LMFDB - Embedded newform 964.1.bh.a.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [964,1,Mod(83,964)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(964, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 37]))

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

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

chi := DirichletCharacter("964.83");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 964 = 2^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	964.bh (of order $60$, degree $16$, 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:	$0.481098672178$
Analytic rank:	$0$
Dimension:	$16$
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:	$\Z[a_1, \ldots, a_{9}]$
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			491.1
Root			$-0.743145 - 0.669131i$ of defining polynomial
Character	$\chi$	$=$	964.491
Dual form			964.1.bh.a.375.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.14988 + 1.58268i) q^{5} -1.00000i q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.14988 + 1.58268i) q^{5} -1.00000i q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.204489 - 1.94558i) q^{10} +(0.0658722 + 0.0813454i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-0.906737 - 1.77957i) q^{17} +(-0.743145 - 0.669131i) q^{18} +(-0.795697 + 1.78716i) q^{20} +(-0.873619 + 2.68872i) q^{25} +(-0.0163743 - 0.103383i) q^{26} +(-0.244415 + 1.14988i) q^{29} +(0.866025 - 0.500000i) q^{32} +(-0.104528 + 1.99452i) q^{34} +(0.309017 + 0.951057i) q^{36} +(0.889993 - 1.09905i) q^{37} +(1.58268 - 1.14988i) q^{40} +(-1.64728 - 0.535233i) q^{41} +(0.795697 + 1.78716i) q^{45} +(-0.994522 - 0.104528i) q^{49} +(2.10094 - 1.89169i) q^{50} +(-0.0375111 + 0.0977196i) q^{52} +(-0.309017 - 0.278240i) q^{53} +(0.786610 - 0.873619i) q^{58} +(0.363271 - 0.500000i) q^{61} -1.00000 q^{64} +(-0.0529982 + 0.197792i) q^{65} +(1.08779 - 1.67504i) q^{68} +(0.207912 - 0.978148i) q^{72} +(1.76007 + 0.278768i) q^{73} +(-1.32028 + 0.506809i) q^{74} +(-1.94558 + 0.204489i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.15897 + 1.28716i) q^{82} +(1.77384 - 3.48137i) q^{85} +(-0.402280 - 1.50133i) q^{89} +(0.204489 - 1.94558i) q^{90} +(-0.669131 + 0.743145i) q^{97} +(0.809017 + 0.587785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 2 * q^9	$ 16 q + 8 q^{4} - 2 q^{9} + 2 q^{10} + 4 q^{13} - 8 q^{16} - 8 q^{17} - 2 q^{26} + 2 q^{34} - 4 q^{36} + 2 q^{37} + 4 q^{40} + 2 q^{52} + 4 q^{53} - 16 q^{64} - 18 q^{65} + 8 q^{68} + 4 q^{73} - 2 q^{74} + 2 q^{81} - 2 q^{85} - 4 q^{89} - 2 q^{90} - 2 q^{97} + 4 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^9 + 2 * q^10 + 4 * q^13 - 8 * q^16 - 8 * q^17 - 2 * q^26 + 2 * q^34 - 4 * q^36 + 2 * q^37 + 4 * q^40 + 2 * q^52 + 4 * q^53 - 16 * q^64 - 18 * q^65 + 8 * q^68 + 4 * q^73 - 2 * q^74 + 2 * q^81 - 2 * q^85 - 4 * q^89 - 2 * q^90 - 2 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/964\mathbb{Z}\right)^\times$.

$n$	$483$	$489$
$\chi(n)$	$-1$	$e\left(\frac{31}{60}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$2$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$3$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$3$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$4$	0.500000	+	0.866025i	0.500000	+	0.866025i
$5$	1.14988	+	1.58268i	1.14988	+	1.58268i	0.743145	+	0.669131i	$0.233333\pi$
$5$	1.14988	+	1.58268i	1.14988	+	1.58268i	0.406737	+	0.913545i	$0.366667\pi$
$6$		0			0
$7$		0			0		0.0523360	−	0.998630i	$-0.483333\pi$
$7$		0			0		−0.0523360	+	0.998630i	$0.516667\pi$
$8$		−	1.00000i		−	1.00000i
$9$	0.978148	+	0.207912i	0.978148	+	0.207912i
$10$	−0.204489	−	1.94558i	−0.204489	−	1.94558i
$11$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$11$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$12$		0			0
$13$	0.0658722	+	0.0813454i	0.0658722	+	0.0813454i	0.809017	−	0.587785i	$-0.200000\pi$
$13$	0.0658722	+	0.0813454i	0.0658722	+	0.0813454i	−0.743145	+	0.669131i	$0.766667\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−0.906737	−	1.77957i	−0.906737	−	1.77957i	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−0.906737	−	1.77957i	−0.906737	−	1.77957i	−0.406737	−	0.913545i	$-0.633333\pi$
$18$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$19$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$19$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$20$	−0.795697	+	1.78716i	−0.795697	+	1.78716i
$21$		0			0
$22$		0			0
$23$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$23$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$24$		0			0
$25$	−0.873619	+	2.68872i	−0.873619	+	2.68872i
$26$	−0.0163743	−	0.103383i	−0.0163743	−	0.103383i
$27$		0			0
$28$		0			0
$29$	−0.244415	+	1.14988i	−0.244415	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$29$	−0.244415	+	1.14988i	−0.244415	+	1.14988i	−0.913545	+	0.406737i	$0.866667\pi$
$30$		0			0
$31$		0			0		−0.998630	−	0.0523360i	$-0.983333\pi$
$31$		0			0		0.998630	+	0.0523360i	$0.0166667\pi$
$32$	0.866025	−	0.500000i	0.866025	−	0.500000i
$33$		0			0
$34$	−0.104528	+	1.99452i	−0.104528	+	1.99452i
$35$		0			0
$36$	0.309017	+	0.951057i	0.309017	+	0.951057i
$37$	0.889993	−	1.09905i	0.889993	−	1.09905i	−0.104528	−	0.994522i	$-0.533333\pi$
$37$	0.889993	−	1.09905i	0.889993	−	1.09905i	0.994522	−	0.104528i	$-0.0333333\pi$
$38$		0			0
$39$		0			0
$40$	1.58268	−	1.14988i	1.58268	−	1.14988i
$41$	−1.64728	−	0.535233i	−1.64728	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$41$	−1.64728	−	0.535233i	−1.64728	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$42$		0			0
$43$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$43$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$44$		0			0
$45$	0.795697	+	1.78716i	0.795697	+	1.78716i
$46$		0			0
$47$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$47$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$48$		0			0
$49$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$50$	2.10094	−	1.89169i	2.10094	−	1.89169i
$51$		0			0
$52$	−0.0375111	+	0.0977196i	−0.0375111	+	0.0977196i
$53$	−0.309017	−	0.278240i	−0.309017	−	0.278240i	0.500000	−	0.866025i	$-0.333333\pi$
$53$	−0.309017	−	0.278240i	−0.309017	−	0.278240i	−0.809017	+	0.587785i	$0.800000\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.786610	−	0.873619i	0.786610	−	0.873619i
$59$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$59$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$60$		0			0
$61$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$61$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−1.00000
$65$	−0.0529982	+	0.197792i	−0.0529982	+	0.197792i
$66$		0			0
$67$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$67$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$68$	1.08779	−	1.67504i	1.08779	−	1.67504i
$69$		0			0
$70$		0			0
$71$		0			0		0.838671	−	0.544639i	$-0.183333\pi$
$71$		0			0		−0.838671	+	0.544639i	$0.816667\pi$
$72$	0.207912	−	0.978148i	0.207912	−	0.978148i
$73$	1.76007	+	0.278768i	1.76007	+	0.278768i	0.951057	−	0.309017i	$-0.100000\pi$
$73$	1.76007	+	0.278768i	1.76007	+	0.278768i	0.809017	+	0.587785i	$0.200000\pi$
$74$	−1.32028	+	0.506809i	−1.32028	+	0.506809i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$	−1.94558	+	0.204489i	−1.94558	+	0.204489i
$81$	0.913545	+	0.406737i	0.913545	+	0.406737i
$82$	1.15897	+	1.28716i	1.15897	+	1.28716i
$83$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$83$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$84$		0			0
$85$	1.77384	−	3.48137i	1.77384	−	3.48137i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.402280	−	1.50133i	−0.402280	−	1.50133i	−0.809017	−	0.587785i	$-0.800000\pi$
$89$	−0.402280	−	1.50133i	−0.402280	−	1.50133i	0.406737	−	0.913545i	$-0.366667\pi$
$90$	0.204489	−	1.94558i	0.204489	−	1.94558i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$97$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$98$	0.809017	+	0.587785i	0.809017	+	0.587785i
$99$		0			0
$100$	−2.76531	+	0.587785i	−2.76531	+	0.587785i
$101$	0.638616	+	0.325391i	0.638616	+	0.325391i	0.743145	−	0.669131i	$-0.233333\pi$
$101$	0.638616	+	0.325391i	0.638616	+	0.325391i	−0.104528	+	0.994522i	$0.533333\pi$
$102$		0			0
$103$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$103$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$104$	0.0813454	−	0.0658722i	0.0813454	−	0.0658722i
$105$		0			0
$106$	0.128496	+	0.395472i	0.128496	+	0.395472i
$107$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$107$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$108$		0			0
$109$	0.571411	+	0.705634i	0.571411	+	0.705634i	0.978148	−	0.207912i	$-0.0666667\pi$
$109$	0.571411	+	0.705634i	0.571411	+	0.705634i	−0.406737	+	0.913545i	$0.633333\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.15897	−	0.669131i	−1.15897	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$113$	−1.15897	−	0.669131i	−1.15897	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$114$		0			0
$115$		0			0
$116$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$117$	0.0475201	+	0.0932634i	0.0475201	+	0.0932634i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.866025	−	0.500000i	0.866025	−	0.500000i
$122$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$123$		0			0
$124$		0			0
$125$	−3.39939	+	1.10453i	−3.39939	+	1.10453i
$126$		0			0
$127$		0			0		−0.933580	−	0.358368i	$-0.883333\pi$
$127$		0			0		0.933580	+	0.358368i	$0.116667\pi$
$128$	0.866025	+	0.500000i	0.866025	+	0.500000i
$129$		0			0
$130$	0.144794	−	0.144794i	0.144794	−	0.144794i
$131$		0			0		−0.358368	−	0.933580i	$-0.616667\pi$
$131$		0			0		0.358368	+	0.933580i	$0.383333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−1.77957	+	0.906737i	−1.77957	+	0.906737i
$137$	−1.45106	+	1.17504i	−1.45106	+	1.17504i	−0.500000	+	0.866025i	$0.666667\pi$
$137$	−1.45106	+	1.17504i	−1.45106	+	1.17504i	−0.951057	+	0.309017i	$0.900000\pi$
$138$		0			0
$139$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$139$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$145$	−2.10094	+	0.935398i	−2.10094	+	0.935398i
$146$	−1.38488	−	1.12146i	−1.38488	−	1.12146i
$147$		0			0
$148$	1.39680	+	0.221232i	1.39680	+	0.221232i
$149$	−0.978148	+	0.792088i	−0.978148	+	0.792088i	−0.978148	−	0.207912i	$-0.933333\pi$
$149$	−0.978148	+	0.792088i	−0.978148	+	0.792088i			1.00000i	$0.5\pi$
$150$		0			0
$151$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$151$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$152$		0			0
$153$	−0.516929	−	1.92920i	−0.516929	−	1.92920i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.01693	+	0.390362i	−1.01693	+	0.390362i	−0.809017	−	0.587785i	$-0.800000\pi$
$157$	−1.01693	+	0.390362i	−1.01693	+	0.390362i	−0.207912	+	0.978148i	$0.566667\pi$
$158$		0			0
$159$		0			0
$160$	1.78716	+	0.795697i	1.78716	+	0.795697i
$161$		0			0
$162$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$163$		0			0		−0.0523360	−	0.998630i	$-0.516667\pi$
$163$		0			0		0.0523360	+	0.998630i	$0.483333\pi$
$164$	−0.360114	−	1.69420i	−0.360114	−	1.69420i
$165$		0			0
$166$		0			0
$167$		0			0		0.933580	−	0.358368i	$-0.116667\pi$
$167$		0			0		−0.933580	+	0.358368i	$0.883333\pi$
$168$		0			0
$169$	0.205634	−	0.967431i	0.205634	−	0.967431i
$170$	−3.27688	+	2.12803i	−3.27688	+	2.12803i
$171$		0			0
$172$		0			0
$173$	0.913545	−	1.40674i	0.913545	−	1.40674i		−	1.00000i	$-0.5\pi$
$173$	0.913545	−	1.40674i	0.913545	−	1.40674i	0.913545	−	0.406737i	$-0.133333\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.402280	+	1.50133i	−0.402280	+	1.50133i
$179$		0			0		−0.838671	−	0.544639i	$-0.816667\pi$
$179$		0			0		0.838671	+	0.544639i	$0.183333\pi$
$180$	−1.14988	+	1.58268i	−1.14988	+	1.58268i
$181$	0.951057	−	1.64728i	0.951057	−	1.64728i	0.207912	−	0.978148i	$-0.433333\pi$
$181$	0.951057	−	1.64728i	0.951057	−	1.64728i	0.743145	−	0.669131i	$-0.233333\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.76283	+	0.144794i	2.76283	+	0.144794i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$191$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$192$		0			0
$193$	0.122881	−	0.169131i	0.122881	−	0.169131i	−0.743145	−	0.669131i	$-0.766667\pi$
$193$	0.122881	−	0.169131i	0.122881	−	0.169131i	0.866025	+	0.500000i	$0.166667\pi$
$194$	0.951057	−	0.309017i	0.951057	−	0.309017i
$195$		0			0
$196$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$197$	−0.889993	−	0.889993i	−0.889993	−	0.889993i	0.104528	−	0.994522i	$-0.466667\pi$
$197$	−0.889993	−	0.889993i	−0.889993	−	0.889993i	−0.994522	+	0.104528i	$0.966667\pi$
$198$		0			0
$199$		0			0		0.629320	−	0.777146i	$-0.283333\pi$
$199$		0			0		−0.629320	+	0.777146i	$0.716667\pi$
$200$	2.68872	+	0.873619i	2.68872	+	0.873619i
$201$		0			0
$202$	−0.390362	−	0.601105i	−0.390362	−	0.601105i
$203$		0			0
$204$		0			0
$205$	−1.04707	−	3.22256i	−1.04707	−	3.22256i
$206$		0			0
$207$		0			0
$208$	−0.103383	+	0.0163743i	−0.103383	+	0.0163743i
$209$		0			0
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	0.0864545	−	0.406737i	0.0864545	−	0.406737i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.142040	−	0.896802i	−0.142040	−	0.896802i
$219$		0			0
$220$		0			0
$221$	0.0850311	−	0.190983i	0.0850311	−	0.190983i
$222$		0			0
$223$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$223$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$224$		0			0
$225$	−1.41355	+	2.44833i	−1.41355	+	2.44833i
$226$	0.669131	+	1.15897i	0.669131	+	1.15897i
$227$		0			0		0.544639	−	0.838671i	$-0.316667\pi$
$227$		0			0		−0.544639	+	0.838671i	$0.683333\pi$
$228$		0			0
$229$	0.809017	+	1.81708i	0.809017	+	1.81708i	0.500000	+	0.866025i	$0.333333\pi$
$229$	0.809017	+	1.81708i	0.809017	+	1.81708i	0.309017	+	0.951057i	$0.400000\pi$
$230$		0			0
$231$		0			0
$232$	1.14988	+	0.244415i	1.14988	+	0.244415i
$233$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$233$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$234$	0.00547810	−	0.104528i	0.00547810	−	0.104528i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−1.00000			−1.00000
$241$	−1.00000			−1.00000
$242$	−1.00000			−1.00000
$243$		0			0
$244$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$245$	−0.978148	−	1.69420i	−0.978148	−	1.69420i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	3.49622	+	0.743145i	3.49622	+	0.743145i
$251$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$251$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	0.669131	−	1.15897i	0.669131	−	1.15897i	−0.309017	−	0.951057i	$-0.600000\pi$
$257$	0.669131	−	1.15897i	0.669131	−	1.15897i	0.978148	−	0.207912i	$-0.0666667\pi$
$258$		0			0
$259$		0			0
$260$	−0.197792	+	0.0529982i	−0.197792	+	0.0529982i
$261$	−0.478148	+	1.07394i	−0.478148	+	1.07394i
$262$		0			0
$263$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$263$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$264$		0			0
$265$	0.0850311	−	0.809017i	0.0850311	−	0.809017i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.66365	−	0.847673i	1.66365	−	0.847673i	0.669131	−	0.743145i	$-0.266667\pi$
$269$	1.66365	−	0.847673i	1.66365	−	0.847673i	0.994522	−	0.104528i	$-0.0333333\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	1.99452	+	0.104528i	1.99452	+	0.104528i
$273$		0			0
$274$	1.84417	−	0.292088i	1.84417	−	0.292088i
$275$		0			0
$276$		0			0
$277$	0.0646021	+	0.198825i	0.0646021	+	0.198825i	0.978148	−	0.207912i	$-0.0666667\pi$
$277$	0.0646021	+	0.198825i	0.0646021	+	0.198825i	−0.913545	+	0.406737i	$0.866667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	−0.866025	−	0.500000i	$-0.833333\pi$
$281$	−0.658114	+	0.478148i	−0.658114	+	0.478148i	0.207912	+	0.978148i	$0.433333\pi$
$282$		0			0
$283$		0			0		0.629320	−	0.777146i	$-0.283333\pi$
$283$		0			0		−0.629320	+	0.777146i	$0.716667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.951057	−	0.309017i	0.951057	−	0.309017i
$289$	−1.75692	+	2.41819i	−1.75692	+	2.41819i
$290$	2.28716	+	0.240391i	2.28716	+	0.240391i
$291$		0			0
$292$	0.638616	+	1.66365i	0.638616	+	1.66365i
$293$	0.669131	−	1.74314i	0.669131	−	1.74314i		−	1.00000i	$-0.5\pi$
$293$	0.669131	−	1.74314i	0.669131	−	1.74314i	0.669131	−	0.743145i	$-0.266667\pi$
$294$		0			0
$295$		0			0
$296$	−1.09905	−	0.889993i	−1.09905	−	0.889993i
$297$		0			0
$298$	1.24314	−	0.196895i	1.24314	−	0.196895i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.20906			1.20906
$306$	−0.516929	+	1.92920i	−0.516929	+	1.92920i
$307$		0			0		−0.933580	−	0.358368i	$-0.883333\pi$
$307$		0			0		0.933580	+	0.358368i	$0.116667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.998630	−	0.0523360i	$-0.0166667\pi$
$311$		0			0		−0.998630	+	0.0523360i	$0.983333\pi$
$312$		0			0
$313$	0.395472	−	1.86055i	0.395472	−	1.86055i	−0.104528	−	0.994522i	$-0.533333\pi$
$313$	0.395472	−	1.86055i	0.395472	−	1.86055i	0.500000	−	0.866025i	$-0.333333\pi$
$314$	1.07587	+	0.170401i	1.07587	+	0.170401i
$315$		0			0
$316$		0			0
$317$	0.642040	+	0.642040i	0.642040	+	0.642040i	0.951057	−	0.309017i	$-0.100000\pi$
$317$	0.642040	+	0.642040i	0.642040	+	0.642040i	−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$	−1.14988	−	1.58268i	−1.14988	−	1.58268i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.104528	+	0.994522i	0.104528	+	0.994522i
$325$	−0.276262	+	0.106047i	−0.276262	+	0.106047i
$326$		0			0
$327$		0			0
$328$	−0.535233	+	1.64728i	−0.535233	+	1.64728i
$329$		0			0
$330$		0			0
$331$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$331$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$332$		0			0
$333$	1.09905	−	0.889993i	1.09905	−	0.889993i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.73767	+	0.773659i	−1.73767	+	0.773659i	−0.743145	+	0.669131i	$0.766667\pi$
$337$	−1.73767	+	0.773659i	−1.73767	+	0.773659i	−0.994522	+	0.104528i	$0.966667\pi$
$338$	−0.661799	+	0.735003i	−0.661799	+	0.735003i
$339$		0			0
$340$	3.90187	−	0.204489i	3.90187	−	0.204489i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.49452	+	0.761497i	−1.49452	+	0.761497i
$347$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$347$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$348$		0			0
$349$	−0.413545	−	1.94558i	−0.413545	−	1.94558i	−0.309017	−	0.951057i	$-0.600000\pi$
$349$	−0.413545	−	1.94558i	−0.413545	−	1.94558i	−0.104528	−	0.994522i	$-0.533333\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.601105	+	0.390362i	0.601105	+	0.390362i	0.809017	−	0.587785i	$-0.200000\pi$
$353$	0.601105	+	0.390362i	0.601105	+	0.390362i	−0.207912	+	0.978148i	$0.566667\pi$
$354$		0			0
$355$		0			0
$356$	1.09905	−	1.09905i	1.09905	−	1.09905i
$357$		0			0
$358$		0			0
$359$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$359$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$360$	1.78716	−	0.795697i	1.78716	−	0.795697i
$361$	0.866025	−	0.500000i	0.866025	−	0.500000i
$362$	−1.64728	+	0.951057i	−1.64728	+	0.951057i
$363$		0			0
$364$		0			0
$365$	1.58268	+	3.10618i	1.58268	+	3.10618i
$366$		0			0
$367$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$367$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$368$		0			0
$369$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$370$	−2.32028	−	1.50681i	−2.32028	−	1.50681i
$371$		0			0
$372$		0			0
$373$	−1.24314	−	1.53516i	−1.24314	−	1.53516i	−0.743145	−	0.669131i	$-0.766667\pi$
$373$	−1.24314	−	1.53516i	−1.24314	−	1.53516i	−0.500000	−	0.866025i	$-0.666667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.109638	+	0.0558632i	−0.109638	+	0.0558632i
$378$		0			0
$379$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$379$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.998630	−	0.0523360i	$-0.0166667\pi$
$383$		0			0		−0.998630	+	0.0523360i	$0.983333\pi$
$384$		0			0
$385$		0			0
$386$	−0.190983	+	0.0850311i	−0.190983	+	0.0850311i
$387$		0			0
$388$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$389$	1.65669	+	0.262394i	1.65669	+	0.262394i	0.913545	−	0.406737i	$-0.133333\pi$
$389$	1.65669	+	0.262394i	1.65669	+	0.262394i	0.743145	+	0.669131i	$0.233333\pi$
$390$		0			0
$391$		0			0
$392$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$393$		0			0
$394$	0.325760	+	1.21575i	0.325760	+	1.21575i
$395$		0			0
$396$		0			0
$397$	−0.896802	+	1.76007i	−0.896802	+	1.76007i	−0.309017	+	0.951057i	$0.600000\pi$
$397$	−0.896802	+	1.76007i	−0.896802	+	1.76007i	−0.587785	+	0.809017i	$0.700000\pi$
$398$		0			0
$399$		0			0
$400$	−1.89169	−	2.10094i	−1.89169	−	2.10094i
$401$	0.743145	+	0.330869i	0.743145	+	0.330869i	0.743145	−	0.669131i	$-0.233333\pi$
$401$	0.743145	+	0.330869i	0.743145	+	0.330869i			1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.0375111	+	0.715754i	0.0375111	+	0.715754i
$405$	0.406737	+	1.91355i	0.406737	+	1.91355i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.90807	−	0.302208i	−1.90807	−	0.302208i	−0.913545	−	0.406737i	$-0.866667\pi$
$409$	−1.90807	−	0.302208i	−1.90807	−	0.302208i	−0.994522	+	0.104528i	$0.966667\pi$
$410$	−0.704489	+	3.31436i	−0.704489	+	3.31436i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.0977196	+	0.0375111i	0.0977196	+	0.0375111i
$417$		0			0
$418$		0			0
$419$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$419$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$420$		0			0
$421$	−0.873619	+	1.20243i	−0.873619	+	1.20243i	0.104528	+	0.994522i	$0.466667\pi$
$421$	−0.873619	+	1.20243i	−0.873619	+	1.20243i	−0.978148	+	0.207912i	$0.933333\pi$
$422$		0			0
$423$		0			0
$424$	−0.278240	+	0.309017i	−0.278240	+	0.309017i
$425$	5.57692	−	0.883297i	5.57692	−	0.883297i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.358368	−	0.933580i	$-0.616667\pi$
$431$		0			0		0.358368	+	0.933580i	$0.383333\pi$
$432$		0			0
$433$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$433$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$434$		0			0
$435$		0			0
$436$	−0.325391	+	0.847673i	−0.325391	+	0.847673i
$437$		0			0
$438$		0			0
$439$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$439$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$440$		0			0
$441$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$442$	−0.169131	+	0.122881i	−0.169131	+	0.122881i
$443$		0			0		−0.544639	−	0.838671i	$-0.683333\pi$
$443$		0			0		0.544639	+	0.838671i	$0.316667\pi$
$444$		0			0
$445$	1.91355	−	2.36303i	1.91355	−	2.36303i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.511265	+	0.0809764i	−0.511265	+	0.0809764i	−0.406737	−	0.913545i	$-0.633333\pi$
$449$	−0.511265	+	0.0809764i	−0.511265	+	0.0809764i	−0.104528	+	0.994522i	$0.533333\pi$
$450$	2.44833	−	1.41355i	2.44833	−	1.41355i
$451$		0			0
$452$		−	1.33826i		−	1.33826i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$457$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$458$	0.207912	−	1.97815i	0.207912	−	1.97815i
$459$		0			0
$460$		0			0
$461$	0.0489435	−	0.309017i	0.0489435	−	0.309017i	−0.951057	−	0.309017i	$-0.900000\pi$
$461$	0.0489435	−	0.309017i	0.0489435	−	0.309017i	1.00000			$0$
$462$		0			0
$463$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$463$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$464$	−0.873619	−	0.786610i	−0.873619	−	0.786610i
$465$		0			0
$466$	0.809017	−	1.40126i	0.809017	−	1.40126i
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$	−0.0570084	+	0.0877853i	−0.0570084	+	0.0877853i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.244415	−	0.336408i	−0.244415	−	0.336408i
$478$		0			0
$479$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$479$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$480$		0			0
$481$	0.148028			0.148028
$482$	0.866025	+	0.500000i	0.866025	+	0.500000i
$483$		0			0
$484$	0.866025	+	0.500000i	0.866025	+	0.500000i
$485$	−1.94558	−	0.204489i	−1.94558	−	0.204489i
$486$		0			0
$487$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$487$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$488$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$489$		0			0
$490$			1.95630i			1.95630i
$491$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$491$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$492$		0			0
$493$	2.26792	−	0.607686i	2.26792	−	0.607686i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$499$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$500$	−2.65624	−	2.39169i	−2.65624	−	2.39169i
$501$		0			0
$502$		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
$505$	0.219344	+	1.38488i	0.219344	+	1.38488i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$509$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			1.00000i
$513$		0			0
$514$	−1.15897	+	0.669131i	−1.15897	+	0.669131i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.197792	+	0.0529982i	0.197792	+	0.0529982i
$521$	0.593263	+	0.913545i	0.593263	+	0.913545i	1.00000			$0$
$521$	0.593263	+	0.913545i	0.593263	+	0.913545i	−0.406737	+	0.913545i	$0.633333\pi$
$522$	0.951057	−	0.690983i	0.951057	−	0.690983i
$523$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$523$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$530$	−0.478148	+	0.658114i	−0.478148	+	0.658114i
$531$		0			0
$532$		0			0
$533$	−0.0649711	−	0.169255i	−0.0649711	−	0.169255i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.86460	−	0.0977196i	−1.86460	−	0.0977196i
$539$		0			0
$540$		0			0
$541$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$541$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$542$		0			0
$543$		0			0
$544$	−1.67504	−	1.08779i	−1.67504	−	1.08779i
$545$	−0.459735	+	1.71575i	−0.459735	+	1.71575i
$546$		0			0
$547$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$547$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$548$	−1.74314	−	0.669131i	−1.74314	−	0.669131i
$549$	0.459289	−	0.413545i	0.459289	−	0.413545i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.0434654	−	0.204489i	0.0434654	−	0.204489i
$555$		0			0
$556$		0			0
$557$	0.169131	−	0.379874i	0.169131	−	0.379874i	−0.809017	−	0.587785i	$-0.800000\pi$
$557$	0.169131	−	0.379874i	0.169131	−	0.379874i	0.978148	+	0.207912i	$0.0666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.809017	−	0.0850311i	0.809017	−	0.0850311i
$563$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$563$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$564$		0			0
$565$	−0.273659	−	2.60369i	−0.273659	−	2.60369i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.459289	+	1.41355i	−0.459289	+	1.41355i	0.406737	+	0.913545i	$0.366667\pi$
$569$	−0.459289	+	1.41355i	−0.459289	+	1.41355i	−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$571$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$577$	−0.557008	−	0.451057i	−0.557008	−	0.451057i	0.309017	−	0.951057i	$-0.400000\pi$
$577$	−0.557008	−	0.451057i	−0.557008	−	0.451057i	−0.866025	+	0.500000i	$0.833333\pi$
$578$	2.73063	−	1.21575i	2.73063	−	1.21575i
$579$		0			0
$580$	−1.86055	−	1.35177i	−1.86055	−	1.35177i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.278768	−	1.76007i	0.278768	−	1.76007i
$585$	−0.0929633	+	0.182451i	−0.0929633	+	0.182451i
$586$	−1.45106	+	1.17504i	−1.45106	+	1.17504i
$587$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$587$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.506809	+	1.32028i	0.506809	+	1.32028i
$593$	−0.889993	+	0.889993i	−0.889993	+	0.889993i	−0.994522	−	0.104528i	$-0.966667\pi$
$593$	−0.889993	+	0.889993i	−0.889993	+	0.889993i	0.104528	+	0.994522i	$0.466667\pi$
$594$		0			0
$595$		0			0
$596$	−1.17504	−	0.451057i	−1.17504	−	0.451057i
$597$		0			0
$598$		0			0
$599$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$599$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$600$		0			0
$601$	−0.379874	+	0.169131i	−0.379874	+	0.169131i	−0.587785	−	0.809017i	$-0.700000\pi$
$601$	−0.379874	+	0.169131i	−0.379874	+	0.169131i	0.207912	+	0.978148i	$0.433333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.78716	+	0.795697i	1.78716	+	0.795697i
$606$		0			0
$607$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$607$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$608$		0			0
$609$		0			0
$610$	−1.04707	−	0.604528i	−1.04707	−	0.604528i
$611$		0			0
$612$	1.41228	−	1.41228i	1.41228	−	1.41228i
$613$	0.185505	+	0.483257i	0.185505	+	0.483257i	0.994522	−	0.104528i	$-0.0333333\pi$
$613$	0.185505	+	0.483257i	0.185505	+	0.483257i	−0.809017	+	0.587785i	$0.800000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$617$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$618$		0			0
$619$		0			0		0.777146	−	0.629320i	$-0.216667\pi$
$619$		0			0		−0.777146	+	0.629320i	$0.783333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−3.36984	−	2.44833i	−3.36984	−	2.44833i
$626$	−1.27276	+	1.41355i	−1.27276	+	1.41355i
$627$		0			0
$628$	−0.846528	−	0.685505i	−0.846528	−	0.685505i
$629$	−2.76283	−	0.587257i	−2.76283	−	0.587257i
$630$		0			0
$631$		0			0		0.777146	−	0.629320i	$-0.216667\pi$
$631$		0			0		−0.777146	+	0.629320i	$0.783333\pi$
$632$		0			0
$633$		0			0
$634$	−0.235003	−	0.877042i	−0.235003	−	0.877042i
$635$		0			0
$636$		0			0
$637$	−0.0570084	−	0.0877853i	−0.0570084	−	0.0877853i
$638$		0			0
$639$		0			0
$640$	0.204489	+	1.94558i	0.204489	+	1.94558i
$641$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$641$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$642$		0			0
$643$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$643$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$	0.406737	−	0.913545i	0.406737	−	0.913545i
$649$		0			0
$650$	0.292274	+	0.0462916i	0.292274	+	0.0462916i
$651$		0			0
$652$		0			0
$653$	−1.55216	+	0.0813454i	−1.55216	+	0.0813454i	−0.809017	−	0.587785i	$-0.800000\pi$
$653$	−1.55216	+	0.0813454i	−1.55216	+	0.0813454i	−0.743145	+	0.669131i	$0.766667\pi$
$654$		0			0
$655$		0			0
$656$	1.28716	−	1.15897i	1.28716	−	1.15897i
$657$	1.66365	+	0.638616i	1.66365	+	0.638616i
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$	1.62019	+	1.05216i	1.62019	+	1.05216i	0.951057	+	0.309017i	$0.100000\pi$
$661$	1.62019	+	1.05216i	1.62019	+	1.05216i	0.669131	+	0.743145i	$0.266667\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.39680	+	0.221232i	−1.39680	+	0.221232i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.459289	−	0.413545i	0.459289	−	0.413545i	−0.406737	−	0.913545i	$-0.633333\pi$
$673$	0.459289	−	0.413545i	0.459289	−	0.413545i	0.866025	+	0.500000i	$0.166667\pi$
$674$	1.89169	+	0.198825i	1.89169	+	0.198825i
$675$		0			0
$676$	0.940637	−	0.305631i	0.940637	−	0.305631i
$677$	−0.112122	+	0.292088i	−0.112122	+	0.292088i	−0.978148	−	0.207912i	$-0.933333\pi$
$677$	−0.112122	+	0.292088i	−0.112122	+	0.292088i	0.866025	+	0.500000i	$0.166667\pi$
$678$		0			0
$679$		0			0
$680$	−3.48137	−	1.77384i	−3.48137	−	1.77384i
$681$		0			0
$682$		0			0
$683$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$683$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$684$		0			0
$685$	−3.52825	−	0.945393i	−3.52825	−	0.945393i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.00227792	−	0.0434654i	0.00227792	−	0.0434654i
$690$		0			0
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$	1.67504	+	0.0877853i	1.67504	+	0.0877853i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.541162	+	3.41676i	0.541162	+	3.41676i
$698$	−0.614648	+	1.89169i	−0.614648	+	1.89169i
$699$		0			0
$700$		0			0
$701$	0.692314	+	0.185505i	0.692314	+	0.185505i	0.587785	−	0.809017i	$-0.300000\pi$
$701$	0.692314	+	0.185505i	0.692314	+	0.185505i	0.104528	+	0.994522i	$0.466667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.325391	−	0.638616i	−0.325391	−	0.638616i
$707$		0			0
$708$		0			0
$709$	−0.846528	+	1.30354i	−0.846528	+	1.30354i	0.104528	+	0.994522i	$0.466667\pi$
$709$	−0.846528	+	1.30354i	−0.846528	+	1.30354i	−0.951057	+	0.309017i	$0.900000\pi$
$710$		0			0
$711$		0			0
$712$	−1.50133	+	0.402280i	−1.50133	+	0.402280i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	−1.94558	−	0.204489i	−1.94558	−	0.204489i
$721$		0			0
$722$	−1.00000			−1.00000
$723$		0			0
$724$	1.90211			1.90211
$725$	−2.87819	−	1.66172i	−2.87819	−	1.66172i
$726$		0			0
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$	0.809017	+	0.587785i	0.809017	+	0.587785i
$730$	0.182451	−	3.48137i	0.182451	−	3.48137i
$731$		0			0
$732$		0			0
$733$	0.181049	+	1.72256i	0.181049	+	1.72256i	0.587785	+	0.809017i	$0.300000\pi$
$733$	0.181049	+	1.72256i	0.181049	+	1.72256i	−0.406737	+	0.913545i	$0.633333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.866025	+	1.50000i	0.866025	+	1.50000i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	1.25602	+	2.46508i	1.25602	+	2.46508i
$741$		0			0
$742$		0			0
$743$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$743$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$744$		0			0
$745$	−2.37837	−	0.637283i	−2.37837	−	0.637283i
$746$	0.309017	+	1.95106i	0.309017	+	1.95106i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$751$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$752$		0			0
$753$		0			0
$754$	0.122881	+	0.00643990i	0.122881	+	0.00643990i
$755$		0			0
$756$		0			0
$757$	0.0932634	−	1.77957i	0.0932634	−	1.77957i	−0.406737	−	0.913545i	$-0.633333\pi$
$757$	0.0932634	−	1.77957i	0.0932634	−	1.77957i	0.500000	−	0.866025i	$-0.333333\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.90807	+	0.511265i	1.90807	+	0.511265i	0.994522	+	0.104528i	$0.0333333\pi$
$761$	1.90807	+	0.511265i	1.90807	+	0.511265i	0.913545	+	0.406737i	$0.133333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	2.45890	−	3.03649i	2.45890	−	3.03649i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.325391	−	0.847673i	0.325391	−	0.847673i	−0.669131	−	0.743145i	$-0.733333\pi$
$769$	0.325391	−	0.847673i	0.325391	−	0.847673i	0.994522	−	0.104528i	$-0.0333333\pi$
$770$		0			0
$771$		0			0
$772$	0.207912	+	0.0218524i	0.207912	+	0.0218524i
$773$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$773$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$774$		0			0
$775$		0			0
$776$	0.743145	+	0.669131i	0.743145	+	0.669131i
$777$		0			0
$778$	−1.30354	−	1.05558i	−1.30354	−	1.05558i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.587785	−	0.809017i	0.587785	−	0.809017i
$785$	−1.78716	−	1.16060i	−1.78716	−	1.16060i
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$	0.325760	−	1.21575i	0.325760	−	1.21575i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.0646021	−	0.00338565i	0.0646021	−	0.00338565i
$794$	1.65669	−	1.07587i	1.65669	−	1.07587i
$795$		0			0
$796$		0			0
$797$	−1.66365	+	0.638616i	−1.66365	+	0.638616i	−0.994522	−	0.104528i	$-0.966667\pi$
$797$	−1.66365	+	0.638616i	−1.66365	+	0.638616i	−0.669131	+	0.743145i	$0.733333\pi$
$798$		0			0
$799$		0			0
$800$	0.587785	+	2.76531i	0.587785	+	2.76531i
$801$	−0.0813454	−	1.55216i	−0.0813454	−	1.55216i
$802$	−0.478148	−	0.658114i	−0.478148	−	0.658114i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.325391	−	0.638616i	0.325391	−	0.638616i
$809$	0.170401	+	0.262394i	0.170401	+	0.262394i	0.913545	−	0.406737i	$-0.133333\pi$
$809$	0.170401	+	0.262394i	0.170401	+	0.262394i	−0.743145	+	0.669131i	$0.766667\pi$
$810$	0.604528	−	1.86055i	0.604528	−	1.86055i
$811$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$811$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.50133	+	1.21575i	1.50133	+	1.21575i
$819$		0			0
$820$	2.26728	−	2.51807i	2.26728	−	2.51807i
$821$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$821$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$822$		0			0
$823$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$823$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.777146	−	0.629320i	$-0.216667\pi$
$827$		0			0		−0.777146	+	0.629320i	$0.783333\pi$
$828$		0			0
$829$	0.251377	+	0.773659i	0.251377	+	0.773659i	0.994522	+	0.104528i	$0.0333333\pi$
$829$	0.251377	+	0.773659i	0.251377	+	0.773659i	−0.743145	+	0.669131i	$0.766667\pi$
$830$		0			0
$831$		0			0
$832$	−0.0658722	−	0.0813454i	−0.0658722	−	0.0813454i
$833$	0.715754	+	1.86460i	0.715754	+	1.86460i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$839$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$840$		0			0
$841$	−0.348943	−	0.155360i	−0.348943	−	0.155360i
$842$	1.35779	−	0.604528i	1.35779	−	0.604528i
$843$		0			0
$844$		0			0
$845$	1.76758	−	0.786979i	1.76758	−	0.786979i
$846$		0			0
$847$		0			0
$848$	0.395472	−	0.128496i	0.395472	−	0.128496i
$849$		0			0
$850$	−5.27140	−	2.02350i	−5.27140	−	2.02350i
$851$		0			0
$852$		0			0
$853$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$853$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.406737	+	0.0864545i	−0.406737	+	0.0864545i	−0.406737	−	0.913545i	$-0.633333\pi$
$857$	−0.406737	+	0.0864545i	−0.406737	+	0.0864545i			1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$859$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$863$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$864$		0			0
$865$	3.27688	−	0.171734i	3.27688	−	0.171734i
$866$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.705634	−	0.571411i	0.705634	−	0.571411i
$873$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.251377	+	0.773659i	−0.251377	+	0.773659i	0.743145	+	0.669131i	$0.233333\pi$
$877$	−0.251377	+	0.773659i	−0.251377	+	0.773659i	−0.994522	+	0.104528i	$0.966667\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.181049	−	1.72256i	−0.181049	−	1.72256i	−0.587785	−	0.809017i	$-0.700000\pi$
$881$	−0.181049	−	1.72256i	−0.181049	−	1.72256i	0.406737	−	0.913545i	$-0.366667\pi$
$882$	0.669131	+	0.743145i	0.669131	+	0.743145i
$883$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$883$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$884$	0.207912	−	0.0218524i	0.207912	−	0.0218524i
$885$		0			0
$886$		0			0
$887$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$887$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$888$		0			0
$889$		0			0
$890$	−2.83869	+	1.08967i	−2.83869	+	1.08967i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.483257	+	0.185505i	0.483257	+	0.185505i
$899$		0			0
$900$	−2.82709			−2.82709
$901$	−0.214951	+	0.802208i	−0.214951	+	0.802208i
$902$		0			0
$903$		0			0
$904$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$905$	3.70071	−	0.388960i	3.70071	−	0.388960i
$906$		0			0
$907$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$907$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$908$		0			0
$909$	0.557008	+	0.451057i	0.557008	+	0.451057i
$910$		0			0
$911$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$911$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$912$		0			0
$913$		0			0
$914$	1.20243	−	1.08268i	1.20243	−	1.08268i
$915$		0			0
$916$	−1.16913	+	1.60917i	−1.16913	+	1.60917i
$917$		0			0
$918$		0			0
$919$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$919$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$920$		0			0
$921$		0			0
$922$	−0.196895	+	0.243145i	−0.196895	+	0.243145i
$923$		0			0
$924$		0			0
$925$	2.17753	+	3.35310i	2.17753	+	3.35310i
$926$		0			0
$927$		0			0
$928$	0.363271	+	1.11803i	0.363271	+	1.11803i
$929$	−0.434128	+	0.281926i	−0.434128	+	0.281926i	−0.743145	−	0.669131i	$-0.766667\pi$
$929$	−0.434128	+	0.281926i	−0.434128	+	0.281926i	0.309017	+	0.951057i	$0.400000\pi$
$930$		0			0
$931$		0			0
$932$	−1.40126	+	0.809017i	−1.40126	+	0.809017i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.0932634	−	0.0475201i	0.0932634	−	0.0475201i
$937$	0.198825	+	0.0646021i	0.198825	+	0.0646021i	0.406737	−	0.913545i	$-0.366667\pi$
$937$	0.198825	+	0.0646021i	0.198825	+	0.0646021i	−0.207912	+	0.978148i	$0.566667\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.302208	+	1.90807i	0.302208	+	1.90807i	0.406737	+	0.913545i	$0.366667\pi$
$941$	0.302208	+	1.90807i	0.302208	+	1.90807i	−0.104528	+	0.994522i	$0.533333\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$947$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$948$		0			0
$949$	0.0932634	+	0.161537i	0.0932634	+	0.161537i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.877042	−	0.235003i	0.877042	−	0.235003i	0.207912	−	0.978148i	$-0.433333\pi$
$953$	0.877042	−	0.235003i	0.877042	−	0.235003i	0.669131	+	0.743145i	$0.266667\pi$
$954$	0.0434654	+	0.413545i	0.0434654	+	0.413545i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.994522	+	0.104528i	0.994522	+	0.104528i
$962$	−0.128196	−	0.0740142i	−0.128196	−	0.0740142i
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$965$	0.408977			0.408977
$966$		0			0
$967$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$967$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$	1.58268	+	1.14988i	1.58268	+	1.14988i
$971$		0			0		0.0523360	−	0.998630i	$-0.483333\pi$
$971$		0			0		−0.0523360	+	0.998630i	$0.516667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.251377	+	0.564602i	0.251377	+	0.564602i
$977$	−1.24314	−	1.53516i	−1.24314	−	1.53516i	−0.743145	−	0.669131i	$-0.766667\pi$
$977$	−1.24314	−	1.53516i	−1.24314	−	1.53516i	−0.500000	−	0.866025i	$-0.666667\pi$
$978$		0			0
$979$		0			0
$980$	0.978148	−	1.69420i	0.978148	−	1.69420i
$981$	0.412215	+	0.809017i	0.412215	+	0.809017i
$982$		0			0
$983$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$983$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$984$		0			0
$985$	0.385184	−	2.43196i	0.385184	−	2.43196i
$986$	−2.26792	−	0.607686i	−2.26792	−	0.607686i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$991$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.511265	−	0.0809764i	0.511265	−	0.0809764i	0.104528	−	0.994522i	$-0.466667\pi$
$997$	0.511265	−	0.0809764i	0.511265	−	0.0809764i	0.406737	+	0.913545i	$0.366667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	964.1.bh.a.491.1	yes	16
4.3	odd	2	CM	964.1.bh.a.491.1	yes	16
241.134	even	60	inner	964.1.bh.a.375.1	✓	16
964.375	odd	60	inner	964.1.bh.a.375.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
964.1.bh.a.375.1	✓	16	241.134	even	60	inner
964.1.bh.a.375.1	✓	16	964.375	odd	60	inner
964.1.bh.a.491.1	yes	16	1.1	even	1	trivial
964.1.bh.a.491.1	yes	16	4.3	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 964 = 2^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	964.bh (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.14988 + 1.58268i) q^{5} -1.00000i q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.14988 + 1.58268i) q^{5} -1.00000i q^{8} +(0.978148 + 0.207912i) q^{9} +(-0.204489 - 1.94558i) q^{10} +(0.0658722 + 0.0813454i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-0.906737 - 1.77957i) q^{17} +(-0.743145 - 0.669131i) q^{18} +(-0.795697 + 1.78716i) q^{20} +(-0.873619 + 2.68872i) q^{25} +(-0.0163743 - 0.103383i) q^{26} +(-0.244415 + 1.14988i) q^{29} +(0.866025 - 0.500000i) q^{32} +(-0.104528 + 1.99452i) q^{34} +(0.309017 + 0.951057i) q^{36} +(0.889993 - 1.09905i) q^{37} +(1.58268 - 1.14988i) q^{40} +(-1.64728 - 0.535233i) q^{41} +(0.795697 + 1.78716i) q^{45} +(-0.994522 - 0.104528i) q^{49} +(2.10094 - 1.89169i) q^{50} +(-0.0375111 + 0.0977196i) q^{52} +(-0.309017 - 0.278240i) q^{53} +(0.786610 - 0.873619i) q^{58} +(0.363271 - 0.500000i) q^{61} -1.00000 q^{64} +(-0.0529982 + 0.197792i) q^{65} +(1.08779 - 1.67504i) q^{68} +(0.207912 - 0.978148i) q^{72} +(1.76007 + 0.278768i) q^{73} +(-1.32028 + 0.506809i) q^{74} +(-1.94558 + 0.204489i) q^{80} +(0.913545 + 0.406737i) q^{81} +(1.15897 + 1.28716i) q^{82} +(1.77384 - 3.48137i) q^{85} +(-0.402280 - 1.50133i) q^{89} +(0.204489 - 1.94558i) q^{90} +(-0.669131 + 0.743145i) q^{97} +(0.809017 + 0.587785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 2 * q^9	\( 16 q + 8 q^{4} - 2 q^{9} + 2 q^{10} + 4 q^{13} - 8 q^{16} - 8 q^{17} - 2 q^{26} + 2 q^{34} - 4 q^{36} + 2 q^{37} + 4 q^{40} + 2 q^{52} + 4 q^{53} - 16 q^{64} - 18 q^{65} + 8 q^{68} + 4 q^{73} - 2 q^{74} + 2 q^{81} - 2 q^{85} - 4 q^{89} - 2 q^{90} - 2 q^{97} + 4 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^9 + 2 * q^10 + 4 * q^13 - 8 * q^16 - 8 * q^17 - 2 * q^26 + 2 * q^34 - 4 * q^36 + 2 * q^37 + 4 * q^40 + 2 * q^52 + 4 * q^53 - 16 * q^64 - 18 * q^65 + 8 * q^68 + 4 * q^73 - 2 * q^74 + 2 * q^81 - 2 * q^85 - 4 * q^89 - 2 * q^90 - 2 * q^97 + 4 * q^98

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