LMFDB - Embedded newform 2527.1.y.d.2050.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2527,1,Mod(62,2527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2527, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("2527.62");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2527 = 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2527.y (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.26113728692$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.17689.1

Embedding invariants

Embedding label			2050.2
Root			$-0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	2527.2050
Dual form			2527.1.y.d.1833.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.342020 + 0.939693i) q^{5} +(0.642788 + 0.766044i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.342020 + 0.939693i) q^{5} +(0.642788 + 0.766044i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.984808 + 0.173648i) q^{10} +(-0.642788 - 0.766044i) q^{13} +(0.342020 + 0.939693i) q^{14} +(0.939693 + 0.342020i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(0.984808 + 0.173648i) q^{17} +(0.173648 - 0.984808i) q^{21} +(-0.939693 - 0.342020i) q^{23} +(0.342020 + 0.939693i) q^{24} +(0.866025 - 0.500000i) q^{26} +(0.866025 + 0.500000i) q^{27} +(0.173648 + 0.984808i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-0.342020 + 0.939693i) q^{34} +(0.766044 + 0.642788i) q^{35} -1.00000 q^{39} +(-0.984808 - 0.173648i) q^{40} +(0.642788 - 0.766044i) q^{41} +(0.939693 + 0.342020i) q^{42} +(-0.939693 + 0.342020i) q^{43} +(0.500000 - 0.866025i) q^{46} +(-0.984808 + 0.173648i) q^{47} +(-0.984808 + 0.173648i) q^{48} +(0.500000 - 0.866025i) q^{49} +(0.766044 - 0.642788i) q^{51} +(-0.939693 - 0.342020i) q^{53} +(-0.642788 + 0.766044i) q^{54} +1.00000i q^{56} -1.00000 q^{58} +(0.984808 + 0.173648i) q^{59} +(-0.342020 + 0.939693i) q^{61} +(-0.500000 - 0.866025i) q^{64} +(0.500000 - 0.866025i) q^{65} +(-0.173648 - 0.984808i) q^{67} +(-0.866025 + 0.500000i) q^{69} +(-0.766044 + 0.642788i) q^{70} +(-0.939693 + 0.342020i) q^{71} +(0.642788 - 0.766044i) q^{73} +(0.173648 - 0.984808i) q^{78} +(-0.766044 - 0.642788i) q^{79} +(0.342020 - 0.939693i) q^{80} +(0.939693 - 0.342020i) q^{81} +(0.642788 + 0.766044i) q^{82} +(0.173648 + 0.984808i) q^{85} +(-0.173648 - 0.984808i) q^{86} +(0.866025 + 0.500000i) q^{87} +(0.642788 + 0.766044i) q^{89} +(-0.939693 - 0.342020i) q^{91} -1.00000i q^{94} +(-0.984808 - 0.173648i) q^{97} +(0.766044 + 0.642788i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{8}+O(q^{10}) $ 12 * q - 6 * q^8	$ 12 q - 6 q^{8} - 6 q^{30} - 12 q^{39} + 6 q^{46} + 6 q^{49} - 12 q^{58} - 6 q^{64} + 6 q^{65}+O(q^{100}) $ 12 * q - 6 * q^8 - 6 * q^30 - 12 * q^39 + 6 * q^46 + 6 * q^49 - 12 * q^58 - 6 * q^64 + 6 * q^65

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2527\mathbb{Z}\right)^\times$.

$n$	$1445$	$1807$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$2$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$3$	0.642788	−	0.766044i	0.642788	−	0.766044i	−0.342020	−	0.939693i	$-0.611111\pi$
$3$	0.642788	−	0.766044i	0.642788	−	0.766044i	0.984808	+	0.173648i	$0.0555556\pi$
$4$		0			0
$5$	0.342020	+	0.939693i	0.342020	+	0.939693i	0.984808	+	0.173648i	$0.0555556\pi$
$5$	0.342020	+	0.939693i	0.342020	+	0.939693i	−0.642788	+	0.766044i	$0.722222\pi$
$6$	0.642788	+	0.766044i	0.642788	+	0.766044i
$7$	0.866025	−	0.500000i	0.866025	−	0.500000i
$7$	0.866025	−	0.500000i	0.866025	−	0.500000i
$8$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$9$		0			0
$10$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$13$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$14$	0.342020	+	0.939693i	0.342020	+	0.939693i
$15$	0.939693	+	0.342020i	0.939693	+	0.342020i
$16$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$17$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$17$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$		0			0
$21$	0.173648	−	0.984808i	0.173648	−	0.984808i
$22$		0			0
$23$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$23$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$24$	0.342020	+	0.939693i	0.342020	+	0.939693i
$25$		0			0
$26$	0.866025	−	0.500000i	0.866025	−	0.500000i
$27$	0.866025	+	0.500000i	0.866025	+	0.500000i
$28$		0			0
$29$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$29$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$30$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$		0			0
$33$		0			0
$34$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$35$	0.766044	+	0.642788i	0.766044	+	0.642788i
$36$		0			0
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$		0			0
$39$	−1.00000			−1.00000
$40$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$41$	0.642788	−	0.766044i	0.642788	−	0.766044i	−0.342020	−	0.939693i	$-0.611111\pi$
$41$	0.642788	−	0.766044i	0.642788	−	0.766044i	0.984808	+	0.173648i	$0.0555556\pi$
$42$	0.939693	+	0.342020i	0.939693	+	0.342020i
$43$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$43$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$44$		0			0
$45$		0			0
$46$	0.500000	−	0.866025i	0.500000	−	0.866025i
$47$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$47$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$48$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$49$	0.500000	−	0.866025i	0.500000	−	0.866025i
$50$		0			0
$51$	0.766044	−	0.642788i	0.766044	−	0.642788i
$52$		0			0
$53$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$53$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$54$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$55$		0			0
$56$			1.00000i			1.00000i
$57$		0			0
$58$	−1.00000			−1.00000
$59$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$59$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$60$		0			0
$61$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	0.642788	+	0.766044i	$0.277778\pi$
$61$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$62$		0			0
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$65$	0.500000	−	0.866025i	0.500000	−	0.866025i
$66$		0			0
$67$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$67$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$68$		0			0
$69$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$70$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$71$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$71$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$72$		0			0
$73$	0.642788	−	0.766044i	0.642788	−	0.766044i	−0.342020	−	0.939693i	$-0.611111\pi$
$73$	0.642788	−	0.766044i	0.642788	−	0.766044i	0.984808	+	0.173648i	$0.0555556\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$	0.173648	−	0.984808i	0.173648	−	0.984808i
$79$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$79$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$80$	0.342020	−	0.939693i	0.342020	−	0.939693i
$81$	0.939693	−	0.342020i	0.939693	−	0.342020i
$82$	0.642788	+	0.766044i	0.642788	+	0.766044i
$83$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$83$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$84$		0			0
$85$	0.173648	+	0.984808i	0.173648	+	0.984808i
$86$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$87$	0.866025	+	0.500000i	0.866025	+	0.500000i
$88$		0			0
$89$	0.642788	+	0.766044i	0.642788	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$89$	0.642788	+	0.766044i	0.642788	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$90$		0			0
$91$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$92$		0			0
$93$		0			0
$94$		−	1.00000i		−	1.00000i
$95$		0			0
$96$		0			0
$97$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$97$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$98$	0.766044	+	0.642788i	0.766044	+	0.642788i
$99$		0			0
$100$		0			0
$101$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$101$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$102$	0.500000	+	0.866025i	0.500000	+	0.866025i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	0.984808	−	0.173648i	0.984808	−	0.173648i
$105$	0.984808	−	0.173648i	0.984808	−	0.173648i
$106$	0.500000	−	0.866025i	0.500000	−	0.866025i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$109$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$110$		0			0
$111$		0			0
$112$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		−	1.00000i		−	1.00000i
$116$		0			0
$117$		0			0
$118$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$119$	0.939693	−	0.342020i	0.939693	−	0.342020i
$120$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$121$	0.500000	+	0.866025i	0.500000	+	0.866025i
$122$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$123$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$124$		0			0
$125$	0.866025	+	0.500000i	0.866025	+	0.500000i
$126$		0			0
$127$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$127$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$128$	0.939693	−	0.342020i	0.939693	−	0.342020i
$129$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$130$	0.766044	+	0.642788i	0.766044	+	0.642788i
$131$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$131$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$132$		0			0
$133$		0			0
$134$	1.00000			1.00000
$135$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$136$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$137$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$137$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$138$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$139$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$139$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$140$		0			0
$141$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$142$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$143$		0			0
$144$		0			0
$145$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$146$	0.642788	+	0.766044i	0.642788	+	0.766044i
$147$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$148$		0			0
$149$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$149$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	−0.984808	−	0.173648i	$-0.944444\pi$
$157$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$158$	0.766044	−	0.642788i	0.766044	−	0.642788i
$159$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$160$		0			0
$161$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$162$	0.173648	+	0.984808i	0.173648	+	0.984808i
$163$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$163$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$167$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$168$	0.766044	+	0.642788i	0.766044	+	0.642788i
$169$		0			0
$170$	−1.00000			−1.00000
$171$		0			0
$172$		0			0
$173$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$173$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$174$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$175$		0			0
$176$		0			0
$177$	0.766044	−	0.642788i	0.766044	−	0.642788i
$178$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$181$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$182$	0.500000	−	0.866025i	0.500000	−	0.866025i
$183$	0.500000	+	0.866025i	0.500000	+	0.866025i
$184$	0.766044	−	0.642788i	0.766044	−	0.642788i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.00000			1.00000
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$193$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$193$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$194$	0.342020	−	0.939693i	0.342020	−	0.939693i
$195$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$196$		0			0
$197$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$197$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$198$		0			0
$199$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$199$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$200$		0			0
$201$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$202$	0.866025	−	0.500000i	0.866025	−	0.500000i
$203$	0.642788	+	0.766044i	0.642788	+	0.766044i
$204$		0			0
$205$	0.939693	+	0.342020i	0.939693	+	0.342020i
$206$		0			0
$207$		0			0
$208$			1.00000i			1.00000i
$209$		0			0
$210$			1.00000i			1.00000i
$211$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$211$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$214$		0			0
$215$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$216$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$217$		0			0
$218$	0.173648	+	0.984808i	0.173648	+	0.984808i
$219$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$220$		0			0
$221$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$222$		0			0
$223$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	−0.984808	−	0.173648i	$-0.944444\pi$
$223$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	0.984808	+	0.173648i	0.984808	+	0.173648i
$231$		0			0
$232$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$233$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$233$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$234$		0			0
$235$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$236$		0			0
$237$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$238$	0.173648	+	0.984808i	0.173648	+	0.984808i
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$241$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	0.342020	−	0.939693i	$-0.388889\pi$
$241$	−0.642788	−	0.766044i	−0.642788	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$242$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$243$		0			0
$244$		0			0
$245$	0.984808	+	0.173648i	0.984808	+	0.173648i
$246$	1.00000			1.00000
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$251$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$251$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$252$		0			0
$253$		0			0
$254$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$255$	0.866025	+	0.500000i	0.866025	+	0.500000i
$256$		0			0
$257$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$257$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$258$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.342020	−	0.939693i	0.342020	−	0.939693i
$263$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$263$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$264$		0			0
$265$		−	1.00000i		−	1.00000i
$266$		0			0
$267$	1.00000			1.00000
$268$		0			0
$269$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$269$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$270$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$271$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	−0.984808	−	0.173648i	$-0.944444\pi$
$271$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$272$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$273$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$274$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$275$		0			0
$276$		0			0
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$	0.866025	−	0.500000i	0.866025	−	0.500000i
$279$		0			0
$280$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$281$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$281$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$282$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$283$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$283$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.173648	−	0.984808i	0.173648	−	0.984808i
$288$		0			0
$289$		0			0
$290$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$291$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$292$		0			0
$293$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$293$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$294$	0.984808	−	0.173648i	0.984808	−	0.173648i
$295$	0.173648	+	0.984808i	0.173648	+	0.984808i
$296$		0			0
$297$		0			0
$298$	0.766044	−	0.642788i	0.766044	−	0.642788i
$299$	0.342020	+	0.939693i	0.342020	+	0.939693i
$300$		0			0
$301$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$302$		0			0
$303$	−1.00000			−1.00000
$304$		0			0
$305$	−1.00000			−1.00000
$306$		0			0
$307$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$307$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$	0.500000	−	0.866025i	0.500000	−	0.866025i
$313$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$313$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$314$	0.984808	−	0.173648i	0.984808	−	0.173648i
$315$		0			0
$316$		0			0
$317$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$317$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$318$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$319$		0			0
$320$	0.642788	−	0.766044i	0.642788	−	0.766044i
$321$		0			0
$322$		−	1.00000i		−	1.00000i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$327$	0.342020	−	0.939693i	0.342020	−	0.939693i
$328$	0.342020	+	0.939693i	0.342020	+	0.939693i
$329$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$330$		0			0
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$		0			0
$333$		0			0
$334$	0.866025	+	0.500000i	0.866025	+	0.500000i
$335$	0.866025	−	0.500000i	0.866025	−	0.500000i
$336$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$337$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$337$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		−	1.00000i		−	1.00000i
$344$	0.173648	−	0.984808i	0.173648	−	0.984808i
$345$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$346$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$347$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$347$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$348$		0			0
$349$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$349$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$350$		0			0
$351$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$352$		0			0
$353$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$353$	−1.73205	−	1.00000i	−1.73205	−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$354$	0.500000	+	0.866025i	0.500000	+	0.866025i
$355$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$356$		0			0
$357$	0.342020	−	0.939693i	0.342020	−	0.939693i
$358$		0			0
$359$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$359$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$360$		0			0
$361$		0			0
$362$			1.00000i			1.00000i
$363$	0.984808	+	0.173648i	0.984808	+	0.173648i
$364$		0			0
$365$	0.939693	+	0.342020i	0.939693	+	0.342020i
$366$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$367$	0.642788	+	0.766044i	0.642788	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$367$	0.642788	+	0.766044i	0.642788	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$368$	0.500000	+	0.866025i	0.500000	+	0.866025i
$369$		0			0
$370$		0			0
$371$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$372$		0			0
$373$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$373$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$374$		0			0
$375$	0.939693	−	0.342020i	0.939693	−	0.342020i
$376$	0.342020	−	0.939693i	0.342020	−	0.939693i
$377$	0.642788	−	0.766044i	0.642788	−	0.766044i
$378$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$			1.00000i			1.00000i
$382$		0			0
$383$	0.642788	−	0.766044i	0.642788	−	0.766044i	−0.342020	−	0.939693i	$-0.611111\pi$
$383$	0.642788	−	0.766044i	0.642788	−	0.766044i	0.984808	+	0.173648i	$0.0555556\pi$
$384$	0.342020	−	0.939693i	0.342020	−	0.939693i
$385$		0			0
$386$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$387$		0			0
$388$		0			0
$389$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$389$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$390$	0.984808	−	0.173648i	0.984808	−	0.173648i
$391$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$392$	0.500000	+	0.866025i	0.500000	+	0.866025i
$393$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$394$		0			0
$395$	0.342020	−	0.939693i	0.342020	−	0.939693i
$396$		0			0
$397$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$397$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$398$			1.00000i			1.00000i
$399$		0			0
$400$		0			0
$401$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$401$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$402$	0.642788	−	0.766044i	0.642788	−	0.766044i
$403$		0			0
$404$		0			0
$405$	0.642788	+	0.766044i	0.642788	+	0.766044i
$406$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$407$		0			0
$408$	0.173648	+	0.984808i	0.173648	+	0.984808i
$409$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$409$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$410$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$411$	0.866025	−	0.500000i	0.866025	−	0.500000i
$412$		0			0
$413$	0.939693	−	0.342020i	0.939693	−	0.342020i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.00000			−1.00000
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$421$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$422$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$423$		0			0
$424$	0.766044	−	0.642788i	0.766044	−	0.642788i
$425$		0			0
$426$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$427$	0.173648	+	0.984808i	0.173648	+	0.984808i
$428$		0			0
$429$		0			0
$430$	0.866025	−	0.500000i	0.866025	−	0.500000i
$431$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$431$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$432$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$433$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$433$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$434$		0			0
$435$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$436$		0			0
$437$		0			0
$438$	1.00000			1.00000
$439$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$439$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$440$		0			0
$441$		0			0
$442$	0.939693	−	0.342020i	0.939693	−	0.342020i
$443$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$443$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$444$		0			0
$445$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$446$	0.984808	−	0.173648i	0.984808	−	0.173648i
$447$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$448$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$449$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$449$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	1.00000i		−	1.00000i
$456$		0			0
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$		0			0
$459$	0.766044	+	0.642788i	0.766044	+	0.642788i
$460$		0			0
$461$	0.342020	+	0.939693i	0.342020	+	0.939693i	0.984808	+	0.173648i	$0.0555556\pi$
$461$	0.342020	+	0.939693i	0.342020	+	0.939693i	−0.642788	+	0.766044i	$0.722222\pi$
$462$		0			0
$463$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$463$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$464$	0.500000	−	0.866025i	0.500000	−	0.866025i
$465$		0			0
$466$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$470$	0.939693	−	0.342020i	0.939693	−	0.342020i
$471$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$472$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$473$		0			0
$474$		−	1.00000i		−	1.00000i
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$479$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$480$		0			0
$481$		0			0
$482$	0.866025	−	0.500000i	0.866025	−	0.500000i
$483$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$484$		0			0
$485$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$486$		0			0
$487$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$487$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$488$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$489$	0.684040	+	1.87939i	0.684040	+	1.87939i
$490$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$491$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$491$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$492$		0			0
$493$			1.00000i			1.00000i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$498$		0			0
$499$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$499$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$500$		0			0
$501$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$502$	0.866025	+	0.500000i	0.866025	+	0.500000i
$503$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$503$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$504$		0			0
$505$	0.500000	−	0.866025i	0.500000	−	0.866025i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	0.642788	+	0.766044i	$0.277778\pi$
$509$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$510$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$511$	0.173648	−	0.984808i	0.173648	−	0.984808i
$512$	1.00000			1.00000
$513$		0			0
$514$			1.00000i			1.00000i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.766044	−	0.642788i	0.766044	−	0.642788i
$520$	0.500000	+	0.866025i	0.500000	+	0.866025i
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$523$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$524$		0			0
$525$		0			0
$526$	0.766044	−	0.642788i	0.766044	−	0.642788i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	0.984808	+	0.173648i	0.984808	+	0.173648i
$531$		0			0
$532$		0			0
$533$	−1.00000			−1.00000
$534$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$535$		0			0
$536$	0.939693	+	0.342020i	0.939693	+	0.342020i
$537$		0			0
$538$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$539$		0			0
$540$		0			0
$541$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$541$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$542$	0.984808	−	0.173648i	0.984808	−	0.173648i
$543$	0.500000	−	0.866025i	0.500000	−	0.866025i
$544$		0			0
$545$	0.642788	+	0.766044i	0.642788	+	0.766044i
$546$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$547$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$547$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		−	1.00000i		−	1.00000i
$553$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$557$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$558$		0			0
$559$	0.866025	+	0.500000i	0.866025	+	0.500000i
$560$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$561$		0			0
$562$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$	0.342020	−	0.939693i	0.342020	−	0.939693i
$567$	0.642788	−	0.766044i	0.642788	−	0.766044i
$568$	0.173648	−	0.984808i	0.173648	−	0.984808i
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$		0			0
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$		0			0
$574$	0.939693	+	0.342020i	0.939693	+	0.342020i
$575$		0			0
$576$		0			0
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$		0			0
$579$	0.984808	−	0.173648i	0.984808	−	0.173648i
$580$		0			0
$581$		0			0
$582$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$583$		0			0
$584$	0.342020	+	0.939693i	0.342020	+	0.939693i
$585$		0			0
$586$	1.28558	−	1.53209i	1.28558	−	1.53209i
$587$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$587$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$588$		0			0
$589$		0			0
$590$	−1.00000			−1.00000
$591$		0			0
$592$		0			0
$593$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	0.642788	+	0.766044i	$0.277778\pi$
$593$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$594$		0			0
$595$	0.642788	+	0.766044i	0.642788	+	0.766044i
$596$		0			0
$597$	0.500000	−	0.866025i	0.500000	−	0.866025i
$598$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$599$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$599$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$600$		0			0
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$603$		0			0
$604$		0			0
$605$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$606$	0.173648	−	0.984808i	0.173648	−	0.984808i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$	1.00000			1.00000
$610$	0.173648	−	0.984808i	0.173648	−	0.984808i
$611$	0.766044	+	0.642788i	0.766044	+	0.642788i
$612$		0			0
$613$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$613$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$614$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$615$	0.866025	−	0.500000i	0.866025	−	0.500000i
$616$		0			0
$617$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$617$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$622$		0			0
$623$	0.939693	+	0.342020i	0.939693	+	0.342020i
$624$	0.766044	+	0.642788i	0.766044	+	0.642788i
$625$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$626$			1.00000i			1.00000i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$631$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$632$	0.939693	−	0.342020i	0.939693	−	0.342020i
$633$	0.642788	+	0.766044i	0.642788	+	0.766044i
$634$	0.500000	+	0.866025i	0.500000	+	0.866025i
$635$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$636$		0			0
$637$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$638$		0			0
$639$		0			0
$640$	0.642788	+	0.766044i	0.642788	+	0.766044i
$641$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$641$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$642$		0			0
$643$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$643$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$644$		0			0
$645$	−1.00000			−1.00000
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	0.866025	+	0.500000i	0.866025	+	0.500000i
$655$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$656$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$657$		0			0
$658$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$659$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$659$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	0.642788	+	0.766044i	$0.277778\pi$
$661$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$662$		0			0
$663$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.173648	−	0.984808i	0.173648	−	0.984808i
$668$		0			0
$669$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$670$	0.342020	+	0.939693i	0.342020	+	0.939693i
$671$		0			0
$672$		0			0
$673$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$673$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$674$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$675$		0			0
$676$		0			0
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$		0			0
$679$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$680$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$681$		0			0
$682$		0			0
$683$	2.00000			2.00000			1.00000			$0$
$683$	2.00000			2.00000			1.00000			$0$
$684$		0			0
$685$			1.00000i			1.00000i
$686$	0.984808	+	0.173648i	0.984808	+	0.173648i
$687$		0			0
$688$	0.939693	+	0.342020i	0.939693	+	0.342020i
$689$	0.342020	+	0.939693i	0.342020	+	0.939693i
$690$	0.766044	−	0.642788i	0.766044	−	0.642788i
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$		0			0
$694$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$695$	0.500000	−	0.866025i	0.500000	−	0.866025i
$696$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$697$	0.766044	−	0.642788i	0.766044	−	0.642788i
$698$		0			0
$699$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$700$		0			0
$701$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$701$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$702$	1.00000			1.00000
$703$		0			0
$704$		0			0
$705$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$706$	1.28558	−	1.53209i	1.28558	−	1.53209i
$707$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$708$		0			0
$709$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$709$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$710$	0.866025	−	0.500000i	0.866025	−	0.500000i
$711$		0			0
$712$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$713$		0			0
$714$	0.866025	+	0.500000i	0.866025	+	0.500000i
$715$		0			0
$716$		0			0
$717$		0			0
$718$	0.939693	+	0.342020i	0.939693	+	0.342020i
$719$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$719$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−1.00000			−1.00000
$724$		0			0
$725$		0			0
$726$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$727$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	−0.984808	−	0.173648i	$-0.944444\pi$
$727$	−0.342020	−	0.939693i	−0.342020	−	0.939693i	0.642788	−	0.766044i	$-0.277778\pi$
$728$	0.766044	−	0.642788i	0.766044	−	0.642788i
$729$	0.500000	+	0.866025i	0.500000	+	0.866025i
$730$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$731$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$732$		0			0
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$735$	0.766044	−	0.642788i	0.766044	−	0.642788i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$739$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$740$		0			0
$741$		0			0
$742$		−	1.00000i		−	1.00000i
$743$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$743$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$744$		0			0
$745$	0.342020	−	0.939693i	0.342020	−	0.939693i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.173648	+	0.984808i	0.173648	+	0.984808i
$751$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$751$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$752$	0.866025	+	0.500000i	0.866025	+	0.500000i
$753$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$754$	0.642788	+	0.766044i	0.642788	+	0.766044i
$755$		0			0
$756$		0			0
$757$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$757$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$761$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$762$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$763$	0.642788	−	0.766044i	0.642788	−	0.766044i
$764$		0			0
$765$		0			0
$766$	0.642788	+	0.766044i	0.642788	+	0.766044i
$767$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$768$		0			0
$769$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$769$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$770$		0			0
$771$	0.500000	−	0.866025i	0.500000	−	0.866025i
$772$		0			0
$773$	0.642788	+	0.766044i	0.642788	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$773$	0.642788	+	0.766044i	0.642788	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$774$		0			0
$775$		0			0
$776$	0.642788	−	0.766044i	0.642788	−	0.766044i
$777$		0			0
$778$	−1.00000			−1.00000
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.642788	−	0.766044i	0.642788	−	0.766044i
$783$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$784$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$785$	0.766044	−	0.642788i	0.766044	−	0.642788i
$786$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$787$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$787$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$790$	0.866025	+	0.500000i	0.866025	+	0.500000i
$791$		0			0
$792$		0			0
$793$	0.939693	−	0.342020i	0.939693	−	0.342020i
$794$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$795$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−1.00000			−1.00000
$800$		0			0
$801$		0			0
$802$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$803$		0			0
$804$		0			0
$805$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$806$		0			0
$807$	0.173648	+	0.984808i	0.173648	+	0.984808i
$808$	0.984808	−	0.173648i	0.984808	−	0.173648i
$809$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$809$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$810$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$811$	0.642788	+	0.766044i	0.642788	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$811$	0.642788	+	0.766044i	0.642788	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$812$		0			0
$813$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$814$		0			0
$815$	−1.96962	−	0.347296i	−1.96962	−	0.347296i
$816$	−1.00000			−1.00000
$817$		0			0
$818$			1.00000i			1.00000i
$819$		0			0
$820$		0			0
$821$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$821$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$822$	0.342020	+	0.939693i	0.342020	+	0.939693i
$823$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$823$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$824$		0			0
$825$		0			0
$826$	0.173648	+	0.984808i	0.173648	+	0.984808i
$827$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$827$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$828$		0			0
$829$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$829$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$830$		0			0
$831$		0			0
$832$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$833$	0.642788	−	0.766044i	0.642788	−	0.766044i
$834$	0.173648	−	0.984808i	0.173648	−	0.984808i
$835$	1.00000			1.00000
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$839$	−0.642788	+	0.766044i	−0.642788	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$840$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$841$		0			0
$842$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$843$	0.866025	−	0.500000i	0.866025	−	0.500000i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.866025	+	0.500000i	0.866025	+	0.500000i
$848$	0.500000	+	0.866025i	0.500000	+	0.866025i
$849$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$853$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$854$	−1.00000			−1.00000
$855$		0			0
$856$		0			0
$857$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$857$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$858$		0			0
$859$	0.342020	−	0.939693i	0.342020	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$859$	0.342020	−	0.939693i	0.342020	−	0.939693i	0.984808	−	0.173648i	$-0.0555556\pi$
$860$		0			0
$861$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$862$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$863$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$863$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$864$		0			0
$865$	0.173648	+	0.984808i	0.173648	+	0.984808i
$866$	0.866025	+	0.500000i	0.866025	+	0.500000i
$867$		0			0
$868$		0			0
$869$		0			0
$870$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$871$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$872$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$873$		0			0
$874$		0			0
$875$	1.00000			1.00000
$876$		0			0
$877$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$877$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$878$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$879$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$880$		0			0
$881$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$881$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$882$		0			0
$883$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$883$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$884$		0			0
$885$	0.866025	+	0.500000i	0.866025	+	0.500000i
$886$	0.500000	+	0.866025i	0.500000	+	0.866025i
$887$	0.642788	+	0.766044i	0.642788	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$887$	0.642788	+	0.766044i	0.642788	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$888$		0			0
$889$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$890$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		−	1.00000i		−	1.00000i
$895$		0			0
$896$	0.642788	−	0.766044i	0.642788	−	0.766044i
$897$	0.939693	+	0.342020i	0.939693	+	0.342020i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$902$		0			0
$903$	0.173648	+	0.984808i	0.173648	+	0.984808i
$904$		0			0
$905$	0.500000	+	0.866025i	0.500000	+	0.866025i
$906$		0			0
$907$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$907$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$908$		0			0
$909$		0			0
$910$	0.984808	+	0.173648i	0.984808	+	0.173648i
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$916$		0			0
$917$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$918$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$919$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$919$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$920$	0.866025	+	0.500000i	0.866025	+	0.500000i
$921$	0.173648	+	0.984808i	0.173648	+	0.984808i
$922$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$923$	0.866025	+	0.500000i	0.866025	+	0.500000i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$929$	0.984808	+	0.173648i	0.984808	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.642788	+	0.766044i	0.642788	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$937$	0.642788	+	0.766044i	0.642788	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$938$	0.866025	−	0.500000i	0.866025	−	0.500000i
$939$	0.500000	−	0.866025i	0.500000	−	0.866025i
$940$		0			0
$941$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$941$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$942$	0.500000	−	0.866025i	0.500000	−	0.866025i
$943$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$944$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$945$	0.342020	+	0.939693i	0.342020	+	0.939693i
$946$		0			0
$947$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$947$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$	−1.00000			−1.00000
$950$		0			0
$951$		−	1.00000i		−	1.00000i
$952$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$953$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$953$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	0.866025	+	0.500000i	0.866025	+	0.500000i
$959$	0.984808	−	0.173648i	0.984808	−	0.173648i
$960$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$966$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$967$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$967$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$	1.00000			1.00000
$971$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$971$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$972$		0			0
$973$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$974$		0			0
$975$		0			0
$976$	0.866025	−	0.500000i	0.866025	−	0.500000i
$977$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$977$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$978$	−1.96962	+	0.347296i	−1.96962	+	0.347296i
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$983$	0.342020	+	0.939693i	0.342020	+	0.939693i	0.984808	+	0.173648i	$0.0555556\pi$
$983$	0.342020	+	0.939693i	0.342020	+	0.939693i	−0.642788	+	0.766044i	$0.722222\pi$
$984$	0.939693	+	0.342020i	0.939693	+	0.342020i
$985$		0			0
$986$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$987$			1.00000i			1.00000i
$988$		0			0
$989$	1.00000			1.00000
$990$		0			0
$991$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$991$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$992$		0			0
$993$		0			0
$994$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$995$	0.500000	+	0.866025i	0.500000	+	0.866025i
$996$		0			0
$997$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$997$	−0.984808	+	0.173648i	−0.984808	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$998$	0.173648	+	0.984808i	0.173648	+	0.984808i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2527.1.y.d.2050.2		12
7.6	odd	2	inner	2527.1.y.d.2050.1		12
19.2	odd	18		133.1.m.a.125.1	yes	4
19.3	odd	18		2527.1.d.e.1084.2		2
19.4	even	9	inner	2527.1.y.d.2400.1		12
19.5	even	9		2527.1.m.d.1014.1		4
19.6	even	9	inner	2527.1.y.d.1182.2		12
19.7	even	3	inner	2527.1.y.d.776.2		12
19.8	odd	6		2527.1.y.e.62.2		12
19.9	even	9	inner	2527.1.y.d.1833.1		12
19.10	odd	18		2527.1.y.e.1833.2		12
19.11	even	3	inner	2527.1.y.d.62.1		12
19.12	odd	6		2527.1.y.e.776.1		12
19.13	odd	18		2527.1.y.e.1182.1		12
19.14	odd	18		133.1.m.a.83.2	yes	4
19.15	odd	18		2527.1.y.e.2400.2		12
19.16	even	9		2527.1.d.b.1084.1		2
19.17	even	9		2527.1.m.d.790.2		4
19.18	odd	2		2527.1.y.e.2050.1		12
57.2	even	18		1197.1.ci.c.1189.1		4
57.14	even	18		1197.1.ci.c.748.2		4
76.59	even	18		2128.1.cy.a.657.2		4
76.71	even	18		2128.1.cy.a.881.1		4
95.2	even	36		3325.1.bi.a.524.1		4
95.14	odd	18		3325.1.bc.a.2876.1		4
95.33	even	36		3325.1.bi.b.349.1		4
95.52	even	36		3325.1.bi.a.349.2		4
95.59	odd	18		3325.1.bc.a.3051.2		4
95.78	even	36		3325.1.bi.b.524.2		4
133.2	odd	18		931.1.t.a.619.2		4
133.6	odd	18	inner	2527.1.y.d.1182.1		12
133.13	even	18		2527.1.y.e.1182.2		12
133.27	even	6		2527.1.y.e.62.1		12
133.33	even	18		931.1.k.a.178.1		4
133.34	even	18		2527.1.y.e.2400.1		12
133.40	even	18		931.1.t.a.619.1		4
133.41	even	18		2527.1.d.e.1084.1		2
133.48	even	18		2527.1.y.e.1833.1		12
133.52	even	18		931.1.t.a.558.2		4
133.55	odd	18		2527.1.m.d.790.1		4
133.59	even	18		931.1.k.a.68.1		4
133.62	odd	18		2527.1.m.d.1014.2		4
133.69	even	6		2527.1.y.e.776.2		12
133.83	odd	6	inner	2527.1.y.d.776.1		12
133.90	even	18		133.1.m.a.83.1	✓	4
133.97	even	18		133.1.m.a.125.2	yes	4
133.104	odd	18	inner	2527.1.y.d.1833.2		12
133.109	odd	18		931.1.t.a.558.1		4
133.111	odd	18		2527.1.d.b.1084.2		2
133.116	odd	18		931.1.k.a.68.2		4
133.118	odd	18	inner	2527.1.y.d.2400.2		12
133.125	odd	6	inner	2527.1.y.d.62.2		12
133.128	odd	18		931.1.k.a.178.2		4
133.132	even	2		2527.1.y.e.2050.2		12
399.230	odd	18		1197.1.ci.c.1189.2		4
399.356	odd	18		1197.1.ci.c.748.1		4
532.223	odd	18		2128.1.cy.a.881.2		4
532.363	odd	18		2128.1.cy.a.657.1		4
665.97	odd	36		3325.1.bi.b.524.1		4
665.223	odd	36		3325.1.bi.a.349.1		4
665.363	odd	36		3325.1.bi.a.524.2		4
665.489	even	18		3325.1.bc.a.2876.2		4
665.622	odd	36		3325.1.bi.b.349.2		4
665.629	even	18		3325.1.bc.a.3051.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.1.m.a.83.1	✓	4	133.90	even	18
133.1.m.a.83.2	yes	4	19.14	odd	18
133.1.m.a.125.1	yes	4	19.2	odd	18
133.1.m.a.125.2	yes	4	133.97	even	18
931.1.k.a.68.1		4	133.59	even	18
931.1.k.a.68.2		4	133.116	odd	18
931.1.k.a.178.1		4	133.33	even	18
931.1.k.a.178.2		4	133.128	odd	18
931.1.t.a.558.1		4	133.109	odd	18
931.1.t.a.558.2		4	133.52	even	18
931.1.t.a.619.1		4	133.40	even	18
931.1.t.a.619.2		4	133.2	odd	18
1197.1.ci.c.748.1		4	399.356	odd	18
1197.1.ci.c.748.2		4	57.14	even	18
1197.1.ci.c.1189.1		4	57.2	even	18
1197.1.ci.c.1189.2		4	399.230	odd	18
2128.1.cy.a.657.1		4	532.363	odd	18
2128.1.cy.a.657.2		4	76.59	even	18
2128.1.cy.a.881.1		4	76.71	even	18
2128.1.cy.a.881.2		4	532.223	odd	18
2527.1.d.b.1084.1		2	19.16	even	9
2527.1.d.b.1084.2		2	133.111	odd	18
2527.1.d.e.1084.1		2	133.41	even	18
2527.1.d.e.1084.2		2	19.3	odd	18
2527.1.m.d.790.1		4	133.55	odd	18
2527.1.m.d.790.2		4	19.17	even	9
2527.1.m.d.1014.1		4	19.5	even	9
2527.1.m.d.1014.2		4	133.62	odd	18
2527.1.y.d.62.1		12	19.11	even	3	inner
2527.1.y.d.62.2		12	133.125	odd	6	inner
2527.1.y.d.776.1		12	133.83	odd	6	inner
2527.1.y.d.776.2		12	19.7	even	3	inner
2527.1.y.d.1182.1		12	133.6	odd	18	inner
2527.1.y.d.1182.2		12	19.6	even	9	inner
2527.1.y.d.1833.1		12	19.9	even	9	inner
2527.1.y.d.1833.2		12	133.104	odd	18	inner
2527.1.y.d.2050.1		12	7.6	odd	2	inner
2527.1.y.d.2050.2		12	1.1	even	1	trivial
2527.1.y.d.2400.1		12	19.4	even	9	inner
2527.1.y.d.2400.2		12	133.118	odd	18	inner
2527.1.y.e.62.1		12	133.27	even	6
2527.1.y.e.62.2		12	19.8	odd	6
2527.1.y.e.776.1		12	19.12	odd	6
2527.1.y.e.776.2		12	133.69	even	6
2527.1.y.e.1182.1		12	19.13	odd	18
2527.1.y.e.1182.2		12	133.13	even	18
2527.1.y.e.1833.1		12	133.48	even	18
2527.1.y.e.1833.2		12	19.10	odd	18
2527.1.y.e.2050.1		12	19.18	odd	2
2527.1.y.e.2050.2		12	133.132	even	2
2527.1.y.e.2400.1		12	133.34	even	18
2527.1.y.e.2400.2		12	19.15	odd	18
3325.1.bc.a.2876.1		4	95.14	odd	18
3325.1.bc.a.2876.2		4	665.489	even	18
3325.1.bc.a.3051.1		4	665.629	even	18
3325.1.bc.a.3051.2		4	95.59	odd	18
3325.1.bi.a.349.1		4	665.223	odd	36
3325.1.bi.a.349.2		4	95.52	even	36
3325.1.bi.a.524.1		4	95.2	even	36
3325.1.bi.a.524.2		4	665.363	odd	36
3325.1.bi.b.349.1		4	95.33	even	36
3325.1.bi.b.349.2		4	665.622	odd	36
3325.1.bi.b.524.1		4	665.97	odd	36
3325.1.bi.b.524.2		4	95.78	even	36

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:	\( N \)	\(=\)	\( 2527 = 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2527.y (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.342020 + 0.939693i) q^{5} +(0.642788 + 0.766044i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.342020 + 0.939693i) q^{5} +(0.642788 + 0.766044i) q^{6} +(0.866025 - 0.500000i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.984808 + 0.173648i) q^{10} +(-0.642788 - 0.766044i) q^{13} +(0.342020 + 0.939693i) q^{14} +(0.939693 + 0.342020i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(0.984808 + 0.173648i) q^{17} +(0.173648 - 0.984808i) q^{21} +(-0.939693 - 0.342020i) q^{23} +(0.342020 + 0.939693i) q^{24} +(0.866025 - 0.500000i) q^{26} +(0.866025 + 0.500000i) q^{27} +(0.173648 + 0.984808i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-0.342020 + 0.939693i) q^{34} +(0.766044 + 0.642788i) q^{35} -1.00000 q^{39} +(-0.984808 - 0.173648i) q^{40} +(0.642788 - 0.766044i) q^{41} +(0.939693 + 0.342020i) q^{42} +(-0.939693 + 0.342020i) q^{43} +(0.500000 - 0.866025i) q^{46} +(-0.984808 + 0.173648i) q^{47} +(-0.984808 + 0.173648i) q^{48} +(0.500000 - 0.866025i) q^{49} +(0.766044 - 0.642788i) q^{51} +(-0.939693 - 0.342020i) q^{53} +(-0.642788 + 0.766044i) q^{54} +1.00000i q^{56} -1.00000 q^{58} +(0.984808 + 0.173648i) q^{59} +(-0.342020 + 0.939693i) q^{61} +(-0.500000 - 0.866025i) q^{64} +(0.500000 - 0.866025i) q^{65} +(-0.173648 - 0.984808i) q^{67} +(-0.866025 + 0.500000i) q^{69} +(-0.766044 + 0.642788i) q^{70} +(-0.939693 + 0.342020i) q^{71} +(0.642788 - 0.766044i) q^{73} +(0.173648 - 0.984808i) q^{78} +(-0.766044 - 0.642788i) q^{79} +(0.342020 - 0.939693i) q^{80} +(0.939693 - 0.342020i) q^{81} +(0.642788 + 0.766044i) q^{82} +(0.173648 + 0.984808i) q^{85} +(-0.173648 - 0.984808i) q^{86} +(0.866025 + 0.500000i) q^{87} +(0.642788 + 0.766044i) q^{89} +(-0.939693 - 0.342020i) q^{91} -1.00000i q^{94} +(-0.984808 - 0.173648i) q^{97} +(0.766044 + 0.642788i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{8}+O(q^{10}) \) 12 * q - 6 * q^8	\( 12 q - 6 q^{8} - 6 q^{30} - 12 q^{39} + 6 q^{46} + 6 q^{49} - 12 q^{58} - 6 q^{64} + 6 q^{65}+O(q^{100}) \) 12 * q - 6 * q^8 - 6 * q^30 - 12 * q^39 + 6 * q^46 + 6 * q^49 - 12 * q^58 - 6 * q^64 + 6 * q^65

Introduction

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