LMFDB - Embedded newform 1512.1.ef.a.517.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,1,Mod(13,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8, 9]))

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

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

chi := DirichletCharacter("1512.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1512.ef (of order $18$, degree $6$, 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:	$0.754586299101$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{9} + \cdots)$

Embedding invariants

Embedding label			517.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1512.517
Dual form			1512.1.ef.a.1357.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.0603074 - 0.342020i) q^{5} +(0.173648 + 0.984808i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.173648 + 0.300767i) q^{10} +(0.173648 - 0.984808i) q^{12} +(0.939693 - 0.342020i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.326352 + 0.118782i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.766044 - 0.642788i) q^{18} +(-0.766044 - 1.32683i) q^{19} +(0.266044 - 0.223238i) q^{20} +(-0.939693 - 0.342020i) q^{21} +(0.266044 + 0.223238i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.826352 + 0.300767i) q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} +0.347296 q^{30} +(0.173648 - 0.984808i) q^{32} +(-0.173648 - 0.300767i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(0.266044 + 1.50881i) q^{38} +(-0.766044 - 0.642788i) q^{39} +(-0.326352 + 0.118782i) q^{40} +(0.766044 + 0.642788i) q^{42} +(0.266044 + 0.223238i) q^{45} +(-0.173648 - 0.300767i) q^{46} +(0.766044 - 0.642788i) q^{48} +(0.173648 - 0.984808i) q^{49} +(-0.673648 - 0.565258i) q^{50} +(0.939693 + 0.342020i) q^{52} +(-0.939693 - 0.342020i) q^{54} +(-0.939693 - 0.342020i) q^{56} +(-0.766044 + 1.32683i) q^{57} +(0.347296 - 1.96962i) q^{59} +(-0.326352 - 0.118782i) q^{60} +(-1.43969 + 1.20805i) q^{61} +(0.173648 + 0.984808i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0603074 - 0.342020i) q^{65} +(0.0603074 - 0.342020i) q^{69} +(0.0603074 + 0.342020i) q^{70} +(-0.173648 + 0.300767i) q^{71} +1.00000 q^{72} +(-0.152704 - 0.866025i) q^{75} +(0.266044 - 1.50881i) q^{76} +(0.500000 + 0.866025i) q^{78} +(-1.43969 - 0.524005i) q^{79} +0.347296 q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.939693 + 0.342020i) q^{83} +(-0.500000 - 0.866025i) q^{84} +(-0.173648 - 0.300767i) q^{90} +(0.500000 - 0.866025i) q^{91} +(0.0603074 + 0.342020i) q^{92} +(-0.500000 + 0.181985i) q^{95} +(-0.939693 + 0.342020i) q^{96} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} + 6 q^{5} - 3 q^{8} - 3 q^{9} - 3 q^{15} - 3 q^{20} - 3 q^{23} - 3 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{38} - 3 q^{40} - 3 q^{45} - 3 q^{50} - 3 q^{60} - 3 q^{61} - 3 q^{64}+ \cdots - 3 q^{98}+O(q^{100}) $ 6 * q - 3 * q^3 + 6 * q^5 - 3 * q^8 - 3 * q^9 - 3 * q^15 - 3 * q^20 - 3 * q^23 - 3 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^38 - 3 * q^40 - 3 * q^45 - 3 * q^50 - 3 * q^60 - 3 * q^61 - 3 * q^64 - 6 * q^65 + 6 * q^69 + 6 * q^70 + 6 * q^72 - 3 * q^75 - 3 * q^76 + 3 * q^78 - 3 * q^79 - 3 * q^81 - 3 * q^84 + 3 * q^91 + 6 * q^92 - 3 * q^95 - 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$	$1$

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 $

$2$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$2$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$3$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$3$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$4$	0.766044	+	0.642788i	0.766044	+	0.642788i
$5$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$5$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$6$	0.173648	+	0.984808i	0.173648	+	0.984808i
$7$	0.766044	−	0.642788i	0.766044	−	0.642788i
$7$	0.766044	−	0.642788i	0.766044	−	0.642788i
$8$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$9$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$10$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$11$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$11$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$12$	0.173648	−	0.984808i	0.173648	−	0.984808i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$14$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$15$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$16$	0.173648	+	0.984808i	0.173648	+	0.984808i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	0.766044	−	0.642788i	0.766044	−	0.642788i
$19$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$19$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$20$	0.266044	−	0.223238i	0.266044	−	0.223238i
$21$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$22$		0			0
$23$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$23$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$25$	0.826352	+	0.300767i	0.826352	+	0.300767i
$26$	−1.00000			−1.00000
$27$	1.00000			1.00000
$28$	1.00000			1.00000
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$	0.347296			0.347296
$31$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$31$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$32$	0.173648	−	0.984808i	0.173648	−	0.984808i
$33$		0			0
$34$		0			0
$35$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$36$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	0.266044	+	1.50881i	0.266044	+	1.50881i
$39$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$40$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$41$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$41$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$42$	0.766044	+	0.642788i	0.766044	+	0.642788i
$43$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$43$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$44$		0			0
$45$	0.266044	+	0.223238i	0.266044	+	0.223238i
$46$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$47$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$47$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$48$	0.766044	−	0.642788i	0.766044	−	0.642788i
$49$	0.173648	−	0.984808i	0.173648	−	0.984808i
$50$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$51$		0			0
$52$	0.939693	+	0.342020i	0.939693	+	0.342020i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$55$		0			0
$56$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$57$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$58$		0			0
$59$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$59$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$60$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$61$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$61$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$62$		0			0
$63$	0.173648	+	0.984808i	0.173648	+	0.984808i
$64$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$65$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$66$		0			0
$67$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$67$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$68$		0			0
$69$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$70$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$71$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$71$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$72$	1.00000			1.00000
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$76$	0.266044	−	1.50881i	0.266044	−	1.50881i
$77$		0			0
$78$	0.500000	+	0.866025i	0.500000	+	0.866025i
$79$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$79$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$80$	0.347296			0.347296
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$		0			0
$83$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$83$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$84$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$91$	0.500000	−	0.866025i	0.500000	−	0.866025i
$92$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$93$		0			0
$94$		0			0
$95$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$96$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$97$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$97$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$98$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$99$		0			0
$100$	0.439693	+	0.761570i	0.439693	+	0.761570i
$101$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$101$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$102$		0			0
$103$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$103$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$104$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$105$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	0.766044	+	0.642788i	0.766044	+	0.642788i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	0.766044	+	0.642788i	0.766044	+	0.642788i
$113$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$113$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$114$	1.17365	−	0.984808i	1.17365	−	0.984808i
$115$	0.0923963	−	0.0775297i	0.0923963	−	0.0775297i
$116$		0			0
$117$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$118$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$119$		0			0
$120$	0.266044	+	0.223238i	0.266044	+	0.223238i
$121$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$122$	1.76604	−	0.642788i	1.76604	−	0.642788i
$123$		0			0
$124$		0			0
$125$	0.326352	−	0.565258i	0.326352	−	0.565258i
$126$	0.173648	−	0.984808i	0.173648	−	0.984808i
$127$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$127$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$128$	0.766044	−	0.642788i	0.766044	−	0.642788i
$129$		0			0
$130$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$131$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$131$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$132$		0			0
$133$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$134$		0			0
$135$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$136$		0			0
$137$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$137$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$138$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$139$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$139$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$140$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$141$		0			0
$142$	0.266044	−	0.223238i	0.266044	−	0.223238i
$143$		0			0
$144$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$145$		0			0
$146$		0			0
$147$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$148$		0			0
$149$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$149$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$150$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$151$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$151$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$152$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$157$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$157$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$158$	1.17365	+	0.984808i	1.17365	+	0.984808i
$159$		0			0
$160$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$161$	0.347296			0.347296
$162$	0.173648	+	0.984808i	0.173648	+	0.984808i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$167$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$167$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$168$	0.173648	+	0.984808i	0.173648	+	0.984808i
$169$		0			0
$170$		0			0
$171$	1.53209			1.53209
$172$		0			0
$173$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$173$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$174$		0			0
$175$	0.826352	−	0.300767i	0.826352	−	0.300767i
$176$		0			0
$177$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$178$		0			0
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$181$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$181$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$182$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$183$	1.76604	+	0.642788i	1.76604	+	0.642788i
$184$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.766044	−	0.642788i	0.766044	−	0.642788i
$190$	0.532089			0.532089
$191$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$191$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$192$	1.00000			1.00000
$193$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$193$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$194$		0			0
$195$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$196$	0.766044	−	0.642788i	0.766044	−	0.642788i
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$201$		0			0
$202$	1.76604	−	0.642788i	1.76604	−	0.642788i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$208$	0.500000	+	0.866025i	0.500000	+	0.866025i
$209$		0			0
$210$	0.266044	−	0.223238i	0.266044	−	0.223238i
$211$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$211$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$212$		0			0
$213$	0.347296			0.347296
$214$		0			0
$215$		0			0
$216$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$223$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$224$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$225$	−0.673648	+	0.565258i	−0.673648	+	0.565258i
$226$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$227$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$227$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$228$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$229$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$229$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$230$	−0.113341	+	0.0412527i	−0.113341	+	0.0412527i
$231$		0			0
$232$		0			0
$233$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$233$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$234$	0.500000	−	0.866025i	0.500000	−	0.866025i
$235$		0			0
$236$	1.53209	−	1.28558i	1.53209	−	1.28558i
$237$	0.266044	+	1.50881i	0.266044	+	1.50881i
$238$		0			0
$239$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$239$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$240$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$241$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$241$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$242$	1.00000			1.00000
$243$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$244$	−1.87939			−1.87939
$245$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$246$		0			0
$247$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$248$		0			0
$249$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$250$	−0.500000	+	0.419550i	−0.500000	+	0.419550i
$251$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$251$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$252$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$253$		0			0
$254$	0.266044	+	1.50881i	0.266044	+	1.50881i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$257$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$257$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$258$		0			0
$259$		0			0
$260$	0.173648	−	0.300767i	0.173648	−	0.300767i
$261$		0			0
$262$	0.939693	+	1.62760i	0.939693	+	1.62760i
$263$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$263$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$264$		0			0
$265$		0			0
$266$	1.17365	+	0.984808i	1.17365	+	0.984808i
$267$		0			0
$268$		0			0
$269$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$269$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$270$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−1.00000			−1.00000
$274$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$275$		0			0
$276$	0.266044	−	0.223238i	0.266044	−	0.223238i
$277$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$277$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$278$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$279$		0			0
$280$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$281$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$282$		0			0
$283$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$284$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$285$	0.407604	+	0.342020i	0.407604	+	0.342020i
$286$		0			0
$287$		0			0
$288$	0.766044	+	0.642788i	0.766044	+	0.642788i
$289$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$293$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$294$	1.00000			1.00000
$295$	−0.652704	−	0.237565i	−0.652704	−	0.237565i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.326352	+	0.118782i	0.326352	+	0.118782i
$300$	0.439693	−	0.761570i	0.439693	−	0.761570i
$301$		0			0
$302$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$303$	1.76604	+	0.642788i	1.76604	+	0.642788i
$304$	1.17365	−	0.984808i	1.17365	−	0.984808i
$305$	0.326352	+	0.565258i	0.326352	+	0.565258i
$306$		0			0
$307$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$307$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$311$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$312$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$313$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$313$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$314$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$315$	0.347296			0.347296
$316$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$317$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$317$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$318$		0			0
$319$		0			0
$320$	0.266044	+	0.223238i	0.266044	+	0.223238i
$321$		0			0
$322$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$323$		0			0
$324$	0.173648	−	0.984808i	0.173648	−	0.984808i
$325$	0.879385			0.879385
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$331$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$332$	0.500000	+	0.866025i	0.500000	+	0.866025i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.173648	−	0.984808i	0.173648	−	0.984808i
$337$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$337$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$338$		0			0
$339$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$340$		0			0
$341$		0			0
$342$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$343$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$344$		0			0
$345$	−0.113341	−	0.0412527i	−0.113341	−	0.0412527i
$346$	0.347296	−	1.96962i	0.347296	−	1.96962i
$347$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$347$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$349$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$350$	−0.879385			−0.879385
$351$	0.939693	−	0.342020i	0.939693	−	0.342020i
$352$		0			0
$353$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$353$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$354$	2.00000			2.00000
$355$	0.0923963	+	0.0775297i	0.0923963	+	0.0775297i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$359$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$360$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$361$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$362$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$363$	0.766044	+	0.642788i	0.766044	+	0.642788i
$364$	0.939693	−	0.342020i	0.939693	−	0.342020i
$365$		0			0
$366$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$367$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$367$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$368$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$373$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$374$		0			0
$375$	−0.652704			−0.652704
$376$		0			0
$377$		0			0
$378$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$381$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$382$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$383$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$383$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$384$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$385$		0			0
$386$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$387$		0			0
$388$		0			0
$389$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$389$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$390$	0.326352	−	0.118782i	0.326352	−	0.118782i
$391$		0			0
$392$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$393$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$394$		0			0
$395$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$396$		0			0
$397$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$397$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$398$		0			0
$399$	0.266044	+	1.50881i	0.266044	+	1.50881i
$400$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$401$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$401$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$402$		0			0
$403$		0			0
$404$	−1.87939			−1.87939
$405$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$409$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$410$		0			0
$411$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$412$		0			0
$413$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$414$	0.347296			0.347296
$415$	0.173648	−	0.300767i	0.173648	−	0.300767i
$416$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$417$	0.266044	−	1.50881i	0.266044	−	1.50881i
$418$		0			0
$419$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$419$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$420$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$421$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$421$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$427$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$431$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$432$	0.173648	+	0.984808i	0.173648	+	0.984808i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$438$		0			0
$439$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$439$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$440$		0			0
$441$	0.766044	+	0.642788i	0.766044	+	0.642788i
$442$		0			0
$443$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$443$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.173648	+	0.984808i	0.173648	+	0.984808i
$449$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$449$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$450$	0.826352	−	0.300767i	0.826352	−	0.300767i
$451$		0			0
$452$	1.17365	−	0.984808i	1.17365	−	0.984808i
$453$	0.266044	−	0.223238i	0.266044	−	0.223238i
$454$	0.266044	−	1.50881i	0.266044	−	1.50881i
$455$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$456$	1.53209			1.53209
$457$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$457$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$458$	−1.87939			−1.87939
$459$		0			0
$460$	0.120615			0.120615
$461$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$461$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$463$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$464$		0			0
$465$		0			0
$466$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$467$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$467$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$468$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$469$		0			0
$470$		0			0
$471$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$472$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$473$		0			0
$474$	0.266044	−	1.50881i	0.266044	−	1.50881i
$475$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$476$		0			0
$477$		0			0
$478$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$479$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$479$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$480$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$481$		0			0
$482$		0			0
$483$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$484$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$485$		0			0
$486$	0.766044	−	0.642788i	0.766044	−	0.642788i
$487$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$487$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$488$	1.76604	+	0.642788i	1.76604	+	0.642788i
$489$		0			0
$490$	0.266044	+	0.223238i	0.266044	+	0.223238i
$491$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$491$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$492$		0			0
$493$		0			0
$494$	0.766044	+	1.32683i	0.766044	+	1.32683i
$495$		0			0
$496$		0			0
$497$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$498$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$499$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$499$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$500$	0.613341	−	0.223238i	0.613341	−	0.223238i
$501$		0			0
$502$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$	0.766044	−	0.642788i	0.766044	−	0.642788i
$505$	0.326352	+	0.565258i	0.326352	+	0.565258i
$506$		0			0
$507$		0			0
$508$	0.266044	−	1.50881i	0.266044	−	1.50881i
$509$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$509$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.53209	−	1.28558i	1.53209	−	1.28558i
$520$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$523$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$524$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$525$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$526$	1.76604	−	0.642788i	1.76604	−	0.642788i
$527$		0			0
$528$		0			0
$529$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$530$		0			0
$531$	1.53209	+	1.28558i	1.53209	+	1.28558i
$532$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$539$		0			0
$540$	0.266044	−	0.223238i	0.266044	−	0.223238i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	0.939693	−	1.62760i	0.939693	−	1.62760i
$544$		0			0
$545$		0			0
$546$	0.939693	+	0.342020i	0.939693	+	0.342020i
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$	0.500000	+	0.866025i	0.500000	+	0.866025i
$549$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$550$		0			0
$551$		0			0
$552$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$553$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$554$		0			0
$555$		0			0
$556$	0.266044	+	1.50881i	0.266044	+	1.50881i
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$	0.266044	−	0.223238i	0.266044	−	0.223238i
$561$		0			0
$562$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$563$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$563$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$564$		0			0
$565$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$566$	0.347296			0.347296
$567$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$568$	0.347296			0.347296
$569$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$569$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$570$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$571$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$571$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$572$		0			0
$573$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$574$		0			0
$575$	0.152704	+	0.264490i	0.152704	+	0.264490i
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.173648	+	0.984808i	0.173648	+	0.984808i
$579$	0.266044	−	1.50881i	0.266044	−	1.50881i
$580$		0			0
$581$	0.939693	−	0.342020i	0.939693	−	0.342020i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.326352	+	0.118782i	0.326352	+	0.118782i
$586$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$587$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$587$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$588$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$589$		0			0
$590$	0.532089	+	0.446476i	0.532089	+	0.446476i
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$599$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$599$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$600$	−0.673648	+	0.565258i	−0.673648	+	0.565258i
$601$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$601$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$602$		0			0
$603$		0			0
$604$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$605$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$606$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$607$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$607$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$608$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$609$		0			0
$610$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	1.17365	−	0.984808i	1.17365	−	0.984808i
$615$		0			0
$616$		0			0
$617$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$617$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$618$		0			0
$619$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$619$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	0.266044	+	0.223238i	0.266044	+	0.223238i
$622$		0			0
$623$		0			0
$624$	0.500000	−	0.866025i	0.500000	−	0.866025i
$625$	0.500000	+	0.419550i	0.500000	+	0.419550i
$626$		0			0
$627$		0			0
$628$	0.266044	−	0.223238i	0.266044	−	0.223238i
$629$		0			0
$630$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$631$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$631$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$632$	0.266044	+	1.50881i	0.266044	+	1.50881i
$633$		0			0
$634$		0			0
$635$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$636$		0			0
$637$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$638$		0			0
$639$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$640$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$641$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$641$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$642$		0			0
$643$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$643$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$644$	0.266044	+	0.223238i	0.266044	+	0.223238i
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$649$		0			0
$650$	−0.826352	−	0.300767i	−0.826352	−	0.300767i
$651$		0			0
$652$		0			0
$653$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$653$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$654$		0			0
$655$	−0.500000	+	0.419550i	−0.500000	+	0.419550i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$661$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$662$		0			0
$663$		0			0
$664$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$665$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$673$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$673$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$674$	−1.00000			−1.00000
$675$	0.826352	+	0.300767i	0.826352	+	0.300767i
$676$		0			0
$677$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$677$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$678$	1.53209			1.53209
$679$		0			0
$680$		0			0
$681$	1.17365	−	0.984808i	1.17365	−	0.984808i
$682$		0			0
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$	1.17365	+	0.984808i	1.17365	+	0.984808i
$685$	0.173648	−	0.300767i	0.173648	−	0.300767i
$686$	0.173648	+	0.984808i	0.173648	+	0.984808i
$687$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$688$		0			0
$689$		0			0
$690$	0.0923963	+	0.0775297i	0.0923963	+	0.0775297i
$691$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$691$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$692$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$693$		0			0
$694$		0			0
$695$	0.407604	−	0.342020i	0.407604	−	0.342020i
$696$		0			0
$697$		0			0
$698$	1.53209	+	1.28558i	1.53209	+	1.28558i
$699$	−1.87939			−1.87939
$700$	0.826352	+	0.300767i	0.826352	+	0.300767i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−1.00000			−1.00000
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$708$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$709$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$709$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$710$	−0.0603074	−	0.104455i	−0.0603074	−	0.104455i
$711$	1.17365	−	0.984808i	1.17365	−	0.984808i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.266044	−	1.50881i	0.266044	−	1.50881i
$718$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$721$		0			0
$722$	1.03209	−	0.866025i	1.03209	−	0.866025i
$723$		0			0
$724$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$725$		0			0
$726$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$727$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$727$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$728$	−1.00000			−1.00000
$729$	1.00000			1.00000
$730$		0			0
$731$		0			0
$732$	0.939693	+	1.62760i	0.939693	+	1.62760i
$733$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$733$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$734$		0			0
$735$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$736$	0.266044	−	0.223238i	0.266044	−	0.223238i
$737$		0			0
$738$		0			0
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$742$		0			0
$743$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$743$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$748$		0			0
$749$		0			0
$750$	0.613341	+	0.223238i	0.613341	+	0.223238i
$751$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$751$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	0.939693	−	1.62760i	0.939693	−	1.62760i
$754$		0			0
$755$	0.120615			0.120615
$756$	1.00000			1.00000
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	0.407604	+	0.342020i	0.407604	+	0.342020i
$761$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$761$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$762$	1.17365	−	0.984808i	1.17365	−	0.984808i
$763$		0			0
$764$	0.939693	+	1.62760i	0.939693	+	1.62760i
$765$		0			0
$766$		0			0
$767$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$768$	0.766044	+	0.642788i	0.766044	+	0.642788i
$769$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$769$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$770$		0			0
$771$		0			0
$772$	0.266044	+	1.50881i	0.266044	+	1.50881i
$773$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$773$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.347296			−0.347296
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$	−0.113341	−	0.0412527i	−0.113341	−	0.0412527i
$786$	0.939693	−	1.62760i	0.939693	−	1.62760i
$787$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$787$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$788$		0			0
$789$	1.76604	+	0.642788i	1.76604	+	0.642788i
$790$	0.407604	−	0.342020i	0.407604	−	0.342020i
$791$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$792$		0			0
$793$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$794$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$795$		0			0
$796$		0			0
$797$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$797$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$798$	0.266044	−	1.50881i	0.266044	−	1.50881i
$799$		0			0
$800$	0.439693	−	0.761570i	0.439693	−	0.761570i
$801$		0			0
$802$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$803$		0			0
$804$		0			0
$805$	0.0209445	−	0.118782i	0.0209445	−	0.118782i
$806$		0			0
$807$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$808$	1.76604	+	0.642788i	1.76604	+	0.642788i
$809$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$809$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$810$	0.347296			0.347296
$811$	2.00000			2.00000			1.00000			$0$
$811$	2.00000			2.00000			1.00000			$0$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.500000	+	0.866025i	0.500000	+	0.866025i
$820$		0			0
$821$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$821$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$822$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$823$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$823$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$824$		0			0
$825$		0			0
$826$	0.347296	+	1.96962i	0.347296	+	1.96962i
$827$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$827$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$828$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$829$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$830$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$831$		0			0
$832$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$833$		0			0
$834$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	1.53209			1.53209
$839$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$839$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$840$	0.347296			0.347296
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$		0			0
$843$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$848$		0			0
$849$	0.266044	+	0.223238i	0.266044	+	0.223238i
$850$		0			0
$851$		0			0
$852$	0.266044	+	0.223238i	0.266044	+	0.223238i
$853$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$853$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$854$	0.939693	−	1.62760i	0.939693	−	1.62760i
$855$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$856$		0			0
$857$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$857$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$858$		0			0
$859$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$859$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$860$		0			0
$861$		0			0
$862$	0.939693	+	0.342020i	0.939693	+	0.342020i
$863$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$863$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$864$	0.173648	−	0.984808i	0.173648	−	0.984808i
$865$	0.694593			0.694593
$866$		0			0
$867$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$875$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$876$		0			0
$877$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$877$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$878$		0			0
$879$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$880$		0			0
$881$		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
$883$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$883$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$884$		0			0
$885$	0.120615	+	0.684040i	0.120615	+	0.684040i
$886$		0			0
$887$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$887$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$888$		0			0
$889$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.173648	−	0.984808i	0.173648	−	0.984808i
$897$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$898$	0.266044	−	0.223238i	0.266044	−	0.223238i
$899$		0			0
$900$	−0.879385			−0.879385
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$905$	0.613341	−	0.223238i	0.613341	−	0.223238i
$906$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$907$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$907$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$908$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$909$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$910$	0.173648	+	0.300767i	0.173648	+	0.300767i
$911$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$911$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$912$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$913$		0			0
$914$	0.266044	+	0.223238i	0.266044	+	0.223238i
$915$	0.326352	−	0.565258i	0.326352	−	0.565258i
$916$	1.76604	+	0.642788i	1.76604	+	0.642788i
$917$	−1.87939			−1.87939
$918$		0			0
$919$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$919$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$920$	−0.113341	−	0.0412527i	−0.113341	−	0.0412527i
$921$	1.53209			1.53209
$922$	0.266044	+	0.223238i	0.266044	+	0.223238i
$923$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$924$		0			0
$925$		0			0
$926$	0.939693	+	1.62760i	0.939693	+	1.62760i
$927$		0			0
$928$		0			0
$929$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$929$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$930$		0			0
$931$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$932$	1.76604	−	0.642788i	1.76604	−	0.642788i
$933$		0			0
$934$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$935$		0			0
$936$	0.939693	−	0.342020i	0.939693	−	0.342020i
$937$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$937$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$941$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$942$	0.347296			0.347296
$943$		0			0
$944$	2.00000			2.00000
$945$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$946$		0			0
$947$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$947$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$948$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$949$		0			0
$950$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$951$		0			0
$952$		0			0
$953$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$954$		0			0
$955$	0.326352	−	0.565258i	0.326352	−	0.565258i
$956$	0.266044	+	1.50881i	0.266044	+	1.50881i
$957$		0			0
$958$		0			0
$959$	0.939693	−	0.342020i	0.939693	−	0.342020i
$960$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$961$	0.173648	+	0.984808i	0.173648	+	0.984808i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.407604	−	0.342020i	0.407604	−	0.342020i
$966$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$967$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$967$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$968$	0.766044	+	0.642788i	0.766044	+	0.642788i
$969$		0			0
$970$		0			0
$971$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$971$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$972$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$973$	1.53209			1.53209
$974$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$975$	−0.439693	−	0.761570i	−0.439693	−	0.761570i
$976$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$977$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$977$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$978$		0			0
$979$		0			0
$980$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$981$		0			0
$982$		0			0
$983$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$983$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$989$		0			0
$990$		0			0
$991$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$991$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$995$		0			0
$996$	0.500000	−	0.866025i	0.500000	−	0.866025i
$997$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$997$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.1.ef.a.517.1	✓	6
7.6	odd	2		1512.1.ef.b.517.1	yes	6
8.5	even	2		1512.1.ef.b.517.1	yes	6
27.7	even	9	inner	1512.1.ef.a.1357.1	yes	6
56.13	odd	2	CM	1512.1.ef.a.517.1	✓	6
189.34	odd	18		1512.1.ef.b.1357.1	yes	6
216.61	even	18		1512.1.ef.b.1357.1	yes	6
1512.1357	odd	18	inner	1512.1.ef.a.1357.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.1.ef.a.517.1	✓	6	1.1	even	1	trivial
1512.1.ef.a.517.1	✓	6	56.13	odd	2	CM
1512.1.ef.a.1357.1	yes	6	27.7	even	9	inner
1512.1.ef.a.1357.1	yes	6	1512.1357	odd	18	inner
1512.1.ef.b.517.1	yes	6	7.6	odd	2
1512.1.ef.b.517.1	yes	6	8.5	even	2
1512.1.ef.b.1357.1	yes	6	189.34	odd	18
1512.1.ef.b.1357.1	yes	6	216.61	even	18

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1512.ef (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.0603074 - 0.342020i) q^{5} +(0.173648 + 0.984808i) q^{6} +(0.766044 - 0.642788i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.173648 + 0.300767i) q^{10} +(0.173648 - 0.984808i) q^{12} +(0.939693 - 0.342020i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(-0.326352 + 0.118782i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.766044 - 0.642788i) q^{18} +(-0.766044 - 1.32683i) q^{19} +(0.266044 - 0.223238i) q^{20} +(-0.939693 - 0.342020i) q^{21} +(0.266044 + 0.223238i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.826352 + 0.300767i) q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} +0.347296 q^{30} +(0.173648 - 0.984808i) q^{32} +(-0.173648 - 0.300767i) q^{35} +(-0.939693 + 0.342020i) q^{36} +(0.266044 + 1.50881i) q^{38} +(-0.766044 - 0.642788i) q^{39} +(-0.326352 + 0.118782i) q^{40} +(0.766044 + 0.642788i) q^{42} +(0.266044 + 0.223238i) q^{45} +(-0.173648 - 0.300767i) q^{46} +(0.766044 - 0.642788i) q^{48} +(0.173648 - 0.984808i) q^{49} +(-0.673648 - 0.565258i) q^{50} +(0.939693 + 0.342020i) q^{52} +(-0.939693 - 0.342020i) q^{54} +(-0.939693 - 0.342020i) q^{56} +(-0.766044 + 1.32683i) q^{57} +(0.347296 - 1.96962i) q^{59} +(-0.326352 - 0.118782i) q^{60} +(-1.43969 + 1.20805i) q^{61} +(0.173648 + 0.984808i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.0603074 - 0.342020i) q^{65} +(0.0603074 - 0.342020i) q^{69} +(0.0603074 + 0.342020i) q^{70} +(-0.173648 + 0.300767i) q^{71} +1.00000 q^{72} +(-0.152704 - 0.866025i) q^{75} +(0.266044 - 1.50881i) q^{76} +(0.500000 + 0.866025i) q^{78} +(-1.43969 - 0.524005i) q^{79} +0.347296 q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.939693 + 0.342020i) q^{83} +(-0.500000 - 0.866025i) q^{84} +(-0.173648 - 0.300767i) q^{90} +(0.500000 - 0.866025i) q^{91} +(0.0603074 + 0.342020i) q^{92} +(-0.500000 + 0.181985i) q^{95} +(-0.939693 + 0.342020i) q^{96} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} + 6 q^{5} - 3 q^{8} - 3 q^{9} - 3 q^{15} - 3 q^{20} - 3 q^{23} - 3 q^{24} + 6 q^{25} - 6 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{38} - 3 q^{40} - 3 q^{45} - 3 q^{50} - 3 q^{60} - 3 q^{61} - 3 q^{64}+ \cdots - 3 q^{98}+O(q^{100}) \) 6 * q - 3 * q^3 + 6 * q^5 - 3 * q^8 - 3 * q^9 - 3 * q^15 - 3 * q^20 - 3 * q^23 - 3 * q^24 + 6 * q^25 - 6 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^38 - 3 * q^40 - 3 * q^45 - 3 * q^50 - 3 * q^60 - 3 * q^61 - 3 * q^64 - 6 * q^65 + 6 * q^69 + 6 * q^70 + 6 * q^72 - 3 * q^75 - 3 * q^76 + 3 * q^78 - 3 * q^79 - 3 * q^81 - 3 * q^84 + 3 * q^91 + 6 * q^92 - 3 * q^95 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more