LMFDB - Embedded newform 2664.1.cg.a.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2664,1,Mod(211,2664)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2664, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("2664.211");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2664 = 2^{3} \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2664.cg (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:	$1.32950919365$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.7096896.2

Embedding invariants

Embedding label			211.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2664.211
Dual form			2664.1.cg.a.2563.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73205 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +2.00000i q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.866025 + 0.500000i) q^{14} +(1.73205 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.73205 - 1.00000i) q^{20} +(0.866025 - 0.500000i) q^{21} -1.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.50000 - 2.59808i) q^{25} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.866025 - 0.500000i) q^{29} +(-1.73205 + 1.00000i) q^{30} +(-0.866025 - 0.500000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -1.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +1.00000 q^{36} +1.00000i q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.73205 - 1.00000i) q^{40} +1.00000i q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{44} +2.00000i q^{45} +(0.866025 - 0.500000i) q^{46} +(0.866025 - 0.500000i) q^{47} -1.00000 q^{48} +(1.50000 + 2.59808i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(-0.866025 + 0.500000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.73205 + 1.00000i) q^{55} -1.00000i q^{56} -1.00000 q^{57} +1.00000i q^{58} +1.00000 q^{59} -2.00000i q^{60} +1.00000i q^{61} +(0.866025 - 0.500000i) q^{62} +(0.866025 + 0.500000i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(0.500000 - 0.866025i) q^{68} -1.00000i q^{69} +2.00000 q^{70} +(-0.866025 - 0.500000i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.866025 - 0.500000i) q^{74} +3.00000 q^{75} +1.00000 q^{76} +(0.866025 - 0.500000i) q^{77} +1.00000i q^{79} +2.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.866025 - 0.500000i) q^{84} +(1.73205 + 1.00000i) q^{85} +1.00000 q^{86} +(0.866025 + 0.500000i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +(-1.73205 - 1.00000i) q^{90} +1.00000i q^{92} -1.00000i q^{93} +1.00000i q^{94} +2.00000i q^{95} +(0.500000 - 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 2 q^{11} + 2 q^{12} - 2 q^{16} + 2 q^{17} - 2 q^{18} - 2 q^{19} - 4 q^{22} + 2 q^{24} + 6 q^{25} - 4 q^{27} - 2 q^{32} - 2 q^{33} - 4 q^{34}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 2 * q^11 + 2 * q^12 - 2 * q^16 + 2 * q^17 - 2 * q^18 - 2 * q^19 - 4 * q^22 + 2 * q^24 + 6 * q^25 - 4 * q^27 - 2 * q^32 - 2 * q^33 - 4 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^38 - 2 * q^43 + 2 * q^44 - 4 * q^48 + 6 * q^50 - 2 * q^51 + 2 * q^54 - 4 * q^57 + 4 * q^59 + 4 * q^64 - 2 * q^66 + 2 * q^68 + 8 * q^70 - 2 * q^72 + 12 * q^75 + 4 * q^76 - 2 * q^81 + 4 * q^86 + 2 * q^88 - 2 * q^89 + 2 * q^96 + 2 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2664\mathbb{Z}\right)^\times$.

$n$	$1297$	$1333$	$1999$	$2369$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$2$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$5$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$6$	−1.00000			−1.00000
$7$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$8$	1.00000			1.00000
$9$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$10$			2.00000i			2.00000i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.500000	−	0.866025i	0.500000	−	0.866025i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	0.866025	+	0.500000i	0.866025	+	0.500000i
$15$	1.73205	+	1.00000i	1.73205	+	1.00000i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$18$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$19$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$19$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$20$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$21$	0.866025	−	0.500000i	0.866025	−	0.500000i
$22$	−1.00000			−1.00000
$23$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$23$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.500000	+	0.866025i	0.500000	+	0.866025i
$25$	1.50000	−	2.59808i	1.50000	−	2.59808i
$26$		0			0
$27$	−1.00000			−1.00000
$28$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$29$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$29$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$30$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$31$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$31$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$32$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$33$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$34$	−1.00000			−1.00000
$35$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$36$	1.00000			1.00000
$37$			1.00000i			1.00000i
$37$			1.00000i			1.00000i
$38$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$39$		0			0
$40$	1.73205	−	1.00000i	1.73205	−	1.00000i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−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	$-0.333333\pi$
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$44$	0.500000	−	0.866025i	0.500000	−	0.866025i
$45$			2.00000i			2.00000i
$46$	0.866025	−	0.500000i	0.866025	−	0.500000i
$47$	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	$0.166667\pi$
$48$	−1.00000			−1.00000
$49$		0			0
$50$	1.50000	+	2.59808i	1.50000	+	2.59808i
$51$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$52$		0			0
$53$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$53$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$54$	0.500000	−	0.866025i	0.500000	−	0.866025i
$55$	1.73205	+	1.00000i	1.73205	+	1.00000i
$56$		−	1.00000i		−	1.00000i
$57$	−1.00000			−1.00000
$58$			1.00000i			1.00000i
$59$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$59$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$60$		−	2.00000i		−	2.00000i
$61$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$61$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$62$	0.866025	−	0.500000i	0.866025	−	0.500000i
$63$	0.866025	+	0.500000i	0.866025	+	0.500000i
$64$	1.00000			1.00000
$65$		0			0
$66$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	0.500000	−	0.866025i	0.500000	−	0.866025i
$69$		−	1.00000i		−	1.00000i
$70$	2.00000			2.00000
$71$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$71$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$72$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$75$	3.00000			3.00000
$76$	1.00000			1.00000
$77$	0.866025	−	0.500000i	0.866025	−	0.500000i
$78$		0			0
$79$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$79$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$80$			2.00000i			2.00000i
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$		0			0
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$85$	1.73205	+	1.00000i	1.73205	+	1.00000i
$86$	1.00000			1.00000
$87$	0.866025	+	0.500000i	0.866025	+	0.500000i
$88$	0.500000	+	0.866025i	0.500000	+	0.866025i
$89$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$89$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$90$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$91$		0			0
$92$			1.00000i			1.00000i
$93$		−	1.00000i		−	1.00000i
$94$			1.00000i			1.00000i
$95$			2.00000i			2.00000i
$96$	0.500000	−	0.866025i	0.500000	−	0.866025i
$97$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$97$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$98$		0			0
$99$	−1.00000			−1.00000
$100$	−3.00000			−3.00000
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$102$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$104$		0			0
$105$	1.00000	−	1.73205i	1.00000	−	1.73205i
$106$		−	1.00000i		−	1.00000i
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$108$	0.500000	+	0.866025i	0.500000	+	0.866025i
$109$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$109$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$110$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$111$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$112$	0.866025	+	0.500000i	0.866025	+	0.500000i
$113$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$113$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$114$	0.500000	−	0.866025i	0.500000	−	0.866025i
$115$	−2.00000			−2.00000
$116$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$117$		0			0
$118$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$119$	0.866025	−	0.500000i	0.866025	−	0.500000i
$120$	1.73205	+	1.00000i	1.73205	+	1.00000i
$121$		0			0
$122$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$123$		0			0
$124$			1.00000i			1.00000i
$125$		−	4.00000i		−	4.00000i
$126$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$127$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$127$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$128$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$129$	0.500000	−	0.866025i	0.500000	−	0.866025i
$130$		0			0
$131$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$132$	1.00000			1.00000
$133$	0.866025	+	0.500000i	0.866025	+	0.500000i
$134$		0			0
$135$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$136$	0.500000	+	0.866025i	0.500000	+	0.866025i
$137$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$137$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$138$	0.866025	+	0.500000i	0.866025	+	0.500000i
$139$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$139$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$140$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$141$	0.866025	+	0.500000i	0.866025	+	0.500000i
$142$	0.866025	−	0.500000i	0.866025	−	0.500000i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$145$	1.00000	−	1.73205i	1.00000	−	1.73205i
$146$		0			0
$147$		0			0
$148$	0.866025	−	0.500000i	0.866025	−	0.500000i
$149$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$149$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$150$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$151$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$151$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$152$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$153$	−1.00000			−1.00000
$154$			1.00000i			1.00000i
$155$	−2.00000			−2.00000
$156$		0			0
$157$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$157$		−	1.00000i		−	1.00000i	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
$160$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$161$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$162$	1.00000			1.00000
$163$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$163$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$			2.00000i			2.00000i
$166$		0			0
$167$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$167$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$168$	0.866025	−	0.500000i	0.866025	−	0.500000i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$171$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$172$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$175$	−2.59808	−	1.50000i	−2.59808	−	1.50000i
$176$	−1.00000			−1.00000
$177$	0.500000	+	0.866025i	0.500000	+	0.866025i
$178$	1.00000			1.00000
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	1.73205	−	1.00000i	1.73205	−	1.00000i
$181$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$181$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$182$		0			0
$183$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$184$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$185$	1.00000	+	1.73205i	1.00000	+	1.73205i
$186$	0.866025	+	0.500000i	0.866025	+	0.500000i
$187$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$188$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$189$			1.00000i			1.00000i
$190$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$191$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$191$	−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			$\pi$
$194$	−1.00000			−1.00000
$195$		0			0
$196$		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	$0.166667\pi$
$198$	0.500000	−	0.866025i	0.500000	−	0.866025i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	1.50000	−	2.59808i	1.50000	−	2.59808i
$201$		0			0
$202$		−	1.00000i		−	1.00000i
$203$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$204$	1.00000			1.00000
$205$		0			0
$206$	0.866025	−	0.500000i	0.866025	−	0.500000i
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$		0			0
$209$	−1.00000			−1.00000
$210$	1.00000	+	1.73205i	1.00000	+	1.73205i
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$211$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$212$	0.866025	+	0.500000i	0.866025	+	0.500000i
$213$		−	1.00000i		−	1.00000i
$214$	0.500000	+	0.866025i	0.500000	+	0.866025i
$215$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$216$	−1.00000			−1.00000
$217$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$218$			1.00000i			1.00000i
$219$		0			0
$220$		−	2.00000i		−	2.00000i
$221$		0			0
$222$		−	1.00000i		−	1.00000i
$223$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$223$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$224$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$225$	1.50000	+	2.59808i	1.50000	+	2.59808i
$226$	0.500000	−	0.866025i	0.500000	−	0.866025i
$227$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$227$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$228$	0.500000	+	0.866025i	0.500000	+	0.866025i
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$	1.00000	−	1.73205i	1.00000	−	1.73205i
$231$	0.866025	+	0.500000i	0.866025	+	0.500000i
$232$	0.866025	−	0.500000i	0.866025	−	0.500000i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	1.00000	−	1.73205i	1.00000	−	1.73205i
$236$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$237$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$238$			1.00000i			1.00000i
$239$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$239$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$240$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$241$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$241$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.500000	−	0.866025i
$244$	0.866025	−	0.500000i	0.866025	−	0.500000i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$249$		0			0
$250$	3.46410	+	2.00000i	3.46410	+	2.00000i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		−	1.00000i		−	1.00000i
$253$		−	1.00000i		−	1.00000i
$254$		−	1.00000i		−	1.00000i
$255$			2.00000i			2.00000i
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$257$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$258$	0.500000	+	0.866025i	0.500000	+	0.866025i
$259$	1.00000			1.00000
$260$		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	$0.166667\pi$
$263$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$265$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$266$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$267$	0.500000	−	0.866025i	0.500000	−	0.866025i
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		−	2.00000i		−	2.00000i
$271$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$271$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$272$	−1.00000			−1.00000
$273$		0			0
$274$	1.00000			1.00000
$275$	3.00000			3.00000
$276$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$277$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$278$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$279$	0.866025	−	0.500000i	0.866025	−	0.500000i
$280$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$			1.00000i			1.00000i
$285$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$286$		0			0
$287$		0			0
$288$	1.00000			1.00000
$289$		0			0
$290$	1.00000	+	1.73205i	1.00000	+	1.73205i
$291$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$	1.73205	−	1.00000i	1.73205	−	1.00000i
$296$			1.00000i			1.00000i
$297$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$298$	0.866025	−	0.500000i	0.866025	−	0.500000i
$299$		0			0
$300$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$301$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$302$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$303$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$304$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$305$	1.00000	+	1.73205i	1.00000	+	1.73205i
$306$	0.500000	−	0.866025i	0.500000	−	0.866025i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$309$		−	1.00000i		−	1.00000i
$310$	1.00000	−	1.73205i	1.00000	−	1.73205i
$311$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$311$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$313$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$314$	0.866025	+	0.500000i	0.866025	+	0.500000i
$315$	2.00000			2.00000
$316$	0.866025	−	0.500000i	0.866025	−	0.500000i
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$	0.866025	−	0.500000i	0.866025	−	0.500000i
$319$	0.866025	+	0.500000i	0.866025	+	0.500000i
$320$	1.73205	−	1.00000i	1.73205	−	1.00000i
$321$	1.00000			1.00000
$322$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$323$	−1.00000			−1.00000
$324$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$325$		0			0
$326$	−1.00000			−1.00000
$327$	0.866025	+	0.500000i	0.866025	+	0.500000i
$328$		0			0
$329$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$330$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$		0			0
$333$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$334$			2.00000i			2.00000i
$335$		0			0
$336$			1.00000i			1.00000i
$337$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$337$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$338$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$339$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$340$		−	2.00000i		−	2.00000i
$341$		−	1.00000i		−	1.00000i
$342$	1.00000			1.00000
$343$		−	1.00000i		−	1.00000i
$344$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$345$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$346$		0			0
$347$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$347$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$348$		−	1.00000i		−	1.00000i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	2.59808	−	1.50000i	2.59808	−	1.50000i
$351$		0			0
$352$	0.500000	−	0.866025i	0.500000	−	0.866025i
$353$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$353$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$354$	−1.00000			−1.00000
$355$	−2.00000			−2.00000
$356$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$357$	0.866025	+	0.500000i	0.866025	+	0.500000i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$			2.00000i			2.00000i
$361$		0			0
$362$	0.866025	−	0.500000i	0.866025	−	0.500000i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		−	1.00000i		−	1.00000i
$367$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$368$	0.866025	−	0.500000i	0.866025	−	0.500000i
$369$		0			0
$370$	−2.00000			−2.00000
$371$	0.500000	+	0.866025i	0.500000	+	0.866025i
$372$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$375$	3.46410	−	2.00000i	3.46410	−	2.00000i
$376$	0.866025	−	0.500000i	0.866025	−	0.500000i
$377$		0			0
$378$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$379$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$379$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$380$	1.73205	−	1.00000i	1.73205	−	1.00000i
$381$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$382$		−	1.00000i		−	1.00000i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	−1.00000			−1.00000
$385$	1.00000	−	1.73205i	1.00000	−	1.73205i
$386$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$387$	1.00000			1.00000
$388$	0.500000	−	0.866025i	0.500000	−	0.866025i
$389$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$390$		0			0
$391$		−	1.00000i		−	1.00000i
$392$		0			0
$393$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$394$			1.00000i			1.00000i
$395$	1.00000	+	1.73205i	1.00000	+	1.73205i
$396$	0.500000	+	0.866025i	0.500000	+	0.866025i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$			1.00000i			1.00000i
$400$	1.50000	+	2.59808i	1.50000	+	2.59808i
$401$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$401$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	0.866025	+	0.500000i	0.866025	+	0.500000i
$405$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$406$	1.00000			1.00000
$407$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$408$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$409$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$409$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$	0.500000	−	0.866025i	0.500000	−	0.866025i
$412$			1.00000i			1.00000i
$413$		−	1.00000i		−	1.00000i
$414$			1.00000i			1.00000i
$415$		0			0
$416$		0			0
$417$	0.500000	+	0.866025i	0.500000	+	0.866025i
$418$	0.500000	−	0.866025i	0.500000	−	0.866025i
$419$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$420$	−2.00000			−2.00000
$421$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$421$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$422$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$423$			1.00000i			1.00000i
$424$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$425$	3.00000			3.00000
$426$	0.866025	+	0.500000i	0.866025	+	0.500000i
$427$	1.00000			1.00000
$428$	−1.00000			−1.00000
$429$		0			0
$430$	1.73205	−	1.00000i	1.73205	−	1.00000i
$431$	−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	$0.833333\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$435$	2.00000			2.00000
$436$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$437$	0.866025	−	0.500000i	0.866025	−	0.500000i
$438$		0			0
$439$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$439$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$440$	1.73205	+	1.00000i	1.73205	+	1.00000i
$441$		0			0
$442$		0			0
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$444$	0.866025	+	0.500000i	0.866025	+	0.500000i
$445$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$446$		−	1.00000i		−	1.00000i
$447$		−	1.00000i		−	1.00000i
$448$		−	1.00000i		−	1.00000i
$449$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$449$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$450$	−3.00000			−3.00000
$451$		0			0
$452$	0.500000	+	0.866025i	0.500000	+	0.866025i
$453$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$454$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$455$		0			0
$456$	−1.00000			−1.00000
$457$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$457$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$460$	1.00000	+	1.73205i	1.00000	+	1.73205i
$461$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$461$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$462$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$			1.00000i			1.00000i
$465$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$		0			0
$470$	1.00000	+	1.73205i	1.00000	+	1.73205i
$471$	0.866025	−	0.500000i	0.866025	−	0.500000i
$472$	1.00000			1.00000
$473$	0.500000	−	0.866025i	0.500000	−	0.866025i
$474$		−	1.00000i		−	1.00000i
$475$	1.50000	+	2.59808i	1.50000	+	2.59808i
$476$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$477$		−	1.00000i		−	1.00000i
$478$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		−	2.00000i		−	2.00000i
$481$		0			0
$482$	0.500000	−	0.866025i	0.500000	−	0.866025i
$483$	−1.00000			−1.00000
$484$		0			0
$485$	1.73205	+	1.00000i	1.73205	+	1.00000i
$486$	0.500000	+	0.866025i	0.500000	+	0.866025i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$			1.00000i			1.00000i
$489$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$490$		0			0
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$492$		0			0
$493$	0.866025	+	0.500000i	0.866025	+	0.500000i
$494$		0			0
$495$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$496$	0.866025	−	0.500000i	0.866025	−	0.500000i
$497$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	−3.46410	+	2.00000i	−3.46410	+	2.00000i
$501$	1.73205	+	1.00000i	1.73205	+	1.00000i
$502$		0			0
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$	0.866025	+	0.500000i	0.866025	+	0.500000i
$505$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$506$	0.866025	+	0.500000i	0.866025	+	0.500000i
$507$	−1.00000			−1.00000
$508$	0.866025	+	0.500000i	0.866025	+	0.500000i
$509$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$509$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$510$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$511$		0			0
$512$	1.00000			1.00000
$513$	0.500000	−	0.866025i	0.500000	−	0.866025i
$514$	0.500000	−	0.866025i	0.500000	−	0.866025i
$515$	−2.00000			−2.00000
$516$	−1.00000			−1.00000
$517$	0.866025	+	0.500000i	0.866025	+	0.500000i
$518$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$519$		0			0
$520$		0			0
$521$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$521$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$522$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$524$	0.500000	+	0.866025i	0.500000	+	0.866025i
$525$		−	3.00000i		−	3.00000i
$526$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$527$		−	1.00000i		−	1.00000i
$528$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$529$		0			0
$530$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$531$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$532$		−	1.00000i		−	1.00000i
$533$		0			0
$534$	0.500000	+	0.866025i	0.500000	+	0.866025i
$535$		−	2.00000i		−	2.00000i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	1.73205	+	1.00000i	1.73205	+	1.00000i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		−	1.00000i		−	1.00000i
$543$		−	1.00000i		−	1.00000i
$544$	0.500000	−	0.866025i	0.500000	−	0.866025i
$545$	1.00000	−	1.73205i	1.00000	−	1.73205i
$546$		0			0
$547$	−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			$\pi$
$548$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$549$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$550$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$551$			1.00000i			1.00000i
$552$		−	1.00000i		−	1.00000i
$553$	1.00000			1.00000
$554$	0.866025	+	0.500000i	0.866025	+	0.500000i
$555$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$556$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$558$			1.00000i			1.00000i
$559$		0			0
$560$	2.00000			2.00000
$561$	−1.00000			−1.00000
$562$		0			0
$563$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$563$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$564$		−	1.00000i		−	1.00000i
$565$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$566$		0			0
$567$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$568$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$569$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$569$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$570$		−	2.00000i		−	2.00000i
$571$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$571$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$574$		0			0
$575$	−2.59808	+	1.50000i	−2.59808	+	1.50000i
$576$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$577$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$577$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$578$		0			0
$579$	−1.00000			−1.00000
$580$	−2.00000			−2.00000
$581$		0			0
$582$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$583$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$587$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$588$		0			0
$589$	0.866025	−	0.500000i	0.866025	−	0.500000i
$590$			2.00000i			2.00000i
$591$	0.866025	+	0.500000i	0.866025	+	0.500000i
$592$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	1.00000			1.00000
$595$	1.00000	−	1.73205i	1.00000	−	1.73205i
$596$			1.00000i			1.00000i
$597$		0			0
$598$		0			0
$599$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$599$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$600$	3.00000			3.00000
$601$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$601$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$602$		−	1.00000i		−	1.00000i
$603$		0			0
$604$	0.866025	−	0.500000i	0.866025	−	0.500000i
$605$		0			0
$606$	0.866025	−	0.500000i	0.866025	−	0.500000i
$607$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$607$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$608$	1.00000			1.00000
$609$	0.500000	−	0.866025i	0.500000	−	0.866025i
$610$	−2.00000			−2.00000
$611$		0			0
$612$	0.500000	+	0.866025i	0.500000	+	0.866025i
$613$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$613$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$614$		0			0
$615$		0			0
$616$	0.866025	−	0.500000i	0.866025	−	0.500000i
$617$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$617$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$618$	0.866025	+	0.500000i	0.866025	+	0.500000i
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$620$	1.00000	+	1.73205i	1.00000	+	1.73205i
$621$	0.866025	+	0.500000i	0.866025	+	0.500000i
$622$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$623$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$624$		0			0
$625$	−2.50000	−	4.33013i	−2.50000	−	4.33013i
$626$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$627$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$628$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$629$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$630$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$632$			1.00000i			1.00000i
$633$	−1.00000			−1.00000
$634$		0			0
$635$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$636$			1.00000i			1.00000i
$637$		0			0
$638$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$639$	0.866025	−	0.500000i	0.866025	−	0.500000i
$640$			2.00000i			2.00000i
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$644$	1.00000			1.00000
$645$		−	2.00000i		−	2.00000i
$646$	0.500000	−	0.866025i	0.500000	−	0.866025i
$647$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$647$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$648$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$649$	0.500000	+	0.866025i	0.500000	+	0.866025i
$650$		0			0
$651$	−1.00000			−1.00000
$652$	0.500000	−	0.866025i	0.500000	−	0.866025i
$653$		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
$655$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$656$		0			0
$657$		0			0
$658$	1.00000			1.00000
$659$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$659$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$660$	1.73205	−	1.00000i	1.73205	−	1.00000i
$661$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$661$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.00000			2.00000
$666$	0.866025	−	0.500000i	0.866025	−	0.500000i
$667$	−1.00000			−1.00000
$668$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$669$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$670$		0			0
$671$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$672$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$673$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$676$	1.00000			1.00000
$677$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$677$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$678$	1.00000			1.00000
$679$	0.866025	−	0.500000i	0.866025	−	0.500000i
$680$	1.73205	+	1.00000i	1.73205	+	1.00000i
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$	0.866025	+	0.500000i	0.866025	+	0.500000i
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$684$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$685$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$686$	0.866025	+	0.500000i	0.866025	+	0.500000i
$687$		0			0
$688$	1.00000			1.00000
$689$		0			0
$690$	2.00000			2.00000
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$		0			0
$693$			1.00000i			1.00000i
$694$	0.500000	+	0.866025i	0.500000	+	0.866025i
$695$	1.73205	−	1.00000i	1.73205	−	1.00000i
$696$	0.866025	+	0.500000i	0.866025	+	0.500000i
$697$		0			0
$698$		0			0
$699$		0			0
$700$			3.00000i			3.00000i
$701$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$701$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$702$		0			0
$703$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$704$	0.500000	+	0.866025i	0.500000	+	0.866025i
$705$	2.00000			2.00000
$706$	1.00000	+	1.73205i	1.00000	+	1.73205i
$707$	0.500000	+	0.866025i	0.500000	+	0.866025i
$708$	0.500000	−	0.866025i	0.500000	−	0.866025i
$709$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$709$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$710$	1.00000	−	1.73205i	1.00000	−	1.73205i
$711$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$712$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$713$	0.500000	+	0.866025i	0.500000	+	0.866025i
$714$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$715$		0			0
$716$		0			0
$717$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$718$		0			0
$719$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$719$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$720$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$721$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$722$		0			0
$723$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$724$			1.00000i			1.00000i
$725$		−	3.00000i		−	3.00000i
$726$		0			0
$727$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$727$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$	0.500000	−	0.866025i	0.500000	−	0.866025i
$732$	0.866025	+	0.500000i	0.866025	+	0.500000i
$733$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$733$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$734$	0.866025	+	0.500000i	0.866025	+	0.500000i
$735$		0			0
$736$			1.00000i			1.00000i
$737$		0			0
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	1.00000	−	1.73205i	1.00000	−	1.73205i
$741$		0			0
$742$	−1.00000			−1.00000
$743$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$743$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$744$		−	1.00000i		−	1.00000i
$745$	−2.00000			−2.00000
$746$		0			0
$747$		0			0
$748$	1.00000			1.00000
$749$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$750$			4.00000i			4.00000i
$751$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$751$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$752$			1.00000i			1.00000i
$753$		0			0
$754$		0			0
$755$	1.00000	+	1.73205i	1.00000	+	1.73205i
$756$	0.866025	−	0.500000i	0.866025	−	0.500000i
$757$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$757$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$758$	1.00000			1.00000
$759$	0.866025	−	0.500000i	0.866025	−	0.500000i
$760$			2.00000i			2.00000i
$761$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$761$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$762$	0.866025	−	0.500000i	0.866025	−	0.500000i
$763$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$764$	0.866025	+	0.500000i	0.866025	+	0.500000i
$765$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$766$		0			0
$767$		0			0
$768$	0.500000	−	0.866025i	0.500000	−	0.866025i
$769$	−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			$\pi$
$770$	1.00000	+	1.73205i	1.00000	+	1.73205i
$771$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$772$	1.00000			1.00000
$773$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$773$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$774$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$775$	−2.59808	+	1.50000i	−2.59808	+	1.50000i
$776$	0.500000	+	0.866025i	0.500000	+	0.866025i
$777$	0.500000	+	0.866025i	0.500000	+	0.866025i
$778$	0.866025	+	0.500000i	0.866025	+	0.500000i
$779$		0			0
$780$		0			0
$781$		−	1.00000i		−	1.00000i
$782$	0.866025	+	0.500000i	0.866025	+	0.500000i
$783$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$784$		0			0
$785$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$786$	1.00000			1.00000
$787$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$787$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$788$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$789$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$790$	−2.00000			−2.00000
$791$			1.00000i			1.00000i
$792$	−1.00000			−1.00000
$793$		0			0
$794$		0			0
$795$	−2.00000			−2.00000
$796$		0			0
$797$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$797$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$798$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$799$	0.866025	+	0.500000i	0.866025	+	0.500000i
$800$	−3.00000			−3.00000
$801$	1.00000			1.00000
$802$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$803$		0			0
$804$		0			0
$805$			2.00000i			2.00000i
$806$		0			0
$807$		0			0
$808$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$810$	1.73205	−	1.00000i	1.73205	−	1.00000i
$811$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$811$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$812$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$813$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$814$		−	1.00000i		−	1.00000i
$815$	1.73205	+	1.00000i	1.73205	+	1.00000i
$816$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$817$	1.00000			1.00000
$818$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$819$		0			0
$820$		0			0
$821$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$821$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$822$	0.500000	+	0.866025i	0.500000	+	0.866025i
$823$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$824$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$825$	1.50000	+	2.59808i	1.50000	+	2.59808i
$826$	0.866025	+	0.500000i	0.866025	+	0.500000i
$827$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$827$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$828$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$829$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$829$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$830$		0			0
$831$	0.866025	−	0.500000i	0.866025	−	0.500000i
$832$		0			0
$833$		0			0
$834$	−1.00000			−1.00000
$835$	2.00000	−	3.46410i	2.00000	−	3.46410i
$836$	0.500000	+	0.866025i	0.500000	+	0.866025i
$837$	0.866025	+	0.500000i	0.866025	+	0.500000i
$838$	0.500000	−	0.866025i	0.500000	−	0.866025i
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$	1.00000	−	1.73205i	1.00000	−	1.73205i
$841$		0			0
$842$		−	1.00000i		−	1.00000i
$843$		0			0
$844$	1.00000			1.00000
$845$			2.00000i			2.00000i
$846$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$847$		0			0
$848$		−	1.00000i		−	1.00000i
$849$		0			0
$850$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$851$	0.500000	−	0.866025i	0.500000	−	0.866025i
$852$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$855$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$856$	0.500000	−	0.866025i	0.500000	−	0.866025i
$857$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$857$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$858$		0			0
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$860$			2.00000i			2.00000i
$861$		0			0
$862$	0.866025	−	0.500000i	0.866025	−	0.500000i
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$864$	0.500000	+	0.866025i	0.500000	+	0.866025i
$865$		0			0
$866$		0			0
$867$		0			0
$868$	1.00000			1.00000
$869$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$870$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$871$		0			0
$872$	0.866025	−	0.500000i	0.866025	−	0.500000i
$873$	−1.00000			−1.00000
$874$			1.00000i			1.00000i
$875$	−4.00000			−4.00000
$876$		0			0
$877$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$877$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$878$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$879$		0			0
$880$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$881$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$881$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$882$		0			0
$883$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$883$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$884$		0			0
$885$	1.73205	+	1.00000i	1.73205	+	1.00000i
$886$	−1.00000			−1.00000
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$889$	0.500000	+	0.866025i	0.500000	+	0.866025i
$890$	1.73205	−	1.00000i	1.73205	−	1.00000i
$891$	0.500000	−	0.866025i	0.500000	−	0.866025i
$892$	0.866025	+	0.500000i	0.866025	+	0.500000i
$893$			1.00000i			1.00000i
$894$	0.866025	+	0.500000i	0.866025	+	0.500000i
$895$		0			0
$896$	0.866025	+	0.500000i	0.866025	+	0.500000i
$897$		0			0
$898$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$899$	−1.00000			−1.00000
$900$	1.50000	−	2.59808i	1.50000	−	2.59808i
$901$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$902$		0			0
$903$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$904$	−1.00000			−1.00000
$905$	−2.00000			−2.00000
$906$		−	1.00000i		−	1.00000i
$907$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$907$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$908$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$909$		−	1.00000i		−	1.00000i
$910$		0			0
$911$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$911$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$912$	0.500000	−	0.866025i	0.500000	−	0.866025i
$913$		0			0
$914$	0.500000	−	0.866025i	0.500000	−	0.866025i
$915$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$916$		0			0
$917$			1.00000i			1.00000i
$918$	1.00000			1.00000
$919$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$919$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$920$	−2.00000			−2.00000
$921$		0			0
$922$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$923$		0			0
$924$		−	1.00000i		−	1.00000i
$925$	2.59808	+	1.50000i	2.59808	+	1.50000i
$926$		0			0
$927$	0.866025	−	0.500000i	0.866025	−	0.500000i
$928$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$929$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$929$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$930$	2.00000			2.00000
$931$		0			0
$932$		0			0
$933$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$934$		0			0
$935$			2.00000i			2.00000i
$936$		0			0
$937$	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
$939$	−2.00000			−2.00000
$940$	−2.00000			−2.00000
$941$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$941$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$942$			1.00000i			1.00000i
$943$		0			0
$944$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$945$	1.00000	+	1.73205i	1.00000	+	1.73205i
$946$	0.500000	+	0.866025i	0.500000	+	0.866025i
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$	0.866025	+	0.500000i	0.866025	+	0.500000i
$949$		0			0
$950$	−3.00000			−3.00000
$951$		0			0
$952$	0.866025	−	0.500000i	0.866025	−	0.500000i
$953$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$953$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$954$	0.866025	+	0.500000i	0.866025	+	0.500000i
$955$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$956$	0.866025	−	0.500000i	0.866025	−	0.500000i
$957$			1.00000i			1.00000i
$958$		0			0
$959$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$960$	1.73205	+	1.00000i	1.73205	+	1.00000i
$961$		0			0
$962$		0			0
$963$	0.500000	+	0.866025i	0.500000	+	0.866025i
$964$	0.500000	+	0.866025i	0.500000	+	0.866025i
$965$			2.00000i			2.00000i
$966$	0.500000	−	0.866025i	0.500000	−	0.866025i
$967$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$967$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$968$		0			0
$969$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$970$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$971$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$971$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$972$	−1.00000			−1.00000
$973$		−	1.00000i		−	1.00000i
$974$		0			0
$975$		0			0
$976$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$977$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$978$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$979$	0.500000	−	0.866025i	0.500000	−	0.866025i
$980$		0			0
$981$			1.00000i			1.00000i
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	1.00000	−	1.73205i
$986$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$987$	0.500000	−	0.866025i	0.500000	−	0.866025i
$988$		0			0
$989$			1.00000i			1.00000i
$990$		−	2.00000i		−	2.00000i
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$992$			1.00000i			1.00000i
$993$		0			0
$994$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$995$		0			0
$996$		0			0
$997$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$997$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$998$		0			0
$999$		−	1.00000i		−	1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2664.1.cg.a.211.2	yes	4
8.3	odd	2	inner	2664.1.cg.a.211.1	yes	4
9.7	even	3		2664.1.bg.a.1987.2	yes	4
37.10	even	3		2664.1.bg.a.787.2	yes	4
72.43	odd	6		2664.1.bg.a.1987.1	yes	4
296.195	odd	6		2664.1.bg.a.787.1	✓	4
333.232	even	3	inner	2664.1.cg.a.2563.1	yes	4
2664.2563	odd	6	inner	2664.1.cg.a.2563.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2664.1.bg.a.787.1	✓	4	296.195	odd	6
2664.1.bg.a.787.2	yes	4	37.10	even	3
2664.1.bg.a.1987.1	yes	4	72.43	odd	6
2664.1.bg.a.1987.2	yes	4	9.7	even	3
2664.1.cg.a.211.1	yes	4	8.3	odd	2	inner
2664.1.cg.a.211.2	yes	4	1.1	even	1	trivial
2664.1.cg.a.2563.1	yes	4	333.232	even	3	inner
2664.1.cg.a.2563.2	yes	4	2664.2563	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2664.cg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.73205 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +2.00000i q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(0.866025 + 0.500000i) q^{14} +(1.73205 + 1.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-1.73205 - 1.00000i) q^{20} +(0.866025 - 0.500000i) q^{21} -1.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.50000 - 2.59808i) q^{25} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.866025 - 0.500000i) q^{29} +(-1.73205 + 1.00000i) q^{30} +(-0.866025 - 0.500000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -1.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +1.00000 q^{36} +1.00000i q^{37} +(-0.500000 - 0.866025i) q^{38} +(1.73205 - 1.00000i) q^{40} +1.00000i q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.500000 - 0.866025i) q^{44} +2.00000i q^{45} +(0.866025 - 0.500000i) q^{46} +(0.866025 - 0.500000i) q^{47} -1.00000 q^{48} +(1.50000 + 2.59808i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(-0.866025 + 0.500000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(1.73205 + 1.00000i) q^{55} -1.00000i q^{56} -1.00000 q^{57} +1.00000i q^{58} +1.00000 q^{59} -2.00000i q^{60} +1.00000i q^{61} +(0.866025 - 0.500000i) q^{62} +(0.866025 + 0.500000i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{66} +(0.500000 - 0.866025i) q^{68} -1.00000i q^{69} +2.00000 q^{70} +(-0.866025 - 0.500000i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.866025 - 0.500000i) q^{74} +3.00000 q^{75} +1.00000 q^{76} +(0.866025 - 0.500000i) q^{77} +1.00000i q^{79} +2.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.866025 - 0.500000i) q^{84} +(1.73205 + 1.00000i) q^{85} +1.00000 q^{86} +(0.866025 + 0.500000i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +(-1.73205 - 1.00000i) q^{90} +1.00000i q^{92} -1.00000i q^{93} +1.00000i q^{94} +2.00000i q^{95} +(0.500000 - 0.866025i) q^{96} +(0.500000 + 0.866025i) q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} + 4 q^{8} - 2 q^{9} + 2 q^{11} + 2 q^{12} - 2 q^{16} + 2 q^{17} - 2 q^{18} - 2 q^{19} - 4 q^{22} + 2 q^{24} + 6 q^{25} - 4 q^{27} - 2 q^{32} - 2 q^{33} - 4 q^{34}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 + 4 * q^8 - 2 * q^9 + 2 * q^11 + 2 * q^12 - 2 * q^16 + 2 * q^17 - 2 * q^18 - 2 * q^19 - 4 * q^22 + 2 * q^24 + 6 * q^25 - 4 * q^27 - 2 * q^32 - 2 * q^33 - 4 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^38 - 2 * q^43 + 2 * q^44 - 4 * q^48 + 6 * q^50 - 2 * q^51 + 2 * q^54 - 4 * q^57 + 4 * q^59 + 4 * q^64 - 2 * q^66 + 2 * q^68 + 8 * q^70 - 2 * q^72 + 12 * q^75 + 4 * q^76 - 2 * q^81 + 4 * q^86 + 2 * q^88 - 2 * q^89 + 2 * q^96 + 2 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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