LMFDB - Embedded newform 2565.1.dy.d.2374.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2565,1,Mod(94,2565)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2565, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8, 9, 9])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2565.94"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 2565 = 3^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2565.dy (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.28010175740$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{72})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{12} + 1 $ x^24 - x^12 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{36}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{36} - \cdots)$

Embedding invariants

Embedding label			2374.4
Root			$0.0871557 - 0.996195i$ of defining polynomial
Character	$\chi$	$=$	2565.2374
Dual form			2565.1.dy.d.94.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.345975 - 1.96212i) q^{2} +(-0.996195 + 0.0871557i) q^{3} +(-2.79053 - 1.01567i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 1.98481i) q^{6} +(-1.96212 + 3.39849i) q^{8} +(0.984808 - 0.173648i) q^{9} +(0.996195 + 1.72546i) q^{10} +(-0.984808 - 0.826352i) q^{11} +(2.86843 + 0.768593i) q^{12} +(0.284489 + 1.61341i) q^{13} +(0.707107 - 0.707107i) q^{15} +(3.71455 + 3.11688i) q^{16} -1.99239i q^{18} +(0.500000 - 0.866025i) q^{19} +(2.79053 - 1.01567i) q^{20} +(-1.96212 + 1.64641i) q^{22} +(1.65846 - 3.55657i) q^{24} +(0.173648 - 0.984808i) q^{25} +3.26414 q^{26} +(-0.965926 + 0.258819i) q^{27} +(-1.14279 - 1.63207i) q^{30} +(4.39469 - 3.68758i) q^{32} +(1.05308 + 0.737376i) q^{33} +(-2.92450 - 0.515668i) q^{36} +(0.0871557 + 0.150958i) q^{37} +(-1.52626 - 1.28068i) q^{38} +(-0.424024 - 1.58248i) q^{39} +(-0.681437 - 3.86462i) q^{40} +(1.90883 + 3.30619i) q^{44} +(-0.642788 + 0.766044i) q^{45} +(-3.97207 - 2.78127i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-1.87223 - 0.681437i) q^{50} +(0.844822 - 4.79122i) q^{52} +0.845237 q^{53} +(0.173648 + 1.98481i) q^{54} +1.28558 q^{55} +(-0.422618 + 0.906308i) q^{57} +(-2.69139 + 1.25501i) q^{60} +(-3.29053 - 5.69936i) q^{64} +(-1.25501 - 1.05308i) q^{65} +(1.81116 - 1.81116i) q^{66} +(0.0898869 + 0.509774i) q^{67} +(-1.34217 + 3.68758i) q^{72} +(0.326352 - 0.118782i) q^{74} +(-0.0871557 + 0.996195i) q^{75} +(-2.27486 + 1.90883i) q^{76} +(-3.25172 + 0.284489i) q^{78} -4.84900 q^{80} +(0.939693 - 0.342020i) q^{81} +(4.74066 - 1.72546i) q^{88} +(1.28068 + 1.52626i) q^{90} +(0.173648 + 0.984808i) q^{95} +(-4.05657 + 4.05657i) q^{96} +(1.47988 + 1.24177i) q^{97} +(-0.996195 - 1.72546i) q^{98} +(-1.11334 - 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{16} + 12 q^{19} + 12 q^{24} - 12 q^{30} - 24 q^{36} + 12 q^{44} - 12 q^{64} + 24 q^{66} + 12 q^{74} - 24 q^{80} - 12 q^{96}+O(q^{100}) $ 24 * q + 12 * q^16 + 12 * q^19 + 12 * q^24 - 12 * q^30 - 24 * q^36 + 12 * q^44 - 12 * q^64 + 24 * q^66 + 12 * q^74 - 24 * q^80 - 12 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2565\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.345975	−	1.96212i	0.345975	−	1.96212i	0.0871557	−	0.996195i	$-0.472222\pi$
$2$	0.345975	−	1.96212i	0.345975	−	1.96212i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−0.996195	+	0.0871557i	−0.996195	+	0.0871557i
$3$	−0.996195	+	0.0871557i	−0.996195	+	0.0871557i
$4$	−2.79053	−	1.01567i	−2.79053	−	1.01567i
$5$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$5$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$6$	−0.173648	+	1.98481i	−0.173648	+	1.98481i
$7$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$7$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$8$	−1.96212	+	3.39849i	−1.96212	+	3.39849i
$9$	0.984808	−	0.173648i	0.984808	−	0.173648i
$10$	0.996195	+	1.72546i	0.996195	+	1.72546i
$11$	−0.984808	−	0.826352i	−0.984808	−	0.826352i		−	1.00000i	$-0.5\pi$
$11$	−0.984808	−	0.826352i	−0.984808	−	0.826352i	−0.984808	+	0.173648i	$0.944444\pi$
$12$	2.86843	+	0.768593i	2.86843	+	0.768593i
$13$	0.284489	+	1.61341i	0.284489	+	1.61341i	0.707107	+	0.707107i	$0.250000\pi$
$13$	0.284489	+	1.61341i	0.284489	+	1.61341i	−0.422618	+	0.906308i	$0.638889\pi$
$14$		0			0
$15$	0.707107	−	0.707107i	0.707107	−	0.707107i
$16$	3.71455	+	3.11688i	3.71455	+	3.11688i
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$		−	1.99239i		−	1.99239i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i
$20$	2.79053	−	1.01567i	2.79053	−	1.01567i
$21$		0			0
$22$	−1.96212	+	1.64641i	−1.96212	+	1.64641i
$23$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$23$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$24$	1.65846	−	3.55657i	1.65846	−	3.55657i
$25$	0.173648	−	0.984808i	0.173648	−	0.984808i
$26$	3.26414			3.26414
$27$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$28$		0			0
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$	−1.14279	−	1.63207i	−1.14279	−	1.63207i
$31$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$31$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$32$	4.39469	−	3.68758i	4.39469	−	3.68758i
$33$	1.05308	+	0.737376i	1.05308	+	0.737376i
$34$		0			0
$35$		0			0
$36$	−2.92450	−	0.515668i	−2.92450	−	0.515668i
$37$	0.0871557	+	0.150958i	0.0871557	+	0.150958i	0.906308	−	0.422618i	$-0.138889\pi$
$37$	0.0871557	+	0.150958i	0.0871557	+	0.150958i	−0.819152	+	0.573576i	$0.805556\pi$
$38$	−1.52626	−	1.28068i	−1.52626	−	1.28068i
$39$	−0.424024	−	1.58248i	−0.424024	−	1.58248i
$40$	−0.681437	−	3.86462i	−0.681437	−	3.86462i
$41$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$41$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$42$		0			0
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	1.90883	+	3.30619i	1.90883	+	3.30619i
$45$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$46$		0			0
$47$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$47$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$48$	−3.97207	−	2.78127i	−3.97207	−	2.78127i
$49$	0.766044	−	0.642788i	0.766044	−	0.642788i
$50$	−1.87223	−	0.681437i	−1.87223	−	0.681437i
$51$		0			0
$52$	0.844822	−	4.79122i	0.844822	−	4.79122i
$53$	0.845237			0.845237			0.422618	−	0.906308i	$-0.361111\pi$
$53$	0.845237			0.845237			0.422618	+	0.906308i	$0.361111\pi$
$54$	0.173648	+	1.98481i	0.173648	+	1.98481i
$55$	1.28558			1.28558
$56$		0			0
$57$	−0.422618	+	0.906308i	−0.422618	+	0.906308i
$58$		0			0
$59$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$59$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$60$	−2.69139	+	1.25501i	−2.69139	+	1.25501i
$61$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$61$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$62$		0			0
$63$		0			0
$64$	−3.29053	−	5.69936i	−3.29053	−	5.69936i
$65$	−1.25501	−	1.05308i	−1.25501	−	1.05308i
$66$	1.81116	−	1.81116i	1.81116	−	1.81116i
$67$	0.0898869	+	0.509774i	0.0898869	+	0.509774i	0.996195	+	0.0871557i	$0.0277778\pi$
$67$	0.0898869	+	0.509774i	0.0898869	+	0.509774i	−0.906308	+	0.422618i	$0.861111\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$	−1.34217	+	3.68758i	−1.34217	+	3.68758i
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$	0.326352	−	0.118782i	0.326352	−	0.118782i
$75$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$76$	−2.27486	+	1.90883i	−2.27486	+	1.90883i
$77$		0			0
$78$	−3.25172	+	0.284489i	−3.25172	+	0.284489i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$	−4.84900			−4.84900
$81$	0.939693	−	0.342020i	0.939693	−	0.342020i
$82$		0			0
$83$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$83$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	4.74066	−	1.72546i	4.74066	−	1.72546i
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$	1.28068	+	1.52626i	1.28068	+	1.52626i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.173648	+	0.984808i	0.173648	+	0.984808i
$96$	−4.05657	+	4.05657i	−4.05657	+	4.05657i
$97$	1.47988	+	1.24177i	1.47988	+	1.24177i	0.906308	+	0.422618i	$0.138889\pi$
$97$	1.47988	+	1.24177i	1.47988	+	1.24177i	0.573576	+	0.819152i	$0.305556\pi$
$98$	−0.996195	−	1.72546i	−0.996195	−	1.72546i
$99$	−1.11334	−	0.642788i	−1.11334	−	0.642788i
$100$	−1.48481	+	2.57176i	−1.48481	+	2.57176i
$101$	1.62760	−	0.592396i	1.62760	−	0.592396i	0.642788	−	0.766044i	$-0.277778\pi$
$101$	1.62760	−	0.592396i	1.62760	−	0.592396i	0.984808	+	0.173648i	$0.0555556\pi$
$102$		0			0
$103$	1.52626	−	1.28068i	1.52626	−	1.28068i	0.707107	−	0.707107i	$-0.250000\pi$
$103$	1.52626	−	1.28068i	1.52626	−	1.28068i	0.819152	−	0.573576i	$-0.194444\pi$
$104$	−6.04138	−	2.19888i	−6.04138	−	2.19888i
$105$		0			0
$106$	0.292431	−	1.65846i	0.292431	−	1.65846i
$107$	−1.81262			−1.81262			−0.906308	−	0.422618i	$-0.861111\pi$
$107$	−1.81262			−1.81262			−0.906308	+	0.422618i	$0.861111\pi$
$108$	2.95832	+	0.258819i	2.95832	+	0.258819i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	0.444777	−	2.52245i	0.444777	−	2.52245i
$111$	−0.0999810	−	0.142788i	−0.0999810	−	0.142788i
$112$		0			0
$113$	0.396534	−	0.332731i	0.396534	−	0.332731i	−0.422618	−	0.906308i	$-0.638889\pi$
$113$	0.396534	−	0.332731i	0.396534	−	0.332731i	0.819152	+	0.573576i	$0.194444\pi$
$114$	1.63207	+	1.14279i	1.63207	+	1.14279i
$115$		0			0
$116$		0			0
$117$	0.560333	+	1.53950i	0.560333	+	1.53950i
$118$		0			0
$119$		0			0
$120$	1.01567	+	3.79053i	1.01567	+	3.79053i
$121$	0.113341	+	0.642788i	0.113341	+	0.642788i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.500000	+	0.866025i	0.500000	+	0.866025i
$126$		0			0
$127$	0.258819	−	0.448288i	0.258819	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$127$	0.258819	−	0.448288i	0.258819	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$128$	−6.93038	+	2.52245i	−6.93038	+	2.52245i
$129$		0			0
$130$	−2.50048	+	2.09815i	−2.50048	+	2.09815i
$131$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$131$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$132$	−2.18972	−	3.12725i	−2.18972	−	3.12725i
$133$		0			0
$134$	1.03134			1.03134
$135$	0.573576	−	0.819152i	0.573576	−	0.819152i
$136$		0			0
$137$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$137$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$138$		0			0
$139$	1.62760	+	0.592396i	1.62760	+	0.592396i	0.984808	−	0.173648i	$-0.0555556\pi$
$139$	1.62760	+	0.592396i	1.62760	+	0.592396i	0.642788	+	0.766044i	$0.277778\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.05308	−	1.82399i	1.05308	−	1.82399i
$144$	4.19936	+	2.42450i	4.19936	+	2.42450i
$145$		0			0
$146$		0			0
$147$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$148$	−0.0898869	−	0.509774i	−0.0898869	−	0.509774i
$149$	0.118782	+	0.673648i	0.118782	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$149$	0.118782	+	0.673648i	0.118782	+	0.673648i	−0.866025	+	0.500000i	$0.833333\pi$
$150$	1.92450	+	0.515668i	1.92450	+	0.515668i
$151$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$151$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$152$	1.96212	+	3.39849i	1.96212	+	3.39849i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.424024	+	4.84662i	−0.424024	+	4.84662i
$157$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$157$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$158$		0			0
$159$	−0.842020	+	0.0736672i	−0.842020	+	0.0736672i
$160$	−0.996195	+	5.64970i	−0.996195	+	5.64970i
$161$		0			0
$162$	−0.345975	−	1.96212i	−0.345975	−	1.96212i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$	−1.28068	+	0.112045i	−1.28068	+	0.112045i
$166$		0			0
$167$	0.878770	−	0.737376i	0.878770	−	0.737376i	−0.0871557	−	0.996195i	$-0.527778\pi$
$167$	0.878770	−	0.737376i	0.878770	−	0.737376i	0.965926	+	0.258819i	$0.0833333\pi$
$168$		0			0
$169$	−1.58248	+	0.575976i	−1.58248	+	0.575976i
$170$		0			0
$171$	0.342020	−	0.939693i	0.342020	−	0.939693i
$172$		0			0
$173$	1.25501	+	1.05308i	1.25501	+	1.05308i	0.996195	+	0.0871557i	$0.0277778\pi$
$173$	1.25501	+	1.05308i	1.25501	+	1.05308i	0.258819	+	0.965926i	$0.416667\pi$
$174$		0			0
$175$		0			0
$176$	−1.08248	−	6.13905i	−1.08248	−	6.13905i
$177$		0			0
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	2.57176	−	1.48481i	2.57176	−	1.48481i
$181$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$181$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.163799	−	0.0596180i	−0.163799	−	0.0596180i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.99239			1.99239
$191$	0.326352	−	1.85083i	0.326352	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$191$	0.326352	−	1.85083i	0.326352	−	1.85083i	0.500000	−	0.866025i	$-0.333333\pi$
$192$	3.77474	+	5.39088i	3.77474	+	5.39088i
$193$	−0.794263	−	0.289088i	−0.794263	−	0.289088i	−0.0871557	−	0.996195i	$-0.527778\pi$
$193$	−0.794263	−	0.289088i	−0.794263	−	0.289088i	−0.707107	+	0.707107i	$0.750000\pi$
$194$	2.94851	−	2.47409i	2.94851	−	2.47409i
$195$	1.34202	+	0.939693i	1.34202	+	0.939693i
$196$	−2.79053	+	1.01567i	−2.79053	+	1.01567i
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$	−1.64641	+	1.96212i	−1.64641	+	1.96212i
$199$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$199$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$200$	3.00614	+	2.52245i	3.00614	+	2.52245i
$201$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$202$	−0.599246	−	3.39849i	−0.599246	−	3.39849i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−1.98481	−	3.43779i	−1.98481	−	3.43779i
$207$		0			0
$208$	−3.97207	+	6.87983i	−3.97207	+	6.87983i
$209$	−1.20805	+	0.439693i	−1.20805	+	0.439693i
$210$		0			0
$211$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$211$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$212$	−2.35865	−	0.858480i	−2.35865	−	0.858480i
$213$		0			0
$214$	−0.627119	+	3.55657i	−0.627119	+	3.55657i
$215$		0			0
$216$	1.01567	−	3.79053i	1.01567	−	3.79053i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−3.58743	−	1.30572i	−3.58743	−	1.30572i
$221$		0			0
$222$	−0.314757	+	0.146774i	−0.314757	+	0.146774i
$223$	−1.07797	+	0.392349i	−1.07797	+	0.392349i	−0.819152	−	0.573576i	$-0.805556\pi$
$223$	−1.07797	+	0.392349i	−1.07797	+	0.392349i	−0.258819	+	0.965926i	$0.583333\pi$
$224$		0			0
$225$		−	1.00000i		−	1.00000i
$226$	−0.515668	−	0.893164i	−0.515668	−	0.893164i
$227$	1.08335	+	0.909039i	1.08335	+	0.909039i	0.996195	−	0.0871557i	$-0.0277778\pi$
$227$	1.08335	+	0.909039i	1.08335	+	0.909039i	0.0871557	+	0.996195i	$0.472222\pi$
$228$	2.09984	−	2.09984i	2.09984	−	2.09984i
$229$	−0.342020	−	1.93969i	−0.342020	−	1.93969i	−0.342020	−	0.939693i	$-0.611111\pi$
$229$	−0.342020	−	1.93969i	−0.342020	−	1.93969i		−	1.00000i	$-0.5\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$	3.21455	−	0.566812i	3.21455	−	0.566812i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$239$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$240$	4.83055	−	0.422618i	4.83055	−	0.422618i
$241$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$241$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$242$	1.30044			1.30044
$243$	−0.906308	+	0.422618i	−0.906308	+	0.422618i
$244$		0			0
$245$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$246$		0			0
$247$	1.53950	+	0.560333i	1.53950	+	0.560333i
$248$		0			0
$249$		0			0
$250$	1.87223	−	0.681437i	1.87223	−	0.681437i
$251$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$251$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$252$		0			0
$253$		0			0
$254$	−0.790050	−	0.662930i	−0.790050	−	0.662930i
$255$		0			0
$256$	1.40883	+	7.98988i	1.40883	+	7.98988i
$257$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	−0.819152	−	0.573576i	$-0.805556\pi$
$257$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$258$		0			0
$259$		0			0
$260$	2.43257	+	4.21333i	2.43257	+	4.21333i
$261$		0			0
$262$	−0.345975	+	0.599246i	−0.345975	+	0.599246i
$263$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$263$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$264$	−4.57224	+	2.13207i	−4.57224	+	2.13207i
$265$	−0.647489	+	0.543308i	−0.647489	+	0.543308i
$266$		0			0
$267$		0			0
$268$	0.266930	−	1.51383i	0.266930	−	1.51383i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−1.40883	−	1.40883i	−1.40883	−	1.40883i
$271$	1.73205			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$271$	1.73205			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.984808	+	0.826352i	−0.984808	+	0.826352i
$276$		0			0
$277$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$277$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$278$	1.72546	−	2.98858i	1.72546	−	2.98858i
$279$		0			0
$280$		0			0
$281$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$281$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$282$		0			0
$283$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$283$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$284$		0			0
$285$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$286$	−3.21455	−	2.69733i	−3.21455	−	2.69733i
$287$		0			0
$288$	3.68758	−	4.39469i	3.68758	−	4.39469i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$		0			0
$291$	−1.58248	−	1.10806i	−1.58248	−	1.10806i
$292$		0			0
$293$	0.486421	+	0.177043i	0.486421	+	0.177043i	0.573576	−	0.819152i	$-0.305556\pi$
$293$	0.486421	+	0.177043i	0.486421	+	0.177043i	−0.0871557	+	0.996195i	$0.527778\pi$
$294$	1.14279	+	1.63207i	1.14279	+	1.63207i
$295$		0			0
$296$	−0.684040			−0.684040
$297$	1.16513	+	0.543308i	1.16513	+	0.543308i
$298$	1.36287			1.36287
$299$		0			0
$300$	1.25501	−	2.69139i	1.25501	−	2.69139i
$301$		0			0
$302$		0			0
$303$	−1.56977	+	0.731996i	−1.56977	+	0.731996i
$304$	4.55657	−	1.65846i	4.55657	−	1.65846i
$305$		0			0
$306$		0			0
$307$	0.422618	+	0.731996i	0.422618	+	0.731996i	0.996195	−	0.0871557i	$-0.0277778\pi$
$307$	0.422618	+	0.731996i	0.422618	+	0.731996i	−0.573576	+	0.819152i	$0.694444\pi$
$308$		0			0
$309$	−1.40883	+	1.40883i	−1.40883	+	1.40883i
$310$		0			0
$311$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$311$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$312$	6.21003	+	1.66397i	6.21003	+	1.66397i
$313$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$313$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$317$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.422618	+	0.906308i	$0.638889\pi$
$318$	−0.146774	+	1.67763i	−0.146774	+	1.67763i
$319$		0			0
$320$	6.18417	+	2.25085i	6.18417	+	2.25085i
$321$	1.80572	−	0.157980i	1.80572	−	0.157980i
$322$		0			0
$323$		0			0
$324$	−2.96962			−2.96962
$325$	1.63830			1.63830
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	−0.223238	+	2.55162i	−0.223238	+	2.55162i
$331$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$331$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$332$		0			0
$333$	0.112045	+	0.133530i	0.112045	+	0.133530i
$334$	−1.14279	−	1.97937i	−1.14279	−	1.97937i
$335$	−0.396534	−	0.332731i	−0.396534	−	0.332731i
$336$		0			0
$337$	0.245576	+	1.39273i	0.245576	+	1.39273i	0.819152	+	0.573576i	$0.194444\pi$
$337$	0.245576	+	1.39273i	0.245576	+	1.39273i	−0.573576	+	0.819152i	$0.694444\pi$
$338$	0.582635	+	3.30429i	0.582635	+	3.30429i
$339$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$340$		0			0
$341$		0			0
$342$	−1.72546	−	0.996195i	−1.72546	−	0.996195i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	2.50048	−	2.09815i	2.50048	−	2.09815i
$347$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$347$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$348$		0			0
$349$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$349$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$350$		0			0
$351$	−0.692377	−	1.48481i	−0.692377	−	1.48481i
$352$	−7.37516			−7.37516
$353$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$353$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$359$	−0.642788	+	1.11334i	−0.642788	+	1.11334i	−0.984808	+	0.173648i	$0.944444\pi$
$360$	−1.34217	−	3.68758i	−1.34217	−	3.68758i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	−0.168932	−	0.630463i	−0.168932	−	0.630463i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$367$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$368$		0			0
$369$		0			0
$370$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$371$		0			0
$372$		0			0
$373$	0.878770	−	0.737376i	0.878770	−	0.737376i	−0.0871557	−	0.996195i	$-0.527778\pi$
$373$	0.878770	−	0.737376i	0.878770	−	0.737376i	0.965926	+	0.258819i	$0.0833333\pi$
$374$		0			0
$375$	−0.573576	−	0.819152i	−0.573576	−	0.819152i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	0.515668	−	2.92450i	0.515668	−	2.92450i
$381$	−0.218763	+	0.469139i	−0.218763	+	0.469139i
$382$	−3.51865	−	1.28068i	−3.51865	−	1.28068i
$383$	0.133530	−	0.112045i	0.133530	−	0.112045i	−0.573576	−	0.819152i	$-0.694444\pi$
$383$	0.133530	−	0.112045i	0.133530	−	0.112045i	0.707107	+	0.707107i	$0.250000\pi$
$384$	6.68417	−	3.11688i	6.68417	−	3.11688i
$385$		0			0
$386$	−0.842020	+	1.45842i	−0.842020	+	1.45842i
$387$		0			0
$388$	−2.86843	−	4.96826i	−2.86843	−	4.96826i
$389$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$389$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$390$	2.30810	−	2.30810i	2.30810	−	2.30810i
$391$		0			0
$392$	0.681437	+	3.86462i	0.681437	+	3.86462i
$393$	0.335463	+	0.0898869i	0.335463	+	0.0898869i
$394$		0			0
$395$		0			0
$396$	2.45395	+	2.92450i	2.45395	+	2.92450i
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	2.86843	−	1.04402i	2.86843	−	1.04402i
$399$		0			0
$400$	3.71455	−	3.11688i	3.71455	−	3.11688i
$401$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$401$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$402$	−1.02741	+	0.0898869i	−1.02741	+	0.0898869i
$403$		0			0
$404$	−5.14352			−5.14352
$405$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$406$		0			0
$407$	0.0389129	−	0.220686i	0.0389129	−	0.220686i
$408$		0			0
$409$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$409$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$410$		0			0
$411$		0			0
$412$	−5.55981	+	2.02361i	−5.55981	+	2.02361i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	7.19983	+	6.04138i	7.19983	+	6.04138i
$417$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$418$	0.444777	+	2.52245i	0.444777	+	2.52245i
$419$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$419$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$420$		0			0
$421$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$421$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$422$		0			0
$423$		0			0
$424$	−1.65846	+	2.87253i	−1.65846	+	2.87253i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	5.05815	+	1.84102i	5.05815	+	1.84102i
$429$	−0.890103	+	1.90883i	−0.890103	+	1.90883i
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−4.39469	−	2.04928i	−4.39469	−	2.04928i
$433$	−1.93185			−1.93185			−0.965926	−	0.258819i	$-0.916667\pi$
$433$	−1.93185			−1.93185			−0.965926	+	0.258819i	$0.916667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$	−2.52245	+	4.36902i	−2.52245	+	4.36902i
$441$	0.642788	−	0.766044i	0.642788	−	0.766044i
$442$		0			0
$443$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$443$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$444$	0.133975	+	0.500000i	0.133975	+	0.500000i
$445$		0			0
$446$	0.396886	+	2.25085i	0.396886	+	2.25085i
$447$	−0.177043	−	0.660732i	−0.177043	−	0.660732i
$448$		0			0
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	−1.96212	−	0.345975i	−1.96212	−	0.345975i
$451$		0			0
$452$	−1.44448	+	0.525749i	−1.44448	+	0.525749i
$453$		0			0
$454$	2.15846	−	1.81116i	2.15846	−	1.81116i
$455$		0			0
$456$	−2.25085	−	3.21455i	−2.25085	−	3.21455i
$457$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$457$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$458$	−3.92424			−3.92424
$459$		0			0
$460$		0			0
$461$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$461$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$463$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$		−	4.86513i		−	4.86513i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$476$		0			0
$477$	0.832395	−	0.146774i	0.832395	−	0.146774i
$478$	1.87223	−	3.24280i	1.87223	−	3.24280i
$479$	−0.642788	+	0.233956i	−0.642788	+	0.233956i	−0.642788	−	0.766044i	$-0.722222\pi$
$479$	−0.642788	+	0.233956i	−0.642788	+	0.233956i			1.00000i	$0.5\pi$
$480$	0.500000	−	5.71503i	0.500000	−	5.71503i
$481$	−0.218763	+	0.183564i	−0.218763	+	0.183564i
$482$		0			0
$483$		0			0
$484$	0.336579	−	1.90883i	0.336579	−	1.90883i
$485$	−1.93185			−1.93185
$486$	0.515668	+	1.92450i	0.515668	+	1.92450i
$487$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$487$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$488$		0			0
$489$		0			0
$490$	1.87223	+	0.681437i	1.87223	+	0.681437i
$491$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$491$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$	1.63207	−	2.82683i	1.63207	−	2.82683i
$495$	1.26604	−	0.223238i	1.26604	−	0.223238i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	−0.984808	−	0.173648i	$-0.944444\pi$
$499$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	0.866025	−	0.500000i	$-0.166667\pi$
$500$	−0.515668	−	2.92450i	−0.515668	−	2.92450i
$501$	−0.811160	+	0.811160i	−0.811160	+	0.811160i
$502$	−0.530064	−	0.444777i	−0.530064	−	0.444777i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$		0			0
$505$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$506$		0			0
$507$	1.52626	−	0.711706i	1.52626	−	0.711706i
$508$	−1.17755	+	0.988084i	−1.17755	+	0.988084i
$509$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$509$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$510$		0			0
$511$		0			0
$512$	8.78937			8.78937
$513$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$514$	−2.81766			−2.81766
$515$	−0.345975	+	1.96212i	−0.345975	+	1.96212i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.34202	−	0.939693i	−1.34202	−	0.939693i
$520$	6.04138	−	2.19888i	6.04138	−	2.19888i
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	−0.422618	−	0.731996i	−0.422618	−	0.731996i	0.573576	−	0.819152i	$-0.305556\pi$
$523$	−0.422618	−	0.731996i	−0.422618	−	0.731996i	−0.996195	+	0.0871557i	$0.972222\pi$
$524$	0.790050	+	0.662930i	0.790050	+	0.662930i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.61341	+	6.02135i	1.61341	+	6.02135i
$529$	0.766044	+	0.642788i	0.766044	+	0.642788i
$530$	0.842020	+	1.45842i	0.842020	+	1.45842i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.38854	−	1.16513i	1.38854	−	1.16513i
$536$	−1.90883	−	0.694758i	−1.90883	−	0.694758i
$537$		0			0
$538$		0			0
$539$	−1.28558			−1.28558
$540$	−2.43257	+	1.70330i	−2.43257	+	1.70330i
$541$	−0.684040			−0.684040			−0.342020	−	0.939693i	$-0.611111\pi$
$541$	−0.684040			−0.684040			−0.342020	+	0.939693i	$0.611111\pi$
$542$	0.599246	−	3.39849i	0.599246	−	3.39849i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.70330	+	0.619951i	−1.70330	+	0.619951i	−0.996195	−	0.0871557i	$-0.972222\pi$
$547$	−1.70330	+	0.619951i	−1.70330	+	0.619951i	−0.707107	+	0.707107i	$0.750000\pi$
$548$		0			0
$549$		0			0
$550$	1.28068	+	2.21821i	1.28068	+	2.21821i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.168372	+	0.0451151i	0.168372	+	0.0451151i
$556$	−3.94017	−	3.30619i	−3.94017	−	3.30619i
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.70330	−	0.619951i	−1.70330	−	0.619951i	−0.707107	−	0.707107i	$-0.750000\pi$
$563$	−1.70330	−	0.619951i	−1.70330	−	0.619951i	−0.996195	+	0.0871557i	$0.972222\pi$
$564$		0			0
$565$	−0.0898869	+	0.509774i	−0.0898869	+	0.509774i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$569$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$570$	−1.98481	+	0.173648i	−1.98481	+	0.173648i
$571$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$571$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.866025	+	0.500000i	$0.166667\pi$
$572$	−4.79122	+	4.02031i	−4.79122	+	4.02031i
$573$	−0.163799	+	1.87223i	−0.163799	+	1.87223i
$574$		0			0
$575$		0			0
$576$	−4.23022	−	5.04138i	−4.23022	−	5.04138i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	1.52626	+	1.28068i	1.52626	+	1.28068i
$579$	0.816436	+	0.218763i	0.816436	+	0.218763i
$580$		0			0
$581$		0			0
$582$	−2.72165	+	2.72165i	−2.72165	+	2.72165i
$583$	−0.832395	−	0.698463i	−0.832395	−	0.698463i
$584$		0			0
$585$	−1.41881	−	0.819152i	−1.41881	−	0.819152i
$586$	0.515668	−	0.893164i	0.515668	−	0.893164i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	2.69139	−	1.25501i	2.69139	−	1.25501i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.146774	+	0.832395i	−0.146774	+	0.832395i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	1.46914	−	2.09815i	1.46914	−	2.09815i
$595$		0			0
$596$	0.352738	−	2.00048i	0.352738	−	2.00048i
$597$	−0.878770	−	1.25501i	−0.878770	−	1.25501i
$598$		0			0
$599$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$599$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$600$	−3.21455	−	2.25085i	−3.21455	−	2.25085i
$601$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$601$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$602$		0			0
$603$	0.177043	+	0.486421i	0.177043	+	0.486421i
$604$		0			0
$605$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$606$	0.893164	+	3.33333i	0.893164	+	3.33333i
$607$	−0.314757	−	1.78508i	−0.314757	−	1.78508i	−0.573576	−	0.819152i	$-0.694444\pi$
$607$	−0.314757	−	1.78508i	−0.314757	−	1.78508i	0.258819	−	0.965926i	$-0.416667\pi$
$608$	−0.996195	−	5.64970i	−0.996195	−	5.64970i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$	1.58248	−	0.575976i	1.58248	−	0.575976i
$615$		0			0
$616$		0			0
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	2.27688	+	3.25172i	2.27688	+	3.25172i
$619$	−0.223238	+	1.26604i	−0.223238	+	1.26604i	0.642788	+	0.766044i	$0.277778\pi$
$619$	−0.223238	+	1.26604i	−0.223238	+	1.26604i	−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	3.35734	−	7.19983i	3.35734	−	7.19983i
$625$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$626$		0			0
$627$	1.16513	−	0.543308i	1.16513	−	0.543308i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.642788	+	1.11334i	0.642788	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$631$	0.642788	+	1.11334i	0.642788	+	1.11334i	−0.342020	+	0.939693i	$0.611111\pi$
$632$		0			0
$633$		0			0
$634$	0.489282	+	2.77486i	0.489282	+	2.77486i
$635$	0.0898869	+	0.509774i	0.0898869	+	0.509774i
$636$	2.42450	+	0.649643i	2.42450	+	0.649643i
$637$	1.25501	+	1.05308i	1.25501	+	1.05308i
$638$		0			0
$639$		0			0
$640$	3.68758	−	6.38708i	3.68758	−	6.38708i
$641$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$641$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$642$	0.314757	−	3.59769i	0.314757	−	3.59769i
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−0.681437	+	3.86462i	−0.681437	+	3.86462i
$649$		0			0
$650$	0.566812	−	3.21455i	0.566812	−	3.21455i
$651$		0			0
$652$		0			0
$653$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$653$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$654$		0			0
$655$	0.326352	−	0.118782i	0.326352	−	0.118782i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$	3.68758	+	0.988084i	3.68758	+	0.988084i
$661$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$661$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.300767	−	0.173648i	0.300767	−	0.173648i
$667$		0			0
$668$	−3.20116	+	1.16513i	−3.20116	+	1.16513i
$669$	1.03967	−	0.484808i	1.03967	−	0.484808i
$670$	−0.790050	+	0.662930i	−0.790050	+	0.662930i
$671$		0			0
$672$		0			0
$673$	0.345975	−	1.96212i	0.345975	−	1.96212i	0.0871557	−	0.996195i	$-0.472222\pi$
$673$	0.345975	−	1.96212i	0.345975	−	1.96212i	0.258819	−	0.965926i	$-0.416667\pi$
$674$	2.81766			2.81766
$675$	0.0871557	+	0.996195i	0.0871557	+	0.996195i
$676$	5.00095			5.00095
$677$	−0.0302689	+	0.171663i	−0.0302689	+	0.171663i	−0.996195	−	0.0871557i	$-0.972222\pi$
$677$	−0.0302689	+	0.171663i	−0.0302689	+	0.171663i	0.965926	+	0.258819i	$0.0833333\pi$
$678$	0.591550	+	0.844822i	0.591550	+	0.844822i
$679$		0			0
$680$		0			0
$681$	−1.15846	−	0.811160i	−1.15846	−	0.811160i
$682$		0			0
$683$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$683$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$684$	−1.90883	+	2.27486i	−1.90883	+	2.27486i
$685$		0			0
$686$		0			0
$687$	0.509774	+	1.90250i	0.509774	+	1.90250i
$688$		0			0
$689$	0.240460	+	1.36372i	0.240460	+	1.36372i
$690$		0			0
$691$	0.524005	+	0.439693i	0.524005	+	0.439693i	0.866025	−	0.500000i	$-0.166667\pi$
$691$	0.524005	+	0.439693i	0.524005	+	0.439693i	−0.342020	+	0.939693i	$0.611111\pi$
$692$	−2.43257	−	4.21333i	−2.43257	−	4.21333i
$693$		0			0
$694$		0			0
$695$	−1.62760	+	0.592396i	−1.62760	+	0.592396i
$696$		0			0
$697$		0			0
$698$	2.86843	+	1.04402i	2.86843	+	1.04402i
$699$		0			0
$700$		0			0
$701$	1.96962			1.96962			0.984808	−	0.173648i	$-0.0555556\pi$
$701$	1.96962			1.96962			0.984808	+	0.173648i	$0.0555556\pi$
$702$	−3.15292	+	0.844822i	−3.15292	+	0.844822i
$703$	0.174311			0.174311
$704$	−1.46914	+	8.33190i	−1.46914	+	8.33190i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$709$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	0.365731	+	2.07417i	0.365731	+	2.07417i
$716$		0			0
$717$	−1.81535	−	0.486421i	−1.81535	−	0.486421i
$718$	1.96212	+	1.64641i	1.96212	+	1.64641i
$719$	0.866025	+	1.50000i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$719$	0.866025	+	1.50000i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$720$	−4.77533	+	0.842020i	−4.77533	+	0.842020i
$721$		0			0
$722$	−1.87223	+	0.681437i	−1.87223	+	0.681437i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−1.29549	+	0.113341i	−1.29549	+	0.113341i
$727$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$727$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$728$		0			0
$729$	0.866025	−	0.500000i	0.866025	−	0.500000i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$733$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$734$		0			0
$735$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$736$		0			0
$737$	0.332731	−	0.576308i	0.332731	−	0.576308i
$738$		0			0
$739$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$739$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$740$	0.396534	+	0.332731i	0.396534	+	0.332731i
$741$	−1.58248	−	0.424024i	−1.58248	−	0.424024i
$742$		0			0
$743$	−0.345975	−	1.96212i	−0.345975	−	1.96212i	−0.258819	−	0.965926i	$-0.583333\pi$
$743$	−0.345975	−	1.96212i	−0.345975	−	1.96212i	−0.0871557	−	0.996195i	$-0.527778\pi$
$744$		0			0
$745$	−0.524005	−	0.439693i	−0.524005	−	0.439693i
$746$	−1.14279	−	1.97937i	−1.14279	−	1.97937i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−1.80572	+	0.842020i	−1.80572	+	0.842020i
$751$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$751$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$752$		0			0
$753$	−0.146774	+	0.314757i	−0.146774	+	0.314757i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	−3.68758	−	1.34217i	−3.68758	−	1.34217i
$761$	−0.524005	+	0.439693i	−0.524005	+	0.439693i	−0.866025	−	0.500000i	$-0.833333\pi$
$761$	−0.524005	+	0.439693i	−0.524005	+	0.439693i	0.342020	+	0.939693i	$0.388889\pi$
$762$	0.844822	+	0.591550i	0.844822	+	0.591550i
$763$		0			0
$764$	−2.79053	+	4.83333i	−2.79053	+	4.83333i
$765$		0			0
$766$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$767$		0			0
$768$	−2.09984	−	7.83669i	−2.09984	−	7.83669i
$769$	−0.300767	−	1.70574i	−0.300767	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$769$	−0.300767	−	1.70574i	−0.300767	−	1.70574i	0.342020	−	0.939693i	$-0.388889\pi$
$770$		0			0
$771$	0.366025	+	1.36603i	0.366025	+	1.36603i
$772$	1.92279	+	1.61341i	1.92279	+	1.61341i
$773$	0.906308	+	1.56977i	0.906308	+	1.56977i	0.819152	+	0.573576i	$0.194444\pi$
$773$	0.906308	+	1.56977i	0.906308	+	1.56977i	0.0871557	+	0.996195i	$0.472222\pi$
$774$		0			0
$775$		0			0
$776$	−7.12386	+	2.59287i	−7.12386	+	2.59287i
$777$		0			0
$778$	−2.86843	+	2.40690i	−2.86843	+	2.40690i
$779$		0			0
$780$	−2.79053	−	3.98528i	−2.79053	−	3.98528i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	4.84900			4.84900
$785$		0			0
$786$	0.292431	−	0.627119i	0.292431	−	0.627119i
$787$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.906308	−	0.422618i	$-0.138889\pi$
$787$	1.32893	+	0.483690i	1.32893	+	0.483690i	0.422618	+	0.906308i	$0.361111\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	4.36902	−	2.52245i	4.36902	−	2.52245i
$793$		0			0
$794$		0			0
$795$	0.597672	−	0.597672i	0.597672	−	0.597672i
$796$	−0.790050	−	4.48059i	−0.790050	−	4.48059i
$797$	0.314757	+	1.78508i	0.314757	+	1.78508i	0.573576	+	0.819152i	$0.305556\pi$
$797$	0.314757	+	1.78508i	0.314757	+	1.78508i	−0.258819	+	0.965926i	$0.583333\pi$
$798$		0			0
$799$		0			0
$800$	−2.86843	−	4.96826i	−2.86843	−	4.96826i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−0.133975	+	1.53134i	−0.133975	+	1.53134i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.18028	+	6.69372i	−1.18028	+	6.69372i
$809$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$809$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$810$	1.52626	+	1.28068i	1.52626	+	1.28068i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	−1.72546	+	0.150958i	−1.72546	+	0.150958i
$814$	−0.419550	−	0.152704i	−0.419550	−	0.152704i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$821$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$822$		0			0
$823$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$823$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$824$	1.35769	+	7.69983i	1.35769	+	7.69983i
$825$	0.909039	−	0.909039i	0.909039	−	0.909039i
$826$		0			0
$827$	0.258819	+	0.448288i	0.258819	+	0.448288i	0.965926	−	0.258819i	$-0.0833333\pi$
$827$	0.258819	+	0.448288i	0.258819	+	0.448288i	−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	8.25931	−	6.93038i	8.25931	−	6.93038i
$833$		0			0
$834$	−1.45842	+	3.12760i	−1.45842	+	3.12760i
$835$	−0.199201	+	1.12973i	−0.199201	+	1.12973i
$836$	3.81766			3.81766
$837$		0			0
$838$	−1.99239			−1.99239
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.842020	−	1.45842i	0.842020	−	1.45842i
$846$		0			0
$847$		0			0
$848$	3.13967	+	2.63450i	3.13967	+	2.63450i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$853$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$854$		0			0
$855$	0.342020	+	0.939693i	0.342020	+	0.939693i
$856$	3.55657	−	6.16016i	3.55657	−	6.16016i
$857$	1.87223	−	0.681437i	1.87223	−	0.681437i	0.906308	−	0.422618i	$-0.138889\pi$
$857$	1.87223	−	0.681437i	1.87223	−	0.681437i	0.965926	−	0.258819i	$-0.0833333\pi$
$858$	3.43741	+	2.40690i	3.43741	+	2.40690i
$859$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.81262			1.81262			0.906308	−	0.422618i	$-0.138889\pi$
$863$	1.81262			1.81262			0.906308	+	0.422618i	$0.138889\pi$
$864$	−3.29053	+	4.69936i	−3.29053	+	4.69936i
$865$	−1.63830			−1.63830
$866$	−0.668372	+	3.79053i	−0.668372	+	3.79053i
$867$	0.422618	−	0.906308i	0.422618	−	0.906308i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−0.796905	+	0.290050i	−0.796905	+	0.290050i
$872$		0			0
$873$	1.67303	+	0.965926i	1.67303	+	0.965926i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	−0.819152	−	0.573576i	$-0.805556\pi$
$877$	−0.245576	−	1.39273i	−0.245576	−	1.39273i	0.573576	−	0.819152i	$-0.305556\pi$
$878$		0			0
$879$	−0.500000	−	0.133975i	−0.500000	−	0.133975i
$880$	4.77533	+	4.00698i	4.77533	+	4.00698i
$881$	0.984808	+	1.70574i	0.984808	+	1.70574i	0.642788	+	0.766044i	$0.277778\pi$
$881$	0.984808	+	1.70574i	0.984808	+	1.70574i	0.342020	+	0.939693i	$0.388889\pi$
$882$	−1.28068	−	1.52626i	−1.28068	−	1.52626i
$883$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$883$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.486421	−	0.177043i	−0.486421	−	0.177043i	0.0871557	−	0.996195i	$-0.472222\pi$
$887$	−0.486421	−	0.177043i	−0.486421	−	0.177043i	−0.573576	+	0.819152i	$0.694444\pi$
$888$	0.681437	−	0.0596180i	0.681437	−	0.0596180i
$889$		0			0
$890$		0			0
$891$	−1.20805	−	0.439693i	−1.20805	−	0.439693i
$892$	3.40660			3.40660
$893$		0			0
$894$	−1.35769	+	0.118782i	−1.35769	+	0.118782i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.01567	+	2.79053i	−1.01567	+	2.79053i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.352738	+	2.00048i	0.352738	+	2.00048i
$905$		0			0
$906$		0			0
$907$	−1.38854	−	1.16513i	−1.38854	−	1.16513i	−0.965926	−	0.258819i	$-0.916667\pi$
$907$	−1.38854	−	1.16513i	−1.38854	−	1.16513i	−0.422618	−	0.906308i	$-0.638889\pi$
$908$	−2.09984	−	3.63702i	−2.09984	−	3.63702i
$909$	1.50000	−	0.866025i	1.50000	−	0.866025i
$910$		0			0
$911$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$911$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$912$	−4.39469	+	2.04928i	−4.39469	+	2.04928i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.01567	+	5.76014i	−1.01567	+	5.76014i
$917$		0			0
$918$		0			0
$919$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$919$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$920$		0			0
$921$	−0.484808	−	0.692377i	−0.484808	−	0.692377i
$922$	1.87223	+	0.681437i	1.87223	+	0.681437i
$923$		0			0
$924$		0			0
$925$	0.163799	−	0.0596180i	0.163799	−	0.0596180i
$926$		0			0
$927$	1.28068	−	1.52626i	1.28068	−	1.52626i
$928$		0			0
$929$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$929$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$930$		0			0
$931$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−6.33143	−	1.11640i	−6.33143	−	1.11640i
$937$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$937$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$941$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$942$		0			0
$943$		0			0
$944$		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
$949$		0			0
$950$	−1.52626	+	1.28068i	−1.52626	+	1.28068i
$951$	1.28171	−	0.597672i	1.28171	−	0.597672i
$952$		0			0
$953$	0.258819	−	0.448288i	0.258819	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$953$	0.258819	−	0.448288i	0.258819	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$954$		−	1.68404i		−	1.68404i
$955$	0.939693	+	1.62760i	0.939693	+	1.62760i
$956$	−4.27533	−	3.58743i	−4.27533	−	3.58743i
$957$		0			0
$958$	0.236661	+	1.34217i	0.236661	+	1.34217i
$959$		0			0
$960$	−6.35681	−	1.70330i	−6.35681	−	1.70330i
$961$	0.766044	+	0.642788i	0.766044	+	0.642788i
$962$	0.284489	+	0.492749i	0.284489	+	0.492749i
$963$	−1.78508	+	0.314757i	−1.78508	+	0.314757i
$964$		0			0
$965$	0.794263	−	0.289088i	0.794263	−	0.289088i
$966$		0			0
$967$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$967$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$968$	−2.40690	−	0.876039i	−2.40690	−	0.876039i
$969$		0			0
$970$	−0.668372	+	3.79053i	−0.668372	+	3.79053i
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	2.95832	−	0.258819i	2.95832	−	0.258819i
$973$		0			0
$974$	0.489282	−	2.77486i	0.489282	−	2.77486i
$975$	−1.63207	+	0.142788i	−1.63207	+	0.142788i
$976$		0			0
$977$	−0.878770	+	0.737376i	−0.878770	+	0.737376i	−0.965926	−	0.258819i	$-0.916667\pi$
$977$	−0.878770	+	0.737376i	−0.878770	+	0.737376i	0.0871557	+	0.996195i	$0.472222\pi$
$978$		0			0
$979$		0			0
$980$	1.48481	−	2.57176i	1.48481	−	2.57176i
$981$		0			0
$982$	1.52626	+	2.64356i	1.52626	+	2.64356i
$983$	−0.878770	−	0.737376i	−0.878770	−	0.737376i	0.0871557	−	0.996195i	$-0.472222\pi$
$983$	−0.878770	−	0.737376i	−0.878770	−	0.737376i	−0.965926	+	0.258819i	$0.916667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−3.72691	−	3.12725i	−3.72691	−	3.12725i
$989$		0			0
$990$		−	2.56137i		−	2.56137i
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$996$		0			0
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$	−1.36287			−1.36287
$999$	−0.123257	−	0.123257i	−0.123257	−	0.123257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2565.1.dy.d.2374.4	yes	24
5.4	even	2	inner	2565.1.dy.d.2374.1	yes	24
19.18	odd	2	inner	2565.1.dy.d.2374.1	yes	24
27.13	even	9	inner	2565.1.dy.d.94.4	yes	24
95.94	odd	2	CM	2565.1.dy.d.2374.4	yes	24
135.94	even	18	inner	2565.1.dy.d.94.1	✓	24
513.94	odd	18	inner	2565.1.dy.d.94.1	✓	24
2565.94	odd	18	inner	2565.1.dy.d.94.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2565.1.dy.d.94.1	✓	24	135.94	even	18	inner
2565.1.dy.d.94.1	✓	24	513.94	odd	18	inner
2565.1.dy.d.94.4	yes	24	27.13	even	9	inner
2565.1.dy.d.94.4	yes	24	2565.94	odd	18	inner
2565.1.dy.d.2374.1	yes	24	5.4	even	2	inner
2565.1.dy.d.2374.1	yes	24	19.18	odd	2	inner
2565.1.dy.d.2374.4	yes	24	1.1	even	1	trivial
2565.1.dy.d.2374.4	yes	24	95.94	odd	2	CM

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2565 = 3^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2565.dy (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.345975 - 1.96212i) q^{2} +(-0.996195 + 0.0871557i) q^{3} +(-2.79053 - 1.01567i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(-0.173648 + 1.98481i) q^{6} +(-1.96212 + 3.39849i) q^{8} +(0.984808 - 0.173648i) q^{9} +(0.996195 + 1.72546i) q^{10} +(-0.984808 - 0.826352i) q^{11} +(2.86843 + 0.768593i) q^{12} +(0.284489 + 1.61341i) q^{13} +(0.707107 - 0.707107i) q^{15} +(3.71455 + 3.11688i) q^{16} -1.99239i q^{18} +(0.500000 - 0.866025i) q^{19} +(2.79053 - 1.01567i) q^{20} +(-1.96212 + 1.64641i) q^{22} +(1.65846 - 3.55657i) q^{24} +(0.173648 - 0.984808i) q^{25} +3.26414 q^{26} +(-0.965926 + 0.258819i) q^{27} +(-1.14279 - 1.63207i) q^{30} +(4.39469 - 3.68758i) q^{32} +(1.05308 + 0.737376i) q^{33} +(-2.92450 - 0.515668i) q^{36} +(0.0871557 + 0.150958i) q^{37} +(-1.52626 - 1.28068i) q^{38} +(-0.424024 - 1.58248i) q^{39} +(-0.681437 - 3.86462i) q^{40} +(1.90883 + 3.30619i) q^{44} +(-0.642788 + 0.766044i) q^{45} +(-3.97207 - 2.78127i) q^{48} +(0.766044 - 0.642788i) q^{49} +(-1.87223 - 0.681437i) q^{50} +(0.844822 - 4.79122i) q^{52} +0.845237 q^{53} +(0.173648 + 1.98481i) q^{54} +1.28558 q^{55} +(-0.422618 + 0.906308i) q^{57} +(-2.69139 + 1.25501i) q^{60} +(-3.29053 - 5.69936i) q^{64} +(-1.25501 - 1.05308i) q^{65} +(1.81116 - 1.81116i) q^{66} +(0.0898869 + 0.509774i) q^{67} +(-1.34217 + 3.68758i) q^{72} +(0.326352 - 0.118782i) q^{74} +(-0.0871557 + 0.996195i) q^{75} +(-2.27486 + 1.90883i) q^{76} +(-3.25172 + 0.284489i) q^{78} -4.84900 q^{80} +(0.939693 - 0.342020i) q^{81} +(4.74066 - 1.72546i) q^{88} +(1.28068 + 1.52626i) q^{90} +(0.173648 + 0.984808i) q^{95} +(-4.05657 + 4.05657i) q^{96} +(1.47988 + 1.24177i) q^{97} +(-0.996195 - 1.72546i) q^{98} +(-1.11334 - 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{16} + 12 q^{19} + 12 q^{24} - 12 q^{30} - 24 q^{36} + 12 q^{44} - 12 q^{64} + 24 q^{66} + 12 q^{74} - 24 q^{80} - 12 q^{96}+O(q^{100}) \) 24 * q + 12 * q^16 + 12 * q^19 + 12 * q^24 - 12 * q^30 - 24 * q^36 + 12 * q^44 - 12 * q^64 + 24 * q^66 + 12 * q^74 - 24 * q^80 - 12 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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