LMFDB - Embedded newform 3960.1.dh.b.2539.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3960,1,Mod(379,3960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3960.379"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3960, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 5, 4])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3960.dh (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.97629745003$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 440)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.23425600.1

Embedding invariants

Embedding label			2539.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	3960.2539
Dual form			3960.1.dh.b.379.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.30902 + 0.951057i) q^{7} +(0.809017 - 0.587785i) q^{8} +1.00000 q^{10} +(0.809017 + 0.587785i) q^{11} +(0.190983 - 0.587785i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.500000 + 0.363271i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-0.809017 + 0.587785i) q^{22} +1.61803 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.500000 + 0.363271i) q^{26} +(-0.500000 - 1.53884i) q^{28} -1.00000 q^{32} +(0.500000 - 1.53884i) q^{35} +(-0.500000 - 0.363271i) q^{37} +(-0.190983 - 0.587785i) q^{38} +(-0.809017 - 0.587785i) q^{40} +(-1.30902 + 0.951057i) q^{41} +(-0.309017 - 0.951057i) q^{44} +(-0.500000 + 1.53884i) q^{46} +(0.500000 - 0.363271i) q^{47} +(0.500000 + 1.53884i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{52} +(0.500000 - 1.53884i) q^{53} +(0.309017 - 0.951057i) q^{55} +1.61803 q^{56} +(0.500000 + 0.363271i) q^{59} +(0.309017 - 0.951057i) q^{64} -0.618034 q^{65} +(1.30902 + 0.951057i) q^{70} +(0.500000 - 0.363271i) q^{74} +0.618034 q^{76} +(0.500000 + 1.53884i) q^{77} +(0.809017 - 0.587785i) q^{80} +(-0.500000 - 1.53884i) q^{82} +1.00000 q^{88} +1.61803 q^{89} +(0.809017 - 0.587785i) q^{91} +(-1.30902 - 0.951057i) q^{92} +(0.190983 + 0.587785i) q^{94} +(0.500000 + 0.363271i) q^{95} -1.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} + q^{5} + 3 q^{7} + q^{8} + 4 q^{10} + q^{11} + 3 q^{13} - 3 q^{14} - q^{16} - 2 q^{19} + q^{20} - q^{22} + 2 q^{23} - q^{25} + 2 q^{26} - 2 q^{28} - 4 q^{32} + 2 q^{35} - 2 q^{37}+ \cdots - 2 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 + q^5 + 3 * q^7 + q^8 + 4 * q^10 + q^11 + 3 * q^13 - 3 * q^14 - q^16 - 2 * q^19 + q^20 - q^22 + 2 * q^23 - q^25 + 2 * q^26 - 2 * q^28 - 4 * q^32 + 2 * q^35 - 2 * q^37 - 3 * q^38 - q^40 - 3 * q^41 + q^44 - 2 * q^46 + 2 * q^47 + 2 * q^49 + q^50 - 2 * q^52 + 2 * q^53 - q^55 + 2 * q^56 + 2 * q^59 - q^64 + 2 * q^65 + 3 * q^70 + 2 * q^74 - 2 * q^76 + 2 * q^77 + q^80 - 2 * q^82 + 4 * q^88 + 2 * q^89 + q^91 - 3 * q^92 + 3 * q^94 + 2 * q^95 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3960\mathbb{Z}\right)^\times$.

$n$	$991$	$1981$	$2377$	$2521$	$3521$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$2$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$5$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$5$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$6$		0			0
$7$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$7$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$8$	0.809017	−	0.587785i	0.809017	−	0.587785i
$9$		0			0
$10$	1.00000			1.00000
$11$	0.809017	+	0.587785i	0.809017	+	0.587785i
$11$	0.809017	+	0.587785i	0.809017	+	0.587785i
$12$		0			0
$13$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$13$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$14$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$15$		0			0
$16$	0.309017	+	0.951057i	0.309017	+	0.951057i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$		0			0
$19$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$19$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$20$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$21$		0			0
$22$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$23$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$23$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$26$	0.500000	+	0.363271i	0.500000	+	0.363271i
$27$		0			0
$28$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$29$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$29$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$30$		0			0
$31$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$31$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$32$	−1.00000			−1.00000
$33$		0			0
$34$		0			0
$35$	0.500000	−	1.53884i	0.500000	−	1.53884i
$36$		0			0
$37$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$37$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$38$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$39$		0			0
$40$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$41$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$41$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$45$		0			0
$46$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$47$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$47$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$48$		0			0
$49$	0.500000	+	1.53884i	0.500000	+	1.53884i
$50$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$51$		0			0
$52$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$53$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$53$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$54$		0			0
$55$	0.309017	−	0.951057i	0.309017	−	0.951057i
$56$	1.61803			1.61803
$57$		0			0
$58$		0			0
$59$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$59$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$60$		0			0
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$		0			0
$64$	0.309017	−	0.951057i	0.309017	−	0.951057i
$65$	−0.618034			−0.618034
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$	1.30902	+	0.951057i	1.30902	+	0.951057i
$71$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$71$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$72$		0			0
$73$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$73$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$74$	0.500000	−	0.363271i	0.500000	−	0.363271i
$75$		0			0
$76$	0.618034			0.618034
$77$	0.500000	+	1.53884i	0.500000	+	1.53884i
$78$		0			0
$79$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$79$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$80$	0.809017	−	0.587785i	0.809017	−	0.587785i
$81$		0			0
$82$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$83$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$83$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.00000			1.00000
$89$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$89$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$90$		0			0
$91$	0.809017	−	0.587785i	0.809017	−	0.587785i
$92$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$93$		0			0
$94$	0.190983	+	0.587785i	0.190983	+	0.587785i
$95$	0.500000	+	0.363271i	0.500000	+	0.363271i
$96$		0			0
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$	−1.61803			−1.61803
$99$		0			0
$100$	1.00000			1.00000
$101$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$101$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$102$		0			0
$103$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$103$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$104$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$105$		0			0
$106$	1.30902	+	0.951057i	1.30902	+	0.951057i
$107$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$107$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$108$		0			0
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	0.809017	+	0.587785i	0.809017	+	0.587785i
$111$		0			0
$112$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$113$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$113$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$116$		0			0
$117$		0			0
$118$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$119$		0			0
$120$		0			0
$121$	0.309017	+	0.951057i	0.309017	+	0.951057i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.809017	+	0.587785i	0.809017	+	0.587785i
$126$		0			0
$127$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$127$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$128$	0.809017	+	0.587785i	0.809017	+	0.587785i
$129$		0			0
$130$	0.190983	−	0.587785i	0.190983	−	0.587785i
$131$	−2.00000			−2.00000			−1.00000			$\pi$
$131$	−2.00000			−2.00000			−1.00000			$\pi$
$132$		0			0
$133$	−1.00000			−1.00000
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$137$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$138$		0			0
$139$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$139$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$140$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$141$		0			0
$142$		0			0
$143$	0.500000	−	0.363271i	0.500000	−	0.363271i
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.190983	+	0.587785i	0.190983	+	0.587785i
$149$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$149$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$150$		0			0
$151$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$151$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$152$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$153$		0			0
$154$	−1.61803			−1.61803
$155$		0			0
$156$		0			0
$157$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$157$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$158$		0			0
$159$		0			0
$160$	0.309017	+	0.951057i	0.309017	+	0.951057i
$161$	2.11803	+	1.53884i	2.11803	+	1.53884i
$162$		0			0
$163$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$163$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$164$	1.61803			1.61803
$165$		0			0
$166$		0			0
$167$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$167$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$168$		0			0
$169$	0.500000	+	0.363271i	0.500000	+	0.363271i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$173$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$174$		0			0
$175$	−1.61803			−1.61803
$176$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$177$		0			0
$178$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$179$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$179$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$180$		0			0
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$	0.309017	+	0.951057i	0.309017	+	0.951057i
$183$		0			0
$184$	1.30902	−	0.951057i	1.30902	−	0.951057i
$185$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$186$		0			0
$187$		0			0
$188$	−0.618034			−0.618034
$189$		0			0
$190$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$		0			0
$193$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$193$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$194$		0			0
$195$		0			0
$196$	0.500000	−	1.53884i	0.500000	−	1.53884i
$197$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$197$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.30902	+	0.951057i	1.30902	+	0.951057i
$206$	0.500000	−	0.363271i	0.500000	−	0.363271i
$207$		0			0
$208$	0.618034			0.618034
$209$	−0.618034			−0.618034
$210$		0			0
$211$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$211$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$212$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$221$		0			0
$222$		0			0
$223$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$223$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$224$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$225$		0			0
$226$		0			0
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$		0			0
$229$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$229$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$230$	1.61803			1.61803
$231$		0			0
$232$		0			0
$233$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$233$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$234$		0			0
$235$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$236$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$237$		0			0
$238$		0			0
$239$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$239$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$240$		0			0
$241$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$241$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$242$	−1.00000			−1.00000
$243$		0			0
$244$		0			0
$245$	1.30902	−	0.951057i	1.30902	−	0.951057i
$246$		0			0
$247$	0.118034	+	0.363271i	0.118034	+	0.363271i
$248$		0			0
$249$		0			0
$250$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$251$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$251$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$252$		0			0
$253$	1.30902	+	0.951057i	1.30902	+	0.951057i
$254$	−0.618034			−0.618034
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$257$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$257$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$258$		0			0
$259$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$260$	0.500000	+	0.363271i	0.500000	+	0.363271i
$261$		0			0
$262$	0.618034	−	1.90211i	0.618034	−	1.90211i
$263$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$263$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$264$		0			0
$265$	−1.61803			−1.61803
$266$	0.309017	−	0.951057i	0.309017	−	0.951057i
$267$		0			0
$268$		0			0
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$271$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.00000			−1.00000
$276$		0			0
$277$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$277$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$278$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$279$		0			0
$280$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$281$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$281$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$282$		0			0
$283$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$283$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$284$		0			0
$285$		0			0
$286$	0.190983	+	0.587785i	0.190983	+	0.587785i
$287$	−2.61803			−2.61803
$288$		0			0
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$293$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$294$		0			0
$295$	0.190983	−	0.587785i	0.190983	−	0.587785i
$296$	−0.618034			−0.618034
$297$		0			0
$298$		0			0
$299$	0.309017	−	0.951057i	0.309017	−	0.951057i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	0.500000	−	1.53884i	0.500000	−	1.53884i
$309$		0			0
$310$		0			0
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$		0			0
$313$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$313$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$314$	0.500000	+	1.53884i	0.500000	+	1.53884i
$315$		0			0
$316$		0			0
$317$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$317$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	−1.00000			−1.00000
$321$		0			0
$322$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$323$		0			0
$324$		0			0
$325$	0.190983	+	0.587785i	0.190983	+	0.587785i
$326$		0			0
$327$		0			0
$328$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$329$	1.00000			1.00000
$330$		0			0
$331$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$331$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$332$		0			0
$333$		0			0
$334$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$335$		0			0
$336$		0			0
$337$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$337$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$338$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$344$		0			0
$345$		0			0
$346$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$347$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$347$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$348$		0			0
$349$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$349$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$350$	0.500000	−	1.53884i	0.500000	−	1.53884i
$351$		0			0
$352$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$357$		0			0
$358$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$359$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$359$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$360$		0			0
$361$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$362$		0			0
$363$		0			0
$364$	−1.00000			−1.00000
$365$		0			0
$366$		0			0
$367$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$367$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$368$	0.500000	+	1.53884i	0.500000	+	1.53884i
$369$		0			0
$370$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$371$	2.11803	−	1.53884i	2.11803	−	1.53884i
$372$		0			0
$373$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$373$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$374$		0			0
$375$		0			0
$376$	0.190983	−	0.587785i	0.190983	−	0.587785i
$377$		0			0
$378$		0			0
$379$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$379$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$380$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$381$		0			0
$382$		0			0
$383$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$383$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$384$		0			0
$385$	1.30902	−	0.951057i	1.30902	−	0.951057i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	1.30902	+	0.951057i	1.30902	+	0.951057i
$393$		0			0
$394$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$395$		0			0
$396$		0			0
$397$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$397$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$401$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$401$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$408$		0			0
$409$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$409$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$410$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$411$		0			0
$412$	0.190983	+	0.587785i	0.190983	+	0.587785i
$413$	0.309017	+	0.951057i	0.309017	+	0.951057i
$414$		0			0
$415$		0			0
$416$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$417$		0			0
$418$	0.190983	−	0.587785i	0.190983	−	0.587785i
$419$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$419$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$	1.61803	+	1.17557i	1.61803	+	1.17557i
$423$		0			0
$424$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$		0			0
$433$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$433$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$441$		0			0
$442$		0			0
$443$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$443$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$444$		0			0
$445$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$446$	0.500000	+	1.53884i	0.500000	+	1.53884i
$447$		0			0
$448$	1.30902	−	0.951057i	1.30902	−	0.951057i
$449$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$449$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$450$		0			0
$451$	−1.61803			−1.61803
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$456$		0			0
$457$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$457$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$		0			0
$460$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$463$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$467$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$468$		0			0
$469$		0			0
$470$	0.500000	−	0.363271i	0.500000	−	0.363271i
$471$		0			0
$472$	0.618034			0.618034
$473$		0			0
$474$		0			0
$475$	0.190983	−	0.587785i	0.190983	−	0.587785i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$479$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$480$		0			0
$481$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$482$	0.500000	−	1.53884i	0.500000	−	1.53884i
$483$		0			0
$484$	0.309017	−	0.951057i	0.309017	−	0.951057i
$485$		0			0
$486$		0			0
$487$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$487$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$488$		0			0
$489$		0			0
$490$	0.500000	+	1.53884i	0.500000	+	1.53884i
$491$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$491$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$	−0.381966			−0.381966
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$499$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$500$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$501$		0			0
$502$	1.30902	+	0.951057i	1.30902	+	0.951057i
$503$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$503$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$504$		0			0
$505$		0			0
$506$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$507$		0			0
$508$	0.190983	−	0.587785i	0.190983	−	0.587785i
$509$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$509$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$513$		0			0
$514$		0			0
$515$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$516$		0			0
$517$	0.618034			0.618034
$518$	1.00000			1.00000
$519$		0			0
$520$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$521$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$521$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$522$		0			0
$523$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$523$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$524$	1.61803	+	1.17557i	1.61803	+	1.17557i
$525$		0			0
$526$	0.190983	−	0.587785i	0.190983	−	0.587785i
$527$		0			0
$528$		0			0
$529$	1.61803			1.61803
$530$	0.500000	−	1.53884i	0.500000	−	1.53884i
$531$		0			0
$532$	0.809017	+	0.587785i	0.809017	+	0.587785i
$533$	0.309017	+	0.951057i	0.309017	+	0.951057i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$540$		0			0
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$547$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$548$		0			0
$549$		0			0
$550$	0.309017	−	0.951057i	0.309017	−	0.951057i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$555$		0			0
$556$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$557$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$557$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$558$		0			0
$559$		0			0
$560$	1.61803			1.61803
$561$		0			0
$562$	2.00000			2.00000
$563$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$563$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$569$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$570$		0			0
$571$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$571$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$572$	−0.618034			−0.618034
$573$		0			0
$574$	0.809017	−	2.48990i	0.809017	−	2.48990i
$575$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$576$		0			0
$577$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$577$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$578$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.30902	−	0.951057i	1.30902	−	0.951057i
$584$		0			0
$585$		0			0
$586$	1.30902	−	0.951057i	1.30902	−	0.951057i
$587$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$587$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$588$		0			0
$589$		0			0
$590$	0.500000	+	0.363271i	0.500000	+	0.363271i
$591$		0			0
$592$	0.190983	−	0.587785i	0.190983	−	0.587785i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.809017	+	0.587785i	0.809017	+	0.587785i
$599$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$599$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$600$		0			0
$601$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$601$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.809017	−	0.587785i	0.809017	−	0.587785i
$606$		0			0
$607$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$607$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$608$	0.500000	−	0.363271i	0.500000	−	0.363271i
$609$		0			0
$610$		0			0
$611$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$612$		0			0
$613$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$613$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$614$		0			0
$615$		0			0
$616$	1.30902	+	0.951057i	1.30902	+	0.951057i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$619$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.11803	+	1.53884i	2.11803	+	1.53884i
$624$		0			0
$625$	0.309017	−	0.951057i	0.309017	−	0.951057i
$626$		0			0
$627$		0			0
$628$	−1.61803			−1.61803
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$		0			0
$633$		0			0
$634$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$635$	0.500000	−	0.363271i	0.500000	−	0.363271i
$636$		0			0
$637$	1.00000			1.00000
$638$		0			0
$639$		0			0
$640$	0.309017	−	0.951057i	0.309017	−	0.951057i
$641$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$642$		0			0
$643$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$643$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$644$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$645$		0			0
$646$		0			0
$647$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$647$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$648$		0			0
$649$	0.190983	+	0.587785i	0.190983	+	0.587785i
$650$	−0.618034			−0.618034
$651$		0			0
$652$		0			0
$653$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$653$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$654$		0			0
$655$	0.618034	+	1.90211i	0.618034	+	1.90211i
$656$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$657$		0			0
$658$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$659$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$659$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$660$		0			0
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$663$		0			0
$664$		0			0
$665$	0.309017	+	0.951057i	0.309017	+	0.951057i
$666$		0			0
$667$		0			0
$668$	0.500000	−	0.363271i	0.500000	−	0.363271i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$673$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$674$		0			0
$675$		0			0
$676$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$677$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$677$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$687$		0			0
$688$		0			0
$689$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$690$		0			0
$691$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$691$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$692$	1.61803			1.61803
$693$		0			0
$694$		0			0
$695$	0.500000	−	1.53884i	0.500000	−	1.53884i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	1.30902	+	0.951057i	1.30902	+	0.951057i
$701$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$701$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$702$		0			0
$703$	0.381966			0.381966
$704$	0.809017	−	0.587785i	0.809017	−	0.587785i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$709$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$		0			0
$712$	1.30902	−	0.951057i	1.30902	−	0.951057i
$713$		0			0
$714$		0			0
$715$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$716$	1.61803			1.61803
$717$		0			0
$718$		0			0
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		0			0
$721$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$722$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$727$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$728$	0.309017	−	0.951057i	0.309017	−	0.951057i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$733$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$734$	1.61803	−	1.17557i	1.61803	−	1.17557i
$735$		0			0
$736$	−1.61803			−1.61803
$737$		0			0
$738$		0			0
$739$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$739$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$740$	0.500000	−	0.363271i	0.500000	−	0.363271i
$741$		0			0
$742$	0.809017	+	2.48990i	0.809017	+	2.48990i
$743$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$743$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$744$		0			0
$745$		0			0
$746$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$751$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$752$	0.500000	+	0.363271i	0.500000	+	0.363271i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$757$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$758$	1.61803			1.61803
$759$		0			0
$760$	0.618034			0.618034
$761$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$761$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.30902	+	0.951057i	1.30902	+	0.951057i
$767$	0.309017	−	0.224514i	0.309017	−	0.224514i
$768$		0			0
$769$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$769$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$770$	0.500000	+	1.53884i	0.500000	+	1.53884i
$771$		0			0
$772$		0			0
$773$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$773$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.309017	−	0.951057i	0.309017	−	0.951057i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$785$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$786$		0			0
$787$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$787$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$788$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.500000	−	1.53884i	0.500000	−	1.53884i
$795$		0			0
$796$		0			0
$797$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$797$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	0.809017	−	0.587785i	0.809017	−	0.587785i
$801$		0			0
$802$	0.618034			0.618034
$803$		0			0
$804$		0			0
$805$	0.809017	−	2.48990i	0.809017	−	2.48990i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$809$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$810$		0			0
$811$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$811$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$812$		0			0
$813$		0			0
$814$	0.618034			0.618034
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.500000	+	0.363271i	0.500000	+	0.363271i
$819$		0			0
$820$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$821$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$821$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$822$		0			0
$823$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$823$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$824$	−0.618034			−0.618034
$825$		0			0
$826$	−1.00000			−1.00000
$827$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$827$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$828$		0			0
$829$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$829$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$830$		0			0
$831$		0			0
$832$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$833$		0			0
$834$		0			0
$835$	0.618034			0.618034
$836$	0.500000	+	0.363271i	0.500000	+	0.363271i
$837$		0			0
$838$	0.190983	−	0.587785i	0.190983	−	0.587785i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$		0			0
$841$	0.309017	+	0.951057i	0.309017	+	0.951057i
$842$		0			0
$843$		0			0
$844$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$845$	0.190983	−	0.587785i	0.190983	−	0.587785i
$846$		0			0
$847$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$848$	1.61803			1.61803
$849$		0			0
$850$		0			0
$851$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$852$		0			0
$853$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$853$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$859$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$863$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$864$		0			0
$865$	1.30902	+	0.951057i	1.30902	+	0.951057i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$875$	0.500000	+	1.53884i	0.500000	+	1.53884i
$876$		0			0
$877$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$877$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$878$		0			0
$879$		0			0
$880$	1.00000			1.00000
$881$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$881$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$882$		0			0
$883$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$883$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$887$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$888$		0			0
$889$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$890$	1.61803			1.61803
$891$		0			0
$892$	−1.61803			−1.61803
$893$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$894$		0			0
$895$	1.30902	+	0.951057i	1.30902	+	0.951057i
$896$	0.500000	+	1.53884i	0.500000	+	1.53884i
$897$		0			0
$898$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	0.500000	−	1.53884i	0.500000	−	1.53884i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$907$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$908$		0			0
$909$		0			0
$910$	0.809017	−	0.587785i	0.809017	−	0.587785i
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.61803	−	1.90211i	−2.61803	−	1.90211i
$918$		0			0
$919$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$919$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$920$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.618034			0.618034
$926$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$927$		0			0
$928$		0			0
$929$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$929$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$937$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$938$		0			0
$939$		0			0
$940$	0.190983	+	0.587785i	0.190983	+	0.587785i
$941$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$941$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$942$		0			0
$943$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$944$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$		0			0
$950$	0.500000	+	0.363271i	0.500000	+	0.363271i
$951$		0			0
$952$		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			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$962$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$963$		0			0
$964$	1.30902	+	0.951057i	1.30902	+	0.951057i
$965$		0			0
$966$		0			0
$967$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$967$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$968$	0.809017	+	0.587785i	0.809017	+	0.587785i
$969$		0			0
$970$		0			0
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$972$		0			0
$973$	0.809017	+	2.48990i	0.809017	+	2.48990i
$974$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$975$		0			0
$976$		0			0
$977$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$977$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$978$		0			0
$979$	1.30902	+	0.951057i	1.30902	+	0.951057i
$980$	−1.61803			−1.61803
$981$		0			0
$982$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$983$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$983$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$984$		0			0
$985$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$986$		0			0
$987$		0			0
$988$	0.118034	−	0.363271i	0.118034	−	0.363271i
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$997$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$998$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3960.1.dh.b.2539.1		4
3.2	odd	2		440.1.bh.a.339.1	✓	4
5.4	even	2		3960.1.dh.a.2539.1		4
8.3	odd	2		3960.1.dh.a.2539.1		4
11.5	even	5	inner	3960.1.dh.b.379.1		4
12.11	even	2		1760.1.cn.a.559.1		4
15.2	even	4		2200.1.cl.c.251.2		8
15.8	even	4		2200.1.cl.c.251.1		8
15.14	odd	2		440.1.bh.b.339.1	yes	4
24.5	odd	2		1760.1.cn.b.559.1		4
24.11	even	2		440.1.bh.b.339.1	yes	4
33.5	odd	10		440.1.bh.a.379.1	yes	4
40.19	odd	2	CM	3960.1.dh.b.2539.1		4
55.49	even	10		3960.1.dh.a.379.1		4
60.59	even	2		1760.1.cn.b.559.1		4
88.27	odd	10		3960.1.dh.a.379.1		4
120.29	odd	2		1760.1.cn.a.559.1		4
120.59	even	2		440.1.bh.a.339.1	✓	4
120.83	odd	4		2200.1.cl.c.251.2		8
120.107	odd	4		2200.1.cl.c.251.1		8
132.71	even	10		1760.1.cn.a.1039.1		4
165.38	even	20		2200.1.cl.c.2051.2		8
165.104	odd	10		440.1.bh.b.379.1	yes	4
165.137	even	20		2200.1.cl.c.2051.1		8
264.5	odd	10		1760.1.cn.b.1039.1		4
264.203	even	10		440.1.bh.b.379.1	yes	4
440.379	odd	10	inner	3960.1.dh.b.379.1		4
660.599	even	10		1760.1.cn.b.1039.1		4
1320.203	odd	20		2200.1.cl.c.2051.1		8
1320.269	odd	10		1760.1.cn.a.1039.1		4
1320.467	odd	20		2200.1.cl.c.2051.2		8
1320.1259	even	10		440.1.bh.a.379.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.1.bh.a.339.1	✓	4	3.2	odd	2
440.1.bh.a.339.1	✓	4	120.59	even	2
440.1.bh.a.379.1	yes	4	33.5	odd	10
440.1.bh.a.379.1	yes	4	1320.1259	even	10
440.1.bh.b.339.1	yes	4	15.14	odd	2
440.1.bh.b.339.1	yes	4	24.11	even	2
440.1.bh.b.379.1	yes	4	165.104	odd	10
440.1.bh.b.379.1	yes	4	264.203	even	10
1760.1.cn.a.559.1		4	12.11	even	2
1760.1.cn.a.559.1		4	120.29	odd	2
1760.1.cn.a.1039.1		4	132.71	even	10
1760.1.cn.a.1039.1		4	1320.269	odd	10
1760.1.cn.b.559.1		4	24.5	odd	2
1760.1.cn.b.559.1		4	60.59	even	2
1760.1.cn.b.1039.1		4	264.5	odd	10
1760.1.cn.b.1039.1		4	660.599	even	10
2200.1.cl.c.251.1		8	15.8	even	4
2200.1.cl.c.251.1		8	120.107	odd	4
2200.1.cl.c.251.2		8	15.2	even	4
2200.1.cl.c.251.2		8	120.83	odd	4
2200.1.cl.c.2051.1		8	165.137	even	20
2200.1.cl.c.2051.1		8	1320.203	odd	20
2200.1.cl.c.2051.2		8	165.38	even	20
2200.1.cl.c.2051.2		8	1320.467	odd	20
3960.1.dh.a.379.1		4	55.49	even	10
3960.1.dh.a.379.1		4	88.27	odd	10
3960.1.dh.a.2539.1		4	5.4	even	2
3960.1.dh.a.2539.1		4	8.3	odd	2
3960.1.dh.b.379.1		4	11.5	even	5	inner
3960.1.dh.b.379.1		4	440.379	odd	10	inner
3960.1.dh.b.2539.1		4	1.1	even	1	trivial
3960.1.dh.b.2539.1		4	40.19	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3960.dh (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.30902 + 0.951057i) q^{7} +(0.809017 - 0.587785i) q^{8} +1.00000 q^{10} +(0.809017 + 0.587785i) q^{11} +(0.190983 - 0.587785i) q^{13} +(-1.30902 + 0.951057i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-0.500000 + 0.363271i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(-0.809017 + 0.587785i) q^{22} +1.61803 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.500000 + 0.363271i) q^{26} +(-0.500000 - 1.53884i) q^{28} -1.00000 q^{32} +(0.500000 - 1.53884i) q^{35} +(-0.500000 - 0.363271i) q^{37} +(-0.190983 - 0.587785i) q^{38} +(-0.809017 - 0.587785i) q^{40} +(-1.30902 + 0.951057i) q^{41} +(-0.309017 - 0.951057i) q^{44} +(-0.500000 + 1.53884i) q^{46} +(0.500000 - 0.363271i) q^{47} +(0.500000 + 1.53884i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{52} +(0.500000 - 1.53884i) q^{53} +(0.309017 - 0.951057i) q^{55} +1.61803 q^{56} +(0.500000 + 0.363271i) q^{59} +(0.309017 - 0.951057i) q^{64} -0.618034 q^{65} +(1.30902 + 0.951057i) q^{70} +(0.500000 - 0.363271i) q^{74} +0.618034 q^{76} +(0.500000 + 1.53884i) q^{77} +(0.809017 - 0.587785i) q^{80} +(-0.500000 - 1.53884i) q^{82} +1.00000 q^{88} +1.61803 q^{89} +(0.809017 - 0.587785i) q^{91} +(-1.30902 - 0.951057i) q^{92} +(0.190983 + 0.587785i) q^{94} +(0.500000 + 0.363271i) q^{95} -1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} + q^{5} + 3 q^{7} + q^{8} + 4 q^{10} + q^{11} + 3 q^{13} - 3 q^{14} - q^{16} - 2 q^{19} + q^{20} - q^{22} + 2 q^{23} - q^{25} + 2 q^{26} - 2 q^{28} - 4 q^{32} + 2 q^{35} - 2 q^{37}+ \cdots - 2 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 + q^5 + 3 * q^7 + q^8 + 4 * q^10 + q^11 + 3 * q^13 - 3 * q^14 - q^16 - 2 * q^19 + q^20 - q^22 + 2 * q^23 - q^25 + 2 * q^26 - 2 * q^28 - 4 * q^32 + 2 * q^35 - 2 * q^37 - 3 * q^38 - q^40 - 3 * q^41 + q^44 - 2 * q^46 + 2 * q^47 + 2 * q^49 + q^50 - 2 * q^52 + 2 * q^53 - q^55 + 2 * q^56 + 2 * q^59 - q^64 + 2 * q^65 + 3 * q^70 + 2 * q^74 - 2 * q^76 + 2 * q^77 + q^80 - 2 * q^82 + 4 * q^88 + 2 * q^89 + q^91 - 3 * q^92 + 3 * q^94 + 2 * q^95 - 2 * q^98

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