LMFDB - Embedded newform 2717.1.db.c.1429.4

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			1429.4
Root			$-0.882948 + 0.469472i$ of defining polynomial
Character	$\chi$	$=$	2717.1429
Dual form			2717.1.db.c.1715.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59381 + 0.580099i) q^{2} +(-0.130100 - 0.737831i) q^{3} +(1.43767 + 1.20635i) q^{4} +(0.220661 - 1.25143i) q^{6} +(-0.241922 + 0.419021i) q^{7} +(0.743520 + 1.28781i) q^{8} +(0.412224 - 0.150037i) q^{9} +O(q^{10})$	\(q+(1.59381 + 0.580099i) q^{2} +(-0.130100 - 0.737831i) q^{3} +(1.43767 + 1.20635i) q^{4} +(0.220661 - 1.25143i) q^{6} +(-0.241922 + 0.419021i) q^{7} +(0.743520 + 1.28781i) q^{8} +(0.412224 - 0.150037i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.703040 - 1.21770i) q^{12} +(-0.173648 + 0.984808i) q^{13} +(-0.628651 + 0.527501i) q^{14} +(0.112076 + 0.635614i) q^{16} +0.744043 q^{18} +(-0.990268 + 0.139173i) q^{19} +(0.340641 + 0.123983i) q^{21} +(0.294524 + 1.67033i) q^{22} +(0.856733 + 0.718885i) q^{23} +(0.853457 - 0.716136i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.848048 + 1.46886i) q^{26} +(-0.538939 - 0.933469i) q^{27} +(-0.853288 + 0.310571i) q^{28} +(0.0681302 - 0.386385i) q^{32} +(0.573931 - 0.481585i) q^{33} +(0.773638 + 0.281581i) q^{36} +(-1.65903 - 0.352638i) q^{38} +0.749213 q^{39} +(-0.333843 - 1.89332i) q^{41} +(0.470994 + 0.395211i) q^{42} +(-0.325893 + 1.84823i) q^{44} +(0.948445 + 1.64275i) q^{46} +(0.454395 - 0.165386i) q^{48} +(0.382948 + 0.663285i) q^{49} +(0.848048 - 1.46886i) q^{50} +(-1.43767 + 1.20635i) q^{52} +(-0.943248 - 0.791479i) q^{53} +(-0.317461 - 1.80041i) q^{54} -0.719495 q^{56} +(0.231520 + 0.712544i) q^{57} +(-0.0368572 + 0.209028i) q^{63} +(0.655438 - 1.13525i) q^{64} +(1.19410 - 0.434618i) q^{66} +(0.418955 - 0.725651i) q^{69} +(0.499717 + 0.419312i) q^{72} +(-0.107320 - 0.608645i) q^{73} -0.749213 q^{75} +(-1.59157 - 0.994522i) q^{76} -0.483844 q^{77} +(1.19410 + 0.434618i) q^{78} +(-0.282579 + 0.237112i) q^{81} +(0.566229 - 3.21125i) q^{82} +(-0.997564 + 1.72783i) q^{83} +(0.340162 + 0.589177i) q^{84} +(-0.743520 + 1.28781i) q^{88} +(-0.370646 - 0.311009i) q^{91} +(0.364474 + 2.06703i) q^{92} -0.293951 q^{96} +(0.225575 + 1.27930i) q^{98} +(0.336048 + 0.281978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.978148	−	0.207912i	$-0.0666667\pi$
$2$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.615661	+	0.788011i	$0.288889\pi$
$3$	−0.130100	−	0.737831i	−0.130100	−	0.737831i	−0.978148	−	0.207912i	$-0.933333\pi$
$3$	−0.130100	−	0.737831i	−0.130100	−	0.737831i	0.848048	−	0.529919i	$-0.177778\pi$
$4$	1.43767	+	1.20635i	1.43767	+	1.20635i
$5$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$5$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$6$	0.220661	−	1.25143i	0.220661	−	1.25143i
$7$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	−0.961262	−	0.275637i	$-0.911111\pi$
$7$	−0.241922	+	0.419021i	−0.241922	+	0.419021i	0.719340	+	0.694658i	$0.244444\pi$
$8$	0.743520	+	1.28781i	0.743520	+	1.28781i
$9$	0.412224	−	0.150037i	0.412224	−	0.150037i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	0.703040	−	1.21770i	0.703040	−	1.21770i
$13$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$13$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$14$	−0.628651	+	0.527501i	−0.628651	+	0.527501i
$15$		0			0
$16$	0.112076	+	0.635614i	0.112076	+	0.635614i
$17$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$17$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$18$	0.744043			0.744043
$19$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$19$	−0.990268	+	0.139173i	−0.990268	+	0.139173i
$20$		0			0
$21$	0.340641	+	0.123983i	0.340641	+	0.123983i
$22$	0.294524	+	1.67033i	0.294524	+	1.67033i
$23$	0.856733	+	0.718885i	0.856733	+	0.718885i	0.961262	−	0.275637i	$-0.0888889\pi$
$23$	0.856733	+	0.718885i	0.856733	+	0.718885i	−0.104528	+	0.994522i	$0.533333\pi$
$24$	0.853457	−	0.716136i	0.853457	−	0.716136i
$25$	0.173648	−	0.984808i	0.173648	−	0.984808i
$26$	−0.848048	+	1.46886i	−0.848048	+	1.46886i
$27$	−0.538939	−	0.933469i	−0.538939	−	0.933469i
$28$	−0.853288	+	0.310571i	−0.853288	+	0.310571i
$29$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$29$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.0681302	−	0.386385i	0.0681302	−	0.386385i
$33$	0.573931	−	0.481585i	0.573931	−	0.481585i
$34$		0			0
$35$		0			0
$36$	0.773638	+	0.281581i	0.773638	+	0.281581i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−1.65903	−	0.352638i	−1.65903	−	0.352638i
$39$	0.749213			0.749213
$40$		0			0
$41$	−0.333843	−	1.89332i	−0.333843	−	1.89332i	−0.438371	−	0.898794i	$-0.644444\pi$
$41$	−0.333843	−	1.89332i	−0.333843	−	1.89332i	0.104528	−	0.994522i	$-0.466667\pi$
$42$	0.470994	+	0.395211i	0.470994	+	0.395211i
$43$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$43$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$44$	−0.325893	+	1.84823i	−0.325893	+	1.84823i
$45$		0			0
$46$	0.948445	+	1.64275i	0.948445	+	1.64275i
$47$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$47$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$48$	0.454395	−	0.165386i	0.454395	−	0.165386i
$49$	0.382948	+	0.663285i	0.382948	+	0.663285i
$50$	0.848048	−	1.46886i	0.848048	−	1.46886i
$51$		0			0
$52$	−1.43767	+	1.20635i	−1.43767	+	1.20635i
$53$	−0.943248	−	0.791479i	−0.943248	−	0.791479i	0.0348995	−	0.999391i	$-0.488889\pi$
$53$	−0.943248	−	0.791479i	−0.943248	−	0.791479i	−0.978148	+	0.207912i	$0.933333\pi$
$54$	−0.317461	−	1.80041i	−0.317461	−	1.80041i
$55$		0			0
$56$	−0.719495			−0.719495
$57$	0.231520	+	0.712544i	0.231520	+	0.712544i
$58$		0			0
$59$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$59$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$60$		0			0
$61$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$61$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$62$		0			0
$63$	−0.0368572	+	0.209028i	−0.0368572	+	0.209028i
$64$	0.655438	−	1.13525i	0.655438	−	1.13525i
$65$		0			0
$66$	1.19410	−	0.434618i	1.19410	−	0.434618i
$67$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$67$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$68$		0			0
$69$	0.418955	−	0.725651i	0.418955	−	0.725651i
$70$		0			0
$71$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$71$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$72$	0.499717	+	0.419312i	0.499717	+	0.419312i
$73$	−0.107320	−	0.608645i	−0.107320	−	0.608645i	−0.990268	−	0.139173i	$-0.955556\pi$
$73$	−0.107320	−	0.608645i	−0.107320	−	0.608645i	0.882948	−	0.469472i	$-0.155556\pi$
$74$		0			0
$75$	−0.749213			−0.749213
$76$	−1.59157	−	0.994522i	−1.59157	−	0.994522i
$77$	−0.483844			−0.483844
$78$	1.19410	+	0.434618i	1.19410	+	0.434618i
$79$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$79$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$80$		0			0
$81$	−0.282579	+	0.237112i	−0.282579	+	0.237112i
$82$	0.566229	−	3.21125i	0.566229	−	3.21125i
$83$	−0.997564	+	1.72783i	−0.997564	+	1.72783i	−0.438371	+	0.898794i	$0.644444\pi$
$83$	−0.997564	+	1.72783i	−0.997564	+	1.72783i	−0.559193	+	0.829038i	$0.688889\pi$
$84$	0.340162	+	0.589177i	0.340162	+	0.589177i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.743520	+	1.28781i	−0.743520	+	1.28781i
$89$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$89$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$90$		0			0
$91$	−0.370646	−	0.311009i	−0.370646	−	0.311009i
$92$	0.364474	+	2.06703i	0.364474	+	2.06703i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.293951			−0.293951
$97$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$97$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$98$	0.225575	+	1.27930i	0.225575	+	1.27930i
$99$	0.336048	+	0.281978i	0.336048	+	0.281978i
$100$	1.43767	−	1.20635i	1.43767	−	1.20635i
$101$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$101$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$102$		0			0
$103$	−0.438371	−	0.759281i	−0.438371	−	0.759281i	0.559193	−	0.829038i	$-0.311111\pi$
$103$	−0.438371	−	0.759281i	−0.438371	−	0.759281i	−0.997564	+	0.0697565i	$0.977778\pi$
$104$	−1.39736	+	0.508597i	−1.39736	+	0.508597i
$105$		0			0
$106$	−1.04422	−	1.80864i	−1.04422	−	1.80864i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.351273	−	1.99217i	0.351273	−	1.99217i
$109$	−1.02517	+	0.860218i	−1.02517	+	0.860218i	−0.990268	−	0.139173i	$-0.955556\pi$
$109$	−1.02517	+	0.860218i	−1.02517	+	0.860218i	−0.0348995	+	0.999391i	$0.511111\pi$
$110$		0			0
$111$		0			0
$112$	−0.293449	−	0.106807i	−0.293449	−	0.106807i
$113$	−1.76590			−1.76590			−0.882948	−	0.469472i	$-0.844444\pi$
$113$	−1.76590			−1.76590			−0.882948	+	0.469472i	$0.844444\pi$
$114$	−0.0443481	+	1.26996i	−0.0443481	+	1.26996i
$115$		0			0
$116$		0			0
$117$	0.0761759	+	0.432015i	0.0761759	+	0.432015i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	−1.35351	+	0.492639i	−1.35351	+	0.492639i
$124$		0			0
$125$		0			0
$126$	−0.180000	+	0.311770i	−0.180000	+	0.311770i
$127$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$127$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$128$	1.40265	−	1.17696i	1.40265	−	1.17696i
$129$		0			0
$130$		0			0
$131$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$131$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$132$	1.40608			1.40608
$133$	0.181251	−	0.448612i	0.181251	−	0.448612i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$137$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$138$	1.08868	−	0.913514i	1.08868	−	0.913514i
$139$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$139$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$144$	0.141566	+	0.245200i	0.141566	+	0.245200i
$145$		0			0
$146$	0.182026	−	1.03232i	0.182026	−	1.03232i
$147$	0.439571	−	0.368844i	0.439571	−	0.368844i
$148$		0			0
$149$	−0.317271	−	1.79933i	−0.317271	−	1.79933i	−0.559193	−	0.829038i	$-0.688889\pi$
$149$	−0.317271	−	1.79933i	−0.317271	−	1.79933i	0.241922	−	0.970296i	$-0.422222\pi$
$150$	−1.19410	−	0.434618i	−1.19410	−	0.434618i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	−0.915513	−	1.17180i	−0.915513	−	1.17180i
$153$		0			0
$154$	−0.771155	−	0.280677i	−0.771155	−	0.280677i
$155$		0			0
$156$	1.07712	+	0.903811i	1.07712	+	0.903811i
$157$	−0.160147	+	0.134379i	−0.160147	+	0.134379i	−0.719340	−	0.694658i	$-0.755556\pi$
$157$	−0.160147	+	0.134379i	−0.160147	+	0.134379i	0.559193	+	0.829038i	$0.311111\pi$
$158$		0			0
$159$	−0.461262	+	0.798929i	−0.461262	+	0.798929i
$160$		0			0
$161$	−0.508490	+	0.185075i	−0.508490	+	0.185075i
$162$	−0.587925	+	0.213987i	−0.587925	+	0.213987i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	1.80404	−	3.12469i	1.80404	−	3.12469i
$165$		0			0
$166$	−2.59224	+	2.17515i	−2.59224	+	2.17515i
$167$	1.35275	+	1.13510i	1.35275	+	1.13510i	0.978148	+	0.207912i	$0.0666667\pi$
$167$	1.35275	+	1.13510i	1.35275	+	1.13510i	0.374607	+	0.927184i	$0.377778\pi$
$168$	0.0936059	+	0.530865i	0.0936059	+	0.530865i
$169$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$170$		0			0
$171$	−0.387331	+	0.205948i	−0.387331	+	0.205948i
$172$		0			0
$173$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$173$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$174$		0			0
$175$	0.370646	+	0.311009i	0.370646	+	0.311009i
$176$	−0.494420	+	0.414868i	−0.494420	+	0.414868i
$177$		0			0
$178$		0			0
$179$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$179$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$180$		0			0
$181$	−0.0655896	+	0.0238727i	−0.0655896	+	0.0238727i	−0.374607	−	0.927184i	$-0.622222\pi$
$181$	−0.0655896	+	0.0238727i	−0.0655896	+	0.0238727i	0.309017	+	0.951057i	$0.400000\pi$
$182$	−0.410323	−	0.710700i	−0.410323	−	0.710700i
$183$		0			0
$184$	−0.288791	+	1.63782i	−0.288791	+	1.63782i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.521524			0.521524
$190$		0			0
$191$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$191$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$192$	−0.922896	−	0.335907i	−0.922896	−	0.335907i
$193$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	−0.913545	−	0.406737i	$-0.866667\pi$
$193$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	0.719340	−	0.694658i	$-0.244444\pi$
$194$		0			0
$195$		0			0
$196$	−0.249600	+	1.41555i	−0.249600	+	1.41555i
$197$	0.0348995	−	0.0604477i	0.0348995	−	0.0604477i	−0.848048	−	0.529919i	$-0.822222\pi$
$197$	0.0348995	−	0.0604477i	0.0348995	−	0.0604477i	0.882948	+	0.469472i	$0.155556\pi$
$198$	0.372021	+	0.644360i	0.372021	+	0.644360i
$199$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.882948	+	0.469472i	$0.844444\pi$
$199$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.978148	+	0.207912i	$0.933333\pi$
$200$	1.39736	−	0.508597i	1.39736	−	0.508597i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.258222	−	1.46445i	−0.258222	−	1.46445i
$207$	0.461025	+	0.167800i	0.461025	+	0.167800i
$208$	−0.645419			−0.645419
$209$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$210$		0			0
$211$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$211$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$212$	−0.401279	−	2.27577i	−0.401279	−	2.27577i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.801423	−	1.38811i	0.801423	−	1.38811i
$217$		0			0
$218$	−2.13293	+	0.776324i	−2.13293	+	0.776324i
$219$	−0.435115	+	0.158369i	−0.435115	+	0.158369i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$223$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$224$	0.145421	+	0.122023i	0.145421	+	0.122023i
$225$	−0.0761759	−	0.432015i	−0.0761759	−	0.432015i
$226$	−2.81450	−	1.02439i	−2.81450	−	1.02439i
$227$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$227$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$228$	−0.526727	+	1.30369i	−0.526727	+	1.30369i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	0.0629478	+	0.356995i	0.0629478	+	0.356995i
$232$		0			0
$233$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$233$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$234$	−0.129202	+	0.732739i	−0.129202	+	0.732739i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.615661	+	0.788011i	$0.288889\pi$
$239$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.374607	+	0.927184i	$0.377778\pi$
$240$		0			0
$241$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.104528	−	0.994522i	$-0.466667\pi$
$241$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.241922	−	0.970296i	$-0.422222\pi$
$242$	−1.29929	+	1.09023i	−1.29929	+	1.09023i
$243$	−0.613990	−	0.515199i	−0.613990	−	0.515199i
$244$		0			0
$245$		0			0
$246$	−2.44302			−2.44302
$247$	0.0348995	−	0.999391i	0.0348995	−	0.999391i
$248$		0			0
$249$	1.40463	+	0.511244i	1.40463	+	0.511244i
$250$		0			0
$251$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.997564	−	0.0697565i	$-0.977778\pi$
$251$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.241922	−	0.970296i	$-0.577778\pi$
$252$	−0.305148	+	0.256050i	−0.305148	+	0.256050i
$253$	−0.194206	+	1.10140i	−0.194206	+	1.10140i
$254$		0			0
$255$		0			0
$256$	1.68648	−	0.613830i	1.68648	−	0.613830i
$257$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.559193	−	0.829038i	$-0.311111\pi$
$257$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.961262	+	0.275637i	$0.0888889\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$263$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$264$	1.04692	+	0.381048i	1.04692	+	0.381048i
$265$		0			0
$266$	0.549119	−	0.609859i	0.549119	−	0.609859i
$267$		0			0
$268$		0			0
$269$	0.333843	+	1.89332i	0.333843	+	1.89332i	0.438371	+	0.898794i	$0.355556\pi$
$269$	0.333843	+	1.89332i	0.333843	+	1.89332i	−0.104528	+	0.994522i	$0.533333\pi$
$270$		0			0
$271$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i	−0.669131	−	0.743145i	$-0.733333\pi$
$271$	−0.0534691	+	0.0448659i	−0.0534691	+	0.0448659i	0.615661	+	0.788011i	$0.288889\pi$
$272$		0			0
$273$	−0.181251	+	0.313936i	−0.181251	+	0.313936i
$274$		0			0
$275$	0.939693	−	0.342020i	0.939693	−	0.342020i
$276$	1.47770	−	0.537840i	1.47770	−	0.537840i
$277$		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
$281$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i	0.615661	−	0.788011i	$-0.288889\pi$
$281$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i	−0.669131	+	0.743145i	$0.733333\pi$
$282$		0			0
$283$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$283$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$284$		0			0
$285$		0			0
$286$	−1.69610			−1.69610
$287$	0.874103	+	0.318147i	0.874103	+	0.318147i
$288$	−0.0298873	−	0.169499i	−0.0298873	−	0.169499i
$289$	0.766044	+	0.642788i	0.766044	+	0.642788i
$290$		0			0
$291$		0			0
$292$	0.579945	−	1.00449i	0.579945	−	1.00449i
$293$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$293$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$294$	0.914558	−	0.332872i	0.914558	−	0.332872i
$295$		0			0
$296$		0			0
$297$	0.538939	−	0.933469i	0.538939	−	0.933469i
$298$	0.538122	−	3.05184i	0.538122	−	3.05184i
$299$	−0.856733	+	0.718885i	−0.856733	+	0.718885i
$300$	−1.07712	−	0.903811i	−1.07712	−	0.903811i
$301$		0			0
$302$	1.59381	+	0.580099i	1.59381	+	0.580099i
$303$		0			0
$304$	−0.199446	−	0.613830i	−0.199446	−	0.613830i
$305$		0			0
$306$		0			0
$307$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$307$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$308$	−0.695607	−	0.583683i	−0.695607	−	0.583683i
$309$	−0.503189	+	0.422226i	−0.503189	+	0.422226i
$310$		0			0
$311$	0.374607	−	0.648838i	0.374607	−	0.648838i	−0.615661	−	0.788011i	$-0.711111\pi$
$311$	0.374607	−	0.648838i	0.374607	−	0.648838i	0.990268	+	0.139173i	$0.0444444\pi$
$312$	0.557055	+	0.964847i	0.557055	+	0.964847i
$313$	−1.71690	+	0.624902i	−1.71690	+	0.624902i	−0.997564	−	0.0697565i	$-0.977778\pi$
$313$	−1.71690	+	0.624902i	−1.71690	+	0.624902i	−0.719340	+	0.694658i	$0.755556\pi$
$314$	−0.333197	+	0.121274i	−0.333197	+	0.121274i
$315$		0			0
$316$		0			0
$317$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$317$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$318$	−1.19862	+	1.00576i	−1.19862	+	1.00576i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−0.917798			−0.917798
$323$		0			0
$324$	−0.692294			−0.692294
$325$	0.939693	+	0.342020i	0.939693	+	0.342020i
$326$		0			0
$327$	0.768069	+	0.644486i	0.768069	+	0.644486i
$328$	2.19002	−	1.83764i	2.19002	−	1.83764i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−3.51853	+	1.28064i	−3.51853	+	1.28064i
$333$		0			0
$334$	1.49756	+	2.59386i	1.49756	+	2.59386i
$335$		0			0
$336$	−0.0406278	+	0.230411i	−0.0406278	+	0.230411i
$337$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$337$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$338$	−1.29929	−	1.09023i	−1.29929	−	1.09023i
$339$	0.229742	+	1.30293i	0.229742	+	1.30293i
$340$		0			0
$341$		0			0
$342$	−0.736802	+	0.103551i	−0.736802	+	0.103551i
$343$	−0.854417			−0.854417
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$347$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$348$		0			0
$349$	0.438371	−	0.759281i	0.438371	−	0.759281i	−0.559193	−	0.829038i	$-0.688889\pi$
$349$	0.438371	−	0.759281i	0.438371	−	0.759281i	0.997564	+	0.0697565i	$0.0222222\pi$
$350$	0.410323	+	0.710700i	0.410323	+	0.710700i
$351$	1.01287	−	0.368656i	1.01287	−	0.368656i
$352$	0.368685	−	0.134190i	0.368685	−	0.134190i
$353$		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
$358$	−0.102287	−	0.580099i	−0.102287	−	0.580099i
$359$	1.05094	+	0.382510i	1.05094	+	0.382510i	0.809017	−	0.587785i	$-0.200000\pi$
$359$	1.05094	+	0.382510i	1.05094	+	0.382510i	0.241922	+	0.970296i	$0.422222\pi$
$360$		0			0
$361$	0.961262	−	0.275637i	0.961262	−	0.275637i
$362$	−0.118386			−0.118386
$363$	0.704030	+	0.256246i	0.704030	+	0.256246i
$364$	−0.157681	−	0.894255i	−0.157681	−	0.894255i
$365$		0			0
$366$		0			0
$367$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$367$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$368$	−0.360914	+	0.625121i	−0.360914	+	0.625121i
$369$	−0.421686	−	0.730381i	−0.421686	−	0.730381i
$370$		0			0
$371$	0.559839	−	0.203765i	0.559839	−	0.203765i
$372$		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
$378$	0.831210	+	0.302536i	0.831210	+	0.302536i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	2.13293	+	0.776324i	2.13293	+	0.776324i
$383$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$383$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$384$	−1.05088	−	0.881794i	−1.05088	−	0.881794i
$385$		0			0
$386$	0.329391	−	1.86807i	0.329391	−	1.86807i
$387$		0			0
$388$		0			0
$389$	1.83832	−	0.669092i	1.83832	−	0.669092i	0.848048	−	0.529919i	$-0.177778\pi$
$389$	1.83832	−	0.669092i	1.83832	−	0.669092i	0.990268	−	0.139173i	$-0.0444444\pi$
$390$		0			0
$391$		0			0
$392$	−0.569458	+	0.986330i	−0.569458	+	0.986330i
$393$		0			0
$394$	0.0906888	−	0.0760969i	0.0906888	−	0.0760969i
$395$		0			0
$396$	0.142963	+	0.810781i	0.142963	+	0.810781i
$397$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$397$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$398$	−3.35918			−3.35918
$399$	−0.354581	−	0.0753684i	−0.354581	−	0.0753684i
$400$	0.645419			0.645419
$401$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$401$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$409$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$410$		0			0
$411$		0			0
$412$	0.285724	−	1.62042i	0.285724	−	1.62042i
$413$		0			0
$414$	0.637446	+	0.534881i	0.637446	+	0.534881i
$415$		0			0
$416$	0.368685	+	0.134190i	0.368685	+	0.134190i
$417$		0			0
$418$	−0.524123	−	1.61308i	−0.524123	−	1.61308i
$419$	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		−0.173648	−	0.984808i	$-0.555556\pi$
$421$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$422$		0			0
$423$		0			0
$424$	0.317954	−	1.80321i	0.317954	−	1.80321i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.374607	+	0.648838i	0.374607	+	0.648838i
$430$		0			0
$431$	−0.152245	+	0.863423i	−0.152245	+	0.863423i	0.809017	+	0.587785i	$0.200000\pi$
$431$	−0.152245	+	0.863423i	−0.152245	+	0.863423i	−0.961262	+	0.275637i	$0.911111\pi$
$432$	0.532924	−	0.447176i	0.532924	−	0.447176i
$433$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.848048	+	0.529919i	$0.177778\pi$
$433$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.669131	+	0.743145i	$0.266667\pi$
$434$		0			0
$435$		0			0
$436$	−2.51157			−2.51157
$437$	−0.948445	−	0.592654i	−0.948445	−	0.592654i
$438$	−0.785359			−0.785359
$439$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$439$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$440$		0			0
$441$	0.257378	+	0.215965i	0.257378	+	0.215965i
$442$		0			0
$443$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.104528	+	0.994522i	$0.533333\pi$
$443$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.241922	+	0.970296i	$0.577778\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.28633	+	0.468185i	−1.28633	+	0.468185i
$448$	0.317130	+	0.549285i	0.317130	+	0.549285i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	0.129202	−	0.732739i	0.129202	−	0.732739i
$451$	1.47274	−	1.23577i	1.47274	−	1.23577i
$452$	−2.53877	−	2.13028i	−2.53877	−	2.13028i
$453$	−0.130100	−	0.737831i	−0.130100	−	0.737831i
$454$	−0.985028	−	0.358521i	−0.985028	−	0.358521i
$455$		0			0
$456$	−0.745485	+	0.827945i	−0.745485	+	0.827945i
$457$	−1.98054			−1.98054			−0.990268	−	0.139173i	$-0.955556\pi$
$457$	−1.98054			−1.98054			−0.990268	+	0.139173i	$0.955556\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.49861	−	1.25748i	1.49861	−	1.25748i	0.615661	−	0.788011i	$-0.288889\pi$
$461$	1.49861	−	1.25748i	1.49861	−	1.25748i	0.882948	−	0.469472i	$-0.155556\pi$
$462$	−0.106766	+	0.605498i	−0.106766	+	0.605498i
$463$		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
$467$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$467$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$468$	−0.411644	+	0.712989i	−0.411644	+	0.712989i
$469$		0			0
$470$		0			0
$471$	0.119984	+	0.100679i	0.119984	+	0.100679i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.0348995	+	0.999391i	−0.0348995	+	0.999391i
$476$		0			0
$477$	−0.507581	−	0.184744i	−0.507581	−	0.184744i
$478$	0.583315	+	3.30815i	0.583315	+	3.30815i
$479$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$479$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	1.69196	−	2.93057i	1.69196	−	2.93057i
$483$	0.202709	+	0.351102i	0.202709	+	0.351102i
$484$	−1.76356	+	0.641884i	−1.76356	+	0.641884i
$485$		0			0
$486$	−0.679717	−	1.17730i	−0.679717	−	1.17730i
$487$		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		−0.173648	−	0.984808i	$-0.555556\pi$
$491$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$492$	−2.54020	−	0.924556i	−2.54020	−	0.924556i
$493$		0			0
$494$	0.635369	−	1.57259i	0.635369	−	1.57259i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.94214	+	1.62965i	1.94214	+	1.62965i
$499$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$499$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$500$		0			0
$501$	0.661516	−	1.14578i	0.661516	−	1.14578i
$502$	−1.37217	−	2.37667i	−1.37217	−	2.37667i
$503$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$503$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$504$	−0.296593	+	0.107951i	−0.296593	+	0.107951i
$505$		0			0
$506$	−0.948445	+	1.64275i	−0.948445	+	1.64275i
$507$	−0.130100	+	0.737831i	−0.130100	+	0.737831i
$508$		0			0
$509$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$509$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$	0.280998	+	0.102275i	0.280998	+	0.102275i
$512$	1.21299			1.21299
$513$	0.663608	+	0.849379i	0.663608	+	0.849379i
$514$	2.74434			2.74434
$515$		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		0.939693	−	0.342020i	$-0.111111\pi$
$523$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$524$		0			0
$525$	0.181251	−	0.313936i	0.181251	−	0.313936i
$526$		0			0
$527$		0			0
$528$	0.370426	+	0.310824i	0.370426	+	0.310824i
$529$	0.0435487	+	0.246977i	0.0435487	+	0.246977i
$530$		0			0
$531$		0			0
$532$	0.801761	−	0.426304i	0.801761	−	0.426304i
$533$	1.92252			1.92252
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.199324	+	0.167253i	−0.199324	+	0.167253i
$538$	−0.566229	+	3.21125i	−0.566229	+	3.21125i
$539$	−0.382948	+	0.663285i	−0.382948	+	0.663285i
$540$		0			0
$541$	−1.35192	+	0.492057i	−1.35192	+	0.492057i	−0.913545	−	0.406737i	$-0.866667\pi$
$541$	−1.35192	+	0.492057i	−1.35192	+	0.492057i	−0.438371	+	0.898794i	$0.644444\pi$
$542$	−0.111246	+	0.0404903i	−0.111246	+	0.0404903i
$543$	0.0261472	+	0.0452882i	0.0261472	+	0.0452882i
$544$		0			0
$545$		0			0
$546$	−0.470994	+	0.395211i	−0.470994	+	0.395211i
$547$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$547$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$548$		0			0
$549$		0			0
$550$	1.69610			1.69610
$551$		0			0
$552$	1.24600			1.24600
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.333843	+	1.89332i	−0.333843	+	1.89332i	0.104528	+	0.994522i	$0.466667\pi$
$557$	−0.333843	+	1.89332i	−0.333843	+	1.89332i	−0.438371	+	0.898794i	$0.644444\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.0591929	−	0.102525i	−0.0591929	−	0.102525i
$563$		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
$567$	−0.0309928	−	0.175769i	−0.0309928	−	0.175769i
$568$		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			$\pi$
$572$	−1.76356	−	0.641884i	−1.76356	−	0.641884i
$573$	−0.174107	−	0.987411i	−0.174107	−	0.987411i
$574$	1.20860	+	1.01413i	1.20860	+	1.01413i
$575$	0.856733	−	0.718885i	0.856733	−	0.718885i
$576$	0.0998572	−	0.566318i	0.0998572	−	0.566318i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.848048	+	1.46886i	0.848048	+	1.46886i
$579$	−0.787377	+	0.286582i	−0.787377	+	0.286582i
$580$		0			0
$581$	−0.482665	−	0.836001i	−0.482665	−	0.836001i
$582$		0			0
$583$	0.213817	−	1.21262i	0.213817	−	1.21262i
$584$	0.704026	−	0.590748i	0.704026	−	0.590748i
$585$		0			0
$586$	0.451237	+	2.55909i	0.451237	+	2.55909i
$587$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$587$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$588$	1.07691			1.07691
$589$		0			0
$590$		0			0
$591$	−0.0491406	−	0.0178857i	−0.0491406	−	0.0178857i
$592$		0			0
$593$	0.160147	+	0.134379i	0.160147	+	0.134379i	0.719340	−	0.694658i	$-0.244444\pi$
$593$	0.160147	+	0.134379i	0.160147	+	0.134379i	−0.559193	+	0.829038i	$0.688889\pi$
$594$	1.40047	−	1.17513i	1.40047	−	1.17513i
$595$		0			0
$596$	1.71449	−	2.96958i	1.71449	−	2.96958i
$597$	0.741922	+	1.28505i	0.741922	+	1.28505i
$598$	−1.78249	+	0.648775i	−1.78249	+	0.648775i
$599$	−1.59381	+	0.580099i	−1.59381	+	0.580099i	−0.978148	−	0.207912i	$-0.933333\pi$
$599$	−1.59381	+	0.580099i	−1.59381	+	0.580099i	−0.615661	+	0.788011i	$0.711111\pi$
$600$	−0.557055	−	0.964847i	−0.557055	−	0.964847i
$601$		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
$604$	1.43767	+	1.20635i	1.43767	+	1.20635i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.0136927	+	0.392107i	−0.0136927	+	0.392107i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.374607	−	0.927184i	$-0.377778\pi$
$613$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.978148	−	0.207912i	$-0.0666667\pi$
$614$	0.102287	−	0.580099i	0.102287	−	0.580099i
$615$		0			0
$616$	−0.359747	−	0.623101i	−0.359747	−	0.623101i
$617$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$617$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$618$	−1.04692	+	0.381048i	−1.04692	+	0.381048i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	0.209330	−	1.18717i	0.209330	−	1.18717i
$622$	0.973442	−	0.816814i	0.973442	−	0.816814i
$623$		0			0
$624$	0.0839687	+	0.476210i	0.0839687	+	0.476210i
$625$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$626$	−3.09892			−3.09892
$627$	−0.501321	+	0.556774i	−0.501321	+	0.556774i
$628$	−0.392346			−0.392346
$629$		0			0
$630$		0			0
$631$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$631$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−1.62693	+	0.592153i	−1.62693	+	0.592153i
$637$	−0.719706	+	0.261952i	−0.719706	+	0.261952i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.671624	−	0.563559i	0.671624	−	0.563559i	−0.241922	−	0.970296i	$-0.577778\pi$
$641$	0.671624	−	0.563559i	0.671624	−	0.563559i	0.913545	+	0.406737i	$0.133333\pi$
$642$		0			0
$643$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$643$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$644$	−0.954305	−	0.347339i	−0.954305	−	0.347339i
$645$		0			0
$646$		0			0
$647$	0.0697990			0.0697990			0.0348995	−	0.999391i	$-0.488889\pi$
$647$	0.0697990			0.0697990			0.0348995	+	0.999391i	$0.488889\pi$
$648$	−0.515459	−	0.187612i	−0.515459	−	0.187612i
$649$		0			0
$650$	1.29929	+	1.09023i	1.29929	+	1.09023i
$651$		0			0
$652$		0			0
$653$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$653$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$654$	0.850289	+	1.47274i	0.850289	+	1.47274i
$655$		0			0
$656$	1.16600	−	0.424390i	1.16600	−	0.424390i
$657$	−0.135559	−	0.234796i	−0.135559	−	0.234796i
$658$		0			0
$659$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$659$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$660$		0			0
$661$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$661$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$662$		0			0
$663$		0			0
$664$	−2.96683			−2.96683
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.575493	+	3.26378i	0.575493	+	3.26378i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.0711131	−	0.123172i	0.0711131	−	0.123172i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−1.01287	+	0.368656i	−1.01287	+	0.368656i
$676$	−0.938371	−	1.62531i	−0.938371	−	1.62531i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.389665	+	2.20990i	−0.389665	+	2.20990i
$679$		0			0
$680$		0			0
$681$	0.0804059	+	0.456005i	0.0804059	+	0.456005i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.805298	−	0.171171i	−0.805298	−	0.171171i
$685$		0			0
$686$	−1.36178	−	0.495647i	−1.36178	−	0.495647i
$687$		0			0
$688$		0			0
$689$	0.943248	−	0.791479i	0.943248	−	0.791479i
$690$		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
$693$	−0.199452	+	0.0725946i	−0.199452	+	0.0725946i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.13914	−	0.955850i	1.13914	−	0.955850i
$699$		0			0
$700$	0.157681	+	0.894255i	0.157681	+	0.894255i
$701$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$701$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$702$	1.82818			1.82818
$703$		0			0
$704$	1.31088			1.31088
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$709$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.113181	−	0.641884i	0.113181	−	0.641884i
$717$	1.13669	−	0.953796i	1.13669	−	0.953796i
$718$	1.45310	+	1.21930i	1.45310	+	1.21930i
$719$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$719$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$	0.424206			0.424206
$722$	1.69196	+	0.118314i	1.69196	+	0.118314i
$723$	−1.49478			−1.49478
$724$	−0.123095	−	0.0448028i	−0.123095	−	0.0448028i
$725$		0			0
$726$	0.973442	+	0.816814i	0.973442	+	0.816814i
$727$	−0.370646	+	0.311009i	−0.370646	+	0.311009i	−0.809017	−	0.587785i	$-0.800000\pi$
$727$	−0.370646	+	0.311009i	−0.370646	+	0.311009i	0.438371	+	0.898794i	$0.355556\pi$
$728$	0.124939	−	0.708564i	0.124939	−	0.708564i
$729$	−0.484690	+	0.839508i	−0.484690	+	0.839508i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.997564	−	1.72783i	−0.997564	−	1.72783i	−0.559193	−	0.829038i	$-0.688889\pi$
$733$	−0.997564	−	1.72783i	−0.997564	−	1.72783i	−0.438371	−	0.898794i	$-0.644444\pi$
$734$	0.524123	−	0.907807i	0.524123	−	0.907807i
$735$		0			0
$736$	0.336136	−	0.282051i	0.336136	−	0.282051i
$737$		0			0
$738$	−0.248393	−	1.40871i	−0.248393	−	1.40871i
$739$	1.80658	+	0.657542i	1.80658	+	0.657542i	0.997564	+	0.0697565i	$0.0222222\pi$
$739$	1.80658	+	0.657542i	1.80658	+	0.657542i	0.809017	+	0.587785i	$0.200000\pi$
$740$		0			0
$741$	−0.741922	+	0.104270i	−0.741922	+	0.104270i
$742$	1.01048			1.01048
$743$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$743$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.151981	+	0.861925i	−0.151981	+	0.861925i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.83832	−	0.669092i	1.83832	−	0.669092i	0.848048	−	0.529919i	$-0.177778\pi$
$751$	1.83832	−	0.669092i	1.83832	−	0.669092i	0.990268	−	0.139173i	$-0.0444444\pi$
$752$		0			0
$753$	−0.606126	+	1.04984i	−0.606126	+	1.04984i
$754$		0			0
$755$		0			0
$756$	0.749779	+	0.629139i	0.749779	+	0.629139i
$757$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$757$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$758$		0			0
$759$	0.837909			0.837909
$760$		0			0
$761$	1.43868			1.43868			0.719340	−	0.694658i	$-0.244444\pi$
$761$	1.43868			1.43868			0.719340	+	0.694658i	$0.244444\pi$
$762$		0			0
$763$	−0.112439	−	0.637672i	−0.112439	−	0.637672i
$764$	1.92398	+	1.61441i	1.92398	+	1.61441i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.672314	−	1.16448i	−0.672314	−	1.16448i
$769$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.809017	−	0.587785i	$-0.200000\pi$
$769$	1.80658	−	0.657542i	1.80658	−	0.657542i	0.997564	−	0.0697565i	$-0.0222222\pi$
$770$		0			0
$771$	−0.606126	−	1.04984i	−0.606126	−	1.04984i
$772$	1.04946	−	1.81772i	1.04946	−	1.81772i
$773$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$773$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	3.31806			3.31806
$779$	0.594092	+	1.82843i	0.594092	+	1.82843i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.378674	+	0.317745i	−0.378674	+	0.317745i
$785$		0			0
$786$		0			0
$787$	−0.241922	−	0.419021i	−0.241922	−	0.419021i	0.719340	−	0.694658i	$-0.244444\pi$
$787$	−0.241922	−	0.419021i	−0.241922	−	0.419021i	−0.961262	+	0.275637i	$0.911111\pi$
$788$	0.123095	−	0.0448028i	0.123095	−	0.0448028i
$789$		0			0
$790$		0			0
$791$	0.427209	−	0.739947i	0.427209	−	0.739947i
$792$	−0.113277	+	0.642423i	−0.113277	+	0.642423i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−3.49280	−	1.27127i	−3.49280	−	1.27127i
$797$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$797$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$798$	−0.521413	−	0.325815i	−0.521413	−	0.325815i
$799$		0			0
$800$	−0.368685	−	0.134190i	−0.368685	−	0.134190i
$801$		0			0
$802$		0			0
$803$	0.473442	−	0.397265i	0.473442	−	0.397265i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.35351	−	0.492639i	1.35351	−	0.492639i
$808$		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
$811$	0.249824	−	1.41682i	0.249824	−	1.41682i	−0.559193	−	0.829038i	$-0.688889\pi$
$811$	0.249824	−	1.41682i	0.249824	−	1.41682i	0.809017	−	0.587785i	$-0.200000\pi$
$812$		0			0
$813$	0.0400598	+	0.0336141i	0.0400598	+	0.0336141i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−3.18762			−3.18762
$819$	−0.199452	−	0.0725946i	−0.199452	−	0.0725946i
$820$		0			0
$821$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$821$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$822$		0			0
$823$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	0.438371	+	0.898794i	$0.355556\pi$
$823$	−0.280969	+	1.59345i	−0.280969	+	1.59345i	−0.719340	+	0.694658i	$0.755556\pi$
$824$	0.651875	−	1.12908i	0.651875	−	1.12908i
$825$	−0.374607	−	0.648838i	−0.374607	−	0.648838i
$826$		0			0
$827$	−1.83832	+	0.669092i	−1.83832	+	0.669092i	−0.848048	+	0.529919i	$0.822222\pi$
$827$	−1.83832	+	0.669092i	−1.83832	+	0.669092i	−0.990268	+	0.139173i	$0.955556\pi$
$828$	0.460377	+	0.797397i	0.460377	+	0.797397i
$829$	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
$832$	1.00419	+	0.842615i	1.00419	+	0.842615i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.0654974	−	1.87560i	0.0654974	−	1.87560i
$837$		0			0
$838$	2.91203	+	1.05989i	2.91203	+	1.05989i
$839$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$839$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$840$		0			0
$841$	0.766044	−	0.642788i	0.766044	−	0.642788i
$842$		0			0
$843$	−0.0261472	+	0.0452882i	−0.0261472	+	0.0452882i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.241922	−	0.419021i	−0.241922	−	0.419021i
$848$	0.397360	−	0.688247i	0.397360	−	0.688247i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.978148	−	0.207912i	$-0.0666667\pi$
$853$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.615661	+	0.788011i	$0.288889\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$857$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$858$	0.220661	+	1.25143i	0.220661	+	1.25143i
$859$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i	0.669131	−	0.743145i	$-0.266667\pi$
$859$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i	−0.615661	+	0.788011i	$0.711111\pi$
$860$		0			0
$861$	0.121019	−	0.686331i	0.121019	−	0.686331i
$862$	−0.743520	+	1.28781i	−0.743520	+	1.28781i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	−0.397397	+	0.144641i	−0.397397	+	0.144641i
$865$		0			0
$866$	1.67959	+	2.90914i	1.67959	+	2.90914i
$867$	0.374607	−	0.648838i	0.374607	−	0.648838i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.87003	−	0.680636i	−1.87003	−	0.680636i
$873$		0			0
$874$	−1.16784	−	1.49477i	−1.16784	−	1.49477i
$875$		0			0
$876$	−0.816598	−	0.297217i	−0.816598	−	0.297217i
$877$	−0.107320	−	0.608645i	−0.107320	−	0.608645i	−0.990268	−	0.139173i	$-0.955556\pi$
$877$	−0.107320	−	0.608645i	−0.107320	−	0.608645i	0.882948	−	0.469472i	$-0.155556\pi$
$878$		0			0
$879$	0.879313	−	0.737831i	0.879313	−	0.737831i
$880$		0			0
$881$	0.615661	−	1.06636i	0.615661	−	1.06636i	−0.374607	−	0.927184i	$-0.622222\pi$
$881$	0.615661	−	1.06636i	0.615661	−	1.06636i	0.990268	−	0.139173i	$-0.0444444\pi$
$882$	0.284929	+	0.493512i	0.284929	+	0.493512i
$883$	0.704030	−	0.256246i	0.704030	−	0.256246i	0.0348995	−	0.999391i	$-0.488889\pi$
$883$	0.704030	−	0.256246i	0.704030	−	0.256246i	0.669131	+	0.743145i	$0.266667\pi$
$884$		0			0
$885$		0			0
$886$	−1.69196	+	2.93057i	−1.69196	+	2.93057i
$887$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$887$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.346634	−	0.126165i	−0.346634	−	0.126165i
$892$		0			0
$893$		0			0
$894$	−2.32175			−2.32175
$895$		0			0
$896$	0.153840	+	0.872471i	0.153840	+	0.872471i
$897$	0.641876	+	0.538598i	0.641876	+	0.538598i
$898$		0			0
$899$		0			0
$900$	0.411644	−	0.712989i	0.411644	−	0.712989i
$901$		0			0
$902$	3.06414	−	1.11525i	3.06414	−	1.11525i
$903$		0			0
$904$	−1.31298	−	2.27414i	−1.31298	−	2.27414i
$905$		0			0
$906$	0.220661	−	1.25143i	0.220661	−	1.25143i
$907$	−1.23949	+	1.04005i	−1.23949	+	1.04005i	−0.241922	+	0.970296i	$0.577778\pi$
$907$	−1.23949	+	1.04005i	−1.23949	+	1.04005i	−0.997564	+	0.0697565i	$0.977778\pi$
$908$	−0.888528	−	0.745563i	−0.888528	−	0.745563i
$909$		0			0
$910$		0			0
$911$	1.11839			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$911$	1.11839			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$912$	−0.426955	+	0.227016i	−0.426955	+	0.227016i
$913$	−1.99513			−1.99513
$914$	−3.15660	−	1.14891i	−3.15660	−	1.14891i
$915$		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
$921$	−0.244507	+	0.0889933i	−0.244507	+	0.0889933i
$922$	3.11796	−	1.13485i	3.11796	−	1.13485i
$923$		0			0
$924$	−0.340162	+	0.589177i	−0.340162	+	0.589177i
$925$		0			0
$926$		0			0
$927$	−0.294628	−	0.247222i	−0.294628	−	0.247222i
$928$		0			0
$929$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$929$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$930$		0			0
$931$	−0.471532	−	0.603534i	−0.471532	−	0.603534i
$932$		0			0
$933$	−0.527469	−	0.191983i	−0.527469	−	0.191983i
$934$	0.553524	+	3.13919i	0.553524	+	3.13919i
$935$		0			0
$936$	−0.499717	+	0.419312i	−0.499717	+	0.419312i
$937$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$937$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$938$		0			0
$939$	0.684440	+	1.18549i	0.684440	+	1.18549i
$940$		0			0
$941$	−1.83832	+	0.669092i	−1.83832	+	0.669092i	−0.848048	+	0.529919i	$0.822222\pi$
$941$	−1.83832	+	0.669092i	−1.83832	+	0.669092i	−0.990268	+	0.139173i	$0.955556\pi$
$942$	0.132828	+	0.230065i	0.132828	+	0.230065i
$943$	1.07506	−	1.86206i	1.07506	−	1.86206i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$947$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$948$		0			0
$949$	0.618034			0.618034
$950$	−0.635369	+	1.57259i	−0.635369	+	1.57259i
$951$		0			0
$952$		0			0
$953$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$953$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$954$	−0.701817	−	0.588894i	−0.701817	−	0.588894i
$955$		0			0
$956$	−0.645443	+	3.66049i	−0.645443	+	3.66049i
$957$		0			0
$958$	−1.29929	−	2.25043i	−1.29929	−	2.25043i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	2.86833	−	2.40682i	2.86833	−	2.40682i
$965$		0			0
$966$	0.119405	+	0.677180i	0.119405	+	0.677180i
$967$	−1.65940	−	0.603972i	−1.65940	−	0.603972i	−0.669131	−	0.743145i	$-0.733333\pi$
$967$	−1.65940	−	0.603972i	−1.65940	−	0.603972i	−0.990268	+	0.139173i	$0.955556\pi$
$968$	−1.48704			−1.48704
$969$		0			0
$970$		0			0
$971$	1.83832	+	0.669092i	1.83832	+	0.669092i	0.990268	+	0.139173i	$0.0444444\pi$
$971$	1.83832	+	0.669092i	1.83832	+	0.669092i	0.848048	+	0.529919i	$0.177778\pi$
$972$	−0.261206	−	1.48137i	−0.261206	−	1.48137i
$973$		0			0
$974$		0			0
$975$	0.130100	−	0.737831i	0.130100	−	0.737831i
$976$		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
$981$	−0.293534	+	0.508416i	−0.293534	+	0.508416i
$982$		0			0
$983$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$983$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$984$	−1.64079	−	1.37679i	−1.64079	−	1.37679i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.25579	−	1.39469i	1.25579	−	1.39469i
$989$		0			0
$990$		0			0
$991$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	−0.882948	−	0.469472i	$-0.844444\pi$
$991$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	0.669131	−	0.743145i	$-0.266667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.40265	+	2.42947i	1.40265	+	2.42947i
$997$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$997$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$998$		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.1429.4	✓	24
11.10	odd	2		2717.1.db.d.1429.1	yes	24
13.12	even	2		2717.1.db.d.1429.1	yes	24
19.5	even	9	inner	2717.1.db.c.1715.4	yes	24
143.142	odd	2	CM	2717.1.db.c.1429.4	✓	24
209.43	odd	18		2717.1.db.d.1715.1	yes	24
247.233	even	18		2717.1.db.d.1715.1	yes	24
2717.1715	odd	18	inner	2717.1.db.c.1715.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.1429.4	✓	24	1.1	even	1	trivial
2717.1.db.c.1429.4	✓	24	143.142	odd	2	CM
2717.1.db.c.1715.4	yes	24	19.5	even	9	inner
2717.1.db.c.1715.4	yes	24	2717.1715	odd	18	inner
2717.1.db.d.1429.1	yes	24	11.10	odd	2
2717.1.db.d.1429.1	yes	24	13.12	even	2
2717.1.db.d.1715.1	yes	24	209.43	odd	18
2717.1.db.d.1715.1	yes	24	247.233	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)

\(f(q)\)	\(=\)	\(q+(1.59381 + 0.580099i) q^{2} +(-0.130100 - 0.737831i) q^{3} +(1.43767 + 1.20635i) q^{4} +(0.220661 - 1.25143i) q^{6} +(-0.241922 + 0.419021i) q^{7} +(0.743520 + 1.28781i) q^{8} +(0.412224 - 0.150037i) q^{9} +O(q^{10})\)	\(q+(1.59381 + 0.580099i) q^{2} +(-0.130100 - 0.737831i) q^{3} +(1.43767 + 1.20635i) q^{4} +(0.220661 - 1.25143i) q^{6} +(-0.241922 + 0.419021i) q^{7} +(0.743520 + 1.28781i) q^{8} +(0.412224 - 0.150037i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.703040 - 1.21770i) q^{12} +(-0.173648 + 0.984808i) q^{13} +(-0.628651 + 0.527501i) q^{14} +(0.112076 + 0.635614i) q^{16} +0.744043 q^{18} +(-0.990268 + 0.139173i) q^{19} +(0.340641 + 0.123983i) q^{21} +(0.294524 + 1.67033i) q^{22} +(0.856733 + 0.718885i) q^{23} +(0.853457 - 0.716136i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.848048 + 1.46886i) q^{26} +(-0.538939 - 0.933469i) q^{27} +(-0.853288 + 0.310571i) q^{28} +(0.0681302 - 0.386385i) q^{32} +(0.573931 - 0.481585i) q^{33} +(0.773638 + 0.281581i) q^{36} +(-1.65903 - 0.352638i) q^{38} +0.749213 q^{39} +(-0.333843 - 1.89332i) q^{41} +(0.470994 + 0.395211i) q^{42} +(-0.325893 + 1.84823i) q^{44} +(0.948445 + 1.64275i) q^{46} +(0.454395 - 0.165386i) q^{48} +(0.382948 + 0.663285i) q^{49} +(0.848048 - 1.46886i) q^{50} +(-1.43767 + 1.20635i) q^{52} +(-0.943248 - 0.791479i) q^{53} +(-0.317461 - 1.80041i) q^{54} -0.719495 q^{56} +(0.231520 + 0.712544i) q^{57} +(-0.0368572 + 0.209028i) q^{63} +(0.655438 - 1.13525i) q^{64} +(1.19410 - 0.434618i) q^{66} +(0.418955 - 0.725651i) q^{69} +(0.499717 + 0.419312i) q^{72} +(-0.107320 - 0.608645i) q^{73} -0.749213 q^{75} +(-1.59157 - 0.994522i) q^{76} -0.483844 q^{77} +(1.19410 + 0.434618i) q^{78} +(-0.282579 + 0.237112i) q^{81} +(0.566229 - 3.21125i) q^{82} +(-0.997564 + 1.72783i) q^{83} +(0.340162 + 0.589177i) q^{84} +(-0.743520 + 1.28781i) q^{88} +(-0.370646 - 0.311009i) q^{91} +(0.364474 + 2.06703i) q^{92} -0.293951 q^{96} +(0.225575 + 1.27930i) q^{98} +(0.336048 + 0.281978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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