LMFDB - Embedded newform 2717.1.db.c.2001.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2717.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.35595963932$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{45})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 $ x^24 - x^21 + x^15 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{45}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{45} - \cdots)$

Embedding invariants

Embedding label			2001.2
Root			$0.559193 + 0.829038i$ of defining polynomial
Character	$\chi$	$=$	2717.2001
Dual form			2717.1.db.c.2144.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.671624 + 0.563559i) q^{2} +(1.35192 + 0.492057i) q^{3} +(-0.0401688 + 0.227809i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(-0.882948 + 1.52931i) q^{7} +(-0.539776 - 0.934920i) q^{8} +(0.819514 + 0.687654i) q^{9} +O(q^{10})$	\(q+(-0.671624 + 0.563559i) q^{2} +(1.35192 + 0.492057i) q^{3} +(-0.0401688 + 0.227809i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(-0.882948 + 1.52931i) q^{7} +(-0.539776 - 0.934920i) q^{8} +(0.819514 + 0.687654i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.166400 + 0.288213i) q^{12} +(0.939693 - 0.342020i) q^{13} +(-0.268848 - 1.52471i) q^{14} +(0.672037 + 0.244601i) q^{16} -0.937938 q^{18} +(-0.961262 - 0.275637i) q^{19} +(-1.94618 + 1.63304i) q^{21} +(-0.823868 - 0.299864i) q^{22} +(-0.130100 + 0.737831i) q^{23} +(-0.269698 - 1.52954i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.438371 + 0.759281i) q^{26} +(0.0502092 + 0.0869649i) q^{27} +(-0.312923 - 0.262574i) q^{28} +(0.425245 - 0.154776i) q^{32} +(0.249824 + 1.41682i) q^{33} +(-0.189572 + 0.159070i) q^{36} +(0.800944 - 0.356603i) q^{38} +1.43868 q^{39} +(1.59381 + 0.580099i) q^{41} +(0.386786 - 2.19357i) q^{42} +(-0.217372 + 0.0791171i) q^{44} +(-0.328433 - 0.568863i) q^{46} +(0.788180 + 0.661361i) q^{48} +(-1.05919 - 1.83458i) q^{49} +(0.438371 - 0.759281i) q^{50} +(0.0401688 + 0.227809i) q^{52} +(-0.0840186 + 0.476493i) q^{53} +(-0.0827315 - 0.0301118i) q^{54} +1.90638 q^{56} +(-1.16392 - 0.845635i) q^{57} +(-1.77522 + 0.646128i) q^{63} +(-0.555962 + 0.962955i) q^{64} +(-0.966251 - 0.810781i) q^{66} +(-0.538939 + 0.933469i) q^{69} +(0.200547 - 1.13736i) q^{72} +(-1.52045 - 0.553400i) q^{73} -1.43868 q^{75} +(0.101405 - 0.207912i) q^{76} -1.76590 q^{77} +(-0.966251 + 0.810781i) q^{78} +(-0.160682 - 0.911271i) q^{81} +(-1.39736 + 0.508597i) q^{82} +(0.990268 - 1.71519i) q^{83} +(-0.293845 - 0.508954i) q^{84} +(0.539776 - 0.934920i) q^{88} +(-0.306644 + 1.73907i) q^{91} +(-0.162858 - 0.0592756i) q^{92} +0.651054 q^{96} +(1.74527 + 0.635227i) q^{98} +(-0.185769 + 1.05355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * q^78 + 6 * q^81 + 3 * q^82 - 12 * q^84 - 3 * q^88 - 6 * q^91 - 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	−0.913545	−	0.406737i	$-0.866667\pi$
$2$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	0.241922	+	0.970296i	$0.422222\pi$
$3$	1.35192	+	0.492057i	1.35192	+	0.492057i	0.913545	−	0.406737i	$-0.133333\pi$
$3$	1.35192	+	0.492057i	1.35192	+	0.492057i	0.438371	+	0.898794i	$0.355556\pi$
$4$	−0.0401688	+	0.227809i	−0.0401688	+	0.227809i
$5$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$5$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$6$	−1.18528	+	0.431408i	−1.18528	+	0.431408i
$7$	−0.882948	+	1.52931i	−0.882948	+	1.52931i	−0.0348995	+	0.999391i	$0.511111\pi$
$7$	−0.882948	+	1.52931i	−0.882948	+	1.52931i	−0.848048	+	0.529919i	$0.822222\pi$
$8$	−0.539776	−	0.934920i	−0.539776	−	0.934920i
$9$	0.819514	+	0.687654i	0.819514	+	0.687654i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	−0.166400	+	0.288213i	−0.166400	+	0.288213i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$13$	0.939693	−	0.342020i	0.939693	−	0.342020i
$14$	−0.268848	−	1.52471i	−0.268848	−	1.52471i
$15$		0			0
$16$	0.672037	+	0.244601i	0.672037	+	0.244601i
$17$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$17$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$18$	−0.937938			−0.937938
$19$	−0.961262	−	0.275637i	−0.961262	−	0.275637i
$19$	−0.961262	−	0.275637i	−0.961262	−	0.275637i
$20$		0			0
$21$	−1.94618	+	1.63304i	−1.94618	+	1.63304i
$22$	−0.823868	−	0.299864i	−0.823868	−	0.299864i
$23$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	0.848048	+	0.529919i	$0.177778\pi$
$23$	−0.130100	+	0.737831i	−0.130100	+	0.737831i	−0.978148	+	0.207912i	$0.933333\pi$
$24$	−0.269698	−	1.52954i	−0.269698	−	1.52954i
$25$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$26$	−0.438371	+	0.759281i	−0.438371	+	0.759281i
$27$	0.0502092	+	0.0869649i	0.0502092	+	0.0869649i
$28$	−0.312923	−	0.262574i	−0.312923	−	0.262574i
$29$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$29$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.425245	−	0.154776i	0.425245	−	0.154776i
$33$	0.249824	+	1.41682i	0.249824	+	1.41682i
$34$		0			0
$35$		0			0
$36$	−0.189572	+	0.159070i	−0.189572	+	0.159070i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.800944	−	0.356603i	0.800944	−	0.356603i
$39$	1.43868			1.43868
$40$		0			0
$41$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.978148	−	0.207912i	$-0.0666667\pi$
$41$	1.59381	+	0.580099i	1.59381	+	0.580099i	0.615661	+	0.788011i	$0.288889\pi$
$42$	0.386786	−	2.19357i	0.386786	−	2.19357i
$43$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$43$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$44$	−0.217372	+	0.0791171i	−0.217372	+	0.0791171i
$45$		0			0
$46$	−0.328433	−	0.568863i	−0.328433	−	0.568863i
$47$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$47$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$48$	0.788180	+	0.661361i	0.788180	+	0.661361i
$49$	−1.05919	−	1.83458i	−1.05919	−	1.83458i
$50$	0.438371	−	0.759281i	0.438371	−	0.759281i
$51$		0			0
$52$	0.0401688	+	0.227809i	0.0401688	+	0.227809i
$53$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	0.913545	+	0.406737i	$0.133333\pi$
$53$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	−0.997564	+	0.0697565i	$0.977778\pi$
$54$	−0.0827315	−	0.0301118i	−0.0827315	−	0.0301118i
$55$		0			0
$56$	1.90638			1.90638
$57$	−1.16392	−	0.845635i	−1.16392	−	0.845635i
$58$		0			0
$59$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$59$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$60$		0			0
$61$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$61$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$62$		0			0
$63$	−1.77522	+	0.646128i	−1.77522	+	0.646128i
$64$	−0.555962	+	0.962955i	−0.555962	+	0.962955i
$65$		0			0
$66$	−0.966251	−	0.810781i	−0.966251	−	0.810781i
$67$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$67$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$68$		0			0
$69$	−0.538939	+	0.933469i	−0.538939	+	0.933469i
$70$		0			0
$71$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$71$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$72$	0.200547	−	1.13736i	0.200547	−	1.13736i
$73$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.559193	−	0.829038i	$-0.688889\pi$
$73$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.961262	+	0.275637i	$0.911111\pi$
$74$		0			0
$75$	−1.43868			−1.43868
$76$	0.101405	−	0.207912i	0.101405	−	0.207912i
$77$	−1.76590			−1.76590
$78$	−0.966251	+	0.810781i	−0.966251	+	0.810781i
$79$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$79$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$80$		0			0
$81$	−0.160682	−	0.911271i	−0.160682	−	0.911271i
$82$	−1.39736	+	0.508597i	−1.39736	+	0.508597i
$83$	0.990268	−	1.71519i	0.990268	−	1.71519i	0.374607	−	0.927184i	$-0.377778\pi$
$83$	0.990268	−	1.71519i	0.990268	−	1.71519i	0.615661	−	0.788011i	$-0.288889\pi$
$84$	−0.293845	−	0.508954i	−0.293845	−	0.508954i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.539776	−	0.934920i	0.539776	−	0.934920i
$89$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$89$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$90$		0			0
$91$	−0.306644	+	1.73907i	−0.306644	+	1.73907i
$92$	−0.162858	−	0.0592756i	−0.162858	−	0.0592756i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.651054			0.651054
$97$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$97$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$98$	1.74527	+	0.635227i	1.74527	+	0.635227i
$99$	−0.185769	+	1.05355i	−0.185769	+	1.05355i
$100$	−0.0401688	−	0.227809i	−0.0401688	−	0.227809i
$101$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$101$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$102$		0			0
$103$	0.615661	+	1.06636i	0.615661	+	1.06636i	0.990268	+	0.139173i	$0.0444444\pi$
$103$	0.615661	+	1.06636i	0.615661	+	1.06636i	−0.374607	+	0.927184i	$0.622222\pi$
$104$	−0.826986	−	0.693923i	−0.826986	−	0.693923i
$105$		0			0
$106$	−0.212103	−	0.367373i	−0.212103	−	0.367373i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−0.0218282	+	0.00794481i	−0.0218282	+	0.00794481i
$109$	0.0363024	+	0.205881i	0.0363024	+	0.205881i	0.997564	−	0.0697565i	$-0.0222222\pi$
$109$	0.0363024	+	0.205881i	0.0363024	+	0.205881i	−0.961262	+	0.275637i	$0.911111\pi$
$110$		0			0
$111$		0			0
$112$	−0.967445	+	0.811783i	−0.967445	+	0.811783i
$113$	1.11839			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$113$	1.11839			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$114$	1.25828	−	0.0879874i	1.25828	−	0.0879874i
$115$		0			0
$116$		0			0
$117$	1.00528	+	0.365893i	1.00528	+	0.365893i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	1.86925	+	1.56849i	1.86925	+	1.56849i
$124$		0			0
$125$		0			0
$126$	0.828150	−	1.43440i	0.828150	−	1.43440i
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	−0.0907025	−	0.514400i	−0.0907025	−	0.514400i
$129$		0			0
$130$		0			0
$131$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$131$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$132$	−0.332800			−0.332800
$133$	1.27028	−	1.22669i	1.27028	−	1.22669i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$137$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$138$	−0.164101	−	0.930664i	−0.164101	−	0.930664i
$139$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$139$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.766044	+	0.642788i	0.766044	+	0.642788i
$144$	0.382542	+	0.662583i	0.382542	+	0.662583i
$145$		0			0
$146$	1.33305	−	0.485189i	1.33305	−	0.485189i
$147$	−0.529224	−	3.00138i	−0.529224	−	3.00138i
$148$		0			0
$149$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.882948	−	0.469472i	$-0.155556\pi$
$149$	1.25755	+	0.457712i	1.25755	+	0.457712i	0.374607	+	0.927184i	$0.377778\pi$
$150$	0.966251	−	0.810781i	0.966251	−	0.810781i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	0.261167	+	1.04749i	0.261167	+	1.04749i
$153$		0			0
$154$	1.18602	−	0.995186i	1.18602	−	0.995186i
$155$		0			0
$156$	−0.0577900	+	0.327744i	−0.0577900	+	0.327744i
$157$	−0.339707	−	1.92657i	−0.339707	−	1.92657i	−0.374607	−	0.927184i	$-0.622222\pi$
$157$	−0.339707	−	1.92657i	−0.339707	−	1.92657i	0.0348995	−	0.999391i	$-0.488889\pi$
$158$		0			0
$159$	−0.348048	+	0.602837i	−0.348048	+	0.602837i
$160$		0			0
$161$	−1.01350	−	0.850429i	−1.01350	−	0.850429i
$162$	0.621473	+	0.521478i	0.621473	+	0.521478i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−0.196173	+	0.339782i	−0.196173	+	0.339782i
$165$		0			0
$166$	0.301526	+	1.71004i	0.301526	+	1.71004i
$167$	−0.194206	+	1.10140i	−0.194206	+	1.10140i	0.719340	+	0.694658i	$0.244444\pi$
$167$	−0.194206	+	1.10140i	−0.194206	+	1.10140i	−0.913545	+	0.406737i	$0.866667\pi$
$168$	2.57726	+	0.938047i	2.57726	+	0.938047i
$169$	0.766044	−	0.642788i	0.766044	−	0.642788i
$170$		0			0
$171$	−0.598224	−	0.886904i	−0.598224	−	0.886904i
$172$		0			0
$173$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$173$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$174$		0			0
$175$	0.306644	−	1.73907i	0.306644	−	1.73907i
$176$	0.124187	+	0.704302i	0.124187	+	0.704302i
$177$		0			0
$178$		0			0
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$180$		0			0
$181$	−1.52836	−	1.28244i	−1.52836	−	1.28244i	−0.809017	−	0.587785i	$-0.800000\pi$
$181$	−1.52836	−	1.28244i	−1.52836	−	1.28244i	−0.719340	−	0.694658i	$-0.755556\pi$
$182$	−0.774117	−	1.34081i	−0.774117	−	1.34081i
$183$		0			0
$184$	0.760038	−	0.276631i	0.760038	−	0.276631i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.177328			−0.177328
$190$		0			0
$191$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$191$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$192$	−1.22544	+	1.02827i	−1.22544	+	1.02827i
$193$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.0348995	−	0.999391i	$-0.511111\pi$
$193$	−0.704030	−	0.256246i	−0.704030	−	0.256246i	−0.669131	+	0.743145i	$0.733333\pi$
$194$		0			0
$195$		0			0
$196$	0.460479	−	0.167601i	0.460479	−	0.167601i
$197$	−0.997564	+	1.72783i	−0.997564	+	1.72783i	−0.438371	+	0.898794i	$0.644444\pi$
$197$	−0.997564	+	1.72783i	−0.997564	+	1.72783i	−0.559193	+	0.829038i	$0.688889\pi$
$198$	−0.468969	−	0.812278i	−0.468969	−	0.812278i
$199$	1.47274	+	1.23577i	1.47274	+	1.23577i	0.913545	+	0.406737i	$0.133333\pi$
$199$	1.47274	+	1.23577i	1.47274	+	1.23577i	0.559193	+	0.829038i	$0.311111\pi$
$200$	0.826986	+	0.693923i	0.826986	+	0.693923i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−1.01445	−	0.369229i	−1.01445	−	0.369229i
$207$	−0.613990	+	0.515199i	−0.613990	+	0.515199i
$208$	0.715167			0.715167
$209$	−0.241922	−	0.970296i	−0.241922	−	0.970296i
$210$		0			0
$211$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$211$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$212$	−0.105174	−	0.0382803i	−0.105174	−	0.0382803i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	0.0542035	−	0.0938832i	0.0542035	−	0.0938832i
$217$		0			0
$218$	−0.140408	−	0.117816i	−0.140408	−	0.117816i
$219$	−1.78322	−	1.49630i	−1.78322	−	1.49630i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$223$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$224$	−0.138768	+	0.786991i	−0.138768	+	0.786991i
$225$	−1.00528	−	0.365893i	−1.00528	−	0.365893i
$226$	−0.751134	+	0.630276i	−0.751134	+	0.630276i
$227$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$228$	0.239396	−	0.231182i	0.239396	−	0.231182i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	−2.38734	−	0.868922i	−2.38734	−	0.868922i
$232$		0			0
$233$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$233$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$234$	−0.881373	+	0.320794i	−0.881373	+	0.320794i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.961262	+	1.66495i	0.961262	+	1.66495i	0.719340	+	0.694658i	$0.244444\pi$
$239$	0.961262	+	1.66495i	0.961262	+	1.66495i	0.241922	+	0.970296i	$0.422222\pi$
$240$		0			0
$241$	1.86110	−	0.677383i	1.86110	−	0.677383i	0.882948	−	0.469472i	$-0.155556\pi$
$241$	1.86110	−	0.677383i	1.86110	−	0.677383i	0.978148	−	0.207912i	$-0.0666667\pi$
$242$	−0.152245	−	0.863423i	−0.152245	−	0.863423i
$243$	0.248607	−	1.40992i	0.248607	−	1.40992i
$244$		0			0
$245$		0			0
$246$	−2.13937			−2.13937
$247$	−0.997564	+	0.0697565i	−0.997564	+	0.0697565i
$248$		0			0
$249$	2.18273	−	1.83153i	2.18273	−	1.83153i
$250$		0			0
$251$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$251$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$252$	−0.0758850	−	0.430365i	−0.0758850	−	0.430365i
$253$	−0.704030	+	0.256246i	−0.704030	+	0.256246i
$254$		0			0
$255$		0			0
$256$	−0.500971	−	0.420364i	−0.500971	−	0.420364i
$257$	0.473442	+	0.397265i	0.473442	+	0.397265i	0.848048	−	0.529919i	$-0.177778\pi$
$257$	0.473442	+	0.397265i	0.473442	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$263$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$264$	1.18977	−	0.998333i	1.18977	−	0.998333i
$265$		0			0
$266$	−0.161835	+	1.53975i	−0.161835	+	1.53975i
$267$		0			0
$268$		0			0
$269$	−1.59381	−	0.580099i	−1.59381	−	0.580099i	−0.615661	−	0.788011i	$-0.711111\pi$
$269$	−1.59381	−	0.580099i	−1.59381	−	0.580099i	−0.978148	+	0.207912i	$0.933333\pi$
$270$		0			0
$271$	0.346450	+	1.96482i	0.346450	+	1.96482i	0.241922	+	0.970296i	$0.422222\pi$
$271$	0.346450	+	1.96482i	0.346450	+	1.96482i	0.104528	+	0.994522i	$0.466667\pi$
$272$		0			0
$273$	−1.27028	+	2.20019i	−1.27028	+	2.20019i
$274$		0			0
$275$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$276$	−0.191004	−	0.160271i	−0.191004	−	0.160271i
$277$		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
$281$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.104528	−	0.994522i	$-0.466667\pi$
$281$	0.346450	−	1.96482i	0.346450	−	1.96482i	0.241922	−	0.970296i	$-0.422222\pi$
$282$		0			0
$283$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$283$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$284$		0			0
$285$		0			0
$286$	−0.876742			−0.876742
$287$	−2.29440	+	1.92523i	−2.29440	+	1.92523i
$288$	0.454926	+	0.165580i	0.454926	+	0.165580i
$289$	0.173648	−	0.984808i	0.173648	−	0.984808i
$290$		0			0
$291$		0			0
$292$	0.187144	−	0.324143i	0.187144	−	0.324143i
$293$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$293$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$294$	2.04689	+	1.71755i	2.04689	+	1.71755i
$295$		0			0
$296$		0			0
$297$	−0.0502092	+	0.0869649i	−0.0502092	+	0.0869649i
$298$	−1.10255	+	0.401296i	−1.10255	+	0.401296i
$299$	0.130100	+	0.737831i	0.130100	+	0.737831i
$300$	0.0577900	−	0.327744i	0.0577900	−	0.327744i
$301$		0			0
$302$	−0.671624	+	0.563559i	−0.671624	+	0.563559i
$303$		0			0
$304$	−0.578582	−	0.420364i	−0.578582	−	0.420364i
$305$		0			0
$306$		0			0
$307$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$308$	0.0709339	−	0.402286i	0.0709339	−	0.402286i
$309$	0.307614	+	1.74457i	0.307614	+	1.74457i
$310$		0			0
$311$	0.719340	−	1.24593i	0.719340	−	1.24593i	−0.241922	−	0.970296i	$-0.577778\pi$
$311$	0.719340	−	1.24593i	0.719340	−	1.24593i	0.961262	−	0.275637i	$-0.0888889\pi$
$312$	−0.776565	−	1.34505i	−0.776565	−	1.34505i
$313$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.990268	−	0.139173i	$-0.0444444\pi$
$313$	1.02517	+	0.860218i	1.02517	+	0.860218i	0.0348995	+	0.999391i	$0.488889\pi$
$314$	1.31389	+	1.10249i	1.31389	+	1.10249i
$315$		0			0
$316$		0			0
$317$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$317$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$318$	−0.105977	−	0.601025i	−0.105977	−	0.601025i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	1.15996			1.15996
$323$		0			0
$324$	0.214050			0.214050
$325$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$326$		0			0
$327$	−0.0522275	+	0.296197i	−0.0522275	+	0.296197i
$328$	−0.317954	−	1.80321i	−0.317954	−	1.80321i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	0.350958	+	0.294489i	0.350958	+	0.294489i
$333$		0			0
$334$	−0.490268	−	0.849169i	−0.490268	−	0.849169i
$335$		0			0
$336$	−1.70735	+	0.621424i	−1.70735	+	0.621424i
$337$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$337$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$338$	−0.152245	+	0.863423i	−0.152245	+	0.863423i
$339$	1.51196	+	0.550310i	1.51196	+	0.550310i
$340$		0			0
$341$		0			0
$342$	0.901604	+	0.258531i	0.901604	+	0.258531i
$343$	1.97495			1.97495
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$347$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$348$		0			0
$349$	−0.615661	+	1.06636i	−0.615661	+	1.06636i	0.374607	+	0.927184i	$0.377778\pi$
$349$	−0.615661	+	1.06636i	−0.615661	+	1.06636i	−0.990268	+	0.139173i	$0.955556\pi$
$350$	0.774117	+	1.34081i	0.774117	+	1.34081i
$351$	0.0769249	+	0.0645477i	0.0769249	+	0.0645477i
$352$	0.346663	+	0.290885i	0.346663	+	0.290885i
$353$		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
$358$	−1.54837	−	0.563559i	−1.54837	−	0.563559i
$359$	0.573931	−	0.481585i	0.573931	−	0.481585i	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	0.573931	−	0.481585i	0.573931	−	0.481585i	0.882948	+	0.469472i	$0.155556\pi$
$360$		0			0
$361$	0.848048	+	0.529919i	0.848048	+	0.529919i
$362$	1.74921			1.74921
$363$	−1.10209	+	0.924765i	−1.10209	+	0.924765i
$364$	−0.383857	−	0.139713i	−0.383857	−	0.139713i
$365$		0			0
$366$		0			0
$367$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.559193	−	0.829038i	$-0.311111\pi$
$367$	1.52045	−	0.553400i	1.52045	−	0.553400i	0.961262	+	0.275637i	$0.0888889\pi$
$368$	−0.267906	+	0.464027i	−0.267906	+	0.464027i
$369$	0.907241	+	1.57139i	0.907241	+	1.57139i
$370$		0			0
$371$	−0.654522	−	0.549209i	−0.654522	−	0.549209i
$372$		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
$378$	0.119098	−	0.0999350i	0.119098	−	0.0999350i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	0.140408	−	0.117816i	0.140408	−	0.117816i
$383$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$383$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$384$	0.130492	−	0.740056i	0.130492	−	0.740056i
$385$		0			0
$386$	0.617253	−	0.224662i	0.617253	−	0.224662i
$387$		0			0
$388$		0			0
$389$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.961262	+	0.275637i	$0.0888889\pi$
$389$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.438371	+	0.898794i	$0.355556\pi$
$390$		0			0
$391$		0			0
$392$	−1.14345	+	1.98052i	−1.14345	+	1.98052i
$393$		0			0
$394$	−0.303748	−	1.72264i	−0.303748	−	1.72264i
$395$		0			0
$396$	−0.232545	−	0.0846394i	−0.232545	−	0.0846394i
$397$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$397$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$398$	−1.68556			−1.68556
$399$	2.32091	−	1.03334i	2.32091	−	1.03334i
$400$	−0.715167			−0.715167
$401$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$401$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$409$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−0.267656	+	0.0974187i	−0.267656	+	0.0974187i
$413$		0			0
$414$	0.122025	−	0.692040i	0.122025	−	0.692040i
$415$		0			0
$416$	0.346663	−	0.290885i	0.346663	−	0.290885i
$417$		0			0
$418$	0.709299	+	0.515336i	0.709299	+	0.515336i
$419$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$419$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$420$		0			0
$421$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$421$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$422$		0			0
$423$		0			0
$424$	0.490834	−	0.178649i	0.490834	−	0.178649i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.719340	+	1.24593i	0.719340	+	1.24593i
$430$		0			0
$431$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.848048	−	0.529919i	$-0.822222\pi$
$431$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.309017	+	0.951057i	$0.600000\pi$
$432$	0.0124707	+	0.0707248i	0.0124707	+	0.0707248i
$433$	0.333843	−	1.89332i	0.333843	−	1.89332i	−0.104528	−	0.994522i	$-0.533333\pi$
$433$	0.333843	−	1.89332i	0.333843	−	1.89332i	0.438371	−	0.898794i	$-0.355556\pi$
$434$		0			0
$435$		0			0
$436$	−0.0483597			−0.0483597
$437$	0.328433	−	0.673388i	0.328433	−	0.673388i
$438$	2.04091			2.04091
$439$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$439$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$440$		0			0
$441$	0.393530	−	2.23182i	0.393530	−	2.23182i
$442$		0			0
$443$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.882948	+	0.469472i	$0.844444\pi$
$443$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.978148	+	0.207912i	$0.933333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.47489	+	1.23758i	1.47489	+	1.23758i
$448$	−0.981771	−	1.70048i	−0.981771	−	1.70048i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	0.881373	−	0.320794i	0.881373	−	0.320794i
$451$	0.294524	+	1.67033i	0.294524	+	1.67033i
$452$	−0.0449242	+	0.254778i	−0.0449242	+	0.254778i
$453$	1.35192	+	0.492057i	1.35192	+	0.492057i
$454$	−1.08671	+	0.911858i	−1.08671	+	0.911858i
$455$		0			0
$456$	−0.162346	+	1.54462i	−0.162346	+	1.54462i
$457$	−1.92252			−1.92252			−0.961262	−	0.275637i	$-0.911111\pi$
$457$	−1.92252			−1.92252			−0.961262	+	0.275637i	$0.911111\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.317271	−	1.79933i	−0.317271	−	1.79933i	−0.559193	−	0.829038i	$-0.688889\pi$
$461$	−0.317271	−	1.79933i	−0.317271	−	1.79933i	0.241922	−	0.970296i	$-0.422222\pi$
$462$	2.09308	−	0.761820i	2.09308	−	0.761820i
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$467$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$468$	−0.123735	+	0.214314i	−0.123735	+	0.214314i
$469$		0			0
$470$		0			0
$471$	0.488730	−	2.77172i	0.488730	−	2.77172i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.997564	−	0.0697565i	0.997564	−	0.0697565i
$476$		0			0
$477$	−0.396517	+	0.332717i	−0.396517	+	0.332717i
$478$	−1.58391	−	0.576495i	−1.58391	−	0.576495i
$479$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$479$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	−0.868210	+	1.50378i	−0.868210	+	1.50378i
$483$	−0.951710	−	1.64841i	−0.951710	−	1.64841i
$484$	−0.177204	−	0.148692i	−0.177204	−	0.148692i
$485$		0			0
$486$	0.627603	+	1.08704i	0.627603	+	1.08704i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$491$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$492$	−0.432402	+	0.362828i	−0.432402	+	0.362828i
$493$		0			0
$494$	0.630676	−	0.609036i	0.630676	−	0.609036i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.433799	+	2.46020i	−0.433799	+	2.46020i
$499$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$499$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$500$		0			0
$501$	−0.804499	+	1.39343i	−0.804499	+	1.39343i
$502$	0.270928	+	0.469262i	0.270928	+	0.469262i
$503$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$503$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$504$	1.56230	+	1.31093i	1.56230	+	1.31093i
$505$		0			0
$506$	0.328433	−	0.568863i	0.328433	−	0.568863i
$507$	1.35192	−	0.492057i	1.35192	−	0.492057i
$508$		0			0
$509$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$509$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$510$		0			0
$511$	2.18880	−	1.83662i	2.18880	−	1.83662i
$512$	1.09570			1.09570
$513$	−0.0242934	−	0.0974355i	−0.0242934	−	0.0974355i
$514$	−0.541857			−0.541857
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$521$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$522$		0			0
$523$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$523$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$524$		0			0
$525$	1.27028	−	2.20019i	1.27028	−	2.20019i
$526$		0			0
$527$		0			0
$528$	−0.178666	+	1.01326i	−0.178666	+	1.01326i
$529$	0.412224	+	0.150037i	0.412224	+	0.150037i
$530$		0			0
$531$		0			0
$532$	0.228426	+	0.338655i	0.228426	+	0.338655i
$533$	1.69610			1.69610
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.469516	+	2.66276i	0.469516	+	2.66276i
$538$	1.39736	−	0.508597i	1.39736	−	0.508597i
$539$	1.05919	−	1.83458i	1.05919	−	1.83458i
$540$		0			0
$541$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i	0.615661	−	0.788011i	$-0.288889\pi$
$541$	−0.0534691	−	0.0448659i	−0.0534691	−	0.0448659i	−0.669131	+	0.743145i	$0.733333\pi$
$542$	−1.33998	−	1.12437i	−1.33998	−	1.12437i
$543$	−1.43518	−	2.48580i	−1.43518	−	2.48580i
$544$		0			0
$545$		0			0
$546$	−0.386786	−	2.19357i	−0.386786	−	2.19357i
$547$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$547$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$548$		0			0
$549$		0			0
$550$	0.876742			0.876742
$551$		0			0
$552$	1.16363			1.16363
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.59381	−	0.580099i	1.59381	−	0.580099i	0.615661	−	0.788011i	$-0.288889\pi$
$557$	1.59381	−	0.580099i	1.59381	−	0.580099i	0.978148	+	0.207912i	$0.0666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.874607	+	1.51486i	0.874607	+	1.51486i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.53549	+	0.558873i	1.53549	+	0.558873i
$568$		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			$\pi$
$572$	−0.177204	+	0.148692i	−0.177204	+	0.148692i
$573$	−0.282628	−	0.102868i	−0.282628	−	0.102868i
$574$	0.455992	−	2.58606i	0.455992	−	2.58606i
$575$	−0.130100	−	0.737831i	−0.130100	−	0.737831i
$576$	−1.11780	+	0.406845i	−1.11780	+	0.406845i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.438371	+	0.759281i	0.438371	+	0.759281i
$579$	−0.825702	−	0.692846i	−0.825702	−	0.692846i
$580$		0			0
$581$	1.74871	+	3.02885i	1.74871	+	3.02885i
$582$		0			0
$583$	−0.454664	+	0.165484i	−0.454664	+	0.165484i
$584$	0.303321	+	1.72022i	0.303321	+	1.72022i
$585$		0			0
$586$	−0.286126	−	0.104142i	−0.286126	−	0.104142i
$587$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$587$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$588$	0.704998			0.704998
$589$		0			0
$590$		0			0
$591$	−2.19882	+	1.84503i	−2.19882	+	1.84503i
$592$		0			0
$593$	0.339707	−	1.92657i	0.339707	−	1.92657i	−0.0348995	−	0.999391i	$-0.511111\pi$
$593$	0.339707	−	1.92657i	0.339707	−	1.92657i	0.374607	−	0.927184i	$-0.377778\pi$
$594$	−0.0152882	−	0.0867035i	−0.0152882	−	0.0867035i
$595$		0			0
$596$	−0.154785	+	0.268096i	−0.154785	+	0.268096i
$597$	1.38295	+	2.39534i	1.38295	+	2.39534i
$598$	−0.503189	−	0.422226i	−0.503189	−	0.422226i
$599$	0.671624	+	0.563559i	0.671624	+	0.563559i	0.913545	−	0.406737i	$-0.133333\pi$
$599$	0.671624	+	0.563559i	0.671624	+	0.563559i	−0.241922	+	0.970296i	$0.577778\pi$
$600$	0.776565	+	1.34505i	0.776565	+	1.34505i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	−0.0401688	+	0.227809i	−0.0401688	+	0.227809i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.451434	+	0.0315673i	−0.451434	+	0.0315673i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	−0.913545	−	0.406737i	$-0.866667\pi$
$613$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	0.719340	−	0.694658i	$-0.244444\pi$
$614$	1.54837	−	0.563559i	1.54837	−	0.563559i
$615$		0			0
$616$	0.953189	+	1.65097i	0.953189	+	1.65097i
$617$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$617$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$618$	−1.18977	−	0.998333i	−1.18977	−	0.998333i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	−0.0706976	+	0.0257318i	−0.0706976	+	0.0257318i
$622$	0.219031	+	1.24219i	0.219031	+	1.24219i
$623$		0			0
$624$	0.966846	+	0.351903i	0.966846	+	0.351903i
$625$	0.766044	−	0.642788i	0.766044	−	0.642788i
$626$	−1.17331			−1.17331
$627$	0.150383	−	1.43080i	0.150383	−	1.43080i
$628$	0.452536			0.452536
$629$		0			0
$630$		0			0
$631$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$631$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.123351	−	0.103504i	−0.123351	−	0.103504i
$637$	−1.62278	−	1.36167i	−1.62278	−	1.36167i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	−0.882948	−	0.469472i	$-0.844444\pi$
$641$	−0.213817	−	1.21262i	−0.213817	−	1.21262i	0.669131	−	0.743145i	$-0.266667\pi$
$642$		0			0
$643$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$643$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$644$	0.234446	−	0.196724i	0.234446	−	0.196724i
$645$		0			0
$646$		0			0
$647$	−1.99513			−1.99513			−0.997564	−	0.0697565i	$-0.977778\pi$
$647$	−1.99513			−1.99513			−0.997564	+	0.0697565i	$0.977778\pi$
$648$	−0.765234	+	0.642107i	−0.765234	+	0.642107i
$649$		0			0
$650$	0.152245	−	0.863423i	0.152245	−	0.863423i
$651$		0			0
$652$		0			0
$653$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$654$	−0.131847	−	0.228366i	−0.131847	−	0.228366i
$655$		0			0
$656$	0.929205	+	0.779696i	0.929205	+	0.779696i
$657$	−0.865486	−	1.49906i	−0.865486	−	1.49906i
$658$		0			0
$659$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$659$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$660$		0			0
$661$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$661$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$662$		0			0
$663$		0			0
$664$	−2.13809			−2.13809
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.243106	−	0.0884835i	−0.243106	−	0.0884835i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.574847	+	0.995664i	−0.574847	+	0.995664i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−0.0769249	−	0.0645477i	−0.0769249	−	0.0645477i
$676$	0.115661	+	0.200332i	0.115661	+	0.200332i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−1.32560	+	0.482480i	−1.32560	+	0.482480i
$679$		0			0
$680$		0			0
$681$	2.18745	+	0.796166i	2.18745	+	0.796166i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.226074	−	0.100655i	0.226074	−	0.100655i
$685$		0			0
$686$	−1.32642	+	1.11300i	−1.32642	+	1.11300i
$687$		0			0
$688$		0			0
$689$	0.0840186	+	0.476493i	0.0840186	+	0.476493i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−1.44718	−	1.21432i	−1.44718	−	1.21432i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.187462	−	1.06315i	−0.187462	−	1.06315i
$699$		0			0
$700$	0.383857	+	0.139713i	0.383857	+	0.139713i
$701$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$701$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$702$	−0.0880410			−0.0880410
$703$		0			0
$704$	−1.11192			−1.11192
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$709$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.408527	+	0.148692i	−0.408527	+	0.148692i
$717$	0.480293	+	2.72388i	0.480293	+	2.72388i
$718$	−0.114064	+	0.646888i	−0.114064	+	0.646888i
$719$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$719$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$	−2.17439			−2.17439
$722$	−0.868210	+	0.122019i	−0.868210	+	0.122019i
$723$	2.84936			2.84936
$724$	0.353544	−	0.296659i	0.353544	−	0.296659i
$725$		0			0
$726$	0.219031	−	1.24219i	0.219031	−	1.24219i
$727$	−0.306644	−	1.73907i	−0.306644	−	1.73907i	−0.615661	−	0.788011i	$-0.711111\pi$
$727$	−0.306644	−	1.73907i	−0.306644	−	1.73907i	0.309017	−	0.951057i	$-0.400000\pi$
$728$	1.79141	−	0.652019i	1.79141	−	0.652019i
$729$	0.567193	−	0.982407i	0.567193	−	0.982407i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.615661	+	0.788011i	$0.288889\pi$
$733$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.374607	+	0.927184i	$0.377778\pi$
$734$	−0.709299	+	1.22854i	−0.709299	+	1.22854i
$735$		0			0
$736$	0.0588747	+	0.333895i	0.0588747	+	0.333895i
$737$		0			0
$738$	−1.49489	−	0.544097i	−1.49489	−	0.544097i
$739$	−1.29929	+	1.09023i	−1.29929	+	1.09023i	−0.309017	+	0.951057i	$0.600000\pi$
$739$	−1.29929	+	1.09023i	−1.29929	+	1.09023i	−0.990268	+	0.139173i	$0.955556\pi$
$740$		0			0
$741$	−1.38295	−	0.396554i	−1.38295	−	0.396554i
$742$	0.749104			0.749104
$743$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.99100	−	0.724664i	1.99100	−	0.724664i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.961262	+	0.275637i	$0.0888889\pi$
$751$	1.39963	+	1.17443i	1.39963	+	1.17443i	0.438371	+	0.898794i	$0.355556\pi$
$752$		0			0
$753$	0.444576	−	0.770029i	0.444576	−	0.770029i
$754$		0			0
$755$		0			0
$756$	0.00712307	−	0.0403969i	0.00712307	−	0.0403969i
$757$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$757$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$758$		0			0
$759$	−1.07788			−1.07788
$760$		0			0
$761$	−0.0697990			−0.0697990			−0.0348995	−	0.999391i	$-0.511111\pi$
$761$	−0.0697990			−0.0697990			−0.0348995	+	0.999391i	$0.511111\pi$
$762$		0			0
$763$	−0.346909	−	0.126264i	−0.346909	−	0.126264i
$764$	0.00839757	−	0.0476250i	0.00839757	−	0.0476250i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.470427	−	0.814804i	−0.470427	−	0.814804i
$769$	−1.29929	−	1.09023i	−1.29929	−	1.09023i	−0.990268	−	0.139173i	$-0.955556\pi$
$769$	−1.29929	−	1.09023i	−1.29929	−	1.09023i	−0.309017	−	0.951057i	$-0.600000\pi$
$770$		0			0
$771$	0.444576	+	0.770029i	0.444576	+	0.770029i
$772$	0.0866551	−	0.150091i	0.0866551	−	0.150091i
$773$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$773$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.60189			−1.60189
$779$	−1.37217	−	0.996940i	−1.37217	−	0.996940i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.263077	−	1.49198i	−0.263077	−	1.49198i
$785$		0			0
$786$		0			0
$787$	−0.882948	−	1.52931i	−0.882948	−	1.52931i	−0.848048	−	0.529919i	$-0.822222\pi$
$787$	−0.882948	−	1.52931i	−0.882948	−	1.52931i	−0.0348995	−	0.999391i	$-0.511111\pi$
$788$	−0.353544	−	0.296659i	−0.353544	−	0.296659i
$789$		0			0
$790$		0			0
$791$	−0.987476	+	1.71036i	−0.987476	+	1.71036i
$792$	1.08526	−	0.395001i	1.08526	−	0.395001i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.340678	+	0.285863i	−0.340678	+	0.285863i
$797$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$797$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$798$	−0.976434	+	2.00199i	−0.976434	+	2.00199i
$799$		0			0
$800$	−0.346663	+	0.290885i	−0.346663	+	0.290885i
$801$		0			0
$802$		0			0
$803$	−0.280969	−	1.59345i	−0.280969	−	1.59345i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.86925	−	1.56849i	−1.86925	−	1.56849i
$808$		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
$811$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	−0.309017	−	0.951057i	$-0.600000\pi$
$811$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	0.374607	+	0.927184i	$0.377778\pi$
$812$		0			0
$813$	−0.498431	+	2.82674i	−0.498431	+	2.82674i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.34325			1.34325
$819$	−1.44718	+	1.21432i	−1.44718	+	1.21432i
$820$		0			0
$821$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$821$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$822$		0			0
$823$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	−0.615661	−	0.788011i	$-0.711111\pi$
$823$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	0.0348995	+	0.999391i	$0.488889\pi$
$824$	0.664639	−	1.15119i	0.664639	−	1.15119i
$825$	−0.719340	−	1.24593i	−0.719340	−	1.24593i
$826$		0			0
$827$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.961262	−	0.275637i	$-0.911111\pi$
$827$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.438371	−	0.898794i	$-0.644444\pi$
$828$	−0.0927035	−	0.160567i	−0.0927035	−	0.160567i
$829$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$829$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$830$		0			0
$831$		0			0
$832$	−0.193084	+	1.09503i	−0.193084	+	1.09503i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.230759	−	0.0161363i	0.230759	−	0.0161363i
$837$		0			0
$838$	−0.898808	+	0.754189i	−0.898808	+	0.754189i
$839$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$839$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$840$		0			0
$841$	0.173648	+	0.984808i	0.173648	+	0.984808i
$842$		0			0
$843$	1.43518	−	2.48580i	1.43518	−	2.48580i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.882948	−	1.52931i	−0.882948	−	1.52931i
$848$	−0.173014	+	0.299670i	−0.173014	+	0.299670i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	−0.913545	−	0.406737i	$-0.866667\pi$
$853$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	0.241922	+	0.970296i	$0.422222\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$857$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$858$	−1.18528	−	0.431408i	−1.18528	−	0.431408i
$859$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.104528	+	0.994522i	$0.533333\pi$
$859$	−0.346450	+	1.96482i	−0.346450	+	1.96482i	−0.241922	+	0.970296i	$0.577778\pi$
$860$		0			0
$861$	−4.04916	+	1.47377i	−4.04916	+	1.47377i
$862$	0.539776	−	0.934920i	0.539776	−	0.934920i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	0.0348113	+	0.0292102i	0.0348113	+	0.0292102i
$865$		0			0
$866$	0.842779	+	1.45974i	0.842779	+	1.45974i
$867$	0.719340	−	1.24593i	0.719340	−	1.24593i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.172887	−	0.145069i	0.172887	−	0.145069i
$873$		0			0
$874$	0.158910	+	0.637355i	0.158910	+	0.637355i
$875$		0			0
$876$	0.412500	−	0.346129i	0.412500	−	0.346129i
$877$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.559193	−	0.829038i	$-0.688889\pi$
$877$	−1.52045	−	0.553400i	−1.52045	−	0.553400i	−0.961262	+	0.275637i	$0.911111\pi$
$878$		0			0
$879$	0.0867630	+	0.492057i	0.0867630	+	0.492057i
$880$		0			0
$881$	0.241922	−	0.419021i	0.241922	−	0.419021i	−0.719340	−	0.694658i	$-0.755556\pi$
$881$	0.241922	−	0.419021i	0.241922	−	0.419021i	0.961262	+	0.275637i	$0.0888889\pi$
$882$	0.993457	+	1.72072i	0.993457	+	1.72072i
$883$	−1.10209	−	0.924765i	−1.10209	−	0.924765i	−0.104528	−	0.994522i	$-0.533333\pi$
$883$	−1.10209	−	0.924765i	−1.10209	−	0.924765i	−0.997564	+	0.0697565i	$0.977778\pi$
$884$		0			0
$885$		0			0
$886$	0.868210	−	1.50378i	0.868210	−	1.50378i
$887$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$887$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.708843	−	0.594790i	0.708843	−	0.594790i
$892$		0			0
$893$		0			0
$894$	−1.68802			−1.68802
$895$		0			0
$896$	0.866762	+	0.315476i	0.866762	+	0.315476i
$897$	−0.187172	+	1.06150i	−0.187172	+	1.06150i
$898$		0			0
$899$		0			0
$900$	0.123735	−	0.214314i	0.123735	−	0.214314i
$901$		0			0
$902$	−1.13914	−	0.955850i	−1.13914	−	0.955850i
$903$		0			0
$904$	−0.603678	−	1.04560i	−0.603678	−	1.04560i
$905$		0			0
$906$	−1.18528	+	0.431408i	−1.18528	+	0.431408i
$907$	0.107320	+	0.608645i	0.107320	+	0.608645i	0.990268	+	0.139173i	$0.0444444\pi$
$907$	0.107320	+	0.608645i	0.107320	+	0.608645i	−0.882948	+	0.469472i	$0.844444\pi$
$908$	−0.0649945	+	0.368602i	−0.0649945	+	0.368602i
$909$		0			0
$910$		0			0
$911$	−0.749213			−0.749213			−0.374607	−	0.927184i	$-0.622222\pi$
$911$	−0.749213			−0.749213			−0.374607	+	0.927184i	$0.622222\pi$
$912$	−0.575351	−	0.852993i	−0.575351	−	0.852993i
$913$	1.98054			1.98054
$914$	1.29121	−	1.08346i	1.29121	−	1.08346i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−2.07126	−	1.73799i	−2.07126	−	1.73799i
$922$	1.22712	+	1.02967i	1.22712	+	1.02967i
$923$		0			0
$924$	0.293845	−	0.508954i	0.293845	−	0.508954i
$925$		0			0
$926$		0			0
$927$	−0.228741	+	1.29726i	−0.228741	+	1.29726i
$928$		0			0
$929$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$929$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$930$		0			0
$931$	0.512484	+	2.05546i	0.512484	+	2.05546i
$932$		0			0
$933$	1.58556	−	1.33044i	1.58556	−	1.33044i
$934$	1.26224	+	0.459418i	1.26224	+	0.459418i
$935$		0			0
$936$	−0.200547	−	1.13736i	−0.200547	−	1.13736i
$937$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$937$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$938$		0			0
$939$	0.962665	+	1.66738i	0.962665	+	1.66738i
$940$		0			0
$941$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.961262	−	0.275637i	$-0.911111\pi$
$941$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.438371	−	0.898794i	$-0.644444\pi$
$942$	1.23379	+	2.13698i	1.23379	+	2.13698i
$943$	−0.635369	+	1.10049i	−0.635369	+	1.10049i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$947$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$948$		0			0
$949$	−1.61803			−1.61803
$950$	−0.630676	+	0.609036i	−0.630676	+	0.609036i
$951$		0			0
$952$		0			0
$953$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$953$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$954$	0.0788042	−	0.446921i	0.0788042	−	0.446921i
$955$		0			0
$956$	−0.417904	+	0.152104i	−0.417904	+	0.152104i
$957$		0			0
$958$	−0.152245	−	0.263696i	−0.152245	−	0.263696i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	0.0795558	+	0.451183i	0.0795558	+	0.451183i
$965$		0			0
$966$	1.56817	+	0.570766i	1.56817	+	0.570766i
$967$	−0.856733	+	0.718885i	−0.856733	+	0.718885i	−0.961262	−	0.275637i	$-0.911111\pi$
$967$	−0.856733	+	0.718885i	−0.856733	+	0.718885i	0.104528	+	0.994522i	$0.466667\pi$
$968$	1.07955			1.07955
$969$		0			0
$970$		0			0
$971$	1.39963	−	1.17443i	1.39963	−	1.17443i	0.438371	−	0.898794i	$-0.355556\pi$
$971$	1.39963	−	1.17443i	1.39963	−	1.17443i	0.961262	−	0.275637i	$-0.0888889\pi$
$972$	0.311206	+	0.113270i	0.311206	+	0.113270i
$973$		0			0
$974$		0			0
$975$	−1.35192	+	0.492057i	−1.35192	+	0.492057i
$976$		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
$981$	−0.111824	+	0.193686i	−0.111824	+	0.193686i
$982$		0			0
$983$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$983$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$984$	0.457434	−	2.59424i	0.457434	−	2.59424i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.0241798	−	0.230056i	0.0241798	−	0.230056i
$989$		0			0
$990$		0			0
$991$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$991$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.329561	+	0.570816i	0.329561	+	0.570816i
$997$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$997$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.c.2001.2	✓	24
11.10	odd	2		2717.1.db.d.2001.3	yes	24
13.12	even	2		2717.1.db.d.2001.3	yes	24
19.16	even	9	inner	2717.1.db.c.2144.2	yes	24
143.142	odd	2	CM	2717.1.db.c.2001.2	✓	24
209.54	odd	18		2717.1.db.d.2144.3	yes	24
247.168	even	18		2717.1.db.d.2144.3	yes	24
2717.2144	odd	18	inner	2717.1.db.c.2144.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.2001.2	✓	24	1.1	even	1	trivial
2717.1.db.c.2001.2	✓	24	143.142	odd	2	CM
2717.1.db.c.2144.2	yes	24	19.16	even	9	inner
2717.1.db.c.2144.2	yes	24	2717.2144	odd	18	inner
2717.1.db.d.2001.3	yes	24	11.10	odd	2
2717.1.db.d.2001.3	yes	24	13.12	even	2
2717.1.db.d.2144.3	yes	24	209.54	odd	18
2717.1.db.d.2144.3	yes	24	247.168	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.671624 + 0.563559i) q^{2} +(1.35192 + 0.492057i) q^{3} +(-0.0401688 + 0.227809i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(-0.882948 + 1.52931i) q^{7} +(-0.539776 - 0.934920i) q^{8} +(0.819514 + 0.687654i) q^{9} +O(q^{10})\)	\(q+(-0.671624 + 0.563559i) q^{2} +(1.35192 + 0.492057i) q^{3} +(-0.0401688 + 0.227809i) q^{4} +(-1.18528 + 0.431408i) q^{6} +(-0.882948 + 1.52931i) q^{7} +(-0.539776 - 0.934920i) q^{8} +(0.819514 + 0.687654i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.166400 + 0.288213i) q^{12} +(0.939693 - 0.342020i) q^{13} +(-0.268848 - 1.52471i) q^{14} +(0.672037 + 0.244601i) q^{16} -0.937938 q^{18} +(-0.961262 - 0.275637i) q^{19} +(-1.94618 + 1.63304i) q^{21} +(-0.823868 - 0.299864i) q^{22} +(-0.130100 + 0.737831i) q^{23} +(-0.269698 - 1.52954i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.438371 + 0.759281i) q^{26} +(0.0502092 + 0.0869649i) q^{27} +(-0.312923 - 0.262574i) q^{28} +(0.425245 - 0.154776i) q^{32} +(0.249824 + 1.41682i) q^{33} +(-0.189572 + 0.159070i) q^{36} +(0.800944 - 0.356603i) q^{38} +1.43868 q^{39} +(1.59381 + 0.580099i) q^{41} +(0.386786 - 2.19357i) q^{42} +(-0.217372 + 0.0791171i) q^{44} +(-0.328433 - 0.568863i) q^{46} +(0.788180 + 0.661361i) q^{48} +(-1.05919 - 1.83458i) q^{49} +(0.438371 - 0.759281i) q^{50} +(0.0401688 + 0.227809i) q^{52} +(-0.0840186 + 0.476493i) q^{53} +(-0.0827315 - 0.0301118i) q^{54} +1.90638 q^{56} +(-1.16392 - 0.845635i) q^{57} +(-1.77522 + 0.646128i) q^{63} +(-0.555962 + 0.962955i) q^{64} +(-0.966251 - 0.810781i) q^{66} +(-0.538939 + 0.933469i) q^{69} +(0.200547 - 1.13736i) q^{72} +(-1.52045 - 0.553400i) q^{73} -1.43868 q^{75} +(0.101405 - 0.207912i) q^{76} -1.76590 q^{77} +(-0.966251 + 0.810781i) q^{78} +(-0.160682 - 0.911271i) q^{81} +(-1.39736 + 0.508597i) q^{82} +(0.990268 - 1.71519i) q^{83} +(-0.293845 - 0.508954i) q^{84} +(0.539776 - 0.934920i) q^{88} +(-0.306644 + 1.73907i) q^{91} +(-0.162858 - 0.0592756i) q^{92} +0.651054 q^{96} +(1.74527 + 0.635227i) q^{98} +(-0.185769 + 1.05355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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