LMFDB - Embedded newform 2717.1.db.c.142.2

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			142.2
Root			$-0.997564 + 0.0697565i$ of defining polynomial
Character	$\chi$	$=$	2717.142
Dual form			2717.1.db.c.2430.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.194206 - 1.10140i) q^{2} +(1.47274 - 1.23577i) q^{3} +(-0.235663 + 0.0857741i) q^{4} +(-1.64709 - 1.38207i) q^{6} +(0.0348995 - 0.0604477i) q^{7} +(-0.418955 - 0.725651i) q^{8} +(0.468172 - 2.65514i) q^{9} +O(q^{10})$	\(q+(-0.194206 - 1.10140i) q^{2} +(1.47274 - 1.23577i) q^{3} +(-0.235663 + 0.0857741i) q^{4} +(-1.64709 - 1.38207i) q^{6} +(0.0348995 - 0.0604477i) q^{7} +(-0.418955 - 0.725651i) q^{8} +(0.468172 - 2.65514i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.241072 + 0.417549i) q^{12} +(-0.766044 - 0.642788i) q^{13} +(-0.0733545 - 0.0266988i) q^{14} +(-0.909979 + 0.763563i) q^{16} -3.01528 q^{18} +(0.241922 + 0.970296i) q^{19} +(-0.0233019 - 0.132152i) q^{21} +(0.856733 - 0.718885i) q^{22} +(-1.86110 + 0.677383i) q^{23} +(-1.51375 - 0.550960i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-0.559193 + 0.968551i) q^{26} +(-1.63039 - 2.82392i) q^{27} +(-0.00303965 + 0.0172387i) q^{28} +(0.375831 + 0.315360i) q^{32} +(1.80658 + 0.657542i) q^{33} +(0.117411 + 0.665873i) q^{36} +(1.02170 - 0.454888i) q^{38} -1.92252 q^{39} +(1.35275 - 1.13510i) q^{41} +(-0.141026 + 0.0513292i) q^{42} +(-0.192114 - 0.161203i) q^{44} +(1.10750 + 1.91825i) q^{46} +(-0.396569 + 2.24906i) q^{48} +(0.497564 + 0.861806i) q^{49} +(0.559193 - 0.968551i) q^{50} +(0.235663 + 0.0857741i) q^{52} +(1.35192 - 0.492057i) q^{53} +(-2.79362 + 2.34413i) q^{54} -0.0584852 q^{56} +(1.55535 + 1.13003i) q^{57} +(-0.144158 - 0.120963i) q^{63} +(-0.319599 + 0.553562i) q^{64} +(0.373365 - 2.11746i) q^{66} +(-1.90381 + 3.29750i) q^{69} +(-2.12284 + 0.772652i) q^{72} +(1.23949 - 1.04005i) q^{73} +1.92252 q^{75} +(-0.140238 - 0.207912i) q^{76} +0.0697990 q^{77} +(0.373365 + 2.11746i) q^{78} +(-3.35737 - 1.22198i) q^{81} +(-1.51290 - 1.26947i) q^{82} +(-0.615661 + 1.06636i) q^{83} +(0.0168266 + 0.0291445i) q^{84} +(0.418955 - 0.725651i) q^{88} +(-0.0655896 + 0.0238727i) q^{91} +(0.380488 - 0.319268i) q^{92} +0.943215 q^{96} +(0.852559 - 0.715382i) q^{98} +(2.53350 - 0.922119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2717\mathbb{Z}\right)^\times$.

$n$	$210$	$287$	$2224$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	−0.913545	−	0.406737i	$-0.866667\pi$
$2$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	0.719340	−	0.694658i	$-0.244444\pi$
$3$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.559193	−	0.829038i	$-0.311111\pi$
$3$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.913545	−	0.406737i	$-0.133333\pi$
$4$	−0.235663	+	0.0857741i	−0.235663	+	0.0857741i
$5$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$5$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$6$	−1.64709	−	1.38207i	−1.64709	−	1.38207i
$7$	0.0348995	−	0.0604477i	0.0348995	−	0.0604477i	−0.848048	−	0.529919i	$-0.822222\pi$
$7$	0.0348995	−	0.0604477i	0.0348995	−	0.0604477i	0.882948	+	0.469472i	$0.155556\pi$
$8$	−0.418955	−	0.725651i	−0.418955	−	0.725651i
$9$	0.468172	−	2.65514i	0.468172	−	2.65514i
$10$		0			0
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$	0.500000	+	0.866025i	0.500000	+	0.866025i
$12$	−0.241072	+	0.417549i	−0.241072	+	0.417549i
$13$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$13$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$14$	−0.0733545	−	0.0266988i	−0.0733545	−	0.0266988i
$15$		0			0
$16$	−0.909979	+	0.763563i	−0.909979	+	0.763563i
$17$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$17$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$18$	−3.01528			−3.01528
$19$	0.241922	+	0.970296i	0.241922	+	0.970296i
$19$	0.241922	+	0.970296i	0.241922	+	0.970296i
$20$		0			0
$21$	−0.0233019	−	0.132152i	−0.0233019	−	0.132152i
$22$	0.856733	−	0.718885i	0.856733	−	0.718885i
$23$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.882948	+	0.469472i	$0.844444\pi$
$23$	−1.86110	+	0.677383i	−1.86110	+	0.677383i	−0.978148	+	0.207912i	$0.933333\pi$
$24$	−1.51375	−	0.550960i	−1.51375	−	0.550960i
$25$	0.766044	+	0.642788i	0.766044	+	0.642788i
$26$	−0.559193	+	0.968551i	−0.559193	+	0.968551i
$27$	−1.63039	−	2.82392i	−1.63039	−	2.82392i
$28$	−0.00303965	+	0.0172387i	−0.00303965	+	0.0172387i
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.375831	+	0.315360i	0.375831	+	0.315360i
$33$	1.80658	+	0.657542i	1.80658	+	0.657542i
$34$		0			0
$35$		0			0
$36$	0.117411	+	0.665873i	0.117411	+	0.665873i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.02170	−	0.454888i	1.02170	−	0.454888i
$39$	−1.92252			−1.92252
$40$		0			0
$41$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.374607	−	0.927184i	$-0.377778\pi$
$41$	1.35275	−	1.13510i	1.35275	−	1.13510i	0.978148	−	0.207912i	$-0.0666667\pi$
$42$	−0.141026	+	0.0513292i	−0.141026	+	0.0513292i
$43$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$43$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$44$	−0.192114	−	0.161203i	−0.192114	−	0.161203i
$45$		0			0
$46$	1.10750	+	1.91825i	1.10750	+	1.91825i
$47$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$47$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$48$	−0.396569	+	2.24906i	−0.396569	+	2.24906i
$49$	0.497564	+	0.861806i	0.497564	+	0.861806i
$50$	0.559193	−	0.968551i	0.559193	−	0.968551i
$51$		0			0
$52$	0.235663	+	0.0857741i	0.235663	+	0.0857741i
$53$	1.35192	−	0.492057i	1.35192	−	0.492057i	0.438371	−	0.898794i	$-0.355556\pi$
$53$	1.35192	−	0.492057i	1.35192	−	0.492057i	0.913545	+	0.406737i	$0.133333\pi$
$54$	−2.79362	+	2.34413i	−2.79362	+	2.34413i
$55$		0			0
$56$	−0.0584852			−0.0584852
$57$	1.55535	+	1.13003i	1.55535	+	1.13003i
$58$		0			0
$59$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$59$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$60$		0			0
$61$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$61$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$62$		0			0
$63$	−0.144158	−	0.120963i	−0.144158	−	0.120963i
$64$	−0.319599	+	0.553562i	−0.319599	+	0.553562i
$65$		0			0
$66$	0.373365	−	2.11746i	0.373365	−	2.11746i
$67$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$67$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$68$		0			0
$69$	−1.90381	+	3.29750i	−1.90381	+	3.29750i
$70$		0			0
$71$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$71$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$72$	−2.12284	+	0.772652i	−2.12284	+	0.772652i
$73$	1.23949	−	1.04005i	1.23949	−	1.04005i	0.241922	−	0.970296i	$-0.422222\pi$
$73$	1.23949	−	1.04005i	1.23949	−	1.04005i	0.997564	−	0.0697565i	$-0.0222222\pi$
$74$		0			0
$75$	1.92252			1.92252
$76$	−0.140238	−	0.207912i	−0.140238	−	0.207912i
$77$	0.0697990			0.0697990
$78$	0.373365	+	2.11746i	0.373365	+	2.11746i
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$		0			0
$81$	−3.35737	−	1.22198i	−3.35737	−	1.22198i
$82$	−1.51290	−	1.26947i	−1.51290	−	1.26947i
$83$	−0.615661	+	1.06636i	−0.615661	+	1.06636i	0.374607	+	0.927184i	$0.377778\pi$
$83$	−0.615661	+	1.06636i	−0.615661	+	1.06636i	−0.990268	+	0.139173i	$0.955556\pi$
$84$	0.0168266	+	0.0291445i	0.0168266	+	0.0291445i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	0.418955	−	0.725651i	0.418955	−	0.725651i
$89$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$89$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$90$		0			0
$91$	−0.0655896	+	0.0238727i	−0.0655896	+	0.0238727i
$92$	0.380488	−	0.319268i	0.380488	−	0.319268i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.943215			0.943215
$97$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$97$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$98$	0.852559	−	0.715382i	0.852559	−	0.715382i
$99$	2.53350	−	0.922119i	2.53350	−	0.922119i
$100$	−0.235663	−	0.0857741i	−0.235663	−	0.0857741i
$101$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$101$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$102$		0			0
$103$	0.374607	+	0.648838i	0.374607	+	0.648838i	0.990268	−	0.139173i	$-0.0444444\pi$
$103$	0.374607	+	0.648838i	0.374607	+	0.648838i	−0.615661	+	0.788011i	$0.711111\pi$
$104$	−0.145501	+	0.825180i	−0.145501	+	0.825180i
$105$		0			0
$106$	−0.804499	−	1.39343i	−0.804499	−	1.39343i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.626442	+	0.525647i	0.626442	+	0.525647i
$109$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	0.241922	−	0.970296i	$-0.422222\pi$
$109$	−0.196449	−	0.0715017i	−0.196449	−	0.0715017i	−0.438371	+	0.898794i	$0.644444\pi$
$110$		0			0
$111$		0			0
$112$	0.0143978	+	0.0816541i	0.0143978	+	0.0816541i
$113$	−1.99513			−1.99513			−0.997564	−	0.0697565i	$-0.977778\pi$
$113$	−1.99513			−1.99513			−0.997564	+	0.0697565i	$0.977778\pi$
$114$	0.942552	−	1.93252i	0.942552	−	1.93252i
$115$		0			0
$116$		0			0
$117$	−2.06533	+	1.73302i	−2.06533	+	1.73302i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$	0.589531	−	3.34340i	0.589531	−	3.34340i
$124$		0			0
$125$		0			0
$126$	−0.105232	+	0.182266i	−0.105232	+	0.182266i
$127$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$127$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$128$	1.13278	+	0.412300i	1.13278	+	0.412300i
$129$		0			0
$130$		0			0
$131$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$131$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$132$	−0.482144			−0.482144
$133$	0.0670951	+	0.0192392i	0.0670951	+	0.0192392i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$137$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$138$	4.00158	+	1.45646i	4.00158	+	1.45646i
$139$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$139$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.173648	−	0.984808i	0.173648	−	0.984808i
$144$	1.60134	+	2.77360i	1.60134	+	2.77360i
$145$		0			0
$146$	−1.38622	−	1.16318i	−1.38622	−	1.16318i
$147$	1.79778	+	0.654338i	1.79778	+	0.654338i
$148$		0			0
$149$	−1.02517	+	0.860218i	−1.02517	+	0.860218i	−0.990268	−	0.139173i	$-0.955556\pi$
$149$	−1.02517	+	0.860218i	−1.02517	+	0.860218i	−0.0348995	+	0.999391i	$0.511111\pi$
$150$	−0.373365	−	2.11746i	−0.373365	−	2.11746i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	0.602742	−	0.582061i	0.602742	−	0.582061i
$153$		0			0
$154$	−0.0135554	−	0.0768763i	−0.0135554	−	0.0768763i
$155$		0			0
$156$	0.453067	−	0.164903i	0.453067	−	0.164903i
$157$	1.83832	+	0.669092i	1.83832	+	0.669092i	0.990268	+	0.139173i	$0.0444444\pi$
$157$	1.83832	+	0.669092i	1.83832	+	0.669092i	0.848048	+	0.529919i	$0.177778\pi$
$158$		0			0
$159$	1.38295	−	2.39534i	1.38295	−	2.39534i
$160$		0			0
$161$	−0.0240050	+	0.136139i	−0.0240050	+	0.136139i
$162$	−0.693865	+	3.93511i	−0.693865	+	3.93511i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$	−0.221432	+	0.383531i	−0.221432	+	0.383531i
$165$		0			0
$166$	1.29405	+	0.470994i	1.29405	+	0.470994i
$167$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.913545	+	0.406737i	$0.866667\pi$
$167$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.961262	+	0.275637i	$0.911111\pi$
$168$	−0.0861334	+	0.0722745i	−0.0861334	+	0.0722745i
$169$	0.173648	+	0.984808i	0.173648	+	0.984808i
$170$		0			0
$171$	2.68953	−	0.188070i	2.68953	−	0.188070i
$172$		0			0
$173$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$173$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$174$		0			0
$175$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i
$176$	−1.11625	−	0.406283i	−1.11625	−	0.406283i
$177$		0			0
$178$		0			0
$179$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$180$		0			0
$181$	0.152245	−	0.863423i	0.152245	−	0.863423i	−0.809017	−	0.587785i	$-0.800000\pi$
$181$	0.152245	−	0.863423i	0.152245	−	0.863423i	0.961262	−	0.275637i	$-0.0888889\pi$
$182$	0.0390311	+	0.0676039i	0.0390311	+	0.0676039i
$183$		0			0
$184$	1.27126	+	1.06671i	1.27126	+	1.06671i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.227599			−0.227599
$190$		0			0
$191$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$191$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$192$	0.213392	+	1.21020i	0.213392	+	1.21020i
$193$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.669131	+	0.743145i	$0.733333\pi$
$193$	−1.51718	+	1.27306i	−1.51718	+	1.27306i	−0.848048	+	0.529919i	$0.822222\pi$
$194$		0			0
$195$		0			0
$196$	−0.191178	−	0.160417i	−0.191178	−	0.160417i
$197$	0.438371	−	0.759281i	0.438371	−	0.759281i	−0.559193	−	0.829038i	$-0.688889\pi$
$197$	0.438371	−	0.759281i	0.438371	−	0.759281i	0.997564	+	0.0697565i	$0.0222222\pi$
$198$	−1.50764	−	2.61131i	−1.50764	−	2.61131i
$199$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	0.913545	+	0.406737i	$0.133333\pi$
$199$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	−0.997564	+	0.0697565i	$0.977778\pi$
$200$	0.145501	−	0.825180i	0.145501	−	0.825180i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.641876	−	0.538598i	0.641876	−	0.538598i
$207$	0.927232	+	5.25859i	0.927232	+	5.25859i
$208$	1.18789			1.18789
$209$	−0.719340	+	0.694658i	−0.719340	+	0.694658i
$210$		0			0
$211$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$211$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$212$	−0.276390	+	0.231919i	−0.276390	+	0.231919i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−1.36612	+	2.36619i	−1.36612	+	2.36619i
$217$		0			0
$218$	−0.0406000	+	0.230254i	−0.0406000	+	0.230254i
$219$	0.540169	−	3.06345i	0.540169	−	3.06345i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$223$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$224$	0.0321791	−	0.0117122i	0.0321791	−	0.0117122i
$225$	2.06533	−	1.73302i	2.06533	−	1.73302i
$226$	0.387465	+	2.19742i	0.387465	+	2.19742i
$227$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$228$	−0.463466	−	0.132897i	−0.463466	−	0.132897i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	0.102796	−	0.0862558i	0.102796	−	0.0862558i
$232$		0			0
$233$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$233$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$234$	2.30984	+	1.93818i	2.30984	+	1.93818i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.241922	−	0.419021i	−0.241922	−	0.419021i	0.719340	−	0.694658i	$-0.244444\pi$
$239$	−0.241922	−	0.419021i	−0.241922	−	0.419021i	−0.961262	+	0.275637i	$0.911111\pi$
$240$		0			0
$241$	0.943248	+	0.791479i	0.943248	+	0.791479i	0.978148	−	0.207912i	$-0.0666667\pi$
$241$	0.943248	+	0.791479i	0.943248	+	0.791479i	−0.0348995	+	0.999391i	$0.511111\pi$
$242$	1.05094	+	0.382510i	1.05094	+	0.382510i
$243$	−3.39049	+	1.23404i	−3.39049	+	1.23404i
$244$		0			0
$245$		0			0
$246$	−3.79689			−3.79689
$247$	0.438371	−	0.898794i	0.438371	−	0.898794i
$248$		0			0
$249$	0.411068	+	2.33128i	0.411068	+	2.33128i
$250$		0			0
$251$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	−0.615661	−	0.788011i	$-0.711111\pi$
$251$	−0.580762	+	0.211380i	−0.580762	+	0.211380i	0.0348995	+	0.999391i	$0.488889\pi$
$252$	0.0443481	+	0.0161414i	0.0443481	+	0.0161414i
$253$	−1.51718	−	1.27306i	−1.51718	−	1.27306i
$254$		0			0
$255$		0			0
$256$	0.123116	−	0.698226i	0.123116	−	0.698226i
$257$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$257$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$263$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$264$	−0.279730	−	1.58643i	−0.279730	−	1.58643i
$265$		0			0
$266$	0.00815972	−	0.0776346i	0.00815972	−	0.0776346i
$267$		0			0
$268$		0			0
$269$	−1.35275	+	1.13510i	−1.35275	+	1.13510i	−0.374607	+	0.927184i	$0.622222\pi$
$269$	−1.35275	+	1.13510i	−1.35275	+	1.13510i	−0.978148	+	0.207912i	$0.933333\pi$
$270$		0			0
$271$	0.823868	+	0.299864i	0.823868	+	0.299864i	0.719340	−	0.694658i	$-0.244444\pi$
$271$	0.823868	+	0.299864i	0.823868	+	0.299864i	0.104528	+	0.994522i	$0.466667\pi$
$272$		0			0
$273$	−0.0670951	+	0.116212i	−0.0670951	+	0.116212i
$274$		0			0
$275$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$276$	0.165817	−	0.940396i	0.165817	−	0.940396i
$277$		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
$281$	0.823868	−	0.299864i	0.823868	−	0.299864i	0.104528	−	0.994522i	$-0.466667\pi$
$281$	0.823868	−	0.299864i	0.823868	−	0.299864i	0.719340	+	0.694658i	$0.244444\pi$
$282$		0			0
$283$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$283$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$284$		0			0
$285$		0			0
$286$	−1.11839			−1.11839
$287$	−0.0214035	−	0.121385i	−0.0214035	−	0.121385i
$288$	1.01328	−	0.850241i	1.01328	−	0.850241i
$289$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$290$		0			0
$291$		0			0
$292$	−0.202891	+	0.351417i	−0.202891	+	0.351417i
$293$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$293$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$294$	0.371546	−	2.10714i	0.371546	−	2.10714i
$295$		0			0
$296$		0			0
$297$	1.63039	−	2.82392i	1.63039	−	2.82392i
$298$	1.14653	+	0.962055i	1.14653	+	0.962055i
$299$	1.86110	+	0.677383i	1.86110	+	0.677383i
$300$	−0.453067	+	0.164903i	−0.453067	+	0.164903i
$301$		0			0
$302$	−0.194206	−	1.10140i	−0.194206	−	1.10140i
$303$		0			0
$304$	−0.961025	−	0.698226i	−0.961025	−	0.698226i
$305$		0			0
$306$		0			0
$307$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$307$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$308$	−0.0164490	+	0.00598695i	−0.0164490	+	0.00598695i
$309$	1.35351	+	0.492639i	1.35351	+	0.492639i
$310$		0			0
$311$	−0.961262	+	1.66495i	−0.961262	+	1.66495i	−0.241922	+	0.970296i	$0.577778\pi$
$311$	−0.961262	+	1.66495i	−0.961262	+	1.66495i	−0.719340	+	0.694658i	$0.755556\pi$
$312$	0.805450	+	1.39508i	0.805450	+	1.39508i
$313$	0.232387	−	1.31793i	0.232387	−	1.31793i	−0.615661	−	0.788011i	$-0.711111\pi$
$313$	0.232387	−	1.31793i	0.232387	−	1.31793i	0.848048	−	0.529919i	$-0.177778\pi$
$314$	0.379924	−	2.15465i	0.379924	−	2.15465i
$315$		0			0
$316$		0			0
$317$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$317$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$318$	−2.90679	−	1.05798i	−2.90679	−	1.05798i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	0.154605			0.154605
$323$		0			0
$324$	0.896021			0.896021
$325$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$326$		0			0
$327$	−0.377678	+	0.137464i	−0.377678	+	0.137464i
$328$	−1.39043	−	0.506074i	−1.39043	−	0.506074i
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	0.0536225	−	0.304108i	0.0536225	−	0.304108i
$333$		0			0
$334$	1.11566	+	1.93238i	1.11566	+	1.93238i
$335$		0			0
$336$	0.122110	+	0.102463i	0.122110	+	0.102463i
$337$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$337$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$338$	1.05094	−	0.382510i	1.05094	−	0.382510i
$339$	−2.93830	+	2.46553i	−2.93830	+	2.46553i
$340$		0			0
$341$		0			0
$342$	−0.729461	−	2.92571i	−0.729461	−	2.92571i
$343$	0.139258			0.139258
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$347$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$348$		0			0
$349$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	−0.990268	−	0.139173i	$-0.955556\pi$
$349$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	0.615661	+	0.788011i	$0.288889\pi$
$350$	−0.0390311	−	0.0676039i	−0.0390311	−	0.0676039i
$351$	−0.566229	+	3.21125i	−0.566229	+	3.21125i
$352$	−0.0851941	+	0.483160i	−0.0851941	+	0.483160i
$353$		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
$358$	−1.31259	+	1.10140i	−1.31259	+	1.10140i
$359$	−0.343916	−	1.95045i	−0.343916	−	1.95045i	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	−0.343916	−	1.95045i	−0.343916	−	1.95045i	−0.0348995	−	0.999391i	$-0.511111\pi$
$360$		0			0
$361$	−0.882948	+	0.469472i	−0.882948	+	0.469472i
$362$	−0.980536			−0.980536
$363$	0.333843	+	1.89332i	0.333843	+	1.89332i
$364$	0.0134094	−	0.0112518i	0.0134094	−	0.0112518i
$365$		0			0
$366$		0			0
$367$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.997564	−	0.0697565i	$-0.977778\pi$
$367$	−1.23949	−	1.04005i	−1.23949	−	1.04005i	−0.241922	−	0.970296i	$-0.577778\pi$
$368$	1.17633	−	2.03747i	1.17633	−	2.03747i
$369$	−2.38051	−	4.12317i	−2.38051	−	4.12317i
$370$		0			0
$371$	0.0174375	−	0.0988928i	0.0174375	−	0.0988928i
$372$		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
$378$	0.0442011	+	0.250677i	0.0442011	+	0.250677i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	0.0406000	+	0.230254i	0.0406000	+	0.230254i
$383$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$383$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$384$	2.17780	−	0.792655i	2.17780	−	0.792655i
$385$		0			0
$386$	1.69679	+	1.42378i	1.69679	+	1.42378i
$387$		0			0
$388$		0			0
$389$	0.317271	−	1.79933i	0.317271	−	1.79933i	−0.241922	−	0.970296i	$-0.577778\pi$
$389$	0.317271	−	1.79933i	0.317271	−	1.79933i	0.559193	−	0.829038i	$-0.311111\pi$
$390$		0			0
$391$		0			0
$392$	0.416914	−	0.722116i	0.416914	−	0.722116i
$393$		0			0
$394$	−0.921403	−	0.335363i	−0.921403	−	0.335363i
$395$		0			0
$396$	−0.517957	+	0.434618i	−0.517957	+	0.434618i
$397$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$397$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$398$	0.541124			0.541124
$399$	0.122589	−	0.0545801i	0.122589	−	0.0545801i
$400$	−1.18789			−1.18789
$401$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$401$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$409$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−0.143934	−	0.120775i	−0.143934	−	0.120775i
$413$		0			0
$414$	5.61172	−	2.04250i	5.61172	−	2.04250i
$415$		0			0
$416$	−0.0851941	−	0.483160i	−0.0851941	−	0.483160i
$417$		0			0
$418$	0.904793	+	0.657371i	0.904793	+	0.657371i
$419$	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		0.766044	−	0.642788i	$-0.222222\pi$
$421$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$422$		0			0
$423$		0			0
$424$	−0.923454	−	0.774870i	−0.923454	−	0.774870i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.961262	−	1.66495i	−0.961262	−	1.66495i
$430$		0			0
$431$	0.573931	+	0.481585i	0.573931	+	0.481585i	0.882948	−	0.469472i	$-0.155556\pi$
$431$	0.573931	+	0.481585i	0.573931	+	0.481585i	−0.309017	+	0.951057i	$0.600000\pi$
$432$	3.63986	+	1.32480i	3.63986	+	1.32480i
$433$	0.454664	−	0.165484i	0.454664	−	0.165484i	−0.104528	−	0.994522i	$-0.533333\pi$
$433$	0.454664	−	0.165484i	0.454664	−	0.165484i	0.559193	+	0.829038i	$0.311111\pi$
$434$		0			0
$435$		0			0
$436$	0.0524287			0.0524287
$437$	−1.10750	−	1.64194i	−1.10750	−	1.64194i
$438$	−3.47897			−3.47897
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	2.52116	−	0.917627i	2.52116	−	0.917627i
$442$		0			0
$443$	−0.943248	−	0.791479i	−0.943248	−	0.791479i	0.0348995	−	0.999391i	$-0.488889\pi$
$443$	−0.943248	−	0.791479i	−0.943248	−	0.791479i	−0.978148	+	0.207912i	$0.933333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.446769	+	2.53375i	−0.446769	+	2.53375i
$448$	0.0223077	+	0.0386381i	0.0223077	+	0.0386381i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−2.30984	−	1.93818i	−2.30984	−	1.93818i
$451$	1.65940	+	0.603972i	1.65940	+	0.603972i
$452$	0.470177	−	0.171130i	0.470177	−	0.171130i
$453$	1.47274	−	1.23577i	1.47274	−	1.23577i
$454$	−0.314231	−	1.78209i	−0.314231	−	1.78209i
$455$		0			0
$456$	0.168385	−	1.60208i	0.168385	−	1.60208i
$457$	0.483844			0.483844			0.241922	−	0.970296i	$-0.422222\pi$
$457$	0.483844			0.483844			0.241922	+	0.970296i	$0.422222\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.997564	−	0.0697565i	$-0.0222222\pi$
$461$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.719340	+	0.694658i	$0.244444\pi$
$462$	−0.114965	−	0.0964673i	−0.114965	−	0.0964673i
$463$		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
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$468$	0.338073	−	0.585559i	0.338073	−	0.585559i
$469$		0			0
$470$		0			0
$471$	3.53421	−	1.28635i	3.53421	−	1.28635i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.438371	+	0.898794i	−0.438371	+	0.898794i
$476$		0			0
$477$	−0.673550	−	3.81989i	−0.673550	−	3.81989i
$478$	−0.414525	+	0.347828i	−0.414525	+	0.347828i
$479$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$479$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$480$		0			0
$481$		0			0
$482$	0.688547	−	1.19260i	0.688547	−	1.19260i
$483$	0.132884	+	0.230162i	0.132884	+	0.230162i
$484$	0.0435487	−	0.246977i	0.0435487	−	0.246977i
$485$		0			0
$486$	2.01761	+	3.49461i	2.01761	+	3.49461i
$487$		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		0.766044	−	0.642788i	$-0.222222\pi$
$491$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$492$	0.147847	+	0.838480i	0.147847	+	0.838480i
$493$		0			0
$494$	−1.07506	−	0.308269i	−1.07506	−	0.308269i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.48783	−	0.905497i	2.48783	−	0.905497i
$499$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$499$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$500$		0			0
$501$	−1.91784	+	3.32180i	−1.91784	+	3.32180i
$502$	0.345600	+	0.598597i	0.345600	+	0.598597i
$503$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$503$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$504$	−0.0273812	+	0.155286i	−0.0273812	+	0.155286i
$505$		0			0
$506$	−1.10750	+	1.91825i	−1.10750	+	1.91825i
$507$	1.47274	+	1.23577i	1.47274	+	1.23577i
$508$		0			0
$509$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$509$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$510$		0			0
$511$	−0.0196113	−	0.111221i	−0.0196113	−	0.111221i
$512$	0.412551			0.412551
$513$	2.34561	−	2.26513i	2.34561	−	2.26513i
$514$	−0.691200			−0.691200
$515$		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		0.173648	−	0.984808i	$-0.444444\pi$
$523$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$524$		0			0
$525$	0.0670951	−	0.116212i	0.0670951	−	0.116212i
$526$		0			0
$527$		0			0
$528$	−2.14602	+	0.781089i	−2.14602	+	0.781089i
$529$	2.23878	−	1.87856i	2.23878	−	1.87856i
$530$		0			0
$531$		0			0
$532$	−0.0174620	+	0.00122106i	−0.0174620	+	0.00122106i
$533$	−1.76590			−1.76590
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.76784	−	1.00741i	−2.76784	−	1.00741i
$538$	1.51290	+	1.26947i	1.51290	+	1.26947i
$539$	−0.497564	+	0.861806i	−0.497564	+	0.861806i
$540$		0			0
$541$	−0.294524	+	1.67033i	−0.294524	+	1.67033i	0.374607	+	0.927184i	$0.377778\pi$
$541$	−0.294524	+	1.67033i	−0.294524	+	1.67033i	−0.669131	+	0.743145i	$0.733333\pi$
$542$	0.170268	−	0.965640i	0.170268	−	0.965640i
$543$	−0.842779	−	1.45974i	−0.842779	−	1.45974i
$544$		0			0
$545$		0			0
$546$	0.141026	+	0.0513292i	0.141026	+	0.0513292i
$547$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$547$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$548$		0			0
$549$		0			0
$550$	1.11839			1.11839
$551$		0			0
$552$	3.19045			3.19045
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.35275	+	1.13510i	1.35275	+	1.13510i	0.978148	+	0.207912i	$0.0666667\pi$
$557$	1.35275	+	1.13510i	1.35275	+	1.13510i	0.374607	+	0.927184i	$0.377778\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.490268	−	0.849169i	−0.490268	−	0.849169i
$563$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$563$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.191037	+	0.160299i	−0.191037	+	0.160299i
$568$		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			$\pi$
$572$	0.0435487	+	0.246977i	0.0435487	+	0.246977i
$573$	−0.307886	+	0.258347i	−0.307886	+	0.258347i
$574$	−0.129536	+	0.0471474i	−0.129536	+	0.0471474i
$575$	−1.86110	−	0.677383i	−1.86110	−	0.677383i
$576$	1.32015	+	1.10774i	1.32015	+	1.10774i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.559193	+	0.968551i	0.559193	+	0.968551i
$579$	−0.661187	+	3.74978i	−0.661187	+	3.74978i
$580$		0			0
$581$	0.0429726	+	0.0744306i	0.0429726	+	0.0744306i
$582$		0			0
$583$	1.10209	+	0.924765i	1.10209	+	0.924765i
$584$	−1.27400	−	0.463699i	−1.27400	−	0.463699i
$585$		0			0
$586$	−1.61013	+	1.35106i	−1.61013	+	1.35106i
$587$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$587$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$588$	−0.479795			−0.479795
$589$		0			0
$590$		0			0
$591$	−0.292694	−	1.65995i	−0.292694	−	1.65995i
$592$		0			0
$593$	−1.83832	+	0.669092i	−1.83832	+	0.669092i	−0.848048	+	0.529919i	$0.822222\pi$
$593$	−1.83832	+	0.669092i	−1.83832	+	0.669092i	−0.990268	+	0.139173i	$0.955556\pi$
$594$	−3.42689	−	1.24728i	−3.42689	−	1.24728i
$595$		0			0
$596$	0.167809	−	0.290654i	0.167809	−	0.290654i
$597$	0.465101	+	0.805578i	0.465101	+	0.805578i
$598$	0.384631	−	2.18135i	0.384631	−	2.18135i
$599$	0.194206	−	1.10140i	0.194206	−	1.10140i	−0.719340	−	0.694658i	$-0.755556\pi$
$599$	0.194206	−	1.10140i	0.194206	−	1.10140i	0.913545	−	0.406737i	$-0.133333\pi$
$600$	−0.805450	−	1.39508i	−0.805450	−	1.39508i
$601$		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
$604$	−0.235663	+	0.0857741i	−0.235663	+	0.0857741i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.215071	+	0.440960i	−0.215071	+	0.440960i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.87481	−	0.682374i	−1.87481	−	0.682374i	−0.961262	−	0.275637i	$-0.911111\pi$
$613$	−1.87481	−	0.682374i	−1.87481	−	0.682374i	−0.913545	−	0.406737i	$-0.866667\pi$
$614$	1.31259	+	1.10140i	1.31259	+	1.10140i
$615$		0			0
$616$	−0.0292426	−	0.0506497i	−0.0292426	−	0.0506497i
$617$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$617$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$618$	0.279730	−	1.58643i	0.279730	−	1.58643i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	4.94719	+	4.15119i	4.94719	+	4.15119i
$622$	2.02045	+	0.735385i	2.02045	+	0.735385i
$623$		0			0
$624$	1.74946	−	1.46797i	1.74946	−	1.46797i
$625$	0.173648	+	0.984808i	0.173648	+	0.984808i
$626$	−1.49669			−1.49669
$627$	−0.200958	+	1.91199i	−0.200958	+	1.91199i
$628$	−0.490613			−0.490613
$629$		0			0
$630$		0			0
$631$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$631$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.120451	+	0.683112i	−0.120451	+	0.683112i
$637$	0.172802	−	0.980010i	0.172802	−	0.980010i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.669131	−	0.743145i	$-0.266667\pi$
$641$	0.704030	+	0.256246i	0.704030	+	0.256246i	0.0348995	+	0.999391i	$0.488889\pi$
$642$		0			0
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$	−0.00602014	−	0.0341419i	−0.00602014	−	0.0341419i
$645$		0			0
$646$		0			0
$647$	0.876742			0.876742			0.438371	−	0.898794i	$-0.355556\pi$
$647$	0.876742			0.876742			0.438371	+	0.898794i	$0.355556\pi$
$648$	0.519853	+	2.94823i	0.519853	+	2.94823i
$649$		0			0
$650$	−1.05094	+	0.382510i	−1.05094	+	0.382510i
$651$		0			0
$652$		0			0
$653$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$653$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$654$	0.224749	+	0.389277i	0.224749	+	0.389277i
$655$		0			0
$656$	−0.364261	+	2.06583i	−0.364261	+	2.06583i
$657$	−2.18119	−	3.77793i	−2.18119	−	3.77793i
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$		0			0
$661$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$661$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$	1.03174			1.03174
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.383292	−	0.321620i	0.383292	−	0.321620i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.0329177	−	0.0570152i	0.0329177	−	0.0570152i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	0.566229	−	3.21125i	0.566229	−	3.21125i
$676$	−0.125393	−	0.217188i	−0.125393	−	0.217188i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	3.28615	+	2.75741i	3.28615	+	2.75741i
$679$		0			0
$680$		0			0
$681$	2.38294	−	1.99952i	2.38294	−	1.99952i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.617690	+	0.275013i	−0.617690	+	0.275013i
$685$		0			0
$686$	−0.0270447	−	0.153378i	−0.0270447	−	0.153378i
$687$		0			0
$688$		0			0
$689$	−1.35192	−	0.492057i	−1.35192	−	0.492057i
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	0.0326779	−	0.185326i	0.0326779	−	0.185326i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.787377	+	0.286582i	0.787377	+	0.286582i
$699$		0			0
$700$	−0.0134094	+	0.0112518i	−0.0134094	+	0.0112518i
$701$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$701$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$702$	3.64682			3.64682
$703$		0			0
$704$	−0.639198			−0.639198
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$709$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.294335	+	0.246977i	0.294335	+	0.246977i
$717$	−0.874103	−	0.318147i	−0.874103	−	0.318147i
$718$	−2.08142	+	0.757576i	−2.08142	+	0.757576i
$719$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$719$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$720$		0			0
$721$	0.0522943			0.0522943
$722$	0.688547	+	0.881300i	0.688547	+	0.881300i
$723$	2.36725			2.36725
$724$	0.0381810	+	0.216535i	0.0381810	+	0.216535i
$725$		0			0
$726$	2.02045	−	0.735385i	2.02045	−	0.735385i
$727$	−0.0655896	−	0.0238727i	−0.0655896	−	0.0238727i	0.309017	−	0.951057i	$-0.400000\pi$
$727$	−0.0655896	−	0.0238727i	−0.0655896	−	0.0238727i	−0.374607	+	0.927184i	$0.622222\pi$
$728$	0.0448023	+	0.0375936i	0.0448023	+	0.0375936i
$729$	−1.68189	+	2.91312i	−1.68189	+	2.91312i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.615661	−	1.06636i	−0.615661	−	1.06636i	−0.990268	−	0.139173i	$-0.955556\pi$
$733$	−0.615661	−	1.06636i	−0.615661	−	1.06636i	0.374607	−	0.927184i	$-0.377778\pi$
$734$	−0.904793	+	1.56715i	−0.904793	+	1.56715i
$735$		0			0
$736$	−0.913078	−	0.332333i	−0.913078	−	0.332333i
$737$		0			0
$738$	−4.07893	+	3.42263i	−4.07893	+	3.42263i
$739$	0.306644	+	1.73907i	0.306644	+	1.73907i	0.615661	+	0.788011i	$0.288889\pi$
$739$	0.306644	+	1.73907i	0.306644	+	1.73907i	−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$	−0.465101	−	1.86542i	−0.465101	−	1.86542i
$742$	−0.112306			−0.112306
$743$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$743$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.54309	+	2.13390i	2.54309	+	2.13390i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	0.317271	−	1.79933i	0.317271	−	1.79933i	−0.241922	−	0.970296i	$-0.577778\pi$
$751$	0.317271	−	1.79933i	0.317271	−	1.79933i	0.559193	−	0.829038i	$-0.311111\pi$
$752$		0			0
$753$	−0.594092	+	1.02900i	−0.594092	+	1.02900i
$754$		0			0
$755$		0			0
$756$	0.0536367	−	0.0195222i	0.0536367	−	0.0195222i
$757$	0.473442	−	0.397265i	0.473442	−	0.397265i	−0.374607	−	0.927184i	$-0.622222\pi$
$757$	0.473442	−	0.397265i	0.473442	−	0.397265i	0.848048	+	0.529919i	$0.177778\pi$
$758$		0			0
$759$	−3.80763			−3.80763
$760$		0			0
$761$	−1.69610			−1.69610			−0.848048	−	0.529919i	$-0.822222\pi$
$761$	−1.69610			−1.69610			−0.848048	+	0.529919i	$0.822222\pi$
$762$		0			0
$763$	−0.0111781	+	0.00937953i	−0.0111781	+	0.00937953i
$764$	0.0492669	−	0.0179317i	0.0492669	−	0.0179317i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.681532	−	1.18045i	−0.681532	−	1.18045i
$769$	0.306644	−	1.73907i	0.306644	−	1.73907i	−0.309017	−	0.951057i	$-0.600000\pi$
$769$	0.306644	−	1.73907i	0.306644	−	1.73907i	0.615661	−	0.788011i	$-0.288889\pi$
$770$		0			0
$771$	−0.594092	−	1.02900i	−0.594092	−	1.02900i
$772$	0.248346	−	0.430148i	0.248346	−	0.430148i
$773$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$773$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−2.04339			−2.04339
$779$	1.42864	+	1.03797i	1.42864	+	1.03797i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−1.11082	−	0.404304i	−1.11082	−	0.404304i
$785$		0			0
$786$		0			0
$787$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i	0.882948	−	0.469472i	$-0.155556\pi$
$787$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i	−0.848048	+	0.529919i	$0.822222\pi$
$788$	−0.0381810	+	0.216535i	−0.0381810	+	0.216535i
$789$		0			0
$790$		0			0
$791$	−0.0696290	+	0.120601i	−0.0696290	+	0.120601i
$792$	−1.73056	−	1.45211i	−1.73056	−	1.45211i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.0210708	−	0.119498i	−0.0210708	−	0.119498i
$797$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$797$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$798$	−0.0839217	−	0.124419i	−0.0839217	−	0.124419i
$799$		0			0
$800$	0.0851941	+	0.483160i	0.0851941	+	0.483160i
$801$		0			0
$802$		0			0
$803$	1.52045	+	0.553400i	1.52045	+	0.553400i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.589531	+	3.34340i	−0.589531	+	3.34340i
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$	−1.29929	−	1.09023i	−1.29929	−	1.09023i	−0.990268	−	0.139173i	$-0.955556\pi$
$811$	−1.29929	−	1.09023i	−1.29929	−	1.09023i	−0.309017	−	0.951057i	$-0.600000\pi$
$812$		0			0
$813$	1.58391	−	0.576495i	1.58391	−	0.576495i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.388411			0.388411
$819$	0.0326779	+	0.185326i	0.0326779	+	0.185326i
$820$		0			0
$821$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$821$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$822$		0			0
$823$	0.473442	+	0.397265i	0.473442	+	0.397265i	0.848048	−	0.529919i	$-0.177778\pi$
$823$	0.473442	+	0.397265i	0.473442	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$824$	0.313886	−	0.543667i	0.313886	−	0.543667i
$825$	0.961262	+	1.66495i	0.961262	+	1.66495i
$826$		0			0
$827$	−0.317271	+	1.79933i	−0.317271	+	1.79933i	0.241922	+	0.970296i	$0.422222\pi$
$827$	−0.317271	+	1.79933i	−0.317271	+	1.79933i	−0.559193	+	0.829038i	$0.688889\pi$
$828$	−0.669565	−	1.15972i	−0.669565	−	1.15972i
$829$	−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
$832$	0.600650	−	0.218619i	0.600650	−	0.218619i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.109938	−	0.225406i	0.109938	−	0.225406i
$837$		0			0
$838$	−0.259898	−	1.47395i	−0.259898	−	1.47395i
$839$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$839$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$840$		0			0
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$	0.842779	−	1.45974i	0.842779	−	1.45974i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.0348995	+	0.0604477i	0.0348995	+	0.0604477i
$848$	−0.854499	+	1.48003i	−0.854499	+	1.48003i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	−0.913545	−	0.406737i	$-0.866667\pi$
$853$	−0.194206	−	1.10140i	−0.194206	−	1.10140i	0.719340	−	0.694658i	$-0.244444\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$857$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$858$	−1.64709	+	1.38207i	−1.64709	+	1.38207i
$859$	−0.823868	+	0.299864i	−0.823868	+	0.299864i	−0.719340	−	0.694658i	$-0.755556\pi$
$859$	−0.823868	+	0.299864i	−0.823868	+	0.299864i	−0.104528	+	0.994522i	$0.533333\pi$
$860$		0			0
$861$	−0.181526	−	0.152319i	−0.181526	−	0.152319i
$862$	0.418955	−	0.725651i	0.418955	−	0.725651i
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	0.277799	−	1.57548i	0.277799	−	1.57548i
$865$		0			0
$866$	−0.270562	−	0.468627i	−0.270562	−	0.468627i
$867$	−0.961262	+	1.66495i	−0.961262	+	1.66495i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.0304181	+	0.172510i	0.0304181	+	0.172510i
$873$		0			0
$874$	−1.59334	+	1.53867i	−1.59334	+	1.53867i
$875$		0			0
$876$	0.135467	+	0.768273i	0.135467	+	0.768273i
$877$	1.23949	−	1.04005i	1.23949	−	1.04005i	0.241922	−	0.970296i	$-0.422222\pi$
$877$	1.23949	−	1.04005i	1.23949	−	1.04005i	0.997564	−	0.0697565i	$-0.0222222\pi$
$878$		0			0
$879$	−3.39526	−	1.23577i	−3.39526	−	1.23577i
$880$		0			0
$881$	0.719340	−	1.24593i	0.719340	−	1.24593i	−0.241922	−	0.970296i	$-0.577778\pi$
$881$	0.719340	−	1.24593i	0.719340	−	1.24593i	0.961262	−	0.275637i	$-0.0888889\pi$
$882$	−1.50029	−	2.59858i	−1.50029	−	2.59858i
$883$	0.333843	−	1.89332i	0.333843	−	1.89332i	−0.104528	−	0.994522i	$-0.533333\pi$
$883$	0.333843	−	1.89332i	0.333843	−	1.89332i	0.438371	−	0.898794i	$-0.355556\pi$
$884$		0			0
$885$		0			0
$886$	−0.688547	+	1.19260i	−0.688547	+	1.19260i
$887$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$887$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.620417	−	3.51856i	−0.620417	−	3.51856i
$892$		0			0
$893$		0			0
$894$	2.87743			2.87743
$895$		0			0
$896$	0.0644561	−	0.0540851i	0.0644561	−	0.0540851i
$897$	3.57800	−	1.30229i	3.57800	−	1.30229i
$898$		0			0
$899$		0			0
$900$	−0.338073	+	0.585559i	−0.338073	+	0.585559i
$901$		0			0
$902$	0.342947	−	1.94495i	0.342947	−	1.94495i
$903$		0			0
$904$	0.835868	+	1.44777i	0.835868	+	1.44777i
$905$		0			0
$906$	−1.64709	−	1.38207i	−1.64709	−	1.38207i
$907$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$907$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$908$	−0.381310	+	0.138785i	−0.381310	+	0.138785i
$909$		0			0
$910$		0			0
$911$	1.98054			1.98054			0.990268	−	0.139173i	$-0.0444444\pi$
$911$	1.98054			1.98054			0.990268	+	0.139173i	$0.0444444\pi$
$912$	−2.27819	+	0.159306i	−2.27819	+	0.159306i
$913$	−1.23132			−1.23132
$914$	−0.0939652	−	0.532903i	−0.0939652	−	0.532903i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−0.511477	+	2.90073i	−0.511477	+	2.90073i
$922$	0.354831	−	2.01235i	0.354831	−	2.01235i
$923$		0			0
$924$	−0.0168266	+	0.0291445i	−0.0168266	+	0.0291445i
$925$		0			0
$926$		0			0
$927$	1.89813	−	0.690864i	1.89813	−	0.690864i
$928$		0			0
$929$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$929$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$930$		0			0
$931$	−0.715835	+	0.691274i	−0.715835	+	0.691274i
$932$		0			0
$933$	0.641820	+	3.63994i	0.641820	+	3.63994i
$934$	−0.297540	+	0.249666i	−0.297540	+	0.249666i
$935$		0			0
$936$	2.12284	+	0.772652i	2.12284	+	0.772652i
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$	−1.28642	−	2.22814i	−1.28642	−	2.22814i
$940$		0			0
$941$	−0.317271	+	1.79933i	−0.317271	+	1.79933i	0.241922	+	0.970296i	$0.422222\pi$
$941$	−0.317271	+	1.79933i	−0.317271	+	1.79933i	−0.559193	+	0.829038i	$0.688889\pi$
$942$	−2.10314	−	3.64274i	−2.10314	−	3.64274i
$943$	−1.74871	+	3.02885i	−1.74871	+	3.02885i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$947$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$948$		0			0
$949$	−1.61803			−1.61803
$950$	1.07506	+	0.308269i	1.07506	+	0.308269i
$951$		0			0
$952$		0			0
$953$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$953$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$954$	−4.07640	+	1.48369i	−4.07640	+	1.48369i
$955$		0			0
$956$	0.0929531	+	0.0779969i	0.0929531	+	0.0779969i
$957$		0			0
$958$	1.05094	+	1.82028i	1.05094	+	1.82028i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	−0.290177	−	0.105616i	−0.290177	−	0.105616i
$965$		0			0
$966$	0.227693	−	0.191057i	0.227693	−	0.191057i
$967$	0.346450	+	1.96482i	0.346450	+	1.96482i	0.241922	+	0.970296i	$0.422222\pi$
$967$	0.346450	+	1.96482i	0.346450	+	1.96482i	0.104528	+	0.994522i	$0.466667\pi$
$968$	0.837909			0.837909
$969$		0			0
$970$		0			0
$971$	0.317271	+	1.79933i	0.317271	+	1.79933i	0.559193	+	0.829038i	$0.311111\pi$
$971$	0.317271	+	1.79933i	0.317271	+	1.79933i	−0.241922	+	0.970296i	$0.577778\pi$
$972$	0.693162	−	0.581632i	0.693162	−	0.581632i
$973$		0			0
$974$		0			0
$975$	−1.47274	−	1.23577i	−1.47274	−	1.23577i
$976$		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
$981$	−0.281819	+	0.488124i	−0.281819	+	0.488124i
$982$		0			0
$983$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$983$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$984$	−2.67313	+	0.972938i	−2.67313	+	0.972938i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.0262144	+	0.249413i	−0.0262144	+	0.249413i
$989$		0			0
$990$		0			0
$991$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.997564	−	0.0697565i	$-0.977778\pi$
$991$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.104528	+	0.994522i	$0.533333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−0.296837	−	0.514137i	−0.296837	−	0.514137i
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$		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.142.2	✓	24
11.10	odd	2		2717.1.db.d.142.3	yes	24
13.12	even	2		2717.1.db.d.142.3	yes	24
19.17	even	9	inner	2717.1.db.c.2430.2	yes	24
143.142	odd	2	CM	2717.1.db.c.142.2	✓	24
209.131	odd	18		2717.1.db.d.2430.3	yes	24
247.207	even	18		2717.1.db.d.2430.3	yes	24
2717.2430	odd	18	inner	2717.1.db.c.2430.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.142.2	✓	24	1.1	even	1	trivial
2717.1.db.c.142.2	✓	24	143.142	odd	2	CM
2717.1.db.c.2430.2	yes	24	19.17	even	9	inner
2717.1.db.c.2430.2	yes	24	2717.2430	odd	18	inner
2717.1.db.d.142.3	yes	24	11.10	odd	2
2717.1.db.d.142.3	yes	24	13.12	even	2
2717.1.db.d.2430.3	yes	24	209.131	odd	18
2717.1.db.d.2430.3	yes	24	247.207	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)

\(f(q)\)	\(=\)	\(q+(-0.194206 - 1.10140i) q^{2} +(1.47274 - 1.23577i) q^{3} +(-0.235663 + 0.0857741i) q^{4} +(-1.64709 - 1.38207i) q^{6} +(0.0348995 - 0.0604477i) q^{7} +(-0.418955 - 0.725651i) q^{8} +(0.468172 - 2.65514i) q^{9} +O(q^{10})\)	\(q+(-0.194206 - 1.10140i) q^{2} +(1.47274 - 1.23577i) q^{3} +(-0.235663 + 0.0857741i) q^{4} +(-1.64709 - 1.38207i) q^{6} +(0.0348995 - 0.0604477i) q^{7} +(-0.418955 - 0.725651i) q^{8} +(0.468172 - 2.65514i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-0.241072 + 0.417549i) q^{12} +(-0.766044 - 0.642788i) q^{13} +(-0.0733545 - 0.0266988i) q^{14} +(-0.909979 + 0.763563i) q^{16} -3.01528 q^{18} +(0.241922 + 0.970296i) q^{19} +(-0.0233019 - 0.132152i) q^{21} +(0.856733 - 0.718885i) q^{22} +(-1.86110 + 0.677383i) q^{23} +(-1.51375 - 0.550960i) q^{24} +(0.766044 + 0.642788i) q^{25} +(-0.559193 + 0.968551i) q^{26} +(-1.63039 - 2.82392i) q^{27} +(-0.00303965 + 0.0172387i) q^{28} +(0.375831 + 0.315360i) q^{32} +(1.80658 + 0.657542i) q^{33} +(0.117411 + 0.665873i) q^{36} +(1.02170 - 0.454888i) q^{38} -1.92252 q^{39} +(1.35275 - 1.13510i) q^{41} +(-0.141026 + 0.0513292i) q^{42} +(-0.192114 - 0.161203i) q^{44} +(1.10750 + 1.91825i) q^{46} +(-0.396569 + 2.24906i) q^{48} +(0.497564 + 0.861806i) q^{49} +(0.559193 - 0.968551i) q^{50} +(0.235663 + 0.0857741i) q^{52} +(1.35192 - 0.492057i) q^{53} +(-2.79362 + 2.34413i) q^{54} -0.0584852 q^{56} +(1.55535 + 1.13003i) q^{57} +(-0.144158 - 0.120963i) q^{63} +(-0.319599 + 0.553562i) q^{64} +(0.373365 - 2.11746i) q^{66} +(-1.90381 + 3.29750i) q^{69} +(-2.12284 + 0.772652i) q^{72} +(1.23949 - 1.04005i) q^{73} +1.92252 q^{75} +(-0.140238 - 0.207912i) q^{76} +0.0697990 q^{77} +(0.373365 + 2.11746i) q^{78} +(-3.35737 - 1.22198i) q^{81} +(-1.51290 - 1.26947i) q^{82} +(-0.615661 + 1.06636i) q^{83} +(0.0168266 + 0.0291445i) q^{84} +(0.418955 - 0.725651i) q^{88} +(-0.0655896 + 0.0238727i) q^{91} +(0.380488 - 0.319268i) q^{92} +0.943215 q^{96} +(0.852559 - 0.715382i) q^{98} +(2.53350 - 0.922119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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