LMFDB - Embedded newform 2667.1.bf.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,1,Mod(107,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2667.107");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2667.bf (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:	$1.33100638869$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.7112889.1

Embedding invariants

Embedding label			107.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2667.107
Dual form			2667.1.bf.a.1670.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +1.00000i q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.866025 + 0.500000i) q^{14} +(0.866025 - 0.500000i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{17} -1.00000i q^{18} +(0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{22} +1.00000i q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000i q^{26} +1.00000 q^{27} +(0.866025 + 0.500000i) q^{29} +1.00000 q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.866025 - 0.500000i) q^{33} +(0.500000 - 0.866025i) q^{34} +(0.866025 - 0.500000i) q^{35} +(0.866025 - 0.500000i) q^{38} +1.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} -1.00000i q^{42} +(0.500000 - 0.866025i) q^{43} +1.00000i q^{45} +(-0.500000 + 0.866025i) q^{46} +(-0.866025 - 0.500000i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.866025 + 0.500000i) q^{51} -1.00000i q^{53} +(0.866025 + 0.500000i) q^{54} +(0.500000 - 0.866025i) q^{55} +(0.866025 + 0.500000i) q^{56} +(0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} -1.00000i q^{59} +(-0.500000 + 0.866025i) q^{61} +(1.73205 - 1.00000i) q^{62} +1.00000 q^{63} -1.00000 q^{64} +1.00000i q^{65} +(-0.500000 - 0.866025i) q^{66} +(-0.866025 - 0.500000i) q^{69} +1.00000 q^{70} +(-0.866025 + 0.500000i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(0.500000 + 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{77} +(0.866025 + 0.500000i) q^{78} +1.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} +(0.866025 + 0.500000i) q^{83} +(-0.500000 + 0.866025i) q^{85} +(0.866025 - 0.500000i) q^{86} +(-0.866025 + 0.500000i) q^{87} +1.00000 q^{88} +(0.866025 + 0.500000i) q^{89} +(-0.500000 + 0.866025i) q^{90} +1.00000 q^{91} +(1.00000 + 1.73205i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.866025 + 0.500000i) q^{95} +(-0.500000 - 0.866025i) q^{97} -1.00000i q^{98} +(0.866025 - 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9} - 2 q^{10} - 2 q^{13} + 2 q^{16} + 2 q^{19} - 2 q^{21} - 2 q^{22} + 4 q^{27} + 4 q^{30} + 4 q^{31} + 2 q^{34} + 4 q^{39} - 2 q^{40} + 2 q^{43} - 2 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{55} + 2 q^{57} + 2 q^{58} - 2 q^{61} + 4 q^{63} - 4 q^{64} - 2 q^{66} + 4 q^{70} + 2 q^{73} + 4 q^{79} - 2 q^{81} - 2 q^{82} - 2 q^{85} + 4 q^{88} - 2 q^{90} + 4 q^{91} + 4 q^{93} - 2 q^{94} - 2 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9 - 2 * q^10 - 2 * q^13 + 2 * q^16 + 2 * q^19 - 2 * q^21 - 2 * q^22 + 4 * q^27 + 4 * q^30 + 4 * q^31 + 2 * q^34 + 4 * q^39 - 2 * q^40 + 2 * q^43 - 2 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^55 + 2 * q^57 + 2 * q^58 - 2 * q^61 + 4 * q^63 - 4 * q^64 - 2 * q^66 + 4 * q^70 + 2 * q^73 + 4 * q^79 - 2 * q^81 - 2 * q^82 - 2 * q^85 + 4 * q^88 - 2 * q^90 + 4 * q^91 + 4 * q^93 - 2 * q^94 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2667\mathbb{Z}\right)^\times$.

$n$	$890$	$1144$	$2416$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$4$		0			0
$5$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$5$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$6$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$7$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$7$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$8$		−	1.00000i		−	1.00000i
$9$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$10$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$11$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$11$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$13$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$14$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$15$	0.866025	−	0.500000i	0.866025	−	0.500000i
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$17$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$18$		−	1.00000i		−	1.00000i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$20$		0			0
$21$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$22$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$23$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$23$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.866025	+	0.500000i	0.866025	+	0.500000i
$25$		0			0
$26$		−	1.00000i		−	1.00000i
$27$	1.00000			1.00000
$28$		0			0
$29$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$29$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$30$	1.00000			1.00000
$31$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$31$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$32$		0			0
$33$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$34$	0.500000	−	0.866025i	0.500000	−	0.866025i
$35$	0.866025	−	0.500000i	0.866025	−	0.500000i
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	0.866025	−	0.500000i	0.866025	−	0.500000i
$39$	1.00000			1.00000
$40$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$42$		−	1.00000i		−	1.00000i
$43$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$43$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$44$		0			0
$45$			1.00000i			1.00000i
$46$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$47$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$47$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$		0			0
$51$	0.866025	+	0.500000i	0.866025	+	0.500000i
$52$		0			0
$53$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$53$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$54$	0.866025	+	0.500000i	0.866025	+	0.500000i
$55$	0.500000	−	0.866025i	0.500000	−	0.866025i
$56$	0.866025	+	0.500000i	0.866025	+	0.500000i
$57$	0.500000	+	0.866025i	0.500000	+	0.866025i
$58$	0.500000	+	0.866025i	0.500000	+	0.866025i
$59$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$59$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$61$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$62$	1.73205	−	1.00000i	1.73205	−	1.00000i
$63$	1.00000			1.00000
$64$	−1.00000			−1.00000
$65$			1.00000i			1.00000i
$66$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$		0			0
$69$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$70$	1.00000			1.00000
$71$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$71$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$72$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$73$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$78$	0.866025	+	0.500000i	0.866025	+	0.500000i
$79$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$79$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$80$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$81$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$82$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$83$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$83$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$84$		0			0
$85$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$86$	0.866025	−	0.500000i	0.866025	−	0.500000i
$87$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$88$	1.00000			1.00000
$89$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$89$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$90$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$91$	1.00000			1.00000
$92$		0			0
$93$	1.00000	+	1.73205i	1.00000	+	1.73205i
$94$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$95$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$96$		0			0
$97$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$97$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$98$		−	1.00000i		−	1.00000i
$99$	0.866025	−	0.500000i	0.866025	−	0.500000i
$100$		0			0
$101$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$102$	0.500000	+	0.866025i	0.500000	+	0.866025i
$103$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$103$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$104$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$105$			1.00000i			1.00000i
$106$	0.500000	−	0.866025i	0.500000	−	0.866025i
$107$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$107$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$109$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$110$	0.866025	−	0.500000i	0.866025	−	0.500000i
$111$		0			0
$112$	0.500000	+	0.866025i	0.500000	+	0.866025i
$113$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$113$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$114$			1.00000i			1.00000i
$115$	0.500000	−	0.866025i	0.500000	−	0.866025i
$116$		0			0
$117$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$118$	0.500000	−	0.866025i	0.500000	−	0.866025i
$119$	0.866025	+	0.500000i	0.866025	+	0.500000i
$120$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$121$		0			0
$122$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$123$	0.866025	−	0.500000i	0.866025	−	0.500000i
$124$		0			0
$125$			1.00000i			1.00000i
$126$	0.866025	+	0.500000i	0.866025	+	0.500000i
$127$	−1.00000			−1.00000
$127$	−1.00000			−1.00000
$128$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$129$	0.500000	+	0.866025i	0.500000	+	0.866025i
$130$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	0.500000	+	0.866025i	0.500000	+	0.866025i
$134$		0			0
$135$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$136$	−1.00000			−1.00000
$137$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$137$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$138$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$139$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$139$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$140$		0			0
$141$	0.866025	−	0.500000i	0.866025	−	0.500000i
$142$	−1.00000			−1.00000
$143$	0.866025	−	0.500000i	0.866025	−	0.500000i
$144$	−1.00000			−1.00000
$145$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$146$			1.00000i			1.00000i
$147$	1.00000			1.00000
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$153$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$154$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$155$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$156$		0			0
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$	0.866025	+	0.500000i	0.866025	+	0.500000i
$159$	0.866025	+	0.500000i	0.866025	+	0.500000i
$160$		0			0
$161$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$162$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$163$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$163$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$164$		0			0
$165$	0.500000	+	0.866025i	0.500000	+	0.866025i
$166$	0.500000	+	0.866025i	0.500000	+	0.866025i
$167$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$167$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$168$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$169$		0			0
$170$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$171$	−1.00000			−1.00000
$172$		0			0
$173$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$173$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$174$	−1.00000			−1.00000
$175$		0			0
$176$	0.866025	+	0.500000i	0.866025	+	0.500000i
$177$	0.866025	+	0.500000i	0.866025	+	0.500000i
$178$	0.500000	+	0.866025i	0.500000	+	0.866025i
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	0.866025	+	0.500000i	0.866025	+	0.500000i
$183$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$184$	1.00000			1.00000
$185$		0			0
$186$			2.00000i			2.00000i
$187$	1.00000			1.00000
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$190$	−1.00000			−1.00000
$191$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$191$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$193$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$194$		−	1.00000i		−	1.00000i
$195$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$196$		0			0
$197$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$197$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$198$	1.00000			1.00000
$199$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$199$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$200$		0			0
$201$		0			0
$202$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$203$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$204$		0			0
$205$	0.500000	+	0.866025i	0.500000	+	0.866025i
$206$	0.866025	+	0.500000i	0.866025	+	0.500000i
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$	−1.00000			−1.00000
$209$	0.866025	+	0.500000i	0.866025	+	0.500000i
$210$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$211$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$212$		0			0
$213$		−	1.00000i		−	1.00000i
$214$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$215$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$216$		−	1.00000i		−	1.00000i
$217$	1.00000	+	1.73205i	1.00000	+	1.73205i
$218$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$219$	−1.00000			−1.00000
$220$		0			0
$221$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$222$		0			0
$223$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$223$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$224$		0			0
$225$		0			0
$226$	1.00000			1.00000
$227$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$227$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$228$		0			0
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$230$	0.866025	−	0.500000i	0.866025	−	0.500000i
$231$	0.866025	−	0.500000i	0.866025	−	0.500000i
$232$	0.500000	−	0.866025i	0.500000	−	0.866025i
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$235$	0.500000	+	0.866025i	0.500000	+	0.866025i
$236$		0			0
$237$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$238$	0.500000	+	0.866025i	0.500000	+	0.866025i
$239$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$239$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$240$		−	1.00000i		−	1.00000i
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$244$		0			0
$245$			1.00000i			1.00000i
$246$	1.00000			1.00000
$247$	−1.00000			−1.00000
$248$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$249$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$250$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$251$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$251$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$252$		0			0
$253$	−1.00000			−1.00000
$254$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$255$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$256$		0			0
$257$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$257$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$258$			1.00000i			1.00000i
$259$		0			0
$260$		0			0
$261$		−	1.00000i		−	1.00000i
$262$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$263$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$264$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$265$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$266$			1.00000i			1.00000i
$267$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$268$		0			0
$269$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$269$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$270$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$273$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$274$	−1.00000			−1.00000
$275$		0			0
$276$		0			0
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$		−	1.00000i		−	1.00000i
$279$	−2.00000			−2.00000
$280$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$281$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$281$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$282$	1.00000			1.00000
$283$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$283$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$284$		0			0
$285$		−	1.00000i		−	1.00000i
$286$	1.00000			1.00000
$287$	0.866025	−	0.500000i	0.866025	−	0.500000i
$288$		0			0
$289$		0			0
$290$		−	1.00000i		−	1.00000i
$291$	1.00000			1.00000
$292$		0			0
$293$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$293$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$294$	0.866025	+	0.500000i	0.866025	+	0.500000i
$295$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$296$		0			0
$297$			1.00000i			1.00000i
$298$		0			0
$299$	0.866025	−	0.500000i	0.866025	−	0.500000i
$300$		0			0
$301$	0.500000	+	0.866025i	0.500000	+	0.866025i
$302$		0			0
$303$	1.73205	−	1.00000i	1.73205	−	1.00000i
$304$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$305$	0.866025	−	0.500000i	0.866025	−	0.500000i
$306$	−1.00000			−1.00000
$307$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$307$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$308$		0			0
$309$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$310$	−2.00000			−2.00000
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$		−	1.00000i		−	1.00000i
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$		0			0
$315$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$316$		0			0
$317$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$317$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$318$	0.500000	+	0.866025i	0.500000	+	0.866025i
$319$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$320$	0.866025	+	0.500000i	0.866025	+	0.500000i
$321$	0.866025	−	0.500000i	0.866025	−	0.500000i
$322$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$323$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.500000	−	0.866025i	0.500000	−	0.866025i
$328$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$329$	0.866025	−	0.500000i	0.866025	−	0.500000i
$330$			1.00000i			1.00000i
$331$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$332$		0			0
$333$		0			0
$334$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$335$		0			0
$336$	−1.00000			−1.00000
$337$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$337$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$338$		0			0
$339$			1.00000i			1.00000i
$340$		0			0
$341$	1.73205	+	1.00000i	1.73205	+	1.00000i
$342$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$343$	1.00000			1.00000
$344$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$345$	0.500000	+	0.866025i	0.500000	+	0.866025i
$346$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$347$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$347$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$352$		0			0
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$	0.500000	+	0.866025i	0.500000	+	0.866025i
$355$	1.00000			1.00000
$356$		0			0
$357$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$358$		0			0
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$	1.00000			1.00000
$361$		0			0
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	1.00000i		−	1.00000i
$366$		−	1.00000i		−	1.00000i
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	0.866025	+	0.500000i	0.866025	+	0.500000i
$369$			1.00000i			1.00000i
$370$		0			0
$371$	0.866025	+	0.500000i	0.866025	+	0.500000i
$372$		0			0
$373$	−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			$\pi$
$374$	0.866025	+	0.500000i	0.866025	+	0.500000i
$375$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$376$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$377$		−	1.00000i		−	1.00000i
$378$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	0.500000	−	0.866025i	0.500000	−	0.866025i
$382$	0.500000	+	0.866025i	0.500000	+	0.866025i
$383$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$383$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$384$	0.866025	−	0.500000i	0.866025	−	0.500000i
$385$	0.500000	+	0.866025i	0.500000	+	0.866025i
$386$		−	1.00000i		−	1.00000i
$387$	−1.00000			−1.00000
$388$		0			0
$389$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$389$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$390$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$391$	1.00000			1.00000
$392$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$393$	0.866025	−	0.500000i	0.866025	−	0.500000i
$394$	1.00000			1.00000
$395$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$396$		0			0
$397$	−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			$\pi$
$398$	0.866025	+	0.500000i	0.866025	+	0.500000i
$399$	−1.00000			−1.00000
$400$		0			0
$401$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$401$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$402$		0			0
$403$	−2.00000			−2.00000
$404$		0			0
$405$	0.866025	−	0.500000i	0.866025	−	0.500000i
$406$	−1.00000			−1.00000
$407$		0			0
$408$	0.500000	−	0.866025i	0.500000	−	0.866025i
$409$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$			1.00000i			1.00000i
$411$		−	1.00000i		−	1.00000i
$412$		0			0
$413$	0.866025	+	0.500000i	0.866025	+	0.500000i
$414$	1.00000			1.00000
$415$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$416$		0			0
$417$	1.00000			1.00000
$418$	0.500000	+	0.866025i	0.500000	+	0.866025i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	0.866025	−	0.500000i	0.866025	−	0.500000i
$423$			1.00000i			1.00000i
$424$	−1.00000			−1.00000
$425$		0			0
$426$	0.500000	−	0.866025i	0.500000	−	0.866025i
$427$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$428$		0			0
$429$			1.00000i			1.00000i
$430$	−1.00000			−1.00000
$431$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$431$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$433$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$434$			2.00000i			2.00000i
$435$	1.00000			1.00000
$436$		0			0
$437$	0.866025	+	0.500000i	0.866025	+	0.500000i
$438$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$441$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$442$	−1.00000			−1.00000
$443$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$443$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$446$			1.00000i			1.00000i
$447$		0			0
$448$	0.500000	−	0.866025i	0.500000	−	0.866025i
$449$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$449$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$450$		0			0
$451$	0.500000	−	0.866025i	0.500000	−	0.866025i
$452$		0			0
$453$		0			0
$454$	−1.00000			−1.00000
$455$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$456$	0.866025	−	0.500000i	0.866025	−	0.500000i
$457$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$457$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$458$	0.866025	−	0.500000i	0.866025	−	0.500000i
$459$		−	1.00000i		−	1.00000i
$460$		0			0
$461$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$461$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$462$	1.00000			1.00000
$463$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$463$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$464$	0.866025	−	0.500000i	0.866025	−	0.500000i
$465$		−	2.00000i		−	2.00000i
$466$		0			0
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$		0			0
$469$		0			0
$470$			1.00000i			1.00000i
$471$		0			0
$472$	−1.00000			−1.00000
$473$	0.866025	+	0.500000i	0.866025	+	0.500000i
$474$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$475$		0			0
$476$		0			0
$477$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$478$	1.00000			1.00000
$479$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$479$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	0.866025	−	0.500000i	0.866025	−	0.500000i
$484$		0			0
$485$			1.00000i			1.00000i
$486$		−	1.00000i		−	1.00000i
$487$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$487$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$488$	0.866025	+	0.500000i	0.866025	+	0.500000i
$489$		0			0
$490$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$491$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$491$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$492$		0			0
$493$	0.500000	−	0.866025i	0.500000	−	0.866025i
$494$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$495$	−1.00000			−1.00000
$496$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$497$		−	1.00000i		−	1.00000i
$498$	−1.00000			−1.00000
$499$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$499$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$502$	−1.00000			−1.00000
$503$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$503$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$504$		−	1.00000i		−	1.00000i
$505$	1.00000	+	1.73205i	1.00000	+	1.73205i
$506$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$507$		0			0
$508$		0			0
$509$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$509$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$510$		−	1.00000i		−	1.00000i
$511$	−1.00000			−1.00000
$512$			1.00000i			1.00000i
$513$	0.500000	−	0.866025i	0.500000	−	0.866025i
$514$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$515$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$516$		0			0
$517$	0.500000	−	0.866025i	0.500000	−	0.866025i
$518$		0			0
$519$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$520$	1.00000			1.00000
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$	0.500000	−	0.866025i	0.500000	−	0.866025i
$523$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$523$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$524$		0			0
$525$		0			0
$526$	0.500000	−	0.866025i	0.500000	−	0.866025i
$527$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$528$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$529$		0			0
$530$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$531$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$532$		0			0
$533$			1.00000i			1.00000i
$534$	−1.00000			−1.00000
$535$	0.500000	+	0.866025i	0.500000	+	0.866025i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.866025	−	0.500000i	0.866025	−	0.500000i
$540$		0			0
$541$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$541$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.866025	+	0.500000i	0.866025	+	0.500000i
$546$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$547$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$547$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$548$		0			0
$549$	1.00000			1.00000
$550$		0			0
$551$	0.866025	−	0.500000i	0.866025	−	0.500000i
$552$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$553$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$557$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$558$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$559$	−1.00000			−1.00000
$560$		−	1.00000i		−	1.00000i
$561$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$562$	1.00000	−	1.73205i	1.00000	−	1.73205i
$563$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$563$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$564$		0			0
$565$	−1.00000			−1.00000
$566$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$567$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$568$	0.500000	+	0.866025i	0.500000	+	0.866025i
$569$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$569$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$570$	0.500000	−	0.866025i	0.500000	−	0.866025i
$571$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$571$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$574$	1.00000			1.00000
$575$		0			0
$576$	0.500000	+	0.866025i	0.500000	+	0.866025i
$577$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$577$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$578$		0			0
$579$	1.00000			1.00000
$580$		0			0
$581$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$582$	0.866025	+	0.500000i	0.866025	+	0.500000i
$583$	1.00000			1.00000
$584$	0.866025	−	0.500000i	0.866025	−	0.500000i
$585$	0.866025	−	0.500000i	0.866025	−	0.500000i
$586$	0.500000	+	0.866025i	0.500000	+	0.866025i
$587$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$587$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$588$		0			0
$589$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$590$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$591$			1.00000i			1.00000i
$592$		0			0
$593$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$593$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$594$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$595$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$596$		0			0
$597$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$598$	1.00000			1.00000
$599$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$599$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$602$			1.00000i			1.00000i
$603$		0			0
$604$		0			0
$605$		0			0
$606$	2.00000			2.00000
$607$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$		−	1.00000i		−	1.00000i
$610$	1.00000			1.00000
$611$			1.00000i			1.00000i
$612$		0			0
$613$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$613$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$614$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$615$	−1.00000			−1.00000
$616$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$617$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$617$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$618$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$619$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$620$		0			0
$621$			1.00000i			1.00000i
$622$		0			0
$623$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$624$	0.500000	−	0.866025i	0.500000	−	0.866025i
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		0			0
$627$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$628$		0			0
$629$		0			0
$630$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$631$	2.00000			2.00000			1.00000			$0$
$631$	2.00000			2.00000			1.00000			$0$
$632$		−	1.00000i		−	1.00000i
$633$	0.500000	+	0.866025i	0.500000	+	0.866025i
$634$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$635$	0.866025	+	0.500000i	0.866025	+	0.500000i
$636$		0			0
$637$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$638$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$639$	0.866025	+	0.500000i	0.866025	+	0.500000i
$640$	0.500000	+	0.866025i	0.500000	+	0.866025i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	1.00000			1.00000
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$		−	1.00000i		−	1.00000i
$646$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$647$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$647$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$648$	0.866025	+	0.500000i	0.866025	+	0.500000i
$649$	1.00000			1.00000
$650$		0			0
$651$	−2.00000			−2.00000
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	0.866025	−	0.500000i	0.866025	−	0.500000i
$655$	0.500000	+	0.866025i	0.500000	+	0.866025i
$656$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$657$	0.500000	−	0.866025i	0.500000	−	0.866025i
$658$	1.00000			1.00000
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	0.866025	−	0.500000i	0.866025	−	0.500000i
$663$		−	1.00000i		−	1.00000i
$664$	0.500000	−	0.866025i	0.500000	−	0.866025i
$665$		−	1.00000i		−	1.00000i
$666$		0			0
$667$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$668$		0			0
$669$	−1.00000			−1.00000
$670$		0			0
$671$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$672$		0			0
$673$	2.00000			2.00000			1.00000			$0$
$673$	2.00000			2.00000			1.00000			$0$
$674$	0.866025	−	0.500000i	0.866025	−	0.500000i
$675$		0			0
$676$		0			0
$677$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$677$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$678$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$679$	1.00000			1.00000
$680$	0.866025	+	0.500000i	0.866025	+	0.500000i
$681$		−	1.00000i		−	1.00000i
$682$	1.00000	+	1.73205i	1.00000	+	1.73205i
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$	1.00000			1.00000
$686$	0.866025	+	0.500000i	0.866025	+	0.500000i
$687$	0.500000	+	0.866025i	0.500000	+	0.866025i
$688$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$689$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$690$			1.00000i			1.00000i
$691$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$691$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$			1.00000i			1.00000i
$694$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$695$			1.00000i			1.00000i
$696$	0.500000	+	0.866025i	0.500000	+	0.866025i
$697$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$701$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$702$		−	1.00000i		−	1.00000i
$703$		0			0
$704$		−	1.00000i		−	1.00000i
$705$	−1.00000			−1.00000
$706$		0			0
$707$	1.73205	−	1.00000i	1.73205	−	1.00000i
$708$		0			0
$709$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$709$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$710$	0.866025	+	0.500000i	0.866025	+	0.500000i
$711$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$712$	0.500000	−	0.866025i	0.500000	−	0.866025i
$713$	1.73205	+	1.00000i	1.73205	+	1.00000i
$714$	−1.00000			−1.00000
$715$	−1.00000			−1.00000
$716$		0			0
$717$			1.00000i			1.00000i
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	0.866025	+	0.500000i	0.866025	+	0.500000i
$721$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$727$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$728$		−	1.00000i		−	1.00000i
$729$	1.00000			1.00000
$730$	0.500000	−	0.866025i	0.500000	−	0.866025i
$731$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$732$		0			0
$733$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$733$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$736$		0			0
$737$		0			0
$738$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$		0			0
$741$	0.500000	−	0.866025i	0.500000	−	0.866025i
$742$	0.500000	+	0.866025i	0.500000	+	0.866025i
$743$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$743$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$744$	1.73205	−	1.00000i	1.73205	−	1.00000i
$745$		0			0
$746$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$747$		−	1.00000i		−	1.00000i
$748$		0			0
$749$	0.866025	−	0.500000i	0.866025	−	0.500000i
$750$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$751$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$752$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$753$		−	1.00000i		−	1.00000i
$754$	0.500000	−	0.866025i	0.500000	−	0.866025i
$755$		0			0
$756$		0			0
$757$		0			0			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$		0			0
$759$	0.500000	−	0.866025i	0.500000	−	0.866025i
$760$	0.500000	+	0.866025i	0.500000	+	0.866025i
$761$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$761$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$762$	0.866025	−	0.500000i	0.866025	−	0.500000i
$763$	0.500000	−	0.866025i	0.500000	−	0.866025i
$764$		0			0
$765$	1.00000			1.00000
$766$	0.500000	+	0.866025i	0.500000	+	0.866025i
$767$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$768$		0			0
$769$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$769$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$770$			1.00000i			1.00000i
$771$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$772$		0			0
$773$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$773$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$774$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$775$		0			0
$776$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$777$		0			0
$778$	1.00000			1.00000
$779$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$780$		0			0
$781$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$782$	0.866025	+	0.500000i	0.866025	+	0.500000i
$783$	0.866025	+	0.500000i	0.866025	+	0.500000i
$784$	−1.00000			−1.00000
$785$		0			0
$786$	1.00000			1.00000
$787$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$787$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$	0.866025	+	0.500000i	0.866025	+	0.500000i
$790$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$791$			1.00000i			1.00000i
$792$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$793$	1.00000			1.00000
$794$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$795$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$796$		0			0
$797$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$797$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$798$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$799$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$800$		0			0
$801$		−	1.00000i		−	1.00000i
$802$	0.500000	+	0.866025i	0.500000	+	0.866025i
$803$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$804$		0			0
$805$	0.500000	+	0.866025i	0.500000	+	0.866025i
$806$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$807$		0			0
$808$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$809$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$809$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$810$	1.00000			1.00000
$811$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$811$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.866025	−	0.500000i	0.866025	−	0.500000i
$817$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$818$		0			0
$819$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$820$		0			0
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$	0.500000	−	0.866025i	0.500000	−	0.866025i
$823$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$823$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$824$		−	1.00000i		−	1.00000i
$825$		0			0
$826$	0.500000	+	0.866025i	0.500000	+	0.866025i
$827$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$827$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$828$		0			0
$829$	−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	$0.666667\pi$
$830$		−	1.00000i		−	1.00000i
$831$		0			0
$832$	0.500000	+	0.866025i	0.500000	+	0.866025i
$833$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$834$	0.866025	+	0.500000i	0.866025	+	0.500000i
$835$	1.00000	−	1.73205i	1.00000	−	1.73205i
$836$		0			0
$837$	1.00000	−	1.73205i	1.00000	−	1.73205i
$838$		0			0
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$	1.00000			1.00000
$841$		0			0
$842$		0			0
$843$	1.73205	+	1.00000i	1.73205	+	1.00000i
$844$		0			0
$845$		0			0
$846$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$847$		0			0
$848$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$849$	0.500000	−	0.866025i	0.500000	−	0.866025i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$853$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$854$		−	1.00000i		−	1.00000i
$855$	0.866025	+	0.500000i	0.866025	+	0.500000i
$856$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$857$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$857$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$858$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$859$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$859$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$			1.00000i			1.00000i
$862$	1.00000			1.00000
$863$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$863$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$864$		0			0
$865$	0.500000	−	0.866025i	0.500000	−	0.866025i
$866$		−	1.00000i		−	1.00000i
$867$		0			0
$868$		0			0
$869$			1.00000i			1.00000i
$870$	0.866025	+	0.500000i	0.866025	+	0.500000i
$871$		0			0
$872$			1.00000i			1.00000i
$873$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$874$	0.500000	+	0.866025i	0.500000	+	0.866025i
$875$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$876$		0			0
$877$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$877$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$880$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$883$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$883$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$884$		0			0
$885$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$886$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$887$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$887$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$	0.500000	−	0.866025i	0.500000	−	0.866025i
$890$		−	1.00000i		−	1.00000i
$891$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$892$		0			0
$893$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$894$		0			0
$895$		0			0
$896$	0.866025	−	0.500000i	0.866025	−	0.500000i
$897$			1.00000i			1.00000i
$898$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$899$	1.73205	−	1.00000i	1.73205	−	1.00000i
$900$		0			0
$901$	−1.00000			−1.00000
$902$	0.866025	−	0.500000i	0.866025	−	0.500000i
$903$	−1.00000			−1.00000
$904$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$905$		0			0
$906$		0			0
$907$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$907$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$			2.00000i			2.00000i
$910$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$912$	1.00000			1.00000
$913$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$914$	0.866025	−	0.500000i	0.866025	−	0.500000i
$915$			1.00000i			1.00000i
$916$		0			0
$917$	0.866025	−	0.500000i	0.866025	−	0.500000i
$918$	0.500000	−	0.866025i	0.500000	−	0.866025i
$919$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$919$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$920$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$921$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$922$	1.00000	−	1.73205i	1.00000	−	1.73205i
$923$	0.866025	+	0.500000i	0.866025	+	0.500000i
$924$		0			0
$925$		0			0
$926$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$927$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$928$		0			0
$929$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$929$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$930$	1.00000	−	1.73205i	1.00000	−	1.73205i
$931$	−1.00000			−1.00000
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$936$	0.866025	+	0.500000i	0.866025	+	0.500000i
$937$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$937$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$941$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$942$		0			0
$943$	0.500000	−	0.866025i	0.500000	−	0.866025i
$944$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$945$	0.866025	−	0.500000i	0.866025	−	0.500000i
$946$	0.500000	+	0.866025i	0.500000	+	0.866025i
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$	0.500000	−	0.866025i	0.500000	−	0.866025i
$950$		0			0
$951$	0.866025	−	0.500000i	0.866025	−	0.500000i
$952$	0.500000	−	0.866025i	0.500000	−	0.866025i
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	−1.00000			−1.00000
$955$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$956$		0			0
$957$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$958$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$959$		−	1.00000i		−	1.00000i
$960$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$961$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$962$		0			0
$963$			1.00000i			1.00000i
$964$		0			0
$965$			1.00000i			1.00000i
$966$	1.00000			1.00000
$967$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$967$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$968$		0			0
$969$	0.866025	−	0.500000i	0.866025	−	0.500000i
$970$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$		0			0
$973$	1.00000			1.00000
$974$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$975$		0			0
$976$	0.500000	+	0.866025i	0.500000	+	0.866025i
$977$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$977$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$978$		0			0
$979$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$980$		0			0
$981$	0.500000	+	0.866025i	0.500000	+	0.866025i
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$984$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$985$	−1.00000			−1.00000
$986$	0.866025	−	0.500000i	0.866025	−	0.500000i
$987$			1.00000i			1.00000i
$988$		0			0
$989$	0.866025	+	0.500000i	0.866025	+	0.500000i
$990$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$	0.500000	+	0.866025i	0.500000	+	0.866025i
$994$	0.500000	−	0.866025i	0.500000	−	0.866025i
$995$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$996$		0			0
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$998$			2.00000i			2.00000i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.1.bf.a.107.2	yes	4
3.2	odd	2	inner	2667.1.bf.a.107.1	✓	4
7.4	even	3		2667.1.bi.a.1250.1	yes	4
21.11	odd	6		2667.1.bi.a.1250.2	yes	4
127.19	even	3		2667.1.bi.a.527.2	yes	4
381.146	odd	6		2667.1.bi.a.527.1	yes	4
889.781	even	3	inner	2667.1.bf.a.1670.1	yes	4
2667.1670	odd	6	inner	2667.1.bf.a.1670.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.1.bf.a.107.1	✓	4	3.2	odd	2	inner
2667.1.bf.a.107.2	yes	4	1.1	even	1	trivial
2667.1.bf.a.1670.1	yes	4	889.781	even	3	inner
2667.1.bf.a.1670.2	yes	4	2667.1670	odd	6	inner
2667.1.bi.a.527.1	yes	4	381.146	odd	6
2667.1.bi.a.527.2	yes	4	127.19	even	3
2667.1.bi.a.1250.1	yes	4	7.4	even	3
2667.1.bi.a.1250.2	yes	4	21.11	odd	6

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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2667.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +1.00000i q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.866025 + 0.500000i) q^{14} +(0.866025 - 0.500000i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{17} -1.00000i q^{18} +(0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(-0.500000 + 0.866025i) q^{22} +1.00000i q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000i q^{26} +1.00000 q^{27} +(0.866025 + 0.500000i) q^{29} +1.00000 q^{30} +(1.00000 - 1.73205i) q^{31} +(-0.866025 - 0.500000i) q^{33} +(0.500000 - 0.866025i) q^{34} +(0.866025 - 0.500000i) q^{35} +(0.866025 - 0.500000i) q^{38} +1.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} -1.00000i q^{42} +(0.500000 - 0.866025i) q^{43} +1.00000i q^{45} +(-0.500000 + 0.866025i) q^{46} +(-0.866025 - 0.500000i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.866025 + 0.500000i) q^{51} -1.00000i q^{53} +(0.866025 + 0.500000i) q^{54} +(0.500000 - 0.866025i) q^{55} +(0.866025 + 0.500000i) q^{56} +(0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} -1.00000i q^{59} +(-0.500000 + 0.866025i) q^{61} +(1.73205 - 1.00000i) q^{62} +1.00000 q^{63} -1.00000 q^{64} +1.00000i q^{65} +(-0.500000 - 0.866025i) q^{66} +(-0.866025 - 0.500000i) q^{69} +1.00000 q^{70} +(-0.866025 + 0.500000i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(0.500000 + 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{77} +(0.866025 + 0.500000i) q^{78} +1.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} +(0.866025 + 0.500000i) q^{83} +(-0.500000 + 0.866025i) q^{85} +(0.866025 - 0.500000i) q^{86} +(-0.866025 + 0.500000i) q^{87} +1.00000 q^{88} +(0.866025 + 0.500000i) q^{89} +(-0.500000 + 0.866025i) q^{90} +1.00000 q^{91} +(1.00000 + 1.73205i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-0.866025 + 0.500000i) q^{95} +(-0.500000 - 0.866025i) q^{97} -1.00000i q^{98} +(0.866025 - 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{7} - 2 q^{9} - 2 q^{10} - 2 q^{13} + 2 q^{16} + 2 q^{19} - 2 q^{21} - 2 q^{22} + 4 q^{27} + 4 q^{30} + 4 q^{31} + 2 q^{34} + 4 q^{39} - 2 q^{40} + 2 q^{43} - 2 q^{46} + 2 q^{48} - 2 q^{49} + 2 q^{55} + 2 q^{57} + 2 q^{58} - 2 q^{61} + 4 q^{63} - 4 q^{64} - 2 q^{66} + 4 q^{70} + 2 q^{73} + 4 q^{79} - 2 q^{81} - 2 q^{82} - 2 q^{85} + 4 q^{88} - 2 q^{90} + 4 q^{91} + 4 q^{93} - 2 q^{94} - 2 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^7 - 2 * q^9 - 2 * q^10 - 2 * q^13 + 2 * q^16 + 2 * q^19 - 2 * q^21 - 2 * q^22 + 4 * q^27 + 4 * q^30 + 4 * q^31 + 2 * q^34 + 4 * q^39 - 2 * q^40 + 2 * q^43 - 2 * q^46 + 2 * q^48 - 2 * q^49 + 2 * q^55 + 2 * q^57 + 2 * q^58 - 2 * q^61 + 4 * q^63 - 4 * q^64 - 2 * q^66 + 4 * q^70 + 2 * q^73 + 4 * q^79 - 2 * q^81 - 2 * q^82 - 2 * q^85 + 4 * q^88 - 2 * q^90 + 4 * q^91 + 4 * q^93 - 2 * q^94 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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