i
$755$		0			0
$756$		0			0
$757$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$757$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.535233	−	1.64728i	0.535233	−	1.64728i	−0.207912	−	0.978148i	$-0.566667\pi$
$761$	0.535233	−	1.64728i	0.535233	−	1.64728i	0.743145	−	0.669131i	$-0.233333\pi$
$762$	0.219344	−	1.38488i	0.219344	−	1.38488i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.393417	−	2.48393i	−0.393417	−	2.48393i
$768$	3.23822	+	0.512884i	3.23822	+	0.512884i
$769$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$769$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$770$		0			0
$771$	−0.530249	−	0.729825i	−0.530249	−	0.729825i
$772$	1.99489	−	3.91519i	1.99489	−	3.91519i
$773$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$773$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$774$		0			0
$775$	−0.658114	−	0.478148i	−0.658114	−	0.478148i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.60917	+	1.16913i	1.60917	+	1.16913i
$784$	2.44833	−	3.36984i	2.44833	−	3.36984i
$785$		0			0
$786$	−0.133078	+	0.261179i	−0.133078	+	0.261179i
$787$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$787$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$788$			4.20188i			4.20188i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	3.73274	−	0.591208i	3.73274	−	0.591208i
$795$		0			0
$796$		0			0
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$		0			0
$800$	−4.35045	+	1.41355i	−4.35045	+	1.41355i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.74902	−	1.74902i	1.74902	−	1.74902i
$807$	−1.27024	+	0.647218i	−1.27024	+	0.647218i
$808$	1.10453	+	6.97372i	1.10453	+	6.97372i
$809$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$809$	1.39680	+	0.221232i	1.39680	+	0.221232i	0.587785	+	0.809017i	$0.300000\pi$
$810$		0			0
$811$		−	1.48629i		−	1.48629i	−0.669131	−	0.743145i	$-0.733333\pi$
$811$		−	1.48629i		−	1.48629i	0.669131	−	0.743145i	$-0.266667\pi$
$812$		0			0
$813$	0.618931	−	1.21472i	0.618931	−	1.21472i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.86055	+	0.604528i	1.86055	+	0.604528i
$819$		0			0
$820$		0			0
$821$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$821$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$822$		0			0
$823$	0.0740142	+	0.0740142i	0.0740142	+	0.0740142i	0.743145	−	0.669131i	$-0.233333\pi$
$823$	0.0740142	+	0.0740142i	0.0740142	+	0.0740142i	−0.669131	+	0.743145i	$0.733333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$827$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$828$	−0.808078	−	1.11222i	−0.808078	−	1.11222i
$829$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$829$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$830$		0			0
$831$	0.575867	+	0.0912084i	0.575867	+	0.0912084i
$832$	−1.16306	−	7.34324i	−1.16306	−	7.34324i
$833$		0			0
$834$	0.412275	−	0.412275i	0.412275	−	0.412275i
$835$		0			0
$836$		0			0
$837$	−0.135562	+	0.855906i	−0.135562	+	0.855906i
$838$		0			0
$839$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$839$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$840$		0			0
$841$	−2.36460	+	0.768306i	−2.36460	+	0.768306i
$842$		0			0
$843$		0			0
$844$	0.401559	−	2.53534i	0.401559	−	2.53534i
$845$		0			0
$846$	−0.0983512	+	0.0155773i	−0.0983512	+	0.0155773i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$			2.20718i			2.20718i
$853$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$853$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$857$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$858$		0			0
$859$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$859$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.89169	−	0.614648i	−1.89169	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$863$	−1.89169	−	0.614648i	−1.89169	−	0.614648i	−0.913545	−	0.406737i	$-0.866667\pi$
$864$	3.44568	+	3.44568i	3.44568	+	3.44568i
$865$		0			0
$866$		0			0
$867$	0.325391	+	0.638616i	0.325391	+	0.638616i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−3.98073	+	0.630486i	−3.98073	+	0.630486i
$877$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$	0.513320	−	3.24098i	0.513320	−	3.24098i
$879$		0			0
$880$		0			0
$881$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$881$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$882$	0.904765	−	0.293976i	0.904765	−	0.293976i
$883$	1.26007	+	0.642040i	1.26007	+	0.642040i	0.951057	−	0.309017i	$-0.100000\pi$
$883$	1.26007	+	0.642040i	1.26007	+	0.642040i	0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$	1.18264	+	3.63978i	1.18264	+	3.63978i
$887$	0.511265	−	0.0809764i	0.511265	−	0.0809764i	0.104528	−	0.994522i	$-0.466667\pi$
$887$	0.511265	−	0.0809764i	0.511265	−	0.0809764i	0.406737	+	0.913545i	$0.366667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	2.68872	−	1.95347i	2.68872	−	1.95347i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.654803	−	0.901259i	0.654803	−	0.901259i
$898$		0			0
$899$	−1.07401	−	1.07401i	−1.07401	−	1.07401i
$900$	−1.30750	−	0.424832i	−1.30750	−	0.424832i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−1.42775	−	1.03732i	−1.42775	−	1.03732i
$907$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$907$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$908$		0			0
$909$	−0.436106	+	0.855906i	−0.436106	+	0.855906i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$919$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$920$		0			0
$921$	−1.21472	−	0.618931i	−1.21472	−	0.618931i
$922$	−2.48990	+	0.809017i	−2.48990	+	0.809017i
$923$	1.61019	−	0.523183i	1.61019	−	0.523183i
$924$		0			0
$925$		0			0
$926$	−0.604528	+	3.81684i	−0.604528	+	3.81684i
$927$		0			0
$928$	−8.43585	+	1.33611i	−8.43585	+	1.33611i
$929$	−0.0740142	+	0.0740142i	−0.0740142	+	0.0740142i	−0.743145	−	0.669131i	$-0.766667\pi$
$929$	−0.0740142	+	0.0740142i	−0.0740142	+	0.0740142i	0.669131	+	0.743145i	$0.266667\pi$
$930$		0			0
$931$		0			0
$932$	5.39428	+	0.854370i	5.39428	+	0.854370i
$933$	−0.972609	+	0.706642i	−0.972609	+	0.706642i
$934$		0			0
$935$		0			0
$936$	1.22650	−	2.40715i	1.22650	−	2.40715i
$937$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$937$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$941$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$942$		0			0
$943$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$944$	−6.73968			−6.73968
$945$		0			0
$946$		0			0
$947$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$947$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$948$		0			0
$949$	1.40354	+	2.75460i	1.40354	+	2.75460i
$950$		0			0
$951$	0.382520	+	0.526494i	0.382520	+	0.526494i
$952$		0			0
$953$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$953$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$954$		0			0
$955$		0			0
$956$	−4.70330	+	2.39645i	−4.70330	+	2.39645i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.104528	+	0.321706i	−0.104528	+	0.321706i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.0809764	+	0.511265i	−0.0809764	+	0.511265i	0.913545	+	0.406737i	$0.133333\pi$
$967$	−0.0809764	+	0.511265i	−0.0809764	+	0.511265i	−0.994522	+	0.104528i	$0.966667\pi$
$968$	−1.10453	−	3.39939i	−1.10453	−	3.39939i
$969$		0			0
$970$		0			0
$971$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$971$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$972$	0.383246	+	2.41972i	0.383246	+	2.41972i
$973$		0			0
$974$	0.330869	−	0.240391i	0.330869	−	0.240391i
$975$		−	1.11402i		−	1.11402i
$976$		0			0
$977$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$977$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$978$	1.26615	+	2.48496i	1.26615	+	2.48496i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−1.51351	−	0.491768i	−1.51351	−	0.491768i
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	−0.134077	−	2.55834i	−0.134077	−	2.55834i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.142040	+	0.278768i	−0.142040	+	0.278768i	−0.951057	−	0.309017i	$-0.900000\pi$
$991$	−0.142040	+	0.278768i	−0.142040	+	0.278768i	0.809017	+	0.587785i	$0.200000\pi$
$992$	−2.18720	−	3.01043i	−2.18720	−	3.01043i
$993$		−	1.43151i		−	1.43151i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.58779	+	0.809017i	−1.58779	+	0.809017i	−0.587785	+	0.809017i	$0.700000\pi$
$997$	−1.58779	+	0.809017i	−1.58779	+	0.809017i	−1.00000			$\pi$
$998$	−2.76283	+	2.76283i	−2.76283	+	2.76283i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	943.1.n.b.390.1	✓	16
23.22	odd	2	CM	943.1.n.b.390.1	✓	16
41.2	even	20	inner	943.1.n.b.781.1	yes	16
943.781	odd	20	inner	943.1.n.b.781.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
943.1.n.b.390.1	✓	16	1.1	even	1	trivial
943.1.n.b.390.1	✓	16	23.22	odd	2	CM
943.1.n.b.781.1	yes	16	41.2	even	20	inner
943.1.n.b.781.1	yes	16	943.781	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 943 = 23 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	943.n (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86055 - 0.604528i) q^{2} +(-0.506809 - 0.506809i) q^{3} +(2.28716 + 1.66172i) q^{4} +(0.636561 + 1.24932i) q^{6} +(-2.10094 - 2.89169i) q^{8} -0.486290i q^{9} +O(q^{10})\)	\(q+(-1.86055 - 0.604528i) q^{2} +(-0.506809 - 0.506809i) q^{3} +(2.28716 + 1.66172i) q^{4} +(0.636561 + 1.24932i) q^{6} +(-2.10094 - 2.89169i) q^{8} -0.486290i q^{9} +(-0.316980 - 2.00133i) q^{12} +(-1.38488 + 0.705634i) q^{13} +(1.28716 + 3.96149i) q^{16} +(-0.293976 + 0.904765i) q^{18} +(0.309017 - 0.951057i) q^{23} +(-0.400762 + 2.53031i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(3.00322 - 0.475663i) q^{26} +(-0.753265 + 0.753265i) q^{27} +(-0.292088 - 1.84417i) q^{29} +(0.658114 - 0.478148i) q^{31} -4.57433i q^{32} +(0.808078 - 1.11222i) q^{36} +(1.05949 + 0.344250i) q^{39} +(-0.978148 + 0.207912i) q^{41} +(-1.14988 + 1.58268i) q^{46} +(0.0475201 + 0.0932634i) q^{47} +(1.35537 - 2.66006i) q^{48} +(-0.587785 - 0.809017i) q^{49} +1.95630i q^{50} +(-4.34003 - 0.687393i) q^{52} +(1.85685 - 0.946115i) q^{54} +(-0.571411 + 3.60775i) q^{58} +(-0.500000 + 1.53884i) q^{59} +(-1.51351 + 0.491768i) q^{62} +(-1.47815 + 4.54927i) q^{64} +(-0.638616 + 0.325391i) q^{69} +(-1.07587 - 0.170401i) q^{71} +(-1.40620 + 1.02166i) q^{72} -1.98904i q^{73} +(-0.325391 + 0.638616i) q^{75} +(-1.76313 - 1.28099i) q^{78} +0.277233 q^{81} +(1.94558 + 0.204489i) q^{82} +(-0.786610 + 1.08268i) q^{87} +(2.28716 - 1.66172i) q^{92} +(-0.575867 - 0.0912084i) q^{93} +(-0.0320330 - 0.202248i) q^{94} +(-2.31831 + 2.31831i) q^{96} +(0.604528 + 1.86055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6	\( 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6} + 2 q^{13} - 6 q^{16} + 6 q^{18} - 4 q^{23} - 22 q^{24} + 4 q^{25} + 12 q^{26} + 6 q^{27} - 8 q^{29} - 10 q^{36} + 2 q^{41} + 2 q^{47} - 18 q^{48} - 6 q^{54} + 2 q^{58} - 8 q^{59} - 10 q^{62} - 6 q^{64} - 2 q^{69} - 2 q^{71} + 16 q^{72} + 2 q^{75} - 2 q^{78} - 12 q^{81} + 10 q^{92} + 6 q^{93} + 18 q^{94} - 10 q^{96} + 6 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 10 * q^4 - 12 * q^6 + 2 * q^13 - 6 * q^16 + 6 * q^18 - 4 * q^23 - 22 * q^24 + 4 * q^25 + 12 * q^26 + 6 * q^27 - 8 * q^29 - 10 * q^36 + 2 * q^41 + 2 * q^47 - 18 * q^48 - 6 * q^54 + 2 * q^58 - 8 * q^59 - 10 * q^62 - 6 * q^64 - 2 * q^69 - 2 * q^71 + 16 * q^72 + 2 * q^75 - 2 * q^78 - 12 * q^81 + 10 * q^92 + 6 * q^93 + 18 * q^94 - 10 * q^96 + 6 * q^98

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