LMFDB - Embedded newform 2717.1.db.a.1715.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2717,1,Mod(142,2717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2717, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 8]))

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

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

chi := DirichletCharacter("2717.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2717 = 11 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2717.db (of order $18$, degree $6$, 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:	$1.35595963932$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{9} - \cdots)$

Embedding invariants

Embedding label			1715.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	2717.1715
Dual form			2717.1.db.a.1429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43969 + 0.524005i) q^{2} +(0.266044 - 1.50881i) q^{3} +(1.03209 - 0.866025i) q^{4} +(0.407604 + 2.31164i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.266044 + 0.460802i) q^{8} +(-1.26604 - 0.460802i) q^{9} +O(q^{10})$	\(q+(-1.43969 + 0.524005i) q^{2} +(0.266044 - 1.50881i) q^{3} +(1.03209 - 0.866025i) q^{4} +(0.407604 + 2.31164i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.266044 + 0.460802i) q^{8} +(-1.26604 - 0.460802i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-1.03209 - 1.78763i) q^{12} +(0.173648 + 0.984808i) q^{13} +(1.79813 + 1.50881i) q^{14} +(-0.0923963 + 0.524005i) q^{16} +2.06418 q^{18} +(0.173648 + 0.984808i) q^{19} +(-2.20574 + 0.802823i) q^{21} +(0.266044 - 1.50881i) q^{22} +(-1.43969 + 1.20805i) q^{23} +(0.624485 + 0.524005i) q^{24} +(0.173648 + 0.984808i) q^{25} +(-0.766044 - 1.32683i) q^{26} +(-0.266044 + 0.460802i) q^{27} +(-1.93969 - 0.705990i) q^{28} +(-0.233956 - 1.32683i) q^{32} +(1.17365 + 0.984808i) q^{33} +(-1.70574 + 0.620838i) q^{36} +(-0.766044 - 1.32683i) q^{38} +1.53209 q^{39} +(-0.326352 + 1.85083i) q^{41} +(2.75490 - 2.31164i) q^{42} +(0.233956 + 1.32683i) q^{44} +(1.43969 - 2.49362i) q^{46} +(0.766044 + 0.278817i) q^{48} +(-0.673648 + 1.16679i) q^{49} +(-0.766044 - 1.32683i) q^{50} +(1.03209 + 0.866025i) q^{52} +(-1.43969 + 1.20805i) q^{53} +(0.141559 - 0.802823i) q^{54} +0.815207 q^{56} +1.53209 q^{57} +(0.358441 + 2.03282i) q^{63} +(0.766044 + 1.32683i) q^{64} +(-2.20574 - 0.802823i) q^{66} +(1.43969 + 2.49362i) q^{69} +(0.549163 - 0.460802i) q^{72} +(0.347296 - 1.96962i) q^{73} +1.53209 q^{75} +(1.03209 + 0.866025i) q^{76} +1.53209 q^{77} +(-2.20574 + 0.802823i) q^{78} +(-0.407604 - 0.342020i) q^{81} +(-0.500000 - 2.83564i) q^{82} +(-0.766044 - 1.32683i) q^{83} +(-1.58125 + 2.73881i) q^{84} +(-0.266044 - 0.460802i) q^{88} +(1.17365 - 0.984808i) q^{91} +(-0.439693 + 2.49362i) q^{92} -2.06418 q^{96} +(0.358441 - 2.03282i) q^{98} +(1.03209 - 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9} - 3 q^{11} + 3 q^{12} - 3 q^{14} + 3 q^{16} - 6 q^{18} - 3 q^{21} - 3 q^{22} - 3 q^{23} - 9 q^{24} + 3 q^{27} - 6 q^{28} - 6 q^{32} + 6 q^{33} - 3 q^{41} + 18 q^{42} + 6 q^{44} + 3 q^{46} - 3 q^{49} - 3 q^{52} - 3 q^{53} + 9 q^{54} + 12 q^{56} - 6 q^{63} - 3 q^{66} + 3 q^{69} + 15 q^{72} - 3 q^{76} - 3 q^{78} - 6 q^{81} - 3 q^{82} - 12 q^{84} + 3 q^{88} + 6 q^{91} + 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9 - 3 * q^11 + 3 * q^12 - 3 * q^14 + 3 * q^16 - 6 * q^18 - 3 * q^21 - 3 * q^22 - 3 * q^23 - 9 * q^24 + 3 * q^27 - 6 * q^28 - 6 * q^32 + 6 * q^33 - 3 * q^41 + 18 * q^42 + 6 * q^44 + 3 * q^46 - 3 * q^49 - 3 * q^52 - 3 * q^53 + 9 * q^54 + 12 * q^56 - 6 * q^63 - 3 * q^66 + 3 * q^69 + 15 * q^72 - 3 * q^76 - 3 * q^78 - 6 * q^81 - 3 * q^82 - 12 * q^84 + 3 * q^88 + 6 * q^91 + 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$2$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$4$	1.03209	−	0.866025i	1.03209	−	0.866025i
$5$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$5$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$6$	0.407604	+	2.31164i	0.407604	+	2.31164i
$7$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$7$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$8$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$9$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$12$	−1.03209	−	1.78763i	−1.03209	−	1.78763i
$13$	0.173648	+	0.984808i	0.173648	+	0.984808i
$13$	0.173648	+	0.984808i	0.173648	+	0.984808i
$14$	1.79813	+	1.50881i	1.79813	+	1.50881i
$15$		0			0
$16$	−0.0923963	+	0.524005i	−0.0923963	+	0.524005i
$17$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$17$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$18$	2.06418			2.06418
$19$	0.173648	+	0.984808i	0.173648	+	0.984808i
$19$	0.173648	+	0.984808i	0.173648	+	0.984808i
$20$		0			0
$21$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$22$	0.266044	−	1.50881i	0.266044	−	1.50881i
$23$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$23$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$24$	0.624485	+	0.524005i	0.624485	+	0.524005i
$25$	0.173648	+	0.984808i	0.173648	+	0.984808i
$26$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$27$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$28$	−1.93969	−	0.705990i	−1.93969	−	0.705990i
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$33$	1.17365	+	0.984808i	1.17365	+	0.984808i
$34$		0			0
$35$		0			0
$36$	−1.70574	+	0.620838i	−1.70574	+	0.620838i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$39$	1.53209			1.53209
$40$		0			0
$41$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$41$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$42$	2.75490	−	2.31164i	2.75490	−	2.31164i
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	0.233956	+	1.32683i	0.233956	+	1.32683i
$45$		0			0
$46$	1.43969	−	2.49362i	1.43969	−	2.49362i
$47$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$47$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$48$	0.766044	+	0.278817i	0.766044	+	0.278817i
$49$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$50$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$51$		0			0
$52$	1.03209	+	0.866025i	1.03209	+	0.866025i
$53$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$53$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$54$	0.141559	−	0.802823i	0.141559	−	0.802823i
$55$		0			0
$56$	0.815207			0.815207
$57$	1.53209			1.53209
$58$		0			0
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$		0			0
$61$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$61$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$62$		0			0
$63$	0.358441	+	2.03282i	0.358441	+	2.03282i
$64$	0.766044	+	1.32683i	0.766044	+	1.32683i
$65$		0			0
$66$	−2.20574	−	0.802823i	−2.20574	−	0.802823i
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$		0			0
$69$	1.43969	+	2.49362i	1.43969	+	2.49362i
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	0.549163	−	0.460802i	0.549163	−	0.460802i
$73$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$73$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$74$		0			0
$75$	1.53209			1.53209
$76$	1.03209	+	0.866025i	1.03209	+	0.866025i
$77$	1.53209			1.53209
$78$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$		0			0
$81$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$82$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$83$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$83$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$84$	−1.58125	+	2.73881i	−1.58125	+	2.73881i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$89$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$89$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$90$		0			0
$91$	1.17365	−	0.984808i	1.17365	−	0.984808i
$92$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−2.06418			−2.06418
$97$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$97$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$98$	0.358441	−	2.03282i	0.358441	−	2.03282i
$99$	1.03209	−	0.866025i	1.03209	−	0.866025i
$100$	1.03209	+	0.866025i	1.03209	+	0.866025i
$101$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$101$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$102$		0			0
$103$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$103$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$104$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$105$		0			0
$106$	1.43969	−	2.49362i	1.43969	−	2.49362i
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	0.124485	+	0.705990i	0.124485	+	0.705990i
$109$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$109$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$110$		0			0
$111$		0			0
$112$	0.766044	−	0.278817i	0.766044	−	0.278817i
$113$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$113$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$114$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$115$		0			0
$116$		0			0
$117$	0.233956	−	1.32683i	0.233956	−	1.32683i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$	2.70574	+	0.984808i	2.70574	+	0.984808i
$124$		0			0
$125$		0			0
$126$	−1.58125	−	2.73881i	−1.58125	−	2.73881i
$127$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$127$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$128$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$129$		0			0
$130$		0			0
$131$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$131$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$132$	2.06418			2.06418
$133$	1.17365	−	0.984808i	1.17365	−	0.984808i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$137$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$138$	−3.37939	−	2.83564i	−3.37939	−	2.83564i
$139$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$139$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$144$	0.358441	−	0.620838i	0.358441	−	0.620838i
$145$		0			0
$146$	0.532089	+	3.01763i	0.532089	+	3.01763i
$147$	1.58125	+	1.32683i	1.58125	+	1.32683i
$148$		0			0
$149$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$149$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$150$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$151$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$151$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$152$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$153$		0			0
$154$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$155$		0			0
$156$	1.58125	−	1.32683i	1.58125	−	1.32683i
$157$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$157$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$158$		0			0
$159$	1.43969	+	2.49362i	1.43969	+	2.49362i
$160$		0			0
$161$	2.70574	+	0.984808i	2.70574	+	0.984808i
$162$	0.766044	+	0.278817i	0.766044	+	0.278817i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	1.26604	+	2.19285i	1.26604	+	2.19285i
$165$		0			0
$166$	1.79813	+	1.50881i	1.79813	+	1.50881i
$167$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$167$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$168$	0.216881	−	1.23000i	0.216881	−	1.23000i
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$		0			0
$171$	0.233956	−	1.32683i	0.233956	−	1.32683i
$172$		0			0
$173$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$173$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$174$		0			0
$175$	1.17365	−	0.984808i	1.17365	−	0.984808i
$176$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$177$		0			0
$178$		0			0
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$180$		0			0
$181$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$181$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$182$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$183$		0			0
$184$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.815207			0.815207
$190$		0			0
$191$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$191$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$192$	2.20574	−	0.802823i	2.20574	−	0.802823i
$193$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$193$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$		0			0
$196$	0.315207	+	1.78763i	0.315207	+	1.78763i
$197$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$197$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$198$	−1.03209	+	1.78763i	−1.03209	+	1.78763i
$199$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$199$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$200$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$207$	2.37939	−	0.866025i	2.37939	−	0.866025i
$208$	−0.532089			−0.532089
$209$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$210$		0			0
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−0.141559	−	0.245188i	−0.141559	−	0.245188i
$217$		0			0
$218$	1.43969	+	0.524005i	1.43969	+	0.524005i
$219$	−2.87939	−	1.04801i	−2.87939	−	1.04801i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$223$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$224$	−1.58125	+	1.32683i	−1.58125	+	1.32683i
$225$	0.233956	−	1.32683i	0.233956	−	1.32683i
$226$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$227$	2.00000			2.00000			1.00000			$0$
$227$	2.00000			2.00000			1.00000			$0$
$228$	1.58125	−	1.32683i	1.58125	−	1.32683i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	0.407604	−	2.31164i	0.407604	−	2.31164i
$232$		0			0
$233$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$233$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$234$	0.358441	+	2.03282i	0.358441	+	2.03282i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$239$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$240$		0			0
$241$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$241$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$242$	1.17365	+	0.984808i	1.17365	+	0.984808i
$243$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$244$		0			0
$245$		0			0
$246$	−4.41147			−4.41147
$247$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$248$		0			0
$249$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$250$		0			0
$251$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$251$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$252$	2.13041	+	1.78763i	2.13041	+	1.78763i
$253$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$257$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$263$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$264$	−0.766044	+	0.278817i	−0.766044	+	0.278817i
$265$		0			0
$266$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$267$		0			0
$268$		0			0
$269$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$269$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$270$		0			0
$271$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$271$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$272$		0			0
$273$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$274$		0			0
$275$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$276$	3.64543	+	1.32683i	3.64543	+	1.32683i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$281$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$282$		0			0
$283$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$283$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$284$		0			0
$285$		0			0
$286$	1.53209			1.53209
$287$	2.70574	−	0.984808i	2.70574	−	0.984808i
$288$	−0.315207	+	1.78763i	−0.315207	+	1.78763i
$289$	0.766044	−	0.642788i	0.766044	−	0.642788i
$290$		0			0
$291$		0			0
$292$	−1.34730	−	2.33359i	−1.34730	−	2.33359i
$293$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$293$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$294$	−2.97178	−	1.08164i	−2.97178	−	1.08164i
$295$		0			0
$296$		0			0
$297$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$298$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$299$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$300$	1.58125	−	1.32683i	1.58125	−	1.32683i
$301$		0			0
$302$	1.43969	−	0.524005i	1.43969	−	0.524005i
$303$		0			0
$304$	−0.532089			−0.532089
$305$		0			0
$306$		0			0
$307$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$307$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$308$	1.58125	−	1.32683i	1.58125	−	1.32683i
$309$	0.407604	+	0.342020i	0.407604	+	0.342020i
$310$		0			0
$311$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$311$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$312$	−0.407604	+	0.705990i	−0.407604	+	0.705990i
$313$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$313$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$314$	1.43969	+	0.524005i	1.43969	+	0.524005i
$315$		0			0
$316$		0			0
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$	−3.37939	−	2.83564i	−3.37939	−	2.83564i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−4.41147			−4.41147
$323$		0			0
$324$	−0.716881			−0.716881
$325$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$326$		0			0
$327$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$328$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−1.93969	−	0.705990i	−1.93969	−	0.705990i
$333$		0			0
$334$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$335$		0			0
$336$	−0.216881	−	1.23000i	−0.216881	−	1.23000i
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	1.17365	−	0.984808i	1.17365	−	0.984808i
$339$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$340$		0			0
$341$		0			0
$342$	0.358441	+	2.03282i	0.358441	+	2.03282i
$343$	0.532089			0.532089
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$347$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$349$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$350$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$351$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$352$	1.26604	+	0.460802i	1.26604	+	0.460802i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$359$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$359$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$360$		0			0
$361$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$362$	−2.87939			−2.87939
$363$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$364$	0.358441	−	2.03282i	0.358441	−	2.03282i
$365$		0			0
$366$		0			0
$367$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$367$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$368$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$369$	1.26604	−	2.19285i	1.26604	−	2.19285i
$370$		0			0
$371$	2.70574	+	0.984808i	2.70574	+	0.984808i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−1.17365	+	0.427173i	−1.17365	+	0.427173i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	1.43969	−	0.524005i	1.43969	−	0.524005i
$383$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$383$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$384$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$385$		0			0
$386$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$387$		0			0
$388$		0			0
$389$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$389$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$390$		0			0
$391$		0			0
$392$	−0.358441	−	0.620838i	−0.358441	−	0.620838i
$393$		0			0
$394$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$395$		0			0
$396$	0.315207	−	1.78763i	0.315207	−	1.78763i
$397$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$397$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$398$	0.532089			0.532089
$399$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$400$	−0.532089			−0.532089
$401$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$401$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$409$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$410$		0			0
$411$		0			0
$412$	0.0812519	+	0.460802i	0.0812519	+	0.460802i
$413$		0			0
$414$	−2.97178	+	2.49362i	−2.97178	+	2.49362i
$415$		0			0
$416$	1.26604	−	0.460802i	1.26604	−	0.460802i
$417$		0			0
$418$	1.53209			1.53209
$419$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$420$		0			0
$421$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$421$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$422$		0			0
$423$		0			0
$424$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$430$		0			0
$431$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$431$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$432$	−0.216881	−	0.181985i	−0.216881	−	0.181985i
$433$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$433$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$434$		0			0
$435$		0			0
$436$	−1.34730			−1.34730
$437$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$438$	4.69459			4.69459
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	1.39053	−	1.16679i	1.39053	−	1.16679i
$442$		0			0
$443$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$443$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.43969	+	0.524005i	1.43969	+	0.524005i
$448$	1.17365	−	2.03282i	1.17365	−	2.03282i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	0.358441	+	2.03282i	0.358441	+	2.03282i
$451$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$452$	0.358441	−	0.300767i	0.358441	−	0.300767i
$453$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$454$	−2.87939	+	1.04801i	−2.87939	+	1.04801i
$455$		0			0
$456$	−0.407604	+	0.705990i	−0.407604	+	0.705990i
$457$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$457$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$461$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$462$	0.624485	+	3.54163i	0.624485	+	3.54163i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$468$	−0.907604	−	1.57202i	−0.907604	−	1.57202i
$469$		0			0
$470$		0			0
$471$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$476$		0			0
$477$	2.37939	−	0.866025i	2.37939	−	0.866025i
$478$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$479$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$479$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$480$		0			0
$481$		0			0
$482$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$483$	2.20574	−	3.82045i	2.20574	−	3.82045i
$484$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$485$		0			0
$486$	1.03209	−	1.78763i	1.03209	−	1.78763i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$491$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$492$	3.64543	−	1.32683i	3.64543	−	1.32683i
$493$		0			0
$494$	1.17365	−	0.984808i	1.17365	−	0.984808i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.75490	−	2.31164i	2.75490	−	2.31164i
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$		0			0
$501$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$502$	−1.53209	+	2.65366i	−1.53209	+	2.65366i
$503$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$503$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$504$	−1.03209	−	0.375650i	−1.03209	−	0.375650i
$505$		0			0
$506$	1.43969	+	2.49362i	1.43969	+	2.49362i
$507$	0.266044	+	1.50881i	0.266044	+	1.50881i
$508$		0			0
$509$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$509$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$510$		0			0
$511$	−2.87939	+	1.04801i	−2.87939	+	1.04801i
$512$	1.00000			1.00000
$513$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$514$	3.06418			3.06418
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$521$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$522$		0			0
$523$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$523$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$524$		0			0
$525$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$526$		0			0
$527$		0			0
$528$	−0.624485	+	0.524005i	−0.624485	+	0.524005i
$529$	0.439693	−	2.49362i	0.439693	−	2.49362i
$530$		0			0
$531$		0			0
$532$	0.358441	−	2.03282i	0.358441	−	2.03282i
$533$	−1.87939			−1.87939
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.407604	+	0.342020i	0.407604	+	0.342020i
$538$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$539$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$540$		0			0
$541$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$541$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$542$	2.70574	+	0.984808i	2.70574	+	0.984808i
$543$	1.43969	−	2.49362i	1.43969	−	2.49362i
$544$		0			0
$545$		0			0
$546$	2.75490	+	2.31164i	2.75490	+	2.31164i
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$		0			0
$549$		0			0
$550$	1.53209			1.53209
$551$		0			0
$552$	−1.53209			−1.53209
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$557$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.43969	−	2.49362i	1.43969	−	2.49362i
$563$		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			0
$567$	−0.141559	+	0.802823i	−0.141559	+	0.802823i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$573$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$574$	−3.37939	+	2.83564i	−3.37939	+	2.83564i
$575$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$576$	−0.358441	−	2.03282i	−0.358441	−	2.03282i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$579$	2.70574	+	0.984808i	2.70574	+	0.984808i
$580$		0			0
$581$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$582$		0			0
$583$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$584$	0.815207	+	0.684040i	0.815207	+	0.684040i
$585$		0			0
$586$	0.407604	−	2.31164i	0.407604	−	2.31164i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	2.78106			2.78106
$589$		0			0
$590$		0			0
$591$	2.70574	−	0.984808i	2.70574	−	0.984808i
$592$		0			0
$593$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$593$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$594$	0.624485	+	0.524005i	0.624485	+	0.524005i
$595$		0			0
$596$	0.673648	+	1.16679i	0.673648	+	1.16679i
$597$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$598$	2.70574	+	0.984808i	2.70574	+	0.984808i
$599$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$599$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$600$	−0.407604	+	0.705990i	−0.407604	+	0.705990i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	1.26604	−	0.460802i	1.26604	−	0.460802i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$613$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$614$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$615$		0			0
$616$	−0.407604	+	0.705990i	−0.407604	+	0.705990i
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	−0.766044	−	0.278817i	−0.766044	−	0.278817i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$622$	1.79813	+	1.50881i	1.79813	+	1.50881i
$623$		0			0
$624$	−0.141559	+	0.802823i	−0.141559	+	0.802823i
$625$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$626$	−1.53209			−1.53209
$627$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$628$	−1.34730			−1.34730
$629$		0			0
$630$		0			0
$631$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$631$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	3.64543	+	1.32683i	3.64543	+	1.32683i
$637$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$641$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$643$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$644$	3.64543	−	1.32683i	3.64543	−	1.32683i
$645$		0			0
$646$		0			0
$647$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$647$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$648$	0.266044	−	0.0968323i	0.266044	−	0.0968323i
$649$		0			0
$650$	1.17365	−	0.984808i	1.17365	−	0.984808i
$651$		0			0
$652$		0			0
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$654$	1.17365	−	2.03282i	1.17365	−	2.03282i
$655$		0			0
$656$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$657$	−1.34730	+	2.33359i	−1.34730	+	2.33359i
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$		0			0
$664$	0.815207			0.815207
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.0812519	−	0.460802i	0.0812519	−	0.460802i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	1.58125	+	2.73881i	1.58125	+	2.73881i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$676$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$	0.141559	+	0.802823i	0.141559	+	0.802823i
$679$		0			0
$680$		0			0
$681$	0.532089	−	3.01763i	0.532089	−	3.01763i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.907604	−	1.57202i	−0.907604	−	1.57202i
$685$		0			0
$686$	−0.766044	+	0.278817i	−0.766044	+	0.278817i
$687$		0			0
$688$		0			0
$689$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$	−1.93969	−	0.705990i	−1.93969	−	0.705990i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.407604	+	0.342020i	0.407604	+	0.342020i
$699$		0			0
$700$	0.358441	−	2.03282i	0.358441	−	2.03282i
$701$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$701$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$702$	0.815207			0.815207
$703$		0			0
$704$	−1.53209			−1.53209
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$709$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0812519	+	0.460802i	0.0812519	+	0.460802i
$717$	0.407604	+	0.342020i	0.407604	+	0.342020i
$718$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$720$		0			0
$721$	0.532089			0.532089
$722$	1.17365	−	0.984808i	1.17365	−	0.984808i
$723$	2.34730			2.34730
$724$	2.37939	−	0.866025i	2.37939	−	0.866025i
$725$		0			0
$726$	1.79813	−	1.50881i	1.79813	−	1.50881i
$727$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$727$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$728$	0.141559	+	0.802823i	0.141559	+	0.802823i
$729$	0.766044	+	1.32683i	0.766044	+	1.32683i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$733$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$734$	−1.53209	−	2.65366i	−1.53209	−	2.65366i
$735$		0			0
$736$	1.93969	+	1.62760i	1.93969	+	1.62760i
$737$		0			0
$738$	−0.673648	+	3.82045i	−0.673648	+	3.82045i
$739$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$739$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$740$		0			0
$741$	0.266044	+	1.50881i	0.266044	+	1.50881i
$742$	−4.41147			−4.41147
$743$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.358441	+	2.03282i	0.358441	+	2.03282i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$751$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$752$		0			0
$753$	−1.53209	−	2.65366i	−1.53209	−	2.65366i
$754$		0			0
$755$		0			0
$756$	0.841367	−	0.705990i	0.841367	−	0.705990i
$757$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$757$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$758$		0			0
$759$	−2.87939			−2.87939
$760$		0			0
$761$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$761$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$762$		0			0
$763$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$764$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$769$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$770$		0			0
$771$	−1.53209	+	2.65366i	−1.53209	+	2.65366i
$772$	1.26604	+	2.19285i	1.26604	+	2.19285i
$773$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$773$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.53209			−1.53209
$779$	−1.87939			−1.87939
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.549163	−	0.460802i	−0.549163	−	0.460802i
$785$		0			0
$786$		0			0
$787$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$787$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$788$	2.37939	+	0.866025i	2.37939	+	0.866025i
$789$		0			0
$790$		0			0
$791$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$792$	0.124485	+	0.705990i	0.124485	+	0.705990i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.439693	+	0.160035i	−0.439693	+	0.160035i
$797$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$797$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$798$	2.75490	+	2.31164i	2.75490	+	2.31164i
$799$		0			0
$800$	1.26604	−	0.460802i	1.26604	−	0.460802i
$801$		0			0
$802$		0			0
$803$	1.53209	+	1.28558i	1.53209	+	1.28558i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.70574	+	0.984808i	2.70574	+	0.984808i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$811$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$812$		0			0
$813$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−2.87939			−2.87939
$819$	−1.93969	+	0.705990i	−1.93969	+	0.705990i
$820$		0			0
$821$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$821$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$822$		0			0
$823$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$823$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$824$	−0.0923963	−	0.160035i	−0.0923963	−	0.160035i
$825$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$826$		0			0
$827$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$827$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$828$	1.70574	−	2.95442i	1.70574	−	2.95442i
$829$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$830$		0			0
$831$		0			0
$832$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$837$		0			0
$838$	1.43969	−	0.524005i	1.43969	−	0.524005i
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$		0			0
$843$	1.43969	+	2.49362i	1.43969	+	2.49362i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$848$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$853$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$857$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$858$	0.407604	−	2.31164i	0.407604	−	2.31164i
$859$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$859$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$860$		0			0
$861$	−0.766044	−	4.34445i	−0.766044	−	4.34445i
$862$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	0.673648	+	0.245188i	0.673648	+	0.245188i
$865$		0			0
$866$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$867$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.500000	−	0.181985i	0.500000	−	0.181985i
$873$		0			0
$874$	2.70574	+	0.984808i	2.70574	+	0.984808i
$875$		0			0
$876$	−3.87939	+	1.41198i	−3.87939	+	1.41198i
$877$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$877$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$878$		0			0
$879$	1.79813	+	1.50881i	1.79813	+	1.50881i
$880$		0			0
$881$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$881$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$882$	−1.39053	+	2.40847i	−1.39053	+	2.40847i
$883$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$883$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$884$		0			0
$885$		0			0
$886$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$887$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$887$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.500000	−	0.181985i	0.500000	−	0.181985i
$892$		0			0
$893$		0			0
$894$	−2.34730			−2.34730
$895$		0			0
$896$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$897$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$898$		0			0
$899$		0			0
$900$	−0.907604	−	1.57202i	−0.907604	−	1.57202i
$901$		0			0
$902$	2.70574	+	0.984808i	2.70574	+	0.984808i
$903$		0			0
$904$	−0.0923963	+	0.160035i	−0.0923963	+	0.160035i
$905$		0			0
$906$	−0.407604	−	2.31164i	−0.407604	−	2.31164i
$907$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$907$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$908$	2.06418	−	1.73205i	2.06418	−	1.73205i
$909$		0			0
$910$		0			0
$911$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$911$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$912$	−0.141559	+	0.802823i	−0.141559	+	0.802823i
$913$	1.53209			1.53209
$914$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$922$	1.43969	+	0.524005i	1.43969	+	0.524005i
$923$		0			0
$924$	−1.58125	−	2.73881i	−1.58125	−	2.73881i
$925$		0			0
$926$		0			0
$927$	0.358441	−	0.300767i	0.358441	−	0.300767i
$928$		0			0
$929$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$929$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$930$		0			0
$931$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$932$		0			0
$933$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$934$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$935$		0			0
$936$	0.549163	+	0.460802i	0.549163	+	0.460802i
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$		0			0
$939$	0.766044	−	1.32683i	0.766044	−	1.32683i
$940$		0			0
$941$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$941$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$942$	1.17365	−	2.03282i	1.17365	−	2.03282i
$943$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$947$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$	2.00000			2.00000
$950$	1.17365	−	0.984808i	1.17365	−	0.984808i
$951$		0			0
$952$		0			0
$953$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$953$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$954$	−2.97178	+	2.49362i	−2.97178	+	2.49362i
$955$		0			0
$956$	0.0812519	+	0.460802i	0.0812519	+	0.460802i
$957$		0			0
$958$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	1.58125	+	1.32683i	1.58125	+	1.32683i
$965$		0			0
$966$	−1.17365	+	6.65609i	−1.17365	+	6.65609i
$967$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$967$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$968$	0.532089			0.532089
$969$		0			0
$970$		0			0
$971$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$971$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$972$	−0.315207	+	1.78763i	−0.315207	+	1.78763i
$973$		0			0
$974$		0			0
$975$	0.266044	+	1.50881i	0.266044	+	1.50881i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.673648	+	1.16679i	0.673648	+	1.16679i
$982$		0			0
$983$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$983$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$984$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$989$		0			0
$990$		0			0
$991$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$991$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−1.58125	+	2.73881i	−1.58125	+	2.73881i
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.a.1715.1	yes	6
11.10	odd	2		2717.1.db.b.1715.1	yes	6
13.12	even	2		2717.1.db.b.1715.1	yes	6
19.4	even	9	inner	2717.1.db.a.1429.1	✓	6
143.142	odd	2	CM	2717.1.db.a.1715.1	yes	6
209.175	odd	18		2717.1.db.b.1429.1	yes	6
247.194	even	18		2717.1.db.b.1429.1	yes	6
2717.1429	odd	18	inner	2717.1.db.a.1429.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.a.1429.1	✓	6	19.4	even	9	inner
2717.1.db.a.1429.1	✓	6	2717.1429	odd	18	inner
2717.1.db.a.1715.1	yes	6	1.1	even	1	trivial
2717.1.db.a.1715.1	yes	6	143.142	odd	2	CM
2717.1.db.b.1429.1	yes	6	209.175	odd	18
2717.1.db.b.1429.1	yes	6	247.194	even	18
2717.1.db.b.1715.1	yes	6	11.10	odd	2
2717.1.db.b.1715.1	yes	6	13.12	even	2

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:	\( N \)	\(=\)	\( 2717 = 11 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2717.db (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43969 + 0.524005i) q^{2} +(0.266044 - 1.50881i) q^{3} +(1.03209 - 0.866025i) q^{4} +(0.407604 + 2.31164i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.266044 + 0.460802i) q^{8} +(-1.26604 - 0.460802i) q^{9} +O(q^{10})\)	\(q+(-1.43969 + 0.524005i) q^{2} +(0.266044 - 1.50881i) q^{3} +(1.03209 - 0.866025i) q^{4} +(0.407604 + 2.31164i) q^{6} +(-0.766044 - 1.32683i) q^{7} +(-0.266044 + 0.460802i) q^{8} +(-1.26604 - 0.460802i) q^{9} +(-0.500000 + 0.866025i) q^{11} +(-1.03209 - 1.78763i) q^{12} +(0.173648 + 0.984808i) q^{13} +(1.79813 + 1.50881i) q^{14} +(-0.0923963 + 0.524005i) q^{16} +2.06418 q^{18} +(0.173648 + 0.984808i) q^{19} +(-2.20574 + 0.802823i) q^{21} +(0.266044 - 1.50881i) q^{22} +(-1.43969 + 1.20805i) q^{23} +(0.624485 + 0.524005i) q^{24} +(0.173648 + 0.984808i) q^{25} +(-0.766044 - 1.32683i) q^{26} +(-0.266044 + 0.460802i) q^{27} +(-1.93969 - 0.705990i) q^{28} +(-0.233956 - 1.32683i) q^{32} +(1.17365 + 0.984808i) q^{33} +(-1.70574 + 0.620838i) q^{36} +(-0.766044 - 1.32683i) q^{38} +1.53209 q^{39} +(-0.326352 + 1.85083i) q^{41} +(2.75490 - 2.31164i) q^{42} +(0.233956 + 1.32683i) q^{44} +(1.43969 - 2.49362i) q^{46} +(0.766044 + 0.278817i) q^{48} +(-0.673648 + 1.16679i) q^{49} +(-0.766044 - 1.32683i) q^{50} +(1.03209 + 0.866025i) q^{52} +(-1.43969 + 1.20805i) q^{53} +(0.141559 - 0.802823i) q^{54} +0.815207 q^{56} +1.53209 q^{57} +(0.358441 + 2.03282i) q^{63} +(0.766044 + 1.32683i) q^{64} +(-2.20574 - 0.802823i) q^{66} +(1.43969 + 2.49362i) q^{69} +(0.549163 - 0.460802i) q^{72} +(0.347296 - 1.96962i) q^{73} +1.53209 q^{75} +(1.03209 + 0.866025i) q^{76} +1.53209 q^{77} +(-2.20574 + 0.802823i) q^{78} +(-0.407604 - 0.342020i) q^{81} +(-0.500000 - 2.83564i) q^{82} +(-0.766044 - 1.32683i) q^{83} +(-1.58125 + 2.73881i) q^{84} +(-0.266044 - 0.460802i) q^{88} +(1.17365 - 0.984808i) q^{91} +(-0.439693 + 2.49362i) q^{92} -2.06418 q^{96} +(0.358441 - 2.03282i) q^{98} +(1.03209 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 6 q^{6} + 3 q^{8} - 3 q^{9} - 3 q^{11} + 3 q^{12} - 3 q^{14} + 3 q^{16} - 6 q^{18} - 3 q^{21} - 3 q^{22} - 3 q^{23} - 9 q^{24} + 3 q^{27} - 6 q^{28} - 6 q^{32} + 6 q^{33} - 3 q^{41} + 18 q^{42} + 6 q^{44} + 3 q^{46} - 3 q^{49} - 3 q^{52} - 3 q^{53} + 9 q^{54} + 12 q^{56} - 6 q^{63} - 3 q^{66} + 3 q^{69} + 15 q^{72} - 3 q^{76} - 3 q^{78} - 6 q^{81} - 3 q^{82} - 12 q^{84} + 3 q^{88} + 6 q^{91} + 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 + 6 * q^6 + 3 * q^8 - 3 * q^9 - 3 * q^11 + 3 * q^12 - 3 * q^14 + 3 * q^16 - 6 * q^18 - 3 * q^21 - 3 * q^22 - 3 * q^23 - 9 * q^24 + 3 * q^27 - 6 * q^28 - 6 * q^32 + 6 * q^33 - 3 * q^41 + 18 * q^42 + 6 * q^44 + 3 * q^46 - 3 * q^49 - 3 * q^52 - 3 * q^53 + 9 * q^54 + 12 * q^56 - 6 * q^63 - 3 * q^66 + 3 * q^69 + 15 * q^72 - 3 * q^76 - 3 * q^78 - 6 * q^81 - 3 * q^82 - 12 * q^84 + 3 * q^88 + 6 * q^91 + 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

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