LMFDB - Embedded newform 2717.1.db.c.1715.3

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			1715.3
Root			$-0.719340 + 0.694658i$ of defining polynomial
Character	$\chi$	$=$	2717.1715
Dual form			2717.1.db.c.1429.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.454664 + 0.165484i) q^{2} +(-0.346450 + 1.96482i) q^{3} +(-0.586710 + 0.492308i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(-0.374607 - 0.648838i) q^{7} +(0.427209 - 0.739947i) q^{8} +(-2.80079 - 1.01940i) q^{9} +O(q^{10})$	\(q+(-0.454664 + 0.165484i) q^{2} +(-0.346450 + 1.96482i) q^{3} +(-0.586710 + 0.492308i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(-0.374607 - 0.648838i) q^{7} +(0.427209 - 0.739947i) q^{8} +(-2.80079 - 1.01940i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.764030 - 1.32334i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(0.277693 + 0.233012i) q^{14} +(0.0612094 - 0.347135i) q^{16} +1.44211 q^{18} +(-0.438371 + 0.898794i) q^{19} +(1.40463 - 0.511244i) q^{21} +(-0.0840186 + 0.476493i) q^{22} +(0.0534691 - 0.0448659i) q^{23} +(1.30585 + 1.09574i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.241922 + 0.419021i) q^{26} +(1.97571 - 3.42203i) q^{27} +(0.539213 + 0.196258i) q^{28} +(0.177984 + 1.00940i) q^{32} +(1.52836 + 1.28244i) q^{33} +(2.14511 - 0.780756i) q^{36} +(0.0505754 - 0.481193i) q^{38} +1.99513 q^{39} +(0.213817 - 1.21262i) q^{41} +(-0.554033 + 0.464889i) q^{42} +(0.132996 + 0.754260i) q^{44} +(-0.0168859 + 0.0292472i) q^{46} +(0.660852 + 0.240530i) q^{48} +(0.219340 - 0.379908i) q^{49} +(-0.241922 - 0.419021i) q^{50} +(0.586710 + 0.492308i) q^{52} +(0.856733 - 0.718885i) q^{53} +(-0.331993 + 1.88283i) q^{54} -0.640141 q^{56} +(-1.61409 - 1.17271i) q^{57} +(0.387766 + 2.19913i) q^{63} +(-0.0717168 - 0.124217i) q^{64} +(-0.907114 - 0.330162i) q^{66} +(0.0696290 + 0.120601i) q^{69} +(-1.95083 + 1.63694i) q^{72} +(0.280969 - 1.59345i) q^{73} -1.99513 q^{75} +(-0.185287 - 0.743145i) q^{76} -0.749213 q^{77} +(-0.907114 + 0.330162i) q^{78} +(3.75596 + 3.15163i) q^{81} +(0.103454 + 0.586717i) q^{82} +(0.848048 + 1.46886i) q^{83} +(-0.572421 + 0.991462i) q^{84} +(-0.427209 - 0.739947i) q^{88} +(-0.573931 + 0.481585i) q^{91} +(-0.00928301 + 0.0526466i) q^{92} -2.04494 q^{96} +(-0.0368572 + 0.209028i) q^{98} +(-2.28322 + 1.91585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.454664	+	0.165484i	−0.454664	+	0.165484i	−0.559193	−	0.829038i	$-0.688889\pi$
$2$	−0.454664	+	0.165484i	−0.454664	+	0.165484i	0.104528	+	0.994522i	$0.466667\pi$
$3$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.104528	+	0.994522i	$0.533333\pi$
$3$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.241922	+	0.970296i	$0.577778\pi$
$4$	−0.586710	+	0.492308i	−0.586710	+	0.492308i
$5$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$5$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$6$	−0.167628	−	0.950665i	−0.167628	−	0.950665i
$7$	−0.374607	−	0.648838i	−0.374607	−	0.648838i	0.615661	−	0.788011i	$-0.288889\pi$
$7$	−0.374607	−	0.648838i	−0.374607	−	0.648838i	−0.990268	+	0.139173i	$0.955556\pi$
$8$	0.427209	−	0.739947i	0.427209	−	0.739947i
$9$	−2.80079	−	1.01940i	−2.80079	−	1.01940i
$10$		0			0
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$12$	−0.764030	−	1.32334i	−0.764030	−	1.32334i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$14$	0.277693	+	0.233012i	0.277693	+	0.233012i
$15$		0			0
$16$	0.0612094	−	0.347135i	0.0612094	−	0.347135i
$17$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$17$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$18$	1.44211			1.44211
$19$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$19$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$20$		0			0
$21$	1.40463	−	0.511244i	1.40463	−	0.511244i
$22$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i
$23$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i	−0.615661	−	0.788011i	$-0.711111\pi$
$23$	0.0534691	−	0.0448659i	0.0534691	−	0.0448659i	0.669131	+	0.743145i	$0.266667\pi$
$24$	1.30585	+	1.09574i	1.30585	+	1.09574i
$25$	0.173648	+	0.984808i	0.173648	+	0.984808i
$26$	0.241922	+	0.419021i	0.241922	+	0.419021i
$27$	1.97571	−	3.42203i	1.97571	−	3.42203i
$28$	0.539213	+	0.196258i	0.539213	+	0.196258i
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	0.177984	+	1.00940i	0.177984	+	1.00940i
$33$	1.52836	+	1.28244i	1.52836	+	1.28244i
$34$		0			0
$35$		0			0
$36$	2.14511	−	0.780756i	2.14511	−	0.780756i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.0505754	−	0.481193i	0.0505754	−	0.481193i
$39$	1.99513			1.99513
$40$		0			0
$41$	0.213817	−	1.21262i	0.213817	−	1.21262i	−0.669131	−	0.743145i	$-0.733333\pi$
$41$	0.213817	−	1.21262i	0.213817	−	1.21262i	0.882948	−	0.469472i	$-0.155556\pi$
$42$	−0.554033	+	0.464889i	−0.554033	+	0.464889i
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	0.132996	+	0.754260i	0.132996	+	0.754260i
$45$		0			0
$46$	−0.0168859	+	0.0292472i	−0.0168859	+	0.0292472i
$47$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$47$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$48$	0.660852	+	0.240530i	0.660852	+	0.240530i
$49$	0.219340	−	0.379908i	0.219340	−	0.379908i
$50$	−0.241922	−	0.419021i	−0.241922	−	0.419021i
$51$		0			0
$52$	0.586710	+	0.492308i	0.586710	+	0.492308i
$53$	0.856733	−	0.718885i	0.856733	−	0.718885i	−0.104528	−	0.994522i	$-0.533333\pi$
$53$	0.856733	−	0.718885i	0.856733	−	0.718885i	0.961262	+	0.275637i	$0.0888889\pi$
$54$	−0.331993	+	1.88283i	−0.331993	+	1.88283i
$55$		0			0
$56$	−0.640141			−0.640141
$57$	−1.61409	−	1.17271i	−1.61409	−	1.17271i
$58$		0			0
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$		0			0
$61$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$61$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$62$		0			0
$63$	0.387766	+	2.19913i	0.387766	+	2.19913i
$64$	−0.0717168	−	0.124217i	−0.0717168	−	0.124217i
$65$		0			0
$66$	−0.907114	−	0.330162i	−0.907114	−	0.330162i
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$		0			0
$69$	0.0696290	+	0.120601i	0.0696290	+	0.120601i
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	−1.95083	+	1.63694i	−1.95083	+	1.63694i
$73$	0.280969	−	1.59345i	0.280969	−	1.59345i	−0.438371	−	0.898794i	$-0.644444\pi$
$73$	0.280969	−	1.59345i	0.280969	−	1.59345i	0.719340	−	0.694658i	$-0.244444\pi$
$74$		0			0
$75$	−1.99513			−1.99513
$76$	−0.185287	−	0.743145i	−0.185287	−	0.743145i
$77$	−0.749213			−0.749213
$78$	−0.907114	+	0.330162i	−0.907114	+	0.330162i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$		0			0
$81$	3.75596	+	3.15163i	3.75596	+	3.15163i
$82$	0.103454	+	0.586717i	0.103454	+	0.586717i
$83$	0.848048	+	1.46886i	0.848048	+	1.46886i	0.882948	+	0.469472i	$0.155556\pi$
$83$	0.848048	+	1.46886i	0.848048	+	1.46886i	−0.0348995	+	0.999391i	$0.511111\pi$
$84$	−0.572421	+	0.991462i	−0.572421	+	0.991462i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.427209	−	0.739947i	−0.427209	−	0.739947i
$89$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$89$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$90$		0			0
$91$	−0.573931	+	0.481585i	−0.573931	+	0.481585i
$92$	−0.00928301	+	0.0526466i	−0.00928301	+	0.0526466i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−2.04494			−2.04494
$97$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$97$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$98$	−0.0368572	+	0.209028i	−0.0368572	+	0.209028i
$99$	−2.28322	+	1.91585i	−2.28322	+	1.91585i
$100$	−0.586710	−	0.492308i	−0.586710	−	0.492308i
$101$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$101$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$102$		0			0
$103$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.0348995	−	0.999391i	$-0.488889\pi$
$103$	0.882948	−	1.52931i	0.882948	−	1.52931i	0.848048	−	0.529919i	$-0.177778\pi$
$104$	−0.802890	−	0.292228i	−0.802890	−	0.292228i
$105$		0			0
$106$	−0.270562	+	0.468627i	−0.270562	+	0.468627i
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	0.525525	+	2.98040i	0.525525	+	2.98040i
$109$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.961262	−	0.275637i	$-0.911111\pi$
$109$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.438371	−	0.898794i	$-0.644444\pi$
$110$		0			0
$111$		0			0
$112$	−0.248164	+	0.0903243i	−0.248164	+	0.0903243i
$113$	−1.43868			−1.43868			−0.719340	−	0.694658i	$-0.755556\pi$
$113$	−1.43868			−1.43868			−0.719340	+	0.694658i	$0.755556\pi$
$114$	0.927935	+	0.266081i	0.927935	+	0.266081i
$115$		0			0
$116$		0			0
$117$	−0.517565	+	2.93526i	−0.517565	+	2.93526i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$	2.30849	+	0.840223i	2.30849	+	0.840223i
$124$		0			0
$125$		0			0
$126$	−0.540225	−	0.935698i	−0.540225	−	0.935698i
$127$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$127$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$128$	−0.732008	−	0.614227i	−0.732008	−	0.614227i
$129$		0			0
$130$		0			0
$131$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$131$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$132$	−1.52806			−1.52806
$133$	0.747388	−	0.0522625i	0.747388	−	0.0522625i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$137$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$138$	−0.0516154	−	0.0433104i	−0.0516154	−	0.0433104i
$139$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$139$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$144$	−0.525306	+	0.909856i	−0.525306	+	0.909856i
$145$		0			0
$146$	0.135945	+	0.770982i	0.135945	+	0.770982i
$147$	0.670459	+	0.562582i	0.670459	+	0.562582i
$148$		0			0
$149$	0.339707	−	1.92657i	0.339707	−	1.92657i	−0.0348995	−	0.999391i	$-0.511111\pi$
$149$	0.339707	−	1.92657i	0.339707	−	1.92657i	0.374607	−	0.927184i	$-0.377778\pi$
$150$	0.907114	−	0.330162i	0.907114	−	0.330162i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	0.477784	+	0.708344i	0.477784	+	0.708344i
$153$		0			0
$154$	0.340641	−	0.123983i	0.340641	−	0.123983i
$155$		0			0
$156$	−1.17056	+	0.982217i	−1.17056	+	0.982217i
$157$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.990268	−	0.139173i	$-0.0444444\pi$
$157$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.0348995	+	0.999391i	$0.488889\pi$
$158$		0			0
$159$	1.11566	+	1.93238i	1.11566	+	1.93238i
$160$		0			0
$161$	−0.0491406	−	0.0178857i	−0.0491406	−	0.0178857i
$162$	−2.22925	−	0.811379i	−2.22925	−	0.811379i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	0.471532	+	0.816718i	0.471532	+	0.816718i
$165$		0			0
$166$	−0.628651	−	0.527501i	−0.628651	−	0.527501i
$167$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.104528	−	0.994522i	$-0.466667\pi$
$167$	1.10209	−	0.924765i	1.10209	−	0.924765i	0.997564	+	0.0697565i	$0.0222222\pi$
$168$	0.221777	−	1.25776i	0.221777	−	1.25776i
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$		0			0
$171$	2.14402	−	2.07045i	2.14402	−	2.07045i
$172$		0			0
$173$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$173$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$174$		0			0
$175$	0.573931	−	0.481585i	0.573931	−	0.481585i
$176$	−0.270023	−	0.226577i	−0.270023	−	0.226577i
$177$		0			0
$178$		0			0
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$180$		0			0
$181$	−1.80658	−	0.657542i	−1.80658	−	0.657542i	−0.997564	−	0.0697565i	$-0.977778\pi$
$181$	−1.80658	−	0.657542i	−1.80658	−	0.657542i	−0.809017	−	0.587785i	$-0.800000\pi$
$182$	0.181251	−	0.313936i	0.181251	−	0.313936i
$183$		0			0
$184$	−0.0103559	−	0.0587314i	−0.0103559	−	0.0587314i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−2.96046			−2.96046
$190$		0			0
$191$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$191$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$192$	0.268911	−	0.0978754i	0.268911	−	0.0978754i
$193$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i	−0.990268	−	0.139173i	$-0.955556\pi$
$193$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i	0.978148	+	0.207912i	$0.0666667\pi$
$194$		0			0
$195$		0			0
$196$	0.0583428	+	0.330878i	0.0583428	+	0.330878i
$197$	0.961262	+	1.66495i	0.961262	+	1.66495i	0.719340	+	0.694658i	$0.244444\pi$
$197$	0.961262	+	1.66495i	0.961262	+	1.66495i	0.241922	+	0.970296i	$0.422222\pi$
$198$	0.721057	−	1.24891i	0.721057	−	1.24891i
$199$	−0.823868	−	0.299864i	−0.823868	−	0.299864i	−0.104528	−	0.994522i	$-0.533333\pi$
$199$	−0.823868	−	0.299864i	−0.823868	−	0.299864i	−0.719340	+	0.694658i	$0.755556\pi$
$200$	0.802890	+	0.292228i	0.802890	+	0.292228i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−0.148368	+	0.841437i	−0.148368	+	0.841437i
$207$	−0.195492	+	0.0711533i	−0.195492	+	0.0711533i
$208$	−0.352491			−0.352491
$209$	0.559193	+	0.829038i	0.559193	+	0.829038i
$210$		0			0
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$	−0.148741	+	0.843553i	−0.148741	+	0.843553i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−1.68808	−	2.92384i	−1.68808	−	2.92384i
$217$		0			0
$218$	0.830713	+	0.302355i	0.830713	+	0.302355i
$219$	3.03350	+	1.10410i	3.03350	+	1.10410i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$223$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$224$	0.588260	−	0.493609i	0.588260	−	0.493609i
$225$	0.517565	−	2.93526i	0.517565	−	2.93526i
$226$	0.654116	−	0.238079i	0.654116	−	0.238079i
$227$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$228$	1.52434	−	0.106592i	1.52434	−	0.106592i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	0.259565	−	1.47207i	0.259565	−	1.47207i
$232$		0			0
$233$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$233$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$234$	−0.250420	−	1.42020i	−0.250420	−	1.42020i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.438371	−	0.759281i	0.438371	−	0.759281i	−0.559193	−	0.829038i	$-0.688889\pi$
$239$	0.438371	−	0.759281i	0.438371	−	0.759281i	0.997564	+	0.0697565i	$0.0222222\pi$
$240$		0			0
$241$	−0.294524	−	1.67033i	−0.294524	−	1.67033i	−0.669131	−	0.743145i	$-0.733333\pi$
$241$	−0.294524	−	1.67033i	−0.294524	−	1.67033i	0.374607	−	0.927184i	$-0.377778\pi$
$242$	0.370646	+	0.311009i	0.370646	+	0.311009i
$243$	−4.46666	+	3.74797i	−4.46666	+	3.74797i
$244$		0			0
$245$		0			0
$246$	−1.18863			−1.18863
$247$	0.961262	+	0.275637i	0.961262	+	0.275637i
$248$		0			0
$249$	−3.17985	+	1.15737i	−3.17985	+	1.15737i
$250$		0			0
$251$	0.473442	−	0.397265i	0.473442	−	0.397265i	−0.374607	−	0.927184i	$-0.622222\pi$
$251$	0.473442	−	0.397265i	0.473442	−	0.397265i	0.848048	+	0.529919i	$0.177778\pi$
$252$	−1.31016	−	1.09935i	−1.31016	−	1.09935i
$253$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i
$254$		0			0
$255$		0			0
$256$	0.569247	+	0.207189i	0.569247	+	0.207189i
$257$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$257$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$263$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$264$	1.60187	−	0.583032i	1.60187	−	0.583032i
$265$		0			0
$266$	−0.331162	+	0.147443i	−0.331162	+	0.147443i
$267$		0			0
$268$		0			0
$269$	−0.213817	+	1.21262i	−0.213817	+	1.21262i	0.669131	+	0.743145i	$0.266667\pi$
$269$	−0.213817	+	1.21262i	−0.213817	+	1.21262i	−0.882948	+	0.469472i	$0.844444\pi$
$270$		0			0
$271$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.913545	−	0.406737i	$-0.866667\pi$
$271$	−1.47274	−	1.23577i	−1.47274	−	1.23577i	−0.559193	−	0.829038i	$-0.688889\pi$
$272$		0			0
$273$	−0.747388	−	1.29451i	−0.747388	−	1.29451i
$274$		0			0
$275$	0.939693	+	0.342020i	0.939693	+	0.342020i
$276$	−0.100225	−	0.0364788i	−0.100225	−	0.0364788i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.47274	+	1.23577i	−1.47274	+	1.23577i	−0.559193	+	0.829038i	$0.688889\pi$
$281$	−1.47274	+	1.23577i	−1.47274	+	1.23577i	−0.913545	+	0.406737i	$0.866667\pi$
$282$		0			0
$283$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$283$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$284$		0			0
$285$		0			0
$286$	0.483844			0.483844
$287$	−0.866888	+	0.315522i	−0.866888	+	0.315522i
$288$	0.530487	−	3.00854i	0.530487	−	3.00854i
$289$	0.766044	−	0.642788i	0.766044	−	0.642788i
$290$		0			0
$291$		0			0
$292$	0.619622	+	1.07322i	0.619622	+	1.07322i
$293$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$293$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$294$	−0.397932	−	0.144836i	−0.397932	−	0.144836i
$295$		0			0
$296$		0			0
$297$	−1.97571	−	3.42203i	−1.97571	−	3.42203i
$298$	0.164365	+	0.932161i	0.164365	+	0.932161i
$299$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i
$300$	1.17056	−	0.982217i	1.17056	−	0.982217i
$301$		0			0
$302$	−0.454664	+	0.165484i	−0.454664	+	0.165484i
$303$		0			0
$304$	0.285171	+	0.207189i	0.285171	+	0.207189i
$305$		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			$\pi$
$308$	0.439571	−	0.368844i	0.439571	−	0.368844i
$309$	2.69892	+	2.26466i	2.69892	+	2.26466i
$310$		0			0
$311$	0.997564	+	1.72783i	0.997564	+	1.72783i	0.559193	+	0.829038i	$0.311111\pi$
$311$	0.997564	+	1.72783i	0.997564	+	1.72783i	0.438371	+	0.898794i	$0.355556\pi$
$312$	0.852336	−	1.47629i	0.852336	−	1.47629i
$313$	1.83832	+	0.669092i	1.83832	+	0.669092i	0.990268	+	0.139173i	$0.0444444\pi$
$313$	1.83832	+	0.669092i	1.83832	+	0.669092i	0.848048	+	0.529919i	$0.177778\pi$
$314$	−0.608460	−	0.221461i	−0.608460	−	0.221461i
$315$		0			0
$316$		0			0
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$	−0.827031	−	0.693961i	−0.827031	−	0.693961i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	0.0253023			0.0253023
$323$		0			0
$324$	−3.75523			−3.75523
$325$	0.939693	−	0.342020i	0.939693	−	0.342020i
$326$		0			0
$327$	2.79245	−	2.34314i	2.79245	−	2.34314i
$328$	−0.805928	−	0.676254i	−0.805928	−	0.676254i
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−1.22069	−	0.444295i	−1.22069	−	0.444295i
$333$		0			0
$334$	−0.348048	+	0.602837i	−0.348048	+	0.602837i
$335$		0			0
$336$	−0.0914943	−	0.518890i	−0.0914943	−	0.518890i
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	0.370646	−	0.311009i	0.370646	−	0.311009i
$339$	0.498431	−	2.82674i	0.498431	−	2.82674i
$340$		0			0
$341$		0			0
$342$	−0.632181	+	1.29616i	−0.632181	+	1.29616i
$343$	−1.07788			−1.07788
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$347$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$	−0.882948	−	1.52931i	−0.882948	−	1.52931i	−0.848048	−	0.529919i	$-0.822222\pi$
$349$	−0.882948	−	1.52931i	−0.882948	−	1.52931i	−0.0348995	−	0.999391i	$-0.511111\pi$
$350$	−0.181251	+	0.313936i	−0.181251	+	0.313936i
$351$	−3.71312	−	1.35147i	−3.71312	−	1.35147i
$352$	0.963155	+	0.350560i	0.963155	+	0.350560i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.0291794	−	0.165484i	0.0291794	−	0.165484i
$359$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	0.374607	+	0.927184i	$0.377778\pi$
$360$		0			0
$361$	−0.615661	−	0.788011i	−0.615661	−	0.788011i
$362$	0.930201			0.930201
$363$	1.87481	−	0.682374i	1.87481	−	0.682374i
$364$	0.0996426	−	0.565101i	0.0996426	−	0.565101i
$365$		0			0
$366$		0			0
$367$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$367$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$368$	−0.0123017	−	0.0213072i	−0.0123017	−	0.0213072i
$369$	−1.83500	+	3.17832i	−1.83500	+	3.17832i
$370$		0			0
$371$	−0.787377	−	0.286582i	−0.787377	−	0.286582i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	1.34602	−	0.489909i	1.34602	−	0.489909i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	−0.830713	+	0.302355i	−0.830713	+	0.302355i
$383$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$383$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$384$	1.46045	−	1.22546i	1.46045	−	1.22546i
$385$		0			0
$386$	−0.00586441	−	0.0332587i	−0.00586441	−	0.0332587i
$387$		0			0
$388$		0			0
$389$	0.196449	+	0.0715017i	0.196449	+	0.0715017i	0.438371	−	0.898794i	$-0.355556\pi$
$389$	0.196449	+	0.0715017i	0.196449	+	0.0715017i	−0.241922	+	0.970296i	$0.577778\pi$
$390$		0			0
$391$		0			0
$392$	−0.187408	−	0.324600i	−0.187408	−	0.324600i
$393$		0			0
$394$	−0.712575	−	0.597922i	−0.712575	−	0.597922i
$395$		0			0
$396$	0.396400	−	2.24810i	0.396400	−	2.24810i
$397$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$397$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$398$	0.424206			0.424206
$399$	−0.156247	+	1.48659i	−0.156247	+	1.48659i
$400$	0.352491			0.352491
$401$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$401$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$409$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	0.234858	+	1.33194i	0.234858	+	1.33194i
$413$		0			0
$414$	0.0771086	−	0.0647018i	0.0771086	−	0.0647018i
$415$		0			0
$416$	0.963155	−	0.350560i	0.963155	−	0.350560i
$417$		0			0
$418$	−0.391438	−	0.284396i	−0.391438	−	0.284396i
$419$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$419$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$420$		0			0
$421$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$421$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$422$		0			0
$423$		0			0
$424$	−0.165933	−	0.941051i	−0.165933	−	0.941051i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.997564	−	1.72783i	0.997564	−	1.72783i
$430$		0			0
$431$	0.306644	+	1.73907i	0.306644	+	1.73907i	0.615661	+	0.788011i	$0.288889\pi$
$431$	0.306644	+	1.73907i	0.306644	+	1.73907i	−0.309017	+	0.951057i	$0.600000\pi$
$432$	−1.06698	−	0.895300i	−1.06698	−	0.895300i
$433$	0.671624	−	0.563559i	0.671624	−	0.563559i	−0.241922	−	0.970296i	$-0.577778\pi$
$433$	0.671624	−	0.563559i	0.671624	−	0.563559i	0.913545	+	0.406737i	$0.133333\pi$
$434$		0			0
$435$		0			0
$436$	1.39936			1.39936
$437$	0.0168859	+	0.0677257i	0.0168859	+	0.0677257i
$438$	−1.56194			−1.56194
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	−1.00160	+	0.840445i	−1.00160	+	0.840445i
$442$		0			0
$443$	0.294524	+	1.67033i	0.294524	+	1.67033i	0.669131	+	0.743145i	$0.266667\pi$
$443$	0.294524	+	1.67033i	0.294524	+	1.67033i	−0.374607	+	0.927184i	$0.622222\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	3.66768	+	1.33492i	3.66768	+	1.33492i
$448$	−0.0537312	+	0.0930652i	−0.0537312	+	0.0930652i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	0.250420	+	1.42020i	0.250420	+	1.42020i
$451$	−0.943248	−	0.791479i	−0.943248	−	0.791479i
$452$	0.844087	−	0.708273i	0.844087	−	0.708273i
$453$	−0.346450	+	1.96482i	−0.346450	+	1.96482i
$454$	−0.735663	+	0.267759i	−0.735663	+	0.267759i
$455$		0			0
$456$	−1.55730	+	0.693353i	−1.55730	+	0.693353i
$457$	−0.876742			−0.876742			−0.438371	−	0.898794i	$-0.644444\pi$
$457$	−0.876742			−0.876742			−0.438371	+	0.898794i	$0.644444\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.160147	+	0.134379i	0.160147	+	0.134379i	0.719340	−	0.694658i	$-0.244444\pi$
$461$	0.160147	+	0.134379i	0.160147	+	0.134379i	−0.559193	+	0.829038i	$0.688889\pi$
$462$	0.125589	+	0.712251i	0.125589	+	0.712251i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$468$	−1.14139	−	1.97694i	−1.14139	−	1.97694i
$469$		0			0
$470$		0			0
$471$	−2.04534	+	1.71624i	−2.04534	+	1.71624i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.961262	−	0.275637i	−0.961262	−	0.275637i
$476$		0			0
$477$	−3.13236	+	1.14009i	−3.13236	+	1.14009i
$478$	−0.0736627	+	0.417762i	−0.0736627	+	0.417762i
$479$	−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
$482$	0.410323	+	0.710700i	0.410323	+	0.710700i
$483$	0.0521669	−	0.0903558i	0.0521669	−	0.0903558i
$484$	0.719706	+	0.261952i	0.719706	+	0.261952i
$485$		0			0
$486$	1.41060	−	2.44323i	1.41060	−	2.44323i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$491$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$492$	−1.76806	+	0.643523i	−1.76806	+	0.643523i
$493$		0			0
$494$	−0.482665	+	0.0337512i	−0.482665	+	0.0337512i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.25424	−	1.05243i	1.25424	−	1.05243i
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$		0			0
$501$	1.43518	+	2.48580i	1.43518	+	2.48580i
$502$	−0.149516	+	0.258969i	−0.149516	+	0.258969i
$503$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$503$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$504$	1.79290	+	0.652562i	1.79290	+	0.652562i
$505$		0			0
$506$	0.0168859	+	0.0292472i	0.0168859	+	0.0292472i
$507$	−0.346450	−	1.96482i	−0.346450	−	1.96482i
$508$		0			0
$509$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$509$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$510$		0			0
$511$	−1.13914	+	0.414615i	−1.13914	+	0.414615i
$512$	0.662466			0.662466
$513$	2.20961	+	3.27588i	2.20961	+	3.27588i
$514$	0.299032			0.299032
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	0.309017	+	0.951057i	$0.400000\pi$
$521$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	−0.978148	+	0.207912i	$0.933333\pi$
$522$		0			0
$523$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$523$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$524$		0			0
$525$	0.747388	+	1.29451i	0.747388	+	1.29451i
$526$		0			0
$527$		0			0
$528$	0.538731	−	0.452049i	0.538731	−	0.452049i
$529$	−0.172802	+	0.980010i	−0.172802	+	0.980010i
$530$		0			0
$531$		0			0
$532$	−0.412771	+	0.398608i	−0.412771	+	0.398608i
$533$	−1.23132			−1.23132
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.530793	−	0.445388i	−0.530793	−	0.445388i
$538$	−0.103454	−	0.586717i	−0.103454	−	0.586717i
$539$	−0.219340	−	0.379908i	−0.219340	−	0.379908i
$540$		0			0
$541$	1.86110	+	0.677383i	1.86110	+	0.677383i	0.978148	+	0.207912i	$0.0666667\pi$
$541$	1.86110	+	0.677383i	1.86110	+	0.677383i	0.882948	+	0.469472i	$0.155556\pi$
$542$	0.874103	+	0.318147i	0.874103	+	0.318147i
$543$	1.91784	−	3.32180i	1.91784	−	3.32180i
$544$		0			0
$545$		0			0
$546$	0.554033	+	0.464889i	0.554033	+	0.464889i
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$		0			0
$549$		0			0
$550$	−0.483844			−0.483844
$551$		0			0
$552$	0.118984			0.118984
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.213817	+	1.21262i	0.213817	+	1.21262i	0.882948	+	0.469472i	$0.155556\pi$
$557$	0.213817	+	1.21262i	0.213817	+	1.21262i	−0.669131	+	0.743145i	$0.733333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.465101	−	0.805578i	0.465101	−	0.805578i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.637886	−	3.61763i	0.637886	−	3.61763i
$568$		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			$\pi$
$572$	0.719706	−	0.261952i	0.719706	−	0.261952i
$573$	−0.632996	+	3.58990i	−0.632996	+	3.58990i
$574$	0.341929	−	0.286913i	0.341929	−	0.286913i
$575$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i
$576$	0.0742362	+	0.421014i	0.0742362	+	0.421014i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.241922	+	0.419021i	−0.241922	+	0.419021i
$579$	−0.130860	−	0.0476290i	−0.130860	−	0.0476290i
$580$		0			0
$581$	0.635369	−	1.10049i	0.635369	−	1.10049i
$582$		0			0
$583$	−0.194206	−	1.10140i	−0.194206	−	1.10140i
$584$	−1.05904	−	0.888639i	−1.05904	−	0.888639i
$585$		0			0
$586$	−0.128724	+	0.730030i	−0.128724	+	0.730030i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	−0.670328			−0.670328
$589$		0			0
$590$		0			0
$591$	−3.60436	+	1.31188i	−3.60436	+	1.31188i
$592$		0			0
$593$	−1.02517	+	0.860218i	−1.02517	+	0.860218i	−0.990268	−	0.139173i	$-0.955556\pi$
$593$	−1.02517	+	0.860218i	−1.02517	+	0.860218i	−0.0348995	+	0.999391i	$0.511111\pi$
$594$	1.46458	+	1.22893i	1.46458	+	1.22893i
$595$		0			0
$596$	0.749159	+	1.29758i	0.749159	+	1.29758i
$597$	0.874607	−	1.51486i	0.874607	−	1.51486i
$598$	0.0317351	+	0.0115506i	0.0317351	+	0.0115506i
$599$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$599$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$600$	−0.852336	+	1.47629i	−0.852336	+	1.47629i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	−0.586710	+	0.492308i	−0.586710	+	0.492308i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.985262	−	0.282519i	−0.985262	−	0.282519i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.10209	+	0.924765i	1.10209	+	0.924765i	0.997564	−	0.0697565i	$-0.0222222\pi$
$613$	1.10209	+	0.924765i	1.10209	+	0.924765i	0.104528	+	0.994522i	$0.466667\pi$
$614$	−0.0291794	−	0.165484i	−0.0291794	−	0.165484i
$615$		0			0
$616$	−0.320070	+	0.554378i	−0.320070	+	0.554378i
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	−1.60187	−	0.583032i	−1.60187	−	0.583032i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−0.0478931	−	0.271615i	−0.0478931	−	0.271615i
$622$	−0.739486	−	0.620502i	−0.739486	−	0.620502i
$623$		0			0
$624$	0.122121	−	0.692580i	0.122121	−	0.692580i
$625$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$626$	−0.946541			−0.946541
$627$	−1.82264	+	0.811492i	−1.82264	+	0.811492i
$628$	−1.02497			−1.02497
$629$		0			0
$630$		0			0
$631$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$631$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−1.60590	−	0.584499i	−1.60590	−	0.584499i
$637$	−0.412224	−	0.150037i	−0.412224	−	0.150037i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.978148	−	0.207912i	$-0.933333\pi$
$641$	−1.35275	−	1.13510i	−1.35275	−	1.13510i	−0.374607	−	0.927184i	$-0.622222\pi$
$642$		0			0
$643$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$643$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$644$	0.0376365	−	0.0136986i	0.0376365	−	0.0136986i
$645$		0			0
$646$		0			0
$647$	1.92252			1.92252			0.961262	−	0.275637i	$-0.0888889\pi$
$647$	1.92252			1.92252			0.961262	+	0.275637i	$0.0888889\pi$
$648$	3.93662	−	1.43281i	3.93662	−	1.43281i
$649$		0			0
$650$	−0.370646	+	0.311009i	−0.370646	+	0.311009i
$651$		0			0
$652$		0			0
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$654$	−0.881873	+	1.52745i	−0.881873	+	1.52745i
$655$		0			0
$656$	−0.407855	−	0.148447i	−0.407855	−	0.148447i
$657$	−2.41130	+	4.17650i	−2.41130	+	4.17650i
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$		0			0
$664$	1.44917			1.44917
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.191339	+	1.08514i	−0.191339	+	1.08514i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.766049	+	1.32684i	0.766049	+	1.32684i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	3.71312	+	1.35147i	3.71312	+	1.35147i
$676$	0.382948	−	0.663285i	0.382948	−	0.663285i
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$	0.241163	+	1.36770i	0.241163	+	1.36770i
$679$		0			0
$680$		0			0
$681$	−0.560568	+	3.17914i	−0.560568	+	3.17914i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.238615	+	2.27027i	−0.238615	+	2.27027i
$685$		0			0
$686$	0.490073	−	0.178372i	0.490073	−	0.178372i
$687$		0			0
$688$		0			0
$689$	−0.856733	−	0.718885i	−0.856733	−	0.718885i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$	2.09839	+	0.763750i	2.09839	+	0.763750i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.654522	+	0.549209i	0.654522	+	0.549209i
$699$		0			0
$700$	−0.0996426	+	0.565101i	−0.0996426	+	0.565101i
$701$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$701$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$702$	1.91187			1.91187
$703$		0			0
$704$	−0.143434			−0.143434
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$709$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0461891	−	0.261952i	−0.0461891	−	0.261952i
$717$	1.33998	+	1.12437i	1.33998	+	1.12437i
$718$	−0.0258707	+	0.0217081i	−0.0258707	+	0.0217081i
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$720$		0			0
$721$	−1.32303			−1.32303
$722$	0.410323	+	0.256398i	0.410323	+	0.256398i
$723$	3.38393			3.38393
$724$	1.38365	−	0.503608i	1.38365	−	0.503608i
$725$		0			0
$726$	−0.739486	+	0.620502i	−0.739486	+	0.620502i
$727$	−0.573931	−	0.481585i	−0.573931	−	0.481585i	0.309017	−	0.951057i	$-0.400000\pi$
$727$	−0.573931	−	0.481585i	−0.573931	−	0.481585i	−0.882948	+	0.469472i	$0.844444\pi$
$728$	0.111159	+	0.630416i	0.111159	+	0.630416i
$729$	−3.36508	−	5.82848i	−3.36508	−	5.82848i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.848048	−	1.46886i	0.848048	−	1.46886i	−0.0348995	−	0.999391i	$-0.511111\pi$
$733$	0.848048	−	1.46886i	0.848048	−	1.46886i	0.882948	−	0.469472i	$-0.155556\pi$
$734$	0.391438	+	0.677990i	0.391438	+	0.677990i
$735$		0			0
$736$	0.0548041	+	0.0459861i	0.0548041	+	0.0459861i
$737$		0			0
$738$	0.308348	−	1.74873i	0.308348	−	1.74873i
$739$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.848048	−	0.529919i	$-0.822222\pi$
$739$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$	−0.874607	+	1.79321i	−0.874607	+	1.79321i
$742$	0.405417			0.405417
$743$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$743$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.877839	−	4.97847i	−0.877839	−	4.97847i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.196449	+	0.0715017i	0.196449	+	0.0715017i	0.438371	−	0.898794i	$-0.355556\pi$
$751$	0.196449	+	0.0715017i	0.196449	+	0.0715017i	−0.241922	+	0.970296i	$0.577778\pi$
$752$		0			0
$753$	0.616528	+	1.06786i	0.616528	+	1.06786i
$754$		0			0
$755$		0			0
$756$	1.73693	−	1.45746i	1.73693	−	1.45746i
$757$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$757$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$758$		0			0
$759$	0.139258			0.139258
$760$		0			0
$761$	−1.98054			−1.98054			−0.990268	−	0.139173i	$-0.955556\pi$
$761$	−1.98054			−1.98054			−0.990268	+	0.139173i	$0.955556\pi$
$762$		0			0
$763$	−0.237704	+	1.34808i	−0.237704	+	1.34808i
$764$	−1.07197	+	0.899491i	−1.07197	+	0.899491i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.604304	+	1.04668i	−0.604304	+	1.04668i
$769$	−1.15707	−	0.421137i	−1.15707	−	0.421137i	−0.309017	−	0.951057i	$-0.600000\pi$
$769$	−1.15707	−	0.421137i	−1.15707	−	0.421137i	−0.848048	+	0.529919i	$0.822222\pi$
$770$		0			0
$771$	0.616528	−	1.06786i	0.616528	−	1.06786i
$772$	−0.0267294	−	0.0462966i	−0.0267294	−	0.0462966i
$773$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$773$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.101151			−0.101151
$779$	0.996161	+	0.723753i	0.996161	+	0.723753i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.118454	−	0.0993945i	−0.118454	−	0.0993945i
$785$		0			0
$786$		0			0
$787$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	−0.990268	−	0.139173i	$-0.955556\pi$
$787$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	0.615661	+	0.788011i	$0.288889\pi$
$788$	−1.38365	−	0.503608i	−1.38365	−	0.503608i
$789$		0			0
$790$		0			0
$791$	0.538939	+	0.933469i	0.538939	+	0.933469i
$792$	0.442216	+	2.50793i	0.442216	+	2.50793i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.630997	−	0.229664i	0.630997	−	0.229664i
$797$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$797$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$798$	−0.174967	−	0.701755i	−0.174967	−	0.701755i
$799$		0			0
$800$	−0.963155	+	0.350560i	−0.963155	+	0.350560i
$801$		0			0
$802$		0			0
$803$	−1.23949	−	1.04005i	−1.23949	−	1.04005i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.30849	−	0.840223i	−2.30849	−	0.840223i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	−0.343916	−	1.95045i	−0.343916	−	1.95045i	−0.309017	−	0.951057i	$-0.600000\pi$
$811$	−0.343916	−	1.95045i	−0.343916	−	1.95045i	−0.0348995	−	0.999391i	$-0.511111\pi$
$812$		0			0
$813$	2.93830	−	2.46553i	2.93830	−	2.46553i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.909329			0.909329
$819$	2.09839	−	0.763750i	2.09839	−	0.763750i
$820$		0			0
$821$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$821$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$822$		0			0
$823$	0.107320	+	0.608645i	0.107320	+	0.608645i	0.990268	+	0.139173i	$0.0444444\pi$
$823$	0.107320	+	0.608645i	0.107320	+	0.608645i	−0.882948	+	0.469472i	$0.844444\pi$
$824$	−0.754406	−	1.30667i	−0.754406	−	1.30667i
$825$	−0.997564	+	1.72783i	−0.997564	+	1.72783i
$826$		0			0
$827$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	0.241922	−	0.970296i	$-0.422222\pi$
$827$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	−0.438371	+	0.898794i	$0.644444\pi$
$828$	0.0796678	−	0.137989i	0.0796678	−	0.137989i
$829$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$829$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$830$		0			0
$831$		0			0
$832$	−0.109877	+	0.0921974i	−0.109877	+	0.0921974i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−0.736226	−	0.211109i	−0.736226	−	0.211109i
$837$		0			0
$838$	0.889458	−	0.323736i	0.889458	−	0.323736i
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$		0			0
$843$	−1.91784	−	3.32180i	−1.91784	−	3.32180i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.374607	+	0.648838i	−0.374607	+	0.648838i
$848$	−0.197110	−	0.341405i	−0.197110	−	0.341405i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.454664	+	0.165484i	−0.454664	+	0.165484i	−0.559193	−	0.829038i	$-0.688889\pi$
$853$	−0.454664	+	0.165484i	−0.454664	+	0.165484i	0.104528	+	0.994522i	$0.466667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$857$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$858$	−0.167628	+	0.950665i	−0.167628	+	0.950665i
$859$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.559193	−	0.829038i	$-0.311111\pi$
$859$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.913545	−	0.406737i	$-0.133333\pi$
$860$		0			0
$861$	−0.319609	−	1.81259i	−0.319609	−	1.81259i
$862$	−0.427209	−	0.739947i	−0.427209	−	0.739947i
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	3.80583	+	1.38521i	3.80583	+	1.38521i
$865$		0			0
$866$	−0.212103	+	0.367373i	−0.212103	+	0.367373i
$867$	0.997564	+	1.72783i	0.997564	+	1.72783i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.46695	+	0.533927i	−1.46695	+	0.533927i
$873$		0			0
$874$	−0.0188850	−	0.0279981i	−0.0188850	−	0.0279981i
$875$		0			0
$876$	−2.32334	+	0.845628i	−2.32334	+	0.845628i
$877$	0.280969	−	1.59345i	0.280969	−	1.59345i	−0.438371	−	0.898794i	$-0.644444\pi$
$877$	0.280969	−	1.59345i	0.280969	−	1.59345i	0.719340	−	0.694658i	$-0.244444\pi$
$878$		0			0
$879$	2.34158	+	1.96482i	2.34158	+	1.96482i
$880$		0			0
$881$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	−0.997564	−	0.0697565i	$-0.977778\pi$
$881$	−0.559193	−	0.968551i	−0.559193	−	0.968551i	0.438371	−	0.898794i	$-0.355556\pi$
$882$	0.316313	−	0.547870i	0.316313	−	0.547870i
$883$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.961262	+	0.275637i	$0.0888889\pi$
$883$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.913545	+	0.406737i	$0.133333\pi$
$884$		0			0
$885$		0			0
$886$	−0.410323	−	0.710700i	−0.410323	−	0.710700i
$887$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$887$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.60737	−	1.67695i	4.60737	−	1.67695i
$892$		0			0
$893$		0			0
$894$	−1.88847			−1.88847
$895$		0			0
$896$	−0.124319	+	0.705048i	−0.124319	+	0.705048i
$897$	0.106678	−	0.0895133i	0.106678	−	0.0895133i
$898$		0			0
$899$		0			0
$900$	1.14139	+	1.97694i	1.14139	+	1.97694i
$901$		0			0
$902$	0.559839	+	0.203765i	0.559839	+	0.203765i
$903$		0			0
$904$	−0.614616	+	1.06455i	−0.614616	+	1.06455i
$905$		0			0
$906$	−0.167628	−	0.950665i	−0.167628	−	0.950665i
$907$	0.473442	+	0.397265i	0.473442	+	0.397265i	0.848048	−	0.529919i	$-0.177778\pi$
$907$	0.473442	+	0.397265i	0.473442	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$908$	−0.949316	+	0.796571i	−0.949316	+	0.796571i
$909$		0			0
$910$		0			0
$911$	0.0697990			0.0697990			0.0348995	−	0.999391i	$-0.488889\pi$
$911$	0.0697990			0.0697990			0.0348995	+	0.999391i	$0.488889\pi$
$912$	−0.505886	+	0.488528i	−0.505886	+	0.488528i
$913$	1.69610			1.69610
$914$	0.398624	−	0.145087i	0.398624	−	0.145087i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	−0.651114	−	0.236986i	−0.651114	−	0.236986i
$922$	−0.0950508	−	0.0345956i	−0.0950508	−	0.0345956i
$923$		0			0
$924$	0.572421	+	0.991462i	0.572421	+	0.991462i
$925$		0			0
$926$		0			0
$927$	−4.03193	+	3.38319i	−4.03193	+	3.38319i
$928$		0			0
$929$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$929$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$930$		0			0
$931$	0.245307	+	0.363682i	0.245307	+	0.363682i
$932$		0			0
$933$	−3.74048	+	1.36142i	−3.74048	+	1.36142i
$934$	−0.157903	+	0.895514i	−0.157903	+	0.895514i
$935$		0			0
$936$	1.95083	+	1.63694i	1.95083	+	1.63694i
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$		0			0
$939$	−1.95153	+	3.38015i	−1.95153	+	3.38015i
$940$		0			0
$941$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	0.241922	−	0.970296i	$-0.422222\pi$
$941$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	−0.438371	+	0.898794i	$0.644444\pi$
$942$	0.645932	−	1.11879i	0.645932	−	1.11879i
$943$	−0.0429726	−	0.0744306i	−0.0429726	−	0.0744306i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$947$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$	−1.61803			−1.61803
$950$	0.482665	−	0.0337512i	0.482665	−	0.0337512i
$951$		0			0
$952$		0			0
$953$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$953$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$954$	1.23551	−	1.03671i	1.23551	−	1.03671i
$955$		0			0
$956$	0.116603	+	0.661291i	0.116603	+	0.661291i
$957$		0			0
$958$	0.370646	−	0.641977i	0.370646	−	0.641977i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	0.995116	+	0.835002i	0.995116	+	0.835002i
$965$		0			0
$966$	−0.00876599	+	0.0497144i	−0.00876599	+	0.0497144i
$967$	−1.35192	+	0.492057i	−1.35192	+	0.492057i	−0.913545	−	0.406737i	$-0.866667\pi$
$967$	−1.35192	+	0.492057i	−1.35192	+	0.492057i	−0.438371	+	0.898794i	$0.644444\pi$
$968$	−0.854417			−0.854417
$969$		0			0
$970$		0			0
$971$	0.196449	−	0.0715017i	0.196449	−	0.0715017i	−0.241922	−	0.970296i	$-0.577778\pi$
$971$	0.196449	−	0.0715017i	0.196449	−	0.0715017i	0.438371	+	0.898794i	$0.355556\pi$
$972$	0.775476	−	4.39794i	0.775476	−	4.39794i
$973$		0			0
$974$		0			0
$975$	0.346450	+	1.96482i	0.346450	+	1.96482i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	2.72286	+	4.71612i	2.72286	+	4.71612i
$982$		0			0
$983$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$983$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$984$	1.60793	−	1.34921i	1.60793	−	1.34921i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.699680	+	0.311518i	−0.699680	+	0.311518i
$989$		0			0
$990$		0			0
$991$	0.194206	−	1.10140i	0.194206	−	1.10140i	−0.719340	−	0.694658i	$-0.755556\pi$
$991$	0.194206	−	1.10140i	0.194206	−	1.10140i	0.913545	−	0.406737i	$-0.133333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.29587	−	2.24451i	1.29587	−	2.24451i
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.c.1715.3	yes	24
11.10	odd	2		2717.1.db.d.1715.2	yes	24
13.12	even	2		2717.1.db.d.1715.2	yes	24
19.4	even	9	inner	2717.1.db.c.1429.3	✓	24
143.142	odd	2	CM	2717.1.db.c.1715.3	yes	24
209.175	odd	18		2717.1.db.d.1429.2	yes	24
247.194	even	18		2717.1.db.d.1429.2	yes	24
2717.1429	odd	18	inner	2717.1.db.c.1429.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.1429.3	✓	24	19.4	even	9	inner
2717.1.db.c.1429.3	✓	24	2717.1429	odd	18	inner
2717.1.db.c.1715.3	yes	24	1.1	even	1	trivial
2717.1.db.c.1715.3	yes	24	143.142	odd	2	CM
2717.1.db.d.1429.2	yes	24	209.175	odd	18
2717.1.db.d.1429.2	yes	24	247.194	even	18
2717.1.db.d.1715.2	yes	24	11.10	odd	2
2717.1.db.d.1715.2	yes	24	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.454664 + 0.165484i) q^{2} +(-0.346450 + 1.96482i) q^{3} +(-0.586710 + 0.492308i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(-0.374607 - 0.648838i) q^{7} +(0.427209 - 0.739947i) q^{8} +(-2.80079 - 1.01940i) q^{9} +O(q^{10})\)	\(q+(-0.454664 + 0.165484i) q^{2} +(-0.346450 + 1.96482i) q^{3} +(-0.586710 + 0.492308i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(-0.374607 - 0.648838i) q^{7} +(0.427209 - 0.739947i) q^{8} +(-2.80079 - 1.01940i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.764030 - 1.32334i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(0.277693 + 0.233012i) q^{14} +(0.0612094 - 0.347135i) q^{16} +1.44211 q^{18} +(-0.438371 + 0.898794i) q^{19} +(1.40463 - 0.511244i) q^{21} +(-0.0840186 + 0.476493i) q^{22} +(0.0534691 - 0.0448659i) q^{23} +(1.30585 + 1.09574i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.241922 + 0.419021i) q^{26} +(1.97571 - 3.42203i) q^{27} +(0.539213 + 0.196258i) q^{28} +(0.177984 + 1.00940i) q^{32} +(1.52836 + 1.28244i) q^{33} +(2.14511 - 0.780756i) q^{36} +(0.0505754 - 0.481193i) q^{38} +1.99513 q^{39} +(0.213817 - 1.21262i) q^{41} +(-0.554033 + 0.464889i) q^{42} +(0.132996 + 0.754260i) q^{44} +(-0.0168859 + 0.0292472i) q^{46} +(0.660852 + 0.240530i) q^{48} +(0.219340 - 0.379908i) q^{49} +(-0.241922 - 0.419021i) q^{50} +(0.586710 + 0.492308i) q^{52} +(0.856733 - 0.718885i) q^{53} +(-0.331993 + 1.88283i) q^{54} -0.640141 q^{56} +(-1.61409 - 1.17271i) q^{57} +(0.387766 + 2.19913i) q^{63} +(-0.0717168 - 0.124217i) q^{64} +(-0.907114 - 0.330162i) q^{66} +(0.0696290 + 0.120601i) q^{69} +(-1.95083 + 1.63694i) q^{72} +(0.280969 - 1.59345i) q^{73} -1.99513 q^{75} +(-0.185287 - 0.743145i) q^{76} -0.749213 q^{77} +(-0.907114 + 0.330162i) q^{78} +(3.75596 + 3.15163i) q^{81} +(0.103454 + 0.586717i) q^{82} +(0.848048 + 1.46886i) q^{83} +(-0.572421 + 0.991462i) q^{84} +(-0.427209 - 0.739947i) q^{88} +(-0.573931 + 0.481585i) q^{91} +(-0.00928301 + 0.0526466i) q^{92} -2.04494 q^{96} +(-0.0368572 + 0.209028i) q^{98} +(-2.28322 + 1.91585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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