LMFDB - Embedded newform 2664.1.bg.a.1987.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2664,1,Mod(787,2664)]

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, 4]))

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

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

chi := DirichletCharacter("2664.787");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2664 = 2^{3} \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2664.bg (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			1987.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2664.1987
Dual form			2664.1.bg.a.787.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

$n$	$1297$	$1333$	$1999$	$2369$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			1.00000
$2$	1.00000			1.00000
$3$	−1.00000			−1.00000
$3$	−1.00000			−1.00000
$4$	1.00000			1.00000
$5$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$5$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$6$	−1.00000			−1.00000
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$	1.00000			1.00000
$9$	1.00000			1.00000
$10$			2.00000i			2.00000i
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$12$	−1.00000			−1.00000
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$15$		−	2.00000i		−	2.00000i
$16$	1.00000			1.00000
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$18$	1.00000			1.00000
$19$	−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			$\pi$
$20$			2.00000i			2.00000i
$21$	0.866025	−	0.500000i	0.866025	−	0.500000i
$22$	0.500000	−	0.866025i	0.500000	−	0.866025i
$23$	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	$0.166667\pi$
$24$	−1.00000			−1.00000
$25$	−3.00000			−3.00000
$26$		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	$0.833333\pi$
$30$		−	2.00000i		−	2.00000i
$31$	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	$0.166667\pi$
$32$	1.00000			1.00000
$33$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$34$	0.500000	+	0.866025i	0.500000	+	0.866025i
$35$	−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
$40$			2.00000i			2.00000i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	0.866025	−	0.500000i	0.866025	−	0.500000i
$43$	−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	$0.833333\pi$
$48$	−1.00000			−1.00000
$49$		0			0
$50$	−3.00000			−3.00000
$51$	−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	$0.5\pi$
$54$	−1.00000			−1.00000
$55$	1.73205	+	1.00000i	1.73205	+	1.00000i
$56$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$57$	0.500000	−	0.866025i	0.500000	−	0.866025i
$58$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$59$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$59$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$60$		−	2.00000i		−	2.00000i
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$62$	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			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$	0.500000	+	0.866025i	0.500000	+	0.866025i
$69$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$70$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$71$	−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	$0.833333\pi$
$72$	1.00000			1.00000
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$			1.00000i			1.00000i
$75$	3.00000			3.00000
$76$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$77$			1.00000i			1.00000i
$78$		0			0
$79$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$79$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$80$			2.00000i			2.00000i
$81$	1.00000			1.00000
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	0.866025	−	0.500000i	0.866025	−	0.500000i
$85$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$86$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$87$	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			$\pi$
$90$			2.00000i			2.00000i
$91$		0			0
$92$	0.866025	−	0.500000i	0.866025	−	0.500000i
$93$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$94$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$95$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$96$	−1.00000			−1.00000
$97$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$97$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$98$		0			0
$99$	0.500000	−	0.866025i	0.500000	−	0.866025i
$100$	−3.00000			−3.00000
$101$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$101$	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	$0.166667\pi$
$104$		0			0
$105$	1.00000	+	1.73205i	1.00000	+	1.73205i
$106$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$107$	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			$0$
$108$	−1.00000			−1.00000
$109$	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
$111$		−	1.00000i		−	1.00000i
$112$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$114$	0.500000	−	0.866025i	0.500000	−	0.866025i
$115$	1.00000	+	1.73205i	1.00000	+	1.73205i
$116$	−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
$120$		−	2.00000i		−	2.00000i
$121$		0			0
$122$	0.866025	−	0.500000i	0.866025	−	0.500000i
$123$		0			0
$124$	0.866025	−	0.500000i	0.866025	−	0.500000i
$125$		−	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	$0.5\pi$
$128$	1.00000			1.00000
$129$	0.500000	−	0.866025i	0.500000	−	0.866025i
$130$		0			0
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$132$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$133$		−	1.00000i		−	1.00000i
$134$		0			0
$135$		−	2.00000i		−	2.00000i
$136$	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
$139$	−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			$\pi$
$140$	−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
$144$	1.00000			1.00000
$145$	1.00000	−	1.73205i	1.00000	−	1.73205i
$146$		0			0
$147$		0			0
$148$			1.00000i			1.00000i
$149$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$149$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$150$	3.00000			3.00000
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$152$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$153$	0.500000	+	0.866025i	0.500000	+	0.866025i
$154$			1.00000i			1.00000i
$155$	1.00000	+	1.73205i	1.00000	+	1.73205i
$156$		0			0
$157$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$157$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$158$	0.866025	−	0.500000i	0.866025	−	0.500000i
$159$	0.866025	−	0.500000i	0.866025	−	0.500000i
$160$			2.00000i			2.00000i
$161$	−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
$165$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$166$		0			0
$167$			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
$169$	1.00000			1.00000
$170$	−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		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	0.866025	+	0.500000i	0.866025	+	0.500000i
$175$	2.59808	−	1.50000i	2.59808	−	1.50000i
$176$	0.500000	−	0.866025i	0.500000	−	0.866025i
$177$	0.500000	−	0.866025i	0.500000	−	0.866025i
$178$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$			2.00000i			2.00000i
$181$	−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
$185$	−2.00000			−2.00000
$186$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$187$	1.00000			1.00000
$188$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$189$	0.866025	−	0.500000i	0.866025	−	0.500000i
$190$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$191$	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	$0.5\pi$
$192$	−1.00000			−1.00000
$193$	−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			$\pi$
$194$	0.500000	−	0.866025i	0.500000	−	0.866025i
$195$		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			$\pi$
$200$	−3.00000			−3.00000
$201$		0			0
$202$	0.866025	+	0.500000i	0.866025	+	0.500000i
$203$	1.00000			1.00000
$204$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$205$		0			0
$206$	0.866025	−	0.500000i	0.866025	−	0.500000i
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$		0			0
$209$	0.500000	+	0.866025i	0.500000	+	0.866025i
$210$	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
$213$	0.866025	+	0.500000i	0.866025	+	0.500000i
$214$	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
$218$	0.866025	−	0.500000i	0.866025	−	0.500000i
$219$		0			0
$220$	1.73205	+	1.00000i	1.73205	+	1.00000i
$221$		0			0
$222$		−	1.00000i		−	1.00000i
$223$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$223$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$224$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$225$	−3.00000			−3.00000
$226$	0.500000	−	0.866025i	0.500000	−	0.866025i
$227$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$227$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$228$	0.500000	−	0.866025i	0.500000	−	0.866025i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	1.00000	+	1.73205i	1.00000	+	1.73205i
$231$		−	1.00000i		−	1.00000i
$232$	−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
$238$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$239$	−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	$0.833333\pi$
$240$		−	2.00000i		−	2.00000i
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$	−1.00000			−1.00000
$244$	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
$250$		−	4.00000i		−	4.00000i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$253$		−	1.00000i		−	1.00000i
$254$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$255$	1.73205	−	1.00000i	1.73205	−	1.00000i
$256$	1.00000			1.00000
$257$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$257$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$258$	0.500000	−	0.866025i	0.500000	−	0.866025i
$259$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$260$		0			0
$261$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$262$	0.500000	−	0.866025i	0.500000	−	0.866025i
$263$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$263$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$264$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$265$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$266$		−	1.00000i		−	1.00000i
$267$	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	$0.5\pi$
$272$	0.500000	+	0.866025i	0.500000	+	0.866025i
$273$		0			0
$274$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$275$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$276$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$277$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$278$	−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			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$	0.866025	+	0.500000i	0.866025	+	0.500000i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$285$	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		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		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
$300$	3.00000			3.00000
$301$		−	1.00000i		−	1.00000i
$302$	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	$0.5\pi$
$308$			1.00000i			1.00000i
$309$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$310$	1.00000	+	1.73205i	1.00000	+	1.73205i
$311$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$311$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	2.00000			2.00000			1.00000			$0$
$313$	2.00000			2.00000			1.00000			$0$
$314$	0.866025	+	0.500000i	0.866025	+	0.500000i
$315$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$316$	0.866025	−	0.500000i	0.866025	−	0.500000i
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$	0.866025	−	0.500000i	0.866025	−	0.500000i
$319$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$320$			2.00000i			2.00000i
$321$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$322$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$323$	−1.00000			−1.00000
$324$	1.00000			1.00000
$325$		0			0
$326$	0.500000	+	0.866025i	0.500000	+	0.866025i
$327$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$328$		0			0
$329$	1.00000			1.00000
$330$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$			1.00000i			1.00000i
$334$			2.00000i			2.00000i
$335$		0			0
$336$	0.866025	−	0.500000i	0.866025	−	0.500000i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	1.00000			1.00000
$339$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$340$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$341$		−	1.00000i		−	1.00000i
$342$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$343$		−	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	1.00000			$0$
$347$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$348$	0.866025	+	0.500000i	0.866025	+	0.500000i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	2.59808	−	1.50000i	2.59808	−	1.50000i
$351$		0			0
$352$	0.500000	−	0.866025i	0.500000	−	0.866025i
$353$	−2.00000			−2.00000			−1.00000			$\pi$
$353$	−2.00000			−2.00000			−1.00000			$\pi$
$354$	0.500000	−	0.866025i	0.500000	−	0.866025i
$355$	1.00000	−	1.73205i	1.00000	−	1.73205i
$356$	−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
$366$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$	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		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	1.00000			1.00000
$375$			4.00000i			4.00000i
$376$	−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
$382$	0.866025	+	0.500000i	0.866025	+	0.500000i
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$	−1.00000			−1.00000
$385$	−2.00000			−2.00000
$386$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$387$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$388$	0.500000	−	0.866025i	0.500000	−	0.866025i
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$390$		0			0
$391$	0.866025	+	0.500000i	0.866025	+	0.500000i
$392$		0			0
$393$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$394$	0.866025	−	0.500000i	0.866025	−	0.500000i
$395$	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
$400$	−3.00000			−3.00000
$401$	−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
$405$			2.00000i			2.00000i
$406$	1.00000			1.00000
$407$	0.866025	+	0.500000i	0.866025	+	0.500000i
$408$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$410$		0			0
$411$	0.500000	−	0.866025i	0.500000	−	0.866025i
$412$	0.866025	−	0.500000i	0.866025	−	0.500000i
$413$		−	1.00000i		−	1.00000i
$414$	0.866025	−	0.500000i	0.866025	−	0.500000i
$415$		0			0
$416$		0			0
$417$	0.500000	−	0.866025i	0.500000	−	0.866025i
$418$	0.500000	+	0.866025i	0.500000	+	0.866025i
$419$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$419$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$420$	1.00000	+	1.73205i	1.00000	+	1.73205i
$421$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$421$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$422$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$423$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$424$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$425$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$426$	0.866025	+	0.500000i	0.866025	+	0.500000i
$427$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$428$	0.500000	−	0.866025i	0.500000	−	0.866025i
$429$		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	$0.833333\pi$
$432$	−1.00000			−1.00000
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$435$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$436$	0.866025	−	0.500000i	0.866025	−	0.500000i
$437$			1.00000i			1.00000i
$438$		0			0
$439$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$439$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$440$	1.73205	+	1.00000i	1.73205	+	1.00000i
$441$		0			0
$442$		0			0
$443$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$444$		−	1.00000i		−	1.00000i
$445$	1.73205	−	1.00000i	1.73205	−	1.00000i
$446$	0.866025	+	0.500000i	0.866025	+	0.500000i
$447$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$448$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$449$	−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
$456$	0.500000	−	0.866025i	0.500000	−	0.866025i
$457$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$457$	0.500000	+	0.866025i	0.500000	+	0.866025i	−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
$461$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$461$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$462$		−	1.00000i		−	1.00000i
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$465$	−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
$472$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$473$	0.500000	+	0.866025i	0.500000	+	0.866025i
$474$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$475$	1.50000	−	2.59808i	1.50000	−	2.59808i
$476$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$477$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$478$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$479$		0			0		1.00000			$0$
$479$		0			0		−1.00000			$\pi$
$480$		−	2.00000i		−	2.00000i
$481$		0			0
$482$	0.500000	+	0.866025i	0.500000	+	0.866025i
$483$	0.500000	−	0.866025i	0.500000	−	0.866025i
$484$		0			0
$485$	1.73205	+	1.00000i	1.73205	+	1.00000i
$486$	−1.00000			−1.00000
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	0.866025	−	0.500000i	0.866025	−	0.500000i
$489$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$490$		0			0
$491$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$491$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		−	1.00000i		−	1.00000i
$494$		0			0
$495$	1.73205	+	1.00000i	1.73205	+	1.00000i
$496$	0.866025	−	0.500000i	0.866025	−	0.500000i
$497$	1.00000			1.00000
$498$		0			0
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$		−	4.00000i		−	4.00000i
$501$		−	2.00000i		−	2.00000i
$502$		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
$506$		−	1.00000i		−	1.00000i
$507$	−1.00000			−1.00000
$508$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$510$	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
$515$	1.00000	+	1.73205i	1.00000	+	1.73205i
$516$	0.500000	−	0.866025i	0.500000	−	0.866025i
$517$	−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
$525$	−2.59808	+	1.50000i	−2.59808	+	1.50000i
$526$	0.866025	−	0.500000i	0.866025	−	0.500000i
$527$	0.866025	+	0.500000i	0.866025	+	0.500000i
$528$	−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
$535$	1.73205	+	1.00000i	1.73205	+	1.00000i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		−	2.00000i		−	2.00000i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$543$	0.866025	+	0.500000i	0.866025	+	0.500000i
$544$	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
$551$	0.866025	−	0.500000i	0.866025	−	0.500000i
$552$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$553$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$554$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$555$	2.00000			2.00000
$556$	−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	$0.5\pi$
$558$	0.866025	−	0.500000i	0.866025	−	0.500000i
$559$		0			0
$560$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$561$	−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			$\pi$
$564$	0.866025	+	0.500000i	0.866025	+	0.500000i
$565$	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	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$570$	1.73205	+	1.00000i	1.73205	+	1.00000i
$571$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$571$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$572$		0			0
$573$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$574$		0			0
$575$	−2.59808	+	1.50000i	−2.59808	+	1.50000i
$576$	1.00000			1.00000
$577$	−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
$579$	0.500000	+	0.866025i	0.500000	+	0.866025i
$580$	1.00000	−	1.73205i	1.00000	−	1.73205i
$581$		0			0
$582$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$583$			1.00000i			1.00000i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$587$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$588$		0			0
$589$			1.00000i			1.00000i
$590$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$591$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$592$			1.00000i			1.00000i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$595$	1.00000	−	1.73205i	1.00000	−	1.73205i
$596$	0.866025	−	0.500000i	0.866025	−	0.500000i
$597$		0			0
$598$		0			0
$599$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$599$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$600$	3.00000			3.00000
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		−	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
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$608$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$609$	−1.00000			−1.00000
$610$	1.00000	+	1.73205i	1.00000	+	1.73205i
$611$		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
$616$			1.00000i			1.00000i
$617$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$618$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$619$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$619$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$620$	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
$625$	5.00000			5.00000
$626$	2.00000			2.00000
$627$	−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	$0.166667\pi$
$632$	0.866025	−	0.500000i	0.866025	−	0.500000i
$633$	0.500000	+	0.866025i	0.500000	+	0.866025i
$634$		0			0
$635$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$636$	0.866025	−	0.500000i	0.866025	−	0.500000i
$637$		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			−	1.00000i	$-0.5\pi$
$641$		0			0				1.00000i	$0.5\pi$
$642$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$643$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$643$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$644$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$645$	1.73205	+	1.00000i	1.73205	+	1.00000i
$646$	−1.00000			−1.00000
$647$	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	$0.5\pi$
$648$	1.00000			1.00000
$649$	0.500000	+	0.866025i	0.500000	+	0.866025i
$650$		0			0
$651$	0.500000	−	0.866025i	0.500000	−	0.866025i
$652$	0.500000	+	0.866025i	0.500000	+	0.866025i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$	−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
$659$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$659$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$660$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$661$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$661$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.00000			2.00000
$666$			1.00000i			1.00000i
$667$	−1.00000			−1.00000
$668$			2.00000i			2.00000i
$669$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$670$		0			0
$671$		−	1.00000i		−	1.00000i
$672$	0.866025	−	0.500000i	0.866025	−	0.500000i
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	3.00000			3.00000
$676$	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	$0.833333\pi$
$678$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$679$			1.00000i			1.00000i
$680$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$		−	1.00000i		−	1.00000i
$683$	−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
$686$		−	1.00000i		−	1.00000i
$687$		0			0
$688$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$689$		0			0
$690$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$		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
$700$	2.59808	−	1.50000i	2.59808	−	1.50000i
$701$	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
$705$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$706$	−2.00000			−2.00000
$707$	−1.00000			−1.00000
$708$	0.500000	−	0.866025i	0.500000	−	0.866025i
$709$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$709$	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	$0.166667\pi$
$720$			2.00000i			2.00000i
$721$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$722$		0			0
$723$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$724$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$725$	2.59808	+	1.50000i	2.59808	+	1.50000i
$726$		0			0
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$	−1.00000			−1.00000
$732$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$733$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$733$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$734$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$735$		0			0
$736$	0.866025	−	0.500000i	0.866025	−	0.500000i
$737$		0			0
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	−2.00000			−2.00000
$741$		0			0
$742$	0.500000	−	0.866025i	0.500000	−	0.866025i
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$745$	1.00000	+	1.73205i	1.00000	+	1.73205i
$746$		0			0
$747$		0			0
$748$	1.00000			1.00000
$749$			1.00000i			1.00000i
$750$			4.00000i			4.00000i
$751$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$751$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$752$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$753$		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	$0.5\pi$
$758$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$759$			1.00000i			1.00000i
$760$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$761$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$761$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$762$	0.866025	−	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
$768$	−1.00000			−1.00000
$769$	−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			$\pi$
$770$	−2.00000			−2.00000
$771$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$772$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$773$	−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
$781$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$782$	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
$786$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$787$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$787$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$788$	0.866025	−	0.500000i	0.866025	−	0.500000i
$789$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$790$	1.00000	+	1.73205i	1.00000	+	1.73205i
$791$			1.00000i			1.00000i
$792$	0.500000	−	0.866025i	0.500000	−	0.866025i
$793$		0			0
$794$		0			0
$795$	1.00000	+	1.73205i	1.00000	+	1.73205i
$796$		0			0
$797$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$797$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$798$			1.00000i			1.00000i
$799$		−	1.00000i		−	1.00000i
$800$	−3.00000			−3.00000
$801$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$802$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$803$		0			0
$804$		0			0
$805$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$806$		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			$0$
$810$			2.00000i			2.00000i
$811$	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			$0$
$812$	1.00000			1.00000
$813$	0.866025	−	0.500000i	0.866025	−	0.500000i
$814$	0.866025	+	0.500000i	0.866025	+	0.500000i
$815$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$816$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$817$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$818$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$819$		0			0
$820$		0			0
$821$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$821$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$822$	0.500000	−	0.866025i	0.500000	−	0.866025i
$823$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$823$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$824$	0.866025	−	0.500000i	0.866025	−	0.500000i
$825$	1.50000	−	2.59808i	1.50000	−	2.59808i
$826$		−	1.00000i		−	1.00000i
$827$	−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
$834$	0.500000	−	0.866025i	0.500000	−	0.866025i
$835$	−4.00000			−4.00000
$836$	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		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$	1.00000	+	1.73205i	1.00000	+	1.73205i
$841$		0			0
$842$	0.866025	+	0.500000i	0.866025	+	0.500000i
$843$		0			0
$844$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$845$			2.00000i			2.00000i
$846$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$847$		0			0
$848$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$849$		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		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	−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	1.00000			$0$
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$860$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$861$		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	$0.166667\pi$
$864$	−1.00000			−1.00000
$865$		0			0
$866$		0			0
$867$		0			0
$868$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$869$		−	1.00000i		−	1.00000i
$870$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$871$		0			0
$872$	0.866025	−	0.500000i	0.866025	−	0.500000i
$873$	0.500000	−	0.866025i	0.500000	−	0.866025i
$874$			1.00000i			1.00000i
$875$	2.00000	+	3.46410i	2.00000	+	3.46410i
$876$		0			0
$877$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$877$	−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
$886$	0.500000	−	0.866025i	0.500000	−	0.866025i
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$		−	1.00000i		−	1.00000i
$889$	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
$893$	0.866025	−	0.500000i	0.866025	−	0.500000i
$894$	−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
$900$	−3.00000			−3.00000
$901$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$902$		0			0
$903$			1.00000i			1.00000i
$904$	0.500000	−	0.866025i	0.500000	−	0.866025i
$905$	1.00000	−	1.73205i	1.00000	−	1.73205i
$906$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$907$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$907$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$908$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$909$	0.866025	+	0.500000i	0.866025	+	0.500000i
$910$		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	$0.833333\pi$
$912$	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
$918$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$919$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$919$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$920$	1.00000	+	1.73205i	1.00000	+	1.73205i
$921$		0			0
$922$		−	2.00000i		−	2.00000i
$923$		0			0
$924$		−	1.00000i		−	1.00000i
$925$		−	3.00000i		−	3.00000i
$926$		0			0
$927$	0.866025	−	0.500000i	0.866025	−	0.500000i
$928$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$929$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$929$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$930$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$931$		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
$940$	1.00000	−	1.73205i	1.00000	−	1.73205i
$941$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$941$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$942$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$943$		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			−	1.00000i	$-0.5\pi$
$947$		0			0				1.00000i	$0.5\pi$
$948$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$949$		0			0
$950$	1.50000	−	2.59808i	1.50000	−	2.59808i
$951$		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
$957$	0.866025	−	0.500000i	0.866025	−	0.500000i
$958$		0			0
$959$		−	1.00000i		−	1.00000i
$960$		−	2.00000i		−	2.00000i
$961$		0			0
$962$		0			0
$963$	0.500000	−	0.866025i	0.500000	−	0.866025i
$964$	0.500000	+	0.866025i	0.500000	+	0.866025i
$965$	1.73205	−	1.00000i	1.73205	−	1.00000i
$966$	0.500000	−	0.866025i	0.500000	−	0.866025i
$967$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$967$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$968$		0			0
$969$	1.00000			1.00000
$970$	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
$977$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$977$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$978$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$979$	−1.00000			−1.00000
$980$		0			0
$981$	0.866025	−	0.500000i	0.866025	−	0.500000i
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$983$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$984$		0			0
$985$	1.00000	+	1.73205i	1.00000	+	1.73205i
$986$		−	1.00000i		−	1.00000i
$987$	−1.00000			−1.00000
$988$		0			0
$989$			1.00000i			1.00000i
$990$	1.73205	+	1.00000i	1.73205	+	1.00000i
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$992$	0.866025	−	0.500000i	0.866025	−	0.500000i
$993$		0			0
$994$	1.00000			1.00000
$995$		0			0
$996$		0			0
$997$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$997$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$998$		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.bg.a.1987.2	yes	4
8.3	odd	2	inner	2664.1.bg.a.1987.1	yes	4
9.4	even	3		2664.1.cg.a.211.2	yes	4
37.10	even	3		2664.1.cg.a.2563.1	yes	4
72.67	odd	6		2664.1.cg.a.211.1	yes	4
296.195	odd	6		2664.1.cg.a.2563.2	yes	4
333.121	even	3	inner	2664.1.bg.a.787.2	yes	4
2664.787	odd	6	inner	2664.1.bg.a.787.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2664.1.bg.a.787.1	✓	4	2664.787	odd	6	inner
2664.1.bg.a.787.2	yes	4	333.121	even	3	inner
2664.1.bg.a.1987.1	yes	4	8.3	odd	2	inner
2664.1.bg.a.1987.2	yes	4	1.1	even	1	trivial
2664.1.cg.a.211.1	yes	4	72.67	odd	6
2664.1.cg.a.211.2	yes	4	9.4	even	3
2664.1.cg.a.2563.1	yes	4	37.10	even	3
2664.1.cg.a.2563.2	yes	4	296.195	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:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2664.bg (of order \(6\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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