LMFDB - Embedded newform 2717.1.db.c.1715.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2717.142");

S:= CuspForms(chi, 1);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1715.1
Root			$0.438371 + 0.898794i$ of defining polynomial
Character	$\chi$	$=$	2717.1715
Dual form			2717.1.db.c.1429.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87481 + 0.682374i) q^{2} +(-0.0840186 + 0.476493i) q^{3} +(2.28322 - 1.91585i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(0.848048 + 1.46886i) q^{7} +(-1.97571 + 3.42203i) q^{8} +(0.719706 + 0.261952i) q^{9} +O(q^{10})$	\(q+(-1.87481 + 0.682374i) q^{2} +(-0.0840186 + 0.476493i) q^{3} +(2.28322 - 1.91585i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(0.848048 + 1.46886i) q^{7} +(-1.97571 + 3.42203i) q^{8} +(0.719706 + 0.261952i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.721057 + 1.24891i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(-2.59224 - 2.17515i) q^{14} +(0.851407 - 4.82857i) q^{16} -1.52806 q^{18} +(0.719340 + 0.694658i) q^{19} +(-0.771155 + 0.280677i) q^{21} +(-0.346450 + 1.96482i) q^{22} +(-0.943248 + 0.791479i) q^{23} +(-1.46458 - 1.22893i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.997564 + 1.72783i) q^{26} +(-0.427209 + 0.739947i) q^{27} +(4.75041 + 1.72901i) q^{28} +(1.01251 + 5.74223i) q^{32} +(0.370646 + 0.311009i) q^{33} +(2.14511 - 0.780756i) q^{36} +(-1.82264 - 0.811492i) q^{38} +0.483844 q^{39} +(-0.0121205 + 0.0687386i) q^{41} +(1.25424 - 1.05243i) q^{42} +(-0.517565 - 2.93526i) q^{44} +(1.22832 - 2.12752i) q^{46} +(2.22925 + 0.811379i) q^{48} +(-0.938371 + 1.62531i) q^{49} +(-0.997564 - 1.72783i) q^{50} +(-2.28322 - 1.91585i) q^{52} +(1.47274 - 1.23577i) q^{53} +(0.296013 - 1.67877i) q^{54} -6.70199 q^{56} +(-0.391438 + 0.284396i) q^{57} +(0.225575 + 1.27930i) q^{63} +(-3.36508 - 5.82848i) q^{64} +(-0.907114 - 0.330162i) q^{66} +(-0.297884 - 0.515950i) q^{69} +(-2.31834 + 1.94532i) q^{72} +(0.280969 - 1.59345i) q^{73} -0.483844 q^{75} +(2.97328 + 0.207912i) q^{76} +1.69610 q^{77} +(-0.907114 + 0.330162i) q^{78} +(0.270023 + 0.226577i) q^{81} +(-0.0241819 - 0.137142i) q^{82} +(-0.374607 - 0.648838i) q^{83} +(-1.22298 + 2.11827i) q^{84} +(1.97571 + 3.42203i) q^{88} +(1.29929 - 1.09023i) q^{91} +(-0.637289 + 3.61425i) q^{92} -2.82120 q^{96} +(0.650198 - 3.68746i) q^{98} +(0.586710 - 0.492308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9	$ 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9} + 12 q^{11} - 3 q^{12} + 3 q^{14} - 3 q^{16} - 6 q^{18} - 3 q^{21} + 3 q^{22} + 3 q^{23} + 6 q^{24} - 3 q^{27} + 9 q^{28} + 9 q^{32} + 6 q^{33} + 30 q^{36} - 3 q^{41} + 12 q^{42} + 6 q^{44} + 3 q^{46} - 12 q^{49} - 3 q^{52} + 3 q^{53} - 21 q^{54} - 12 q^{56} - 6 q^{63} - 15 q^{64} - 12 q^{66} - 3 q^{69} - 15 q^{72} - 3 q^{76} - 12 q^{78} + 6 q^{81} + 3 q^{82} - 12 q^{84} - 3 q^{88} - 6 q^{91} - 3 q^{92} + 6 q^{96} - 6 q^{98} - 3 q^{99}+O(q^{100}) $ 24 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 24 * q^6 + 3 * q^8 + 3 * q^9 + 12 * q^11 - 3 * q^12 + 3 * q^14 - 3 * q^16 - 6 * q^18 - 3 * q^21 + 3 * q^22 + 3 * q^23 + 6 * q^24 - 3 * q^27 + 9 * q^28 + 9 * q^32 + 6 * q^33 + 30 * q^36 - 3 * q^41 + 12 * q^42 + 6 * q^44 + 3 * q^46 - 12 * q^49 - 3 * q^52 + 3 * q^53 - 21 * q^54 - 12 * q^56 - 6 * q^63 - 15 * q^64 - 12 * q^66 - 3 * q^69 - 15 * q^72 - 3 * q^76 - 12 * q^78 + 6 * q^81 + 3 * q^82 - 12 * q^84 - 3 * q^88 - 6 * q^91 - 3 * q^92 + 6 * q^96 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.913545	+	0.406737i	$0.866667\pi$
$2$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.961262	+	0.275637i	$0.911111\pi$
$3$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	0.913545	+	0.406737i	$0.133333\pi$
$3$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i	−0.997564	+	0.0697565i	$0.977778\pi$
$4$	2.28322	−	1.91585i	2.28322	−	1.91585i
$5$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$5$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$6$	−0.167628	−	0.950665i	−0.167628	−	0.950665i
$7$	0.848048	+	1.46886i	0.848048	+	1.46886i	0.882948	+	0.469472i	$0.155556\pi$
$7$	0.848048	+	1.46886i	0.848048	+	1.46886i	−0.0348995	+	0.999391i	$0.511111\pi$
$8$	−1.97571	+	3.42203i	−1.97571	+	3.42203i
$9$	0.719706	+	0.261952i	0.719706	+	0.261952i
$10$		0			0
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$	0.500000	−	0.866025i	0.500000	−	0.866025i
$12$	0.721057	+	1.24891i	0.721057	+	1.24891i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$14$	−2.59224	−	2.17515i	−2.59224	−	2.17515i
$15$		0			0
$16$	0.851407	−	4.82857i	0.851407	−	4.82857i
$17$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$17$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$18$	−1.52806			−1.52806
$19$	0.719340	+	0.694658i	0.719340	+	0.694658i
$19$	0.719340	+	0.694658i	0.719340	+	0.694658i
$20$		0			0
$21$	−0.771155	+	0.280677i	−0.771155	+	0.280677i
$22$	−0.346450	+	1.96482i	−0.346450	+	1.96482i
$23$	−0.943248	+	0.791479i	−0.943248	+	0.791479i	−0.978148	−	0.207912i	$-0.933333\pi$
$23$	−0.943248	+	0.791479i	−0.943248	+	0.791479i	0.0348995	+	0.999391i	$0.488889\pi$
$24$	−1.46458	−	1.22893i	−1.46458	−	1.22893i
$25$	0.173648	+	0.984808i	0.173648	+	0.984808i
$26$	0.997564	+	1.72783i	0.997564	+	1.72783i
$27$	−0.427209	+	0.739947i	−0.427209	+	0.739947i
$28$	4.75041	+	1.72901i	4.75041	+	1.72901i
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	1.01251	+	5.74223i	1.01251	+	5.74223i
$33$	0.370646	+	0.311009i	0.370646	+	0.311009i
$34$		0			0
$35$		0			0
$36$	2.14511	−	0.780756i	2.14511	−	0.780756i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−1.82264	−	0.811492i	−1.82264	−	0.811492i
$39$	0.483844			0.483844
$40$		0			0
$41$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i	−0.990268	−	0.139173i	$-0.955556\pi$
$41$	−0.0121205	+	0.0687386i	−0.0121205	+	0.0687386i	0.978148	+	0.207912i	$0.0666667\pi$
$42$	1.25424	−	1.05243i	1.25424	−	1.05243i
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	−0.517565	−	2.93526i	−0.517565	−	2.93526i
$45$		0			0
$46$	1.22832	−	2.12752i	1.22832	−	2.12752i
$47$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$47$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$48$	2.22925	+	0.811379i	2.22925	+	0.811379i
$49$	−0.938371	+	1.62531i	−0.938371	+	1.62531i
$50$	−0.997564	−	1.72783i	−0.997564	−	1.72783i
$51$		0			0
$52$	−2.28322	−	1.91585i	−2.28322	−	1.91585i
$53$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.559193	−	0.829038i	$-0.311111\pi$
$53$	1.47274	−	1.23577i	1.47274	−	1.23577i	0.913545	−	0.406737i	$-0.133333\pi$
$54$	0.296013	−	1.67877i	0.296013	−	1.67877i
$55$		0			0
$56$	−6.70199			−6.70199
$57$	−0.391438	+	0.284396i	−0.391438	+	0.284396i
$58$		0			0
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$		0			0
$61$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$61$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$62$		0			0
$63$	0.225575	+	1.27930i	0.225575	+	1.27930i
$64$	−3.36508	−	5.82848i	−3.36508	−	5.82848i
$65$		0			0
$66$	−0.907114	−	0.330162i	−0.907114	−	0.330162i
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$		0			0
$69$	−0.297884	−	0.515950i	−0.297884	−	0.515950i
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	−2.31834	+	1.94532i	−2.31834	+	1.94532i
$73$	0.280969	−	1.59345i	0.280969	−	1.59345i	−0.438371	−	0.898794i	$-0.644444\pi$
$73$	0.280969	−	1.59345i	0.280969	−	1.59345i	0.719340	−	0.694658i	$-0.244444\pi$
$74$		0			0
$75$	−0.483844			−0.483844
$76$	2.97328	+	0.207912i	2.97328	+	0.207912i
$77$	1.69610			1.69610
$78$	−0.907114	+	0.330162i	−0.907114	+	0.330162i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$		0			0
$81$	0.270023	+	0.226577i	0.270023	+	0.226577i
$82$	−0.0241819	−	0.137142i	−0.0241819	−	0.137142i
$83$	−0.374607	−	0.648838i	−0.374607	−	0.648838i	0.615661	−	0.788011i	$-0.288889\pi$
$83$	−0.374607	−	0.648838i	−0.374607	−	0.648838i	−0.990268	+	0.139173i	$0.955556\pi$
$84$	−1.22298	+	2.11827i	−1.22298	+	2.11827i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.97571	+	3.42203i	1.97571	+	3.42203i
$89$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$89$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$90$		0			0
$91$	1.29929	−	1.09023i	1.29929	−	1.09023i
$92$	−0.637289	+	3.61425i	−0.637289	+	3.61425i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−2.82120			−2.82120
$97$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$97$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$98$	0.650198	−	3.68746i	0.650198	−	3.68746i
$99$	0.586710	−	0.492308i	0.586710	−	0.492308i
$100$	2.28322	+	1.91585i	2.28322	+	1.91585i
$101$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$101$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$102$		0			0
$103$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.374607	+	0.927184i	$0.622222\pi$
$103$	−0.990268	+	1.71519i	−0.990268	+	1.71519i	−0.615661	+	0.788011i	$0.711111\pi$
$104$	3.71312	+	1.35147i	3.71312	+	1.35147i
$105$		0			0
$106$	−1.91784	+	3.32180i	−1.91784	+	3.32180i
$107$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$107$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$108$	0.442216	+	2.50793i	0.442216	+	2.50793i
$109$	0.160147	+	0.134379i	0.160147	+	0.134379i	0.719340	−	0.694658i	$-0.244444\pi$
$109$	0.160147	+	0.134379i	0.160147	+	0.134379i	−0.559193	+	0.829038i	$0.688889\pi$
$110$		0			0
$111$		0			0
$112$	7.81454	−	2.84426i	7.81454	−	2.84426i
$113$	0.876742			0.876742			0.438371	−	0.898794i	$-0.355556\pi$
$113$	0.876742			0.876742			0.438371	+	0.898794i	$0.355556\pi$
$114$	0.539806	−	0.800295i	0.539806	−	0.800295i
$115$		0			0
$116$		0			0
$117$	0.132996	−	0.754260i	0.132996	−	0.754260i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$	−0.0317351	−	0.0115506i	−0.0317351	−	0.0115506i
$124$		0			0
$125$		0			0
$126$	−1.29587	−	2.24451i	−1.29587	−	2.24451i
$127$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$127$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$128$	5.81941	+	4.88307i	5.81941	+	4.88307i
$129$		0			0
$130$		0			0
$131$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$131$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$132$	1.44211			1.44211
$133$	−0.410323	+	1.64571i	−0.410323	+	1.64571i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$137$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$138$	0.910546	+	0.764039i	0.910546	+	0.764039i
$139$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$139$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$144$	1.87761	−	3.25212i	1.87761	−	3.25212i
$145$		0			0
$146$	0.560568	+	3.17914i	0.560568	+	3.17914i
$147$	−0.695607	−	0.583683i	−0.695607	−	0.583683i
$148$		0			0
$149$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	0.615661	+	0.788011i	$0.288889\pi$
$149$	−0.232387	+	1.31793i	−0.232387	+	1.31793i	−0.848048	+	0.529919i	$0.822222\pi$
$150$	0.907114	−	0.330162i	0.907114	−	0.330162i
$151$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$152$	−3.79835	+	1.08916i	−3.79835	+	1.08916i
$153$		0			0
$154$	−3.17985	+	1.15737i	−3.17985	+	1.15737i
$155$		0			0
$156$	1.10472	−	0.926973i	1.10472	−	0.926973i
$157$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.882948	−	0.469472i	$-0.844444\pi$
$157$	−1.49861	−	1.25748i	−1.49861	−	1.25748i	−0.615661	−	0.788011i	$-0.711111\pi$
$158$		0			0
$159$	0.465101	+	0.805578i	0.465101	+	0.805578i
$160$		0			0
$161$	−1.96249	−	0.714289i	−1.96249	−	0.714289i
$162$	−0.660852	−	0.240530i	−0.660852	−	0.240530i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	0.104019	+	0.180167i	0.104019	+	0.180167i
$165$		0			0
$166$	1.14507	+	0.960824i	1.14507	+	0.960824i
$167$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	−0.913545	−	0.406737i	$-0.866667\pi$
$167$	−0.671624	+	0.563559i	−0.671624	+	0.563559i	0.241922	+	0.970296i	$0.422222\pi$
$168$	0.563092	−	3.19345i	0.563092	−	3.19345i
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$		0			0
$171$	0.335746	+	0.688382i	0.335746	+	0.688382i
$172$		0			0
$173$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$173$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$174$		0			0
$175$	−1.29929	+	1.09023i	−1.29929	+	1.09023i
$176$	−3.75596	−	3.15163i	−3.75596	−	3.15163i
$177$		0			0
$178$		0			0
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$179$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$180$		0			0
$181$	−1.05094	−	0.382510i	−1.05094	−	0.382510i	−0.241922	−	0.970296i	$-0.577778\pi$
$181$	−1.05094	−	0.382510i	−1.05094	−	0.382510i	−0.809017	+	0.587785i	$0.800000\pi$
$182$	−1.69196	+	2.93057i	−1.69196	+	2.93057i
$183$		0			0
$184$	−0.844881	−	4.79156i	−0.844881	−	4.79156i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.44917			−1.44917
$190$		0			0
$191$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$191$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$192$	3.05996	−	1.11373i	3.05996	−	1.11373i
$193$	0.213817	−	1.21262i	0.213817	−	1.21262i	−0.669131	−	0.743145i	$-0.733333\pi$
$193$	0.213817	−	1.21262i	0.213817	−	1.21262i	0.882948	−	0.469472i	$-0.155556\pi$
$194$		0			0
$195$		0			0
$196$	0.971336	+	5.50872i	0.971336	+	5.50872i
$197$	0.559193	+	0.968551i	0.559193	+	0.968551i	0.997564	+	0.0697565i	$0.0222222\pi$
$197$	0.559193	+	0.968551i	0.559193	+	0.968551i	−0.438371	+	0.898794i	$0.644444\pi$
$198$	−0.764030	+	1.32334i	−0.764030	+	1.32334i
$199$	1.35192	+	0.492057i	1.35192	+	0.492057i	0.913545	−	0.406737i	$-0.133333\pi$
$199$	1.35192	+	0.492057i	1.35192	+	0.492057i	0.438371	+	0.898794i	$0.355556\pi$
$200$	−3.71312	−	1.35147i	−3.71312	−	1.35147i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	0.686157	−	3.89139i	0.686157	−	3.89139i
$207$	−0.886191	+	0.322547i	−0.886191	+	0.322547i
$208$	−4.90306			−4.90306
$209$	0.961262	−	0.275637i	0.961262	−	0.275637i
$210$		0			0
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$	0.995030	−	5.64310i	0.995030	−	5.64310i
$213$		0			0
$214$		0			0
$215$		0			0
$216$	−1.68808	−	2.92384i	−1.68808	−	2.92384i
$217$		0			0
$218$	−0.391941	−	0.142655i	−0.391941	−	0.142655i
$219$	0.735663	+	0.267759i	0.735663	+	0.267759i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$223$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$224$	−7.57588	+	6.35692i	−7.57588	+	6.35692i
$225$	−0.132996	+	0.754260i	−0.132996	+	0.754260i
$226$	−1.64372	+	0.598266i	−1.64372	+	0.598266i
$227$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$227$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$228$	−0.348879	+	1.39928i	−0.348879	+	1.39928i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$	−0.142504	+	0.808178i	−0.142504	+	0.808178i
$232$		0			0
$233$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$233$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$234$	0.265345	+	1.50484i	0.265345	+	1.50484i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.719340	+	1.24593i	−0.719340	+	1.24593i	0.241922	+	0.970296i	$0.422222\pi$
$239$	−0.719340	+	1.24593i	−0.719340	+	1.24593i	−0.961262	+	0.275637i	$0.911111\pi$
$240$		0			0
$241$	0.130100	+	0.737831i	0.130100	+	0.737831i	0.978148	+	0.207912i	$0.0666667\pi$
$241$	0.130100	+	0.737831i	0.130100	+	0.737831i	−0.848048	+	0.529919i	$0.822222\pi$
$242$	1.52836	+	1.28244i	1.52836	+	1.28244i
$243$	−0.785171	+	0.658837i	−0.785171	+	0.658837i
$244$		0			0
$245$		0			0
$246$	0.0673791			0.0673791
$247$	0.559193	−	0.829038i	0.559193	−	0.829038i
$248$		0			0
$249$	0.340641	−	0.123983i	0.340641	−	0.123983i
$250$		0			0
$251$	0.473442	−	0.397265i	0.473442	−	0.397265i	−0.374607	−	0.927184i	$-0.622222\pi$
$251$	0.473442	−	0.397265i	0.473442	−	0.397265i	0.848048	+	0.529919i	$0.177778\pi$
$252$	2.96598	+	2.48875i	2.96598	+	2.48875i
$253$	0.213817	+	1.21262i	0.213817	+	1.21262i
$254$		0			0
$255$		0			0
$256$	−7.91808	−	2.88195i	−7.91808	−	2.88195i
$257$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	0.0348995	−	0.999391i	$-0.488889\pi$
$257$	−0.580762	−	0.211380i	−0.580762	−	0.211380i	−0.615661	+	0.788011i	$0.711111\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$263$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$264$	−1.79657	+	0.653899i	−1.79657	+	0.653899i
$265$		0			0
$266$	−0.353717	−	3.36539i	−0.353717	−	3.36539i
$267$		0			0
$268$		0			0
$269$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	−0.978148	−	0.207912i	$-0.933333\pi$
$269$	0.0121205	−	0.0687386i	0.0121205	−	0.0687386i	0.990268	+	0.139173i	$0.0444444\pi$
$270$		0			0
$271$	−0.856733	−	0.718885i	−0.856733	−	0.718885i	0.104528	−	0.994522i	$-0.466667\pi$
$271$	−0.856733	−	0.718885i	−0.856733	−	0.718885i	−0.961262	+	0.275637i	$0.911111\pi$
$272$		0			0
$273$	0.410323	+	0.710700i	0.410323	+	0.710700i
$274$		0			0
$275$	0.939693	+	0.342020i	0.939693	+	0.342020i
$276$	−1.66862	−	0.607328i	−1.66862	−	0.607328i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.856733	+	0.718885i	−0.856733	+	0.718885i	−0.961262	−	0.275637i	$-0.911111\pi$
$281$	−0.856733	+	0.718885i	−0.856733	+	0.718885i	0.104528	+	0.994522i	$0.466667\pi$
$282$		0			0
$283$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$283$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$284$		0			0
$285$		0			0
$286$	1.99513			1.99513
$287$	−0.111246	+	0.0404903i	−0.111246	+	0.0404903i
$288$	−0.775476	+	4.39794i	−0.775476	+	4.39794i
$289$	0.766044	−	0.642788i	0.766044	−	0.642788i
$290$		0			0
$291$		0			0
$292$	−2.41130	−	4.17650i	−2.41130	−	4.17650i
$293$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$293$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$294$	1.70242	+	0.619630i	1.70242	+	0.619630i
$295$		0			0
$296$		0			0
$297$	0.427209	+	0.739947i	0.427209	+	0.739947i
$298$	−0.463641	−	2.62944i	−0.463641	−	2.62944i
$299$	0.943248	+	0.791479i	0.943248	+	0.791479i
$300$	−1.10472	+	0.926973i	−1.10472	+	0.926973i
$301$		0			0
$302$	−1.87481	+	0.682374i	−1.87481	+	0.682374i
$303$		0			0
$304$	3.96666	−	2.88195i	3.96666	−	2.88195i
$305$		0			0
$306$		0			0
$307$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$307$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$308$	3.87257	−	3.24947i	3.87257	−	3.24947i
$309$	−0.734077	−	0.615964i	−0.734077	−	0.615964i
$310$		0			0
$311$	0.241922	+	0.419021i	0.241922	+	0.419021i	0.961262	−	0.275637i	$-0.0888889\pi$
$311$	0.241922	+	0.419021i	0.241922	+	0.419021i	−0.719340	+	0.694658i	$0.755556\pi$
$312$	−0.955936	+	1.65573i	−0.955936	+	1.65573i
$313$	−1.25755	−	0.457712i	−1.25755	−	0.457712i	−0.374607	−	0.927184i	$-0.622222\pi$
$313$	−1.25755	−	0.457712i	−1.25755	−	0.457712i	−0.882948	+	0.469472i	$0.844444\pi$
$314$	3.66768	+	1.33492i	3.66768	+	1.33492i
$315$		0			0
$316$		0			0
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$	−1.42168	−	1.19293i	−1.42168	−	1.19293i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	4.16671			4.16671
$323$		0			0
$324$	1.05061			1.05061
$325$	0.939693	−	0.342020i	0.939693	−	0.342020i
$326$		0			0
$327$	−0.0774861	+	0.0650185i	−0.0774861	+	0.0650185i
$328$	−0.211279	−	0.177284i	−0.211279	−	0.177284i
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−2.09839	−	0.763750i	−2.09839	−	0.763750i
$333$		0			0
$334$	0.874607	−	1.51486i	0.874607	−	1.51486i
$335$		0			0
$336$	0.698704	+	3.96255i	0.698704	+	3.96255i
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	1.52836	−	1.28244i	1.52836	−	1.28244i
$339$	−0.0736627	+	0.417762i	−0.0736627	+	0.417762i
$340$		0			0
$341$		0			0
$342$	−1.09919	−	1.06148i	−1.09919	−	1.06148i
$343$	−1.48704			−1.48704
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$347$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.615661	+	0.788011i	$0.288889\pi$
$349$	0.990268	+	1.71519i	0.990268	+	1.71519i	0.374607	+	0.927184i	$0.377778\pi$
$350$	1.69196	−	2.93057i	1.69196	−	2.93057i
$351$	0.802890	+	0.292228i	0.802890	+	0.292228i
$352$	5.47917	+	1.99425i	5.47917	+	1.99425i
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.120321	−	0.682374i	0.120321	−	0.682374i
$359$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.848048	−	0.529919i	$-0.822222\pi$
$359$	−1.15707	+	0.421137i	−1.15707	+	0.421137i	−0.309017	+	0.951057i	$0.600000\pi$
$360$		0			0
$361$	0.0348995	+	0.999391i	0.0348995	+	0.999391i
$362$	2.23132			2.23132
$363$	0.454664	−	0.165484i	0.454664	−	0.165484i
$364$	0.877839	−	4.97847i	0.877839	−	4.97847i
$365$		0			0
$366$		0			0
$367$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	−0.719340	−	0.694658i	$-0.755556\pi$
$367$	−0.280969	−	1.59345i	−0.280969	−	1.59345i	0.438371	−	0.898794i	$-0.355556\pi$
$368$	3.01862	+	5.22841i	3.01862	+	5.22841i
$369$	−0.0267294	+	0.0462966i	−0.0267294	+	0.0462966i
$370$		0			0
$371$	3.06414	+	1.11525i	3.06414	+	1.11525i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	2.71692	−	0.988879i	2.71692	−	0.988879i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	0.391941	−	0.142655i	0.391941	−	0.142655i
$383$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$383$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$384$	−2.81569	+	2.36264i	−2.81569	+	2.36264i
$385$		0			0
$386$	0.426592	+	2.41933i	0.426592	+	2.41933i
$387$		0			0
$388$		0			0
$389$	−1.71690	−	0.624902i	−1.71690	−	0.624902i	−0.719340	−	0.694658i	$-0.755556\pi$
$389$	−1.71690	−	0.624902i	−1.71690	−	0.624902i	−0.997564	+	0.0697565i	$0.977778\pi$
$390$		0			0
$391$		0			0
$392$	−3.70790	−	6.42227i	−3.70790	−	6.42227i
$393$		0			0
$394$	−1.70929	−	1.43427i	−1.70929	−	1.43427i
$395$		0			0
$396$	0.396400	−	2.24810i	0.396400	−	2.24810i
$397$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$397$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$398$	−2.87035			−2.87035
$399$	−0.749697	−	0.333787i	−0.749697	−	0.333787i
$400$	4.90306			4.90306
$401$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$401$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$409$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	1.02506	+	5.81338i	1.02506	+	5.81338i
$413$		0			0
$414$	1.44134	−	1.20943i	1.44134	−	1.20943i
$415$		0			0
$416$	5.47917	−	1.99425i	5.47917	−	1.99425i
$417$		0			0
$418$	−1.61409	+	1.17271i	−1.61409	+	1.17271i
$419$	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		0.173648	−	0.984808i	$-0.444444\pi$
$421$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$422$		0			0
$423$		0			0
$424$	1.31915	+	7.48129i	1.31915	+	7.48129i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.241922	−	0.419021i	0.241922	−	0.419021i
$430$		0			0
$431$	−0.343916	−	1.95045i	−0.343916	−	1.95045i	−0.309017	−	0.951057i	$-0.600000\pi$
$431$	−0.343916	−	1.95045i	−0.343916	−	1.95045i	−0.0348995	−	0.999391i	$-0.511111\pi$
$432$	3.20916	+	2.69280i	3.20916	+	2.69280i
$433$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.997564	−	0.0697565i	$-0.977778\pi$
$433$	−1.10209	+	0.924765i	−1.10209	+	0.924765i	−0.104528	+	0.994522i	$0.533333\pi$
$434$		0			0
$435$		0			0
$436$	0.623102			0.623102
$437$	−1.22832	−	0.0858927i	−1.22832	−	0.0858927i
$438$	−1.56194			−1.56194
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	−1.10110	+	0.923935i	−1.10110	+	0.923935i
$442$		0			0
$443$	−0.130100	−	0.737831i	−0.130100	−	0.737831i	−0.978148	−	0.207912i	$-0.933333\pi$
$443$	−0.130100	−	0.737831i	−0.130100	−	0.737831i	0.848048	−	0.529919i	$-0.177778\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.608460	−	0.221461i	−0.608460	−	0.221461i
$448$	5.70749	−	9.88566i	5.70749	−	9.88566i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	−0.265345	−	1.50484i	−0.265345	−	1.50484i
$451$	0.0534691	+	0.0448659i	0.0534691	+	0.0448659i
$452$	2.00180	−	1.67971i	2.00180	−	1.67971i
$453$	−0.0840186	+	0.476493i	−0.0840186	+	0.476493i
$454$	−3.03350	+	1.10410i	−3.03350	+	1.10410i
$455$		0			0
$456$	−0.199845	−	1.90140i	−0.199845	−	1.90140i
$457$	1.43868			1.43868			0.719340	−	0.694658i	$-0.244444\pi$
$457$	1.43868			1.43868			0.719340	+	0.694658i	$0.244444\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.961262	−	0.275637i	$-0.911111\pi$
$461$	−1.39963	−	1.17443i	−1.39963	−	1.17443i	−0.438371	−	0.898794i	$-0.644444\pi$
$462$	−0.284313	−	1.61242i	−0.284313	−	1.61242i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$468$	−1.14139	−	1.97694i	−1.14139	−	1.97694i
$469$		0			0
$470$		0			0
$471$	0.725093	−	0.608425i	0.725093	−	0.608425i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.559193	+	0.829038i	−0.559193	+	0.829038i
$476$		0			0
$477$	1.38365	−	0.503608i	1.38365	−	0.503608i
$478$	0.498431	−	2.82674i	0.498431	−	2.82674i
$479$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$479$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$480$		0			0
$481$		0			0
$482$	−0.747388	−	1.29451i	−0.747388	−	1.29451i
$483$	0.505240	−	0.875101i	0.505240	−	0.875101i
$484$	−2.80079	−	1.01940i	−2.80079	−	1.01940i
$485$		0			0
$486$	1.02247	−	1.77097i	1.02247	−	1.77097i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$491$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$492$	−0.0945877	+	0.0344271i	−0.0945877	+	0.0344271i
$493$		0			0
$494$	−0.482665	+	1.93586i	−0.482665	+	1.93586i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.554033	+	0.464889i	−0.554033	+	0.464889i
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$		0			0
$501$	−0.212103	−	0.367373i	−0.212103	−	0.367373i
$502$	−0.616528	+	1.06786i	−0.616528	+	1.06786i
$503$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$503$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$504$	−4.82347	−	1.75560i	−4.82347	−	1.75560i
$505$		0			0
$506$	−1.22832	−	2.12752i	−1.22832	−	2.12752i
$507$	−0.0840186	−	0.476493i	−0.0840186	−	0.476493i
$508$		0			0
$509$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$509$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$510$		0			0
$511$	2.57884	−	0.938620i	2.57884	−	0.938620i
$512$	9.21474			9.21474
$513$	−0.821319	+	0.235509i	−0.821319	+	0.235509i
$514$	1.23306			1.23306
$515$		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	0.309017	−	0.951057i	$-0.400000\pi$
$521$	0.978148	−	1.69420i	0.978148	−	1.69420i	0.669131	−	0.743145i	$-0.266667\pi$
$522$		0			0
$523$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$523$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$524$		0			0
$525$	−0.410323	−	0.710700i	−0.410323	−	0.710700i
$526$		0			0
$527$		0			0
$528$	1.81730	−	1.52489i	1.81730	−	1.52489i
$529$	0.0896296	−	0.508315i	0.0896296	−	0.508315i
$530$		0			0
$531$		0			0
$532$	2.21609	+	4.54365i	2.21609	+	4.54365i
$533$	0.0697990			0.0697990
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.128724	−	0.108012i	−0.128724	−	0.108012i
$538$	0.0241819	+	0.137142i	0.0241819	+	0.137142i
$539$	0.938371	+	1.62531i	0.938371	+	1.62531i
$540$		0			0
$541$	−1.65940	−	0.603972i	−1.65940	−	0.603972i	−0.669131	−	0.743145i	$-0.733333\pi$
$541$	−1.65940	−	0.603972i	−1.65940	−	0.603972i	−0.990268	+	0.139173i	$0.955556\pi$
$542$	2.09676	+	0.763157i	2.09676	+	0.763157i
$543$	0.270562	−	0.468627i	0.270562	−	0.468627i
$544$		0			0
$545$		0			0
$546$	−1.25424	−	1.05243i	−1.25424	−	1.05243i
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$		0			0
$549$		0			0
$550$	−1.99513			−1.99513
$551$		0			0
$552$	2.35413			2.35413
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i	0.978148	−	0.207912i	$-0.0666667\pi$
$557$	−0.0121205	−	0.0687386i	−0.0121205	−	0.0687386i	−0.990268	+	0.139173i	$0.955556\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.11566	−	1.93238i	1.11566	−	1.93238i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.103817	+	0.588775i	−0.103817	+	0.588775i
$568$		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			$\pi$
$572$	−2.80079	+	1.01940i	−2.80079	+	1.01940i
$573$	0.0175647	−	0.0996142i	0.0175647	−	0.0996142i
$574$	0.180936	−	0.151823i	0.180936	−	0.151823i
$575$	−0.943248	−	0.791479i	−0.943248	−	0.791479i
$576$	−0.895085	−	5.07628i	−0.895085	−	5.07628i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.997564	+	1.72783i	−0.997564	+	1.72783i
$579$	0.559839	+	0.203765i	0.559839	+	0.203765i
$580$		0			0
$581$	0.635369	−	1.10049i	0.635369	−	1.10049i
$582$		0			0
$583$	−0.333843	−	1.89332i	−0.333843	−	1.89332i
$584$	4.89773	+	4.10969i	4.89773	+	4.10969i
$585$		0			0
$586$	−0.530793	+	3.01028i	−0.530793	+	3.01028i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	−2.70648			−2.70648
$589$		0			0
$590$		0			0
$591$	−0.508490	+	0.185075i	−0.508490	+	0.185075i
$592$		0			0
$593$	1.49861	−	1.25748i	1.49861	−	1.25748i	0.615661	−	0.788011i	$-0.288889\pi$
$593$	1.49861	−	1.25748i	1.49861	−	1.25748i	0.882948	−	0.469472i	$-0.155556\pi$
$594$	−1.30585	−	1.09574i	−1.30585	−	1.09574i
$595$		0			0
$596$	1.99437	+	3.45435i	1.99437	+	3.45435i
$597$	−0.348048	+	0.602837i	−0.348048	+	0.602837i
$598$	−2.30849	−	0.840223i	−2.30849	−	0.840223i
$599$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.961262	+	0.275637i	$0.0888889\pi$
$599$	1.87481	+	0.682374i	1.87481	+	0.682374i	0.913545	+	0.406737i	$0.133333\pi$
$600$	0.955936	−	1.65573i	0.955936	−	1.65573i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	2.28322	−	1.91585i	2.28322	−	1.91585i
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−3.26055	+	4.83396i	−3.26055	+	4.83396i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.671624	−	0.563559i	−0.671624	−	0.563559i	0.241922	−	0.970296i	$-0.422222\pi$
$613$	−0.671624	−	0.563559i	−0.671624	−	0.563559i	−0.913545	+	0.406737i	$0.866667\pi$
$614$	−0.120321	−	0.682374i	−0.120321	−	0.682374i
$615$		0			0
$616$	−3.35100	+	5.80410i	−3.35100	+	5.80410i
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	1.79657	+	0.653899i	1.79657	+	0.653899i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−0.182689	−	1.03608i	−0.182689	−	1.03608i
$622$	−0.739486	−	0.620502i	−0.739486	−	0.620502i
$623$		0			0
$624$	0.411948	−	2.33627i	0.411948	−	2.33627i
$625$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$626$	2.67000			2.67000
$627$	0.0505754	+	0.481193i	0.0505754	+	0.481193i
$628$	−5.83081			−5.83081
$629$		0			0
$630$		0			0
$631$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$631$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	2.60530	+	0.948250i	2.60530	+	0.948250i
$637$	1.76356	+	0.641884i	1.76356	+	0.641884i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.848048	+	0.529919i	$0.177778\pi$
$641$	1.51718	+	1.27306i	1.51718	+	1.27306i	0.669131	+	0.743145i	$0.266667\pi$
$642$		0			0
$643$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$643$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$644$	−5.84928	+	2.12897i	−5.84928	+	2.12897i
$645$		0			0
$646$		0			0
$647$	1.11839			1.11839			0.559193	−	0.829038i	$-0.311111\pi$
$647$	1.11839			1.11839			0.559193	+	0.829038i	$0.311111\pi$
$648$	−1.30884	+	0.476379i	−1.30884	+	0.476379i
$649$		0			0
$650$	−1.52836	+	1.28244i	−1.52836	+	1.28244i
$651$		0			0
$652$		0			0
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$653$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$654$	0.100904	−	0.174772i	0.100904	−	0.174772i
$655$		0			0
$656$	0.321590	+	0.117049i	0.321590	+	0.117049i
$657$	0.619622	−	1.07322i	0.619622	−	1.07322i
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$		0			0
$664$	2.96046			2.96046
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.453771	+	2.57346i	−0.453771	+	2.57346i
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−2.39251	−	4.14396i	−2.39251	−	4.14396i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−0.802890	−	0.292228i	−0.802890	−	0.292228i
$676$	−1.49027	+	2.58122i	−1.49027	+	2.58122i
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$	−0.146966	−	0.833488i	−0.146966	−	0.833488i
$679$		0			0
$680$		0			0
$681$	−0.135945	+	0.770982i	−0.135945	+	0.770982i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	2.08542	+	0.928490i	2.08542	+	0.928490i
$685$		0			0
$686$	2.78791	−	1.01472i	2.78791	−	1.01472i
$687$		0			0
$688$		0			0
$689$	−1.47274	−	1.23577i	−1.47274	−	1.23577i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$	1.22069	+	0.444295i	1.22069	+	0.444295i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−3.02697	−	2.53993i	−3.02697	−	2.53993i
$699$		0			0
$700$	−0.877839	+	4.97847i	−0.877839	+	4.97847i
$701$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$701$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$702$	−1.70467			−1.70467
$703$		0			0
$704$	−6.73015			−6.73015
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$709$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.179748	+	1.01940i	0.179748	+	1.01940i
$717$	−0.533241	−	0.447442i	−0.533241	−	0.447442i
$718$	1.88190	−	1.57910i	1.88190	−	1.57910i
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$720$		0			0
$721$	−3.35918			−3.35918
$722$	−0.747388	−	1.84985i	−0.747388	−	1.84985i
$723$	−0.362502			−0.362502
$724$	−3.13236	+	1.14009i	−3.13236	+	1.14009i
$725$		0			0
$726$	−0.739486	+	0.620502i	−0.739486	+	0.620502i
$727$	1.29929	+	1.09023i	1.29929	+	1.09023i	0.990268	+	0.139173i	$0.0444444\pi$
$727$	1.29929	+	1.09023i	1.29929	+	1.09023i	0.309017	+	0.951057i	$0.400000\pi$
$728$	1.16379	+	6.60018i	1.16379	+	6.60018i
$729$	−0.0717168	−	0.124217i	−0.0717168	−	0.124217i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	−0.990268	−	0.139173i	$-0.955556\pi$
$733$	−0.374607	+	0.648838i	−0.374607	+	0.648838i	0.615661	+	0.788011i	$0.288889\pi$
$734$	1.61409	+	2.79569i	1.61409	+	2.79569i
$735$		0			0
$736$	−5.49990	−	4.61496i	−5.49990	−	4.61496i
$737$		0			0
$738$	0.0185208	−	0.105037i	0.0185208	−	0.105037i
$739$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	−0.309017	−	0.951057i	$-0.600000\pi$
$739$	0.0655896	−	0.0238727i	0.0655896	−	0.0238727i	0.374607	+	0.927184i	$0.377778\pi$
$740$		0			0
$741$	0.348048	+	0.336106i	0.348048	+	0.336106i
$742$	−6.50568			−6.50568
$743$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$743$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0996426	−	0.565101i	−0.0996426	−	0.565101i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.71690	−	0.624902i	−1.71690	−	0.624902i	−0.719340	−	0.694658i	$-0.755556\pi$
$751$	−1.71690	−	0.624902i	−1.71690	−	0.624902i	−0.997564	+	0.0697565i	$0.977778\pi$
$752$		0			0
$753$	0.149516	+	0.258969i	0.149516	+	0.258969i
$754$		0			0
$755$		0			0
$756$	−3.30879	+	2.77640i	−3.30879	+	2.77640i
$757$	0.107320	−	0.608645i	0.107320	−	0.608645i	−0.882948	−	0.469472i	$-0.844444\pi$
$757$	0.107320	−	0.608645i	0.107320	−	0.608645i	0.990268	−	0.139173i	$-0.0444444\pi$
$758$		0			0
$759$	−0.595768			−0.595768
$760$		0			0
$761$	1.76590			1.76590			0.882948	−	0.469472i	$-0.155556\pi$
$761$	1.76590			1.76590			0.882948	+	0.469472i	$0.155556\pi$
$762$		0			0
$763$	−0.0615723	+	0.349194i	−0.0615723	+	0.349194i
$764$	−0.477324	+	0.400522i	−0.477324	+	0.400522i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	2.03849	−	3.53077i	2.03849	−	3.53077i
$769$	0.0655896	+	0.0238727i	0.0655896	+	0.0238727i	0.374607	−	0.927184i	$-0.377778\pi$
$769$	0.0655896	+	0.0238727i	0.0655896	+	0.0238727i	−0.309017	+	0.951057i	$0.600000\pi$
$770$		0			0
$771$	0.149516	−	0.258969i	0.149516	−	0.258969i
$772$	−1.83500	−	3.17832i	−1.83500	−	3.17832i
$773$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$773$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	3.64528			3.64528
$779$	−0.0564686	+	0.0410268i	−0.0564686	+	0.0410268i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	7.04897	+	5.91479i	7.04897	+	5.91479i
$785$		0			0
$786$		0			0
$787$	0.848048	−	1.46886i	0.848048	−	1.46886i	−0.0348995	−	0.999391i	$-0.511111\pi$
$787$	0.848048	−	1.46886i	0.848048	−	1.46886i	0.882948	−	0.469472i	$-0.155556\pi$
$788$	3.13236	+	1.14009i	3.13236	+	1.14009i
$789$		0			0
$790$		0			0
$791$	0.743520	+	1.28781i	0.743520	+	1.28781i
$792$	0.525525	+	2.98040i	0.525525	+	2.98040i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	4.02944	−	1.46659i	4.02944	−	1.46659i
$797$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$797$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$798$	1.63330	+	0.114212i	1.63330	+	0.114212i
$799$		0			0
$800$	−5.47917	+	1.99425i	−5.47917	+	1.99425i
$801$		0			0
$802$		0			0
$803$	−1.23949	−	1.04005i	−1.23949	−	1.04005i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.0317351	+	0.0115506i	0.0317351	+	0.0115506i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	0.306644	+	1.73907i	0.306644	+	1.73907i	0.615661	+	0.788011i	$0.288889\pi$
$811$	0.306644	+	1.73907i	0.306644	+	1.73907i	−0.309017	+	0.951057i	$0.600000\pi$
$812$		0			0
$813$	0.414525	−	0.347828i	0.414525	−	0.347828i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	3.74961			3.74961
$819$	1.22069	−	0.444295i	1.22069	−	0.444295i
$820$		0			0
$821$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$821$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$822$		0			0
$823$	0.107320	+	0.608645i	0.107320	+	0.608645i	0.990268	+	0.139173i	$0.0444444\pi$
$823$	0.107320	+	0.608645i	0.107320	+	0.608645i	−0.882948	+	0.469472i	$0.844444\pi$
$824$	−3.91297	−	6.77746i	−3.91297	−	6.77746i
$825$	−0.241922	+	0.419021i	−0.241922	+	0.419021i
$826$		0			0
$827$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.997564	−	0.0697565i	$-0.0222222\pi$
$827$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.719340	+	0.694658i	$0.244444\pi$
$828$	−1.40542	+	2.43426i	−1.40542	+	2.43426i
$829$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$829$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$830$		0			0
$831$		0			0
$832$	−5.15559	+	4.32606i	−5.15559	+	4.32606i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	1.66669	−	2.47098i	1.66669	−	2.47098i
$837$		0			0
$838$	−2.50898	+	0.913195i	−2.50898	+	0.913195i
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$		0			0
$843$	−0.270562	−	0.468627i	−0.270562	−	0.468627i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.848048	−	1.46886i	0.848048	−	1.46886i
$848$	−4.71312	−	8.16337i	−4.71312	−	8.16337i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.913545	+	0.406737i	$0.866667\pi$
$853$	−1.87481	+	0.682374i	−1.87481	+	0.682374i	−0.961262	+	0.275637i	$0.911111\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$857$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$858$	−0.167628	+	0.950665i	−0.167628	+	0.950665i
$859$	0.856733	−	0.718885i	0.856733	−	0.718885i	−0.104528	−	0.994522i	$-0.533333\pi$
$859$	0.856733	−	0.718885i	0.856733	−	0.718885i	0.961262	+	0.275637i	$0.0888889\pi$
$860$		0			0
$861$	−0.00994661	−	0.0564100i	−0.00994661	−	0.0564100i
$862$	1.97571	+	3.42203i	1.97571	+	3.42203i
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	−4.68150	−	1.70393i	−4.68150	−	1.70393i
$865$		0			0
$866$	1.43518	−	2.48580i	1.43518	−	2.48580i
$867$	0.241922	+	0.419021i	0.241922	+	0.419021i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.776254	+	0.282533i	−0.776254	+	0.282533i
$873$		0			0
$874$	2.36148	−	0.677144i	2.36148	−	0.677144i
$875$		0			0
$876$	2.19267	−	0.798066i	2.19267	−	0.798066i
$877$	0.280969	−	1.59345i	0.280969	−	1.59345i	−0.438371	−	0.898794i	$-0.644444\pi$
$877$	0.280969	−	1.59345i	0.280969	−	1.59345i	0.719340	−	0.694658i	$-0.244444\pi$
$878$		0			0
$879$	0.567862	+	0.476493i	0.567862	+	0.476493i
$880$		0			0
$881$	−0.961262	−	1.66495i	−0.961262	−	1.66495i	−0.719340	−	0.694658i	$-0.755556\pi$
$881$	−0.961262	−	1.66495i	−0.961262	−	1.66495i	−0.241922	−	0.970296i	$-0.577778\pi$
$882$	1.43389	−	2.48356i	1.43389	−	2.48356i
$883$	0.454664	+	0.165484i	0.454664	+	0.165484i	0.559193	−	0.829038i	$-0.311111\pi$
$883$	0.454664	+	0.165484i	0.454664	+	0.165484i	−0.104528	+	0.994522i	$0.533333\pi$
$884$		0			0
$885$		0			0
$886$	0.747388	+	1.29451i	0.747388	+	1.29451i
$887$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$887$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.331233	−	0.120559i	0.331233	−	0.120559i
$892$		0			0
$893$		0			0
$894$	1.29186			1.29186
$895$		0			0
$896$	−2.23741	+	12.6890i	−2.23741	+	12.6890i
$897$	−0.456385	+	0.382952i	−0.456385	+	0.382952i
$898$		0			0
$899$		0			0
$900$	1.14139	+	1.97694i	1.14139	+	1.97694i
$901$		0			0
$902$	−0.130860	−	0.0476290i	−0.130860	−	0.0476290i
$903$		0			0
$904$	−1.73219	+	3.00024i	−1.73219	+	3.00024i
$905$		0			0
$906$	−0.167628	−	0.950665i	−0.167628	−	0.950665i
$907$	0.473442	+	0.397265i	0.473442	+	0.397265i	0.848048	−	0.529919i	$-0.177778\pi$
$907$	0.473442	+	0.397265i	0.473442	+	0.397265i	−0.374607	+	0.927184i	$0.622222\pi$
$908$	3.69433	−	3.09991i	3.69433	−	3.09991i
$909$		0			0
$910$		0			0
$911$	−1.23132			−1.23132			−0.615661	−	0.788011i	$-0.711111\pi$
$911$	−1.23132			−1.23132			−0.615661	+	0.788011i	$0.711111\pi$
$912$	1.03995	+	2.13222i	1.03995	+	2.13222i
$913$	−0.749213			−0.749213
$914$	−2.69725	+	0.981718i	−2.69725	+	0.981718i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$	−0.157903	−	0.0574721i	−0.157903	−	0.0574721i
$922$	3.42544	+	1.24676i	3.42544	+	1.24676i
$923$		0			0
$924$	1.22298	+	2.11827i	1.22298	+	2.11827i
$925$		0			0
$926$		0			0
$927$	−1.16200	+	0.975034i	−1.16200	+	0.975034i
$928$		0			0
$929$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$929$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$930$		0			0
$931$	−1.80404	+	0.517300i	−1.80404	+	0.517300i
$932$		0			0
$933$	−0.219987	+	0.0800686i	−0.219987	+	0.0800686i
$934$	−0.651114	+	3.69265i	−0.651114	+	3.69265i
$935$		0			0
$936$	2.31834	+	1.94532i	2.31834	+	1.94532i
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$		0			0
$939$	0.323755	−	0.560760i	0.323755	−	0.560760i
$940$		0			0
$941$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.997564	−	0.0697565i	$-0.0222222\pi$
$941$	1.71690	+	0.624902i	1.71690	+	0.624902i	0.719340	+	0.694658i	$0.244444\pi$
$942$	−0.944236	+	1.63546i	−0.944236	+	1.63546i
$943$	−0.0429726	−	0.0744306i	−0.0429726	−	0.0744306i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$947$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$948$		0			0
$949$	−1.61803			−1.61803
$950$	0.482665	−	1.93586i	0.482665	−	1.93586i
$951$		0			0
$952$		0			0
$953$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$953$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$954$	−2.25043	+	1.88834i	−2.25043	+	1.88834i
$955$		0			0
$956$	0.744610	+	4.22289i	0.744610	+	4.22289i
$957$		0			0
$958$	1.52836	−	2.64719i	1.52836	−	2.64719i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	1.71062	+	1.43538i	1.71062	+	1.43538i
$965$		0			0
$966$	−0.350081	+	1.98541i	−0.350081	+	1.98541i
$967$	0.823868	−	0.299864i	0.823868	−	0.299864i	0.104528	−	0.994522i	$-0.466667\pi$
$967$	0.823868	−	0.299864i	0.823868	−	0.299864i	0.719340	+	0.694658i	$0.244444\pi$
$968$	3.95142			3.95142
$969$		0			0
$970$		0			0
$971$	−1.71690	+	0.624902i	−1.71690	+	0.624902i	−0.997564	−	0.0697565i	$-0.977778\pi$
$971$	−1.71690	+	0.624902i	−1.71690	+	0.624902i	−0.719340	+	0.694658i	$0.755556\pi$
$972$	−0.530487	+	3.00854i	−0.530487	+	3.00854i
$973$		0			0
$974$		0			0
$975$	0.0840186	+	0.476493i	0.0840186	+	0.476493i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.0800578	+	0.138664i	0.0800578	+	0.138664i
$982$		0			0
$983$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$983$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$984$	0.102226	−	0.0857779i	0.102226	−	0.0857779i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.311551	−	2.96421i	−0.311551	−	2.96421i
$989$		0			0
$990$		0			0
$991$	0.333843	−	1.89332i	0.333843	−	1.89332i	−0.104528	−	0.994522i	$-0.533333\pi$
$991$	0.333843	−	1.89332i	0.333843	−	1.89332i	0.438371	−	0.898794i	$-0.355556\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.540225	−	0.935698i	0.540225	−	0.935698i
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2717.1.db.c.1715.1	yes	24
11.10	odd	2		2717.1.db.d.1715.4	yes	24
13.12	even	2		2717.1.db.d.1715.4	yes	24
19.4	even	9	inner	2717.1.db.c.1429.1	✓	24
143.142	odd	2	CM	2717.1.db.c.1715.1	yes	24
209.175	odd	18		2717.1.db.d.1429.4	yes	24
247.194	even	18		2717.1.db.d.1429.4	yes	24
2717.1429	odd	18	inner	2717.1.db.c.1429.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2717.1.db.c.1429.1	✓	24	19.4	even	9	inner
2717.1.db.c.1429.1	✓	24	2717.1429	odd	18	inner
2717.1.db.c.1715.1	yes	24	1.1	even	1	trivial
2717.1.db.c.1715.1	yes	24	143.142	odd	2	CM
2717.1.db.d.1429.4	yes	24	209.175	odd	18
2717.1.db.d.1429.4	yes	24	247.194	even	18
2717.1.db.d.1715.4	yes	24	11.10	odd	2
2717.1.db.d.1715.4	yes	24	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.87481 + 0.682374i) q^{2} +(-0.0840186 + 0.476493i) q^{3} +(2.28322 - 1.91585i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(0.848048 + 1.46886i) q^{7} +(-1.97571 + 3.42203i) q^{8} +(0.719706 + 0.261952i) q^{9} +O(q^{10})\)	\(q+(-1.87481 + 0.682374i) q^{2} +(-0.0840186 + 0.476493i) q^{3} +(2.28322 - 1.91585i) q^{4} +(-0.167628 - 0.950665i) q^{6} +(0.848048 + 1.46886i) q^{7} +(-1.97571 + 3.42203i) q^{8} +(0.719706 + 0.261952i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.721057 + 1.24891i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(-2.59224 - 2.17515i) q^{14} +(0.851407 - 4.82857i) q^{16} -1.52806 q^{18} +(0.719340 + 0.694658i) q^{19} +(-0.771155 + 0.280677i) q^{21} +(-0.346450 + 1.96482i) q^{22} +(-0.943248 + 0.791479i) q^{23} +(-1.46458 - 1.22893i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.997564 + 1.72783i) q^{26} +(-0.427209 + 0.739947i) q^{27} +(4.75041 + 1.72901i) q^{28} +(1.01251 + 5.74223i) q^{32} +(0.370646 + 0.311009i) q^{33} +(2.14511 - 0.780756i) q^{36} +(-1.82264 - 0.811492i) q^{38} +0.483844 q^{39} +(-0.0121205 + 0.0687386i) q^{41} +(1.25424 - 1.05243i) q^{42} +(-0.517565 - 2.93526i) q^{44} +(1.22832 - 2.12752i) q^{46} +(2.22925 + 0.811379i) q^{48} +(-0.938371 + 1.62531i) q^{49} +(-0.997564 - 1.72783i) q^{50} +(-2.28322 - 1.91585i) q^{52} +(1.47274 - 1.23577i) q^{53} +(0.296013 - 1.67877i) q^{54} -6.70199 q^{56} +(-0.391438 + 0.284396i) q^{57} +(0.225575 + 1.27930i) q^{63} +(-3.36508 - 5.82848i) q^{64} +(-0.907114 - 0.330162i) q^{66} +(-0.297884 - 0.515950i) q^{69} +(-2.31834 + 1.94532i) q^{72} +(0.280969 - 1.59345i) q^{73} -0.483844 q^{75} +(2.97328 + 0.207912i) q^{76} +1.69610 q^{77} +(-0.907114 + 0.330162i) q^{78} +(0.270023 + 0.226577i) q^{81} +(-0.0241819 - 0.137142i) q^{82} +(-0.374607 - 0.648838i) q^{83} +(-1.22298 + 2.11827i) q^{84} +(1.97571 + 3.42203i) q^{88} +(1.29929 - 1.09023i) q^{91} +(-0.637289 + 3.61425i) q^{92} -2.82120 q^{96} +(0.650198 - 3.68746i) q^{98} +(0.586710 - 0.492308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 24 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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