LMFDB - Embedded newform 819.1.ek.a.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,1,Mod(139,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("819.139");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	819.ek (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.408734245346$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.670761.1

Embedding invariants

Embedding label			139.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	819.139
Dual form			819.1.ek.a.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.866025 - 0.500000i) q^{10} -1.00000 q^{11} +(-0.866025 + 0.500000i) q^{13} +(-0.500000 + 0.866025i) q^{14} +1.00000 q^{15} -1.00000 q^{16} +(-0.866025 + 0.500000i) q^{17} +(0.500000 - 0.866025i) q^{18} +(0.866025 - 0.500000i) q^{19} -1.00000i q^{21} -1.00000 q^{22} +(0.866025 - 0.500000i) q^{24} +(-0.866025 + 0.500000i) q^{26} +1.00000i q^{27} -1.00000 q^{29} +1.00000 q^{30} +(0.866025 + 0.500000i) q^{31} +(0.866025 - 0.500000i) q^{33} +(-0.866025 + 0.500000i) q^{34} +(0.866025 - 0.500000i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.866025 + 0.500000i) q^{40} -1.00000i q^{42} +(-0.866025 + 0.500000i) q^{45} +(0.866025 - 0.500000i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{51} +1.00000i q^{54} +(0.866025 + 0.500000i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-0.500000 + 0.866025i) q^{57} -1.00000 q^{58} +1.00000i q^{59} +(-1.73205 - 1.00000i) q^{61} +(0.866025 + 0.500000i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +1.00000 q^{65} +(0.866025 - 0.500000i) q^{66} +(1.00000 + 1.73205i) q^{67} +(0.866025 - 0.500000i) q^{70} +(-0.500000 - 0.866025i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.500000 + 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{77} +(0.500000 - 0.866025i) q^{78} +(0.500000 + 0.866025i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{83} +1.00000 q^{85} +(0.866025 - 0.500000i) q^{87} +1.00000 q^{88} +(0.866025 + 0.500000i) q^{89} +(-0.866025 + 0.500000i) q^{90} -1.00000i q^{91} -1.00000 q^{93} +(0.866025 - 0.500000i) q^{94} -1.00000 q^{95} +(-0.500000 - 0.866025i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^7 - 4 * q^8 + 2 * q^9	$ 4 q + 4 q^{2} - 2 q^{7} - 4 q^{8} + 2 q^{9} - 4 q^{11} - 2 q^{14} + 4 q^{15} - 4 q^{16} + 2 q^{18} - 4 q^{22} - 4 q^{29} + 4 q^{30} - 2 q^{37} + 2 q^{39} - 2 q^{49} + 2 q^{51} + 2 q^{56} - 2 q^{57} - 4 q^{58} + 2 q^{63} + 4 q^{64} + 4 q^{65} + 4 q^{67} - 2 q^{71} - 2 q^{72} - 2 q^{74} + 2 q^{77} + 2 q^{78} + 2 q^{79} - 2 q^{81} + 4 q^{85} + 4 q^{88} - 4 q^{93} - 4 q^{95} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^7 - 4 * q^8 + 2 * q^9 - 4 * q^11 - 2 * q^14 + 4 * q^15 - 4 * q^16 + 2 * q^18 - 4 * q^22 - 4 * q^29 + 4 * q^30 - 2 * q^37 + 2 * q^39 - 2 * q^49 + 2 * q^51 + 2 * q^56 - 2 * q^57 - 4 * q^58 + 2 * q^63 + 4 * q^64 + 4 * q^65 + 4 * q^67 - 2 * q^71 - 2 * q^72 - 2 * q^74 + 2 * q^77 + 2 * q^78 + 2 * q^79 - 2 * q^81 + 4 * q^85 + 4 * q^88 - 4 * q^93 - 4 * q^95 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.1.ek.a.139.1	yes	4
3.2	odd	2		2457.1.ek.a.685.2		4
7.6	odd	2	inner	819.1.ek.a.139.2	yes	4
9.2	odd	6		2457.1.cj.a.1504.1		4
9.7	even	3		819.1.cj.a.412.1	yes	4
13.3	even	3		819.1.cj.a.328.1	✓	4
21.20	even	2		2457.1.ek.a.685.1		4
39.29	odd	6		2457.1.cj.a.874.2		4
63.20	even	6		2457.1.cj.a.1504.2		4
63.34	odd	6		819.1.cj.a.412.2	yes	4
91.55	odd	6		819.1.cj.a.328.2	yes	4
117.16	even	3	inner	819.1.ek.a.601.2	yes	4
117.29	odd	6		2457.1.ek.a.1693.1		4
273.146	even	6		2457.1.cj.a.874.1		4
819.146	even	6		2457.1.ek.a.1693.2		4
819.601	odd	6	inner	819.1.ek.a.601.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.1.cj.a.328.1	✓	4	13.3	even	3
819.1.cj.a.328.2	yes	4	91.55	odd	6
819.1.cj.a.412.1	yes	4	9.7	even	3
819.1.cj.a.412.2	yes	4	63.34	odd	6
819.1.ek.a.139.1	yes	4	1.1	even	1	trivial
819.1.ek.a.139.2	yes	4	7.6	odd	2	inner
819.1.ek.a.601.1	yes	4	819.601	odd	6	inner
819.1.ek.a.601.2	yes	4	117.16	even	3	inner
2457.1.cj.a.874.1		4	273.146	even	6
2457.1.cj.a.874.2		4	39.29	odd	6
2457.1.cj.a.1504.1		4	9.2	odd	6
2457.1.cj.a.1504.2		4	63.20	even	6
2457.1.ek.a.685.1		4	21.20	even	2
2457.1.ek.a.685.2		4	3.2	odd	2
2457.1.ek.a.1693.1		4	117.29	odd	6
2457.1.ek.a.1693.2		4	819.146	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	819.ek (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.866025 - 0.500000i) q^{10} -1.00000 q^{11} +(-0.866025 + 0.500000i) q^{13} +(-0.500000 + 0.866025i) q^{14} +1.00000 q^{15} -1.00000 q^{16} +(-0.866025 + 0.500000i) q^{17} +(0.500000 - 0.866025i) q^{18} +(0.866025 - 0.500000i) q^{19} -1.00000i q^{21} -1.00000 q^{22} +(0.866025 - 0.500000i) q^{24} +(-0.866025 + 0.500000i) q^{26} +1.00000i q^{27} -1.00000 q^{29} +1.00000 q^{30} +(0.866025 + 0.500000i) q^{31} +(0.866025 - 0.500000i) q^{33} +(-0.866025 + 0.500000i) q^{34} +(0.866025 - 0.500000i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.866025 + 0.500000i) q^{40} -1.00000i q^{42} +(-0.866025 + 0.500000i) q^{45} +(0.866025 - 0.500000i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{51} +1.00000i q^{54} +(0.866025 + 0.500000i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-0.500000 + 0.866025i) q^{57} -1.00000 q^{58} +1.00000i q^{59} +(-1.73205 - 1.00000i) q^{61} +(0.866025 + 0.500000i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +1.00000 q^{65} +(0.866025 - 0.500000i) q^{66} +(1.00000 + 1.73205i) q^{67} +(0.866025 - 0.500000i) q^{70} +(-0.500000 - 0.866025i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-0.500000 + 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{77} +(0.500000 - 0.866025i) q^{78} +(0.500000 + 0.866025i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{83} +1.00000 q^{85} +(0.866025 - 0.500000i) q^{87} +1.00000 q^{88} +(0.866025 + 0.500000i) q^{89} +(-0.866025 + 0.500000i) q^{90} -1.00000i q^{91} -1.00000 q^{93} +(0.866025 - 0.500000i) q^{94} -1.00000 q^{95} +(-0.500000 - 0.866025i) q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^7 - 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} - 2 q^{7} - 4 q^{8} + 2 q^{9} - 4 q^{11} - 2 q^{14} + 4 q^{15} - 4 q^{16} + 2 q^{18} - 4 q^{22} - 4 q^{29} + 4 q^{30} - 2 q^{37} + 2 q^{39} - 2 q^{49} + 2 q^{51} + 2 q^{56} - 2 q^{57} - 4 q^{58} + 2 q^{63} + 4 q^{64} + 4 q^{65} + 4 q^{67} - 2 q^{71} - 2 q^{72} - 2 q^{74} + 2 q^{77} + 2 q^{78} + 2 q^{79} - 2 q^{81} + 4 q^{85} + 4 q^{88} - 4 q^{93} - 4 q^{95} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^7 - 4 * q^8 + 2 * q^9 - 4 * q^11 - 2 * q^14 + 4 * q^15 - 4 * q^16 + 2 * q^18 - 4 * q^22 - 4 * q^29 + 4 * q^30 - 2 * q^37 + 2 * q^39 - 2 * q^49 + 2 * q^51 + 2 * q^56 - 2 * q^57 - 4 * q^58 + 2 * q^63 + 4 * q^64 + 4 * q^65 + 4 * q^67 - 2 * q^71 - 2 * q^72 - 2 * q^74 + 2 * q^77 + 2 * q^78 + 2 * q^79 - 2 * q^81 + 4 * q^85 + 4 * q^88 - 4 * q^93 - 4 * q^95 - 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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