LMFDB - Embedded newform 1560.1.du.b.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1560,1,Mod(29,1560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1560, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 3, 2]))

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

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

chi := DirichletCharacter("1560.29");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1560.du (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.778541419707$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.20280.1
Artin image:	$C_6\times S_3$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{12} - \cdots)$

Embedding invariants

Embedding label			269.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1560.269
Dual form			1560.1.du.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{12} -1.00000 q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +1.00000 q^{25} +(0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +2.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(-0.500000 + 0.866025i) q^{39} -1.00000 q^{40} +(-0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(0.500000 + 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} -1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{55} +(-0.500000 - 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{59} +1.00000 q^{60} +(0.500000 - 0.866025i) q^{62} +1.00000 q^{64} +1.00000 q^{65} -1.00000 q^{66} +(1.00000 - 1.73205i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-0.500000 - 0.866025i) q^{69} +(-0.500000 - 0.866025i) q^{72} +(-0.500000 - 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-0.500000 - 0.866025i) q^{78} -1.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{85} +1.00000 q^{86} +(0.500000 + 0.866025i) q^{87} +(-0.500000 + 0.866025i) q^{88} -1.00000 q^{90} -1.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(0.500000 - 0.866025i) q^{94} -1.00000 q^{96} +(-0.500000 - 0.866025i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} + 2 q^{8} - q^{9} + q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + q^{20} - q^{22} + q^{23} + q^{24} + 2 q^{25} + q^{26} - 2 q^{27} - q^{29} - q^{30} - 2 q^{31} - q^{32} + q^{33} + 4 q^{34} - q^{36} - q^{37} - q^{39} - 2 q^{40} - q^{43} + 2 q^{44} + q^{45} + q^{46} - 2 q^{47} + q^{48} - q^{49} - q^{50} - 4 q^{51} + q^{52} + q^{54} + q^{55} - q^{58} - q^{59} + 2 q^{60} + q^{62} + 2 q^{64} + 2 q^{65} - 2 q^{66} + 2 q^{67} - 2 q^{68} - q^{69} - q^{72} - q^{74} + q^{75} - q^{78} - 2 q^{79} + q^{80} - q^{81} + 2 q^{85} + 2 q^{86} + q^{87} - q^{88} - 2 q^{90} - 2 q^{92} - q^{93} + q^{94} - 2 q^{96} - q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 + 2 * q^8 - q^9 + q^10 - q^11 - 2 * q^12 - 2 * q^13 - q^15 - q^16 - 2 * q^17 + 2 * q^18 + q^20 - q^22 + q^23 + q^24 + 2 * q^25 + q^26 - 2 * q^27 - q^29 - q^30 - 2 * q^31 - q^32 + q^33 + 4 * q^34 - q^36 - q^37 - q^39 - 2 * q^40 - q^43 + 2 * q^44 + q^45 + q^46 - 2 * q^47 + q^48 - q^49 - q^50 - 4 * q^51 + q^52 + q^54 + q^55 - q^58 - q^59 + 2 * q^60 + q^62 + 2 * q^64 + 2 * q^65 - 2 * q^66 + 2 * q^67 - 2 * q^68 - q^69 - q^72 - q^74 + q^75 - q^78 - 2 * q^79 + q^80 - q^81 + 2 * q^85 + 2 * q^86 + q^87 - q^88 - 2 * q^90 - 2 * q^92 - q^93 + q^94 - 2 * q^96 - q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$.

$n$	$391$	$521$	$781$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$3$	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
$5$	−1.00000			−1.00000
$5$	−1.00000			−1.00000
$6$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$	1.00000			1.00000
$9$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$10$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$12$	−1.00000			−1.00000
$13$	−1.00000			−1.00000
$13$	−1.00000			−1.00000
$14$		0			0
$15$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$18$	1.00000			1.00000
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.500000	+	0.866025i	0.500000	+	0.866025i
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$23$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$23$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$24$	0.500000	−	0.866025i	0.500000	−	0.866025i
$25$	1.00000			1.00000
$26$	0.500000	−	0.866025i	0.500000	−	0.866025i
$27$	−1.00000			−1.00000
$28$		0			0
$29$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$29$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$30$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$31$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$31$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$32$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$33$	0.500000	+	0.866025i	0.500000	+	0.866025i
$34$	2.00000			2.00000
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$38$		0			0
$39$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$40$	−1.00000			−1.00000
$41$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$41$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$44$	1.00000			1.00000
$45$	0.500000	+	0.866025i	0.500000	+	0.866025i
$46$	0.500000	+	0.866025i	0.500000	+	0.866025i
$47$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$47$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$51$	−2.00000			−2.00000
$52$	0.500000	+	0.866025i	0.500000	+	0.866025i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.500000	−	0.866025i	0.500000	−	0.866025i
$55$	0.500000	−	0.866025i	0.500000	−	0.866025i
$56$		0			0
$57$		0			0
$58$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$60$	1.00000			1.00000
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$	0.500000	−	0.866025i	0.500000	−	0.866025i
$63$		0			0
$64$	1.00000			1.00000
$65$	1.00000			1.00000
$66$	−1.00000			−1.00000
$67$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$67$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$68$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$69$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$70$		0			0
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$75$	0.500000	−	0.866025i	0.500000	−	0.866025i
$76$		0			0
$77$		0			0
$78$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$79$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$79$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$80$	0.500000	−	0.866025i	0.500000	−	0.866025i
$81$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	1.00000	+	1.73205i	1.00000	+	1.73205i
$86$	1.00000			1.00000
$87$	0.500000	+	0.866025i	0.500000	+	0.866025i
$88$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$	−1.00000			−1.00000
$91$		0			0
$92$	−1.00000			−1.00000
$93$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$94$	0.500000	−	0.866025i	0.500000	−	0.866025i
$95$		0			0
$96$	−1.00000			−1.00000
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$99$	1.00000			1.00000
$100$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$101$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$101$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$102$	1.00000	−	1.73205i	1.00000	−	1.73205i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−1.00000			−1.00000
$105$		0			0
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.500000	+	0.866025i	0.500000	+	0.866025i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	0.500000	+	0.866025i	0.500000	+	0.866025i
$111$	0.500000	+	0.866025i	0.500000	+	0.866025i
$112$		0			0
$113$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$113$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$116$	1.00000			1.00000
$117$	0.500000	+	0.866025i	0.500000	+	0.866025i
$118$	1.00000			1.00000
$119$		0			0
$120$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$121$		0			0
$122$		0			0
$123$		0			0
$124$	0.500000	+	0.866025i	0.500000	+	0.866025i
$125$	−1.00000			−1.00000
$126$		0			0
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$	−1.00000			−1.00000
$130$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$131$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$131$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$132$	0.500000	−	0.866025i	0.500000	−	0.866025i
$133$		0			0
$134$	1.00000	+	1.73205i	1.00000	+	1.73205i
$135$	1.00000			1.00000
$136$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$137$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$137$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$138$	1.00000			1.00000
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$142$		0			0
$143$	0.500000	−	0.866025i	0.500000	−	0.866025i
$144$	1.00000			1.00000
$145$	0.500000	−	0.866025i	0.500000	−	0.866025i
$146$		0			0
$147$	0.500000	+	0.866025i	0.500000	+	0.866025i
$148$	1.00000			1.00000
$149$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$149$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$150$	0.500000	+	0.866025i	0.500000	+	0.866025i
$151$	2.00000			2.00000			1.00000			$0$
$151$	2.00000			2.00000			1.00000			$0$
$152$		0			0
$153$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$154$		0			0
$155$	1.00000			1.00000
$156$	1.00000			1.00000
$157$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$157$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$158$	0.500000	−	0.866025i	0.500000	−	0.866025i
$159$		0			0
$160$	0.500000	+	0.866025i	0.500000	+	0.866025i
$161$		0			0
$162$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$164$		0			0
$165$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$166$		0			0
$167$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$167$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$168$		0			0
$169$	1.00000			1.00000
$170$	−2.00000			−2.00000
$171$		0			0
$172$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$173$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$173$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$174$	−1.00000			−1.00000
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$177$	−1.00000			−1.00000
$178$		0			0
$179$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$179$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$180$	0.500000	−	0.866025i	0.500000	−	0.866025i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$		0			0
$184$	0.500000	−	0.866025i	0.500000	−	0.866025i
$185$	0.500000	−	0.866025i	0.500000	−	0.866025i
$186$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$187$	2.00000			2.00000
$188$	0.500000	+	0.866025i	0.500000	+	0.866025i
$189$		0			0
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$	0.500000	−	0.866025i	0.500000	−	0.866025i
$196$	1.00000			1.00000
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$199$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$199$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$200$	1.00000			1.00000
$201$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$202$	1.00000	+	1.73205i	1.00000	+	1.73205i
$203$		0			0
$204$	1.00000	+	1.73205i	1.00000	+	1.73205i
$205$		0			0
$206$		0			0
$207$	−1.00000			−1.00000
$208$	0.500000	−	0.866025i	0.500000	−	0.866025i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.500000	+	0.866025i	0.500000	+	0.866025i
$216$	−1.00000			−1.00000
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.00000			−1.00000
$221$	1.00000	+	1.73205i	1.00000	+	1.73205i
$222$	−1.00000			−1.00000
$223$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$223$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$226$	−1.00000			−1.00000
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$231$		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	$0.666667\pi$
$234$	−1.00000			−1.00000
$235$	1.00000			1.00000
$236$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$237$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.500000	+	0.866025i
$244$		0			0
$245$	0.500000	−	0.866025i	0.500000	−	0.866025i
$246$		0			0
$247$		0			0
$248$	−1.00000			−1.00000
$249$		0			0
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$251$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$252$		0			0
$253$	0.500000	+	0.866025i	0.500000	+	0.866025i
$254$		0			0
$255$	2.00000			2.00000
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$258$	0.500000	−	0.866025i	0.500000	−	0.866025i
$259$		0			0
$260$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$261$	1.00000			1.00000
$262$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$264$	0.500000	+	0.866025i	0.500000	+	0.866025i
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−2.00000			−2.00000
$269$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$269$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$270$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$271$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$271$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$272$	2.00000			2.00000
$273$		0			0
$274$	−1.00000			−1.00000
$275$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$276$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$277$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$277$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$278$		0			0
$279$	0.500000	+	0.866025i	0.500000	+	0.866025i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$283$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$283$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$284$		0			0
$285$		0			0
$286$	0.500000	+	0.866025i	0.500000	+	0.866025i
$287$		0			0
$288$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$289$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$290$	0.500000	+	0.866025i	0.500000	+	0.866025i
$291$		0			0
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−1.00000			−1.00000
$295$	0.500000	+	0.866025i	0.500000	+	0.866025i
$296$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$297$	0.500000	−	0.866025i	0.500000	−	0.866025i
$298$	1.00000			1.00000
$299$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$300$	−1.00000			−1.00000
$301$		0			0
$302$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$303$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$304$		0			0
$305$		0			0
$306$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$315$		0			0
$316$	0.500000	+	0.866025i	0.500000	+	0.866025i
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$320$	−1.00000			−1.00000
$321$		0			0
$322$		0			0
$323$		0			0
$324$	1.00000			1.00000
$325$	−1.00000			−1.00000
$326$	1.00000			1.00000
$327$		0			0
$328$		0			0
$329$		0			0
$330$	1.00000			1.00000
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$		0			0
$333$	1.00000			1.00000
$334$	0.500000	+	0.866025i	0.500000	+	0.866025i
$335$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$339$	1.00000			1.00000
$340$	1.00000	−	1.73205i	1.00000	−	1.73205i
$341$	0.500000	−	0.866025i	0.500000	−	0.866025i
$342$		0			0
$343$		0			0
$344$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$345$	0.500000	+	0.866025i	0.500000	+	0.866025i
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	0.500000	−	0.866025i	0.500000	−	0.866025i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$	1.00000			1.00000
$352$	1.00000			1.00000
$353$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$353$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$354$	0.500000	−	0.866025i	0.500000	−	0.866025i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	0.500000	+	0.866025i	0.500000	+	0.866025i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	0.500000	+	0.866025i	0.500000	+	0.866025i
$369$		0			0
$370$	0.500000	+	0.866025i	0.500000	+	0.866025i
$371$		0			0
$372$	1.00000			1.00000
$373$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$373$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$374$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$375$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$376$	−1.00000			−1.00000
$377$	0.500000	−	0.866025i	0.500000	−	0.866025i
$378$		0			0
$379$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$379$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$383$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$384$	0.500000	+	0.866025i	0.500000	+	0.866025i
$385$		0			0
$386$		0			0
$387$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$388$		0			0
$389$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$389$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$390$	0.500000	+	0.866025i	0.500000	+	0.866025i
$391$	−2.00000			−2.00000
$392$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$393$	0.500000	−	0.866025i	0.500000	−	0.866025i
$394$		0			0
$395$	1.00000			1.00000
$396$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$397$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$397$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$398$	2.00000			2.00000
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$	2.00000			2.00000
$403$	1.00000			1.00000
$404$	−2.00000			−2.00000
$405$	0.500000	−	0.866025i	0.500000	−	0.866025i
$406$		0			0
$407$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$408$	−2.00000			−2.00000
$409$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$409$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$410$		0			0
$411$	1.00000			1.00000
$412$		0			0
$413$		0			0
$414$	0.500000	−	0.866025i	0.500000	−	0.866025i
$415$		0			0
$416$	0.500000	+	0.866025i	0.500000	+	0.866025i
$417$		0			0
$418$		0			0
$419$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$419$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$	0.500000	+	0.866025i	0.500000	+	0.866025i
$424$		0			0
$425$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$430$	−1.00000			−1.00000
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$433$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$434$		0			0
$435$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$439$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$440$	0.500000	−	0.866025i	0.500000	−	0.866025i
$441$	1.00000			1.00000
$442$	−2.00000			−2.00000
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	0.500000	−	0.866025i	0.500000	−	0.866025i
$445$		0			0
$446$		0			0
$447$	−1.00000			−1.00000
$448$		0			0
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	1.00000			1.00000
$451$		0			0
$452$	0.500000	−	0.866025i	0.500000	−	0.866025i
$453$	1.00000	−	1.73205i	1.00000	−	1.73205i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$	1.00000	+	1.73205i	1.00000	+	1.73205i
$460$	1.00000			1.00000
$461$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$461$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$465$	0.500000	−	0.866025i	0.500000	−	0.866025i
$466$	0.500000	−	0.866025i	0.500000	−	0.866025i
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$	0.500000	−	0.866025i	0.500000	−	0.866025i
$469$		0			0
$470$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$471$	0.500000	−	0.866025i	0.500000	−	0.866025i
$472$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$473$	1.00000			1.00000
$474$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	1.00000			1.00000
$481$	0.500000	−	0.866025i	0.500000	−	0.866025i
$482$	−1.00000			−1.00000
$483$		0			0
$484$		0			0
$485$		0			0
$486$	−1.00000			−1.00000
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$	−1.00000			−1.00000
$490$	0.500000	+	0.866025i	0.500000	+	0.866025i
$491$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$491$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$492$		0			0
$493$	2.00000			2.00000
$494$		0			0
$495$	−1.00000			−1.00000
$496$	0.500000	−	0.866025i	0.500000	−	0.866025i
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	0.500000	+	0.866025i	0.500000	+	0.866025i
$501$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$502$	1.00000			1.00000
$503$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$503$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$504$		0			0
$505$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$506$	−1.00000			−1.00000
$507$	0.500000	−	0.866025i	0.500000	−	0.866025i
$508$		0			0
$509$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$509$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$510$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$511$		0			0
$512$	1.00000			1.00000
$513$		0			0
$514$	0.500000	+	0.866025i	0.500000	+	0.866025i
$515$		0			0
$516$	0.500000	+	0.866025i	0.500000	+	0.866025i
$517$	0.500000	−	0.866025i	0.500000	−	0.866025i
$518$		0			0
$519$		0			0
$520$	1.00000			1.00000
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$524$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$525$		0			0
$526$	0.500000	+	0.866025i	0.500000	+	0.866025i
$527$	1.00000	+	1.73205i	1.00000	+	1.73205i
$528$	−1.00000			−1.00000
$529$		0			0
$530$		0			0
$531$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.00000	−	1.73205i	1.00000	−	1.73205i
$537$	0.500000	+	0.866025i	0.500000	+	0.866025i
$538$	−2.00000			−2.00000
$539$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$540$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$	0.500000	+	0.866025i	0.500000	+	0.866025i
$543$		0			0
$544$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$545$		0			0
$546$		0			0
$547$	−2.00000			−2.00000			−1.00000			$\pi$
$547$	−2.00000			−2.00000			−1.00000			$\pi$
$548$	0.500000	−	0.866025i	0.500000	−	0.866025i
$549$		0			0
$550$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$551$		0			0
$552$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$553$		0			0
$554$	1.00000			1.00000
$555$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$	−1.00000			−1.00000
$559$	0.500000	+	0.866025i	0.500000	+	0.866025i
$560$		0			0
$561$	1.00000	−	1.73205i	1.00000	−	1.73205i
$562$		0			0
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$	1.00000			1.00000
$565$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$566$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$567$		0			0
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	−1.00000			−1.00000
$573$		0			0
$574$		0			0
$575$	0.500000	−	0.866025i	0.500000	−	0.866025i
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$579$		0			0
$580$	−1.00000			−1.00000
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$586$		0			0
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	0.500000	−	0.866025i	0.500000	−	0.866025i
$589$		0			0
$590$	−1.00000			−1.00000
$591$		0			0
$592$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$593$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$593$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$594$	0.500000	+	0.866025i	0.500000	+	0.866025i
$595$		0			0
$596$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$597$	−2.00000			−2.00000
$598$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	0.500000	−	0.866025i	0.500000	−	0.866025i
$601$	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
$603$	−2.00000			−2.00000
$604$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$605$		0			0
$606$	2.00000			2.00000
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.00000			1.00000
$612$	2.00000			2.00000
$613$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$613$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$614$	1.00000	−	1.73205i	1.00000	−	1.73205i
$615$		0			0
$616$		0			0
$617$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$617$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$621$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$622$		0			0
$623$		0			0
$624$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$625$	1.00000			1.00000
$626$		0			0
$627$		0			0
$628$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$629$	2.00000			2.00000
$630$		0			0
$631$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$632$	−1.00000			−1.00000
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.500000	−	0.866025i	0.500000	−	0.866025i
$638$	1.00000			1.00000
$639$		0			0
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$641$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$643$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$644$		0			0
$645$	1.00000			1.00000
$646$		0			0
$647$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$647$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$648$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$649$	1.00000			1.00000
$650$	0.500000	−	0.866025i	0.500000	−	0.866025i
$651$		0			0
$652$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	−1.00000			−1.00000
$656$		0			0
$657$		0			0
$658$		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			$\pi$
$660$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$661$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$661$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$662$		0			0
$663$	2.00000			2.00000
$664$		0			0
$665$		0			0
$666$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$667$	0.500000	+	0.866025i	0.500000	+	0.866025i
$668$	−1.00000			−1.00000
$669$		0			0
$670$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$671$		0			0
$672$		0			0
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−1.00000			−1.00000
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$679$		0			0
$680$	1.00000	+	1.73205i	1.00000	+	1.73205i
$681$		0			0
$682$	0.500000	+	0.866025i	0.500000	+	0.866025i
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$		0			0
$685$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$686$		0			0
$687$		0			0
$688$	1.00000			1.00000
$689$		0			0
$690$	−1.00000			−1.00000
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.500000	+	0.866025i	0.500000	+	0.866025i
$697$		0			0
$698$		0			0
$699$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$700$		0			0
$701$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$701$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$702$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$703$		0			0
$704$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$705$	0.500000	−	0.866025i	0.500000	−	0.866025i
$706$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$707$		0			0
$708$	0.500000	+	0.866025i	0.500000	+	0.866025i
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$		0			0
$711$	0.500000	+	0.866025i	0.500000	+	0.866025i
$712$		0			0
$713$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$714$		0			0
$715$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$716$	1.00000			1.00000
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	−1.00000			−1.00000
$721$		0			0
$722$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$723$	1.00000			1.00000
$724$		0			0
$725$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$732$		0			0
$733$	−2.00000			−2.00000			−1.00000			$\pi$
$733$	−2.00000			−2.00000			−1.00000			$\pi$
$734$		0			0
$735$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$736$	−1.00000			−1.00000
$737$	1.00000	+	1.73205i	1.00000	+	1.73205i
$738$		0			0
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	−1.00000			−1.00000
$741$		0			0
$742$		0			0
$743$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$744$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$745$	0.500000	+	0.866025i	0.500000	+	0.866025i
$746$	1.00000			1.00000
$747$		0			0
$748$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$749$		0			0
$750$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$752$	0.500000	−	0.866025i	0.500000	−	0.866025i
$753$	−1.00000			−1.00000
$754$	0.500000	+	0.866025i	0.500000	+	0.866025i
$755$	−2.00000			−2.00000
$756$		0			0
$757$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$757$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$758$		0			0
$759$	1.00000			1.00000
$760$		0			0
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.00000	−	1.73205i	1.00000	−	1.73205i
$766$	−1.00000			−1.00000
$767$	0.500000	+	0.866025i	0.500000	+	0.866025i
$768$	−1.00000			−1.00000
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$770$		0			0
$771$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$775$	−1.00000			−1.00000
$776$		0			0
$777$		0			0
$778$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$779$		0			0
$780$	−1.00000			−1.00000
$781$		0			0
$782$	1.00000	−	1.73205i	1.00000	−	1.73205i
$783$	0.500000	−	0.866025i	0.500000	−	0.866025i
$784$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$785$	−1.00000			−1.00000
$786$	0.500000	+	0.866025i	0.500000	+	0.866025i
$787$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$787$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$788$		0			0
$789$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$790$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$791$		0			0
$792$	1.00000			1.00000
$793$		0			0
$794$	1.00000			1.00000
$795$		0			0
$796$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$797$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$797$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$798$		0			0
$799$	1.00000	+	1.73205i	1.00000	+	1.73205i
$800$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$805$		0			0
$806$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$807$	2.00000			2.00000
$808$	1.00000	−	1.73205i	1.00000	−	1.73205i
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$	0.500000	+	0.866025i	0.500000	+	0.866025i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$814$	1.00000			1.00000
$815$	0.500000	+	0.866025i	0.500000	+	0.866025i
$816$	1.00000	−	1.73205i	1.00000	−	1.73205i
$817$		0			0
$818$	2.00000			2.00000
$819$		0			0
$820$		0			0
$821$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$821$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$822$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	0.500000	+	0.866025i	0.500000	+	0.866025i
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.500000	+	0.866025i	0.500000	+	0.866025i
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$	−1.00000			−1.00000
$832$	−1.00000			−1.00000
$833$	2.00000			2.00000
$834$		0			0
$835$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$836$		0			0
$837$	1.00000			1.00000
$838$	1.00000	+	1.73205i	1.00000	+	1.73205i
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$		0			0
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.00000			−1.00000
$846$	−1.00000			−1.00000
$847$		0			0
$848$		0			0
$849$	0.500000	+	0.866025i	0.500000	+	0.866025i
$850$	2.00000			2.00000
$851$	0.500000	+	0.866025i	0.500000	+	0.866025i
$852$		0			0
$853$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$853$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$857$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$858$	1.00000			1.00000
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	0.500000	−	0.866025i	0.500000	−	0.866025i
$861$		0			0
$862$		0			0
$863$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$863$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$864$	0.500000	+	0.866025i	0.500000	+	0.866025i
$865$		0			0
$866$		0			0
$867$	1.50000	+	2.59808i	1.50000	+	2.59808i
$868$		0			0
$869$	0.500000	−	0.866025i	0.500000	−	0.866025i
$870$	1.00000			1.00000
$871$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$877$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$878$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$879$		0			0
$880$	0.500000	+	0.866025i	0.500000	+	0.866025i
$881$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$881$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$882$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$883$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$883$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$884$	1.00000	−	1.73205i	1.00000	−	1.73205i
$885$	1.00000			1.00000
$886$		0			0
$887$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$887$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$888$	0.500000	+	0.866025i	0.500000	+	0.866025i
$889$		0			0
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$892$		0			0
$893$		0			0
$894$	0.500000	−	0.866025i	0.500000	−	0.866025i
$895$	0.500000	−	0.866025i	0.500000	−	0.866025i
$896$		0			0
$897$	0.500000	+	0.866025i	0.500000	+	0.866025i
$898$		0			0
$899$	0.500000	−	0.866025i	0.500000	−	0.866025i
$900$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.500000	+	0.866025i	0.500000	+	0.866025i
$905$		0			0
$906$	1.00000	+	1.73205i	1.00000	+	1.73205i
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$908$		0			0
$909$	−2.00000			−2.00000
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−2.00000			−2.00000
$919$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$919$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$920$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$921$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$922$	1.00000			1.00000
$923$		0			0
$924$		0			0
$925$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$926$		0			0
$927$		0			0
$928$	1.00000			1.00000
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$	0.500000	+	0.866025i	0.500000	+	0.866025i
$931$		0			0
$932$	0.500000	+	0.866025i	0.500000	+	0.866025i
$933$		0			0
$934$		0			0
$935$	−2.00000			−2.00000
$936$	0.500000	+	0.866025i	0.500000	+	0.866025i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$941$	−2.00000			−2.00000			−1.00000			$\pi$
$941$	−2.00000			−2.00000			−1.00000			$\pi$
$942$	0.500000	+	0.866025i	0.500000	+	0.866025i
$943$		0			0
$944$	1.00000			1.00000
$945$		0			0
$946$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$	1.00000			1.00000
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$953$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.00000			−1.00000
$958$		0			0
$959$		0			0
$960$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$961$		0			0
$962$	0.500000	+	0.866025i	0.500000	+	0.866025i
$963$		0			0
$964$	0.500000	−	0.866025i	0.500000	−	0.866025i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$971$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$972$	0.500000	−	0.866025i	0.500000	−	0.866025i
$973$		0			0
$974$		0			0
$975$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$976$		0			0
$977$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$977$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$978$	0.500000	−	0.866025i	0.500000	−	0.866025i
$979$		0			0
$980$	−1.00000			−1.00000
$981$		0			0
$982$	1.00000	+	1.73205i	1.00000	+	1.73205i
$983$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$983$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$987$		0			0
$988$		0			0
$989$	−1.00000			−1.00000
$990$	0.500000	−	0.866025i	0.500000	−	0.866025i
$991$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$992$	0.500000	+	0.866025i	0.500000	+	0.866025i
$993$		0			0
$994$		0			0
$995$	1.00000	+	1.73205i	1.00000	+	1.73205i
$996$		0			0
$997$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$997$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$	0.500000	−	0.866025i	0.500000	−	0.866025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1560.1.du.b.269.1	yes	2
3.2	odd	2		1560.1.du.d.269.1	yes	2
5.4	even	2		1560.1.du.c.269.1	yes	2
8.5	even	2		1560.1.du.a.269.1	yes	2
13.3	even	3	inner	1560.1.du.b.29.1	yes	2
15.14	odd	2		1560.1.du.a.269.1	yes	2
24.5	odd	2		1560.1.du.c.269.1	yes	2
39.29	odd	6		1560.1.du.d.29.1	yes	2
40.29	even	2		1560.1.du.d.269.1	yes	2
65.29	even	6		1560.1.du.c.29.1	yes	2
104.29	even	6		1560.1.du.a.29.1	✓	2
120.29	odd	2	CM	1560.1.du.b.269.1	yes	2
195.29	odd	6		1560.1.du.a.29.1	✓	2
312.29	odd	6		1560.1.du.c.29.1	yes	2
520.29	even	6		1560.1.du.d.29.1	yes	2
1560.29	odd	6	inner	1560.1.du.b.29.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1560.1.du.a.29.1	✓	2	104.29	even	6
1560.1.du.a.29.1	✓	2	195.29	odd	6
1560.1.du.a.269.1	yes	2	8.5	even	2
1560.1.du.a.269.1	yes	2	15.14	odd	2
1560.1.du.b.29.1	yes	2	13.3	even	3	inner
1560.1.du.b.29.1	yes	2	1560.29	odd	6	inner
1560.1.du.b.269.1	yes	2	1.1	even	1	trivial
1560.1.du.b.269.1	yes	2	120.29	odd	2	CM
1560.1.du.c.29.1	yes	2	65.29	even	6
1560.1.du.c.29.1	yes	2	312.29	odd	6
1560.1.du.c.269.1	yes	2	5.4	even	2
1560.1.du.c.269.1	yes	2	24.5	odd	2
1560.1.du.d.29.1	yes	2	39.29	odd	6
1560.1.du.d.29.1	yes	2	520.29	even	6
1560.1.du.d.269.1	yes	2	3.2	odd	2
1560.1.du.d.269.1	yes	2	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1560.du (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{12} -1.00000 q^{13} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +1.00000 q^{18} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +1.00000 q^{25} +(0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +2.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 + 0.866025i) q^{37} +(-0.500000 + 0.866025i) q^{39} -1.00000 q^{40} +(-0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(0.500000 + 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} -1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(0.500000 - 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{55} +(-0.500000 - 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{59} +1.00000 q^{60} +(0.500000 - 0.866025i) q^{62} +1.00000 q^{64} +1.00000 q^{65} -1.00000 q^{66} +(1.00000 - 1.73205i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-0.500000 - 0.866025i) q^{69} +(-0.500000 - 0.866025i) q^{72} +(-0.500000 - 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{75} +(-0.500000 - 0.866025i) q^{78} -1.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{85} +1.00000 q^{86} +(0.500000 + 0.866025i) q^{87} +(-0.500000 + 0.866025i) q^{88} -1.00000 q^{90} -1.00000 q^{92} +(-0.500000 + 0.866025i) q^{93} +(0.500000 - 0.866025i) q^{94} -1.00000 q^{96} +(-0.500000 - 0.866025i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + q^{6} + 2 q^{8} - q^{9} + q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + q^{20} - q^{22} + q^{23} + q^{24} + 2 q^{25} + q^{26} - 2 q^{27} - q^{29} - q^{30} - 2 q^{31} - q^{32} + q^{33} + 4 q^{34} - q^{36} - q^{37} - q^{39} - 2 q^{40} - q^{43} + 2 q^{44} + q^{45} + q^{46} - 2 q^{47} + q^{48} - q^{49} - q^{50} - 4 q^{51} + q^{52} + q^{54} + q^{55} - q^{58} - q^{59} + 2 q^{60} + q^{62} + 2 q^{64} + 2 q^{65} - 2 q^{66} + 2 q^{67} - 2 q^{68} - q^{69} - q^{72} - q^{74} + q^{75} - q^{78} - 2 q^{79} + q^{80} - q^{81} + 2 q^{85} + 2 q^{86} + q^{87} - q^{88} - 2 q^{90} - 2 q^{92} - q^{93} + q^{94} - 2 q^{96} - q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^5 + q^6 + 2 * q^8 - q^9 + q^10 - q^11 - 2 * q^12 - 2 * q^13 - q^15 - q^16 - 2 * q^17 + 2 * q^18 + q^20 - q^22 + q^23 + q^24 + 2 * q^25 + q^26 - 2 * q^27 - q^29 - q^30 - 2 * q^31 - q^32 + q^33 + 4 * q^34 - q^36 - q^37 - q^39 - 2 * q^40 - q^43 + 2 * q^44 + q^45 + q^46 - 2 * q^47 + q^48 - q^49 - q^50 - 4 * q^51 + q^52 + q^54 + q^55 - q^58 - q^59 + 2 * q^60 + q^62 + 2 * q^64 + 2 * q^65 - 2 * q^66 + 2 * q^67 - 2 * q^68 - q^69 - q^72 - q^74 + q^75 - q^78 - 2 * q^79 + q^80 - q^81 + 2 * q^85 + 2 * q^86 + q^87 - q^88 - 2 * q^90 - 2 * q^92 - q^93 + q^94 - 2 * q^96 - q^98 + 2 * q^99

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