LMFDB - Embedded newform 2717.1.db.c.2001.1

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			2001.1
Root			$-0.615661 + 0.788011i$ of defining polynomial
Character	$\chi$	$=$	2717.2001
Dual form			2717.1.db.c.2144.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51718 + 1.27306i) q^{2} +(1.65940 + 0.603972i) q^{3} +(0.507491 - 2.87812i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(0.438371 - 0.759281i) q^{7} +(1.90381 + 3.29750i) q^{8} +(1.62278 + 1.36167i) q^{9} +O(q^{10})$	\(q+(-1.51718 + 1.27306i) q^{2} +(1.65940 + 0.603972i) q^{3} +(0.507491 - 2.87812i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(0.438371 - 0.759281i) q^{7} +(1.90381 + 3.29750i) q^{8} +(1.62278 + 1.36167i) q^{9} +(0.500000 + 0.866025i) q^{11} +(2.58043 - 4.46944i) q^{12} +(0.939693 - 0.342020i) q^{13} +(0.301526 + 1.71004i) q^{14} +(-4.34008 - 1.57966i) q^{16} -4.19554 q^{18} +(-0.0348995 - 0.999391i) q^{19} +(1.18602 - 0.995186i) q^{21} +(-1.86110 - 0.677383i) q^{22} +(-0.0840186 + 0.476493i) q^{23} +(1.16759 + 6.62172i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.990268 + 1.71519i) q^{26} +(0.987476 + 1.71036i) q^{27} +(-1.96284 - 1.64701i) q^{28} +(5.01769 - 1.82629i) q^{32} +(0.306644 + 1.73907i) q^{33} +(4.74261 - 3.97952i) q^{36} +(1.32524 + 1.47183i) q^{38} +1.76590 q^{39} +(-1.87481 - 0.682374i) q^{41} +(-0.532464 + 3.01975i) q^{42} +(2.74627 - 0.999562i) q^{44} +(-0.479135 - 0.829886i) q^{46} +(-6.24786 - 5.24257i) q^{48} +(0.115661 + 0.200332i) q^{49} +(0.990268 - 1.71519i) q^{50} +(-0.507491 - 2.87812i) q^{52} +(0.294524 - 1.67033i) q^{53} +(-3.67557 - 1.33780i) q^{54} +3.33831 q^{56} +(0.545692 - 1.67947i) q^{57} +(1.74527 - 0.635227i) q^{63} +(-2.97844 + 5.15881i) q^{64} +(-2.67918 - 2.24810i) q^{66} +(-0.427209 + 0.739947i) q^{69} +(-1.40065 + 7.94348i) q^{72} +(0.580762 + 0.211380i) q^{73} -1.76590 q^{75} +(-2.89408 - 0.406737i) q^{76} +0.876742 q^{77} +(-2.67918 + 2.24810i) q^{78} +(0.237754 + 1.34837i) q^{81} +(3.71312 - 1.35147i) q^{82} +(-0.719340 + 1.24593i) q^{83} +(-2.26238 - 3.91855i) q^{84} +(-1.90381 + 3.29750i) q^{88} +(0.152245 - 0.863423i) q^{91} +(1.32877 + 0.483632i) q^{92} +9.42938 q^{96} +(-0.430514 - 0.156694i) q^{98} +(-0.367854 + 2.08620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 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}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * 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 $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.669131	+	0.743145i	$0.733333\pi$
$2$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.848048	+	0.529919i	$0.822222\pi$
$3$	1.65940	+	0.603972i	1.65940	+	0.603972i	0.990268	−	0.139173i	$-0.0444444\pi$
$3$	1.65940	+	0.603972i	1.65940	+	0.603972i	0.669131	+	0.743145i	$0.266667\pi$
$4$	0.507491	−	2.87812i	0.507491	−	2.87812i
$5$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$5$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$6$	−3.28650	+	1.19619i	−3.28650	+	1.19619i
$7$	0.438371	−	0.759281i	0.438371	−	0.759281i	−0.559193	−	0.829038i	$-0.688889\pi$
$7$	0.438371	−	0.759281i	0.438371	−	0.759281i	0.997564	+	0.0697565i	$0.0222222\pi$
$8$	1.90381	+	3.29750i	1.90381	+	3.29750i
$9$	1.62278	+	1.36167i	1.62278	+	1.36167i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	2.58043	−	4.46944i	2.58043	−	4.46944i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$14$	0.301526	+	1.71004i	0.301526	+	1.71004i
$15$		0			0
$16$	−4.34008	−	1.57966i	−4.34008	−	1.57966i
$17$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$17$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$18$	−4.19554			−4.19554
$19$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$19$	−0.0348995	−	0.999391i	−0.0348995	−	0.999391i
$20$		0			0
$21$	1.18602	−	0.995186i	1.18602	−	0.995186i
$22$	−1.86110	−	0.677383i	−1.86110	−	0.677383i
$23$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	0.913545	+	0.406737i	$0.133333\pi$
$23$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	−0.997564	+	0.0697565i	$0.977778\pi$
$24$	1.16759	+	6.62172i	1.16759	+	6.62172i
$25$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$26$	−0.990268	+	1.71519i	−0.990268	+	1.71519i
$27$	0.987476	+	1.71036i	0.987476	+	1.71036i
$28$	−1.96284	−	1.64701i	−1.96284	−	1.64701i
$29$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$29$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	5.01769	−	1.82629i	5.01769	−	1.82629i
$33$	0.306644	+	1.73907i	0.306644	+	1.73907i
$34$		0			0
$35$		0			0
$36$	4.74261	−	3.97952i	4.74261	−	3.97952i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.32524	+	1.47183i	1.32524	+	1.47183i
$39$	1.76590			1.76590
$40$		0			0
$41$	−1.87481	−	0.682374i	−1.87481	−	0.682374i	−0.961262	−	0.275637i	$-0.911111\pi$
$41$	−1.87481	−	0.682374i	−1.87481	−	0.682374i	−0.913545	−	0.406737i	$-0.866667\pi$
$42$	−0.532464	+	3.01975i	−0.532464	+	3.01975i
$43$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$43$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$44$	2.74627	−	0.999562i	2.74627	−	0.999562i
$45$		0			0
$46$	−0.479135	−	0.829886i	−0.479135	−	0.829886i
$47$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$47$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$48$	−6.24786	−	5.24257i	−6.24786	−	5.24257i
$49$	0.115661	+	0.200332i	0.115661	+	0.200332i
$50$	0.990268	−	1.71519i	0.990268	−	1.71519i
$51$		0			0
$52$	−0.507491	−	2.87812i	−0.507491	−	2.87812i
$53$	0.294524	−	1.67033i	0.294524	−	1.67033i	−0.374607	−	0.927184i	$-0.622222\pi$
$53$	0.294524	−	1.67033i	0.294524	−	1.67033i	0.669131	−	0.743145i	$-0.266667\pi$
$54$	−3.67557	−	1.33780i	−3.67557	−	1.33780i
$55$		0			0
$56$	3.33831			3.33831
$57$	0.545692	−	1.67947i	0.545692	−	1.67947i
$58$		0			0
$59$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$59$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$60$		0			0
$61$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$61$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$62$		0			0
$63$	1.74527	−	0.635227i	1.74527	−	0.635227i
$64$	−2.97844	+	5.15881i	−2.97844	+	5.15881i
$65$		0			0
$66$	−2.67918	−	2.24810i	−2.67918	−	2.24810i
$67$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$67$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$68$		0			0
$69$	−0.427209	+	0.739947i	−0.427209	+	0.739947i
$70$		0			0
$71$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$71$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$72$	−1.40065	+	7.94348i	−1.40065	+	7.94348i
$73$	0.580762	+	0.211380i	0.580762	+	0.211380i	0.615661	−	0.788011i	$-0.288889\pi$
$73$	0.580762	+	0.211380i	0.580762	+	0.211380i	−0.0348995	+	0.999391i	$0.511111\pi$
$74$		0			0
$75$	−1.76590			−1.76590
$76$	−2.89408	−	0.406737i	−2.89408	−	0.406737i
$77$	0.876742			0.876742
$78$	−2.67918	+	2.24810i	−2.67918	+	2.24810i
$79$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$79$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$80$		0			0
$81$	0.237754	+	1.34837i	0.237754	+	1.34837i
$82$	3.71312	−	1.35147i	3.71312	−	1.35147i
$83$	−0.719340	+	1.24593i	−0.719340	+	1.24593i	0.241922	+	0.970296i	$0.422222\pi$
$83$	−0.719340	+	1.24593i	−0.719340	+	1.24593i	−0.961262	+	0.275637i	$0.911111\pi$
$84$	−2.26238	−	3.91855i	−2.26238	−	3.91855i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−1.90381	+	3.29750i	−1.90381	+	3.29750i
$89$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$89$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$90$		0			0
$91$	0.152245	−	0.863423i	0.152245	−	0.863423i
$92$	1.32877	+	0.483632i	1.32877	+	0.483632i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	9.42938			9.42938
$97$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$97$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$98$	−0.430514	−	0.156694i	−0.430514	−	0.156694i
$99$	−0.367854	+	2.08620i	−0.367854	+	2.08620i
$100$	0.507491	+	2.87812i	0.507491	+	2.87812i
$101$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$101$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$102$		0			0
$103$	−0.961262	−	1.66495i	−0.961262	−	1.66495i	−0.719340	−	0.694658i	$-0.755556\pi$
$103$	−0.961262	−	1.66495i	−0.961262	−	1.66495i	−0.241922	−	0.970296i	$-0.577778\pi$
$104$	2.91681	+	2.44750i	2.91681	+	2.44750i
$105$		0			0
$106$	1.67959	+	2.90914i	1.67959	+	2.90914i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	5.42376	−	1.97409i	5.42376	−	1.97409i
$109$	0.339707	+	1.92657i	0.339707	+	1.92657i	0.374607	+	0.927184i	$0.377778\pi$
$109$	0.339707	+	1.92657i	0.339707	+	1.92657i	−0.0348995	+	0.999391i	$0.511111\pi$
$110$		0			0
$111$		0			0
$112$	−3.10197	+	2.60287i	−3.10197	+	2.60287i
$113$	−1.23132			−1.23132			−0.615661	−	0.788011i	$-0.711111\pi$
$113$	−1.23132			−1.23132			−0.615661	+	0.788011i	$0.711111\pi$
$114$	1.31016	+	3.24275i	1.31016	+	3.24275i
$115$		0			0
$116$		0			0
$117$	1.99063	+	0.724531i	1.99063	+	0.724531i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	−2.69892	−	2.26466i	−2.69892	−	2.26466i
$124$		0			0
$125$		0			0
$126$	−1.83920	+	3.18559i	−1.83920	+	3.18559i
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	−1.12144	−	6.35999i	−1.12144	−	6.35999i
$129$		0			0
$130$		0			0
$131$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$131$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$132$	5.16087			5.16087
$133$	−0.774117	−	0.411606i	−0.774117	−	0.411606i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$137$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$138$	−0.293848	−	1.66650i	−0.293848	−	1.66650i
$139$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$139$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.766044	+	0.642788i	0.766044	+	0.642788i
$144$	−4.89201	−	8.47321i	−4.89201	−	8.47321i
$145$		0			0
$146$	−1.15022	+	0.418646i	−1.15022	+	0.418646i
$147$	0.0709339	+	0.402286i	0.0709339	+	0.402286i
$148$		0			0
$149$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	0.241922	−	0.970296i	$-0.422222\pi$
$149$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	−0.438371	+	0.898794i	$0.644444\pi$
$150$	2.67918	−	2.24810i	2.67918	−	2.24810i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	3.22905	−	2.01773i	3.22905	−	2.01773i
$153$		0			0
$154$	−1.33017	+	1.11615i	−1.33017	+	1.11615i
$155$		0			0
$156$	0.896176	−	5.08246i	0.896176	−	5.08246i
$157$	0.317271	+	1.79933i	0.317271	+	1.79933i	0.559193	+	0.829038i	$0.311111\pi$
$157$	0.317271	+	1.79933i	0.317271	+	1.79933i	−0.241922	+	0.970296i	$0.577778\pi$
$158$		0			0
$159$	1.49756	−	2.59386i	1.49756	−	2.59386i
$160$		0			0
$161$	0.324961	+	0.272675i	0.324961	+	0.272675i
$162$	−2.07728	−	1.74304i	−2.07728	−	1.74304i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−2.91540	+	5.04963i	−2.91540	+	5.04963i
$165$		0			0
$166$	−0.494786	−	2.80607i	−0.494786	−	2.80607i
$167$	0.213817	−	1.21262i	0.213817	−	1.21262i	−0.669131	−	0.743145i	$-0.733333\pi$
$167$	0.213817	−	1.21262i	0.213817	−	1.21262i	0.882948	−	0.469472i	$-0.155556\pi$
$168$	5.53958	+	2.01624i	5.53958	+	2.01624i
$169$	0.766044	−	0.642788i	0.766044	−	0.642788i
$170$		0			0
$171$	1.30421	−	1.66931i	1.30421	−	1.66931i
$172$		0			0
$173$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$173$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$174$		0			0
$175$	−0.152245	+	0.863423i	−0.152245	+	0.863423i
$176$	−0.802015	−	4.54845i	−0.802015	−	4.54845i
$177$		0			0
$178$		0			0
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$180$		0			0
$181$	−0.573931	−	0.481585i	−0.573931	−	0.481585i	0.309017	−	0.951057i	$-0.400000\pi$
$181$	−0.573931	−	0.481585i	−0.573931	−	0.481585i	−0.882948	+	0.469472i	$0.844444\pi$
$182$	0.868210	+	1.50378i	0.868210	+	1.50378i
$183$		0			0
$184$	−1.73119	+	0.630103i	−1.73119	+	0.630103i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.73152			1.73152
$190$		0			0
$191$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$191$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$192$	−8.05820	+	6.76163i	−8.05820	+	6.76163i
$193$	−0.454664	−	0.165484i	−0.454664	−	0.165484i	0.104528	−	0.994522i	$-0.466667\pi$
$193$	−0.454664	−	0.165484i	−0.454664	−	0.165484i	−0.559193	+	0.829038i	$0.688889\pi$
$194$		0			0
$195$		0			0
$196$	0.635276	−	0.231222i	0.635276	−	0.231222i
$197$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	−0.990268	−	0.139173i	$-0.955556\pi$
$197$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	0.615661	+	0.788011i	$0.288889\pi$
$198$	−2.09777	−	3.63344i	−2.09777	−	3.63344i
$199$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i	0.669131	−	0.743145i	$-0.266667\pi$
$199$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i	−0.615661	+	0.788011i	$0.711111\pi$
$200$	−2.91681	−	2.44750i	−2.91681	−	2.44750i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	3.57800	+	1.30229i	3.57800	+	1.30229i
$207$	−0.785171	+	0.658837i	−0.785171	+	0.658837i
$208$	−4.61862			−4.61862
$209$	0.848048	−	0.529919i	0.848048	−	0.529919i
$210$		0			0
$211$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$211$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$212$	−4.65794	−	1.69535i	−4.65794	−	1.69535i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−3.75994	+	6.51241i	−3.75994	+	6.51241i
$217$		0			0
$218$	−2.96805	−	2.49049i	−2.96805	−	2.49049i
$219$	0.836048	+	0.701528i	0.836048	+	0.701528i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$223$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$224$	0.812943	−	4.61043i	0.812943	−	4.61043i
$225$	−1.99063	−	0.724531i	−1.99063	−	0.724531i
$226$	1.86814	−	1.56755i	1.86814	−	1.56755i
$227$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$227$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$228$	−4.55678	−	2.42288i	−4.55678	−	2.42288i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	1.45487	+	0.529528i	1.45487	+	0.529528i
$232$		0			0
$233$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$233$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$234$	−3.94252	+	1.43496i	−3.94252	+	1.43496i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i	0.882948	−	0.469472i	$-0.155556\pi$
$239$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i	−0.848048	+	0.529919i	$0.822222\pi$
$240$		0			0
$241$	−1.35192	+	0.492057i	−1.35192	+	0.492057i	−0.913545	−	0.406737i	$-0.866667\pi$
$241$	−1.35192	+	0.492057i	−1.35192	+	0.492057i	−0.438371	+	0.898794i	$0.644444\pi$
$242$	−0.343916	−	1.95045i	−0.343916	−	1.95045i
$243$	−0.0769024	+	0.436135i	−0.0769024	+	0.436135i
$244$		0			0
$245$		0			0
$246$	6.97780			6.97780
$247$	−0.374607	−	0.927184i	−0.374607	−	0.927184i
$248$		0			0
$249$	−1.94618	+	1.63304i	−1.94618	+	1.63304i
$250$		0			0
$251$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	0.438371	+	0.898794i	$0.355556\pi$
$251$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	−0.719340	+	0.694658i	$0.755556\pi$
$252$	−0.942552	−	5.34548i	−0.942552	−	5.34548i
$253$	−0.454664	+	0.165484i	−0.454664	+	0.165484i
$254$		0			0
$255$		0			0
$256$	5.23486	+	4.39257i	5.23486	+	4.39257i
$257$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.997564	−	0.0697565i	$-0.977778\pi$
$257$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.241922	−	0.970296i	$-0.577778\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$263$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$264$	−5.15078	+	4.32202i	−5.15078	+	4.32202i
$265$		0			0
$266$	1.69847	−	0.361022i	1.69847	−	0.361022i
$267$		0			0
$268$		0			0
$269$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.961262	+	0.275637i	$0.0888889\pi$
$269$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.913545	+	0.406737i	$0.133333\pi$
$270$		0			0
$271$	0.130100	+	0.737831i	0.130100	+	0.737831i	0.978148	+	0.207912i	$0.0666667\pi$
$271$	0.130100	+	0.737831i	0.130100	+	0.737831i	−0.848048	+	0.529919i	$0.822222\pi$
$272$		0			0
$273$	0.774117	−	1.34081i	0.774117	−	1.34081i
$274$		0			0
$275$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$276$	1.91286	+	1.60508i	1.91286	+	1.60508i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.130100	−	0.737831i	0.130100	−	0.737831i	−0.848048	−	0.529919i	$-0.822222\pi$
$281$	0.130100	−	0.737831i	0.130100	−	0.737831i	0.978148	−	0.207912i	$-0.0666667\pi$
$282$		0			0
$283$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$283$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$284$		0			0
$285$		0			0
$286$	−1.98054			−1.98054
$287$	−1.33998	+	1.12437i	−1.33998	+	1.12437i
$288$	10.6294	+	3.86879i	10.6294	+	3.86879i
$289$	0.173648	−	0.984808i	0.173648	−	0.984808i
$290$		0			0
$291$		0			0
$292$	0.903109	−	1.56423i	0.903109	−	1.56423i
$293$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$293$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$294$	−0.619755	−	0.520037i	−0.619755	−	0.520037i
$295$		0			0
$296$		0			0
$297$	−0.987476	+	1.71036i	−0.987476	+	1.71036i
$298$	0.389075	−	0.141612i	0.389075	−	0.141612i
$299$	0.0840186	+	0.476493i	0.0840186	+	0.476493i
$300$	−0.896176	+	5.08246i	−0.896176	+	5.08246i
$301$		0			0
$302$	−1.51718	+	1.27306i	−1.51718	+	1.27306i
$303$		0			0
$304$	−1.42723	+	4.39257i	−1.42723	+	4.39257i
$305$		0			0
$306$		0			0
$307$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$308$	0.444939	−	2.52337i	0.444939	−	2.52337i
$309$	−0.589531	−	3.34340i	−0.589531	−	3.34340i
$310$		0			0
$311$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.0348995	−	0.999391i	$-0.488889\pi$
$311$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.848048	−	0.529919i	$-0.177778\pi$
$312$	3.36194	+	5.82304i	3.36194	+	5.82304i
$313$	−0.160147	−	0.134379i	−0.160147	−	0.134379i	0.559193	−	0.829038i	$-0.311111\pi$
$313$	−0.160147	−	0.134379i	−0.160147	−	0.134379i	−0.719340	+	0.694658i	$0.755556\pi$
$314$	−2.77202	−	2.32600i	−2.77202	−	2.32600i
$315$		0			0
$316$		0			0
$317$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$317$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$318$	1.03007	+	5.84184i	1.03007	+	5.84184i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−0.840156			−0.840156
$323$		0			0
$324$	4.00144			4.00144
$325$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$326$		0			0
$327$	−0.599887	+	3.40213i	−0.599887	+	3.40213i
$328$	−1.31915	−	7.48129i	−1.31915	−	7.48129i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	3.22089	+	2.70265i	3.22089	+	2.70265i
$333$		0			0
$334$	1.21934	+	2.11196i	1.21934	+	2.11196i
$335$		0			0
$336$	−6.71947	+	2.44569i	−6.71947	+	2.44569i
$337$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$337$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$338$	−0.343916	+	1.95045i	−0.343916	+	1.95045i
$339$	−2.04326	−	0.743684i	−2.04326	−	0.743684i
$340$		0			0
$341$		0			0
$342$	0.146422	+	4.19298i	0.146422	+	4.19298i
$343$	1.07955			1.07955
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$347$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$348$		0			0
$349$	0.961262	−	1.66495i	0.961262	−	1.66495i	0.241922	−	0.970296i	$-0.422222\pi$
$349$	0.961262	−	1.66495i	0.961262	−	1.66495i	0.719340	−	0.694658i	$-0.244444\pi$
$350$	−0.868210	−	1.50378i	−0.868210	−	1.50378i
$351$	1.51290	+	1.26947i	1.51290	+	1.26947i
$352$	4.09046	+	3.43230i	4.09046	+	3.43230i
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−3.49771	−	1.27306i	−3.49771	−	1.27306i
$359$	0.370646	−	0.311009i	0.370646	−	0.311009i	−0.438371	−	0.898794i	$-0.644444\pi$
$359$	0.370646	−	0.311009i	0.370646	−	0.311009i	0.809017	+	0.587785i	$0.200000\pi$
$360$		0			0
$361$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$362$	1.48384			1.48384
$363$	−1.35275	+	1.13510i	−1.35275	+	1.13510i
$364$	−2.40777	−	0.876358i	−2.40777	−	0.876358i
$365$		0			0
$366$		0			0
$367$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	−0.615661	−	0.788011i	$-0.711111\pi$
$367$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	0.0348995	+	0.999391i	$0.488889\pi$
$368$	1.11735	−	1.93530i	1.11735	−	1.93530i
$369$	−2.11323	−	3.66021i	−2.11323	−	3.66021i
$370$		0			0
$371$	−1.13914	−	0.955850i	−1.13914	−	0.955850i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−2.62703	+	2.20434i	−2.62703	+	2.20434i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	2.96805	−	2.49049i	2.96805	−	2.49049i
$383$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$383$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$384$	1.98034	−	11.2311i	1.98034	−	11.2311i
$385$		0			0
$386$	0.900479	−	0.327748i	0.900479	−	0.327748i
$387$		0			0
$388$		0			0
$389$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.990268	−	0.139173i	$-0.0444444\pi$
$389$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.0348995	+	0.999391i	$0.488889\pi$
$390$		0			0
$391$		0			0
$392$	−0.440396	+	0.762788i	−0.440396	+	0.762788i
$393$		0			0
$394$	−0.257667	−	1.46130i	−0.257667	−	1.46130i
$395$		0			0
$396$	5.81767	+	2.11746i	5.81767	+	2.11746i
$397$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$397$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$398$	−0.138239			−0.138239
$399$	−1.03597	−	1.15056i	−1.03597	−	1.15056i
$400$	4.61862			4.61862
$401$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$401$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$409$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−5.27978	+	1.92168i	−5.27978	+	1.92168i
$413$		0			0
$414$	0.352503	−	1.99915i	0.352503	−	1.99915i
$415$		0			0
$416$	4.09046	−	3.43230i	4.09046	−	3.43230i
$417$		0			0
$418$	−0.612019	+	1.88360i	−0.612019	+	1.88360i
$419$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$419$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$420$		0			0
$421$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$421$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$422$		0			0
$423$		0			0
$424$	6.06863	−	2.20880i	6.06863	−	2.20880i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.882948	+	1.52931i	0.882948	+	1.52931i
$430$		0			0
$431$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.809017	−	0.587785i	$-0.200000\pi$
$431$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.997564	−	0.0697565i	$-0.0222222\pi$
$432$	−1.58394	−	8.98298i	−1.58394	−	8.98298i
$433$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$433$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$434$		0			0
$435$		0			0
$436$	5.71732			5.71732
$437$	0.479135	+	0.0673380i	0.479135	+	0.0673380i
$438$	−2.16152			−2.16152
$439$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$439$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$440$		0			0
$441$	−0.0850930	+	0.482587i	−0.0850930	+	0.482587i
$442$		0			0
$443$	1.35192	−	0.492057i	1.35192	−	0.492057i	0.438371	−	0.898794i	$-0.355556\pi$
$443$	1.35192	−	0.492057i	1.35192	−	0.492057i	0.913545	+	0.406737i	$0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.282803	−	0.237300i	−0.282803	−	0.237300i
$448$	2.61132	+	4.52295i	2.61132	+	4.52295i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	3.94252	−	1.43496i	3.94252	−	1.43496i
$451$	−0.346450	−	1.96482i	−0.346450	−	1.96482i
$452$	−0.624885	+	3.54390i	−0.624885	+	3.54390i
$453$	1.65940	+	0.603972i	1.65940	+	0.603972i
$454$	0.937668	−	0.786797i	0.937668	−	0.786797i
$455$		0			0
$456$	6.57694	−	1.39797i	6.57694	−	1.39797i
$457$	−0.0697990			−0.0697990			−0.0348995	−	0.999391i	$-0.511111\pi$
$457$	−0.0697990			−0.0697990			−0.0348995	+	0.999391i	$0.511111\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.232387	−	1.31793i	−0.232387	−	1.31793i	−0.848048	−	0.529919i	$-0.822222\pi$
$461$	−0.232387	−	1.31793i	−0.232387	−	1.31793i	0.615661	−	0.788011i	$-0.288889\pi$
$462$	−2.88141	+	1.04875i	−2.88141	+	1.04875i
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$467$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$468$	3.09552	−	5.36159i	3.09552	−	5.36159i
$469$		0			0
$470$		0			0
$471$	−0.560267	+	3.17743i	−0.560267	+	3.17743i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.374607	+	0.927184i	0.374607	+	0.927184i
$476$		0			0
$477$	2.75239	−	2.30953i	2.75239	−	2.30953i
$478$	−0.129903	−	0.0472807i	−0.129903	−	0.0472807i
$479$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$479$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	1.42468	−	2.46762i	1.42468	−	2.46762i
$483$	0.374552	+	0.648743i	0.374552	+	0.648743i
$484$	2.23878	+	1.87856i	2.23878	+	1.87856i
$485$		0			0
$486$	−0.438553	−	0.759597i	−0.438553	−	0.759597i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$491$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$492$	−7.88765	+	6.61852i	−7.88765	+	6.61852i
$493$		0			0
$494$	1.74871	+	0.929805i	1.74871	+	0.929805i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.873740	−	4.95522i	0.873740	−	4.95522i
$499$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$499$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$500$		0			0
$501$	1.08719	−	1.88307i	1.08719	−	1.88307i
$502$	−1.60229	−	2.77524i	−1.60229	−	2.77524i
$503$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$503$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$504$	5.41733	+	4.54568i	5.41733	+	4.54568i
$505$		0			0
$506$	0.479135	−	0.829886i	0.479135	−	0.829886i
$507$	1.65940	−	0.603972i	1.65940	−	0.603972i
$508$		0			0
$509$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$509$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$510$		0			0
$511$	0.415086	−	0.348299i	0.415086	−	0.348299i
$512$	−7.07614			−7.07614
$513$	1.67485	−	1.04657i	1.67485	−	1.04657i
$514$	3.20457			3.20457
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$521$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$522$		0			0
$523$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$523$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$524$		0			0
$525$	−0.774117	+	1.34081i	−0.774117	+	1.34081i
$526$		0			0
$527$		0			0
$528$	1.41627	−	8.03209i	1.41627	−	8.03209i
$529$	0.719706	+	0.261952i	0.719706	+	0.261952i
$530$		0			0
$531$		0			0
$532$	−1.57751	+	2.01912i	−1.57751	+	2.01912i
$533$	−1.99513			−1.99513
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.576303	+	3.26838i	0.576303	+	3.26838i
$538$	−3.71312	+	1.35147i	−3.71312	+	1.35147i
$539$	−0.115661	+	0.200332i	−0.115661	+	0.200332i
$540$		0			0
$541$	−0.856733	−	0.718885i	−0.856733	−	0.718885i	0.104528	−	0.994522i	$-0.466667\pi$
$541$	−0.856733	−	0.718885i	−0.856733	−	0.718885i	−0.961262	+	0.275637i	$0.911111\pi$
$542$	−1.13669	−	0.953796i	−1.13669	−	0.953796i
$543$	−0.661516	−	1.14578i	−0.661516	−	1.14578i
$544$		0			0
$545$		0			0
$546$	0.532464	+	3.01975i	0.532464	+	3.01975i
$547$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$547$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$548$		0			0
$549$		0			0
$550$	1.98054			1.98054
$551$		0			0
$552$	−3.25330			−3.25330
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.913545	+	0.406737i	$0.866667\pi$
$557$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.961262	+	0.275637i	$0.911111\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.741922	+	1.28505i	0.741922	+	1.28505i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.12802	+	0.410565i	1.12802	+	0.410565i
$568$		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			$\pi$
$572$	2.23878	−	1.87856i	2.23878	−	1.87856i
$573$	−3.24627	−	1.18155i	−3.24627	−	1.18155i
$574$	0.601583	−	3.41175i	0.601583	−	3.41175i
$575$	−0.0840186	−	0.476493i	−0.0840186	−	0.476493i
$576$	−11.8580	+	4.31594i	−11.8580	+	4.31594i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.990268	+	1.71519i	0.990268	+	1.71519i
$579$	−0.654522	−	0.549209i	−0.654522	−	0.549209i
$580$		0			0
$581$	0.630676	+	1.09236i	0.630676	+	1.09236i
$582$		0			0
$583$	1.59381	−	0.580099i	1.59381	−	0.580099i
$584$	0.408636	+	2.31749i	0.408636	+	2.31749i
$585$		0			0
$586$	−0.646352	−	0.235253i	−0.646352	−	0.235253i
$587$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$587$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$588$	1.19383			1.19383
$589$		0			0
$590$		0			0
$591$	−1.01350	+	0.850429i	−1.01350	+	0.850429i
$592$		0			0
$593$	−0.317271	+	1.79933i	−0.317271	+	1.79933i	0.241922	+	0.970296i	$0.422222\pi$
$593$	−0.317271	+	1.79933i	−0.317271	+	1.79933i	−0.559193	+	0.829038i	$0.688889\pi$
$594$	−0.679219	−	3.85204i	−0.679219	−	3.85204i
$595$		0			0
$596$	−0.305487	+	0.529119i	−0.305487	+	0.529119i
$597$	0.0616289	+	0.106744i	0.0616289	+	0.106744i
$598$	−0.734077	−	0.615964i	−0.734077	−	0.615964i
$599$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.848048	+	0.529919i	$0.177778\pi$
$599$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.669131	+	0.743145i	$0.266667\pi$
$600$	−3.36194	−	5.82304i	−3.36194	−	5.82304i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	0.507491	−	2.87812i	0.507491	−	2.87812i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−2.00029	−	4.95090i	−2.00029	−	4.95090i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.213817	+	1.21262i	0.213817	+	1.21262i	0.882948	+	0.469472i	$0.155556\pi$
$613$	0.213817	+	1.21262i	0.213817	+	1.21262i	−0.669131	+	0.743145i	$0.733333\pi$
$614$	3.49771	−	1.27306i	3.49771	−	1.27306i
$615$		0			0
$616$	1.66915	+	2.89106i	1.66915	+	2.89106i
$617$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$617$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$618$	5.15078	+	4.32202i	5.15078	+	4.32202i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	−0.897940	+	0.326824i	−0.897940	+	0.326824i
$622$	0.607320	+	3.44429i	0.607320	+	3.44429i
$623$		0			0
$624$	−7.66413	−	2.78952i	−7.66413	−	2.78952i
$625$	0.766044	−	0.642788i	0.766044	−	0.642788i
$626$	0.414045			0.414045
$627$	1.72731	−	0.367150i	1.72731	−	0.367150i
$628$	5.33972			5.33972
$629$		0			0
$630$		0			0
$631$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$631$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−6.70544	−	5.62653i	−6.70544	−	5.62653i
$637$	0.177204	+	0.148692i	0.177204	+	0.148692i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.333843	+	1.89332i	0.333843	+	1.89332i	0.438371	+	0.898794i	$0.355556\pi$
$641$	0.333843	+	1.89332i	0.333843	+	1.89332i	−0.104528	+	0.994522i	$0.533333\pi$
$642$		0			0
$643$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$643$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$644$	0.949706	−	0.796898i	0.949706	−	0.796898i
$645$		0			0
$646$		0			0
$647$	−0.749213			−0.749213			−0.374607	−	0.927184i	$-0.622222\pi$
$647$	−0.749213			−0.749213			−0.374607	+	0.927184i	$0.622222\pi$
$648$	−3.99362	+	3.35104i	−3.99362	+	3.35104i
$649$		0			0
$650$	0.343916	−	1.95045i	0.343916	−	1.95045i
$651$		0			0
$652$		0			0
$653$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$654$	−3.42099	−	5.92533i	−3.42099	−	5.92533i
$655$		0			0
$656$	7.05890	+	5.92312i	7.05890	+	5.92312i
$657$	0.654617	+	1.13383i	0.654617	+	1.13383i
$658$		0			0
$659$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$659$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$660$		0			0
$661$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$661$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$662$		0			0
$663$		0			0
$664$	−5.47796			−5.47796
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−3.38155	−	1.23078i	−3.38155	−	1.23078i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	4.13357	−	7.15955i	4.13357	−	7.15955i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−1.51290	−	1.26947i	−1.51290	−	1.26947i
$676$	−1.46126	−	2.53098i	−1.46126	−	2.53098i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	4.04674	−	1.47289i	4.04674	−	1.47289i
$679$		0			0
$680$		0			0
$681$	−1.02556	−	0.373275i	−1.02556	−	0.373275i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−4.14261	−	4.60083i	−4.14261	−	4.60083i
$685$		0			0
$686$	−1.63787	+	1.37434i	−1.63787	+	1.37434i
$687$		0			0
$688$		0			0
$689$	−0.294524	−	1.67033i	−0.294524	−	1.67033i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	1.42276	+	1.19384i	1.42276	+	1.19384i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.661187	+	3.74978i	0.661187	+	3.74978i
$699$		0			0
$700$	2.40777	+	0.876358i	2.40777	+	0.876358i
$701$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$701$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$702$	−3.91146			−3.91146
$703$		0			0
$704$	−5.95688			−5.95688
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$709$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	5.16131	−	1.87856i	5.16131	−	1.87856i
$717$	0.0214035	+	0.121385i	0.0214035	+	0.121385i
$718$	−0.166402	+	0.943712i	−0.166402	+	0.943712i
$719$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$719$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$	−1.68556			−1.68556
$722$	1.42468	−	1.37580i	1.42468	−	1.37580i
$723$	−2.54056			−2.54056
$724$	−1.67733	+	1.40744i	−1.67733	+	1.40744i
$725$		0			0
$726$	0.607320	−	3.44429i	0.607320	−	3.44429i
$727$	0.152245	+	0.863423i	0.152245	+	0.863423i	0.961262	+	0.275637i	$0.0888889\pi$
$727$	0.152245	+	0.863423i	0.152245	+	0.863423i	−0.809017	+	0.587785i	$0.800000\pi$
$728$	3.13698	−	1.14177i	3.13698	−	1.14177i
$729$	0.293561	−	0.508463i	0.293561	−	0.508463i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.719340	−	1.24593i	−0.719340	−	1.24593i	−0.961262	−	0.275637i	$-0.911111\pi$
$733$	−0.719340	−	1.24593i	−0.719340	−	1.24593i	0.241922	−	0.970296i	$-0.422222\pi$
$734$	0.612019	−	1.06005i	0.612019	−	1.06005i
$735$		0			0
$736$	0.448635	+	2.54434i	0.448635	+	2.54434i
$737$		0			0
$738$	7.86583	+	2.86293i	7.86583	+	2.86293i
$739$	1.52836	−	1.28244i	1.52836	−	1.28244i	0.719340	−	0.694658i	$-0.244444\pi$
$739$	1.52836	−	1.28244i	1.52836	−	1.28244i	0.809017	−	0.587785i	$-0.200000\pi$
$740$		0			0
$741$	−0.0616289	−	1.76482i	−0.0616289	−	1.76482i
$742$	2.94514			2.94514
$743$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.86388	+	1.04237i	−2.86388	+	1.04237i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.990268	−	0.139173i	$-0.0444444\pi$
$751$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.0348995	+	0.999391i	$0.488889\pi$
$752$		0			0
$753$	−1.42864	+	2.47448i	−1.42864	+	2.47448i
$754$		0			0
$755$		0			0
$756$	0.878733	−	4.98354i	0.878733	−	4.98354i
$757$	1.52045	+	0.553400i	1.52045	+	0.553400i	0.961262	−	0.275637i	$-0.0888889\pi$
$757$	1.52045	+	0.553400i	1.52045	+	0.553400i	0.559193	+	0.829038i	$0.311111\pi$
$758$		0			0
$759$	−0.854417			−0.854417
$760$		0			0
$761$	−1.11839			−1.11839			−0.559193	−	0.829038i	$-0.688889\pi$
$761$	−1.11839			−1.11839			−0.559193	+	0.829038i	$0.688889\pi$
$762$		0			0
$763$	1.61173	+	0.586622i	1.61173	+	0.586622i
$764$	−0.992802	+	5.63046i	−0.992802	+	5.63046i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	6.03373	+	10.4507i	6.03373	+	10.4507i
$769$	1.52836	+	1.28244i	1.52836	+	1.28244i	0.809017	+	0.587785i	$0.200000\pi$
$769$	1.52836	+	1.28244i	1.52836	+	1.28244i	0.719340	+	0.694658i	$0.244444\pi$
$770$		0			0
$771$	−1.42864	−	2.47448i	−1.42864	−	2.47448i
$772$	−0.707022	+	1.22460i	−0.707022	+	1.22460i
$773$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$773$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−2.65047			−2.65047
$779$	−0.616528	+	1.89748i	−0.616528	+	1.89748i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.185524	−	1.05216i	−0.185524	−	1.05216i
$785$		0			0
$786$		0			0
$787$	0.438371	+	0.759281i	0.438371	+	0.759281i	0.997564	−	0.0697565i	$-0.0222222\pi$
$787$	0.438371	+	0.759281i	0.438371	+	0.759281i	−0.559193	+	0.829038i	$0.688889\pi$
$788$	1.67733	+	1.40744i	1.67733	+	1.40744i
$789$		0			0
$790$		0			0
$791$	−0.539776	+	0.934920i	−0.539776	+	0.934920i
$792$	−7.57958	+	2.75874i	−7.57958	+	2.75874i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.156265	−	0.131122i	0.156265	−	0.131122i
$797$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$797$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$798$	3.03649	+	0.426751i	3.03649	+	0.426751i
$799$		0			0
$800$	−4.09046	+	3.43230i	−4.09046	+	3.43230i
$801$		0			0
$802$		0			0
$803$	0.107320	+	0.608645i	0.107320	+	0.608645i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.69892	+	2.26466i	2.69892	+	2.26466i
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$	1.05094	−	0.382510i	1.05094	−	0.382510i	0.241922	−	0.970296i	$-0.422222\pi$
$811$	1.05094	−	0.382510i	1.05094	−	0.382510i	0.809017	+	0.587785i	$0.200000\pi$
$812$		0			0
$813$	−0.229742	+	1.30293i	−0.229742	+	1.30293i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	3.03436			3.03436
$819$	1.42276	−	1.19384i	1.42276	−	1.19384i
$820$		0			0
$821$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$821$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$822$		0			0
$823$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.559193	−	0.829038i	$-0.311111\pi$
$823$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.961262	+	0.275637i	$0.0888889\pi$
$824$	3.66013	−	6.33952i	3.66013	−	6.33952i
$825$	−0.882948	−	1.52931i	−0.882948	−	1.52931i
$826$		0			0
$827$	−1.02517	−	0.860218i	−1.02517	−	0.860218i	−0.0348995	−	0.999391i	$-0.511111\pi$
$827$	−1.02517	−	0.860218i	−1.02517	−	0.860218i	−0.990268	+	0.139173i	$0.955556\pi$
$828$	1.49775	+	2.59417i	1.49775	+	2.59417i
$829$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$829$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$830$		0			0
$831$		0			0
$832$	−1.03440	+	5.86638i	−1.03440	+	5.86638i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−1.09480	−	2.70972i	−1.09480	−	2.70972i
$837$		0			0
$838$	0.317177	−	0.266143i	0.317177	−	0.266143i
$839$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$839$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$840$		0			0
$841$	0.173648	+	0.984808i	0.173648	+	0.984808i
$842$		0			0
$843$	0.661516	−	1.14578i	0.661516	−	1.14578i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.438371	+	0.759281i	0.438371	+	0.759281i
$848$	−3.91681	+	6.78412i	−3.91681	+	6.78412i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.669131	+	0.743145i	$0.733333\pi$
$853$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.848048	+	0.529919i	$0.822222\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$857$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$858$	−3.28650	−	1.19619i	−3.28650	−	1.19619i
$859$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	0.848048	+	0.529919i	$0.177778\pi$
$859$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	−0.978148	+	0.207912i	$0.933333\pi$
$860$		0			0
$861$	−2.90264	+	1.05648i	−2.90264	+	1.05648i
$862$	−1.90381	+	3.29750i	−1.90381	+	3.29750i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	8.07846	+	6.77863i	8.07846	+	6.77863i
$865$		0			0
$866$	0.0691197	+	0.119719i	0.0691197	+	0.119719i
$867$	0.882948	−	1.52931i	0.882948	−	1.52931i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−5.70614	+	4.78802i	−5.70614	+	4.78802i
$873$		0			0
$874$	−0.812659	+	0.507806i	−0.812659	+	0.507806i
$875$		0			0
$876$	2.44337	−	2.05023i	2.44337	−	2.05023i
$877$	0.580762	+	0.211380i	0.580762	+	0.211380i	0.615661	−	0.788011i	$-0.288889\pi$
$877$	0.580762	+	0.211380i	0.580762	+	0.211380i	−0.0348995	+	0.999391i	$0.511111\pi$
$878$		0			0
$879$	0.106497	+	0.603972i	0.106497	+	0.603972i
$880$		0			0
$881$	−0.848048	+	1.46886i	−0.848048	+	1.46886i	0.0348995	+	0.999391i	$0.488889\pi$
$881$	−0.848048	+	1.46886i	−0.848048	+	1.46886i	−0.882948	+	0.469472i	$0.844444\pi$
$882$	−0.485262	−	0.840499i	−0.485262	−	0.840499i
$883$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.978148	−	0.207912i	$-0.933333\pi$
$883$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.374607	−	0.927184i	$-0.622222\pi$
$884$		0			0
$885$		0			0
$886$	−1.42468	+	2.46762i	−1.42468	+	2.46762i
$887$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$887$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.04885	+	0.880087i	−1.04885	+	0.880087i
$892$		0			0
$893$		0			0
$894$	0.731160			0.731160
$895$		0			0
$896$	−5.32063	−	1.93655i	−5.32063	−	1.93655i
$897$	−0.148368	+	0.841437i	−0.148368	+	0.841437i
$898$		0			0
$899$		0			0
$900$	−3.09552	+	5.36159i	−3.09552	+	5.36159i
$901$		0			0
$902$	3.02697	+	2.53993i	3.02697	+	2.53993i
$903$		0			0
$904$	−2.34421	−	4.06029i	−2.34421	−	4.06029i
$905$		0			0
$906$	−3.28650	+	1.19619i	−3.28650	+	1.19619i
$907$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$907$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$908$	−0.313647	+	1.77878i	−0.313647	+	1.77878i
$909$		0			0
$910$		0			0
$911$	−0.483844			−0.483844			−0.241922	−	0.970296i	$-0.577778\pi$
$911$	−0.483844			−0.483844			−0.241922	+	0.970296i	$0.577778\pi$
$912$	−5.02133	+	6.42701i	−5.02133	+	6.42701i
$913$	−1.43868			−1.43868
$914$	0.105898	−	0.0888586i	0.105898	−	0.0888586i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−2.54235	−	2.13328i	−2.54235	−	2.13328i
$922$	2.03038	+	1.70369i	2.03038	+	1.70369i
$923$		0			0
$924$	2.26238	−	3.91855i	2.26238	−	3.91855i
$925$		0			0
$926$		0			0
$927$	0.707208	−	4.01077i	0.707208	−	4.01077i
$928$		0			0
$929$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$929$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$930$		0			0
$931$	0.196173	−	0.122582i	0.196173	−	0.122582i
$932$		0			0
$933$	2.38882	−	2.00446i	2.38882	−	2.00446i
$934$	2.85136	+	1.03781i	2.85136	+	1.03781i
$935$		0			0
$936$	1.40065	+	7.94348i	1.40065	+	7.94348i
$937$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$937$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$938$		0			0
$939$	−0.184586	−	0.319713i	−0.184586	−	0.319713i
$940$		0			0
$941$	−1.02517	−	0.860218i	−1.02517	−	0.860218i	−0.0348995	−	0.999391i	$-0.511111\pi$
$941$	−1.02517	−	0.860218i	−1.02517	−	0.860218i	−0.990268	+	0.139173i	$0.955556\pi$
$942$	−3.19505	−	5.53399i	−3.19505	−	5.53399i
$943$	0.482665	−	0.836001i	0.482665	−	0.836001i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$947$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$948$		0			0
$949$	0.618034			0.618034
$950$	−1.74871	−	0.929805i	−1.74871	−	0.929805i
$951$		0			0
$952$		0			0
$953$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$953$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$954$	−1.23569	+	7.00793i	−1.23569	+	7.00793i
$955$		0			0
$956$	0.191687	−	0.0697684i	0.191687	−	0.0697684i
$957$		0			0
$958$	−0.343916	−	0.595681i	−0.343916	−	0.595681i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	0.730117	+	4.14070i	0.730117	+	4.14070i
$965$		0			0
$966$	−1.39415	−	0.507430i	−1.39415	−	0.507430i
$967$	0.943248	−	0.791479i	0.943248	−	0.791479i	−0.0348995	−	0.999391i	$-0.511111\pi$
$967$	0.943248	−	0.791479i	0.943248	−	0.791479i	0.978148	+	0.207912i	$0.0666667\pi$
$968$	−3.80763			−3.80763
$969$		0			0
$970$		0			0
$971$	1.02517	−	0.860218i	1.02517	−	0.860218i	0.0348995	−	0.999391i	$-0.488889\pi$
$971$	1.02517	−	0.860218i	1.02517	−	0.860218i	0.990268	+	0.139173i	$0.0444444\pi$
$972$	1.21622	+	0.442669i	1.21622	+	0.442669i
$973$		0			0
$974$		0			0
$975$	−1.65940	+	0.603972i	−1.65940	+	0.603972i
$976$		0			0
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−2.07209	+	3.58897i	−2.07209	+	3.58897i
$982$		0			0
$983$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$983$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$984$	2.32949	−	13.2112i	2.32949	−	13.2112i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−2.85866	+	0.607627i	−2.85866	+	0.607627i
$989$		0			0
$990$		0			0
$991$	−1.59381	−	0.580099i	−1.59381	−	0.580099i	−0.615661	−	0.788011i	$-0.711111\pi$
$991$	−1.59381	−	0.580099i	−1.59381	−	0.580099i	−0.978148	+	0.207912i	$0.933333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	3.71242	+	6.43010i	3.71242	+	6.43010i
$997$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$997$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.c.2001.1	✓	24
11.10	odd	2		2717.1.db.d.2001.4	yes	24
13.12	even	2		2717.1.db.d.2001.4	yes	24
19.16	even	9	inner	2717.1.db.c.2144.1	yes	24
143.142	odd	2	CM	2717.1.db.c.2001.1	✓	24
209.54	odd	18		2717.1.db.d.2144.4	yes	24
247.168	even	18		2717.1.db.d.2144.4	yes	24
2717.2144	odd	18	inner	2717.1.db.c.2144.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.2001.1	✓	24	1.1	even	1	trivial
2717.1.db.c.2001.1	✓	24	143.142	odd	2	CM
2717.1.db.c.2144.1	yes	24	19.16	even	9	inner
2717.1.db.c.2144.1	yes	24	2717.2144	odd	18	inner
2717.1.db.d.2001.4	yes	24	11.10	odd	2
2717.1.db.d.2001.4	yes	24	13.12	even	2
2717.1.db.d.2144.4	yes	24	209.54	odd	18
2717.1.db.d.2144.4	yes	24	247.168	even	18

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)

\(f(q)\)	\(=\)	\(q+(-1.51718 + 1.27306i) q^{2} +(1.65940 + 0.603972i) q^{3} +(0.507491 - 2.87812i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(0.438371 - 0.759281i) q^{7} +(1.90381 + 3.29750i) q^{8} +(1.62278 + 1.36167i) q^{9} +O(q^{10})\)	\(q+(-1.51718 + 1.27306i) q^{2} +(1.65940 + 0.603972i) q^{3} +(0.507491 - 2.87812i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(0.438371 - 0.759281i) q^{7} +(1.90381 + 3.29750i) q^{8} +(1.62278 + 1.36167i) q^{9} +(0.500000 + 0.866025i) q^{11} +(2.58043 - 4.46944i) q^{12} +(0.939693 - 0.342020i) q^{13} +(0.301526 + 1.71004i) q^{14} +(-4.34008 - 1.57966i) q^{16} -4.19554 q^{18} +(-0.0348995 - 0.999391i) q^{19} +(1.18602 - 0.995186i) q^{21} +(-1.86110 - 0.677383i) q^{22} +(-0.0840186 + 0.476493i) q^{23} +(1.16759 + 6.62172i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.990268 + 1.71519i) q^{26} +(0.987476 + 1.71036i) q^{27} +(-1.96284 - 1.64701i) q^{28} +(5.01769 - 1.82629i) q^{32} +(0.306644 + 1.73907i) q^{33} +(4.74261 - 3.97952i) q^{36} +(1.32524 + 1.47183i) q^{38} +1.76590 q^{39} +(-1.87481 - 0.682374i) q^{41} +(-0.532464 + 3.01975i) q^{42} +(2.74627 - 0.999562i) q^{44} +(-0.479135 - 0.829886i) q^{46} +(-6.24786 - 5.24257i) q^{48} +(0.115661 + 0.200332i) q^{49} +(0.990268 - 1.71519i) q^{50} +(-0.507491 - 2.87812i) q^{52} +(0.294524 - 1.67033i) q^{53} +(-3.67557 - 1.33780i) q^{54} +3.33831 q^{56} +(0.545692 - 1.67947i) q^{57} +(1.74527 - 0.635227i) q^{63} +(-2.97844 + 5.15881i) q^{64} +(-2.67918 - 2.24810i) q^{66} +(-0.427209 + 0.739947i) q^{69} +(-1.40065 + 7.94348i) q^{72} +(0.580762 + 0.211380i) q^{73} -1.76590 q^{75} +(-2.89408 - 0.406737i) q^{76} +0.876742 q^{77} +(-2.67918 + 2.24810i) q^{78} +(0.237754 + 1.34837i) q^{81} +(3.71312 - 1.35147i) q^{82} +(-0.719340 + 1.24593i) q^{83} +(-2.26238 - 3.91855i) q^{84} +(-1.90381 + 3.29750i) q^{88} +(0.152245 - 0.863423i) q^{91} +(1.32877 + 0.483632i) q^{92} +9.42938 q^{96} +(-0.430514 - 0.156694i) q^{98} +(-0.367854 + 2.08620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * 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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