LMFDB - Embedded newform 943.1.n.b.367.1

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			367.1
Root			$0.994522 + 0.104528i$ of defining polynomial
Character	$\chi$	$=$	943.367
Dual form			943.1.n.b.758.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27276 + 0.413545i) q^{2} +(1.09905 + 1.09905i) q^{3} +(0.639886 - 0.464905i) q^{4} +(-1.85334 - 0.944322i) q^{6} +(0.164446 - 0.226341i) q^{8} +1.41582i q^{9} +O(q^{10})$	\(q+(-1.27276 + 0.413545i) q^{2} +(1.09905 + 1.09905i) q^{3} +(0.639886 - 0.464905i) q^{4} +(-1.85334 - 0.944322i) q^{6} +(0.164446 - 0.226341i) q^{8} +1.41582i q^{9} +(1.21422 + 0.192314i) q^{12} +(-0.325391 + 0.638616i) q^{13} +(-0.360114 + 1.10832i) q^{16} +(-0.585507 - 1.80201i) q^{18} +(0.309017 + 0.951057i) q^{23} +(0.429495 - 0.0680253i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(0.150049 - 0.947371i) q^{26} +(-0.457011 + 0.457011i) q^{27} +(-1.24314 - 0.196895i) q^{29} +(1.60917 + 1.16913i) q^{31} -1.27977i q^{32} +(0.658223 + 0.905966i) q^{36} +(-1.05949 + 0.344250i) q^{39} +(0.669131 - 0.743145i) q^{41} +(-0.786610 - 1.08268i) q^{46} +(-0.970554 - 0.494522i) q^{47} +(-1.61388 + 0.822312i) q^{48} +(0.587785 - 0.809017i) q^{49} -1.33826i q^{50} +(0.0886823 + 0.559918i) q^{52} +(0.392671 - 0.770661i) q^{54} +(1.66365 - 0.263497i) q^{58} +(-0.500000 - 1.53884i) q^{59} +(-2.53158 - 0.822560i) q^{62} +(0.169131 + 0.520530i) q^{64} +(-0.705634 + 1.38488i) q^{69} +(-0.0163743 - 0.103383i) q^{71} +(0.320459 + 0.232827i) q^{72} -0.813473i q^{73} +(-1.38488 + 0.705634i) q^{75} +(1.20612 - 0.876297i) q^{78} +0.411268 q^{81} +(-0.544320 + 1.22256i) q^{82} +(-1.14988 - 1.58268i) q^{87} +(0.639886 + 0.464905i) q^{92} +(0.483626 + 3.05349i) q^{93} +(1.43979 + 0.228041i) q^{94} +(1.40653 - 1.40653i) q^{96} +(-0.413545 + 1.27276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/943\mathbb{Z}\right)^\times$.

$n$	$47$	$534$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	−1.27276	+	0.413545i	−1.27276	+	0.413545i	−0.866025	−	0.500000i	$-0.833333\pi$
$2$	−1.27276	+	0.413545i	−1.27276	+	0.413545i	−0.406737	+	0.913545i	$0.633333\pi$
$3$	1.09905	+	1.09905i	1.09905	+	1.09905i	0.994522	+	0.104528i	$0.0333333\pi$
$3$	1.09905	+	1.09905i	1.09905	+	1.09905i	0.104528	+	0.994522i	$0.466667\pi$
$4$	0.639886	−	0.464905i	0.639886	−	0.464905i
$5$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$5$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$6$	−1.85334	−	0.944322i	−1.85334	−	0.944322i
$7$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$7$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$8$	0.164446	−	0.226341i	0.164446	−	0.226341i
$9$			1.41582i			1.41582i
$10$		0			0
$11$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$11$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$12$	1.21422	+	0.192314i	1.21422	+	0.192314i
$13$	−0.325391	+	0.638616i	−0.325391	+	0.638616i	−0.994522	−	0.104528i	$-0.966667\pi$
$13$	−0.325391	+	0.638616i	−0.325391	+	0.638616i	0.669131	+	0.743145i	$0.266667\pi$
$14$		0			0
$15$		0			0
$16$	−0.360114	+	1.10832i	−0.360114	+	1.10832i
$17$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$17$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$18$	−0.585507	−	1.80201i	−0.585507	−	1.80201i
$19$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$19$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$20$		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
$24$	0.429495	−	0.0680253i	0.429495	−	0.0680253i
$25$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$26$	0.150049	−	0.947371i	0.150049	−	0.947371i
$27$	−0.457011	+	0.457011i	−0.457011	+	0.457011i
$28$		0			0
$29$	−1.24314	−	0.196895i	−1.24314	−	0.196895i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	−1.24314	−	0.196895i	−1.24314	−	0.196895i	−0.743145	+	0.669131i	$0.766667\pi$
$30$		0			0
$31$	1.60917	+	1.16913i	1.60917	+	1.16913i	0.866025	+	0.500000i	$0.166667\pi$
$31$	1.60917	+	1.16913i	1.60917	+	1.16913i	0.743145	+	0.669131i	$0.233333\pi$
$32$		−	1.27977i		−	1.27977i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.658223	+	0.905966i	0.658223	+	0.905966i
$37$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$37$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$38$		0			0
$39$	−1.05949	+	0.344250i	−1.05949	+	0.344250i
$40$		0			0
$41$	0.669131	−	0.743145i	0.669131	−	0.743145i
$41$	0.669131	−	0.743145i	0.669131	−	0.743145i
$42$		0			0
$43$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$43$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$44$		0			0
$45$		0			0
$46$	−0.786610	−	1.08268i	−0.786610	−	1.08268i
$47$	−0.970554	−	0.494522i	−0.970554	−	0.494522i	−0.104528	−	0.994522i	$-0.533333\pi$
$47$	−0.970554	−	0.494522i	−0.970554	−	0.494522i	−0.866025	+	0.500000i	$0.833333\pi$
$48$	−1.61388	+	0.822312i	−1.61388	+	0.822312i
$49$	0.587785	−	0.809017i	0.587785	−	0.809017i
$50$		−	1.33826i		−	1.33826i
$51$		0			0
$52$	0.0886823	+	0.559918i	0.0886823	+	0.559918i
$53$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$53$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$54$	0.392671	−	0.770661i	0.392671	−	0.770661i
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.66365	−	0.263497i	1.66365	−	0.263497i
$59$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$60$		0			0
$61$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$61$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$62$	−2.53158	−	0.822560i	−2.53158	−	0.822560i
$63$		0			0
$64$	0.169131	+	0.520530i	0.169131	+	0.520530i
$65$		0			0
$66$		0			0
$67$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$67$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$68$		0			0
$69$	−0.705634	+	1.38488i	−0.705634	+	1.38488i
$70$		0			0
$71$	−0.0163743	−	0.103383i	−0.0163743	−	0.103383i	0.978148	−	0.207912i	$-0.0666667\pi$
$71$	−0.0163743	−	0.103383i	−0.0163743	−	0.103383i	−0.994522	+	0.104528i	$0.966667\pi$
$72$	0.320459	+	0.232827i	0.320459	+	0.232827i
$73$		−	0.813473i		−	0.813473i	−0.913545	−	0.406737i	$-0.866667\pi$
$73$		−	0.813473i		−	0.813473i	0.913545	−	0.406737i	$-0.133333\pi$
$74$		0			0
$75$	−1.38488	+	0.705634i	−1.38488	+	0.705634i
$76$		0			0
$77$		0			0
$78$	1.20612	−	0.876297i	1.20612	−	0.876297i
$79$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$79$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$80$		0			0
$81$	0.411268			0.411268
$82$	−0.544320	+	1.22256i	−0.544320	+	1.22256i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.14988	−	1.58268i	−1.14988	−	1.58268i
$88$		0			0
$89$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$89$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$90$		0			0
$91$		0			0
$92$	0.639886	+	0.464905i	0.639886	+	0.464905i
$93$	0.483626	+	3.05349i	0.483626	+	3.05349i
$94$	1.43979	+	0.228041i	1.43979	+	0.228041i
$95$		0			0
$96$	1.40653	−	1.40653i	1.40653	−	1.40653i
$97$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$97$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$98$	−0.413545	+	1.27276i	−0.413545	+	1.27276i
$99$		0			0
$100$	0.244415	+	0.752232i	0.244415	+	0.752232i
$101$	0.142040	+	0.278768i	0.142040	+	0.278768i	0.951057	−	0.309017i	$-0.100000\pi$
$101$	0.142040	+	0.278768i	0.142040	+	0.278768i	−0.809017	+	0.587785i	$0.800000\pi$
$102$		0			0
$103$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$103$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$104$	0.0910356	+	0.178667i	0.0910356	+	0.178667i
$105$		0			0
$106$		0			0
$107$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$107$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$108$	−0.0799685	+	0.504901i	−0.0799685	+	0.504901i
$109$		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	$-0.800000\pi$
$113$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$114$		0			0
$115$		0			0
$116$	−0.887009	+	0.451954i	−0.887009	+	0.451954i
$117$	−0.904168	−	0.460697i	−0.904168	−	0.460697i
$118$	1.27276	+	1.75181i	1.27276	+	1.75181i
$119$		0			0
$120$		0			0
$121$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$122$		0			0
$123$	1.55216	−	0.0813454i	1.55216	−	0.0813454i
$124$	1.57322			1.57322
$125$		0			0
$126$		0			0
$127$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$127$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$128$	0.321706	+	0.442790i	0.321706	+	0.442790i
$129$		0			0
$130$		0			0
$131$	1.07394	−	1.47815i	1.07394	−	1.47815i	0.207912	−	0.978148i	$-0.433333\pi$
$131$	1.07394	−	1.47815i	1.07394	−	1.47815i	0.866025	−	0.500000i	$-0.166667\pi$
$132$		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	$0.750000\pi$
$138$	0.325391	−	2.05444i	0.325391	−	2.05444i
$139$	0.459289	−	1.41355i	0.459289	−	1.41355i	−0.406737	−	0.913545i	$-0.633333\pi$
$139$	0.459289	−	1.41355i	0.459289	−	1.41355i	0.866025	−	0.500000i	$-0.166667\pi$
$140$		0			0
$141$	−0.523183	−	1.61019i	−0.523183	−	1.61019i
$142$	0.0635942	+	0.124811i	0.0635942	+	0.124811i
$143$		0			0
$144$	−1.56918	−	0.509857i	−1.56918	−	0.509857i
$145$		0			0
$146$	0.336408	+	1.03536i	0.336408	+	1.03536i
$147$	1.53516	−	0.243145i	1.53516	−	0.243145i
$148$		0			0
$149$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$149$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$150$	1.47082	−	1.47082i	1.47082	−	1.47082i
$151$	0.847673	−	1.66365i	0.847673	−	1.66365i	0.104528	−	0.994522i	$-0.466667\pi$
$151$	0.847673	−	1.66365i	0.847673	−	1.66365i	0.743145	−	0.669131i	$-0.233333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.517912	+	0.712844i	−0.517912	+	0.712844i
$157$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$157$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.523446	+	0.170078i	−0.523446	+	0.170078i
$163$	0.813473			0.813473			0.406737	−	0.913545i	$-0.366667\pi$
$163$	0.813473			0.813473			0.406737	+	0.913545i	$0.366667\pi$
$164$	0.0826761	−	0.786610i	0.0826761	−	0.786610i
$165$		0			0
$166$		0			0
$167$	0.221232	+	0.221232i	0.221232	+	0.221232i	0.809017	−	0.587785i	$-0.200000\pi$
$167$	0.221232	+	0.221232i	0.221232	+	0.221232i	−0.587785	+	0.809017i	$0.700000\pi$
$168$		0			0
$169$	0.285834	+	0.393417i	0.285834	+	0.393417i
$170$		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
$177$	1.14174	−	2.24079i	1.14174	−	2.24079i
$178$		0			0
$179$	0.302208	−	1.90807i	0.302208	−	1.90807i	−0.104528	−	0.994522i	$-0.533333\pi$
$179$	0.302208	−	1.90807i	0.302208	−	1.90807i	0.406737	−	0.913545i	$-0.366667\pi$
$180$		0			0
$181$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$181$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$182$		0			0
$183$		0			0
$184$	0.266080	+	0.0864545i	0.266080	+	0.0864545i
$185$		0			0
$186$	−1.87830	−	3.68637i	−1.87830	−	3.68637i
$187$		0			0
$188$	−0.850950	+	0.134777i	−0.850950	+	0.134777i
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$	−0.386206	+	0.757972i	−0.386206	+	0.757972i
$193$	0.707912	+	0.112122i	0.707912	+	0.112122i	0.500000	−	0.866025i	$-0.333333\pi$
$193$	0.707912	+	0.112122i	0.707912	+	0.112122i	0.207912	+	0.978148i	$0.433333\pi$
$194$		0			0
$195$		0			0
$196$		−	0.790943i		−	0.790943i
$197$	0.244415	−	0.336408i	0.244415	−	0.336408i	−0.669131	−	0.743145i	$-0.733333\pi$
$197$	0.244415	−	0.336408i	0.244415	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$198$		0			0
$199$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$199$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$200$	0.164446	+	0.226341i	0.164446	+	0.226341i
$201$		0			0
$202$	−0.296066	−	0.296066i	−0.296066	−	0.296066i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.34653	+	0.437513i	−1.34653	+	0.437513i
$208$	−0.590611	−	0.590611i	−0.590611	−	0.590611i
$209$		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
$213$	0.0956272	−	0.131620i	0.0956272	−	0.131620i
$214$		0			0
$215$		0			0
$216$	0.0282865	+	0.178594i	0.0282865	+	0.178594i
$217$		0			0
$218$		0			0
$219$	0.894048	−	0.894048i	0.894048	−	0.894048i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$223$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$224$		0			0
$225$	−1.34653	−	0.437513i	−1.34653	−	0.437513i
$226$		0			0
$227$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$227$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$228$		0			0
$229$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$229$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$230$		0			0
$231$		0			0
$232$	−0.248996	+	0.248996i	−0.248996	+	0.248996i
$233$	−0.877042	+	1.72129i	−0.877042	+	1.72129i	−0.207912	+	0.978148i	$0.566667\pi$
$233$	−0.877042	+	1.72129i	−0.877042	+	1.72129i	−0.669131	+	0.743145i	$0.733333\pi$
$234$	1.34131	+	0.212443i	1.34131	+	0.212443i
$235$		0			0
$236$	−1.03536	−	0.752232i	−1.03536	−	0.752232i
$237$		0			0
$238$		0			0
$239$	1.12146	−	0.571411i	1.12146	−	0.571411i	0.207912	−	0.978148i	$-0.433333\pi$
$239$	1.12146	−	0.571411i	1.12146	−	0.571411i	0.913545	+	0.406737i	$0.133333\pi$
$240$		0			0
$241$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$241$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$242$	1.08268	−	0.786610i	1.08268	−	0.786610i
$243$	0.909015	+	0.909015i	0.909015	+	0.909015i
$244$		0			0
$245$		0			0
$246$	−1.94189	+	0.745423i	−1.94189	+	0.745423i
$247$		0			0
$248$	0.529244	−	0.171962i	0.529244	−	0.171962i
$249$		0			0
$250$		0			0
$251$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$251$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$252$		0			0
$253$		0			0
$254$	0.786610	−	1.08268i	0.786610	−	1.08268i
$255$		0			0
$256$	−1.03536	−	0.752232i	−1.03536	−	0.752232i
$257$	0.292088	+	1.84417i	0.292088	+	1.84417i	0.500000	+	0.866025i	$0.333333\pi$
$257$	0.292088	+	1.84417i	0.292088	+	1.84417i	−0.207912	+	0.978148i	$0.566667\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.278768	−	1.76007i	0.278768	−	1.76007i
$262$	−0.755585	+	2.32545i	−0.755585	+	2.32545i
$263$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$263$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.251377	+	0.773659i	0.251377	+	0.773659i	0.994522	+	0.104528i	$0.0333333\pi$
$269$	0.251377	+	0.773659i	0.251377	+	0.773659i	−0.743145	+	0.669131i	$0.766667\pi$
$270$		0			0
$271$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$271$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.192314	+	1.21422i	0.192314	+	1.21422i
$277$	−1.60917	−	1.16913i	−1.60917	−	1.16913i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$	−1.60917	−	1.16913i	−1.60917	−	1.16913i	−0.743145	−	0.669131i	$-0.766667\pi$
$278$			1.98904i			1.98904i
$279$	−1.65528	+	2.27830i	−1.65528	+	2.27830i
$280$		0			0
$281$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$281$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$282$	1.33178	+	1.83303i	1.33178	+	1.83303i
$283$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$283$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$284$	−0.0585410	−	0.0585410i	−0.0585410	−	0.0585410i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.81193			1.81193
$289$	0.951057	−	0.309017i	0.951057	−	0.309017i
$290$		0			0
$291$		0			0
$292$	−0.378188	−	0.520530i	−0.378188	−	0.520530i
$293$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$293$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$294$	−1.85334	+	0.944322i	−1.85334	+	0.944322i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.707912	−	0.112122i	−0.707912	−	0.112122i
$300$	−0.558116	+	1.09536i	−0.558116	+	1.09536i
$301$		0			0
$302$	−0.390890	+	2.46799i	−0.390890	+	2.46799i
$303$	−0.150272	+	0.462489i	−0.150272	+	0.462489i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.80902	+	0.587785i	1.80902	+	0.587785i	1.00000			$0$
$307$	1.80902	+	0.587785i	1.80902	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.97267	+	0.312440i	−1.97267	+	0.312440i	−0.978148	+	0.207912i	$0.933333\pi$
$311$	−1.97267	+	0.312440i	−1.97267	+	0.312440i	−0.994522	+	0.104528i	$0.966667\pi$
$312$	−0.0963118	+	0.296417i	−0.0963118	+	0.296417i
$313$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$313$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.278768	+	1.76007i	0.278768	+	1.76007i	0.587785	+	0.809017i	$0.300000\pi$
$317$	0.278768	+	1.76007i	0.278768	+	1.76007i	−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.263164	−	0.191200i	0.263164	−	0.191200i
$325$	−0.506809	−	0.506809i	−0.506809	−	0.506809i
$326$	−1.03536	+	0.336408i	−1.03536	+	0.336408i
$327$		0			0
$328$	−0.0581680	−	0.273659i	−0.0581680	−	0.273659i
$329$		0			0
$330$		0			0
$331$	−1.18606	−	1.18606i	−1.18606	−	1.18606i	−0.978148	−	0.207912i	$-0.933333\pi$
$331$	−1.18606	−	1.18606i	−1.18606	−	1.18606i	−0.207912	−	0.978148i	$-0.566667\pi$
$332$		0			0
$333$		0			0
$334$	−0.373065	−	0.190086i	−0.373065	−	0.190086i
$335$		0			0
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−0.526494	−	0.382520i	−0.526494	−	0.382520i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.255585	−	0.786610i	−0.255585	−	0.786610i
$347$	−0.896802	−	1.76007i	−0.896802	−	1.76007i	−0.587785	−	0.809017i	$-0.700000\pi$
$347$	−0.896802	−	1.76007i	−0.896802	−	1.76007i	−0.309017	−	0.951057i	$-0.600000\pi$
$348$	−1.47159	−	0.478148i	−1.47159	−	0.478148i
$349$	1.73767	+	0.564602i	1.73767	+	0.564602i	0.994522	−	0.104528i	$-0.0333333\pi$
$349$	1.73767	+	0.564602i	1.73767	+	0.564602i	0.743145	+	0.669131i	$0.233333\pi$
$350$		0			0
$351$	−0.143147	−	0.440562i	−0.143147	−	0.440562i
$352$		0			0
$353$	−0.459289	+	1.41355i	−0.459289	+	1.41355i	0.406737	+	0.913545i	$0.366667\pi$
$353$	−0.459289	+	1.41355i	−0.459289	+	1.41355i	−0.866025	+	0.500000i	$0.833333\pi$
$354$	−0.526494	+	3.32415i	−0.526494	+	3.32415i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.404433	+	2.55349i	0.404433	+	2.55349i
$359$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$359$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$360$		0			0
$361$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$362$		0			0
$363$	−1.38488	−	0.705634i	−1.38488	−	0.705634i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$367$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$368$	−1.16535			−1.16535
$369$	1.05216	+	0.947371i	1.05216	+	0.947371i
$370$		0			0
$371$		0			0
$372$	1.72905	+	1.72905i	1.72905	+	1.72905i
$373$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$373$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$374$		0			0
$375$		0			0
$376$	−0.271535	+	0.138354i	−0.271535	+	0.138354i
$377$	0.530249	−	0.729825i	0.530249	−	0.729825i
$378$		0			0
$379$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$379$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$380$		0			0
$381$	−1.53516	−	0.243145i	−1.53516	−	0.243145i
$382$		0			0
$383$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$383$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$384$	−0.133078	+	0.840219i	−0.133078	+	0.840219i
$385$		0			0
$386$	−0.947371	+	0.150049i	−0.947371	+	0.150049i
$387$		0			0
$388$		0			0
$389$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$389$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$390$		0			0
$391$		0			0
$392$	−0.0864545	−	0.266080i	−0.0864545	−	0.266080i
$393$	2.80487	−	0.444248i	2.80487	−	0.444248i
$394$	−0.171962	+	0.529244i	−0.171962	+	0.529244i
$395$		0			0
$396$		0			0
$397$	0.877042	−	1.72129i	0.877042	−	1.72129i	0.207912	−	0.978148i	$-0.433333\pi$
$397$	0.877042	−	1.72129i	0.877042	−	1.72129i	0.669131	−	0.743145i	$-0.266667\pi$
$398$		0			0
$399$		0			0
$400$	−0.942790	−	0.684977i	−0.942790	−	0.684977i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	−1.27024	+	0.647218i	−1.27024	+	0.647218i
$404$	0.220490	+	0.112345i	0.220490	+	0.112345i
$405$		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
$414$	1.53288	−	1.11370i	1.53288	−	1.11370i
$415$		0			0
$416$	0.817284	+	0.416427i	0.817284	+	0.416427i
$417$	2.05834	−	1.04878i	2.05834	−	1.04878i
$418$		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	$-0.550000\pi$
$421$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$422$	2.35544	+	0.373065i	2.35544	+	0.373065i
$423$	0.700156	−	1.37413i	0.700156	−	1.37413i
$424$		0			0
$425$		0			0
$426$	−0.0672800	+	0.207067i	−0.0672800	+	0.207067i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$431$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$432$	−0.341936	−	0.671088i	−0.341936	−	0.671088i
$433$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$433$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.768181	+	1.50764i	−0.768181	+	1.50764i
$439$	−1.97267	−	0.312440i	−1.97267	−	0.312440i	−0.994522	−	0.104528i	$-0.966667\pi$
$439$	−1.97267	−	0.312440i	−1.97267	−	0.312440i	−0.978148	−	0.207912i	$-0.933333\pi$
$440$		0			0
$441$	1.14543	+	0.832200i	1.14543	+	0.832200i
$442$		0			0
$443$	−0.786610	+	1.08268i	−0.786610	+	1.08268i	0.207912	+	0.978148i	$0.433333\pi$
$443$	−0.786610	+	1.08268i	−0.786610	+	1.08268i	−0.994522	+	0.104528i	$0.966667\pi$
$444$		0			0
$445$		0			0
$446$	0.924716	+	1.27276i	0.924716	+	1.27276i
$447$		0			0
$448$		0			0
$449$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$449$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$450$	1.89474			1.89474
$451$		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	$-0.850000\pi$
$457$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.58268	−	1.14988i	−1.58268	−	1.14988i	−0.913545	−	0.406737i	$-0.866667\pi$
$461$	−1.58268	−	1.14988i	−1.58268	−	1.14988i	−0.669131	−	0.743145i	$-0.733333\pi$
$462$		0			0
$463$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i		−	1.00000i	$-0.5\pi$
$463$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i	−0.309017	+	0.951057i	$0.600000\pi$
$464$	0.665895	−	1.30689i	0.665895	−	1.30689i
$465$		0			0
$466$	0.404433	−	2.55349i	0.404433	−	2.55349i
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	−0.792745	+	0.125558i	−0.792745	+	0.125558i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.430526	−	0.139886i	−0.430526	−	0.139886i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.19104	+	1.19104i	−1.19104	+	1.19104i
$479$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$479$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.464905	+	0.639886i	−0.464905	+	0.639886i
$485$		0			0
$486$	−1.53288	−	0.781040i	−1.53288	−	0.781040i
$487$	−1.07394	−	1.47815i	−1.07394	−	1.47815i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$	−1.07394	−	1.47815i	−1.07394	−	1.47815i	−0.207912	−	0.978148i	$-0.566667\pi$
$488$		0			0
$489$	0.894048	+	0.894048i	0.894048	+	0.894048i
$490$		0			0
$491$	1.98904			1.98904			0.994522	−	0.104528i	$-0.0333333\pi$
$491$	1.98904			1.98904			0.994522	+	0.104528i	$0.0333333\pi$
$492$	0.955389	−	0.773659i	0.955389	−	0.773659i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−1.87525	+	1.36245i	−1.87525	+	1.36245i
$497$		0			0
$498$		0			0
$499$	1.49452	−	0.761497i	1.49452	−	0.761497i	0.500000	−	0.866025i	$-0.333333\pi$
$499$	1.49452	−	0.761497i	1.49452	−	0.761497i	0.994522	+	0.104528i	$0.0333333\pi$
$500$		0			0
$501$			0.486290i			0.486290i
$502$		0			0
$503$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$503$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.118239	+	0.746530i	−0.118239	+	0.746530i
$508$	−0.244415	+	0.752232i	−0.244415	+	0.752232i
$509$	−0.511265	+	0.0809764i	−0.511265	+	0.0809764i	−0.406737	−	0.913545i	$-0.633333\pi$
$509$	−0.511265	+	0.0809764i	−0.511265	+	0.0809764i	−0.104528	+	0.994522i	$0.533333\pi$
$510$		0			0
$511$		0			0
$512$	1.10832	+	0.360114i	1.10832	+	0.360114i
$513$		0			0
$514$	−1.13441	−	2.22640i	−1.13441	−	2.22640i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.679250	+	0.679250i	−0.679250	+	0.679250i
$520$		0			0
$521$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$521$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$522$	0.373065	+	2.35544i	0.373065	+	2.35544i
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$		−	1.44512i		−	1.44512i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$530$		0			0
$531$	2.17873	−	0.707912i	2.17873	−	0.707912i
$532$		0			0
$533$	0.256855	+	0.669131i	0.256855	+	0.669131i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.42920	−	1.76492i	2.42920	−	1.76492i
$538$	−0.639886	−	0.880728i	−0.639886	−	0.880728i
$539$		0			0
$540$		0			0
$541$	−1.01807	+	1.40126i	−1.01807	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$541$	−1.01807	+	1.40126i	−1.01807	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$542$		−	2.54552i		−	2.54552i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.32028	+	1.32028i	−1.32028	+	1.32028i	−0.406737	+	0.913545i	$0.633333\pi$
$547$	−1.32028	+	1.32028i	−1.32028	+	1.32028i	−0.913545	+	0.406737i	$0.866667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	0.197417	+	0.387453i	0.197417	+	0.387453i
$553$		0			0
$554$	2.53158	+	0.822560i	2.53158	+	0.822560i
$555$		0			0
$556$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$557$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$557$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$558$	1.16460	−	3.58427i	1.16460	−	3.58427i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$563$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$564$	−1.08336	−	0.787110i	−1.08336	−	0.787110i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−0.0260925	−	0.0132948i	−0.0260925	−	0.0132948i
$569$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$569$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$570$		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
$576$	−0.736979	+	0.239459i	−0.736979	+	0.239459i
$577$	0.0740142	+	0.0740142i	0.0740142	+	0.0740142i	0.743145	−	0.669131i	$-0.233333\pi$
$577$	0.0740142	+	0.0740142i	0.0740142	+	0.0740142i	−0.669131	+	0.743145i	$0.733333\pi$
$578$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$579$	0.654803	+	0.901259i	0.654803	+	0.901259i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.184122	−	0.133773i	−0.184122	−	0.133773i
$585$		0			0
$586$		0			0
$587$	−0.906737	+	1.77957i	−0.906737	+	1.77957i	−0.406737	+	0.913545i	$0.633333\pi$
$587$	−0.906737	+	1.77957i	−0.906737	+	1.77957i	−0.500000	+	0.866025i	$0.666667\pi$
$588$	0.869286	−	0.869286i	0.869286	−	0.869286i
$589$		0			0
$590$		0			0
$591$	0.638354	−	0.101105i	0.638354	−	0.101105i
$592$		0			0
$593$	−0.809017	−	1.58779i	−0.809017	−	1.58779i	−0.809017	−	0.587785i	$-0.800000\pi$
$593$	−0.809017	−	1.58779i	−0.809017	−	1.58779i		−	1.00000i	$-0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.947371	−	0.150049i	0.947371	−	0.150049i
$599$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$599$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$600$	−0.0680253	+	0.429495i	−0.0680253	+	0.429495i
$601$	0.889993	−	0.889993i	0.889993	−	0.889993i	−0.104528	−	0.994522i	$-0.533333\pi$
$601$	0.889993	−	0.889993i	0.889993	−	0.889993i	0.994522	+	0.104528i	$0.0333333\pi$
$602$		0			0
$603$		0			0
$604$	−0.231025	−	1.45864i	−0.231025	−	1.45864i
$605$		0			0
$606$		−	0.650783i		−	0.650783i
$607$	−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			$1.00000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.631620	−	0.458898i	0.631620	−	0.458898i
$612$		0			0
$613$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$613$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$614$	−2.54552			−2.54552
$615$		0			0
$616$		0			0
$617$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$617$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$618$		0			0
$619$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$619$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$620$		0			0
$621$	−0.575867	−	0.293419i	−0.575867	−	0.293419i
$622$	2.38153	−	1.21345i	2.38153	−	1.21345i
$623$		0			0
$624$		−	1.29822i		−	1.29822i
$625$	−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	$-0.400000\pi$
$631$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$632$		0			0
$633$	−0.855906	−	2.63421i	−0.855906	−	2.63421i
$634$	−1.08268	−	2.12487i	−1.08268	−	2.12487i
$635$		0			0
$636$		0			0
$637$	0.325391	+	0.638616i	0.325391	+	0.638616i
$638$		0			0
$639$	0.146372	−	0.0231831i	0.146372	−	0.0231831i
$640$		0			0
$641$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$641$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$642$		0			0
$643$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$643$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$644$		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	$0.666667\pi$
$648$	0.0676314	−	0.0930867i	0.0676314	−	0.0930867i
$649$		0			0
$650$	0.854636	+	0.435459i	0.854636	+	0.435459i
$651$		0			0
$652$	0.520530	−	0.378188i	0.520530	−	0.378188i
$653$	−1.41228	−	1.41228i	−1.41228	−	1.41228i	−0.743145	−	0.669131i	$-0.766667\pi$
$653$	−1.41228	−	1.41228i	−1.41228	−	1.41228i	−0.669131	−	0.743145i	$-0.733333\pi$
$654$		0			0
$655$		0			0
$656$	0.582676	+	1.00922i	0.582676	+	1.00922i
$657$	1.15173			1.15173
$658$		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	$-0.700000\pi$
$661$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$662$	2.00006	+	1.01908i	2.00006	+	1.01908i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.196895	−	1.24314i	−0.196895	−	1.24314i
$668$	0.244415	+	0.0387115i	0.244415	+	0.0387115i
$669$	0.829522	−	1.62803i	0.829522	−	1.62803i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.84417	−	0.292088i	1.84417	−	0.292088i	0.866025	−	0.500000i	$-0.166667\pi$
$673$	1.84417	−	0.292088i	1.84417	−	0.292088i	0.978148	+	0.207912i	$0.0666667\pi$
$674$		0			0
$675$	−0.293419	−	0.575867i	−0.293419	−	0.575867i
$676$	0.365802	+	0.118856i	0.365802	+	0.118856i
$677$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$677$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.09905	−	1.09905i	1.09905	−	1.09905i	0.104528	−	0.994522i	$-0.466667\pi$
$683$	1.09905	−	1.09905i	1.09905	−	1.09905i	0.994522	−	0.104528i	$-0.0333333\pi$
$684$		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	−0.309017	−	0.951057i	$-0.600000\pi$
$691$	−1.26007	−	0.642040i	−1.26007	−	0.642040i	−0.951057	+	0.309017i	$0.900000\pi$
$692$	0.287327	+	0.395472i	0.287327	+	0.395472i
$693$		0			0
$694$	1.86929	+	1.86929i	1.86929	+	1.86929i
$695$		0			0
$696$	−0.547318			−0.547318
$697$		0			0
$698$	−2.44512			−2.44512
$699$	−2.85570	+	0.927873i	−2.85570	+	0.927873i
$700$		0			0
$701$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$701$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$702$	0.364385	+	0.501533i	0.364385	+	0.501533i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		−	1.98904i		−	1.98904i
$707$		0			0
$708$	−0.311170	−	1.96465i	−0.311170	−	1.96465i
$709$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$709$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.614648	+	1.89169i	−0.614648	+	1.89169i
$714$		0			0
$715$		0			0
$716$	−0.693691	−	1.36144i	−0.693691	−	1.36144i
$717$	1.86055	+	0.604528i	1.86055	+	0.604528i
$718$		0			0
$719$	0.809017	+	1.58779i	0.809017	+	1.58779i	0.809017	+	0.587785i	$0.200000\pi$
$719$	0.809017	+	1.58779i	0.809017	+	1.58779i			1.00000i	$0.500000\pi$
$720$		0			0
$721$		0			0
$722$	0.413545	−	1.27276i	0.413545	−	1.27276i
$723$		0			0
$724$		0			0
$725$	0.571411	−	1.12146i	0.571411	−	1.12146i
$726$	2.05444	+	0.325391i	2.05444	+	0.325391i
$727$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$727$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$728$		0			0
$729$			1.58684i			1.58684i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$733$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$734$		0			0
$735$		0			0
$736$	1.21714	−	0.395472i	1.21714	−	0.395472i
$737$		0			0
$738$	−1.73093	−	0.770661i	−1.73093	−	0.770661i
$739$	0.209057			0.209057			0.104528	−	0.994522i	$-0.466667\pi$
$739$	0.209057			0.209057			0.104528	+	0.994522i	$0.466667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$743$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$744$	0.770661	+	0.392671i	0.770661	+	0.392671i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$751$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$752$	0.897596	−	0.897596i	0.897596	−	0.897596i
$753$		0			0
$754$	−0.373065	+	1.14818i	−0.373065	+	1.14818i
$755$		0			0
$756$		0			0
$757$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$757$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.535233	+	1.64728i	0.535233	+	1.64728i	0.743145	+	0.669131i	$0.233333\pi$
$761$	0.535233	+	1.64728i	0.535233	+	1.64728i	−0.207912	+	0.978148i	$0.566667\pi$
$762$	2.05444	−	0.325391i	2.05444	−	0.325391i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.14543	+	0.181418i	1.14543	+	0.181418i
$768$	−0.311170	−	1.96465i	−0.311170	−	1.96465i
$769$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$769$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$770$		0			0
$771$	−1.70582	+	2.34786i	−1.70582	+	2.34786i
$772$	0.505109	−	0.257366i	0.505109	−	0.257366i
$773$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$773$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$774$		0			0
$775$	−1.60917	+	1.16913i	−1.60917	+	1.16913i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.658114	−	0.478148i	0.658114	−	0.478148i
$784$	0.684977	+	0.942790i	0.684977	+	0.942790i
$785$		0			0
$786$	−3.38621	+	1.72536i	−3.38621	+	1.72536i
$787$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$787$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$788$		−	0.328893i		−	0.328893i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.404433	+	2.55349i	−0.404433	+	2.55349i
$795$		0			0
$796$		0			0
$797$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$797$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$798$		0			0
$799$		0			0
$800$	1.21714	+	0.395472i	1.21714	+	0.395472i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.34905	−	1.34905i	1.34905	−	1.34905i
$807$	−0.574014	+	1.12657i	−0.574014	+	1.12657i
$808$	0.0864545	+	0.0136931i	0.0864545	+	0.0136931i
$809$	0.221232	+	1.39680i	0.221232	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$809$	0.221232	+	1.39680i	0.221232	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$810$		0			0
$811$			0.415823i			0.415823i	0.978148	+	0.207912i	$0.0666667\pi$
$811$			0.415823i			0.415823i	−0.978148	+	0.207912i	$0.933333\pi$
$812$		0			0
$813$	−2.63421	+	1.34220i	−2.63421	+	1.34220i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.27276	−	0.413545i	1.27276	−	0.413545i
$819$		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
$823$	0.770236	+	0.770236i	0.770236	+	0.770236i	0.978148	−	0.207912i	$-0.0666667\pi$
$823$	0.770236	+	0.770236i	0.770236	+	0.770236i	−0.207912	+	0.978148i	$0.566667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$827$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$828$	−0.658223	+	0.905966i	−0.658223	+	0.905966i
$829$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$829$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$830$		0			0
$831$	−0.483626	−	3.05349i	−0.483626	−	3.05349i
$832$	−0.387453	−	0.0613665i	−0.387453	−	0.0613665i
$833$		0			0
$834$	−2.18606	+	2.18606i	−2.18606	+	2.18606i
$835$		0			0
$836$		0			0
$837$	−1.26971	+	0.201103i	−1.26971	+	0.201103i
$838$		0			0
$839$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$839$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$840$		0			0
$841$	0.555585	+	0.180521i	0.555585	+	0.180521i
$842$		0			0
$843$		0			0
$844$	−1.39212	+	0.220490i	−1.39212	+	0.220490i
$845$		0			0
$846$	−0.322865	+	2.03849i	−0.322865	+	2.03849i
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		−	0.128679i		−	0.128679i
$853$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$853$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.978148	−	0.207912i	$-0.933333\pi$
$857$	−1.08268	+	0.786610i	−1.08268	+	0.786610i	−0.104528	+	0.994522i	$0.533333\pi$
$858$		0			0
$859$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$859$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.773659	−	0.251377i	0.773659	−	0.251377i	0.104528	−	0.994522i	$-0.466667\pi$
$863$	0.773659	−	0.251377i	0.773659	−	0.251377i	0.669131	+	0.743145i	$0.266667\pi$
$864$	0.584870	+	0.584870i	0.584870	+	0.584870i
$865$		0			0
$866$		0			0
$867$	1.38488	+	0.705634i	1.38488	+	0.705634i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.156442	−	0.987736i	0.156442	−	0.987736i
$877$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$877$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$878$	2.63995	−	0.418127i	2.63995	−	0.418127i
$879$		0			0
$880$		0			0
$881$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$881$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$882$	−1.80201	−	0.585507i	−1.80201	−	0.585507i
$883$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	−0.951057	−	0.309017i	$-0.900000\pi$
$883$	−0.642040	−	1.26007i	−0.642040	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$884$		0			0
$885$		0			0
$886$	0.553432	−	1.70329i	0.553432	−	1.70329i
$887$	0.0809764	−	0.511265i	0.0809764	−	0.511265i	−0.913545	−	0.406737i	$-0.866667\pi$
$887$	0.0809764	−	0.511265i	0.0809764	−	0.511265i	0.994522	−	0.104528i	$-0.0333333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	−0.752232	−	0.546528i	−0.752232	−	0.546528i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.654803	−	0.901259i	−0.654803	−	0.901259i
$898$		0			0
$899$	−1.77024	−	1.77024i	−1.77024	−	1.77024i
$900$	−1.06503	+	0.346048i	−1.06503	+	0.346048i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−3.14205	+	2.28283i	−3.14205	+	2.28283i
$907$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$907$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$908$		0			0
$909$	−0.394687	+	0.201103i	−0.394687	+	0.201103i
$910$		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	$-0.0500000\pi$
$919$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$920$		0			0
$921$	1.34220	+	2.63421i	1.34220	+	2.63421i
$922$	2.48990	+	0.809017i	2.48990	+	0.809017i
$923$	0.0713503	+	0.0231831i	0.0713503	+	0.0231831i
$924$		0			0
$925$		0			0
$926$	0.413545	−	0.0654992i	0.413545	−	0.0654992i
$927$		0			0
$928$	−0.251981	+	1.59094i	−0.251981	+	1.59094i
$929$	−0.770236	+	0.770236i	−0.770236	+	0.770236i	−0.978148	−	0.207912i	$-0.933333\pi$
$929$	−0.770236	+	0.770236i	−0.770236	+	0.770236i	0.207912	+	0.978148i	$0.433333\pi$
$930$		0			0
$931$		0			0
$932$	0.239029	+	1.50917i	0.239029	+	1.50917i
$933$	−2.51145	−	1.82468i	−2.51145	−	1.82468i
$934$		0			0
$935$		0			0
$936$	−0.252962	+	0.128890i	−0.252962	+	0.128890i
$937$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$937$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$941$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$942$		0			0
$943$	0.913545	+	0.406737i	0.913545	+	0.406737i
$944$	1.88558			1.88558
$945$		0			0
$946$		0			0
$947$	0.169131	−	0.122881i	0.169131	−	0.122881i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.169131	−	0.122881i	0.169131	−	0.122881i	0.669131	+	0.743145i	$0.266667\pi$
$948$		0			0
$949$	0.519497	+	0.264697i	0.519497	+	0.264697i
$950$		0			0
$951$	−1.62803	+	2.24079i	−1.62803	+	2.24079i
$952$		0			0
$953$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$953$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$954$		0			0
$955$		0			0
$956$	0.451954	−	0.887009i	0.451954	−	0.887009i
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.913545	+	2.81160i	0.913545	+	2.81160i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.511265	+	0.0809764i	−0.511265	+	0.0809764i	−0.406737	−	0.913545i	$-0.633333\pi$
$967$	−0.511265	+	0.0809764i	−0.511265	+	0.0809764i	−0.104528	+	0.994522i	$0.533333\pi$
$968$	−0.0864545	+	0.266080i	−0.0864545	+	0.266080i
$969$		0			0
$970$		0			0
$971$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$971$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$972$	1.00427	+	0.159061i	1.00427	+	0.159061i
$973$		0			0
$974$	1.97815	+	1.43721i	1.97815	+	1.43721i
$975$		−	1.11402i		−	1.11402i
$976$		0			0
$977$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$977$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$978$	−1.50764	−	0.768181i	−1.50764	−	0.768181i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−2.53158	+	0.822560i	−2.53158	+	0.822560i
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	0.236836	−	0.364695i	0.236836	−	0.364695i
$985$		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	0.809017	−	0.587785i	$-0.200000\pi$
$991$	1.76007	−	0.896802i	1.76007	−	0.896802i	0.951057	−	0.309017i	$-0.100000\pi$
$992$	1.49622	−	2.05937i	1.49622	−	2.05937i
$993$		−	2.60708i		−	2.60708i
$994$		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			$\pi$
$998$	−1.58726	+	1.58726i	−1.58726	+	1.58726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	943.1.n.b.367.1	✓	16
23.22	odd	2	CM	943.1.n.b.367.1	✓	16
41.20	even	20	inner	943.1.n.b.758.1	yes	16
943.758	odd	20	inner	943.1.n.b.758.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
943.1.n.b.367.1	✓	16	1.1	even	1	trivial
943.1.n.b.367.1	✓	16	23.22	odd	2	CM
943.1.n.b.758.1	yes	16	41.20	even	20	inner
943.1.n.b.758.1	yes	16	943.758	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)

\(f(q)\)	\(=\)	\(q+(-1.27276 + 0.413545i) q^{2} +(1.09905 + 1.09905i) q^{3} +(0.639886 - 0.464905i) q^{4} +(-1.85334 - 0.944322i) q^{6} +(0.164446 - 0.226341i) q^{8} +1.41582i q^{9} +O(q^{10})\)	\(q+(-1.27276 + 0.413545i) q^{2} +(1.09905 + 1.09905i) q^{3} +(0.639886 - 0.464905i) q^{4} +(-1.85334 - 0.944322i) q^{6} +(0.164446 - 0.226341i) q^{8} +1.41582i q^{9} +(1.21422 + 0.192314i) q^{12} +(-0.325391 + 0.638616i) q^{13} +(-0.360114 + 1.10832i) q^{16} +(-0.585507 - 1.80201i) q^{18} +(0.309017 + 0.951057i) q^{23} +(0.429495 - 0.0680253i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(0.150049 - 0.947371i) q^{26} +(-0.457011 + 0.457011i) q^{27} +(-1.24314 - 0.196895i) q^{29} +(1.60917 + 1.16913i) q^{31} -1.27977i q^{32} +(0.658223 + 0.905966i) q^{36} +(-1.05949 + 0.344250i) q^{39} +(0.669131 - 0.743145i) q^{41} +(-0.786610 - 1.08268i) q^{46} +(-0.970554 - 0.494522i) q^{47} +(-1.61388 + 0.822312i) q^{48} +(0.587785 - 0.809017i) q^{49} -1.33826i q^{50} +(0.0886823 + 0.559918i) q^{52} +(0.392671 - 0.770661i) q^{54} +(1.66365 - 0.263497i) q^{58} +(-0.500000 - 1.53884i) q^{59} +(-2.53158 - 0.822560i) q^{62} +(0.169131 + 0.520530i) q^{64} +(-0.705634 + 1.38488i) q^{69} +(-0.0163743 - 0.103383i) q^{71} +(0.320459 + 0.232827i) q^{72} -0.813473i q^{73} +(-1.38488 + 0.705634i) q^{75} +(1.20612 - 0.876297i) q^{78} +0.411268 q^{81} +(-0.544320 + 1.22256i) q^{82} +(-1.14988 - 1.58268i) q^{87} +(0.639886 + 0.464905i) q^{92} +(0.483626 + 3.05349i) q^{93} +(1.43979 + 0.228041i) q^{94} +(1.40653 - 1.40653i) q^{96} +(-0.413545 + 1.27276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 10 q^{4} - 12 q^{6}+O(q^{10}) \) 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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