LMFDB - Embedded newform 2717.1.db.c.2001.4

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			2001.4
Root			$0.0348995 - 0.999391i$ of defining polynomial
Character	$\chi$	$=$	2717.2001
Dual form			2717.1.db.c.2144.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35275 - 1.13510i) q^{2} +(-1.86110 - 0.677383i) q^{3} +(0.367854 - 2.08620i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(-0.719340 + 1.24593i) q^{7} +(-0.987476 - 1.71036i) q^{8} +(2.23878 + 1.87856i) q^{9} +O(q^{10})$	\(q+(1.35275 - 1.13510i) q^{2} +(-1.86110 - 0.677383i) q^{3} +(0.367854 - 2.08620i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(-0.719340 + 1.24593i) q^{7} +(-0.987476 - 1.71036i) q^{8} +(2.23878 + 1.87856i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-2.09777 + 3.63344i) q^{12} +(0.939693 - 0.342020i) q^{13} +(0.441163 + 2.50196i) q^{14} +(-1.28660 - 0.468285i) q^{16} +5.16087 q^{18} +(0.615661 + 0.788011i) q^{19} +(2.18273 - 1.83153i) q^{21} +(1.65940 + 0.603972i) q^{22} +(-0.346450 + 1.96482i) q^{23} +(0.679219 + 3.85204i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(0.882948 - 1.52931i) q^{26} +(-1.90381 - 3.29750i) q^{27} +(2.33466 + 1.95901i) q^{28} +(-0.416155 + 0.151468i) q^{32} +(-0.343916 - 1.95045i) q^{33} +(4.74261 - 3.97952i) q^{36} +(1.72731 + 0.367150i) q^{38} -1.98054 q^{39} +(-0.454664 - 0.165484i) q^{41} +(0.873740 - 4.95522i) q^{42} +(1.99063 - 0.724531i) q^{44} +(1.76159 + 3.05117i) q^{46} +(2.07728 + 1.74304i) q^{48} +(-0.534899 - 0.926473i) q^{49} +(-0.882948 + 1.52931i) q^{50} +(-0.367854 - 2.08620i) q^{52} +(-0.130100 + 0.737831i) q^{53} +(-6.31837 - 2.29970i) q^{54} +2.84132 q^{56} +(-0.612019 - 1.88360i) q^{57} +(-3.95101 + 1.43805i) q^{63} +(0.293561 - 0.508463i) q^{64} +(-2.67918 - 2.24810i) q^{66} +(1.97571 - 3.42203i) q^{69} +(1.00227 - 5.68416i) q^{72} +(0.580762 + 0.211380i) q^{73} +1.98054 q^{75} +(1.87042 - 0.994522i) q^{76} -1.43868 q^{77} +(-2.67918 + 2.24810i) q^{78} +(0.802015 + 4.54845i) q^{81} +(-0.802890 + 0.292228i) q^{82} +(0.438371 - 0.759281i) q^{83} +(-3.01802 - 5.22736i) q^{84} +(0.987476 - 1.71036i) q^{88} +(-0.249824 + 1.41682i) q^{91} +(3.97156 + 1.44553i) q^{92} +0.877107 q^{96} +(-1.77522 - 0.646128i) q^{98} +(-0.507491 + 2.87812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.374607	−	0.927184i	$-0.377778\pi$
$2$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.978148	−	0.207912i	$-0.0666667\pi$
$3$	−1.86110	−	0.677383i	−1.86110	−	0.677383i	−0.978148	−	0.207912i	$-0.933333\pi$
$3$	−1.86110	−	0.677383i	−1.86110	−	0.677383i	−0.882948	−	0.469472i	$-0.844444\pi$
$4$	0.367854	−	2.08620i	0.367854	−	2.08620i
$5$		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
$7$	−0.719340	+	1.24593i	−0.719340	+	1.24593i	0.241922	+	0.970296i	$0.422222\pi$
$7$	−0.719340	+	1.24593i	−0.719340	+	1.24593i	−0.961262	+	0.275637i	$0.911111\pi$
$8$	−0.987476	−	1.71036i	−0.987476	−	1.71036i
$9$	2.23878	+	1.87856i	2.23878	+	1.87856i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	−2.09777	+	3.63344i	−2.09777	+	3.63344i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$14$	0.441163	+	2.50196i	0.441163	+	2.50196i
$15$		0			0
$16$	−1.28660	−	0.468285i	−1.28660	−	0.468285i
$17$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$17$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$18$	5.16087			5.16087
$19$	0.615661	+	0.788011i	0.615661	+	0.788011i
$19$	0.615661	+	0.788011i	0.615661	+	0.788011i
$20$		0			0
$21$	2.18273	−	1.83153i	2.18273	−	1.83153i
$22$	1.65940	+	0.603972i	1.65940	+	0.603972i
$23$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.104528	+	0.994522i	$0.533333\pi$
$23$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.241922	+	0.970296i	$0.577778\pi$
$24$	0.679219	+	3.85204i	0.679219	+	3.85204i
$25$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$26$	0.882948	−	1.52931i	0.882948	−	1.52931i
$27$	−1.90381	−	3.29750i	−1.90381	−	3.29750i
$28$	2.33466	+	1.95901i	2.33466	+	1.95901i
$29$		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	$0.666667\pi$
$32$	−0.416155	+	0.151468i	−0.416155	+	0.151468i
$33$	−0.343916	−	1.95045i	−0.343916	−	1.95045i
$34$		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			$\pi$
$38$	1.72731	+	0.367150i	1.72731	+	0.367150i
$39$	−1.98054			−1.98054
$40$		0			0
$41$	−0.454664	−	0.165484i	−0.454664	−	0.165484i	0.104528	−	0.994522i	$-0.466667\pi$
$41$	−0.454664	−	0.165484i	−0.454664	−	0.165484i	−0.559193	+	0.829038i	$0.688889\pi$
$42$	0.873740	−	4.95522i	0.873740	−	4.95522i
$43$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$43$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$44$	1.99063	−	0.724531i	1.99063	−	0.724531i
$45$		0			0
$46$	1.76159	+	3.05117i	1.76159	+	3.05117i
$47$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$47$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$48$	2.07728	+	1.74304i	2.07728	+	1.74304i
$49$	−0.534899	−	0.926473i	−0.534899	−	0.926473i
$50$	−0.882948	+	1.52931i	−0.882948	+	1.52931i
$51$		0			0
$52$	−0.367854	−	2.08620i	−0.367854	−	2.08620i
$53$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	0.848048	+	0.529919i	$0.177778\pi$
$53$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	−0.978148	+	0.207912i	$0.933333\pi$
$54$	−6.31837	−	2.29970i	−6.31837	−	2.29970i
$55$		0			0
$56$	2.84132			2.84132
$57$	−0.612019	−	1.88360i	−0.612019	−	1.88360i
$58$		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
$63$	−3.95101	+	1.43805i	−3.95101	+	1.43805i
$64$	0.293561	−	0.508463i	0.293561	−	0.508463i
$65$		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
$69$	1.97571	−	3.42203i	1.97571	−	3.42203i
$70$		0			0
$71$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$71$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$72$	1.00227	−	5.68416i	1.00227	−	5.68416i
$73$	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
$75$	1.98054			1.98054
$76$	1.87042	−	0.994522i	1.87042	−	0.994522i
$77$	−1.43868			−1.43868
$78$	−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
$81$	0.802015	+	4.54845i	0.802015	+	4.54845i
$82$	−0.802890	+	0.292228i	−0.802890	+	0.292228i
$83$	0.438371	−	0.759281i	0.438371	−	0.759281i	−0.559193	−	0.829038i	$-0.688889\pi$
$83$	0.438371	−	0.759281i	0.438371	−	0.759281i	0.997564	+	0.0697565i	$0.0222222\pi$
$84$	−3.01802	−	5.22736i	−3.01802	−	5.22736i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.987476	−	1.71036i	0.987476	−	1.71036i
$89$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$89$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$90$		0			0
$91$	−0.249824	+	1.41682i	−0.249824	+	1.41682i
$92$	3.97156	+	1.44553i	3.97156	+	1.44553i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.877107			0.877107
$97$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$97$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$98$	−1.77522	−	0.646128i	−1.77522	−	0.646128i
$99$	−0.507491	+	2.87812i	−0.507491	+	2.87812i
$100$	0.367854	+	2.08620i	0.367854	+	2.08620i
$101$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$101$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$102$		0			0
$103$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	−0.997564	−	0.0697565i	$-0.977778\pi$
$103$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	0.438371	−	0.898794i	$-0.355556\pi$
$104$	−1.51290	−	1.26947i	−1.51290	−	1.26947i
$105$		0			0
$106$	0.661516	+	1.14578i	0.661516	+	1.14578i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−7.57958	+	2.75874i	−7.57958	+	2.75874i
$109$	−0.232387	−	1.31793i	−0.232387	−	1.31793i	−0.848048	−	0.529919i	$-0.822222\pi$
$109$	−0.232387	−	1.31793i	−0.232387	−	1.31793i	0.615661	−	0.788011i	$-0.288889\pi$
$110$		0			0
$111$		0			0
$112$	1.50895	−	1.26616i	1.50895	−	1.26616i
$113$	0.0697990			0.0697990			0.0348995	−	0.999391i	$-0.488889\pi$
$113$	0.0697990			0.0697990			0.0348995	+	0.999391i	$0.488889\pi$
$114$	−2.96598	−	1.85335i	−2.96598	−	1.85335i
$115$		0			0
$116$		0			0
$117$	2.74627	+	0.999562i	2.74627	+	0.999562i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	0.734077	+	0.615964i	0.734077	+	0.615964i
$124$		0			0
$125$		0			0
$126$	−3.71242	+	6.43010i	−3.71242	+	6.43010i
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	−0.256940	−	1.45718i	−0.256940	−	1.45718i
$129$		0			0
$130$		0			0
$131$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$131$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$132$	−4.19554			−4.19554
$133$	−1.42468	+	0.200226i	−1.42468	+	0.200226i
$134$		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	$0.555556\pi$
$138$	−1.21168	−	6.87179i	−1.21168	−	6.87179i
$139$		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
$144$	−2.00072	−	3.46535i	−2.00072	−	3.46535i
$145$		0			0
$146$	1.02556	−	0.373275i	1.02556	−	0.373275i
$147$	0.367922	+	2.08659i	0.367922	+	2.08659i
$148$		0			0
$149$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.997564	−	0.0697565i	$-0.0222222\pi$
$149$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.719340	+	0.694658i	$0.244444\pi$
$150$	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	$0.333333\pi$
$152$	0.739830	−	1.83114i	0.739830	−	1.83114i
$153$		0			0
$154$	−1.94618	+	1.63304i	−1.94618	+	1.63304i
$155$		0			0
$156$	−0.728548	+	4.13180i	−0.728548	+	4.13180i
$157$	−0.0363024	−	0.205881i	−0.0363024	−	0.205881i	0.961262	−	0.275637i	$-0.0888889\pi$
$157$	−0.0363024	−	0.205881i	−0.0363024	−	0.205881i	−0.997564	+	0.0697565i	$0.977778\pi$
$158$		0			0
$159$	0.741922	−	1.28505i	0.741922	−	1.28505i
$160$		0			0
$161$	−2.19882	−	1.84503i	−2.19882	−	1.84503i
$162$	6.24786	+	5.24257i	6.24786	+	5.24257i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−0.512484	+	0.887648i	−0.512484	+	0.887648i
$165$		0			0
$166$	−0.268848	−	1.52471i	−0.268848	−	1.52471i
$167$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i	−0.990268	−	0.139173i	$-0.955556\pi$
$167$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i	0.978148	+	0.207912i	$0.0666667\pi$
$168$	−5.28797	−	1.92466i	−5.28797	−	1.92466i
$169$	0.766044	−	0.642788i	0.766044	−	0.642788i
$170$		0			0
$171$	−0.101995	+	2.92074i	−0.101995	+	2.92074i
$172$		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
$175$	0.249824	−	1.41682i	0.249824	−	1.41682i
$176$	−0.237754	−	1.34837i	−0.237754	−	1.34837i
$177$		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
$181$	1.29929	+	1.09023i	1.29929	+	1.09023i	0.990268	+	0.139173i	$0.0444444\pi$
$181$	1.29929	+	1.09023i	1.29929	+	1.09023i	0.309017	+	0.951057i	$0.400000\pi$
$182$	1.27028	+	2.20019i	1.27028	+	2.20019i
$183$		0			0
$184$	3.70265	−	1.34766i	3.70265	−	1.34766i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	5.47796			5.47796
$190$		0			0
$191$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$191$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$192$	−0.890770	+	0.747445i	−0.890770	+	0.747445i
$193$	−1.87481	−	0.682374i	−1.87481	−	0.682374i	−0.961262	−	0.275637i	$-0.911111\pi$
$193$	−1.87481	−	0.682374i	−1.87481	−	0.682374i	−0.913545	−	0.406737i	$-0.866667\pi$
$194$		0			0
$195$		0			0
$196$	−2.12958	+	0.775102i	−2.12958	+	0.775102i
$197$	0.848048	−	1.46886i	0.848048	−	1.46886i	−0.0348995	−	0.999391i	$-0.511111\pi$
$197$	0.848048	−	1.46886i	0.848048	−	1.46886i	0.882948	−	0.469472i	$-0.155556\pi$
$198$	2.58043	+	4.46944i	2.58043	+	4.46944i
$199$	−0.943248	−	0.791479i	−0.943248	−	0.791479i	0.0348995	−	0.999391i	$-0.488889\pi$
$199$	−0.943248	−	0.791479i	−0.943248	−	0.791479i	−0.978148	+	0.207912i	$0.933333\pi$
$200$	1.51290	+	1.26947i	1.51290	+	1.26947i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−1.85585	−	0.675473i	−1.85585	−	0.675473i
$207$	−4.46666	+	3.74797i	−4.46666	+	3.74797i
$208$	−1.36917			−1.36917
$209$	−0.374607	+	0.927184i	−0.374607	+	0.927184i
$210$		0			0
$211$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$211$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$212$	1.49141	+	0.542828i	1.49141	+	0.542828i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−3.75994	+	6.51241i	−3.75994	+	6.51241i
$217$		0			0
$218$	−1.81034	−	1.51905i	−1.81034	−	1.51905i
$219$	−0.937668	−	0.786797i	−0.937668	−	0.786797i
$220$		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	$0.444444\pi$
$224$	0.110638	−	0.627459i	0.110638	−	0.627459i
$225$	−2.74627	−	0.999562i	−2.74627	−	0.999562i
$226$	0.0944209	−	0.0792285i	0.0944209	−	0.0792285i
$227$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$227$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$228$	−4.15471	+	0.583906i	−4.15471	+	0.583906i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	2.67752	+	0.974537i	2.67752	+	0.974537i
$232$		0			0
$233$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$233$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$234$	4.84963	−	1.76512i	4.84963	−	1.76512i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.615661	−	1.06636i	−0.615661	−	1.06636i	−0.990268	−	0.139173i	$-0.955556\pi$
$239$	−0.615661	−	1.06636i	−0.615661	−	1.06636i	0.374607	−	0.927184i	$-0.377778\pi$
$240$		0			0
$241$	0.823868	−	0.299864i	0.823868	−	0.299864i	0.104528	−	0.994522i	$-0.466667\pi$
$241$	0.823868	−	0.299864i	0.823868	−	0.299864i	0.719340	+	0.694658i	$0.244444\pi$
$242$	0.306644	+	1.73907i	0.306644	+	1.73907i
$243$	0.927232	−	5.25859i	0.927232	−	5.25859i
$244$		0			0
$245$		0			0
$246$	1.69220			1.69220
$247$	0.848048	+	0.529919i	0.848048	+	0.529919i
$248$		0			0
$249$	−1.33017	+	1.11615i	−1.33017	+	1.11615i
$250$		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	$0.755556\pi$
$252$	1.54667	+	8.77160i	1.54667	+	8.77160i
$253$	−1.87481	+	0.682374i	−1.87481	+	0.682374i
$254$		0			0
$255$		0			0
$256$	−1.55185	−	1.30216i	−1.55185	−	1.30216i
$257$	−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	$0.111111\pi$
$264$	−2.99636	+	2.51424i	−2.99636	+	2.51424i
$265$		0			0
$266$	−1.69996	+	1.88800i	−1.69996	+	1.88800i
$267$		0			0
$268$		0			0
$269$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$269$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$270$		0			0
$271$	−0.294524	−	1.67033i	−0.294524	−	1.67033i	−0.669131	−	0.743145i	$-0.733333\pi$
$271$	−0.294524	−	1.67033i	−0.294524	−	1.67033i	0.374607	−	0.927184i	$-0.377778\pi$
$272$		0			0
$273$	1.42468	−	2.46762i	1.42468	−	2.46762i
$274$		0			0
$275$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$276$	−6.41228	−	5.38054i	−6.41228	−	5.38054i
$277$		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
$281$	−0.294524	+	1.67033i	−0.294524	+	1.67033i	0.374607	+	0.927184i	$0.377778\pi$
$281$	−0.294524	+	1.67033i	−0.294524	+	1.67033i	−0.669131	+	0.743145i	$0.733333\pi$
$282$		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
$286$	1.76590			1.76590
$287$	0.533241	−	0.447442i	0.533241	−	0.447442i
$288$	−1.21622	−	0.442669i	−1.21622	−	0.442669i
$289$	0.173648	−	0.984808i	0.173648	−	0.984808i
$290$		0			0
$291$		0			0
$292$	0.654617	−	1.13383i	0.654617	−	1.13383i
$293$	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	$0.777778\pi$
$294$	2.86618	+	2.40501i	2.86618	+	2.40501i
$295$		0			0
$296$		0			0
$297$	1.90381	−	3.29750i	1.90381	−	3.29750i
$298$	3.03187	−	1.10351i	3.03187	−	1.10351i
$299$	0.346450	+	1.96482i	0.346450	+	1.96482i
$300$	0.728548	−	4.13180i	0.728548	−	4.13180i
$301$		0			0
$302$	1.35275	−	1.13510i	1.35275	−	1.13510i
$303$		0			0
$304$	−0.423098	−	1.30216i	−0.423098	−	1.30216i
$305$		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			$\pi$
$308$	−0.529224	+	3.00138i	−0.529224	+	3.00138i
$309$	0.384631	+	2.18135i	0.384631	+	2.18135i
$310$		0			0
$311$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.374607	+	0.927184i	$0.622222\pi$
$311$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.615661	+	0.788011i	$0.711111\pi$
$312$	1.95573	+	3.38743i	1.95573	+	3.38743i
$313$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.961262	+	0.275637i	$0.0888889\pi$
$313$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.438371	+	0.898794i	$0.355556\pi$
$314$	−0.282803	−	0.237300i	−0.282803	−	0.237300i
$315$		0			0
$316$		0			0
$317$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$317$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$318$	−0.455013	−	2.58050i	−0.455013	−	2.58050i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−5.06874			−5.06874
$323$		0			0
$324$	9.78402			9.78402
$325$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$326$		0			0
$327$	−0.460250	+	2.61021i	−0.460250	+	2.61021i
$328$	0.165933	+	0.941051i	0.165933	+	0.941051i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−1.42276	−	1.19384i	−1.42276	−	1.19384i
$333$		0			0
$334$	0.0616289	+	0.106744i	0.0616289	+	0.106744i
$335$		0			0
$336$	−3.66599	+	1.33431i	−3.66599	+	1.33431i
$337$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$337$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$338$	0.306644	−	1.73907i	0.306644	−	1.73907i
$339$	−0.129903	−	0.0472807i	−0.129903	−	0.0472807i
$340$		0			0
$341$		0			0
$342$	3.17735	+	4.06682i	3.17735	+	4.06682i
$343$	0.100418			0.100418
$344$		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
$349$	0.559193	−	0.968551i	0.559193	−	0.968551i	−0.438371	−	0.898794i	$-0.644444\pi$
$349$	0.559193	−	0.968551i	0.559193	−	0.968551i	0.997564	−	0.0697565i	$-0.0222222\pi$
$350$	−1.27028	−	2.20019i	−1.27028	−	2.20019i
$351$	−2.91681	−	2.44750i	−2.91681	−	2.44750i
$352$	−0.339253	−	0.284667i	−0.339253	−	0.284667i
$353$		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
$358$	3.11865	+	1.13510i	3.11865	+	1.13510i
$359$	1.52836	−	1.28244i	1.52836	−	1.28244i	0.719340	−	0.694658i	$-0.244444\pi$
$359$	1.52836	−	1.28244i	1.52836	−	1.28244i	0.809017	−	0.587785i	$-0.200000\pi$
$360$		0			0
$361$	−0.241922	+	0.970296i	−0.241922	+	0.970296i
$362$	2.99513			2.99513
$363$	1.51718	−	1.27306i	1.51718	−	1.27306i
$364$	2.86388	+	1.04237i	2.86388	+	1.04237i
$365$		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	$0.488889\pi$
$368$	1.36584	−	2.36570i	1.36584	−	2.36570i
$369$	−0.707022	−	1.22460i	−0.707022	−	1.22460i
$370$		0			0
$371$	−0.825702	−	0.692846i	−0.825702	−	0.692846i
$372$		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
$378$	7.41033	−	6.21800i	7.41033	−	6.21800i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	1.81034	−	1.51905i	1.81034	−	1.51905i
$383$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$383$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$384$	−0.508880	+	2.88600i	−0.508880	+	2.88600i
$385$		0			0
$386$	−3.31071	+	1.20500i	−3.31071	+	1.20500i
$387$		0			0
$388$		0			0
$389$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.882948	−	0.469472i	$-0.844444\pi$
$389$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.615661	−	0.788011i	$-0.711111\pi$
$390$		0			0
$391$		0			0
$392$	−1.05640	+	1.82974i	−1.05640	+	1.82974i
$393$		0			0
$394$	−0.520099	−	2.94963i	−0.520099	−	2.94963i
$395$		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	$0.777778\pi$
$398$	−2.17439			−2.17439
$399$	2.78709	+	0.592415i	2.78709	+	0.592415i
$400$	1.36917			1.36917
$401$		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
$412$	−2.22629	+	0.810305i	−2.22629	+	0.810305i
$413$		0			0
$414$	−1.78799	+	10.1402i	−1.78799	+	10.1402i
$415$		0			0
$416$	−0.339253	+	0.284667i	−0.339253	+	0.284667i
$417$		0			0
$418$	0.545692	+	1.67947i	0.545692	+	1.67947i
$419$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$419$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$420$		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
$424$	1.39043	−	0.506074i	1.39043	−	0.506074i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.990268	−	1.71519i	−0.990268	−	1.71519i
$430$		0			0
$431$	1.05094	−	0.382510i	1.05094	−	0.382510i	0.241922	−	0.970296i	$-0.422222\pi$
$431$	1.05094	−	0.382510i	1.05094	−	0.382510i	0.809017	+	0.587785i	$0.200000\pi$
$432$	0.905280	+	5.13410i	0.905280	+	5.13410i
$433$	−0.213817	+	1.21262i	−0.213817	+	1.21262i	0.669131	+	0.743145i	$0.266667\pi$
$433$	−0.213817	+	1.21262i	−0.213817	+	1.21262i	−0.882948	+	0.469472i	$0.844444\pi$
$434$		0			0
$435$		0			0
$436$	−2.83495			−2.83495
$437$	−1.76159	+	0.936656i	−1.76159	+	0.936656i
$438$	−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
$441$	0.542913	−	3.07901i	0.542913	−	3.07901i
$442$		0			0
$443$	−0.823868	+	0.299864i	−0.823868	+	0.299864i	−0.719340	−	0.694658i	$-0.755556\pi$
$443$	−0.823868	+	0.299864i	−0.823868	+	0.299864i	−0.104528	+	0.994522i	$0.533333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.77202	−	2.32600i	−2.77202	−	2.32600i
$448$	0.422341	+	0.731515i	0.422341	+	0.731515i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−4.84963	+	1.76512i	−4.84963	+	1.76512i
$451$	−0.0840186	−	0.476493i	−0.0840186	−	0.476493i
$452$	0.0256758	−	0.145615i	0.0256758	−	0.145615i
$453$	−1.86110	−	0.677383i	−1.86110	−	0.677383i
$454$	−0.836048	+	0.701528i	−0.836048	+	0.701528i
$455$		0			0
$456$	−2.61728	+	2.90678i	−2.61728	+	2.90678i
$457$	1.23132			1.23132			0.615661	−	0.788011i	$-0.288889\pi$
$457$	1.23132			1.23132			0.615661	+	0.788011i	$0.288889\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.339707	+	1.92657i	0.339707	+	1.92657i	0.374607	+	0.927184i	$0.377778\pi$
$461$	0.339707	+	1.92657i	0.339707	+	1.92657i	−0.0348995	+	0.999391i	$0.511111\pi$
$462$	4.72822	−	1.72093i	4.72822	−	1.72093i
$463$		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
$471$	−0.0718981	+	0.407755i	−0.0718981	+	0.407755i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.848048	−	0.529919i	−0.848048	−	0.529919i
$476$		0			0
$477$	−1.67733	+	1.40744i	−1.67733	+	1.40744i
$478$	−2.04326	−	0.743684i	−2.04326	−	0.743684i
$479$	−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
$482$	0.774117	−	1.34081i	0.774117	−	1.34081i
$483$	2.84242	+	4.92321i	2.84242	+	4.92321i
$484$	1.62278	+	1.36167i	1.62278	+	1.36167i
$485$		0			0
$486$	−4.71469	−	8.16608i	−4.71469	−	8.16608i
$487$		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	$0.111111\pi$
$492$	1.55506	−	1.30485i	1.55506	−	1.30485i
$493$		0			0
$494$	1.74871	−	0.245765i	1.74871	−	0.245765i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.532464	+	3.01975i	−0.532464	+	3.01975i
$499$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$499$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$500$		0			0
$501$	0.0691197	−	0.119719i	0.0691197	−	0.119719i
$502$	1.42864	+	2.47448i	1.42864	+	2.47448i
$503$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$503$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$504$	6.36111	+	5.33760i	6.36111	+	5.33760i
$505$		0			0
$506$	−1.76159	+	3.05117i	−1.76159	+	3.05117i
$507$	−1.86110	+	0.677383i	−1.86110	+	0.677383i
$508$		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
$511$	−0.681131	+	0.571536i	−0.681131	+	0.571536i
$512$	−2.09769			−2.09769
$513$	1.42636	−	3.53037i	1.42636	−	3.53037i
$514$	−2.85728			−2.85728
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$521$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$522$		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
$525$	−1.42468	+	2.46762i	−1.42468	+	2.46762i
$526$		0			0
$527$		0			0
$528$	−0.470881	+	2.67050i	−0.470881	+	2.67050i
$529$	−2.80079	−	1.01940i	−2.80079	−	1.01940i
$530$		0			0
$531$		0			0
$532$	−0.106362	+	3.04582i	−0.106362	+	3.04582i
$533$	−0.483844			−0.483844
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.646352	−	3.66564i	−0.646352	−	3.66564i
$538$	0.802890	−	0.292228i	0.802890	−	0.292228i
$539$	0.534899	−	0.926473i	0.534899	−	0.926473i
$540$		0			0
$541$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.913545	−	0.406737i	$-0.866667\pi$
$541$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.559193	−	0.829038i	$-0.688889\pi$
$542$	−2.29440	−	1.92523i	−2.29440	−	1.92523i
$543$	−1.67959	−	2.90914i	−1.67959	−	2.90914i
$544$		0			0
$545$		0			0
$546$	−0.873740	−	4.95522i	−0.873740	−	4.95522i
$547$		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
$550$	−1.76590			−1.76590
$551$		0			0
$552$	−7.80387			−7.80387
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.454664	+	0.165484i	−0.454664	+	0.165484i	−0.559193	−	0.829038i	$-0.688889\pi$
$557$	−0.454664	+	0.165484i	−0.454664	+	0.165484i	0.104528	+	0.994522i	$0.466667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.49756	+	2.59386i	1.49756	+	2.59386i
$563$		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
$567$	−6.24399	−	2.27263i	−6.24399	−	2.27263i
$568$		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			$\pi$
$572$	1.62278	−	1.36167i	1.62278	−	1.36167i
$573$	−2.49063	−	0.906516i	−2.49063	−	0.906516i
$574$	0.213454	−	1.21056i	0.213454	−	1.21056i
$575$	−0.346450	−	1.96482i	−0.346450	−	1.96482i
$576$	1.61240	−	0.586865i	1.61240	−	0.586865i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	−0.882948	−	1.52931i	−0.882948	−	1.52931i
$579$	3.02697	+	2.53993i	3.02697	+	2.53993i
$580$		0			0
$581$	0.630676	+	1.09236i	0.630676	+	1.09236i
$582$		0			0
$583$	−0.704030	+	0.256246i	−0.704030	+	0.256246i
$584$	−0.211953	−	1.20204i	−0.211953	−	1.20204i
$585$		0			0
$586$	0.576303	+	0.209757i	0.576303	+	0.209757i
$587$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$587$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$588$	4.48838			4.48838
$589$		0			0
$590$		0			0
$591$	−2.57328	+	2.15924i	−2.57328	+	2.15924i
$592$		0			0
$593$	0.0363024	−	0.205881i	0.0363024	−	0.205881i	−0.961262	−	0.275637i	$-0.911111\pi$
$593$	0.0363024	−	0.205881i	0.0363024	−	0.205881i	0.997564	+	0.0697565i	$0.0222222\pi$
$594$	−1.16759	−	6.62172i	−1.16759	−	6.62172i
$595$		0			0
$596$	1.93524	−	3.35194i	1.93524	−	3.35194i
$597$	1.21934	+	2.11196i	1.21934	+	2.11196i
$598$	2.69892	+	2.26466i	2.69892	+	2.26466i
$599$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.978148	−	0.207912i	$-0.933333\pi$
$599$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.374607	−	0.927184i	$-0.622222\pi$
$600$	−1.95573	−	3.38743i	−1.95573	−	3.38743i
$601$		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
$604$	0.367854	−	2.08620i	0.367854	−	2.08620i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.375569	−	0.234682i	−0.375569	−	0.234682i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i	0.978148	−	0.207912i	$-0.0666667\pi$
$613$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i	−0.990268	+	0.139173i	$0.955556\pi$
$614$	−3.11865	+	1.13510i	−3.11865	+	1.13510i
$615$		0			0
$616$	1.42066	+	2.46066i	1.42066	+	2.46066i
$617$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$617$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$618$	2.99636	+	2.51424i	2.99636	+	2.51424i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	7.13857	−	2.59823i	7.13857	−	2.59823i
$622$	0.607320	+	3.44429i	0.607320	+	3.44429i
$623$		0			0
$624$	2.54816	+	0.927455i	2.54816	+	0.927455i
$625$	0.766044	−	0.642788i	0.766044	−	0.642788i
$626$	3.22645			3.22645
$627$	1.32524	−	1.47183i	1.32524	−	1.47183i
$628$	−0.442863			−0.442863
$629$		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
$636$	−2.40795	−	2.02051i	−2.40795	−	2.02051i
$637$	−0.819514	−	0.687654i	−0.819514	−	0.687654i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.194206	+	1.10140i	0.194206	+	1.10140i	0.913545	+	0.406737i	$0.133333\pi$
$641$	0.194206	+	1.10140i	0.194206	+	1.10140i	−0.719340	+	0.694658i	$0.755556\pi$
$642$		0			0
$643$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$643$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$644$	−4.65794	+	3.90848i	−4.65794	+	3.90848i
$645$		0			0
$646$		0			0
$647$	1.69610			1.69610			0.848048	−	0.529919i	$-0.177778\pi$
$647$	1.69610			1.69610			0.848048	+	0.529919i	$0.177778\pi$
$648$	6.98751	−	5.86322i	6.98751	−	5.86322i
$649$		0			0
$650$	−0.306644	+	1.73907i	−0.306644	+	1.73907i
$651$		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	$0.222222\pi$
$654$	2.34023	+	4.05340i	2.34023	+	4.05340i
$655$		0			0
$656$	0.507478	+	0.425825i	0.507478	+	0.425825i
$657$	0.903109	+	1.56423i	0.903109	+	1.56423i
$658$		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
$664$	−1.73152			−1.73152
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.138944	+	0.0505715i	0.138944	+	0.0505715i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.630938	+	1.09282i	−0.630938	+	1.09282i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	2.91681	+	2.44750i	2.91681	+	2.44750i
$676$	−1.05919	−	1.83458i	−1.05919	−	1.83458i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.229394	+	0.0834927i	−0.229394	+	0.0834927i
$679$		0			0
$680$		0			0
$681$	1.15022	+	0.418646i	1.15022	+	0.418646i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	6.05574	+	1.28719i	6.05574	+	1.28719i
$685$		0			0
$686$	0.135841	−	0.113984i	0.135841	−	0.113984i
$687$		0			0
$688$		0			0
$689$	0.130100	+	0.737831i	0.130100	+	0.737831i
$690$		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
$693$	−3.22089	−	2.70265i	−3.22089	−	2.70265i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.342947	−	1.94495i	−0.342947	−	1.94495i
$699$		0			0
$700$	−2.86388	−	1.04237i	−2.86388	−	1.04237i
$701$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$701$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$702$	−6.72387			−6.72387
$703$		0			0
$704$	0.587123			0.587123
$705$		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
$716$	3.74116	−	1.36167i	3.74116	−	1.36167i
$717$	0.423472	+	2.40163i	0.423472	+	2.40163i
$718$	0.611795	−	3.46966i	0.611795	−	3.46966i
$719$	−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
$721$	1.60900			1.60900
$722$	0.774117	+	1.58718i	0.774117	+	1.58718i
$723$	−1.73642			−1.73642
$724$	2.75239	−	2.30953i	2.75239	−	2.30953i
$725$		0			0
$726$	0.607320	−	3.44429i	0.607320	−	3.44429i
$727$	−0.249824	−	1.41682i	−0.249824	−	1.41682i	−0.809017	−	0.587785i	$-0.800000\pi$
$727$	−0.249824	−	1.41682i	−0.249824	−	1.41682i	0.559193	−	0.829038i	$-0.311111\pi$
$728$	2.66997	−	0.971790i	2.66997	−	0.971790i
$729$	−2.97844	+	5.15881i	−2.97844	+	5.15881i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.438371	+	0.759281i	0.438371	+	0.759281i	0.997564	−	0.0697565i	$-0.0222222\pi$
$733$	0.438371	+	0.759281i	0.438371	+	0.759281i	−0.559193	+	0.829038i	$0.688889\pi$
$734$	−0.545692	+	0.945166i	−0.545692	+	0.945166i
$735$		0			0
$736$	−0.153430	−	0.870145i	−0.153430	−	0.870145i
$737$		0			0
$738$	−2.34646	−	0.854043i	−2.34646	−	0.854043i
$739$	0.370646	−	0.311009i	0.370646	−	0.311009i	−0.438371	−	0.898794i	$-0.644444\pi$
$739$	0.370646	−	0.311009i	0.370646	−	0.311009i	0.809017	+	0.587785i	$0.200000\pi$
$740$		0			0
$741$	−1.21934	−	1.56068i	−1.21934	−	1.56068i
$742$	−1.90342			−1.90342
$743$	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
$747$	2.40777	−	0.876358i	2.40777	−	0.876358i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.882948	−	0.469472i	$-0.844444\pi$
$751$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.615661	−	0.788011i	$-0.711111\pi$
$752$		0			0
$753$	1.60229	−	2.77524i	1.60229	−	2.77524i
$754$		0			0
$755$		0			0
$756$	2.01509	−	11.4281i	2.01509	−	11.4281i
$757$	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
$759$	3.95142			3.95142
$760$		0			0
$761$	−1.92252			−1.92252			−0.961262	−	0.275637i	$-0.911111\pi$
$761$	−1.92252			−1.92252			−0.961262	+	0.275637i	$0.911111\pi$
$762$		0			0
$763$	1.80922	+	0.658501i	1.80922	+	0.658501i
$764$	0.492285	−	2.79188i	0.492285	−	2.79188i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	2.00609	+	3.47464i	2.00609	+	3.47464i
$769$	0.370646	+	0.311009i	0.370646	+	0.311009i	0.809017	−	0.587785i	$-0.200000\pi$
$769$	0.370646	+	0.311009i	0.370646	+	0.311009i	−0.438371	+	0.898794i	$0.644444\pi$
$770$		0			0
$771$	1.60229	+	2.77524i	1.60229	+	2.77524i
$772$	−2.11323	+	3.66021i	−2.11323	+	3.66021i
$773$		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
$778$	−3.45461			−3.45461
$779$	−0.149516	−	0.460163i	−0.149516	−	0.460163i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.254349	+	1.44249i	0.254349	+	1.44249i
$785$		0			0
$786$		0			0
$787$	−0.719340	−	1.24593i	−0.719340	−	1.24593i	−0.961262	−	0.275637i	$-0.911111\pi$
$787$	−0.719340	−	1.24593i	−0.719340	−	1.24593i	0.241922	−	0.970296i	$-0.422222\pi$
$788$	−2.75239	−	2.30953i	−2.75239	−	2.30953i
$789$		0			0
$790$		0			0
$791$	−0.0502092	+	0.0869649i	−0.0502092	+	0.0869649i
$792$	5.42376	−	1.97409i	5.42376	−	1.97409i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−1.99816	+	1.67666i	−1.99816	+	1.67666i
$797$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$797$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$798$	4.44270	−	2.36222i	4.44270	−	2.36222i
$799$		0			0
$800$	0.339253	−	0.284667i	0.339253	−	0.284667i
$801$		0			0
$802$		0			0
$803$	0.107320	+	0.608645i	0.107320	+	0.608645i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.734077	−	0.615964i	−0.734077	−	0.615964i
$808$		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
$811$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.809017	−	0.587785i	$-0.200000\pi$
$811$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.997564	−	0.0697565i	$-0.0222222\pi$
$812$		0			0
$813$	−0.583315	+	3.30815i	−0.583315	+	3.30815i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−2.70551			−2.70551
$819$	−3.22089	+	2.70265i	−3.22089	+	2.70265i
$820$		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	$0.0888889\pi$
$824$	−1.10438	+	1.91284i	−1.10438	+	1.91284i
$825$	0.990268	+	1.71519i	0.990268	+	1.71519i
$826$		0			0
$827$	1.49861	+	1.25748i	1.49861	+	1.25748i	0.882948	+	0.469472i	$0.155556\pi$
$827$	1.49861	+	1.25748i	1.49861	+	1.25748i	0.615661	+	0.788011i	$0.288889\pi$
$828$	6.17595	+	10.6971i	6.17595	+	10.6971i
$829$	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
$832$	0.101953	−	0.578203i	0.101953	−	0.578203i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	1.79649	+	1.12257i	1.79649	+	1.12257i
$837$		0			0
$838$	2.47160	−	2.07392i	2.47160	−	2.07392i
$839$		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
$843$	1.67959	−	2.90914i	1.67959	−	2.90914i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.719340	−	1.24593i	−0.719340	−	1.24593i
$848$	0.512901	−	0.888371i	0.512901	−	0.888371i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.374607	−	0.927184i	$-0.377778\pi$
$853$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.978148	−	0.207912i	$-0.0666667\pi$
$854$		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
$859$	0.294524	−	1.67033i	0.294524	−	1.67033i	−0.374607	−	0.927184i	$-0.622222\pi$
$859$	0.294524	−	1.67033i	0.294524	−	1.67033i	0.669131	−	0.743145i	$-0.266667\pi$
$860$		0			0
$861$	−1.29550	+	0.471524i	−1.29550	+	0.471524i
$862$	0.987476	−	1.71036i	0.987476	−	1.71036i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	1.29175	+	1.08391i	1.29175	+	1.08391i
$865$		0			0
$866$	1.08719	+	1.88307i	1.08719	+	1.88307i
$867$	−0.990268	+	1.71519i	−0.990268	+	1.71519i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−2.02466	+	1.69889i	−2.02466	+	1.69889i
$873$		0			0
$874$	−1.31981	+	3.26664i	−1.31981	+	3.26664i
$875$		0			0
$876$	−1.98634	+	1.66674i	−1.98634	+	1.66674i
$877$	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
$879$	−0.119441	−	0.677383i	−0.119441	−	0.677383i
$880$		0			0
$881$	0.374607	−	0.648838i	0.374607	−	0.648838i	−0.615661	−	0.788011i	$-0.711111\pi$
$881$	0.374607	−	0.648838i	0.374607	−	0.648838i	0.990268	+	0.139173i	$0.0444444\pi$
$882$	−2.76055	−	4.78141i	−2.76055	−	4.78141i
$883$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.848048	+	0.529919i	$0.177778\pi$
$883$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.669131	+	0.743145i	$0.266667\pi$
$884$		0			0
$885$		0			0
$886$	−0.774117	+	1.34081i	−0.774117	+	1.34081i
$887$		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
$891$	−3.53807	+	2.96879i	−3.53807	+	2.96879i
$892$		0			0
$893$		0			0
$894$	−6.39010			−6.39010
$895$		0			0
$896$	2.00038	+	0.728078i	2.00038	+	0.728078i
$897$	0.686157	−	3.89139i	0.686157	−	3.89139i
$898$		0			0
$899$		0			0
$900$	−3.09552	+	5.36159i	−3.09552	+	5.36159i
$901$		0			0
$902$	−0.654522	−	0.549209i	−0.654522	−	0.549209i
$903$		0			0
$904$	−0.0689248	−	0.119381i	−0.0689248	−	0.119381i
$905$		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	$-0.355556\pi$
$908$	−0.227346	+	1.28934i	−0.227346	+	1.28934i
$909$		0			0
$910$		0			0
$911$	−1.99513			−1.99513			−0.997564	−	0.0697565i	$-0.977778\pi$
$911$	−1.99513			−1.99513			−0.997564	+	0.0697565i	$0.977778\pi$
$912$	−0.0946368	+	2.71004i	−0.0946368	+	2.71004i
$913$	0.876742			0.876742
$914$	1.66568	−	1.39767i	1.66568	−	1.39767i
$915$		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
$921$	2.85136	+	2.39258i	2.85136	+	2.39258i
$922$	2.64639	+	2.22058i	2.64639	+	2.22058i
$923$		0			0
$924$	3.01802	−	5.22736i	3.01802	−	5.22736i
$925$		0			0
$926$		0			0
$927$	0.567571	−	3.21885i	0.567571	−	3.21885i
$928$		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
$931$	0.400754	−	0.991900i	0.400754	−	0.991900i
$932$		0			0
$933$	3.00483	−	2.52135i	3.00483	−	2.52135i
$934$	−2.54235	−	0.925338i	−2.54235	−	0.925338i
$935$		0			0
$936$	−1.00227	−	5.68416i	−1.00227	−	5.68416i
$937$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$937$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$938$		0			0
$939$	−1.80931	−	3.13382i	−1.80931	−	3.13382i
$940$		0			0
$941$	1.49861	+	1.25748i	1.49861	+	1.25748i	0.882948	+	0.469472i	$0.155556\pi$
$941$	1.49861	+	1.25748i	1.49861	+	1.25748i	0.615661	+	0.788011i	$0.288889\pi$
$942$	0.365580	+	0.633203i	0.365580	+	0.633203i
$943$	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	+	0.245765i	−1.74871	+	0.245765i
$951$		0			0
$952$		0			0
$953$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$953$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$954$	−0.671427	+	3.80785i	−0.671427	+	3.80785i
$955$		0			0
$956$	−2.45111	+	0.892131i	−2.45111	+	0.892131i
$957$		0			0
$958$	0.306644	+	0.531124i	0.306644	+	0.531124i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	−0.322513	−	1.82906i	−0.322513	−	1.82906i
$965$		0			0
$966$	9.43340	+	3.43348i	9.43340	+	3.43348i
$967$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i	−0.669131	−	0.743145i	$-0.733333\pi$
$967$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i	0.615661	+	0.788011i	$0.288889\pi$
$968$	1.97495			1.97495
$969$		0			0
$970$		0			0
$971$	−1.49861	+	1.25748i	−1.49861	+	1.25748i	−0.615661	+	0.788011i	$0.711111\pi$
$971$	−1.49861	+	1.25748i	−1.49861	+	1.25748i	−0.882948	+	0.469472i	$0.844444\pi$
$972$	−10.6294	−	3.86879i	−10.6294	−	3.86879i
$973$		0			0
$974$		0			0
$975$	1.86110	−	0.677383i	1.86110	−	0.677383i
$976$		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
$981$	1.95555	−	3.38711i	1.95555	−	3.38711i
$982$		0			0
$983$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$983$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$984$	0.328636	−	1.86379i	0.328636	−	1.86379i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.41748	−	1.57427i	1.41748	−	1.57427i
$989$		0			0
$990$		0			0
$991$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.669131	−	0.743145i	$-0.266667\pi$
$991$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.0348995	+	0.999391i	$0.488889\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.83920	+	3.18559i	1.83920	+	3.18559i
$997$		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.2001.4	✓	24
11.10	odd	2		2717.1.db.d.2001.1	yes	24
13.12	even	2		2717.1.db.d.2001.1	yes	24
19.16	even	9	inner	2717.1.db.c.2144.4	yes	24
143.142	odd	2	CM	2717.1.db.c.2001.4	✓	24
209.54	odd	18		2717.1.db.d.2144.1	yes	24
247.168	even	18		2717.1.db.d.2144.1	yes	24
2717.2144	odd	18	inner	2717.1.db.c.2144.4	yes	24

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

\(f(q)\)	\(=\)	\(q+(1.35275 - 1.13510i) q^{2} +(-1.86110 - 0.677383i) q^{3} +(0.367854 - 2.08620i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(-0.719340 + 1.24593i) q^{7} +(-0.987476 - 1.71036i) q^{8} +(2.23878 + 1.87856i) q^{9} +O(q^{10})\)	\(q+(1.35275 - 1.13510i) q^{2} +(-1.86110 - 0.677383i) q^{3} +(0.367854 - 2.08620i) q^{4} +(-3.28650 + 1.19619i) q^{6} +(-0.719340 + 1.24593i) q^{7} +(-0.987476 - 1.71036i) q^{8} +(2.23878 + 1.87856i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-2.09777 + 3.63344i) q^{12} +(0.939693 - 0.342020i) q^{13} +(0.441163 + 2.50196i) q^{14} +(-1.28660 - 0.468285i) q^{16} +5.16087 q^{18} +(0.615661 + 0.788011i) q^{19} +(2.18273 - 1.83153i) q^{21} +(1.65940 + 0.603972i) q^{22} +(-0.346450 + 1.96482i) q^{23} +(0.679219 + 3.85204i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(0.882948 - 1.52931i) q^{26} +(-1.90381 - 3.29750i) q^{27} +(2.33466 + 1.95901i) q^{28} +(-0.416155 + 0.151468i) q^{32} +(-0.343916 - 1.95045i) q^{33} +(4.74261 - 3.97952i) q^{36} +(1.72731 + 0.367150i) q^{38} -1.98054 q^{39} +(-0.454664 - 0.165484i) q^{41} +(0.873740 - 4.95522i) q^{42} +(1.99063 - 0.724531i) q^{44} +(1.76159 + 3.05117i) q^{46} +(2.07728 + 1.74304i) q^{48} +(-0.534899 - 0.926473i) q^{49} +(-0.882948 + 1.52931i) q^{50} +(-0.367854 - 2.08620i) q^{52} +(-0.130100 + 0.737831i) q^{53} +(-6.31837 - 2.29970i) q^{54} +2.84132 q^{56} +(-0.612019 - 1.88360i) q^{57} +(-3.95101 + 1.43805i) q^{63} +(0.293561 - 0.508463i) q^{64} +(-2.67918 - 2.24810i) q^{66} +(1.97571 - 3.42203i) q^{69} +(1.00227 - 5.68416i) q^{72} +(0.580762 + 0.211380i) q^{73} +1.98054 q^{75} +(1.87042 - 0.994522i) q^{76} -1.43868 q^{77} +(-2.67918 + 2.24810i) q^{78} +(0.802015 + 4.54845i) q^{81} +(-0.802890 + 0.292228i) q^{82} +(0.438371 - 0.759281i) q^{83} +(-3.01802 - 5.22736i) q^{84} +(0.987476 - 1.71036i) q^{88} +(-0.249824 + 1.41682i) q^{91} +(3.97156 + 1.44553i) q^{92} +0.877107 q^{96} +(-1.77522 - 0.646128i) q^{98} +(-0.507491 + 2.87812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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