LMFDB - Embedded newform 399.1.n.a.254.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,1,Mod(11,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("399.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	399.n (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:	$0.199126940041$
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 4.0.159201.1

Embedding invariants

Embedding label			254.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	399.254
Dual form			399.1.n.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.500000 + 0.866025i) q^{13} +1.00000i q^{14} +(0.500000 - 0.866025i) q^{15} -1.00000 q^{16} +(0.866025 - 0.500000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(-0.866025 - 0.500000i) q^{21} +(0.500000 + 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +(0.866025 + 0.500000i) q^{26} +1.00000i q^{27} +(0.866025 + 0.500000i) q^{29} +(-0.866025 - 0.500000i) q^{30} +(-0.500000 - 0.866025i) q^{31} -1.00000 q^{33} +1.00000i q^{35} +(0.500000 - 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(-0.866025 + 0.500000i) q^{39} -1.00000 q^{40} +(-0.866025 + 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.866025 - 0.500000i) q^{45} +(-1.73205 + 1.00000i) q^{47} +(-0.866025 - 0.500000i) q^{48} +1.00000 q^{49} -1.00000i q^{53} +1.00000 q^{54} +(0.500000 + 0.866025i) q^{55} +1.00000i q^{56} +1.00000i q^{57} +(0.500000 - 0.866025i) q^{58} +(-0.866025 + 0.500000i) q^{62} +(-0.500000 - 0.866025i) q^{63} -1.00000 q^{64} +(0.866025 + 0.500000i) q^{65} +1.00000i q^{66} +1.00000 q^{67} +1.00000 q^{70} +(0.866025 - 0.500000i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-0.866025 - 0.500000i) q^{74} +(0.866025 - 0.500000i) q^{77} +(0.500000 + 0.866025i) q^{78} -1.00000 q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +(-0.866025 + 0.500000i) q^{86} +(0.500000 + 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{90} +(0.500000 - 0.866025i) q^{91} -1.00000i q^{93} +(1.00000 + 1.73205i) q^{94} +(0.866025 - 0.500000i) q^{95} +(-0.500000 - 0.866025i) q^{97} -1.00000i q^{98} +(-0.866025 - 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{6} - 4 q^{7} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^6 - 4 * q^7 + 2 * q^9	$ 4 q + 2 q^{6} - 4 q^{7} + 2 q^{9} - 4 q^{10} - 2 q^{13} + 2 q^{15} - 4 q^{16} + 2 q^{19} + 2 q^{22} + 2 q^{24} - 2 q^{31} - 4 q^{33} + 2 q^{37} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 4 q^{49} + 4 q^{54} + 2 q^{55} + 2 q^{58} - 2 q^{63} - 4 q^{64} + 4 q^{67} + 4 q^{70} + 2 q^{78} - 4 q^{79} - 2 q^{81} + 2 q^{82} + 2 q^{87} + 2 q^{88} - 2 q^{90} + 2 q^{91} + 4 q^{94} - 2 q^{97}+O(q^{100}) $ 4 * q + 2 * q^6 - 4 * q^7 + 2 * q^9 - 4 * q^10 - 2 * q^13 + 2 * q^15 - 4 * q^16 + 2 * q^19 + 2 * q^22 + 2 * q^24 - 2 * q^31 - 4 * q^33 + 2 * q^37 - 4 * q^40 - 2 * q^42 - 2 * q^43 + 4 * q^49 + 4 * q^54 + 2 * q^55 + 2 * q^58 - 2 * q^63 - 4 * q^64 + 4 * q^67 + 4 * q^70 + 2 * q^78 - 4 * q^79 - 2 * q^81 + 2 * q^82 + 2 * q^87 + 2 * q^88 - 2 * q^90 + 2 * q^91 + 4 * q^94 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.1.n.a.254.1	yes	4
3.2	odd	2	inner	399.1.n.a.254.2	yes	4
7.2	even	3		2793.1.bf.c.197.1		4
7.3	odd	6		2793.1.bi.c.2762.2		4
7.4	even	3		399.1.bi.a.368.2	yes	4
7.5	odd	6		2793.1.bf.b.197.1		4
7.6	odd	2		2793.1.n.c.1451.1		4
19.11	even	3		399.1.bi.a.296.1	yes	4
21.2	odd	6		2793.1.bf.c.197.2		4
21.5	even	6		2793.1.bf.b.197.2		4
21.11	odd	6		399.1.bi.a.368.1	yes	4
21.17	even	6		2793.1.bi.c.2762.1		4
21.20	even	2		2793.1.n.c.1451.2		4
57.11	odd	6		399.1.bi.a.296.2	yes	4
133.11	even	3	inner	399.1.n.a.11.1	✓	4
133.30	even	3		2793.1.bf.c.638.2		4
133.68	odd	6		2793.1.bf.b.638.2		4
133.87	odd	6		2793.1.n.c.410.1		4
133.125	odd	6		2793.1.bi.c.1892.1		4
399.11	odd	6	inner	399.1.n.a.11.2	yes	4
399.68	even	6		2793.1.bf.b.638.1		4
399.125	even	6		2793.1.bi.c.1892.2		4
399.296	odd	6		2793.1.bf.c.638.1		4
399.353	even	6		2793.1.n.c.410.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.1.n.a.11.1	✓	4	133.11	even	3	inner
399.1.n.a.11.2	yes	4	399.11	odd	6	inner
399.1.n.a.254.1	yes	4	1.1	even	1	trivial
399.1.n.a.254.2	yes	4	3.2	odd	2	inner
399.1.bi.a.296.1	yes	4	19.11	even	3
399.1.bi.a.296.2	yes	4	57.11	odd	6
399.1.bi.a.368.1	yes	4	21.11	odd	6
399.1.bi.a.368.2	yes	4	7.4	even	3
2793.1.n.c.410.1		4	133.87	odd	6
2793.1.n.c.410.2		4	399.353	even	6
2793.1.n.c.1451.1		4	7.6	odd	2
2793.1.n.c.1451.2		4	21.20	even	2
2793.1.bf.b.197.1		4	7.5	odd	6
2793.1.bf.b.197.2		4	21.5	even	6
2793.1.bf.b.638.1		4	399.68	even	6
2793.1.bf.b.638.2		4	133.68	odd	6
2793.1.bf.c.197.1		4	7.2	even	3
2793.1.bf.c.197.2		4	21.2	odd	6
2793.1.bf.c.638.1		4	399.296	odd	6
2793.1.bf.c.638.2		4	133.30	even	3
2793.1.bi.c.1892.1		4	133.125	odd	6
2793.1.bi.c.1892.2		4	399.125	even	6
2793.1.bi.c.2762.1		4	21.17	even	6
2793.1.bi.c.2762.2		4	7.3	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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	399.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000i q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +(-0.866025 + 0.500000i) q^{11} +(-0.500000 + 0.866025i) q^{13} +1.00000i q^{14} +(0.500000 - 0.866025i) q^{15} -1.00000 q^{16} +(0.866025 - 0.500000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(-0.866025 - 0.500000i) q^{21} +(0.500000 + 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +(0.866025 + 0.500000i) q^{26} +1.00000i q^{27} +(0.866025 + 0.500000i) q^{29} +(-0.866025 - 0.500000i) q^{30} +(-0.500000 - 0.866025i) q^{31} -1.00000 q^{33} +1.00000i q^{35} +(0.500000 - 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(-0.866025 + 0.500000i) q^{39} -1.00000 q^{40} +(-0.866025 + 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.866025 - 0.500000i) q^{45} +(-1.73205 + 1.00000i) q^{47} +(-0.866025 - 0.500000i) q^{48} +1.00000 q^{49} -1.00000i q^{53} +1.00000 q^{54} +(0.500000 + 0.866025i) q^{55} +1.00000i q^{56} +1.00000i q^{57} +(0.500000 - 0.866025i) q^{58} +(-0.866025 + 0.500000i) q^{62} +(-0.500000 - 0.866025i) q^{63} -1.00000 q^{64} +(0.866025 + 0.500000i) q^{65} +1.00000i q^{66} +1.00000 q^{67} +1.00000 q^{70} +(0.866025 - 0.500000i) q^{71} +(0.866025 - 0.500000i) q^{72} +(-0.866025 - 0.500000i) q^{74} +(0.866025 - 0.500000i) q^{77} +(0.500000 + 0.866025i) q^{78} -1.00000 q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +(-0.866025 + 0.500000i) q^{86} +(0.500000 + 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{90} +(0.500000 - 0.866025i) q^{91} -1.00000i q^{93} +(1.00000 + 1.73205i) q^{94} +(0.866025 - 0.500000i) q^{95} +(-0.500000 - 0.866025i) q^{97} -1.00000i q^{98} +(-0.866025 - 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{6} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^6 - 4 * q^7 + 2 * q^9	\( 4 q + 2 q^{6} - 4 q^{7} + 2 q^{9} - 4 q^{10} - 2 q^{13} + 2 q^{15} - 4 q^{16} + 2 q^{19} + 2 q^{22} + 2 q^{24} - 2 q^{31} - 4 q^{33} + 2 q^{37} - 4 q^{40} - 2 q^{42} - 2 q^{43} + 4 q^{49} + 4 q^{54} + 2 q^{55} + 2 q^{58} - 2 q^{63} - 4 q^{64} + 4 q^{67} + 4 q^{70} + 2 q^{78} - 4 q^{79} - 2 q^{81} + 2 q^{82} + 2 q^{87} + 2 q^{88} - 2 q^{90} + 2 q^{91} + 4 q^{94} - 2 q^{97}+O(q^{100}) \) 4 * q + 2 * q^6 - 4 * q^7 + 2 * q^9 - 4 * q^10 - 2 * q^13 + 2 * q^15 - 4 * q^16 + 2 * q^19 + 2 * q^22 + 2 * q^24 - 2 * q^31 - 4 * q^33 + 2 * q^37 - 4 * q^40 - 2 * q^42 - 2 * q^43 + 4 * q^49 + 4 * q^54 + 2 * q^55 + 2 * q^58 - 2 * q^63 - 4 * q^64 + 4 * q^67 + 4 * q^70 + 2 * q^78 - 4 * q^79 - 2 * q^81 + 2 * q^82 + 2 * q^87 + 2 * q^88 - 2 * q^90 + 2 * q^91 + 4 * q^94 - 2 * q^97

Introduction

L-functions

Modular forms

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