LMFDB - Embedded newform 3528.1.cg.d.2059.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3528,1,Mod(2059,3528)] 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("3528.2059"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3528, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4, 0])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3528.cg (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.76070136457$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 504)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.254016.3

Embedding invariants

Embedding label			2059.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3528.2059
Dual form			3528.1.cg.d.3235.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{17} +(-0.866025 + 0.500000i) q^{18} +1.00000 q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.866025 - 0.500000i) q^{22} +(-0.866025 + 0.500000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.866025 + 0.500000i) q^{32} +1.00000 q^{33} +(-0.866025 - 0.500000i) q^{34} -1.00000 q^{36} -1.00000i q^{37} +(0.866025 + 0.500000i) q^{38} +(-0.866025 - 0.500000i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} -1.00000i q^{45} -1.00000 q^{46} -1.00000 q^{48} +(-0.500000 - 0.866025i) q^{51} +(-0.866025 - 0.500000i) q^{52} +1.00000i q^{53} +(-0.866025 - 0.500000i) q^{54} +1.00000i q^{55} +(0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} -1.00000i q^{60} -1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.866025 + 0.500000i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.866025 - 0.500000i) q^{69} +(-0.866025 - 0.500000i) q^{72} +1.00000 q^{73} +(0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-0.500000 - 0.866025i) q^{78} +(1.73205 + 1.00000i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +1.00000i q^{82} +(0.500000 - 0.866025i) q^{83} +(0.866025 - 0.500000i) q^{85} +(0.866025 - 0.500000i) q^{86} +1.00000i q^{87} +(0.866025 + 0.500000i) q^{88} +1.00000 q^{89} +(0.500000 - 0.866025i) q^{90} +(-0.866025 - 0.500000i) q^{92} +(-0.866025 + 0.500000i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{16} - 4 q^{17} + 4 q^{19} - 4 q^{26} - 4 q^{27} - 2 q^{30} + 4 q^{33} - 4 q^{36} - 2 q^{40} + 2 q^{41} + 2 q^{43} + 4 q^{44} - 4 q^{46}+ \cdots + 2 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^16 - 4 * q^17 + 4 * q^19 - 4 * q^26 - 4 * q^27 - 2 * q^30 + 4 * q^33 - 4 * q^36 - 2 * q^40 + 2 * q^41 + 2 * q^43 + 4 * q^44 - 4 * q^46 - 4 * q^48 - 2 * q^51 + 2 * q^57 + 2 * q^58 - 4 * q^64 + 2 * q^65 - 2 * q^68 + 4 * q^73 + 2 * q^74 + 2 * q^76 - 2 * q^78 - 2 * q^81 + 2 * q^83 + 4 * q^89 + 2 * q^90 - 2 * q^97 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$1765$	$2647$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.866025	+	0.500000i
$2$	0.866025	+	0.500000i	0.866025	+	0.500000i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$4$	0.500000	+	0.866025i	0.500000	+	0.866025i
$5$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$5$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$			1.00000i			1.00000i
$7$		0			0
$7$		0			0
$8$			1.00000i			1.00000i
$9$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$10$	−1.00000			−1.00000
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$12$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$13$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$13$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$14$		0			0
$15$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$18$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$19$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$19$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$20$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$21$		0			0
$22$	0.866025	−	0.500000i	0.866025	−	0.500000i
$23$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$23$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$24$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$25$		0			0
$26$	−1.00000			−1.00000
$27$	−1.00000			−1.00000
$28$		0			0
$29$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$29$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$30$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$33$	1.00000			1.00000
$34$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$35$		0			0
$36$	−1.00000			−1.00000
$37$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$37$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$38$	0.866025	+	0.500000i	0.866025	+	0.500000i
$39$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$40$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$41$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$41$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$42$		0			0
$43$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$43$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$44$	1.00000			1.00000
$45$		−	1.00000i		−	1.00000i
$46$	−1.00000			−1.00000
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−1.00000			−1.00000
$49$		0			0
$50$		0			0
$51$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$52$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$53$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$53$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$54$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$55$			1.00000i			1.00000i
$56$		0			0
$57$	0.500000	+	0.866025i	0.500000	+	0.866025i
$58$	0.500000	+	0.866025i	0.500000	+	0.866025i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		−	1.00000i		−	1.00000i
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−1.00000
$65$	0.500000	−	0.866025i	0.500000	−	0.866025i
$66$	0.866025	+	0.500000i	0.866025	+	0.500000i
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$69$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$73$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$73$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$74$	0.500000	−	0.866025i	0.500000	−	0.866025i
$75$		0			0
$76$	0.500000	+	0.866025i	0.500000	+	0.866025i
$77$		0			0
$78$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$79$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$79$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$80$		−	1.00000i		−	1.00000i
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$			1.00000i			1.00000i
$83$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$84$		0			0
$85$	0.866025	−	0.500000i	0.866025	−	0.500000i
$86$	0.866025	−	0.500000i	0.866025	−	0.500000i
$87$			1.00000i			1.00000i
$88$	0.866025	+	0.500000i	0.866025	+	0.500000i
$89$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$89$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$90$	0.500000	−	0.866025i	0.500000	−	0.866025i
$91$		0			0
$92$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$93$		0			0
$94$		0			0
$95$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$96$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$97$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$97$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$98$		0			0
$99$	0.500000	+	0.866025i	0.500000	+	0.866025i
$100$		0			0
$101$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$101$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$102$		−	1.00000i		−	1.00000i
$103$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$103$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$104$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$105$		0			0
$106$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$107$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$107$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$108$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$109$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$109$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$110$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$111$	0.866025	−	0.500000i	0.866025	−	0.500000i
$112$		0			0
$113$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$113$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$114$			1.00000i			1.00000i
$115$	0.500000	−	0.866025i	0.500000	−	0.866025i
$116$			1.00000i			1.00000i
$117$		−	1.00000i		−	1.00000i
$118$		0			0
$119$		0			0
$120$	0.500000	−	0.866025i	0.500000	−	0.866025i
$121$		0			0
$122$		0			0
$123$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$124$		0			0
$125$		−	1.00000i		−	1.00000i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$129$	1.00000			1.00000
$130$	0.866025	−	0.500000i	0.866025	−	0.500000i
$131$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$131$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$132$	0.500000	+	0.866025i	0.500000	+	0.866025i
$133$		0			0
$134$		0			0
$135$	0.866025	−	0.500000i	0.866025	−	0.500000i
$136$		−	1.00000i		−	1.00000i
$137$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$137$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$138$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			1.00000i			1.00000i
$144$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$145$	−1.00000			−1.00000
$146$	0.866025	+	0.500000i	0.866025	+	0.500000i
$147$		0			0
$148$	0.866025	−	0.500000i	0.866025	−	0.500000i
$149$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$149$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$151$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$152$			1.00000i			1.00000i
$153$	0.500000	−	0.866025i	0.500000	−	0.866025i
$154$		0			0
$155$		0			0
$156$		−	1.00000i		−	1.00000i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	1.00000	+	1.73205i	1.00000	+	1.73205i
$159$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$160$	0.500000	−	0.866025i	0.500000	−	0.866025i
$161$		0			0
$162$		−	1.00000i		−	1.00000i
$163$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$163$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$164$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$165$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$166$	0.866025	−	0.500000i	0.866025	−	0.500000i
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$168$		0			0
$169$		0			0
$170$	1.00000			1.00000
$171$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$172$	1.00000			1.00000
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$175$		0			0
$176$	0.500000	+	0.866025i	0.500000	+	0.866025i
$177$		0			0
$178$	0.866025	+	0.500000i	0.866025	+	0.500000i
$179$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$179$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$180$	0.866025	−	0.500000i	0.866025	−	0.500000i
$181$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$181$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$182$		0			0
$183$		0			0
$184$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$185$	0.500000	+	0.866025i	0.500000	+	0.866025i
$186$		0			0
$187$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$188$		0			0
$189$		0			0
$190$	−1.00000			−1.00000
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$195$	1.00000			1.00000
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$			1.00000i			1.00000i
$199$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$199$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$		0			0
$202$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$203$		0			0
$204$	0.500000	−	0.866025i	0.500000	−	0.866025i
$205$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$206$	1.00000			1.00000
$207$		−	1.00000i		−	1.00000i
$208$		−	1.00000i		−	1.00000i
$209$	0.500000	−	0.866025i	0.500000	−	0.866025i
$210$		0			0
$211$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$211$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$212$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$213$		0			0
$214$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$215$			1.00000i			1.00000i
$216$		−	1.00000i		−	1.00000i
$217$		0			0
$218$	0.500000	−	0.866025i	0.500000	−	0.866025i
$219$	0.500000	+	0.866025i	0.500000	+	0.866025i
$220$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$221$	0.866025	−	0.500000i	0.866025	−	0.500000i
$222$	1.00000			1.00000
$223$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$223$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$224$		0			0
$225$		0			0
$226$		−	1.00000i		−	1.00000i
$227$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$227$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$228$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$229$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$229$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$230$	0.866025	−	0.500000i	0.866025	−	0.500000i
$231$		0			0
$232$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$233$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$233$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$234$	0.500000	−	0.866025i	0.500000	−	0.866025i
$235$		0			0
$236$		0			0
$237$			2.00000i			2.00000i
$238$		0			0
$239$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$239$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$240$	0.866025	−	0.500000i	0.866025	−	0.500000i
$241$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$241$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$242$		0			0
$243$	0.500000	−	0.866025i	0.500000	−	0.866025i
$244$		0			0
$245$		0			0
$246$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$247$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$248$		0			0
$249$	1.00000			1.00000
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$			1.00000i			1.00000i
$254$		0			0
$255$	0.866025	+	0.500000i	0.866025	+	0.500000i
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$258$	0.866025	+	0.500000i	0.866025	+	0.500000i
$259$		0			0
$260$	1.00000			1.00000
$261$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$262$			1.00000i			1.00000i
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$			1.00000i			1.00000i
$265$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$266$		0			0
$267$	0.500000	+	0.866025i	0.500000	+	0.866025i
$268$		0			0
$269$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$269$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$270$	1.00000			1.00000
$271$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$271$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$272$	0.500000	−	0.866025i	0.500000	−	0.866025i
$273$		0			0
$274$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$275$		0			0
$276$		−	1.00000i		−	1.00000i
$277$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$277$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$278$			1.00000i			1.00000i
$279$		0			0
$280$		0			0
$281$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$281$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$282$		0			0
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$286$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$287$		0			0
$288$		−	1.00000i		−	1.00000i
$289$		0			0
$290$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$291$	−1.00000			−1.00000
$292$	0.500000	+	0.866025i	0.500000	+	0.866025i
$293$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$293$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$		0			0
$296$	1.00000			1.00000
$297$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$298$	1.00000			1.00000
$299$	0.500000	−	0.866025i	0.500000	−	0.866025i
$300$		0			0
$301$		0			0
$302$	0.500000	+	0.866025i	0.500000	+	0.866025i
$303$		−	1.00000i		−	1.00000i
$304$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$305$		0			0
$306$	0.866025	−	0.500000i	0.866025	−	0.500000i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	0.866025	+	0.500000i	0.866025	+	0.500000i
$310$		0			0
$311$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$311$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$312$	0.500000	−	0.866025i	0.500000	−	0.866025i
$313$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$313$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$314$		0			0
$315$		0			0
$316$			2.00000i			2.00000i
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$	−1.00000			−1.00000
$319$	0.866025	−	0.500000i	0.866025	−	0.500000i
$320$	0.866025	−	0.500000i	0.866025	−	0.500000i
$321$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$322$		0			0
$323$	−1.00000			−1.00000
$324$	0.500000	−	0.866025i	0.500000	−	0.866025i
$325$		0			0
$326$	0.866025	+	0.500000i	0.866025	+	0.500000i
$327$	0.866025	−	0.500000i	0.866025	−	0.500000i
$328$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$329$		0			0
$330$	−1.00000			−1.00000
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$	1.00000			1.00000
$333$	0.866025	+	0.500000i	0.866025	+	0.500000i
$334$	−1.00000			−1.00000
$335$		0			0
$336$		0			0
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$338$		0			0
$339$	0.500000	−	0.866025i	0.500000	−	0.866025i
$340$	0.866025	+	0.500000i	0.866025	+	0.500000i
$341$		0			0
$342$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$343$		0			0
$344$	0.866025	+	0.500000i	0.866025	+	0.500000i
$345$	1.00000			1.00000
$346$		0			0
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$349$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$349$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$350$		0			0
$351$	0.866025	−	0.500000i	0.866025	−	0.500000i
$352$			1.00000i			1.00000i
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$354$		0			0
$355$		0			0
$356$	0.500000	+	0.866025i	0.500000	+	0.866025i
$357$		0			0
$358$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$359$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$359$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$360$	1.00000			1.00000
$361$		0			0
$362$	1.00000	−	1.73205i	1.00000	−	1.73205i
$363$		0			0
$364$		0			0
$365$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$366$		0			0
$367$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$367$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$368$		−	1.00000i		−	1.00000i
$369$	−1.00000			−1.00000
$370$			1.00000i			1.00000i
$371$		0			0
$372$		0			0
$373$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$373$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$374$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$375$	0.866025	−	0.500000i	0.866025	−	0.500000i
$376$		0			0
$377$	−1.00000			−1.00000
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$381$		0			0
$382$		0			0
$383$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$383$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$384$		−	1.00000i		−	1.00000i
$385$		0			0
$386$		0			0
$387$	0.500000	+	0.866025i	0.500000	+	0.866025i
$388$	−1.00000			−1.00000
$389$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$389$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$390$	0.866025	+	0.500000i	0.866025	+	0.500000i
$391$	0.866025	−	0.500000i	0.866025	−	0.500000i
$392$		0			0
$393$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$394$		0			0
$395$	−2.00000			−2.00000
$396$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$397$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$397$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$398$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$399$		0			0
$400$		0			0
$401$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$401$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$		−	1.00000i		−	1.00000i
$405$	0.866025	+	0.500000i	0.866025	+	0.500000i
$406$		0			0
$407$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$408$	0.866025	−	0.500000i	0.866025	−	0.500000i
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$411$	−1.00000			−1.00000
$412$	0.866025	+	0.500000i	0.866025	+	0.500000i
$413$		0			0
$414$	0.500000	−	0.866025i	0.500000	−	0.866025i
$415$			1.00000i			1.00000i
$416$	0.500000	−	0.866025i	0.500000	−	0.866025i
$417$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$418$	0.866025	−	0.500000i	0.866025	−	0.500000i
$419$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$419$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$420$		0			0
$421$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$421$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$422$			1.00000i			1.00000i
$423$		0			0
$424$	−1.00000			−1.00000
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$429$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$430$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$431$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$431$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$436$	0.866025	−	0.500000i	0.866025	−	0.500000i
$437$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$438$			1.00000i			1.00000i
$439$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$439$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$440$	−1.00000			−1.00000
$441$		0			0
$442$	1.00000			1.00000
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$	0.866025	+	0.500000i	0.866025	+	0.500000i
$445$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$446$	0.500000	+	0.866025i	0.500000	+	0.866025i
$447$	0.866025	+	0.500000i	0.866025	+	0.500000i
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	1.00000			1.00000
$452$	0.500000	−	0.866025i	0.500000	−	0.866025i
$453$			1.00000i			1.00000i
$454$	0.866025	−	0.500000i	0.866025	−	0.500000i
$455$		0			0
$456$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$457$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$457$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$458$	1.00000			1.00000
$459$	1.00000			1.00000
$460$	1.00000			1.00000
$461$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$461$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$462$		0			0
$463$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$463$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$464$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$465$		0			0
$466$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$467$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$467$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$468$	0.866025	−	0.500000i	0.866025	−	0.500000i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$474$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$475$		0			0
$476$		0			0
$477$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$478$	−1.00000			−1.00000
$479$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$479$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$480$	1.00000			1.00000
$481$	0.500000	+	0.866025i	0.500000	+	0.866025i
$482$	0.866025	−	0.500000i	0.866025	−	0.500000i
$483$		0			0
$484$		0			0
$485$		−	1.00000i		−	1.00000i
$486$	0.866025	−	0.500000i	0.866025	−	0.500000i
$487$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$487$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$488$		0			0
$489$	0.500000	+	0.866025i	0.500000	+	0.866025i
$490$		0			0
$491$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$491$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$492$	−1.00000			−1.00000
$493$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$494$	−1.00000			−1.00000
$495$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$496$		0			0
$497$		0			0
$498$	0.866025	+	0.500000i	0.866025	+	0.500000i
$499$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$499$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$500$	0.866025	−	0.500000i	0.866025	−	0.500000i
$501$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$	1.00000			1.00000
$506$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$507$		0			0
$508$		0			0
$509$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$510$	0.500000	+	0.866025i	0.500000	+	0.866025i
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$	−1.00000			−1.00000
$514$			1.00000i			1.00000i
$515$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$516$	0.500000	+	0.866025i	0.500000	+	0.866025i
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.866025	+	0.500000i	0.866025	+	0.500000i
$521$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$521$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$522$	−1.00000			−1.00000
$523$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$523$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$524$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$525$		0			0
$526$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$527$		0			0
$528$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$529$		0			0
$530$		−	1.00000i		−	1.00000i
$531$		0			0
$532$		0			0
$533$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$534$			1.00000i			1.00000i
$535$	0.866025	−	0.500000i	0.866025	−	0.500000i
$536$		0			0
$537$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$538$	0.500000	−	0.866025i	0.500000	−	0.866025i
$539$		0			0
$540$	0.866025	+	0.500000i	0.866025	+	0.500000i
$541$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$541$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$542$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$543$	1.73205	−	1.00000i	1.73205	−	1.00000i
$544$	0.866025	−	0.500000i	0.866025	−	0.500000i
$545$	0.500000	+	0.866025i	0.500000	+	0.866025i
$546$		0			0
$547$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$547$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$548$	−1.00000			−1.00000
$549$		0			0
$550$		0			0
$551$	0.866025	+	0.500000i	0.866025	+	0.500000i
$552$	0.500000	−	0.866025i	0.500000	−	0.866025i
$553$		0			0
$554$	0.500000	+	0.866025i	0.500000	+	0.866025i
$555$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$556$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$557$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$558$		0			0
$559$			1.00000i			1.00000i
$560$		0			0
$561$	−1.00000			−1.00000
$562$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$	0.866025	+	0.500000i	0.866025	+	0.500000i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$569$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$570$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$571$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$571$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$572$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.500000	−	0.866025i	0.500000	−	0.866025i
$577$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$577$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			0
$579$		0			0
$580$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$581$		0			0
$582$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$583$	0.866025	+	0.500000i	0.866025	+	0.500000i
$584$			1.00000i			1.00000i
$585$	0.500000	+	0.866025i	0.500000	+	0.866025i
$586$	1.00000			1.00000
$587$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$587$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.866025	+	0.500000i	0.866025	+	0.500000i
$593$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$593$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$594$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$595$		0			0
$596$	0.866025	+	0.500000i	0.866025	+	0.500000i
$597$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$598$	0.866025	−	0.500000i	0.866025	−	0.500000i
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$			1.00000i			1.00000i
$605$		0			0
$606$	0.500000	−	0.866025i	0.500000	−	0.866025i
$607$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$607$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$608$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.00000			1.00000
$613$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$613$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$614$		0			0
$615$		−	1.00000i		−	1.00000i
$616$		0			0
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$618$	0.500000	+	0.866025i	0.500000	+	0.866025i
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$620$		0			0
$621$	0.866025	−	0.500000i	0.866025	−	0.500000i
$622$	2.00000			2.00000
$623$		0			0
$624$	0.866025	−	0.500000i	0.866025	−	0.500000i
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$		0			0
$627$	1.00000			1.00000
$628$		0			0
$629$			1.00000i			1.00000i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$633$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$634$		0			0
$635$		0			0
$636$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$637$		0			0
$638$	1.00000			1.00000
$639$		0			0
$640$	1.00000			1.00000
$641$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$642$		−	1.00000i		−	1.00000i
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$644$		0			0
$645$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$646$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$647$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$647$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$648$	0.866025	−	0.500000i	0.866025	−	0.500000i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.500000	+	0.866025i	0.500000	+	0.866025i
$653$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$653$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$654$	1.00000			1.00000
$655$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$656$	−1.00000			−1.00000
$657$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$658$		0			0
$659$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$659$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$660$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$	0.866025	+	0.500000i	0.866025	+	0.500000i
$664$	0.866025	+	0.500000i	0.866025	+	0.500000i
$665$		0			0
$666$	0.500000	+	0.866025i	0.500000	+	0.866025i
$667$	−1.00000			−1.00000
$668$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$669$			1.00000i			1.00000i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$674$		−	1.00000i		−	1.00000i
$675$		0			0
$676$		0			0
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	0.866025	−	0.500000i	0.866025	−	0.500000i
$679$		0			0
$680$	0.500000	+	0.866025i	0.500000	+	0.866025i
$681$	1.00000			1.00000
$682$		0			0
$683$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$683$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$684$	−1.00000			−1.00000
$685$		−	1.00000i		−	1.00000i
$686$		0			0
$687$	0.866025	+	0.500000i	0.866025	+	0.500000i
$688$	0.500000	+	0.866025i	0.500000	+	0.866025i
$689$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$690$	0.866025	+	0.500000i	0.866025	+	0.500000i
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$696$	−1.00000			−1.00000
$697$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$698$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$699$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	1.00000			1.00000
$703$		−	1.00000i		−	1.00000i
$704$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$705$		0			0
$706$	0.866025	−	0.500000i	0.866025	−	0.500000i
$707$		0			0
$708$		0			0
$709$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$709$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$710$		0			0
$711$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$712$			1.00000i			1.00000i
$713$		0			0
$714$		0			0
$715$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$716$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$717$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$718$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$719$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$720$	0.866025	+	0.500000i	0.866025	+	0.500000i
$721$		0			0
$722$		0			0
$723$	1.00000			1.00000
$724$	1.73205	−	1.00000i	1.73205	−	1.00000i
$725$		0			0
$726$		0			0
$727$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$727$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$	−1.00000			−1.00000
$731$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$732$		0			0
$733$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$733$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$734$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$735$		0			0
$736$	0.500000	−	0.866025i	0.500000	−	0.866025i
$737$		0			0
$738$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$739$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$739$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$740$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$741$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$742$		0			0
$743$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$744$		0			0
$745$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$746$	−1.00000			−1.00000
$747$	0.500000	+	0.866025i	0.500000	+	0.866025i
$748$	−1.00000			−1.00000
$749$		0			0
$750$	1.00000			1.00000
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$752$		0			0
$753$		0			0
$754$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$755$	−1.00000			−1.00000
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$760$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$761$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$761$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$			1.00000i			1.00000i
$766$	1.00000			1.00000
$767$		0			0
$768$	0.500000	−	0.866025i	0.500000	−	0.866025i
$769$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$769$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$772$		0			0
$773$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$773$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$774$			1.00000i			1.00000i
$775$		0			0
$776$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$777$		0			0
$778$	0.500000	+	0.866025i	0.500000	+	0.866025i
$779$	0.500000	+	0.866025i	0.500000	+	0.866025i
$780$	0.500000	+	0.866025i	0.500000	+	0.866025i
$781$		0			0
$782$	1.00000			1.00000
$783$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$784$		0			0
$785$		0			0
$786$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$787$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$787$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$788$		0			0
$789$		−	1.00000i		−	1.00000i
$790$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$791$		0			0
$792$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$793$		0			0
$794$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$795$	0.500000	−	0.866025i	0.500000	−	0.866025i
$796$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$797$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$797$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$802$		−	1.00000i		−	1.00000i
$803$	0.500000	−	0.866025i	0.500000	−	0.866025i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.866025	−	0.500000i	0.866025	−	0.500000i
$808$	0.500000	−	0.866025i	0.500000	−	0.866025i
$809$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$809$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$810$	0.500000	+	0.866025i	0.500000	+	0.866025i
$811$	−2.00000			−2.00000			−1.00000			$\pi$
$811$	−2.00000			−2.00000			−1.00000			$\pi$
$812$		0			0
$813$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$814$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$815$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$816$	1.00000			1.00000
$817$	0.500000	−	0.866025i	0.500000	−	0.866025i
$818$		0			0
$819$		0			0
$820$		−	1.00000i		−	1.00000i
$821$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$821$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$822$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$	0.500000	+	0.866025i	0.500000	+	0.866025i
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$	0.866025	−	0.500000i	0.866025	−	0.500000i
$829$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$829$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$830$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$831$			1.00000i			1.00000i
$832$	0.866025	−	0.500000i	0.866025	−	0.500000i
$833$		0			0
$834$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$835$	0.500000	−	0.866025i	0.500000	−	0.866025i
$836$	1.00000			1.00000
$837$		0			0
$838$			1.00000i			1.00000i
$839$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$839$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$		0			0
$842$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$843$	−1.00000			−1.00000
$844$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$849$		0			0
$850$		0			0
$851$	0.500000	+	0.866025i	0.500000	+	0.866025i
$852$		0			0
$853$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$853$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$854$		0			0
$855$		−	1.00000i		−	1.00000i
$856$		−	1.00000i		−	1.00000i
$857$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$858$	−1.00000			−1.00000
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$860$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$861$		0			0
$862$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$863$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$863$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$864$	0.866025	−	0.500000i	0.866025	−	0.500000i
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.73205	−	1.00000i	1.73205	−	1.00000i
$870$		−	1.00000i		−	1.00000i
$871$		0			0
$872$	1.00000			1.00000
$873$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$874$	−1.00000			−1.00000
$875$		0			0
$876$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$877$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$877$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$878$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$879$	0.866025	+	0.500000i	0.866025	+	0.500000i
$880$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$	0.866025	+	0.500000i	0.866025	+	0.500000i
$885$		0			0
$886$		0			0
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$	0.500000	+	0.866025i	0.500000	+	0.866025i
$889$		0			0
$890$	−1.00000			−1.00000
$891$	−1.00000			−1.00000
$892$			1.00000i			1.00000i
$893$		0			0
$894$	0.500000	+	0.866025i	0.500000	+	0.866025i
$895$	0.866025	−	0.500000i	0.866025	−	0.500000i
$896$		0			0
$897$	1.00000			1.00000
$898$		0			0
$899$		0			0
$900$		0			0
$901$		−	1.00000i		−	1.00000i
$902$	0.866025	+	0.500000i	0.866025	+	0.500000i
$903$		0			0
$904$	0.866025	−	0.500000i	0.866025	−	0.500000i
$905$	1.00000	+	1.73205i	1.00000	+	1.73205i
$906$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$907$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$907$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$908$	1.00000			1.00000
$909$	0.866025	−	0.500000i	0.866025	−	0.500000i
$910$		0			0
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$912$	−1.00000			−1.00000
$913$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$914$	1.73205	−	1.00000i	1.73205	−	1.00000i
$915$		0			0
$916$	0.866025	+	0.500000i	0.866025	+	0.500000i
$917$		0			0
$918$	0.866025	+	0.500000i	0.866025	+	0.500000i
$919$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$919$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$920$	0.866025	+	0.500000i	0.866025	+	0.500000i
$921$		0			0
$922$	0.500000	+	0.866025i	0.500000	+	0.866025i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.00000			1.00000
$927$			1.00000i			1.00000i
$928$	−1.00000			−1.00000
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$		0			0
$932$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$933$	1.73205	+	1.00000i	1.73205	+	1.00000i
$934$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$935$		−	1.00000i		−	1.00000i
$936$	1.00000			1.00000
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$		0			0
$943$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$944$		0			0
$945$		0			0
$946$		−	1.00000i		−	1.00000i
$947$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$947$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$948$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$949$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$955$		0			0
$956$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$957$	0.866025	+	0.500000i	0.866025	+	0.500000i
$958$	0.500000	+	0.866025i	0.500000	+	0.866025i
$959$		0			0
$960$	0.866025	+	0.500000i	0.866025	+	0.500000i
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$			1.00000i			1.00000i
$963$	0.500000	−	0.866025i	0.500000	−	0.866025i
$964$	1.00000			1.00000
$965$		0			0
$966$		0			0
$967$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$967$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$968$		0			0
$969$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$970$	0.500000	−	0.866025i	0.500000	−	0.866025i
$971$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$971$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$972$	1.00000			1.00000
$973$		0			0
$974$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$975$		0			0
$976$		0			0
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$			1.00000i			1.00000i
$979$	0.500000	−	0.866025i	0.500000	−	0.866025i
$980$		0			0
$981$	0.866025	+	0.500000i	0.866025	+	0.500000i
$982$		−	1.00000i		−	1.00000i
$983$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$983$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$984$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$985$		0			0
$986$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$987$		0			0
$988$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$989$			1.00000i			1.00000i
$990$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$991$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$991$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$996$	0.500000	+	0.866025i	0.500000	+	0.866025i
$997$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$997$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$998$		−	1.00000i		−	1.00000i
$999$			1.00000i			1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3528.1.cg.d.2059.2		4
7.2	even	3		504.1.ce.a.403.1	yes	4
7.3	odd	6		3528.1.ba.d.1843.1		4
7.4	even	3		504.1.ba.a.331.1	yes	4
7.5	odd	6		3528.1.ce.c.2419.1		4
7.6	odd	2		3528.1.cg.c.2059.2		4
8.3	odd	2	inner	3528.1.cg.d.2059.1		4
9.4	even	3	inner	3528.1.cg.d.3235.1		4
21.2	odd	6		1512.1.ce.a.235.2		4
21.11	odd	6		1512.1.ba.a.667.2		4
28.11	odd	6		2016.1.bi.a.79.1		4
28.23	odd	6		2016.1.cm.a.655.2		4
56.3	even	6		3528.1.ba.d.1843.2		4
56.11	odd	6		504.1.ba.a.331.2	yes	4
56.19	even	6		3528.1.ce.c.2419.2		4
56.27	even	2		3528.1.cg.c.2059.1		4
56.37	even	6		2016.1.cm.a.655.1		4
56.51	odd	6		504.1.ce.a.403.2	yes	4
56.53	even	6		2016.1.bi.a.79.2		4
63.4	even	3		504.1.ce.a.499.1	yes	4
63.13	odd	6		3528.1.cg.c.3235.1		4
63.23	odd	6		1512.1.ba.a.739.1		4
63.31	odd	6		3528.1.ce.c.3019.1		4
63.32	odd	6		1512.1.ce.a.1171.2		4
63.40	odd	6		3528.1.ba.d.67.2		4
63.58	even	3		504.1.ba.a.67.2	yes	4
72.67	odd	6	inner	3528.1.cg.d.3235.2		4
168.11	even	6		1512.1.ba.a.667.1		4
168.107	even	6		1512.1.ce.a.235.1		4
252.67	odd	6		2016.1.cm.a.751.1		4
252.247	odd	6		2016.1.bi.a.1327.1		4
504.67	odd	6		504.1.ce.a.499.2	yes	4
504.139	even	6		3528.1.cg.c.3235.2		4
504.275	even	6		1512.1.ba.a.739.2		4
504.283	even	6		3528.1.ce.c.3019.2		4
504.347	even	6		1512.1.ce.a.1171.1		4
504.355	even	6		3528.1.ba.d.67.1		4
504.373	even	6		2016.1.bi.a.1327.2		4
504.445	even	6		2016.1.cm.a.751.2		4
504.499	odd	6		504.1.ba.a.67.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.1.ba.a.67.1	✓	4	504.499	odd	6
504.1.ba.a.67.2	yes	4	63.58	even	3
504.1.ba.a.331.1	yes	4	7.4	even	3
504.1.ba.a.331.2	yes	4	56.11	odd	6
504.1.ce.a.403.1	yes	4	7.2	even	3
504.1.ce.a.403.2	yes	4	56.51	odd	6
504.1.ce.a.499.1	yes	4	63.4	even	3
504.1.ce.a.499.2	yes	4	504.67	odd	6
1512.1.ba.a.667.1		4	168.11	even	6
1512.1.ba.a.667.2		4	21.11	odd	6
1512.1.ba.a.739.1		4	63.23	odd	6
1512.1.ba.a.739.2		4	504.275	even	6
1512.1.ce.a.235.1		4	168.107	even	6
1512.1.ce.a.235.2		4	21.2	odd	6
1512.1.ce.a.1171.1		4	504.347	even	6
1512.1.ce.a.1171.2		4	63.32	odd	6
2016.1.bi.a.79.1		4	28.11	odd	6
2016.1.bi.a.79.2		4	56.53	even	6
2016.1.bi.a.1327.1		4	252.247	odd	6
2016.1.bi.a.1327.2		4	504.373	even	6
2016.1.cm.a.655.1		4	56.37	even	6
2016.1.cm.a.655.2		4	28.23	odd	6
2016.1.cm.a.751.1		4	252.67	odd	6
2016.1.cm.a.751.2		4	504.445	even	6
3528.1.ba.d.67.1		4	504.355	even	6
3528.1.ba.d.67.2		4	63.40	odd	6
3528.1.ba.d.1843.1		4	7.3	odd	6
3528.1.ba.d.1843.2		4	56.3	even	6
3528.1.ce.c.2419.1		4	7.5	odd	6
3528.1.ce.c.2419.2		4	56.19	even	6
3528.1.ce.c.3019.1		4	63.31	odd	6
3528.1.ce.c.3019.2		4	504.283	even	6
3528.1.cg.c.2059.1		4	56.27	even	2
3528.1.cg.c.2059.2		4	7.6	odd	2
3528.1.cg.c.3235.1		4	63.13	odd	6
3528.1.cg.c.3235.2		4	504.139	even	6
3528.1.cg.d.2059.1		4	8.3	odd	2	inner
3528.1.cg.d.2059.2		4	1.1	even	1	trivial
3528.1.cg.d.3235.1		4	9.4	even	3	inner
3528.1.cg.d.3235.2		4	72.67	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3528.cg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.00000i q^{6} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(-0.866025 - 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{17} +(-0.866025 + 0.500000i) q^{18} +1.00000 q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.866025 - 0.500000i) q^{22} +(-0.866025 + 0.500000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -1.00000 q^{26} -1.00000 q^{27} +(0.866025 + 0.500000i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.866025 + 0.500000i) q^{32} +1.00000 q^{33} +(-0.866025 - 0.500000i) q^{34} -1.00000 q^{36} -1.00000i q^{37} +(0.866025 + 0.500000i) q^{38} +(-0.866025 - 0.500000i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} -1.00000i q^{45} -1.00000 q^{46} -1.00000 q^{48} +(-0.500000 - 0.866025i) q^{51} +(-0.866025 - 0.500000i) q^{52} +1.00000i q^{53} +(-0.866025 - 0.500000i) q^{54} +1.00000i q^{55} +(0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} -1.00000i q^{60} -1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.866025 + 0.500000i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-0.866025 - 0.500000i) q^{69} +(-0.866025 - 0.500000i) q^{72} +1.00000 q^{73} +(0.500000 - 0.866025i) q^{74} +(0.500000 + 0.866025i) q^{76} +(-0.500000 - 0.866025i) q^{78} +(1.73205 + 1.00000i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +1.00000i q^{82} +(0.500000 - 0.866025i) q^{83} +(0.866025 - 0.500000i) q^{85} +(0.866025 - 0.500000i) q^{86} +1.00000i q^{87} +(0.866025 + 0.500000i) q^{88} +1.00000 q^{89} +(0.500000 - 0.866025i) q^{90} +(-0.866025 - 0.500000i) q^{92} +(-0.866025 + 0.500000i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 2 q^{9} - 4 q^{10} + 2 q^{11} - 2 q^{12} - 2 q^{16} - 4 q^{17} + 4 q^{19} - 4 q^{26} - 4 q^{27} - 2 q^{30} + 4 q^{33} - 4 q^{36} - 2 q^{40} + 2 q^{41} + 2 q^{43} + 4 q^{44} - 4 q^{46}+ \cdots + 2 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 2 * q^9 - 4 * q^10 + 2 * q^11 - 2 * q^12 - 2 * q^16 - 4 * q^17 + 4 * q^19 - 4 * q^26 - 4 * q^27 - 2 * q^30 + 4 * q^33 - 4 * q^36 - 2 * q^40 + 2 * q^41 + 2 * q^43 + 4 * q^44 - 4 * q^46 - 4 * q^48 - 2 * q^51 + 2 * q^57 + 2 * q^58 - 4 * q^64 + 2 * q^65 - 2 * q^68 + 4 * q^73 + 2 * q^74 + 2 * q^76 - 2 * q^78 - 2 * q^81 + 2 * q^83 + 4 * q^89 + 2 * q^90 - 2 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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