LMFDB - Embedded newform 943.1.n.b.758.2

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			758.2
Root			$-0.406737 + 0.913545i$ of defining polynomial
Character	$\chi$	$=$	943.758
Dual form			943.1.n.b.367.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86055 + 0.604528i) q^{2} +(-1.32028 + 1.32028i) q^{3} +(2.28716 + 1.66172i) q^{4} +(-3.25460 + 1.65830i) q^{6} +(2.10094 + 2.89169i) q^{8} -2.48629i q^{9} +O(q^{10})$	\(q+(1.86055 + 0.604528i) q^{2} +(-1.32028 + 1.32028i) q^{3} +(2.28716 + 1.66172i) q^{4} +(-3.25460 + 1.65830i) q^{6} +(2.10094 + 2.89169i) q^{8} -2.48629i q^{9} +(-5.21364 + 0.825760i) q^{12} +(-0.571411 - 1.12146i) q^{13} +(1.28716 + 3.96149i) q^{16} +(1.50303 - 4.62586i) q^{18} +(0.309017 - 0.951057i) q^{23} +(-6.59168 - 1.04402i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.385184 - 2.43196i) q^{26} +(1.96232 + 1.96232i) q^{27} +(-0.707912 + 0.112122i) q^{29} +(-0.658114 + 0.478148i) q^{31} +4.57433i q^{32} +(4.13152 - 5.68655i) q^{36} +(2.23506 + 0.726216i) q^{39} +(-0.978148 + 0.207912i) q^{41} +(1.14988 - 1.58268i) q^{46} +(1.77957 - 0.906737i) q^{47} +(-6.92970 - 3.53086i) q^{48} +(0.587785 + 0.809017i) q^{49} -1.95630i q^{50} +(0.556639 - 3.51448i) q^{52} +(2.46471 + 4.83727i) q^{54} +(-1.38488 - 0.219344i) q^{58} +(-0.500000 + 1.53884i) q^{59} +(-1.51351 + 0.491768i) q^{62} +(-1.47815 + 4.54927i) q^{64} +(0.847673 + 1.66365i) q^{69} +(-0.262394 + 1.65669i) q^{71} +(7.18959 - 5.22354i) q^{72} -1.98904i q^{73} +(1.66365 + 0.847673i) q^{75} +(3.71942 + 2.70232i) q^{78} -2.69535 q^{81} +(-1.94558 - 0.204489i) q^{82} +(0.786610 - 1.08268i) q^{87} +(2.28716 - 1.66172i) q^{92} +(0.237606 - 1.50019i) q^{93} +(3.85912 - 0.611225i) q^{94} +(-6.03940 - 6.03940i) q^{96} +(0.604528 + 1.86055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/943\mathbb{Z}\right)^\times$.

$n$	$47$	$534$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$-1$

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	$0.0333333\pi$
$2$	1.86055	+	0.604528i	1.86055	+	0.604528i	0.866025	+	0.500000i	$0.166667\pi$
$3$	−1.32028	+	1.32028i	−1.32028	+	1.32028i	−0.406737	+	0.913545i	$0.633333\pi$
$3$	−1.32028	+	1.32028i	−1.32028	+	1.32028i	−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	$0.700000\pi$
$6$	−3.25460	+	1.65830i	−3.25460	+	1.65830i
$7$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$7$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$8$	2.10094	+	2.89169i	2.10094	+	2.89169i
$9$		−	2.48629i		−	2.48629i
$10$		0			0
$11$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$11$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$12$	−5.21364	+	0.825760i	−5.21364	+	0.825760i
$13$	−0.571411	−	1.12146i	−0.571411	−	1.12146i	−0.978148	−	0.207912i	$-0.933333\pi$
$13$	−0.571411	−	1.12146i	−0.571411	−	1.12146i	0.406737	−	0.913545i	$-0.366667\pi$
$14$		0			0
$15$		0			0
$16$	1.28716	+	3.96149i	1.28716	+	3.96149i
$17$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$17$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$18$	1.50303	−	4.62586i	1.50303	−	4.62586i
$19$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$19$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$20$		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
$24$	−6.59168	−	1.04402i	−6.59168	−	1.04402i
$25$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$26$	−0.385184	−	2.43196i	−0.385184	−	2.43196i
$27$	1.96232	+	1.96232i	1.96232	+	1.96232i
$28$		0			0
$29$	−0.707912	+	0.112122i	−0.707912	+	0.112122i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−0.707912	+	0.112122i	−0.707912	+	0.112122i	−0.207912	+	0.978148i	$0.566667\pi$
$30$		0			0
$31$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	−0.866025	−	0.500000i	$-0.833333\pi$
$31$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	0.207912	+	0.978148i	$0.433333\pi$
$32$			4.57433i			4.57433i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	4.13152	−	5.68655i	4.13152	−	5.68655i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$		0			0
$39$	2.23506	+	0.726216i	2.23506	+	0.726216i
$40$		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
$47$	1.77957	−	0.906737i	1.77957	−	0.906737i	0.866025	−	0.500000i	$-0.166667\pi$
$47$	1.77957	−	0.906737i	1.77957	−	0.906737i	0.913545	−	0.406737i	$-0.133333\pi$
$48$	−6.92970	−	3.53086i	−6.92970	−	3.53086i
$49$	0.587785	+	0.809017i	0.587785	+	0.809017i
$50$		−	1.95630i		−	1.95630i
$51$		0			0
$52$	0.556639	−	3.51448i	0.556639	−	3.51448i
$53$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$53$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$54$	2.46471	+	4.83727i	2.46471	+	4.83727i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−1.38488	−	0.219344i	−1.38488	−	0.219344i
$59$	−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		−0.156434	−	0.987688i	$-0.550000\pi$
$67$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$68$		0			0
$69$	0.847673	+	1.66365i	0.847673	+	1.66365i
$70$		0			0
$71$	−0.262394	+	1.65669i	−0.262394	+	1.65669i	0.406737	+	0.913545i	$0.366667\pi$
$71$	−0.262394	+	1.65669i	−0.262394	+	1.65669i	−0.669131	+	0.743145i	$0.733333\pi$
$72$	7.18959	−	5.22354i	7.18959	−	5.22354i
$73$		−	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
$75$	1.66365	+	0.847673i	1.66365	+	0.847673i
$76$		0			0
$77$		0			0
$78$	3.71942	+	2.70232i	3.71942	+	2.70232i
$79$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$79$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$80$		0			0
$81$	−2.69535			−2.69535
$82$	−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		−0.891007	−	0.453990i	$-0.850000\pi$
$89$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$90$		0			0
$91$		0			0
$92$	2.28716	−	1.66172i	2.28716	−	1.66172i
$93$	0.237606	−	1.50019i	0.237606	−	1.50019i
$94$	3.85912	−	0.611225i	3.85912	−	0.611225i
$95$		0			0
$96$	−6.03940	−	6.03940i	−6.03940	−	6.03940i
$97$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$97$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$98$	0.604528	+	1.86055i	0.604528	+	1.86055i
$99$		0			0
$100$	0.873619	−	2.68872i	0.873619	−	2.68872i
$101$	0.142040	−	0.278768i	0.142040	−	0.278768i	−0.809017	−	0.587785i	$-0.800000\pi$
$101$	0.142040	−	0.278768i	0.142040	−	0.278768i	0.951057	+	0.309017i	$0.100000\pi$
$102$		0			0
$103$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$103$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$104$	2.04241	−	4.00846i	2.04241	−	4.00846i
$105$		0			0
$106$		0			0
$107$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$107$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$108$	1.22732	+	7.74899i	1.22732	+	7.74899i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$		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
$116$	−1.80543	−	0.919911i	−1.80543	−	0.919911i
$117$	−2.78827	+	1.42069i	−2.78827	+	1.42069i
$118$	−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
$123$	1.01693	−	1.56593i	1.01693	−	1.56593i
$124$	−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	0.743145	−	0.669131i	$-0.233333\pi$
$131$	−0.122881	−	0.169131i	−0.122881	−	0.169131i	−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	0.571411	+	3.60775i	0.571411	+	3.60775i
$139$	0.128496	+	0.395472i	0.128496	+	0.395472i	0.994522	−	0.104528i	$-0.0333333\pi$
$139$	0.128496	+	0.395472i	0.128496	+	0.395472i	−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$	−1.15239	+	3.54668i	−1.15239	+	3.54668i
$142$	−1.48971	+	2.92373i	−1.48971	+	2.92373i
$143$		0			0
$144$	9.84940	−	3.20026i	9.84940	−	3.20026i
$145$		0			0
$146$	1.20243	−	3.70071i	1.20243	−	3.70071i
$147$	−1.84417	−	0.292088i	−1.84417	−	0.292088i
$148$		0			0
$149$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$149$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$150$	2.58286	+	2.58286i	2.58286	+	2.58286i
$151$	−0.705634	−	1.38488i	−0.705634	−	1.38488i	−0.913545	−	0.406737i	$-0.866667\pi$
$151$	−0.705634	−	1.38488i	−0.705634	−	1.38488i	0.207912	−	0.978148i	$-0.433333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	3.90519	+	5.37503i	3.90519	+	5.37503i
$157$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$157$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−5.01482	−	1.62941i	−5.01482	−	1.62941i
$163$	−1.98904			−1.98904			−0.994522	−	0.104528i	$-0.966667\pi$
$163$	−1.98904			−1.98904			−0.994522	+	0.104528i	$0.966667\pi$
$164$	−2.58268	−	1.14988i	−2.58268	−	1.14988i
$165$		0			0
$166$		0			0
$167$	0.221232	−	0.221232i	0.221232	−	0.221232i	−0.587785	−	0.809017i	$-0.700000\pi$
$167$	0.221232	−	0.221232i	0.221232	−	0.221232i	0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	−0.343370	+	0.472609i	−0.343370	+	0.472609i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$173$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$174$	2.11803	−	1.53884i	2.11803	−	1.53884i
$175$		0			0
$176$		0			0
$177$	−1.37156	−	2.69185i	−1.37156	−	2.69185i
$178$		0			0
$179$	−0.0809764	−	0.511265i	−0.0809764	−	0.511265i	−0.994522	−	0.104528i	$-0.966667\pi$
$179$	−0.0809764	−	0.511265i	−0.0809764	−	0.511265i	0.913545	−	0.406737i	$-0.133333\pi$
$180$		0			0
$181$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$181$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$182$		0			0
$183$		0			0
$184$	3.39939	−	1.10453i	3.39939	−	1.10453i
$185$		0			0
$186$	1.34898	−	2.64753i	1.34898	−	2.64753i
$187$		0			0
$188$	5.57692	+	0.883297i	5.57692	+	0.883297i
$189$		0			0
$190$		0			0
$191$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$191$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$192$	−4.05475	−	7.95789i	−4.05475	−	7.95789i
$193$	1.24314	−	0.196895i	1.24314	−	0.196895i	0.500000	−	0.866025i	$-0.333333\pi$
$193$	1.24314	−	0.196895i	1.24314	−	0.196895i	0.743145	+	0.669131i	$0.233333\pi$
$194$		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		0.891007	−	0.453990i	$-0.150000\pi$
$199$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$200$	2.10094	−	2.89169i	2.10094	−	2.89169i
$201$		0			0
$202$	0.432795	−	0.432795i	0.432795	−	0.432795i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.36460	−	0.768306i	−2.36460	−	0.768306i
$208$	3.70714	−	3.70714i	3.70714	−	3.70714i
$209$		0			0
$210$		0			0
$211$	−1.58779	+	0.809017i	−1.58779	+	0.809017i	−0.587785	+	0.809017i	$0.700000\pi$
$211$	−1.58779	+	0.809017i	−1.58779	+	0.809017i	−1.00000			$\pi$
$212$		0			0
$213$	−1.84086	−	2.53373i	−1.84086	−	2.53373i
$214$		0			0
$215$		0			0
$216$	−1.55172	+	9.79715i	−1.55172	+	9.79715i
$217$		0			0
$218$		0			0
$219$	2.62610	+	2.62610i	2.62610	+	2.62610i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$223$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$224$		0			0
$225$	−2.36460	+	0.768306i	−2.36460	+	0.768306i
$226$		0			0
$227$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$227$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$228$		0			0
$229$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$229$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$230$		0			0
$231$		0			0
$232$	−1.81150	−	1.81150i	−1.81150	−	1.81150i
$233$	0.235003	+	0.461219i	0.235003	+	0.461219i	0.978148	−	0.207912i	$-0.0666667\pi$
$233$	0.235003	+	0.461219i	0.235003	+	0.461219i	−0.743145	+	0.669131i	$0.766667\pi$
$234$	−6.04655	+	0.957680i	−6.04655	+	0.957680i
$235$		0			0
$236$	−3.70071	+	2.68872i	−3.70071	+	2.68872i
$237$		0			0
$238$		0			0
$239$	0.638616	+	0.325391i	0.638616	+	0.325391i	0.743145	−	0.669131i	$-0.233333\pi$
$239$	0.638616	+	0.325391i	0.638616	+	0.325391i	−0.104528	+	0.994522i	$0.533333\pi$
$240$		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
$243$	1.59630	−	1.59630i	1.59630	−	1.59630i
$244$		0			0
$245$		0			0
$246$	2.83869	−	2.29873i	2.83869	−	2.29873i
$247$		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
$257$	−0.243145	+	1.53516i	−0.243145	+	1.53516i	0.500000	+	0.866025i	$0.333333\pi$
$257$	−0.243145	+	1.53516i	−0.243145	+	1.53516i	−0.743145	+	0.669131i	$0.766667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.278768	+	1.76007i	0.278768	+	1.76007i
$262$	−0.126381	−	0.388960i	−0.126381	−	0.388960i
$263$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$263$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$264$		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	$0.566667\pi$
$269$	−0.614648	+	1.89169i	−0.614648	+	1.89169i	−0.406737	+	0.913545i	$0.633333\pi$
$270$		0			0
$271$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$271$	−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
$276$	−0.825760	+	5.21364i	−0.825760	+	5.21364i
$277$	0.658114	−	0.478148i	0.658114	−	0.478148i	−0.207912	−	0.978148i	$-0.566667\pi$
$277$	0.658114	−	0.478148i	0.658114	−	0.478148i	0.866025	+	0.500000i	$0.166667\pi$
$278$			0.813473i			0.813473i
$279$	1.18881	+	1.63626i	1.18881	+	1.63626i
$280$		0			0
$281$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$281$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$282$	−4.28814	+	5.90212i	−4.28814	+	5.90212i
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$	−3.35310	+	3.35310i	−3.35310	+	3.35310i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	11.3731			11.3731
$289$	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		0.891007	−	0.453990i	$-0.150000\pi$
$293$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$294$	−3.25460	−	1.65830i	−3.25460	−	1.65830i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.24314	+	0.196895i	−1.24314	+	0.196895i
$300$	2.39645	+	4.70330i	2.39645	+	4.70330i
$301$		0			0
$302$	−0.475663	−	3.00322i	−0.475663	−	3.00322i
$303$	0.180521	+	0.555585i	0.180521	+	0.555585i
$304$		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
$311$	1.07587	+	0.170401i	1.07587	+	0.170401i	0.669131	−	0.743145i	$-0.266667\pi$
$311$	1.07587	+	0.170401i	1.07587	+	0.170401i	0.406737	+	0.913545i	$0.366667\pi$
$312$	2.59574	+	7.98885i	2.59574	+	7.98885i
$313$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$313$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.278768	−	1.76007i	0.278768	−	1.76007i	−0.309017	−	0.951057i	$-0.600000\pi$
$317$	0.278768	−	1.76007i	0.278768	−	1.76007i	0.587785	−	0.809017i	$-0.300000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−6.16470	−	4.47892i	−6.16470	−	4.47892i
$325$	−0.889993	+	0.889993i	−0.889993	+	0.889993i
$326$	−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
$331$	−0.0740142	+	0.0740142i	−0.0740142	+	0.0740142i	−0.743145	−	0.669131i	$-0.766667\pi$
$331$	−0.0740142	+	0.0740142i	−0.0740142	+	0.0740142i	0.669131	+	0.743145i	$0.266667\pi$
$332$		0			0
$333$		0			0
$334$	0.545353	−	0.277871i	0.545353	−	0.277871i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−0.924562	+	0.671734i	−0.924562	+	0.671734i
$339$		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
$347$	−0.896802	+	1.76007i	−0.896802	+	1.76007i	−0.309017	+	0.951057i	$0.600000\pi$
$347$	−0.896802	+	1.76007i	−0.896802	+	1.76007i	−0.587785	+	0.809017i	$0.700000\pi$
$348$	3.59821	−	1.16913i	3.59821	−	1.16913i
$349$	−0.198825	+	0.0646021i	−0.198825	+	0.0646021i	−0.406737	−	0.913545i	$-0.633333\pi$
$349$	−0.198825	+	0.0646021i	−0.198825	+	0.0646021i	0.207912	+	0.978148i	$0.433333\pi$
$350$		0			0
$351$	1.07937	−	3.32195i	1.07937	−	3.32195i
$352$		0			0
$353$	−0.128496	−	0.395472i	−0.128496	−	0.395472i	0.866025	−	0.500000i	$-0.166667\pi$
$353$	−0.128496	−	0.395472i	−0.128496	−	0.395472i	−0.994522	+	0.104528i	$0.966667\pi$
$354$	−0.924562	−	5.83746i	−0.924562	−	5.83746i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.158414	−	1.00019i	0.158414	−	1.00019i
$359$		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
$363$	1.66365	−	0.847673i	1.66365	−	0.847673i
$364$		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
$369$	0.516929	+	2.43196i	0.516929	+	2.43196i
$370$		0			0
$371$		0			0
$372$	3.03634	−	3.03634i	3.03634	−	3.03634i
$373$		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
$376$	6.36077	+	3.24098i	6.36077	+	3.24098i
$377$	0.530249	+	0.729825i	0.530249	+	0.729825i
$378$		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
$381$	1.84417	−	0.292088i	1.84417	−	0.292088i
$382$		0			0
$383$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$383$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$384$	−1.39717	−	8.82139i	−1.39717	−	8.82139i
$385$		0			0
$386$	2.43196	+	0.385184i	2.43196	+	0.385184i
$387$		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
$393$	0.385537	+	0.0610631i	0.385537	+	0.0610631i
$394$	0.898504	+	2.76531i	0.898504	+	2.76531i
$395$		0			0
$396$		0			0
$397$	−0.235003	−	0.461219i	−0.235003	−	0.461219i	0.743145	−	0.669131i	$-0.233333\pi$
$397$	−0.235003	−	0.461219i	−0.235003	−	0.461219i	−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
$403$	0.912275	+	0.464828i	0.912275	+	0.464828i
$404$	0.788103	−	0.401559i	0.788103	−	0.401559i
$405$		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
$414$	−3.93499	−	2.85894i	−3.93499	−	2.85894i
$415$		0			0
$416$	5.12991	−	2.61382i	5.12991	−	2.61382i
$417$	−0.691786	−	0.352482i	−0.691786	−	0.352482i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$421$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$422$	−3.44322	+	0.545353i	−3.44322	+	0.545353i
$423$	−2.25441	−	4.42453i	−2.25441	−	4.42453i
$424$		0			0
$425$		0			0
$426$	−1.89330	−	5.82698i	−1.89330	−	5.82698i
$427$		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	$0.900000\pi$
$432$	−5.24788	+	10.2995i	−5.24788	+	10.2995i
$433$		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
$438$	3.29843	+	6.47353i	3.29843	+	6.47353i
$439$	1.07587	−	0.170401i	1.07587	−	0.170401i	0.406737	−	0.913545i	$-0.366667\pi$
$439$	1.07587	−	0.170401i	1.07587	−	0.170401i	0.669131	+	0.743145i	$0.266667\pi$
$440$		0			0
$441$	2.01145	−	1.46140i	2.01145	−	1.46140i
$442$		0			0
$443$	1.14988	+	1.58268i	1.14988	+	1.58268i	0.743145	+	0.669131i	$0.233333\pi$
$443$	1.14988	+	1.58268i	1.14988	+	1.58268i	0.406737	+	0.913545i	$0.366667\pi$
$444$		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	$0.600000\pi$
$450$	−4.86392			−4.86392
$451$		0			0
$452$		0			0
$453$	2.76007	+	0.896802i	2.76007	+	0.896802i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$457$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$458$		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	+	0.0489435i	−0.309017	+	0.0489435i	−0.309017	−	0.951057i	$-0.600000\pi$
$463$	−0.309017	+	0.0489435i	−0.309017	+	0.0489435i			1.00000i	$0.5\pi$
$464$	−1.35537	−	2.66006i	−1.35537	−	2.66006i
$465$		0			0
$466$	0.158414	+	1.00019i	0.158414	+	1.00019i
$467$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$	−8.73802	−	1.38397i	−8.73802	−	1.38397i
$469$		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
$478$	0.991468	+	0.991468i	0.991468	+	0.991468i
$479$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$479$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.66172	−	2.28716i	−1.66172	−	2.28716i
$485$		0			0
$486$	3.93499	−	2.00498i	3.93499	−	2.00498i
$487$	0.122881	−	0.169131i	0.122881	−	0.169131i	−0.743145	−	0.669131i	$-0.766667\pi$
$487$	0.122881	−	0.169131i	0.122881	−	0.169131i	0.866025	+	0.500000i	$0.166667\pi$
$488$		0			0
$489$	2.62610	−	2.62610i	2.62610	−	2.62610i
$490$		0			0
$491$	−0.813473			−0.813473			−0.406737	−	0.913545i	$-0.633333\pi$
$491$	−0.813473			−0.813473			−0.406737	+	0.913545i	$0.633333\pi$
$492$	4.92803	−	1.89169i	4.92803	−	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
$499$	0.0932634	+	0.0475201i	0.0932634	+	0.0475201i	0.500000	−	0.866025i	$-0.333333\pi$
$499$	0.0932634	+	0.0475201i	0.0932634	+	0.0475201i	−0.406737	+	0.913545i	$0.633333\pi$
$500$		0			0
$501$			0.584177i			0.584177i
$502$		0			0
$503$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$503$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.170631	−	1.07732i	−0.170631	−	1.07732i
$508$	−0.873619	−	2.68872i	−0.873619	−	2.68872i
$509$	1.90807	+	0.302208i	1.90807	+	0.302208i	0.994522	−	0.104528i	$-0.0333333\pi$
$509$	1.90807	+	0.302208i	1.90807	+	0.302208i	0.913545	+	0.406737i	$0.133333\pi$
$510$		0			0
$511$		0			0
$512$	−3.96149	+	1.28716i	−3.96149	+	1.28716i
$513$		0			0
$514$	−1.38043	+	2.70924i	−1.38043	+	2.70924i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.815979	+	0.815979i	0.815979	+	0.815979i
$520$		0			0
$521$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$521$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$522$	−0.545353	+	3.44322i	−0.545353	+	3.44322i
$523$		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
$531$	3.82601	+	1.24314i	3.82601	+	1.24314i
$532$		0			0
$533$	0.792088	+	0.978148i	0.792088	+	0.978148i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.781926	+	0.568102i	0.781926	+	0.568102i
$538$	−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
$547$	1.09905	+	1.09905i	1.09905	+	1.09905i	0.994522	+	0.104528i	$0.0333333\pi$
$547$	1.09905	+	1.09905i	1.09905	+	1.09905i	0.104528	+	0.994522i	$0.466667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−3.02986	+	5.94644i	−3.02986	+	5.94644i
$553$		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		−0.987688	−	0.156434i	$-0.950000\pi$
$557$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$558$	1.22268	+	3.76301i	1.22268	+	3.76301i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$563$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$564$	−8.52930	+	6.19690i	−8.52930	+	6.19690i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−5.34191	+	2.72184i	−5.34191	+	2.72184i
$569$		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	$-0.250000\pi$
$571$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.00000			−1.00000
$576$	11.3108	+	3.67510i	11.3108	+	3.67510i
$577$	1.18606	−	1.18606i	1.18606	−	1.18606i	0.207912	−	0.978148i	$-0.433333\pi$
$577$	1.18606	−	1.18606i	1.18606	−	1.18606i	0.978148	−	0.207912i	$-0.0666667\pi$
$578$	1.58268	+	1.14988i	1.58268	+	1.14988i
$579$	−1.38135	+	1.90126i	−1.38135	+	1.90126i
$580$		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
$587$	0.494522	+	0.970554i	0.494522	+	0.970554i	0.994522	+	0.104528i	$0.0333333\pi$
$587$	0.494522	+	0.970554i	0.494522	+	0.970554i	−0.500000	+	0.866025i	$0.666667\pi$
$588$	−3.73256	−	3.73256i	−3.73256	−	3.73256i
$589$		0			0
$590$		0			0
$591$	−2.74098	−	0.434128i	−2.74098	−	0.434128i
$592$		0			0
$593$	−0.809017	+	1.58779i	−0.809017	+	1.58779i			1.00000i	$0.5\pi$
$593$	−0.809017	+	1.58779i	−0.809017	+	1.58779i	−0.809017	+	0.587785i	$0.800000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−2.43196	−	0.385184i	−2.43196	−	0.385184i
$599$	0.587785	+	1.80902i	0.587785	+	1.80902i	0.587785	+	0.809017i	$0.300000\pi$
$599$	0.587785	+	1.80902i	0.587785	+	1.80902i			1.00000i	$0.5\pi$
$600$	1.04402	+	6.59168i	1.04402	+	6.59168i
$601$	0.506809	+	0.506809i	0.506809	+	0.506809i	0.913545	−	0.406737i	$-0.133333\pi$
$601$	0.506809	+	0.506809i	0.506809	+	0.506809i	−0.406737	+	0.913545i	$0.633333\pi$
$602$		0			0
$603$		0			0
$604$	0.687393	−	4.34003i	0.687393	−	4.34003i
$605$		0			0
$606$			1.14282i			1.14282i
$607$	−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
$611$	−2.03373	−	1.47759i	−2.03373	−	1.47759i
$612$		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
$621$	2.47267	−	1.25989i	2.47267	−	1.25989i
$622$	1.89869	+	0.967431i	1.89869	+	0.967431i
$623$		0			0
$624$			9.78893i			9.78893i
$625$	−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
$633$	1.02819	−	3.16446i	1.02819	−	3.16446i
$634$	1.58268	−	3.10618i	1.58268	−	3.10618i
$635$		0			0
$636$		0			0
$637$	0.571411	−	1.12146i	0.571411	−	1.12146i
$638$		0			0
$639$	4.11901	+	0.652387i	4.11901	+	0.652387i
$640$		0			0
$641$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$641$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$642$		0			0
$643$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$643$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$644$		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	$0.666667\pi$
$648$	−5.66276	−	7.79411i	−5.66276	−	7.79411i
$649$		0			0
$650$	−2.19390	+	1.11785i	−2.19390	+	1.11785i
$651$		0			0
$652$	−4.54927	−	3.30524i	−4.54927	−	3.30524i
$653$	0.770236	−	0.770236i	0.770236	−	0.770236i	−0.207912	−	0.978148i	$-0.566667\pi$
$653$	0.770236	−	0.770236i	0.770236	−	0.770236i	0.978148	+	0.207912i	$0.0666667\pi$
$654$		0			0
$655$		0			0
$656$	−2.08268	−	3.60730i	−2.08268	−	3.60730i
$657$	−4.94534			−4.94534
$658$		0			0
$659$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$659$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$660$		0			0
$661$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$661$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$662$	−0.182451	+	0.0929633i	−0.182451	+	0.0929633i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.112122	+	0.707912i	−0.112122	+	0.707912i
$668$	0.873619	−	0.138368i	0.873619	−	0.138368i
$669$	−0.996500	−	1.95574i	−0.996500	−	1.95574i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.53516	−	0.243145i	−1.53516	−	0.243145i	−0.669131	−	0.743145i	$-0.733333\pi$
$673$	−1.53516	−	0.243145i	−1.53516	−	0.243145i	−0.866025	+	0.500000i	$0.833333\pi$
$674$		0			0
$675$	1.25989	−	2.47267i	1.25989	−	2.47267i
$676$	−1.57069	+	0.510348i	−1.57069	+	0.510348i
$677$		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
$683$	−1.32028	−	1.32028i	−1.32028	−	1.32028i	−0.913545	−	0.406737i	$-0.866667\pi$
$683$	−1.32028	−	1.32028i	−1.32028	−	1.32028i	−0.406737	−	0.913545i	$-0.633333\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−1.26007	+	0.642040i	−1.26007	+	0.642040i	−0.951057	−	0.309017i	$-0.900000\pi$
$691$	−1.26007	+	0.642040i	−1.26007	+	0.642040i	−0.309017	+	0.951057i	$0.600000\pi$
$692$	1.02700	−	1.41355i	1.02700	−	1.41355i
$693$		0			0
$694$	−2.73256	+	2.73256i	−2.73256	+	2.73256i
$695$		0			0
$696$	4.78339			4.78339
$697$		0			0
$698$	−0.408977			−0.408977
$699$	−0.919209	−	0.298669i	−0.919209	−	0.298669i
$700$		0			0
$701$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$701$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$702$	4.01643	−	5.52814i	4.01643	−	5.52814i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		−	0.813473i		−	0.813473i
$707$		0			0
$708$	1.33611	−	8.43585i	1.33611	−	8.43585i
$709$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$709$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.251377	+	0.773659i	0.251377	+	0.773659i
$714$		0			0
$715$		0			0
$716$	0.664374	−	1.30391i	0.664374	−	1.30391i
$717$	−1.27276	+	0.413545i	−1.27276	+	0.413545i
$718$		0			0
$719$	0.809017	−	1.58779i	0.809017	−	1.58779i		−	1.00000i	$-0.5\pi$
$719$	0.809017	−	1.58779i	0.809017	−	1.58779i	0.809017	−	0.587785i	$-0.200000\pi$
$720$		0			0
$721$		0			0
$722$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$723$		0			0
$724$		0			0
$725$	0.325391	+	0.638616i	0.325391	+	0.638616i
$726$	3.60775	−	0.571411i	3.60775	−	0.571411i
$727$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$727$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$728$		0			0
$729$			1.51978i			1.51978i
$730$		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
$738$	−0.508418	+	4.83727i	−0.508418	+	4.83727i
$739$	−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	$0.700000\pi$
$744$	4.83727	−	2.46471i	4.83727	−	2.46471i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$751$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$752$	5.88262	+	5.88262i	5.88262	+	5.88262i
$753$		0			0
$754$	0.545353	+	1.67842i	0.545353	+	1.67842i
$755$		0			0
$756$		0			0
$757$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$757$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.535233	+	1.64728i	−0.535233	+	1.64728i	0.207912	+	0.978148i	$0.433333\pi$
$761$	−0.535233	+	1.64728i	−0.535233	+	1.64728i	−0.743145	+	0.669131i	$0.766667\pi$
$762$	3.60775	+	0.571411i	3.60775	+	0.571411i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.01145	−	0.318582i	2.01145	−	0.318582i
$768$	1.33611	−	8.43585i	1.33611	−	8.43585i
$769$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$769$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$770$		0			0
$771$	−1.70582	−	2.34786i	−1.70582	−	2.34786i
$772$	3.17046	+	1.61543i	3.17046	+	1.61543i
$773$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$773$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$774$		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
$786$	0.680396	+	0.346679i	0.680396	+	0.346679i
$787$		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
$794$	−0.158414	−	1.00019i	−0.158414	−	1.00019i
$795$		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
$806$	1.41633	+	1.41633i	1.41633	+	1.41633i
$807$	−1.68606	−	3.30908i	−1.68606	−	3.30908i
$808$	1.10453	−	0.174940i	1.10453	−	0.174940i
$809$	0.221232	−	1.39680i	0.221232	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$809$	0.221232	−	1.39680i	0.221232	−	1.39680i	0.809017	−	0.587785i	$-0.200000\pi$
$810$		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
$813$	3.16446	+	1.61237i	3.16446	+	1.61237i
$814$		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	$-0.300000\pi$
$821$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$822$		0			0
$823$	−1.41228	+	1.41228i	−1.41228	+	1.41228i	−0.669131	+	0.743145i	$0.733333\pi$
$823$	−1.41228	+	1.41228i	−1.41228	+	1.41228i	−0.743145	+	0.669131i	$0.766667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$827$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$828$	−4.13152	−	5.68655i	−4.13152	−	5.68655i
$829$		−	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
$831$	−0.237606	+	1.50019i	−0.237606	+	1.50019i
$832$	5.94644	−	0.941824i	5.94644	−	0.941824i
$833$		0			0
$834$	−1.07401	−	1.07401i	−1.07401	−	1.07401i
$835$		0			0
$836$		0			0
$837$	−2.22971	−	0.353151i	−2.22971	−	0.353151i
$838$		0			0
$839$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$839$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$840$		0			0
$841$	−0.462489	+	0.150272i	−0.462489	+	0.150272i
$842$		0			0
$843$		0			0
$844$	−4.97589	−	0.788103i	−4.97589	−	0.788103i
$845$		0			0
$846$	−1.51968	−	9.59490i	−1.51968	−	9.59490i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		−	8.85407i		−	8.85407i
$853$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$853$	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	−0.207912	−	0.978148i	$-0.566667\pi$
$859$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$860$		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	$-0.866667\pi$
$864$	−8.97631	+	8.97631i	−8.97631	+	8.97631i
$865$		0			0
$866$		0			0
$867$	−1.66365	+	0.847673i	−1.66365	+	0.847673i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	1.64247	+	10.3702i	1.64247	+	10.3702i
$877$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$	2.10471	+	0.333354i	2.10471	+	0.333354i
$879$		0			0
$880$		0			0
$881$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$881$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$882$	4.62586	−	1.50303i	4.62586	−	1.50303i
$883$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	0.309017	+	0.951057i	$0.400000\pi$
$883$	−0.642040	+	1.26007i	−0.642040	+	1.26007i	−0.951057	+	0.309017i	$0.900000\pi$
$884$		0			0
$885$		0			0
$886$	1.18264	+	3.63978i	1.18264	+	3.63978i
$887$	−0.302208	−	1.90807i	−0.302208	−	1.90807i	−0.406737	−	0.913545i	$-0.633333\pi$
$887$	−0.302208	−	1.90807i	−0.302208	−	1.90807i	0.104528	−	0.994522i	$-0.466667\pi$
$888$		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
$897$	1.38135	−	1.90126i	1.38135	−	1.90126i
$898$		0			0
$899$	0.412275	−	0.412275i	0.412275	−	0.412275i
$900$	−6.68494	−	2.17207i	−6.68494	−	2.17207i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	4.59310	+	3.33709i	4.59310	+	3.33709i
$907$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$907$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$908$		0			0
$909$	−0.693099	−	0.353151i	−0.693099	−	0.353151i
$910$		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		−0.987688	−	0.156434i	$-0.950000\pi$
$919$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$920$		0			0
$921$	−1.61237	+	3.16446i	−1.61237	+	3.16446i
$922$	2.48990	−	0.809017i	2.48990	−	0.809017i
$923$	2.00784	−	0.652387i	2.00784	−	0.652387i
$924$		0			0
$925$		0			0
$926$	−0.604528	−	0.0957479i	−0.604528	−	0.0957479i
$927$		0			0
$928$	−0.512884	−	3.23822i	−0.512884	−	3.23822i
$929$	1.41228	+	1.41228i	1.41228	+	1.41228i	0.743145	+	0.669131i	$0.233333\pi$
$929$	1.41228	+	1.41228i	1.41228	+	1.41228i	0.669131	+	0.743145i	$0.266667\pi$
$930$		0			0
$931$		0			0
$932$	−0.228928	+	1.44539i	−0.228928	+	1.44539i
$933$	−1.64543	+	1.19547i	−1.64543	+	1.19547i
$934$		0			0
$935$		0			0
$936$	−9.96619	−	5.07802i	−9.96619	−	5.07802i
$937$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$937$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$938$		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
$949$	−2.23063	+	1.13656i	−2.23063	+	1.13656i
$950$		0			0
$951$	1.95574	+	2.69185i	1.95574	+	2.69185i
$952$		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
$956$	0.919911	+	1.80543i	0.919911	+	1.80543i
$957$		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
$967$	1.90807	+	0.302208i	1.90807	+	0.302208i	0.994522	−	0.104528i	$-0.0333333\pi$
$967$	1.90807	+	0.302208i	1.90807	+	0.302208i	0.913545	+	0.406737i	$0.133333\pi$
$968$	−1.10453	−	3.39939i	−1.10453	−	3.39939i
$969$		0			0
$970$		0			0
$971$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$971$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$972$	6.30359	−	0.998391i	6.30359	−	0.998391i
$973$		0			0
$974$	0.330869	−	0.240391i	0.330869	−	0.240391i
$975$		−	2.35008i		−	2.35008i
$976$		0			0
$977$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$977$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$978$	6.47353	−	3.29843i	6.47353	−	3.29843i
$979$		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			$\pi$
$984$	6.66470	−	0.349282i	6.66470	−	0.349282i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.76007	+	0.896802i	1.76007	+	0.896802i	0.951057	+	0.309017i	$0.100000\pi$
$991$	1.76007	+	0.896802i	1.76007	+	0.896802i	0.809017	+	0.587785i	$0.200000\pi$
$992$	−2.18720	−	3.01043i	−2.18720	−	3.01043i
$993$		−	0.195439i		−	0.195439i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.412215	−	0.809017i	−0.412215	−	0.809017i	0.587785	−	0.809017i	$-0.300000\pi$
$997$	−0.412215	−	0.809017i	−0.412215	−	0.809017i	−1.00000			$\pi$
$998$	0.144794	+	0.144794i	0.144794	+	0.144794i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	943.1.n.b.758.2	yes	16
23.22	odd	2	CM	943.1.n.b.758.2	yes	16
41.39	even	20	inner	943.1.n.b.367.2	✓	16
943.367	odd	20	inner	943.1.n.b.367.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
943.1.n.b.367.2	✓	16	41.39	even	20	inner
943.1.n.b.367.2	✓	16	943.367	odd	20	inner
943.1.n.b.758.2	yes	16	1.1	even	1	trivial
943.1.n.b.758.2	yes	16	23.22	odd	2	CM

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Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.86055 + 0.604528i) q^{2} +(-1.32028 + 1.32028i) q^{3} +(2.28716 + 1.66172i) q^{4} +(-3.25460 + 1.65830i) q^{6} +(2.10094 + 2.89169i) q^{8} -2.48629i q^{9} +O(q^{10})\)	\(q+(1.86055 + 0.604528i) q^{2} +(-1.32028 + 1.32028i) q^{3} +(2.28716 + 1.66172i) q^{4} +(-3.25460 + 1.65830i) q^{6} +(2.10094 + 2.89169i) q^{8} -2.48629i q^{9} +(-5.21364 + 0.825760i) q^{12} +(-0.571411 - 1.12146i) q^{13} +(1.28716 + 3.96149i) q^{16} +(1.50303 - 4.62586i) q^{18} +(0.309017 - 0.951057i) q^{23} +(-6.59168 - 1.04402i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.385184 - 2.43196i) q^{26} +(1.96232 + 1.96232i) q^{27} +(-0.707912 + 0.112122i) q^{29} +(-0.658114 + 0.478148i) q^{31} +4.57433i q^{32} +(4.13152 - 5.68655i) q^{36} +(2.23506 + 0.726216i) q^{39} +(-0.978148 + 0.207912i) q^{41} +(1.14988 - 1.58268i) q^{46} +(1.77957 - 0.906737i) q^{47} +(-6.92970 - 3.53086i) q^{48} +(0.587785 + 0.809017i) q^{49} -1.95630i q^{50} +(0.556639 - 3.51448i) q^{52} +(2.46471 + 4.83727i) q^{54} +(-1.38488 - 0.219344i) q^{58} +(-0.500000 + 1.53884i) q^{59} +(-1.51351 + 0.491768i) q^{62} +(-1.47815 + 4.54927i) q^{64} +(0.847673 + 1.66365i) q^{69} +(-0.262394 + 1.65669i) q^{71} +(7.18959 - 5.22354i) q^{72} -1.98904i q^{73} +(1.66365 + 0.847673i) q^{75} +(3.71942 + 2.70232i) q^{78} -2.69535 q^{81} +(-1.94558 - 0.204489i) q^{82} +(0.786610 - 1.08268i) q^{87} +(2.28716 - 1.66172i) q^{92} +(0.237606 - 1.50019i) q^{93} +(3.85912 - 0.611225i) q^{94} +(-6.03940 - 6.03940i) q^{96} +(0.604528 + 1.86055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6}+O(q^{10}) \) 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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