LMFDB - Embedded newform 1071.1.ci.a.727.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,1,Mod(13,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 6, 3]))

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

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

chi := DirichletCharacter("1071.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1071.ci (of order $12$, degree $4$, 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:	$0.534498628530$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.2785671.1

Embedding invariants

Embedding label			727.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1071.727
Dual form			1071.1.ci.a.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.965926 - 0.258819i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.965926 - 0.258819i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.965926 - 0.258819i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.965926 - 0.258819i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(0.707107 + 0.707107i) q^{10} +(-0.366025 - 1.36603i) q^{11} +(-0.965926 - 0.258819i) q^{14} +(-0.866025 - 0.500000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.707107 - 0.707107i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{21} +(-0.366025 + 1.36603i) q^{22} +(1.36603 + 0.366025i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(0.707107 + 0.707107i) q^{27} +(1.36603 - 0.366025i) q^{29} +(0.500000 + 0.866025i) q^{30} -1.41421i q^{33} +(0.258819 + 0.965926i) q^{34} -1.00000 q^{35} +(-1.00000 - 1.00000i) q^{37} +(0.258819 - 0.965926i) q^{40} +(-0.258819 + 0.965926i) q^{41} +(-0.866025 - 0.500000i) q^{42} +(-0.707107 - 0.707107i) q^{45} +(-1.00000 - 1.00000i) q^{46} +(-1.22474 - 0.707107i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-0.500000 - 0.866025i) q^{51} -1.00000i q^{53} +(-0.258819 - 0.965926i) q^{54} +1.41421i q^{55} +(0.258819 + 0.965926i) q^{56} +(-1.36603 - 0.366025i) q^{58} +(0.707107 + 1.22474i) q^{59} +(0.965926 - 0.258819i) q^{61} +(0.965926 + 0.258819i) q^{63} -1.00000 q^{64} +(-0.707107 + 1.22474i) q^{66} +(1.22474 + 0.707107i) q^{69} +(0.866025 + 0.500000i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-0.707107 + 0.707107i) q^{73} +(0.366025 + 1.36603i) q^{74} +(-0.707107 - 1.22474i) q^{77} +(-0.707107 + 0.707107i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.707107 - 0.707107i) q^{82} +(0.500000 + 0.866025i) q^{85} +1.41421 q^{87} +(1.36603 - 0.366025i) q^{88} +(0.258819 + 0.965926i) q^{90} +(0.707107 + 1.22474i) q^{94} +(0.258819 + 0.965926i) q^{97} -1.00000 q^{98} +(0.366025 - 1.36603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 4 q^{11} + 4 q^{16} - 4 q^{18} + 8 q^{21} + 4 q^{22} + 4 q^{23} + 4 q^{29} + 4 q^{30} - 8 q^{35} - 8 q^{37} - 8 q^{46} - 4 q^{51} - 4 q^{58} - 8 q^{64} - 4 q^{72} - 4 q^{74} + 4 q^{81} + 4 q^{85} + 4 q^{88} - 8 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^11 + 4 * q^16 - 4 * q^18 + 8 * q^21 + 4 * q^22 + 4 * q^23 + 4 * q^29 + 4 * q^30 - 8 * q^35 - 8 * q^37 - 8 * q^46 - 4 * q^51 - 4 * q^58 - 8 * q^64 - 4 * q^72 - 4 * q^74 + 4 * q^81 + 4 * q^85 + 4 * q^88 - 8 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.965926	+	0.258819i	0.965926	+	0.258819i
$3$	0.965926	+	0.258819i	0.965926	+	0.258819i
$4$		0			0
$5$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$5$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$6$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$7$	0.965926	−	0.258819i	0.965926	−	0.258819i
$7$	0.965926	−	0.258819i	0.965926	−	0.258819i
$8$			1.00000i			1.00000i
$9$	0.866025	+	0.500000i	0.866025	+	0.500000i
$10$	0.707107	+	0.707107i	0.707107	+	0.707107i
$11$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$11$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$12$		0			0
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$15$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$17$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$18$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		0			0
$21$	1.00000			1.00000
$22$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$23$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$23$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.707107	+	0.707107i
$28$		0			0
$29$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$29$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$30$	0.500000	+	0.866025i	0.500000	+	0.866025i
$31$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$31$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$32$		0			0
$33$		−	1.41421i		−	1.41421i
$34$	0.258819	+	0.965926i	0.258819	+	0.965926i
$35$	−1.00000			−1.00000
$36$		0			0
$37$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$37$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$	0.258819	−	0.965926i	0.258819	−	0.965926i
$41$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$41$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$42$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$		0			0
$45$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$46$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$47$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$47$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$48$	0.707107	−	0.707107i	0.707107	−	0.707107i
$49$	0.866025	−	0.500000i	0.866025	−	0.500000i
$50$		0			0
$51$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$52$		0			0
$53$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$53$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$54$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$55$			1.41421i			1.41421i
$56$	0.258819	+	0.965926i	0.258819	+	0.965926i
$57$		0			0
$58$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$59$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$59$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$60$		0			0
$61$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$61$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$62$		0			0
$63$	0.965926	+	0.258819i	0.965926	+	0.258819i
$64$	−1.00000			−1.00000
$65$		0			0
$66$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	1.22474	+	0.707107i	1.22474	+	0.707107i
$70$	0.866025	+	0.500000i	0.866025	+	0.500000i
$71$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$71$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$72$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$73$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$73$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$74$	0.366025	+	1.36603i	0.366025	+	1.36603i
$75$		0			0
$76$		0			0
$77$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$78$		0			0
$79$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$79$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$80$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$81$	0.500000	+	0.866025i	0.500000	+	0.866025i
$82$	0.707107	−	0.707107i	0.707107	−	0.707107i
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$	0.500000	+	0.866025i	0.500000	+	0.866025i
$86$		0			0
$87$	1.41421			1.41421
$88$	1.36603	−	0.366025i	1.36603	−	0.366025i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	0.258819	+	0.965926i	0.258819	+	0.965926i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	0.707107	+	1.22474i	0.707107	+	1.22474i
$95$		0			0
$96$		0			0
$97$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$97$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$98$	−1.00000			−1.00000
$99$	0.366025	−	1.36603i	0.366025	−	1.36603i
$100$		0			0
$101$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$101$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$102$			1.00000i			1.00000i
$103$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$103$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$104$		0			0
$105$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$106$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$107$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$107$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$108$		0			0
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$	0.707107	−	1.22474i	0.707107	−	1.22474i
$111$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$112$	0.258819	−	0.965926i	0.258819	−	0.965926i
$113$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$113$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$114$		0			0
$115$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$116$		0			0
$117$		0			0
$118$		−	1.41421i		−	1.41421i
$119$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$120$	0.500000	−	0.866025i	0.500000	−	0.866025i
$121$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$122$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$123$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$124$		0			0
$125$	0.707107	+	0.707107i	0.707107	+	0.707107i
$126$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$127$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$127$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$128$	0.866025	+	0.500000i	0.866025	+	0.500000i
$129$		0			0
$130$		0			0
$131$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$131$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$136$	0.707107	−	0.707107i	0.707107	−	0.707107i
$137$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$137$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$138$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$139$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$139$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$140$		0			0
$141$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$142$		0			0
$143$		0			0
$144$	0.866025	−	0.500000i	0.866025	−	0.500000i
$145$	−1.41421			−1.41421
$146$	0.965926	−	0.258819i	0.965926	−	0.258819i
$147$	0.965926	−	0.258819i	0.965926	−	0.258819i
$148$		0			0
$149$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$149$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$150$		0			0
$151$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$151$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$152$		0			0
$153$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$154$			1.41421i			1.41421i
$155$		0			0
$156$		0			0
$157$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$157$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$158$		0			0
$159$	0.258819	−	0.965926i	0.258819	−	0.965926i
$160$		0			0
$161$	1.41421			1.41421
$162$		−	1.00000i		−	1.00000i
$163$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$163$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$164$		0			0
$165$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$166$		0			0
$167$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$167$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$168$			1.00000i			1.00000i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$		−	1.00000i		−	1.00000i
$171$		0			0
$172$		0			0
$173$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$173$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$174$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$175$		0			0
$176$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$177$	0.366025	+	1.36603i	0.366025	+	1.36603i
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$181$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$182$		0			0
$183$	1.00000			1.00000
$184$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$185$	0.707107	+	1.22474i	0.707107	+	1.22474i
$186$		0			0
$187$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$188$		0			0
$189$	0.866025	+	0.500000i	0.866025	+	0.500000i
$190$		0			0
$191$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$191$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$192$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$193$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$193$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$194$	0.258819	−	0.965926i	0.258819	−	0.965926i
$195$		0			0
$196$		0			0
$197$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$197$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$198$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$199$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$199$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$200$		0			0
$201$		0			0
$202$	0.707107	+	1.22474i	0.707107	+	1.22474i
$203$	1.22474	−	0.707107i	1.22474	−	0.707107i
$204$		0			0
$205$	0.500000	−	0.866025i	0.500000	−	0.866025i
$206$	1.41421			1.41421
$207$	1.00000	+	1.00000i	1.00000	+	1.00000i
$208$		0			0
$209$		0			0
$210$	0.707107	+	0.707107i	0.707107	+	0.707107i
$211$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$211$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$212$		0			0
$213$		0			0
$214$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$215$		0			0
$216$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$217$		0			0
$218$		0			0
$219$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$220$		0			0
$221$		0			0
$222$			1.41421i			1.41421i
$223$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$223$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$227$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$228$		0			0
$229$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$229$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$230$	0.707107	+	1.22474i	0.707107	+	1.22474i
$231$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$232$	0.366025	+	1.36603i	0.366025	+	1.36603i
$233$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		0			0
$235$	1.00000	+	1.00000i	1.00000	+	1.00000i
$236$		0			0
$237$		0			0
$238$	0.500000	+	0.866025i	0.500000	+	0.866025i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$241$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$241$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$242$	1.00000			1.00000
$243$	0.258819	+	0.965926i	0.258819	+	0.965926i
$244$		0			0
$245$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$246$	0.866025	−	0.500000i	0.866025	−	0.500000i
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$251$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$251$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$252$		0			0
$253$		−	2.00000i		−	2.00000i
$254$	0.500000	−	0.866025i	0.500000	−	0.866025i
$255$	0.258819	+	0.965926i	0.258819	+	0.965926i
$256$		0			0
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$260$		0			0
$261$	1.36603	+	0.366025i	1.36603	+	0.366025i
$262$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$	1.41421			1.41421
$265$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$269$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$270$			1.00000i			1.00000i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$273$		0			0
$274$	1.73205	−	1.00000i	1.73205	−	1.00000i
$275$		0			0
$276$		0			0
$277$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$277$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$278$	0.707107	+	0.707107i	0.707107	+	0.707107i
$279$		0			0
$280$		−	1.00000i		−	1.00000i
$281$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$281$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$282$	0.366025	+	1.36603i	0.366025	+	1.36603i
$283$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$283$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			1.00000i			1.00000i
$288$		0			0
$289$			1.00000i			1.00000i
$290$	1.22474	+	0.707107i	1.22474	+	0.707107i
$291$			1.00000i			1.00000i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$295$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$296$	1.00000	−	1.00000i	1.00000	−	1.00000i
$297$	0.707107	−	1.22474i	0.707107	−	1.22474i
$298$		−	1.00000i		−	1.00000i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$303$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$304$		0			0
$305$	−1.00000			−1.00000
$306$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$307$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$307$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$308$		0			0
$309$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$310$		0			0
$311$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$311$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$312$		0			0
$313$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$313$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$314$	−1.41421			−1.41421
$315$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$316$		0			0
$317$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$317$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$318$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$319$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$320$	0.965926	+	0.258819i	0.965926	+	0.258819i
$321$	0.707107	+	1.22474i	0.707107	+	1.22474i
$322$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$329$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$330$	1.00000	−	1.00000i	1.00000	−	1.00000i
$331$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$331$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$332$		0			0
$333$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$334$		0			0
$335$		0			0
$336$	0.500000	−	0.866025i	0.500000	−	0.866025i
$337$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$337$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$338$	0.866025	−	0.500000i	0.866025	−	0.500000i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.707107	−	0.707107i	0.707107	−	0.707107i
$344$		0			0
$345$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$346$	0.258819	−	0.965926i	0.258819	−	0.965926i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$349$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$353$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$354$	0.366025	−	1.36603i	0.366025	−	1.36603i
$355$		0			0
$356$		0			0
$357$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	0.707107	−	0.707107i	0.707107	−	0.707107i
$361$	−1.00000			−1.00000
$362$	0.258819	+	0.965926i	0.258819	+	0.965926i
$363$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$364$		0			0
$365$	0.866025	−	0.500000i	0.866025	−	0.500000i
$366$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$367$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$367$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$368$	1.00000	−	1.00000i	1.00000	−	1.00000i
$369$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$370$		−	1.41421i		−	1.41421i
$371$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$372$		0			0
$373$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$373$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$374$	1.22474	−	0.707107i	1.22474	−	0.707107i
$375$	0.500000	+	0.866025i	0.500000	+	0.866025i
$376$	0.707107	−	1.22474i	0.707107	−	1.22474i
$377$		0			0
$378$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$379$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$379$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$380$		0			0
$381$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$382$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$383$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$383$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$384$	0.707107	+	0.707107i	0.707107	+	0.707107i
$385$	0.366025	+	1.36603i	0.366025	+	1.36603i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$392$	0.500000	+	0.866025i	0.500000	+	0.866025i
$393$	0.866025	+	0.500000i	0.866025	+	0.500000i
$394$	1.36603	−	0.366025i	1.36603	−	0.366025i
$395$		0			0
$396$		0			0
$397$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$397$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$398$	0.965926	−	0.258819i	0.965926	−	0.258819i
$399$		0			0
$400$		0			0
$401$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$401$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$406$	−1.41421			−1.41421
$407$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$408$	0.866025	−	0.500000i	0.866025	−	0.500000i
$409$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$409$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$410$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$411$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$412$		0			0
$413$	1.00000	+	1.00000i	1.00000	+	1.00000i
$414$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$415$		0			0
$416$		0			0
$417$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$418$		0			0
$419$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$419$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$420$		0			0
$421$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$421$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$422$		0			0
$423$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$424$	1.00000			1.00000
$425$		0			0
$426$		0			0
$427$	0.866025	−	0.500000i	0.866025	−	0.500000i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$431$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$432$	0.965926	−	0.258819i	0.965926	−	0.258819i
$433$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$433$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$436$		0			0
$437$		0			0
$438$	1.00000			1.00000
$439$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$439$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$440$	−1.41421			−1.41421
$441$	1.00000			1.00000
$442$		0			0
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.258819	+	0.965926i	0.258819	+	0.965926i
$448$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$449$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$449$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$450$		0			0
$451$	1.41421			1.41421
$452$		0			0
$453$	0.707107	+	0.707107i	0.707107	+	0.707107i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$457$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$458$		0			0
$459$		−	1.00000i		−	1.00000i
$460$		0			0
$461$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$461$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$462$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$463$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$463$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$464$	0.366025	−	1.36603i	0.366025	−	1.36603i
$465$		0			0
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$		0			0
$470$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$471$	1.36603	−	0.366025i	1.36603	−	0.366025i
$472$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.500000	−	0.866025i	0.500000	−	0.866025i
$478$		0			0
$479$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$479$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$480$		0			0
$481$		0			0
$482$	0.258819	−	0.965926i	0.258819	−	0.965926i
$483$	1.36603	+	0.366025i	1.36603	+	0.366025i
$484$		0			0
$485$		−	1.00000i		−	1.00000i
$486$	0.258819	−	0.965926i	0.258819	−	0.965926i
$487$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$487$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$488$	0.258819	+	0.965926i	0.258819	+	0.965926i
$489$		0			0
$490$	0.965926	+	0.258819i	0.965926	+	0.258819i
$491$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$491$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$492$		0			0
$493$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$494$		0			0
$495$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$500$		0			0
$501$		0			0
$502$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$505$	1.00000	+	1.00000i	1.00000	+	1.00000i
$506$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$507$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$	0.258819	−	0.965926i	0.258819	−	0.965926i
$511$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$512$		−	1.00000i		−	1.00000i
$513$		0			0
$514$		0			0
$515$	1.36603	−	0.366025i	1.36603	−	0.366025i
$516$		0			0
$517$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$518$	0.707107	+	1.22474i	0.707107	+	1.22474i
$519$			1.00000i			1.00000i
$520$		0			0
$521$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$521$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$522$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$		0			0
$525$		0			0
$526$	0.500000	+	0.866025i	0.500000	+	0.866025i
$527$		0			0
$528$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$529$	0.866025	+	0.500000i	0.866025	+	0.500000i
$530$	0.707107	−	0.707107i	0.707107	−	0.707107i
$531$			1.41421i			1.41421i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$536$		0			0
$537$		0			0
$538$	0.965926	−	0.258819i	0.965926	−	0.258819i
$539$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$540$		0			0
$541$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$541$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$542$		0			0
$543$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$547$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$	0.965926	+	0.258819i	0.965926	+	0.258819i
$550$		0			0
$551$		0			0
$552$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$553$		0			0
$554$		0			0
$555$	0.366025	+	1.36603i	0.366025	+	1.36603i
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$561$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$562$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$		0			0
$566$	0.707107	−	0.707107i	0.707107	−	0.707107i
$567$	0.707107	+	0.707107i	0.707107	+	0.707107i
$568$		0			0
$569$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$569$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$570$		0			0
$571$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$571$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$	0.707107	−	0.707107i	0.707107	−	0.707107i
$574$	0.500000	−	0.866025i	0.500000	−	0.866025i
$575$		0			0
$576$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$577$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$577$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$578$	0.500000	−	0.866025i	0.500000	−	0.866025i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	0.500000	−	0.866025i	0.500000	−	0.866025i
$583$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$584$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$585$		0			0
$586$		0			0
$587$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$587$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$588$		0			0
$589$		0			0
$590$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$591$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$592$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$593$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$593$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$594$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$595$	0.707107	+	0.707107i	0.707107	+	0.707107i
$596$		0			0
$597$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$598$		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
$601$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$601$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.965926	−	0.258819i	0.965926	−	0.258819i
$606$	0.366025	+	1.36603i	0.366025	+	1.36603i
$607$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$607$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$608$		0			0
$609$	1.36603	−	0.366025i	1.36603	−	0.366025i
$610$	0.866025	+	0.500000i	0.866025	+	0.500000i
$611$		0			0
$612$		0			0
$613$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$613$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$614$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$615$	0.707107	−	0.707107i	0.707107	−	0.707107i
$616$	1.22474	−	0.707107i	1.22474	−	0.707107i
$617$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$617$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$618$	1.36603	+	0.366025i	1.36603	+	0.366025i
$619$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$619$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$620$		0			0
$621$	0.707107	+	1.22474i	0.707107	+	1.22474i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.41421i			1.41421i
$630$	0.500000	+	0.866025i	0.500000	+	0.866025i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$635$	0.258819	−	0.965926i	0.258819	−	0.965926i
$636$		0			0
$637$		0			0
$638$			2.00000i			2.00000i
$639$		0			0
$640$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$641$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$641$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$642$		−	1.41421i		−	1.41421i
$643$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$643$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$647$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$648$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$649$	1.41421	−	1.41421i	1.41421	−	1.41421i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$654$		0			0
$655$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$656$	0.707107	+	0.707107i	0.707107	+	0.707107i
$657$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$658$	1.00000	+	1.00000i	1.00000	+	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
$661$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$661$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$662$	0.500000	+	0.866025i	0.500000	+	0.866025i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$667$	2.00000			2.00000
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$672$		0			0
$673$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$673$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$674$	1.00000	−	1.00000i	1.00000	−	1.00000i
$675$		0			0
$676$		0			0
$677$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$677$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$678$		0			0
$679$	0.500000	+	0.866025i	0.500000	+	0.866025i
$680$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$681$		0			0
$682$		0			0
$683$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$683$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$684$		0			0
$685$	1.41421	−	1.41421i	1.41421	−	1.41421i
$686$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$687$		0			0
$688$		0			0
$689$		0			0
$690$	0.366025	+	1.36603i	0.366025	+	1.36603i
$691$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$691$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$692$		0			0
$693$		−	1.41421i		−	1.41421i
$694$		0			0
$695$	0.866025	+	0.500000i	0.866025	+	0.500000i
$696$			1.41421i			1.41421i
$697$	0.866025	−	0.500000i	0.866025	−	0.500000i
$698$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$699$		0			0
$700$		0			0
$701$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$701$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$702$		0			0
$703$		0			0
$704$	0.366025	+	1.36603i	0.366025	+	1.36603i
$705$	0.707107	+	1.22474i	0.707107	+	1.22474i
$706$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$707$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$708$		0			0
$709$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$709$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$	0.258819	+	0.965926i	0.258819	+	0.965926i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$719$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$720$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$721$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$722$	0.866025	+	0.500000i	0.866025	+	0.500000i
$723$			1.00000i			1.00000i
$724$		0			0
$725$		0			0
$726$	0.965926	+	0.258819i	0.965926	+	0.258819i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$			1.00000i			1.00000i
$730$	−1.00000			−1.00000
$731$		0			0
$732$		0			0
$733$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$733$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$734$		0			0
$735$	−1.00000			−1.00000
$736$		0			0
$737$		0			0
$738$	0.965926	−	0.258819i	0.965926	−	0.258819i
$739$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$739$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$740$		0			0
$741$		0			0
$742$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$743$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$743$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$744$		0			0
$745$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.22474	+	0.707107i	1.22474	+	0.707107i
$750$		−	1.00000i		−	1.00000i
$751$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$752$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$753$	0.366025	−	1.36603i	0.366025	−	1.36603i
$754$		0			0
$755$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$756$		0			0
$757$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$757$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$758$	0.366025	+	1.36603i	0.366025	+	1.36603i
$759$	0.517638	−	1.93185i	0.517638	−	1.93185i
$760$		0			0
$761$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$761$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$762$	0.707107	−	0.707107i	0.707107	−	0.707107i
$763$		0			0
$764$		0			0
$765$			1.00000i			1.00000i
$766$			1.41421i			1.41421i
$767$		0			0
$768$		0			0
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$	0.366025	−	1.36603i	0.366025	−	1.36603i
$771$		0			0
$772$		0			0
$773$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$773$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$774$		0			0
$775$		0			0
$776$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$777$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$			1.41421i			1.41421i
$783$	1.22474	+	0.707107i	1.22474	+	0.707107i
$784$		−	1.00000i		−	1.00000i
$785$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$786$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$787$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$787$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$788$		0			0
$789$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$790$		0			0
$791$		0			0
$792$	1.36603	+	0.366025i	1.36603	+	0.366025i
$793$		0			0
$794$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$795$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$796$		0			0
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$	0.366025	+	1.36603i	0.366025	+	1.36603i
$800$		0			0
$801$		0			0
$802$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$803$	1.22474	+	0.707107i	1.22474	+	0.707107i
$804$		0			0
$805$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$806$		0			0
$807$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$808$	0.707107	−	1.22474i	0.707107	−	1.22474i
$809$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$809$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$810$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$		0			0
$813$		0			0
$814$	1.73205	−	1.00000i	1.73205	−	1.00000i
$815$		0			0
$816$	−1.00000			−1.00000
$817$		0			0
$818$	−1.41421			−1.41421
$819$		0			0
$820$		0			0
$821$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$821$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$822$	1.93185	−	0.517638i	1.93185	−	0.517638i
$823$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$823$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$824$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$825$		0			0
$826$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$827$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$827$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$834$	0.500000	+	0.866025i	0.500000	+	0.866025i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$839$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$839$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$840$	0.258819	−	0.965926i	0.258819	−	0.965926i
$841$	0.866025	−	0.500000i	0.866025	−	0.500000i
$842$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$843$	0.707107	+	0.707107i	0.707107	+	0.707107i
$844$		0			0
$845$	0.707107	−	0.707107i	0.707107	−	0.707107i
$846$			1.41421i			1.41421i
$847$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$848$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$849$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$850$		0			0
$851$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$852$		0			0
$853$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$853$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$854$	−1.00000			−1.00000
$855$		0			0
$856$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$857$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$857$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$858$		0			0
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$		0			0
$861$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$862$		0			0
$863$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$863$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$		−	1.00000i		−	1.00000i
$866$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$867$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$868$		0			0
$869$		0			0
$870$	1.00000	+	1.00000i	1.00000	+	1.00000i
$871$		0			0
$872$		0			0
$873$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$874$		0			0
$875$	0.866025	+	0.500000i	0.866025	+	0.500000i
$876$		0			0
$877$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$877$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$	1.22474	+	0.707107i	1.22474	+	0.707107i
$881$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$881$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$882$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$883$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$883$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$884$		0			0
$885$		−	1.41421i		−	1.41421i
$886$		0			0
$887$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$887$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$888$	1.22474	−	0.707107i	1.22474	−	0.707107i
$889$	0.258819	+	0.965926i	0.258819	+	0.965926i
$890$		0			0
$891$	1.00000	−	1.00000i	1.00000	−	1.00000i
$892$		0			0
$893$		0			0
$894$	0.258819	−	0.965926i	0.258819	−	0.965926i
$895$		0			0
$896$	0.965926	+	0.258819i	0.965926	+	0.258819i
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$902$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$903$		0			0
$904$		0			0
$905$	0.500000	+	0.866025i	0.500000	+	0.866025i
$906$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$907$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$907$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$908$		0			0
$909$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$910$		0			0
$911$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$911$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$912$		0			0
$913$		0			0
$914$	0.500000	+	0.866025i	0.500000	+	0.866025i
$915$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$916$		0			0
$917$	1.00000			1.00000
$918$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	0.707107	−	1.22474i	0.707107	−	1.22474i
$921$	0.366025	−	1.36603i	0.366025	−	1.36603i
$922$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$923$		0			0
$924$		0			0
$925$		0			0
$926$			1.00000i			1.00000i
$927$	−1.41421			−1.41421
$928$		0			0
$929$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$929$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.00000	−	1.00000i	1.00000	−	1.00000i
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$941$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$942$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$943$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$944$	1.41421			1.41421
$945$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$946$		0			0
$947$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$947$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		−	1.41421i		−	1.41421i
$952$	0.500000	−	0.866025i	0.500000	−	0.866025i
$953$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$954$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$955$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$956$		0			0
$957$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$958$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$959$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$960$	0.866025	+	0.500000i	0.866025	+	0.500000i
$961$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$962$		0			0
$963$	0.366025	+	1.36603i	0.366025	+	1.36603i
$964$		0			0
$965$		0			0
$966$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$967$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$967$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$		0			0
$970$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$	−1.00000			−1.00000
$974$	1.36603	−	0.366025i	1.36603	−	0.366025i
$975$		0			0
$976$	0.258819	−	0.965926i	0.258819	−	0.965926i
$977$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$977$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.00000			1.00000
$983$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$983$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$984$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$985$	1.22474	−	0.707107i	1.22474	−	0.707107i
$986$	0.707107	+	1.22474i	0.707107	+	1.22474i
$987$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$988$		0			0
$989$		0			0
$990$	1.22474	−	0.707107i	1.22474	−	0.707107i
$991$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$991$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$992$		0			0
$993$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$994$		0			0
$995$	0.866025	−	0.500000i	0.866025	−	0.500000i
$996$		0			0
$997$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$997$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$998$	1.00000	+	1.00000i	1.00000	+	1.00000i
$999$		−	1.41421i		−	1.41421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.1.ci.a.727.2	yes	8
3.2	odd	2		3213.1.cl.a.370.2		8
7.6	odd	2	inner	1071.1.ci.a.727.1	yes	8
9.4	even	3	inner	1071.1.ci.a.13.1	✓	8
9.5	odd	6		3213.1.cl.a.1441.1		8
17.4	even	4	inner	1071.1.ci.a.412.2	yes	8
21.20	even	2		3213.1.cl.a.370.1		8
51.38	odd	4		3213.1.cl.a.1126.2		8
63.13	odd	6	inner	1071.1.ci.a.13.2	yes	8
63.41	even	6		3213.1.cl.a.1441.2		8
119.55	odd	4	inner	1071.1.ci.a.412.1	yes	8
153.4	even	12	inner	1071.1.ci.a.769.1	yes	8
153.140	odd	12		3213.1.cl.a.2197.1		8
357.293	even	4		3213.1.cl.a.1126.1		8
1071.293	even	12		3213.1.cl.a.2197.2		8
1071.769	odd	12	inner	1071.1.ci.a.769.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1071.1.ci.a.13.1	✓	8	9.4	even	3	inner
1071.1.ci.a.13.2	yes	8	63.13	odd	6	inner
1071.1.ci.a.412.1	yes	8	119.55	odd	4	inner
1071.1.ci.a.412.2	yes	8	17.4	even	4	inner
1071.1.ci.a.727.1	yes	8	7.6	odd	2	inner
1071.1.ci.a.727.2	yes	8	1.1	even	1	trivial
1071.1.ci.a.769.1	yes	8	153.4	even	12	inner
1071.1.ci.a.769.2	yes	8	1071.769	odd	12	inner
3213.1.cl.a.370.1		8	21.20	even	2
3213.1.cl.a.370.2		8	3.2	odd	2
3213.1.cl.a.1126.1		8	357.293	even	4
3213.1.cl.a.1126.2		8	51.38	odd	4
3213.1.cl.a.1441.1		8	9.5	odd	6
3213.1.cl.a.1441.2		8	63.41	even	6
3213.1.cl.a.2197.1		8	153.140	odd	12
3213.1.cl.a.2197.2		8	1071.293	even	12

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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1071.ci (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.965926 - 0.258819i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.965926 - 0.258819i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.965926 - 0.258819i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(0.965926 - 0.258819i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(0.707107 + 0.707107i) q^{10} +(-0.366025 - 1.36603i) q^{11} +(-0.965926 - 0.258819i) q^{14} +(-0.866025 - 0.500000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.707107 - 0.707107i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{21} +(-0.366025 + 1.36603i) q^{22} +(1.36603 + 0.366025i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(0.707107 + 0.707107i) q^{27} +(1.36603 - 0.366025i) q^{29} +(0.500000 + 0.866025i) q^{30} -1.41421i q^{33} +(0.258819 + 0.965926i) q^{34} -1.00000 q^{35} +(-1.00000 - 1.00000i) q^{37} +(0.258819 - 0.965926i) q^{40} +(-0.258819 + 0.965926i) q^{41} +(-0.866025 - 0.500000i) q^{42} +(-0.707107 - 0.707107i) q^{45} +(-1.00000 - 1.00000i) q^{46} +(-1.22474 - 0.707107i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.866025 - 0.500000i) q^{49} +(-0.500000 - 0.866025i) q^{51} -1.00000i q^{53} +(-0.258819 - 0.965926i) q^{54} +1.41421i q^{55} +(0.258819 + 0.965926i) q^{56} +(-1.36603 - 0.366025i) q^{58} +(0.707107 + 1.22474i) q^{59} +(0.965926 - 0.258819i) q^{61} +(0.965926 + 0.258819i) q^{63} -1.00000 q^{64} +(-0.707107 + 1.22474i) q^{66} +(1.22474 + 0.707107i) q^{69} +(0.866025 + 0.500000i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-0.707107 + 0.707107i) q^{73} +(0.366025 + 1.36603i) q^{74} +(-0.707107 - 1.22474i) q^{77} +(-0.707107 + 0.707107i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.707107 - 0.707107i) q^{82} +(0.500000 + 0.866025i) q^{85} +1.41421 q^{87} +(1.36603 - 0.366025i) q^{88} +(0.258819 + 0.965926i) q^{90} +(0.707107 + 1.22474i) q^{94} +(0.258819 + 0.965926i) q^{97} -1.00000 q^{98} +(0.366025 - 1.36603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 4 q^{11} + 4 q^{16} - 4 q^{18} + 8 q^{21} + 4 q^{22} + 4 q^{23} + 4 q^{29} + 4 q^{30} - 8 q^{35} - 8 q^{37} - 8 q^{46} - 4 q^{51} - 4 q^{58} - 8 q^{64} - 4 q^{72} - 4 q^{74} + 4 q^{81} + 4 q^{85} + 4 q^{88} - 8 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^11 + 4 * q^16 - 4 * q^18 + 8 * q^21 + 4 * q^22 + 4 * q^23 + 4 * q^29 + 4 * q^30 - 8 * q^35 - 8 * q^37 - 8 * q^46 - 4 * q^51 - 4 * q^58 - 8 * q^64 - 4 * q^72 - 4 * q^74 + 4 * q^81 + 4 * q^85 + 4 * q^88 - 8 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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