LMFDB - Embedded newform 1564.1.w.c.1291.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1564,1,Mod(271,1564)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1564, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

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

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

chi := DirichletCharacter("1564.271");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1564 = 2^{2} \cdot 17 \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1564.w (of order $22$, degree $10$, 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:	$0.780537679758$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{22}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{22} - \cdots)$

Embedding invariants

Embedding label			1291.1
Root			$-0.989821 - 0.142315i$ of defining polynomial
Character	$\chi$	$=$	1564.1291
Dual form			1564.1.w.c.951.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-0.449181 + 0.983568i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.03748 - 0.304632i) q^{6} +(0.474017 - 0.304632i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.110783 - 0.127850i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-0.449181 + 0.983568i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.03748 - 0.304632i) q^{6} +(0.474017 - 0.304632i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.110783 - 0.127850i) q^{9} +(-0.258908 + 1.80075i) q^{11} +(0.153882 - 1.07028i) q^{12} +(1.61435 + 1.03748i) q^{13} +(0.368991 + 0.425839i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-0.959493 - 0.281733i) q^{17} +(0.110783 - 0.127850i) q^{18} +(0.0867074 + 0.603063i) q^{21} -1.81926 q^{22} +(-0.281733 + 0.959493i) q^{23} +1.08128 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.797176 + 1.74557i) q^{26} +(-0.861971 + 0.253098i) q^{27} +(-0.368991 + 0.425839i) q^{28} +(-0.755750 - 1.65486i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.65486 - 1.06351i) q^{33} +(0.142315 - 0.989821i) q^{34} +(0.142315 + 0.0914602i) q^{36} +(-1.74557 + 1.12181i) q^{39} +(-0.584585 + 0.171650i) q^{42} +(-0.258908 - 1.80075i) q^{44} +(-0.989821 - 0.142315i) q^{46} +(0.153882 + 1.07028i) q^{48} +(-0.283524 + 0.620830i) q^{49} +(0.959493 - 0.281733i) q^{50} +(0.708089 - 0.817178i) q^{51} +(-1.84125 - 0.540641i) q^{52} +(0.698939 - 0.449181i) q^{53} +(-0.373193 - 0.817178i) q^{54} +(-0.474017 - 0.304632i) q^{56} +(1.53046 - 0.983568i) q^{62} +(-0.0914602 - 0.0268551i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.817178 - 1.78937i) q^{66} +1.00000 q^{68} +(-0.817178 - 0.708089i) q^{69} +(-0.0702757 + 0.153882i) q^{72} +(1.03748 + 0.304632i) q^{75} +(0.425839 + 0.932456i) q^{77} +(-1.35881 - 1.56815i) q^{78} +(1.66538 + 1.07028i) q^{79} +(0.162317 - 1.12894i) q^{81} +(-0.253098 - 0.554206i) q^{84} +(1.74557 - 0.512546i) q^{88} +(-0.345139 + 0.755750i) q^{89} +1.08128 q^{91} -1.00000i q^{92} +1.96714 q^{93} +(-1.03748 + 0.304632i) q^{96} +(-0.654861 - 0.192284i) q^{98} +(0.258908 - 0.166390i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 + 2 * q^9	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} + 4 q^{13} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 22 q^{33} + 2 q^{34} + 2 q^{36} - 22 q^{42} + 2 q^{49} + 2 q^{50} - 18 q^{52} - 4 q^{53} - 2 q^{64} + 20 q^{68} + 20 q^{72} - 2 q^{81} - 18 q^{89} - 2 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 + 2 * q^9 + 4 * q^13 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 22 * q^33 + 2 * q^34 + 2 * q^36 - 22 * q^42 + 2 * q^49 + 2 * q^50 - 18 * q^52 - 4 * q^53 - 2 * q^64 + 20 * q^68 + 20 * q^72 - 2 * q^81 - 18 * q^89 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1564\mathbb{Z}\right)^\times$.

$n$	$783$	$921$	$1293$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.142315	+	0.989821i	0.142315	+	0.989821i
$2$	0.142315	+	0.989821i	0.142315	+	0.989821i
$3$	−0.449181	+	0.983568i	−0.449181	+	0.983568i	0.540641	+	0.841254i	$0.318182\pi$
$3$	−0.449181	+	0.983568i	−0.449181	+	0.983568i	−0.989821	+	0.142315i	$0.954545\pi$
$4$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$5$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$5$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$6$	−1.03748	−	0.304632i	−1.03748	−	0.304632i
$7$	0.474017	−	0.304632i	0.474017	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$7$	0.474017	−	0.304632i	0.474017	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$8$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$9$	−0.110783	−	0.127850i	−0.110783	−	0.127850i
$10$		0			0
$11$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	0.281733	+	0.959493i	$0.409091\pi$
$11$	−0.258908	+	1.80075i	−0.258908	+	1.80075i	−0.540641	+	0.841254i	$0.681818\pi$
$12$	0.153882	−	1.07028i	0.153882	−	1.07028i
$13$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$13$	1.61435	+	1.03748i	1.61435	+	1.03748i	0.654861	+	0.755750i	$0.272727\pi$
$14$	0.368991	+	0.425839i	0.368991	+	0.425839i
$15$		0			0
$16$	0.841254	−	0.540641i	0.841254	−	0.540641i
$17$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$17$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$18$	0.110783	−	0.127850i	0.110783	−	0.127850i
$19$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$19$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$20$		0			0
$21$	0.0867074	+	0.603063i	0.0867074	+	0.603063i
$22$	−1.81926			−1.81926
$23$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$23$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$24$	1.08128			1.08128
$25$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$26$	−0.797176	+	1.74557i	−0.797176	+	1.74557i
$27$	−0.861971	+	0.253098i	−0.861971	+	0.253098i
$28$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$29$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$29$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$30$		0			0
$31$	−0.755750	−	1.65486i	−0.755750	−	1.65486i	−0.755750	−	0.654861i	$-0.772727\pi$
$31$	−0.755750	−	1.65486i	−0.755750	−	1.65486i		−	1.00000i	$-0.5\pi$
$32$	0.654861	+	0.755750i	0.654861	+	0.755750i
$33$	−1.65486	−	1.06351i	−1.65486	−	1.06351i
$34$	0.142315	−	0.989821i	0.142315	−	0.989821i
$35$		0			0
$36$	0.142315	+	0.0914602i	0.142315	+	0.0914602i
$37$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$37$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$38$		0			0
$39$	−1.74557	+	1.12181i	−1.74557	+	1.12181i
$40$		0			0
$41$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$41$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$42$	−0.584585	+	0.171650i	−0.584585	+	0.171650i
$43$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$43$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$44$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$45$		0			0
$46$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.153882	+	1.07028i	0.153882	+	1.07028i
$49$	−0.283524	+	0.620830i	−0.283524	+	0.620830i
$50$	0.959493	−	0.281733i	0.959493	−	0.281733i
$51$	0.708089	−	0.817178i	0.708089	−	0.817178i
$52$	−1.84125	−	0.540641i	−1.84125	−	0.540641i
$53$	0.698939	−	0.449181i	0.698939	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$53$	0.698939	−	0.449181i	0.698939	−	0.449181i	0.841254	+	0.540641i	$0.181818\pi$
$54$	−0.373193	−	0.817178i	−0.373193	−	0.817178i
$55$		0			0
$56$	−0.474017	−	0.304632i	−0.474017	−	0.304632i
$57$		0			0
$58$		0			0
$59$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$59$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$60$		0			0
$61$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$61$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$62$	1.53046	−	0.983568i	1.53046	−	0.983568i
$63$	−0.0914602	−	0.0268551i	−0.0914602	−	0.0268551i
$64$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$65$		0			0
$66$	0.817178	−	1.78937i	0.817178	−	1.78937i
$67$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$67$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$68$	1.00000			1.00000
$69$	−0.817178	−	0.708089i	−0.817178	−	0.708089i
$70$		0			0
$71$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$71$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$72$	−0.0702757	+	0.153882i	−0.0702757	+	0.153882i
$73$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$73$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$74$		0			0
$75$	1.03748	+	0.304632i	1.03748	+	0.304632i
$76$		0			0
$77$	0.425839	+	0.932456i	0.425839	+	0.932456i
$78$	−1.35881	−	1.56815i	−1.35881	−	1.56815i
$79$	1.66538	+	1.07028i	1.66538	+	1.07028i	0.909632	+	0.415415i	$0.136364\pi$
$79$	1.66538	+	1.07028i	1.66538	+	1.07028i	0.755750	+	0.654861i	$0.227273\pi$
$80$		0			0
$81$	0.162317	−	1.12894i	0.162317	−	1.12894i
$82$		0			0
$83$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$83$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$84$	−0.253098	−	0.554206i	−0.253098	−	0.554206i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	1.74557	−	0.512546i	1.74557	−	0.512546i
$89$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	0.654861	+	0.755750i	$0.272727\pi$
$89$	−0.345139	+	0.755750i	−0.345139	+	0.755750i	−1.00000			$\pi$
$90$		0			0
$91$	1.08128			1.08128
$92$		−	1.00000i		−	1.00000i
$93$	1.96714			1.96714
$94$		0			0
$95$		0			0
$96$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$97$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$97$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$98$	−0.654861	−	0.192284i	−0.654861	−	0.192284i
$99$	0.258908	−	0.166390i	0.258908	−	0.166390i
$100$	0.415415	+	0.909632i	0.415415	+	0.909632i
$101$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$101$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$102$	0.909632	+	0.584585i	0.909632	+	0.584585i
$103$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$103$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$104$	0.273100	−	1.89945i	0.273100	−	1.89945i
$105$		0			0
$106$	0.544078	+	0.627899i	0.544078	+	0.627899i
$107$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$107$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$108$	0.755750	−	0.485691i	0.755750	−	0.485691i
$109$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$109$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$110$		0			0
$111$		0			0
$112$	0.234072	−	0.512546i	0.234072	−	0.512546i
$113$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$113$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.0462003	−	0.321330i	−0.0462003	−	0.321330i
$118$		0			0
$119$	−0.540641	+	0.158746i	−0.540641	+	0.158746i
$120$		0			0
$121$	−2.21616	−	0.650724i	−2.21616	−	0.650724i
$122$		0			0
$123$		0			0
$124$	1.19136	+	1.37491i	1.19136	+	1.37491i
$125$		0			0
$126$	0.0135656	−	0.0943511i	0.0135656	−	0.0943511i
$127$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$127$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$128$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$129$		0			0
$130$		0			0
$131$	1.27155	−	0.817178i	1.27155	−	0.817178i	0.281733	−	0.959493i	$-0.409091\pi$
$131$	1.27155	−	0.817178i	1.27155	−	0.817178i	0.989821	+	0.142315i	$0.0454545\pi$
$132$	1.88745	+	0.554206i	1.88745	+	0.554206i
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.142315	+	0.989821i	0.142315	+	0.989821i
$137$	0.284630			0.284630			0.142315	−	0.989821i	$-0.454545\pi$
$137$	0.284630			0.284630			0.142315	+	0.989821i	$0.454545\pi$
$138$	0.584585	−	0.909632i	0.584585	−	0.909632i
$139$	1.51150			1.51150			0.755750	−	0.654861i	$-0.227273\pi$
$139$	1.51150			1.51150			0.755750	+	0.654861i	$0.227273\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.28621	+	2.63843i	−2.28621	+	2.63843i
$144$	−0.162317	−	0.0476607i	−0.162317	−	0.0476607i
$145$		0			0
$146$		0			0
$147$	−0.483276	−	0.557730i	−0.483276	−	0.557730i
$148$		0			0
$149$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	0.415415	+	0.909632i	$0.363636\pi$
$149$	−0.239446	+	1.66538i	−0.239446	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$150$	−0.153882	+	1.07028i	−0.153882	+	1.07028i
$151$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$151$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$152$		0			0
$153$	0.0702757	+	0.153882i	0.0702757	+	0.153882i
$154$	−0.862362	+	0.554206i	−0.862362	+	0.554206i
$155$		0			0
$156$	1.35881	−	1.56815i	1.35881	−	1.56815i
$157$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.959493	−	0.281733i	$-0.909091\pi$
$157$	−1.61435	+	0.474017i	−1.61435	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$158$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$159$	0.127850	+	0.889217i	0.127850	+	0.889217i
$160$		0			0
$161$	0.158746	+	0.540641i	0.158746	+	0.540641i
$162$	1.14055			1.14055
$163$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i	−0.989821	−	0.142315i	$-0.954545\pi$
$163$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.989821	+	0.142315i	$0.0454545\pi$
$167$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$168$	0.512546	−	0.329393i	0.512546	−	0.329393i
$169$	1.11435	+	2.44009i	1.11435	+	2.44009i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$173$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$174$		0			0
$175$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$176$	0.755750	+	1.65486i	0.755750	+	1.65486i
$177$		0			0
$178$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$179$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$179$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$180$		0			0
$181$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$181$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$182$	0.153882	+	1.07028i	0.153882	+	1.07028i
$183$		0			0
$184$	0.989821	−	0.142315i	0.989821	−	0.142315i
$185$		0			0
$186$	0.279953	+	1.94711i	0.279953	+	1.94711i
$187$	0.755750	−	1.65486i	0.755750	−	1.65486i
$188$		0			0
$189$	−0.331487	+	0.382557i	−0.331487	+	0.382557i
$190$		0			0
$191$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$191$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$192$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$193$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$193$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$194$		0			0
$195$		0			0
$196$	0.0971309	−	0.675560i	0.0971309	−	0.675560i
$197$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$197$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$198$	0.201543	+	0.232593i	0.201543	+	0.232593i
$199$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	−0.989821	−	0.142315i	$-0.954545\pi$
$199$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$200$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$201$		0			0
$202$	0.186393	−	0.215109i	0.186393	−	0.215109i
$203$		0			0
$204$	−0.449181	+	0.983568i	−0.449181	+	0.983568i
$205$		0			0
$206$		0			0
$207$	0.153882	−	0.0702757i	0.153882	−	0.0702757i
$208$	1.91899			1.91899
$209$		0			0
$210$		0			0
$211$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$211$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$212$	−0.544078	+	0.627899i	−0.544078	+	0.627899i
$213$		0			0
$214$	1.27155	−	0.817178i	1.27155	−	0.817178i
$215$		0			0
$216$	0.588302	+	0.678936i	0.588302	+	0.678936i
$217$	−0.862362	−	0.554206i	−0.862362	−	0.554206i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.25667	−	1.45027i	−1.25667	−	1.45027i
$222$		0			0
$223$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$223$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$224$	0.540641	+	0.158746i	0.540641	+	0.158746i
$225$	−0.110783	+	0.127850i	−0.110783	+	0.127850i
$226$		0			0
$227$	0.449181	−	0.983568i	0.449181	−	0.983568i	−0.540641	−	0.841254i	$-0.681818\pi$
$227$	0.449181	−	0.983568i	0.449181	−	0.983568i	0.989821	−	0.142315i	$-0.0454545\pi$
$228$		0			0
$229$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$229$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$230$		0			0
$231$	−1.10841			−1.10841
$232$		0			0
$233$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$233$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$234$	0.311485	−	0.0914602i	0.311485	−	0.0914602i
$235$		0			0
$236$		0			0
$237$	−1.80075	+	1.15727i	−1.80075	+	1.15727i
$238$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$239$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$239$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$240$		0			0
$241$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$241$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$242$	0.328708	−	2.28621i	0.328708	−	2.28621i
$243$	0.281733	+	0.181059i	0.281733	+	0.181059i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	−1.19136	+	1.37491i	−1.19136	+	1.37491i
$249$		0			0
$250$		0			0
$251$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$251$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$252$	0.0953214			0.0953214
$253$	−1.65486	−	0.755750i	−1.65486	−	0.755750i
$254$		0			0
$255$		0			0
$256$	0.415415	−	0.909632i	0.415415	−	0.909632i
$257$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$257$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.989821	+	1.14231i	0.989821	+	1.14231i
$263$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$263$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$264$	−0.279953	+	1.94711i	−0.279953	+	1.94711i
$265$		0			0
$266$		0			0
$267$	−0.588302	−	0.678936i	−0.588302	−	0.678936i
$268$		0			0
$269$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$269$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$270$		0			0
$271$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$271$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$272$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$273$	−0.485691	+	1.06351i	−0.485691	+	1.06351i
$274$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$275$	1.81926			1.81926
$276$	0.983568	+	0.449181i	0.983568	+	0.449181i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	0.215109	+	1.49611i	0.215109	+	1.49611i
$279$	−0.127850	+	0.279953i	−0.127850	+	0.279953i
$280$		0			0
$281$	0.857685	−	0.989821i	0.857685	−	0.989821i	−0.142315	−	0.989821i	$-0.545455\pi$
$281$	0.857685	−	0.989821i	0.857685	−	0.989821i	1.00000			$0$
$282$		0			0
$283$	−1.66538	+	1.07028i	−1.66538	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$283$	−1.66538	+	1.07028i	−1.66538	+	1.07028i	−0.909632	+	0.415415i	$0.863636\pi$
$284$		0			0
$285$		0			0
$286$	−2.93694	−	1.88745i	−2.93694	−	1.88745i
$287$		0			0
$288$	0.0240754	−	0.167448i	0.0240754	−	0.167448i
$289$	0.841254	+	0.540641i	0.841254	+	0.540641i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	0.415415	−	0.909632i	$-0.363636\pi$
$293$	0.273100	+	0.0801894i	0.273100	+	0.0801894i	−0.142315	+	0.989821i	$0.545455\pi$
$294$	0.483276	−	0.557730i	0.483276	−	0.557730i
$295$		0			0
$296$		0			0
$297$	−0.232593	−	1.61772i	−0.232593	−	1.61772i
$298$	−1.68251			−1.68251
$299$	−1.45027	+	1.25667i	−1.45027	+	1.25667i
$300$	−1.08128			−1.08128
$301$		0			0
$302$		0			0
$303$	0.295298	−	0.0867074i	0.295298	−	0.0867074i
$304$		0			0
$305$		0			0
$306$	−0.142315	+	0.0914602i	−0.142315	+	0.0914602i
$307$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$307$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$308$	−0.671292	−	0.774713i	−0.671292	−	0.774713i
$309$		0			0
$310$		0			0
$311$	0.0801894	−	0.557730i	0.0801894	−	0.557730i	−0.909632	−	0.415415i	$-0.863636\pi$
$311$	0.0801894	−	0.557730i	0.0801894	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$312$	1.74557	+	1.12181i	1.74557	+	1.12181i
$313$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$313$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$314$	−0.698939	−	1.53046i	−0.698939	−	1.53046i
$315$		0			0
$316$	−1.89945	−	0.557730i	−1.89945	−	0.557730i
$317$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$317$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$318$	−0.861971	+	0.253098i	−0.861971	+	0.253098i
$319$		0			0
$320$		0			0
$321$	1.63436			1.63436
$322$	−0.512546	+	0.234072i	−0.512546	+	0.234072i
$323$		0			0
$324$	0.162317	+	1.12894i	0.162317	+	1.12894i
$325$	0.797176	−	1.74557i	0.797176	−	1.74557i
$326$	0.540641	−	0.158746i	0.540641	−	0.158746i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$331$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$332$		0			0
$333$		0			0
$334$	−0.281733	+	1.95949i	−0.281733	+	1.95949i
$335$		0			0
$336$	0.398983	+	0.460451i	0.398983	+	0.460451i
$337$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$337$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$338$	−2.25667	+	1.45027i	−2.25667	+	1.45027i
$339$		0			0
$340$		0			0
$341$	3.17565	−	0.932456i	3.17565	−	0.932456i
$342$		0			0
$343$	0.134919	+	0.938384i	0.134919	+	0.938384i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.258908	+	1.80075i	0.258908	+	1.80075i	0.540641	+	0.841254i	$0.318182\pi$
$347$	0.258908	+	1.80075i	0.258908	+	1.80075i	−0.281733	+	0.959493i	$0.590909\pi$
$348$		0			0
$349$	1.84125	−	0.540641i	1.84125	−	0.540641i	0.841254	−	0.540641i	$-0.181818\pi$
$349$	1.84125	−	0.540641i	1.84125	−	0.540641i	1.00000			$0$
$350$	0.368991	−	0.425839i	0.368991	−	0.425839i
$351$	−1.65411	−	0.485691i	−1.65411	−	0.485691i
$352$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$353$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$353$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$354$		0			0
$355$		0			0
$356$	0.118239	−	0.822373i	0.118239	−	0.822373i
$357$	0.0867074	−	0.603063i	0.0867074	−	0.603063i
$358$		0			0
$359$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$359$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$360$		0			0
$361$	0.841254	−	0.540641i	0.841254	−	0.540641i
$362$		0			0
$363$	1.63549	−	1.88745i	1.63549	−	1.88745i
$364$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$365$		0			0
$366$		0			0
$367$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$367$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$368$	0.281733	+	0.959493i	0.281733	+	0.959493i
$369$		0			0
$370$		0			0
$371$	0.194474	−	0.425839i	0.194474	−	0.425839i
$372$	−1.88745	+	0.554206i	−1.88745	+	0.554206i
$373$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	−0.841254	−	0.540641i	$-0.818182\pi$
$373$	−0.186393	+	0.215109i	−0.186393	+	0.215109i	0.654861	+	0.755750i	$0.272727\pi$
$374$	1.74557	+	0.512546i	1.74557	+	0.512546i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−0.425839	−	0.273670i	−0.425839	−	0.273670i
$379$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$379$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$383$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$384$	0.909632	−	0.584585i	0.909632	−	0.584585i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.239446	+	1.66538i	0.239446	+	1.66538i	0.654861	+	0.755750i	$0.272727\pi$
$389$	0.239446	+	1.66538i	0.239446	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$390$		0			0
$391$	0.540641	−	0.841254i	0.540641	−	0.841254i
$392$	0.682507			0.682507
$393$	0.232593	+	1.61772i	0.232593	+	1.61772i
$394$		0			0
$395$		0			0
$396$	−0.201543	+	0.232593i	−0.201543	+	0.232593i
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$	0.909632	−	0.584585i	0.909632	−	0.584585i
$399$		0			0
$400$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$401$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$401$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$402$		0			0
$403$	0.496841	−	3.45561i	0.496841	−	3.45561i
$404$	0.239446	+	0.153882i	0.239446	+	0.153882i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.03748	−	0.304632i	−1.03748	−	0.304632i
$409$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$409$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$410$		0			0
$411$	−0.127850	+	0.279953i	−0.127850	+	0.279953i
$412$		0			0
$413$		0			0
$414$	0.0914602	+	0.142315i	0.0914602	+	0.142315i
$415$		0			0
$416$	0.273100	+	1.89945i	0.273100	+	1.89945i
$417$	−0.678936	+	1.48666i	−0.678936	+	1.48666i
$418$		0			0
$419$	1.19136	−	1.37491i	1.19136	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$419$	1.19136	−	1.37491i	1.19136	−	1.37491i	0.909632	−	0.415415i	$-0.136364\pi$
$420$		0			0
$421$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−0.415415	+	0.909632i	$0.636364\pi$
$421$	−1.41542	+	0.909632i	−1.41542	+	0.909632i	−1.00000			$\pi$
$422$	0.822373	+	1.80075i	0.822373	+	1.80075i
$423$		0			0
$424$	−0.698939	−	0.449181i	−0.698939	−	0.449181i
$425$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$426$		0			0
$427$		0			0
$428$	0.989821	+	1.14231i	0.989821	+	1.14231i
$429$	−1.56815	−	3.43378i	−1.56815	−	3.43378i
$430$		0			0
$431$	−1.03748	−	0.304632i	−1.03748	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$431$	−1.03748	−	0.304632i	−1.03748	−	0.304632i	−0.755750	+	0.654861i	$0.772727\pi$
$432$	−0.588302	+	0.678936i	−0.588302	+	0.678936i
$433$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.841254	−	0.540641i	$-0.818182\pi$
$433$	−1.25667	+	0.368991i	−1.25667	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$434$	0.425839	−	0.932456i	0.425839	−	0.932456i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.258908	−	1.80075i	−0.258908	−	1.80075i	−0.540641	−	0.841254i	$-0.681818\pi$
$439$	−0.258908	−	1.80075i	−0.258908	−	1.80075i	0.281733	−	0.959493i	$-0.409091\pi$
$440$		0			0
$441$	0.110783	−	0.0325288i	0.110783	−	0.0325288i
$442$	1.25667	−	1.45027i	1.25667	−	1.45027i
$443$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$443$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.53046	−	0.983568i	−1.53046	−	0.983568i
$448$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i
$449$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$449$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$450$	−0.142315	−	0.0914602i	−0.142315	−	0.0914602i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.03748	+	0.304632i	1.03748	+	0.304632i
$455$		0			0
$456$		0			0
$457$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$457$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$458$	0.273100	+	1.89945i	0.273100	+	1.89945i
$459$	0.898361			0.898361
$460$		0			0
$461$	−1.30972			−1.30972			−0.654861	−	0.755750i	$-0.727273\pi$
$461$	−1.30972			−1.30972			−0.654861	+	0.755750i	$0.727273\pi$
$462$	−0.157744	−	1.09713i	−0.157744	−	1.09713i
$463$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$463$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$467$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$468$	0.134858	+	0.295298i	0.134858	+	0.295298i
$469$		0			0
$470$		0			0
$471$	0.258908	−	1.80075i	0.258908	−	1.80075i
$472$		0			0
$473$		0			0
$474$	−1.40176	−	1.61772i	−1.40176	−	1.61772i
$475$		0			0
$476$	0.474017	−	0.304632i	0.474017	−	0.304632i
$477$	−0.134858	−	0.0395979i	−0.134858	−	0.0395979i
$478$		0			0
$479$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$479$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.603063	−	0.0867074i	−0.603063	−	0.0867074i
$484$	2.30972			2.30972
$485$		0			0
$486$	−0.139121	+	0.304632i	−0.139121	+	0.304632i
$487$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$487$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$488$		0			0
$489$	0.584585	+	0.171650i	0.584585	+	0.171650i
$490$		0			0
$491$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$491$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−1.53046	−	0.983568i	−1.53046	−	0.983568i
$497$		0			0
$498$		0			0
$499$	0.474017	−	0.304632i	0.474017	−	0.304632i	−0.281733	−	0.959493i	$-0.590909\pi$
$499$	0.474017	−	0.304632i	0.474017	−	0.304632i	0.755750	+	0.654861i	$0.227273\pi$
$500$		0			0
$501$	−1.40176	+	1.61772i	−1.40176	+	1.61772i
$502$		0			0
$503$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$503$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$504$	0.0135656	+	0.0943511i	0.0135656	+	0.0943511i
$505$		0			0
$506$	0.512546	−	1.74557i	0.512546	−	1.74557i
$507$	−2.90055			−2.90055
$508$		0			0
$509$	0.345139	−	0.755750i	0.345139	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$509$	0.345139	−	0.755750i	0.345139	−	0.755750i	1.00000			$0$
$510$		0			0
$511$		0			0
$512$	0.959493	+	0.281733i	0.959493	+	0.281733i
$513$		0			0
$514$	0.698939	+	1.53046i	0.698939	+	1.53046i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$521$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$522$		0			0
$523$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$523$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$524$	−0.989821	+	1.14231i	−0.989821	+	1.14231i
$525$	0.584585	−	0.171650i	0.584585	−	0.171650i
$526$		0			0
$527$	0.258908	+	1.80075i	0.258908	+	1.80075i
$528$	−1.96714			−1.96714
$529$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.588302	−	0.678936i	0.588302	−	0.678936i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.04455	−	0.671292i	−1.04455	−	0.671292i
$540$		0			0
$541$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$541$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$542$		0			0
$543$		0			0
$544$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$545$		0			0
$546$	−1.12181	−	0.329393i	−1.12181	−	0.329393i
$547$	−1.29639	+	1.49611i	−1.29639	+	1.49611i	−0.540641	+	0.841254i	$0.681818\pi$
$547$	−1.29639	+	1.49611i	−1.29639	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$548$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i
$549$		0			0
$550$	0.258908	+	1.80075i	0.258908	+	1.80075i
$551$		0			0
$552$	−0.304632	+	1.03748i	−0.304632	+	1.03748i
$553$	1.11546			1.11546
$554$		0			0
$555$		0			0
$556$	−1.45027	+	0.425839i	−1.45027	+	0.425839i
$557$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	0.142315	+	0.989821i	$0.454545\pi$
$557$	−0.857685	+	0.989821i	−0.857685	+	0.989821i	−1.00000			$\pi$
$558$	−0.295298	−	0.0867074i	−0.295298	−	0.0867074i
$559$		0			0
$560$		0			0
$561$	1.28820	+	1.48666i	1.28820	+	1.48666i
$562$	1.10181	+	0.708089i	1.10181	+	0.708089i
$563$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$563$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$564$		0			0
$565$		0			0
$566$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$567$	−0.266971	−	0.584585i	−0.266971	−	0.584585i
$568$		0			0
$569$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$569$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$570$		0			0
$571$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$571$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$572$	1.45027	−	3.17565i	1.45027	−	3.17565i
$573$		0			0
$574$		0			0
$575$	0.989821	+	0.142315i	0.989821	+	0.142315i
$576$	0.169170			0.169170
$577$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	0.959493	−	0.281733i	$-0.0909091\pi$
$577$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i	−1.00000			$\pi$
$578$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.627899	+	1.37491i	0.627899	+	1.37491i
$584$		0			0
$585$		0			0
$586$	−0.0405070	+	0.281733i	−0.0405070	+	0.281733i
$587$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$587$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$588$	0.620830	+	0.398983i	0.620830	+	0.398983i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$593$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$594$	1.56815	−	0.460451i	1.56815	−	0.460451i
$595$		0			0
$596$	−0.239446	−	1.66538i	−0.239446	−	1.66538i
$597$	1.16917			1.16917
$598$	−1.45027	−	1.25667i	−1.45027	−	1.25667i
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.153882	−	1.07028i	−0.153882	−	1.07028i
$601$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$601$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	0.127850	+	0.279953i	0.127850	+	0.279953i
$607$	−1.29639	−	1.49611i	−1.29639	−	1.49611i	−0.755750	−	0.654861i	$-0.772727\pi$
$607$	−1.29639	−	1.49611i	−1.29639	−	1.49611i	−0.540641	−	0.841254i	$-0.681818\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.110783	−	0.127850i	−0.110783	−	0.127850i
$613$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$613$	−0.118239	−	0.258908i	−0.118239	−	0.258908i	−0.959493	+	0.281733i	$0.909091\pi$
$614$		0			0
$615$		0			0
$616$	0.671292	−	0.774713i	0.671292	−	0.774713i
$617$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$617$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$618$		0			0
$619$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	−0.755750	−	0.654861i	$-0.772727\pi$
$619$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	0.540641	−	0.841254i	$-0.318182\pi$
$620$		0			0
$621$		−	0.898361i		−	0.898361i
$622$	0.563465			0.563465
$623$	0.0666238	+	0.463379i	0.0666238	+	0.463379i
$624$	−0.861971	+	1.88745i	−0.861971	+	1.88745i
$625$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$626$		0			0
$627$		0			0
$628$	1.41542	−	0.909632i	1.41542	−	0.909632i
$629$		0			0
$630$		0			0
$631$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$631$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$632$	0.281733	−	1.95949i	0.281733	−	1.95949i
$633$	−0.304632	+	2.11876i	−0.304632	+	2.11876i
$634$		0			0
$635$		0			0
$636$	−0.373193	−	0.817178i	−0.373193	−	0.817178i
$637$	−1.10181	+	0.708089i	−1.10181	+	0.708089i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$641$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$642$	0.232593	+	1.61772i	0.232593	+	1.61772i
$643$	−0.563465			−0.563465			−0.281733	−	0.959493i	$-0.590909\pi$
$643$	−0.563465			−0.563465			−0.281733	+	0.959493i	$0.590909\pi$
$644$	−0.304632	−	0.474017i	−0.304632	−	0.474017i
$645$		0			0
$646$		0			0
$647$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$647$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$648$	−1.09435	+	0.321330i	−1.09435	+	0.321330i
$649$		0			0
$650$	1.84125	+	0.540641i	1.84125	+	0.540641i
$651$	0.932456	−	0.599253i	0.932456	−	0.599253i
$652$	0.234072	+	0.512546i	0.234072	+	0.512546i
$653$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$653$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$659$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$660$		0			0
$661$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$661$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$662$		0			0
$663$	1.99091	−	0.584585i	1.99091	−	0.584585i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.97964			−1.97964
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.398983	+	0.460451i	−0.398983	+	0.460451i
$673$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$673$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$674$		0			0
$675$	0.373193	+	0.817178i	0.373193	+	0.817178i
$676$	−1.75667	−	2.02730i	−1.75667	−	2.02730i
$677$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$677$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.765644	+	0.883600i	0.765644	+	0.883600i
$682$	1.37491	+	3.01063i	1.37491	+	3.01063i
$683$	−1.66538	+	1.07028i	−1.66538	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$683$	−1.66538	+	1.07028i	−1.66538	+	1.07028i	−0.909632	+	0.415415i	$0.863636\pi$
$684$		0			0
$685$		0			0
$686$	−0.909632	+	0.267092i	−0.909632	+	0.267092i
$687$	−0.861971	+	1.88745i	−0.861971	+	1.88745i
$688$		0			0
$689$	1.59435			1.59435
$690$		0			0
$691$	−0.563465			−0.563465			−0.281733	−	0.959493i	$-0.590909\pi$
$691$	−0.563465			−0.563465			−0.281733	+	0.959493i	$0.590909\pi$
$692$		0			0
$693$	0.0720391	−	0.157744i	0.0720391	−	0.157744i
$694$	−1.74557	+	0.512546i	−1.74557	+	0.512546i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.797176	+	1.74557i	0.797176	+	1.74557i
$699$		0			0
$700$	0.474017	+	0.304632i	0.474017	+	0.304632i
$701$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	0.142315	+	0.989821i	$0.454545\pi$
$701$	−0.273100	+	1.89945i	−0.273100	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$702$	0.245343	−	1.70640i	0.245343	−	1.70640i
$703$		0			0
$704$	−1.19136	−	1.37491i	−1.19136	−	1.37491i
$705$		0			0
$706$	1.10181	−	0.708089i	1.10181	−	0.708089i
$707$	−0.153882	−	0.0451840i	−0.153882	−	0.0451840i
$708$		0			0
$709$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$709$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$710$		0			0
$711$	−0.0476607	−	0.331487i	−0.0476607	−	0.331487i
$712$	0.830830			0.830830
$713$	1.80075	−	0.258908i	1.80075	−	0.258908i
$714$	0.609264			0.609264
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.540641	−	0.158746i	−0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$719$	−0.540641	−	0.158746i	−0.540641	−	0.158746i	−0.540641	+	0.841254i	$0.681818\pi$
$720$		0			0
$721$		0			0
$722$	0.654861	+	0.755750i	0.654861	+	0.755750i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	2.10100	+	1.35023i	2.10100	+	1.35023i
$727$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$727$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$728$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$729$	0.654861	−	0.420853i	0.654861	−	0.420853i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.142315	+	0.989821i	$0.545455\pi$
$733$	−0.797176	+	1.74557i	−0.797176	+	1.74557i	−0.654861	+	0.755750i	$0.727273\pi$
$734$	−0.215109	−	1.49611i	−0.215109	−	1.49611i
$735$		0			0
$736$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$737$		0			0
$738$		0			0
$739$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$739$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$740$		0			0
$741$		0			0
$742$	0.449181	+	0.131891i	0.449181	+	0.131891i
$743$	−0.909632	+	0.584585i	−0.909632	+	0.584585i	−0.909632	−	0.415415i	$-0.863636\pi$
$743$	−0.909632	+	0.584585i	−0.909632	+	0.584585i			1.00000i	$0.5\pi$
$744$	−0.817178	−	1.78937i	−0.817178	−	1.78937i
$745$		0			0
$746$	−0.239446	−	0.153882i	−0.239446	−	0.153882i
$747$		0			0
$748$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$749$	−0.716476	−	0.460451i	−0.716476	−	0.460451i
$750$		0			0
$751$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	0.755750	−	0.654861i	$-0.227273\pi$
$751$	−0.234072	−	0.512546i	−0.234072	−	0.512546i	−0.989821	+	0.142315i	$0.954545\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.210281	−	0.460451i	0.210281	−	0.460451i
$757$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$757$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$758$	−1.51150			−1.51150
$759$	1.48666	−	1.28820i	1.48666	−	1.28820i
$760$		0			0
$761$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	−0.415415	−	0.909632i	$-0.636364\pi$
$761$	−0.273100	−	1.89945i	−0.273100	−	1.89945i	0.142315	−	0.989821i	$-0.454545\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.708089	+	0.817178i	0.708089	+	0.817178i
$769$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−0.415415	−	0.909632i	$-0.636364\pi$
$769$	−1.41542	−	0.909632i	−1.41542	−	0.909632i	−1.00000			$\pi$
$770$		0			0
$771$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$772$		0			0
$773$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	0.654861	−	0.755750i	$-0.272727\pi$
$773$	−0.186393	−	0.215109i	−0.186393	−	0.215109i	−0.841254	+	0.540641i	$0.818182\pi$
$774$		0			0
$775$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$776$		0			0
$777$		0			0
$778$	−1.61435	+	0.474017i	−1.61435	+	0.474017i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	0.909632	+	0.415415i	0.909632	+	0.415415i
$783$		0			0
$784$	0.0971309	+	0.675560i	0.0971309	+	0.675560i
$785$		0			0
$786$	−1.56815	+	0.460451i	−1.56815	+	0.460451i
$787$	0.368991	−	0.425839i	0.368991	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$787$	0.368991	−	0.425839i	0.368991	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.258908	−	0.166390i	−0.258908	−	0.166390i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.708089	+	0.817178i	0.708089	+	0.817178i
$797$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.654861	−	0.755750i	$-0.727273\pi$
$797$	−0.797176	−	1.74557i	−0.797176	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$798$		0			0
$799$		0			0
$800$	0.654861	−	0.755750i	0.654861	−	0.755750i
$801$	0.134858	−	0.0395979i	0.134858	−	0.0395979i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	3.49114			3.49114
$807$		0			0
$808$	−0.118239	+	0.258908i	−0.118239	+	0.258908i
$809$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$809$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$810$		0			0
$811$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$811$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.153882	−	1.07028i	0.153882	−	1.07028i
$817$		0			0
$818$	0.239446	+	0.153882i	0.239446	+	0.153882i
$819$	−0.119787	−	0.138242i	−0.119787	−	0.138242i
$820$		0			0
$821$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$821$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$822$	−0.295298	−	0.0867074i	−0.295298	−	0.0867074i
$823$	0.989821	−	1.14231i	0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$823$	0.989821	−	1.14231i	0.989821	−	1.14231i	0.989821	−	0.142315i	$-0.0454545\pi$
$824$		0			0
$825$	−0.817178	+	1.78937i	−0.817178	+	1.78937i
$826$		0			0
$827$	−1.97964			−1.97964			−0.989821	−	0.142315i	$-0.954545\pi$
$827$	−1.97964			−1.97964			−0.989821	+	0.142315i	$0.954545\pi$
$828$	−0.127850	+	0.110783i	−0.127850	+	0.110783i
$829$	0.830830			0.830830			0.415415	−	0.909632i	$-0.363636\pi$
$829$	0.830830			0.830830			0.415415	+	0.909632i	$0.363636\pi$
$830$		0			0
$831$		0			0
$832$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$833$	0.446947	−	0.515804i	0.446947	−	0.515804i
$834$	−1.56815	−	0.460451i	−1.56815	−	0.460451i
$835$		0			0
$836$		0			0
$837$	1.07028	+	1.23516i	1.07028	+	1.23516i
$838$	1.53046	+	0.983568i	1.53046	+	0.983568i
$839$	0.215109	−	1.49611i	0.215109	−	1.49611i	−0.540641	−	0.841254i	$-0.681818\pi$
$839$	0.215109	−	1.49611i	0.215109	−	1.49611i	0.755750	−	0.654861i	$-0.227273\pi$
$840$		0			0
$841$	0.841254	+	0.540641i	0.841254	+	0.540641i
$842$	−1.10181	−	1.27155i	−1.10181	−	1.27155i
$843$	0.588302	+	1.28820i	0.588302	+	1.28820i
$844$	−1.66538	+	1.07028i	−1.66538	+	1.07028i
$845$		0			0
$846$		0			0
$847$	−1.24873	+	0.366660i	−1.24873	+	0.366660i
$848$	0.345139	−	0.755750i	0.345139	−	0.755750i
$849$	−0.304632	−	2.11876i	−0.304632	−	2.11876i
$850$	−1.00000			−1.00000
$851$		0			0
$852$		0			0
$853$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$853$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$854$		0			0
$855$		0			0
$856$	−0.989821	+	1.14231i	−0.989821	+	1.14231i
$857$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$857$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$858$	3.17565	−	2.04087i	3.17565	−	2.04087i
$859$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$859$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$860$		0			0
$861$		0			0
$862$	0.153882	−	1.07028i	0.153882	−	1.07028i
$863$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$863$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$864$	−0.755750	−	0.485691i	−0.755750	−	0.485691i
$865$		0			0
$866$	−0.544078	−	1.19136i	−0.544078	−	1.19136i
$867$	−0.909632	+	0.584585i	−0.909632	+	0.584585i
$868$	0.983568	+	0.288802i	0.983568	+	0.288802i
$869$	−2.35848	+	2.72183i	−2.35848	+	2.72183i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$877$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$878$	1.74557	−	0.512546i	1.74557	−	0.512546i
$879$	−0.201543	+	0.232593i	−0.201543	+	0.232593i
$880$		0			0
$881$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$881$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$882$	0.0479637	+	0.105026i	0.0479637	+	0.105026i
$883$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$883$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$884$	1.61435	+	1.03748i	1.61435	+	1.03748i
$885$		0			0
$886$		0			0
$887$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$887$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.99091	+	0.584585i	1.99091	+	0.584585i
$892$		0			0
$893$		0			0
$894$	0.755750	−	1.65486i	0.755750	−	1.65486i
$895$		0			0
$896$	−0.563465			−0.563465
$897$	−0.584585	−	1.99091i	−0.584585	−	1.99091i
$898$		0			0
$899$		0			0
$900$	0.0702757	−	0.153882i	0.0702757	−	0.153882i
$901$	−0.797176	+	0.234072i	−0.797176	+	0.234072i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.909632	+	0.584585i	0.909632	+	0.584585i	0.909632	−	0.415415i	$-0.136364\pi$
$907$	0.909632	+	0.584585i	0.909632	+	0.584585i			1.00000i	$0.5\pi$
$908$	−0.153882	+	1.07028i	−0.153882	+	1.07028i
$909$	−0.00685257	+	0.0476607i	−0.00685257	+	0.0476607i
$910$		0			0
$911$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.755750	+	0.654861i	$0.227273\pi$
$911$	1.29639	+	1.49611i	1.29639	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$912$		0			0
$913$		0			0
$914$	1.84125	+	0.540641i	1.84125	+	0.540641i
$915$		0			0
$916$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$917$	0.353799	−	0.774713i	0.353799	−	0.774713i
$918$	0.127850	+	0.889217i	0.127850	+	0.889217i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−0.186393	−	1.29639i	−0.186393	−	1.29639i
$923$		0			0
$924$	1.06351	−	0.312276i	1.06351	−	0.312276i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$929$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	0.512546	+	0.329393i	0.512546	+	0.329393i
$934$		0			0
$935$		0			0
$936$	−0.273100	+	0.175511i	−0.273100	+	0.175511i
$937$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$937$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$941$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$942$	1.81926			1.81926
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$947$	1.45027	−	0.425839i	1.45027	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$948$	1.40176	−	1.61772i	1.40176	−	1.61772i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.368991	+	0.425839i	0.368991	+	0.425839i
$953$	−1.68251	−	1.08128i	−1.68251	−	1.08128i	−0.841254	−	0.540641i	$-0.818182\pi$
$953$	−1.68251	−	1.08128i	−1.68251	−	1.08128i	−0.841254	−	0.540641i	$-0.818182\pi$
$954$	0.0200026	−	0.139121i	0.0200026	−	0.139121i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.134919	−	0.0867074i	0.134919	−	0.0867074i
$960$		0			0
$961$	−1.51255	+	1.74557i	−1.51255	+	1.74557i
$962$		0			0
$963$	−0.106222	+	0.232593i	−0.106222	+	0.232593i
$964$		0			0
$965$		0			0
$966$		−	0.609264i		−	0.609264i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.328708	+	2.28621i	0.328708	+	2.28621i
$969$		0			0
$970$		0			0
$971$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$971$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$972$	−0.321330	−	0.0943511i	−0.321330	−	0.0943511i
$973$	0.716476	−	0.460451i	0.716476	−	0.460451i
$974$	0.234072	+	0.512546i	0.234072	+	0.512546i
$975$	1.35881	+	1.56815i	1.35881	+	1.56815i
$976$		0			0
$977$	0.186393	−	1.29639i	0.186393	−	1.29639i	−0.654861	−	0.755750i	$-0.727273\pi$
$977$	0.186393	−	1.29639i	0.186393	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$978$	−0.0867074	+	0.603063i	−0.0867074	+	0.603063i
$979$	−1.27155	−	0.817178i	−1.27155	−	0.817178i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.03748	+	0.304632i	1.03748	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$983$	1.03748	+	0.304632i	1.03748	+	0.304632i	0.281733	+	0.959493i	$0.409091\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.281733	+	1.95949i	0.281733	+	1.95949i	0.281733	+	0.959493i	$0.409091\pi$
$991$	0.281733	+	1.95949i	0.281733	+	1.95949i			1.00000i	$0.500000\pi$
$992$	0.755750	−	1.65486i	0.755750	−	1.65486i
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$997$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$998$	0.368991	+	0.425839i	0.368991	+	0.425839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1564.1.w.c.1291.1	yes	20
4.3	odd	2	inner	1564.1.w.c.1291.2	yes	20
17.16	even	2	inner	1564.1.w.c.1291.2	yes	20
23.8	even	11	inner	1564.1.w.c.951.1	✓	20
68.67	odd	2	CM	1564.1.w.c.1291.1	yes	20
92.31	odd	22	inner	1564.1.w.c.951.2	yes	20
391.169	even	22	inner	1564.1.w.c.951.2	yes	20
1564.951	odd	22	inner	1564.1.w.c.951.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1564.1.w.c.951.1	✓	20	23.8	even	11	inner
1564.1.w.c.951.1	✓	20	1564.951	odd	22	inner
1564.1.w.c.951.2	yes	20	92.31	odd	22	inner
1564.1.w.c.951.2	yes	20	391.169	even	22	inner
1564.1.w.c.1291.1	yes	20	1.1	even	1	trivial
1564.1.w.c.1291.1	yes	20	68.67	odd	2	CM
1564.1.w.c.1291.2	yes	20	4.3	odd	2	inner
1564.1.w.c.1291.2	yes	20	17.16	even	2	inner

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:	\( N \)	\(=\)	\( 1564 = 2^{2} \cdot 17 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1564.w (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.449181 + 0.983568i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.03748 - 0.304632i) q^{6} +(0.474017 - 0.304632i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.110783 - 0.127850i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.449181 + 0.983568i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.03748 - 0.304632i) q^{6} +(0.474017 - 0.304632i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.110783 - 0.127850i) q^{9} +(-0.258908 + 1.80075i) q^{11} +(0.153882 - 1.07028i) q^{12} +(1.61435 + 1.03748i) q^{13} +(0.368991 + 0.425839i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-0.959493 - 0.281733i) q^{17} +(0.110783 - 0.127850i) q^{18} +(0.0867074 + 0.603063i) q^{21} -1.81926 q^{22} +(-0.281733 + 0.959493i) q^{23} +1.08128 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-0.797176 + 1.74557i) q^{26} +(-0.861971 + 0.253098i) q^{27} +(-0.368991 + 0.425839i) q^{28} +(-0.755750 - 1.65486i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-1.65486 - 1.06351i) q^{33} +(0.142315 - 0.989821i) q^{34} +(0.142315 + 0.0914602i) q^{36} +(-1.74557 + 1.12181i) q^{39} +(-0.584585 + 0.171650i) q^{42} +(-0.258908 - 1.80075i) q^{44} +(-0.989821 - 0.142315i) q^{46} +(0.153882 + 1.07028i) q^{48} +(-0.283524 + 0.620830i) q^{49} +(0.959493 - 0.281733i) q^{50} +(0.708089 - 0.817178i) q^{51} +(-1.84125 - 0.540641i) q^{52} +(0.698939 - 0.449181i) q^{53} +(-0.373193 - 0.817178i) q^{54} +(-0.474017 - 0.304632i) q^{56} +(1.53046 - 0.983568i) q^{62} +(-0.0914602 - 0.0268551i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(0.817178 - 1.78937i) q^{66} +1.00000 q^{68} +(-0.817178 - 0.708089i) q^{69} +(-0.0702757 + 0.153882i) q^{72} +(1.03748 + 0.304632i) q^{75} +(0.425839 + 0.932456i) q^{77} +(-1.35881 - 1.56815i) q^{78} +(1.66538 + 1.07028i) q^{79} +(0.162317 - 1.12894i) q^{81} +(-0.253098 - 0.554206i) q^{84} +(1.74557 - 0.512546i) q^{88} +(-0.345139 + 0.755750i) q^{89} +1.08128 q^{91} -1.00000i q^{92} +1.96714 q^{93} +(-1.03748 + 0.304632i) q^{96} +(-0.654861 - 0.192284i) q^{98} +(0.258908 - 0.166390i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 + 2 * q^9	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{8} + 2 q^{9} + 4 q^{13} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 22 q^{33} + 2 q^{34} + 2 q^{36} - 22 q^{42} + 2 q^{49} + 2 q^{50} - 18 q^{52} - 4 q^{53} - 2 q^{64} + 20 q^{68} + 20 q^{72} - 2 q^{81} - 18 q^{89} - 2 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^8 + 2 * q^9 + 4 * q^13 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 2 * q^25 - 4 * q^26 + 2 * q^32 - 22 * q^33 + 2 * q^34 + 2 * q^36 - 22 * q^42 + 2 * q^49 + 2 * q^50 - 18 * q^52 - 4 * q^53 - 2 * q^64 + 20 * q^68 + 20 * q^72 - 2 * q^81 - 18 * q^89 - 2 * q^98

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