LMFDB - Embedded newform 2565.1.dy.d.949.1

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			949.1
Root			$-0.573576 - 0.819152i$ of defining polynomial
Character	$\chi$	$=$	2565.949
Dual form			2565.1.dy.d.1519.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.53950 - 0.560333i) q^{2} +(-0.819152 - 0.573576i) q^{3} +(1.29005 + 1.08248i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.939693 + 1.34202i) q^{6} +(-0.560333 - 0.970525i) q^{8} +(0.342020 + 0.939693i) q^{9} +(0.819152 - 1.41881i) q^{10} +(-0.342020 - 1.93969i) q^{11} +(-0.435862 - 1.62666i) q^{12} +(0.794263 - 0.289088i) q^{13} +(0.707107 - 0.707107i) q^{15} +(0.0263861 + 0.149643i) q^{16} -1.63830i q^{18} +(0.500000 + 0.866025i) q^{19} +(-1.29005 + 1.08248i) q^{20} +(-0.560333 + 3.17781i) q^{22} +(-0.0976725 + 1.11640i) q^{24} +(-0.939693 - 0.342020i) q^{25} -1.38475 q^{26} +(0.258819 - 0.965926i) q^{27} +(-1.48481 + 0.692377i) q^{30} +(-0.151373 + 0.858480i) q^{32} +(-0.832395 + 1.78508i) q^{33} +(-0.575976 + 1.58248i) q^{36} +(-0.573576 + 0.993464i) q^{37} +(-0.284489 - 1.61341i) q^{38} +(-0.816436 - 0.218763i) q^{39} +(1.05308 - 0.383290i) q^{40} +(1.65846 - 2.87253i) q^{44} +(-0.984808 + 0.173648i) q^{45} +(0.0642174 - 0.137715i) q^{48} +(0.173648 - 0.984808i) q^{49} +(1.25501 + 1.05308i) q^{50} +(1.33757 + 0.486836i) q^{52} -0.174311 q^{53} +(-0.939693 + 1.34202i) q^{54} +1.96962 q^{55} +(0.0871557 - 0.996195i) q^{57} +(1.67763 - 0.146774i) q^{60} +(0.790050 - 1.36841i) q^{64} +(0.146774 + 0.832395i) q^{65} +(2.28171 - 2.28171i) q^{66} +(1.81535 - 0.660732i) q^{67} +(0.720350 - 0.858480i) q^{72} +(1.43969 - 1.20805i) q^{74} +(0.573576 + 0.819152i) q^{75} +(-0.292431 + 1.65846i) q^{76} +(1.13432 + 0.794263i) q^{78} -0.151951 q^{80} +(-0.766044 + 0.642788i) q^{81} +(-1.69088 + 1.41881i) q^{88} +(1.61341 + 0.284489i) q^{90} +(-0.939693 + 0.342020i) q^{95} +(0.616402 - 0.616402i) q^{96} +(-0.0898869 - 0.509774i) q^{97} +(-0.819152 + 1.41881i) q^{98} +(1.70574 - 0.984808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2565\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.53950	−	0.560333i	−1.53950	−	0.560333i	−0.573576	−	0.819152i	$-0.694444\pi$
$2$	−1.53950	−	0.560333i	−1.53950	−	0.560333i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	−0.819152	−	0.573576i	−0.819152	−	0.573576i
$3$	−0.819152	−	0.573576i	−0.819152	−	0.573576i
$4$	1.29005	+	1.08248i	1.29005	+	1.08248i
$5$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$5$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$6$	0.939693	+	1.34202i	0.939693	+	1.34202i
$7$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$7$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$8$	−0.560333	−	0.970525i	−0.560333	−	0.970525i
$9$	0.342020	+	0.939693i	0.342020	+	0.939693i
$10$	0.819152	−	1.41881i	0.819152	−	1.41881i
$11$	−0.342020	−	1.93969i	−0.342020	−	1.93969i	−0.342020	−	0.939693i	$-0.611111\pi$
$11$	−0.342020	−	1.93969i	−0.342020	−	1.93969i		−	1.00000i	$-0.5\pi$
$12$	−0.435862	−	1.62666i	−0.435862	−	1.62666i
$13$	0.794263	−	0.289088i	0.794263	−	0.289088i	0.0871557	−	0.996195i	$-0.472222\pi$
$13$	0.794263	−	0.289088i	0.794263	−	0.289088i	0.707107	+	0.707107i	$0.250000\pi$
$14$		0			0
$15$	0.707107	−	0.707107i	0.707107	−	0.707107i
$16$	0.0263861	+	0.149643i	0.0263861	+	0.149643i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		−	1.63830i		−	1.63830i
$19$	0.500000	+	0.866025i	0.500000	+	0.866025i
$19$	0.500000	+	0.866025i	0.500000	+	0.866025i
$20$	−1.29005	+	1.08248i	−1.29005	+	1.08248i
$21$		0			0
$22$	−0.560333	+	3.17781i	−0.560333	+	3.17781i
$23$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$23$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$24$	−0.0976725	+	1.11640i	−0.0976725	+	1.11640i
$25$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$26$	−1.38475			−1.38475
$27$	0.258819	−	0.965926i	0.258819	−	0.965926i
$28$		0			0
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$	−1.48481	+	0.692377i	−1.48481	+	0.692377i
$31$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$31$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$32$	−0.151373	+	0.858480i	−0.151373	+	0.858480i
$33$	−0.832395	+	1.78508i	−0.832395	+	1.78508i
$34$		0			0
$35$		0			0
$36$	−0.575976	+	1.58248i	−0.575976	+	1.58248i
$37$	−0.573576	+	0.993464i	−0.573576	+	0.993464i	0.422618	+	0.906308i	$0.361111\pi$
$37$	−0.573576	+	0.993464i	−0.573576	+	0.993464i	−0.996195	+	0.0871557i	$0.972222\pi$
$38$	−0.284489	−	1.61341i	−0.284489	−	1.61341i
$39$	−0.816436	−	0.218763i	−0.816436	−	0.218763i
$40$	1.05308	−	0.383290i	1.05308	−	0.383290i
$41$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$41$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$42$		0			0
$43$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$43$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$44$	1.65846	−	2.87253i	1.65846	−	2.87253i
$45$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$46$		0			0
$47$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$47$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$48$	0.0642174	−	0.137715i	0.0642174	−	0.137715i
$49$	0.173648	−	0.984808i	0.173648	−	0.984808i
$50$	1.25501	+	1.05308i	1.25501	+	1.05308i
$51$		0			0
$52$	1.33757	+	0.486836i	1.33757	+	0.486836i
$53$	−0.174311			−0.174311			−0.0871557	−	0.996195i	$-0.527778\pi$
$53$	−0.174311			−0.174311			−0.0871557	+	0.996195i	$0.527778\pi$
$54$	−0.939693	+	1.34202i	−0.939693	+	1.34202i
$55$	1.96962			1.96962
$56$		0			0
$57$	0.0871557	−	0.996195i	0.0871557	−	0.996195i
$58$		0			0
$59$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$59$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$60$	1.67763	−	0.146774i	1.67763	−	0.146774i
$61$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$61$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$62$		0			0
$63$		0			0
$64$	0.790050	−	1.36841i	0.790050	−	1.36841i
$65$	0.146774	+	0.832395i	0.146774	+	0.832395i
$66$	2.28171	−	2.28171i	2.28171	−	2.28171i
$67$	1.81535	−	0.660732i	1.81535	−	0.660732i	0.819152	−	0.573576i	$-0.194444\pi$
$67$	1.81535	−	0.660732i	1.81535	−	0.660732i	0.996195	−	0.0871557i	$-0.0277778\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$71$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$72$	0.720350	−	0.858480i	0.720350	−	0.858480i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$	1.43969	−	1.20805i	1.43969	−	1.20805i
$75$	0.573576	+	0.819152i	0.573576	+	0.819152i
$76$	−0.292431	+	1.65846i	−0.292431	+	1.65846i
$77$		0			0
$78$	1.13432	+	0.794263i	1.13432	+	0.794263i
$79$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$79$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$80$	−0.151951			−0.151951
$81$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$82$		0			0
$83$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$83$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−1.69088	+	1.41881i	−1.69088	+	1.41881i
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	1.61341	+	0.284489i	1.61341	+	0.284489i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$96$	0.616402	−	0.616402i	0.616402	−	0.616402i
$97$	−0.0898869	−	0.509774i	−0.0898869	−	0.509774i	−0.996195	−	0.0871557i	$-0.972222\pi$
$97$	−0.0898869	−	0.509774i	−0.0898869	−	0.509774i	0.906308	−	0.422618i	$-0.138889\pi$
$98$	−0.819152	+	1.41881i	−0.819152	+	1.41881i
$99$	1.70574	−	0.984808i	1.70574	−	0.984808i
$100$	−0.842020	−	1.45842i	−0.842020	−	1.45842i
$101$	1.32683	−	1.11334i	1.32683	−	1.11334i	0.342020	−	0.939693i	$-0.388889\pi$
$101$	1.32683	−	1.11334i	1.32683	−	1.11334i	0.984808	−	0.173648i	$-0.0555556\pi$
$102$		0			0
$103$	0.284489	−	1.61341i	0.284489	−	1.61341i	−0.422618	−	0.906308i	$-0.638889\pi$
$103$	0.284489	−	1.61341i	0.284489	−	1.61341i	0.707107	−	0.707107i	$-0.250000\pi$
$104$	−0.725619	−	0.608866i	−0.725619	−	0.608866i
$105$		0			0
$106$	0.268353	+	0.0976725i	0.268353	+	0.0976725i
$107$	1.99239			1.99239			0.996195	−	0.0871557i	$-0.0277778\pi$
$107$	1.99239			1.99239			0.996195	+	0.0871557i	$0.0277778\pi$
$108$	1.37949	−	0.965926i	1.37949	−	0.965926i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−3.03223	−	1.10364i	−3.03223	−	1.10364i
$111$	1.03967	−	0.484808i	1.03967	−	0.484808i
$112$		0			0
$113$	−0.335463	+	1.90250i	−0.335463	+	1.90250i	0.0871557	+	0.996195i	$0.472222\pi$
$113$	−0.335463	+	1.90250i	−0.335463	+	1.90250i	−0.422618	+	0.906308i	$0.638889\pi$
$114$	−0.692377	+	1.48481i	−0.692377	+	1.48481i
$115$		0			0
$116$		0			0
$117$	0.543308	+	0.647489i	0.543308	+	0.647489i
$118$		0			0
$119$		0			0
$120$	−1.08248	−	0.290050i	−1.08248	−	0.290050i
$121$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.500000	−	0.866025i	0.500000	−	0.866025i
$126$		0			0
$127$	−0.965926	−	1.67303i	−0.965926	−	1.67303i	−0.707107	−	0.707107i	$-0.750000\pi$
$127$	−0.965926	−	1.67303i	−0.965926	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$128$	−1.31527	+	1.10364i	−1.31527	+	1.10364i
$129$		0			0
$130$	0.240460	−	1.36372i	0.240460	−	1.36372i
$131$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$131$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$132$	−3.00614	+	1.40179i	−3.00614	+	1.40179i
$133$		0			0
$134$	−3.16496			−3.16496
$135$	0.906308	+	0.422618i	0.906308	+	0.422618i
$136$		0			0
$137$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$137$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$138$		0			0
$139$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$139$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.832395	−	1.44175i	−0.832395	−	1.44175i
$144$	−0.131594	+	0.0759757i	−0.131594	+	0.0759757i
$145$		0			0
$146$		0			0
$147$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$148$	−1.81535	+	0.660732i	−1.81535	+	0.660732i
$149$	1.20805	−	0.439693i	1.20805	−	0.439693i	0.342020	−	0.939693i	$-0.388889\pi$
$149$	1.20805	−	0.439693i	1.20805	−	0.439693i	0.866025	+	0.500000i	$0.166667\pi$
$150$	−0.424024	−	1.58248i	−0.424024	−	1.58248i
$151$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$151$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$152$	0.560333	−	0.970525i	0.560333	−	0.970525i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.816436	−	1.16599i	−0.816436	−	1.16599i
$157$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$157$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$158$		0			0
$159$	0.142788	+	0.0999810i	0.142788	+	0.0999810i
$160$	−0.819152	−	0.298147i	−0.819152	−	0.298147i
$161$		0			0
$162$	1.53950	−	0.560333i	1.53950	−	0.560333i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$	−1.61341	−	1.12973i	−1.61341	−	1.12973i
$166$		0			0
$167$	0.314757	−	1.78508i	0.314757	−	1.78508i	−0.258819	−	0.965926i	$-0.583333\pi$
$167$	0.314757	−	1.78508i	0.314757	−	1.78508i	0.573576	−	0.819152i	$-0.305556\pi$
$168$		0			0
$169$	−0.218763	+	0.183564i	−0.218763	+	0.183564i
$170$		0			0
$171$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$172$		0			0
$173$	−0.146774	−	0.832395i	−0.146774	−	0.832395i	−0.965926	−	0.258819i	$-0.916667\pi$
$173$	−0.146774	−	0.832395i	−0.146774	−	0.832395i	0.819152	−	0.573576i	$-0.194444\pi$
$174$		0			0
$175$		0			0
$176$	0.281237	−	0.102362i	0.281237	−	0.102362i
$177$		0			0
$178$		0			0
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	−1.45842	−	0.842020i	−1.45842	−	0.842020i
$181$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$181$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.878770	−	0.737376i	−0.878770	−	0.737376i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.63830			1.63830
$191$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$191$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$192$	−1.43206	+	0.667779i	−1.43206	+	0.667779i
$193$	−0.133530	−	0.112045i	−0.133530	−	0.112045i	0.573576	−	0.819152i	$-0.305556\pi$
$193$	−0.133530	−	0.112045i	−0.133530	−	0.112045i	−0.707107	+	0.707107i	$0.750000\pi$
$194$	−0.147262	+	0.835165i	−0.147262	+	0.835165i
$195$	0.357212	−	0.766044i	0.357212	−	0.766044i
$196$	1.29005	−	1.08248i	1.29005	−	1.08248i
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$	−3.17781	+	0.560333i	−3.17781	+	0.560333i
$199$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$199$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$200$	0.194602	+	1.10364i	0.194602	+	1.10364i
$201$	−1.86603	−	0.500000i	−1.86603	−	0.500000i
$202$	−2.66650	+	0.970525i	−2.66650	+	0.970525i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−1.34202	+	2.32445i	−1.34202	+	2.32445i
$207$		0			0
$208$	0.0642174	+	0.111228i	0.0642174	+	0.111228i
$209$	1.50881	−	1.26604i	1.50881	−	1.26604i
$210$		0			0
$211$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$211$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$212$	−0.224870	−	0.188689i	−0.224870	−	0.188689i
$213$		0			0
$214$	−3.06729	−	1.11640i	−3.06729	−	1.11640i
$215$		0			0
$216$	−1.08248	+	0.290050i	−1.08248	+	0.290050i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	2.54090	+	2.13207i	2.54090	+	2.13207i
$221$		0			0
$222$	−1.87223	+	0.163799i	−1.87223	+	0.163799i
$223$	1.38854	−	1.16513i	1.38854	−	1.16513i	0.422618	−	0.906308i	$-0.361111\pi$
$223$	1.38854	−	1.16513i	1.38854	−	1.16513i	0.965926	−	0.258819i	$-0.0833333\pi$
$224$		0			0
$225$		−	1.00000i		−	1.00000i
$226$	1.58248	−	2.74094i	1.58248	−	2.74094i
$227$	0.245576	+	1.39273i	0.245576	+	1.39273i	0.819152	+	0.573576i	$0.194444\pi$
$227$	0.245576	+	1.39273i	0.245576	+	1.39273i	−0.573576	+	0.819152i	$0.694444\pi$
$228$	1.19080	−	1.19080i	1.19080	−	1.19080i
$229$	0.642788	−	0.233956i	0.642788	−	0.233956i		−	1.00000i	$-0.5\pi$
$229$	0.642788	−	0.233956i	0.642788	−	0.233956i	0.642788	+	0.766044i	$0.277778\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$233$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$234$	−0.473614	−	1.30124i	−0.473614	−	1.30124i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$239$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$240$	0.124471	+	0.0871557i	0.124471	+	0.0871557i
$241$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$241$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$242$	4.71731			4.71731
$243$	0.996195	−	0.0871557i	0.996195	−	0.0871557i
$244$		0			0
$245$	0.939693	+	0.342020i	0.939693	+	0.342020i
$246$		0			0
$247$	0.647489	+	0.543308i	0.647489	+	0.543308i
$248$		0			0
$249$		0			0
$250$	−1.25501	+	1.05308i	−1.25501	+	1.05308i
$251$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$251$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$252$		0			0
$253$		0			0
$254$	0.549590	+	3.11688i	0.549590	+	3.11688i
$255$		0			0
$256$	1.15846	−	0.421643i	1.15846	−	0.421643i
$257$	1.32893	−	0.483690i	1.32893	−	0.483690i	0.422618	−	0.906308i	$-0.361111\pi$
$257$	1.32893	−	0.483690i	1.32893	−	0.483690i	0.906308	+	0.422618i	$0.138889\pi$
$258$		0			0
$259$		0			0
$260$	−0.711706	+	1.23271i	−0.711706	+	1.23271i
$261$		0			0
$262$	1.53950	+	2.66650i	1.53950	+	2.66650i
$263$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$263$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$264$	2.19888	−	0.192377i	2.19888	−	0.192377i
$265$	0.0302689	−	0.171663i	0.0302689	−	0.171663i
$266$		0			0
$267$		0			0
$268$	3.05712	+	1.11270i	3.05712	+	1.11270i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−1.15846	−	1.15846i	−1.15846	−	1.15846i
$271$	−1.73205			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$271$	−1.73205			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.342020	+	1.93969i	−0.342020	+	1.93969i
$276$		0			0
$277$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$277$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$278$	−1.41881	−	2.45746i	−1.41881	−	2.45746i
$279$		0			0
$280$		0			0
$281$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$281$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$282$		0			0
$283$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$283$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$284$		0			0
$285$	0.965926	+	0.258819i	0.965926	+	0.258819i
$286$	0.473614	+	2.68600i	0.473614	+	2.68600i
$287$		0			0
$288$	−0.858480	+	0.151373i	−0.858480	+	0.151373i
$289$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$290$		0			0
$291$	−0.218763	+	0.469139i	−0.218763	+	0.469139i
$292$		0			0
$293$	1.47988	+	1.24177i	1.47988	+	1.24177i	0.906308	+	0.422618i	$0.138889\pi$
$293$	1.47988	+	1.24177i	1.47988	+	1.24177i	0.573576	+	0.819152i	$0.305556\pi$
$294$	1.48481	−	0.692377i	1.48481	−	0.692377i
$295$		0			0
$296$	1.28558			1.28558
$297$	−1.96212	−	0.171663i	−1.96212	−	0.171663i
$298$	−2.10616			−2.10616
$299$		0			0
$300$	−0.146774	+	1.67763i	−0.146774	+	1.67763i
$301$		0			0
$302$		0			0
$303$	−1.72546	+	0.150958i	−1.72546	+	0.150958i
$304$	−0.116402	+	0.0976725i	−0.116402	+	0.0976725i
$305$		0			0
$306$		0			0
$307$	−0.0871557	+	0.150958i	−0.0871557	+	0.150958i	−0.906308	−	0.422618i	$-0.861111\pi$
$307$	−0.0871557	+	0.150958i	−0.0871557	+	0.150958i	0.819152	+	0.573576i	$0.194444\pi$
$308$		0			0
$309$	−1.15846	+	1.15846i	−1.15846	+	1.15846i
$310$		0			0
$311$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$311$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$312$	0.245161	+	0.914952i	0.245161	+	0.914952i
$313$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$313$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.0871557	−	0.996195i	$-0.472222\pi$
$317$	1.08335	−	0.909039i	1.08335	−	0.909039i	0.996195	+	0.0871557i	$0.0277778\pi$
$318$	−0.163799	−	0.233930i	−0.163799	−	0.233930i
$319$		0			0
$320$	1.21043	+	1.01567i	1.21043	+	1.01567i
$321$	−1.63207	−	1.14279i	−1.63207	−	1.14279i
$322$		0			0
$323$		0			0
$324$	−1.68404			−1.68404
$325$	−0.845237			−0.845237
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	1.85083	+	2.64326i	1.85083	+	2.64326i
$331$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$331$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$332$		0			0
$333$	−1.12973	−	0.199201i	−1.12973	−	0.199201i
$334$	−1.48481	+	2.57176i	−1.48481	+	2.57176i
$335$	0.335463	+	1.90250i	0.335463	+	1.90250i
$336$		0			0
$337$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.906308	−	0.422618i	$-0.861111\pi$
$337$	−1.32893	+	0.483690i	−1.32893	+	0.483690i	−0.422618	+	0.906308i	$0.638889\pi$
$338$	0.439644	−	0.160017i	0.439644	−	0.160017i
$339$	1.36603	−	1.36603i	1.36603	−	1.36603i
$340$		0			0
$341$		0			0
$342$	1.41881	−	0.819152i	1.41881	−	0.819152i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.240460	+	1.36372i	−0.240460	+	1.36372i
$347$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$347$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$349$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$350$		0			0
$351$	−0.0736672	−	0.842020i	−0.0736672	−	0.842020i
$352$	1.71696			1.71696
$353$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$353$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$359$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.342020	−	0.939693i	$-0.611111\pi$
$360$	0.720350	+	0.858480i	0.720350	+	0.858480i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	2.78127	+	0.745240i	2.78127	+	0.745240i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$367$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$368$		0			0
$369$		0			0
$370$	0.939693	+	1.62760i	0.939693	+	1.62760i
$371$		0			0
$372$		0			0
$373$	0.314757	−	1.78508i	0.314757	−	1.78508i	−0.258819	−	0.965926i	$-0.583333\pi$
$373$	0.314757	−	1.78508i	0.314757	−	1.78508i	0.573576	−	0.819152i	$-0.305556\pi$
$374$		0			0
$375$	−0.906308	+	0.422618i	−0.906308	+	0.422618i
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−1.58248	−	0.575976i	−1.58248	−	0.575976i
$381$	−0.168372	+	1.92450i	−0.168372	+	1.92450i
$382$	−1.92279	−	1.61341i	−1.92279	−	1.61341i
$383$	−0.199201	+	1.12973i	−0.199201	+	1.12973i	0.707107	+	0.707107i	$0.250000\pi$
$383$	−0.199201	+	1.12973i	−0.199201	+	1.12973i	−0.906308	+	0.422618i	$0.861111\pi$
$384$	1.71043	−	0.149643i	1.71043	−	0.149643i
$385$		0			0
$386$	0.142788	+	0.247315i	0.142788	+	0.247315i
$387$		0			0
$388$	0.435862	−	0.754935i	0.435862	−	0.754935i
$389$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$389$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$390$	−0.979169	+	0.979169i	−0.979169	+	0.979169i
$391$		0			0
$392$	−1.05308	+	0.383290i	−1.05308	+	0.383290i
$393$	0.486421	+	1.81535i	0.486421	+	1.81535i
$394$		0			0
$395$		0			0
$396$	3.26652	+	0.575976i	3.26652	+	0.575976i
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$	−0.435862	+	0.365731i	−0.435862	+	0.365731i
$399$		0			0
$400$	0.0263861	−	0.149643i	0.0263861	−	0.149643i
$401$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$401$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$402$	2.59258	+	1.81535i	2.59258	+	1.81535i
$403$		0			0
$404$	2.91684			2.91684
$405$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$406$		0			0
$407$	2.12319	+	0.772777i	2.12319	+	0.772777i
$408$		0			0
$409$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$409$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$410$		0			0
$411$		0			0
$412$	2.11349	−	1.77343i	2.11349	−	1.77343i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.127946	+	0.725619i	0.127946	+	0.725619i
$417$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$418$	−3.03223	+	1.10364i	−3.03223	+	1.10364i
$419$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$419$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$420$		0			0
$421$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$421$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$422$		0			0
$423$		0			0
$424$	0.0976725	+	0.169174i	0.0976725	+	0.169174i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.57028	+	2.15672i	2.57028	+	2.15672i
$429$	−0.145096	+	1.65846i	−0.145096	+	1.65846i
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	0.151373	+	0.0132434i	0.151373	+	0.0132434i
$433$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$433$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$439$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$440$	−1.10364	−	1.91156i	−1.10364	−	1.91156i
$441$	0.984808	−	0.173648i	0.984808	−	0.173648i
$442$		0			0
$443$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$443$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$444$	1.86603	+	0.500000i	1.86603	+	0.500000i
$445$		0			0
$446$	−2.79053	+	1.01567i	−2.79053	+	1.01567i
$447$	−1.24177	−	0.332731i	−1.24177	−	0.332731i
$448$		0			0
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.560333	+	1.53950i	−0.560333	+	1.53950i
$451$		0			0
$452$	−2.49218	+	2.09119i	−2.49218	+	2.09119i
$453$		0			0
$454$	0.402328	−	2.28171i	0.402328	−	2.28171i
$455$		0			0
$456$	−1.01567	+	0.473614i	−1.01567	+	0.473614i
$457$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$457$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$458$	−1.12067			−1.12067
$459$		0			0
$460$		0			0
$461$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$461$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$462$		0			0
$463$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$463$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$			1.42341i			1.42341i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$476$		0			0
$477$	−0.0596180	−	0.163799i	−0.0596180	−	0.163799i
$478$	−1.25501	−	2.17375i	−1.25501	−	2.17375i
$479$	−0.984808	+	0.826352i	−0.984808	+	0.826352i	−0.984808	−	0.173648i	$-0.944444\pi$
$479$	−0.984808	+	0.826352i	−0.984808	+	0.826352i			1.00000i	$0.5\pi$
$480$	0.500000	+	0.714074i	0.500000	+	0.714074i
$481$	−0.168372	+	0.954885i	−0.168372	+	0.954885i
$482$		0			0
$483$		0			0
$484$	−4.55657	−	1.65846i	−4.55657	−	1.65846i
$485$	0.517638			0.517638
$486$	−1.58248	−	0.424024i	−1.58248	−	0.424024i
$487$	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
$490$	−1.25501	−	1.05308i	−1.25501	−	1.05308i
$491$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$491$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$	−0.692377	−	1.19923i	−0.692377	−	1.19923i
$495$	0.673648	+	1.85083i	0.673648	+	1.85083i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.20805	+	0.439693i	−1.20805	+	0.439693i	−0.866025	−	0.500000i	$-0.833333\pi$
$499$	−1.20805	+	0.439693i	−1.20805	+	0.439693i	−0.342020	+	0.939693i	$0.611111\pi$
$500$	1.58248	−	0.575976i	1.58248	−	0.575976i
$501$	−1.28171	+	1.28171i	−1.28171	+	1.28171i
$502$	0.534664	+	3.03223i	0.534664	+	3.03223i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$		0			0
$505$	0.866025	+	1.50000i	0.866025	+	1.50000i
$506$		0			0
$507$	0.284489	−	0.0248895i	0.284489	−	0.0248895i
$508$	0.564932	−	3.20389i	0.564932	−	3.20389i
$509$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$509$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$		0			0
$512$	−0.302746			−0.302746
$513$	0.965926	−	0.258819i	0.965926	−	0.258819i
$514$	−2.31691			−2.31691
$515$	1.53950	+	0.560333i	1.53950	+	0.560333i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.357212	+	0.766044i	−0.357212	+	0.766044i
$520$	0.725619	−	0.608866i	0.725619	−	0.608866i
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$	0.0871557	−	0.150958i	0.0871557	−	0.150958i	−0.819152	−	0.573576i	$-0.805556\pi$
$523$	0.0871557	−	0.150958i	0.0871557	−	0.150958i	0.906308	+	0.422618i	$0.138889\pi$
$524$	−0.549590	−	3.11688i	−0.549590	−	3.11688i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.289088	−	0.0774609i	−0.289088	−	0.0774609i
$529$	0.173648	+	0.984808i	0.173648	+	0.984808i
$530$	−0.142788	+	0.247315i	−0.142788	+	0.247315i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.345975	+	1.96212i	−0.345975	+	1.96212i
$536$	−1.65846	−	1.39161i	−1.65846	−	1.39161i
$537$		0			0
$538$		0			0
$539$	−1.96962			−1.96962
$540$	0.711706	+	1.52626i	0.711706	+	1.52626i
$541$	1.28558			1.28558			0.642788	−	0.766044i	$-0.277778\pi$
$541$	1.28558			1.28558			0.642788	+	0.766044i	$0.277778\pi$
$542$	2.66650	+	0.970525i	2.66650	+	0.970525i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.52626	+	1.28068i	−1.52626	+	1.28068i	−0.707107	+	0.707107i	$0.750000\pi$
$547$	−1.52626	+	1.28068i	−1.52626	+	1.28068i	−0.819152	+	0.573576i	$0.805556\pi$
$548$		0			0
$549$		0			0
$550$	1.61341	−	2.79452i	1.61341	−	2.79452i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.296905	+	1.10806i	0.296905	+	1.10806i
$556$	0.506505	+	2.87253i	0.506505	+	2.87253i
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.52626	−	1.28068i	−1.52626	−	1.28068i	−0.819152	−	0.573576i	$-0.805556\pi$
$563$	−1.52626	−	1.28068i	−1.52626	−	1.28068i	−0.707107	−	0.707107i	$-0.750000\pi$
$564$		0			0
$565$	−1.81535	−	0.660732i	−1.81535	−	0.660732i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$569$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$570$	−1.34202	−	0.939693i	−1.34202	−	0.939693i
$571$	−0.524005	−	0.439693i	−0.524005	−	0.439693i	0.342020	−	0.939693i	$-0.388889\pi$
$571$	−0.524005	−	0.439693i	−0.524005	−	0.439693i	−0.866025	+	0.500000i	$0.833333\pi$
$572$	0.486836	−	2.76098i	0.486836	−	2.76098i
$573$	−0.878770	−	1.25501i	−0.878770	−	1.25501i
$574$		0			0
$575$		0			0
$576$	1.55609	+	0.274381i	1.55609	+	0.274381i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.284489	+	1.61341i	0.284489	+	1.61341i
$579$	0.0451151	+	0.168372i	0.0451151	+	0.168372i
$580$		0			0
$581$		0			0
$582$	0.599661	−	0.599661i	0.599661	−	0.599661i
$583$	0.0596180	+	0.338111i	0.0596180	+	0.338111i
$584$		0			0
$585$	−0.731996	+	0.422618i	−0.731996	+	0.422618i
$586$	−1.58248	−	2.74094i	−1.58248	−	2.74094i
$587$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$587$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$588$	−1.67763	+	0.146774i	−1.67763	+	0.146774i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.163799	−	0.0596180i	−0.163799	−	0.0596180i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	2.92450	+	1.36372i	2.92450	+	1.36372i
$595$		0			0
$596$	2.03440	+	0.740460i	2.03440	+	0.740460i
$597$	−0.314757	+	0.146774i	−0.314757	+	0.146774i
$598$		0			0
$599$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$599$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$600$	0.473614	−	1.01567i	0.473614	−	1.01567i
$601$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$601$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$602$		0			0
$603$	1.24177	+	1.47988i	1.24177	+	1.47988i
$604$		0			0
$605$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$606$	2.74094	+	0.734432i	2.74094	+	0.734432i
$607$	−1.87223	+	0.681437i	−1.87223	+	0.681437i	−0.906308	+	0.422618i	$0.861111\pi$
$607$	−1.87223	+	0.681437i	−1.87223	+	0.681437i	−0.965926	+	0.258819i	$0.916667\pi$
$608$	−0.819152	+	0.298147i	−0.819152	+	0.298147i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	0.218763	−	0.183564i	0.218763	−	0.183564i
$615$		0			0
$616$		0			0
$617$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$617$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$618$	2.43257	−	1.13432i	2.43257	−	1.13432i
$619$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$619$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	0.0111938	−	0.127946i	0.0111938	−	0.127946i
$625$	0.766044	+	0.642788i	0.766044	+	0.642788i
$626$		0			0
$627$	−1.96212	+	0.171663i	−1.96212	+	0.171663i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.984808	−	1.70574i	0.984808	−	1.70574i	0.342020	−	0.939693i	$-0.388889\pi$
$631$	0.984808	−	1.70574i	0.984808	−	1.70574i	0.642788	−	0.766044i	$-0.277778\pi$
$632$		0			0
$633$		0			0
$634$	−2.17718	+	0.792431i	−2.17718	+	0.792431i
$635$	1.81535	−	0.660732i	1.81535	−	0.660732i
$636$	0.0759757	+	0.283545i	0.0759757	+	0.283545i
$637$	−0.146774	−	0.832395i	−0.146774	−	0.832395i
$638$		0			0
$639$		0			0
$640$	−0.858480	−	1.48693i	−0.858480	−	1.48693i
$641$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$641$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$642$	1.87223	+	2.67383i	1.87223	+	2.67383i
$643$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$643$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	1.05308	+	0.383290i	1.05308	+	0.383290i
$649$		0			0
$650$	1.30124	+	0.473614i	1.30124	+	0.473614i
$651$		0			0
$652$		0			0
$653$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$653$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$654$		0			0
$655$	1.43969	−	1.20805i	1.43969	−	1.20805i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$	−0.858480	−	3.20389i	−0.858480	−	3.20389i
$661$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$661$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.62760	+	0.939693i	1.62760	+	0.939693i
$667$		0			0
$668$	2.33836	−	1.96212i	2.33836	−	1.96212i
$669$	−1.80572	+	0.157980i	−1.80572	+	0.157980i
$670$	0.549590	−	3.11688i	0.549590	−	3.11688i
$671$		0			0
$672$		0			0
$673$	−1.53950	−	0.560333i	−1.53950	−	0.560333i	−0.573576	−	0.819152i	$-0.694444\pi$
$673$	−1.53950	−	0.560333i	−1.53950	−	0.560333i	−0.965926	+	0.258819i	$0.916667\pi$
$674$	2.31691			2.31691
$675$	−0.573576	+	0.819152i	−0.573576	+	0.819152i
$676$	−0.480920			−0.480920
$677$	−1.07797	−	0.392349i	−1.07797	−	0.392349i	−0.258819	−	0.965926i	$-0.583333\pi$
$677$	−1.07797	−	0.392349i	−1.07797	−	0.392349i	−0.819152	+	0.573576i	$0.805556\pi$
$678$	−2.86843	+	1.33757i	−2.86843	+	1.33757i
$679$		0			0
$680$		0			0
$681$	0.597672	−	1.28171i	0.597672	−	1.28171i
$682$		0			0
$683$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$683$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$684$	−1.65846	+	0.292431i	−1.65846	+	0.292431i
$685$		0			0
$686$		0			0
$687$	−0.660732	−	0.177043i	−0.660732	−	0.177043i
$688$		0			0
$689$	−0.138449	+	0.0503913i	−0.138449	+	0.0503913i
$690$		0			0
$691$	−0.223238	−	1.26604i	−0.223238	−	1.26604i	−0.866025	−	0.500000i	$-0.833333\pi$
$691$	−0.223238	−	1.26604i	−0.223238	−	1.26604i	0.642788	−	0.766044i	$-0.277778\pi$
$692$	0.711706	−	1.23271i	0.711706	−	1.23271i
$693$		0			0
$694$		0			0
$695$	−1.32683	+	1.11334i	−1.32683	+	1.11334i
$696$		0			0
$697$		0			0
$698$	−0.435862	−	0.365731i	−0.435862	−	0.365731i
$699$		0			0
$700$		0			0
$701$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$701$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$702$	−0.358401	+	1.33757i	−0.358401	+	1.33757i
$703$	−1.14715			−1.14715
$704$	−2.92450	−	1.06443i	−2.92450	−	1.06443i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$709$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	1.56439	−	0.569392i	1.56439	−	0.569392i
$716$		0			0
$717$	−0.396534	−	1.47988i	−0.396534	−	1.47988i
$718$	0.560333	+	3.17781i	0.560333	+	3.17781i
$719$	−0.866025	+	1.50000i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$719$	−0.866025	+	1.50000i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$720$	−0.0519704	−	0.142788i	−0.0519704	−	0.142788i
$721$		0			0
$722$	1.25501	−	1.05308i	1.25501	−	1.05308i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−3.86419	−	2.70574i	−3.86419	−	2.70574i
$727$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$727$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$728$		0			0
$729$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$733$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$734$		0			0
$735$	−0.573576	−	0.819152i	−0.573576	−	0.819152i
$736$		0			0
$737$	−1.90250	−	3.29523i	−1.90250	−	3.29523i
$738$		0			0
$739$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$739$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$740$	−0.335463	−	1.90250i	−0.335463	−	1.90250i
$741$	−0.218763	−	0.816436i	−0.218763	−	0.816436i
$742$		0			0
$743$	1.53950	−	0.560333i	1.53950	−	0.560333i	0.573576	−	0.819152i	$-0.305556\pi$
$743$	1.53950	−	0.560333i	1.53950	−	0.560333i	0.965926	+	0.258819i	$0.0833333\pi$
$744$		0			0
$745$	0.223238	+	1.26604i	0.223238	+	1.26604i
$746$	−1.48481	+	2.57176i	−1.48481	+	2.57176i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	1.63207	−	0.142788i	1.63207	−	0.142788i
$751$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$751$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$752$		0			0
$753$	−0.163799	+	1.87223i	−0.163799	+	1.87223i
$754$		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
$760$	0.858480	+	0.720350i	0.858480	+	0.720350i
$761$	0.223238	−	1.26604i	0.223238	−	1.26604i	−0.642788	−	0.766044i	$-0.722222\pi$
$761$	0.223238	−	1.26604i	0.223238	−	1.26604i	0.866025	−	0.500000i	$-0.166667\pi$
$762$	1.33757	−	2.86843i	1.33757	−	2.86843i
$763$		0			0
$764$	1.29005	+	2.23443i	1.29005	+	2.23443i
$765$		0			0
$766$	0.939693	−	1.62760i	0.939693	−	1.62760i
$767$		0			0
$768$	−1.19080	−	0.319073i	−1.19080	−	0.319073i
$769$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.984808	−	0.173648i	$-0.944444\pi$
$769$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.642788	+	0.766044i	$0.722222\pi$
$770$		0			0
$771$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$772$	−0.0509740	−	0.289088i	−0.0509740	−	0.289088i
$773$	−0.996195	+	1.72546i	−0.996195	+	1.72546i	−0.422618	+	0.906308i	$0.638889\pi$
$773$	−0.996195	+	1.72546i	−0.996195	+	1.72546i	−0.573576	+	0.819152i	$0.694444\pi$
$774$		0			0
$775$		0			0
$776$	−0.444382	+	0.372881i	−0.444382	+	0.372881i
$777$		0			0
$778$	0.435862	−	2.47189i	0.435862	−	2.47189i
$779$		0			0
$780$	1.29005	−	0.601560i	1.29005	−	0.601560i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.151951			0.151951
$785$		0			0
$786$	0.268353	−	3.06729i	0.268353	−	3.06729i
$787$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.0871557	−	0.996195i	$-0.527778\pi$
$787$	−1.08335	−	0.909039i	−1.08335	−	0.909039i	−0.996195	+	0.0871557i	$0.972222\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.91156	−	1.10364i	−1.91156	−	1.10364i
$793$		0			0
$794$		0			0
$795$	−0.123257	+	0.123257i	−0.123257	+	0.123257i
$796$	0.549590	−	0.200034i	0.549590	−	0.200034i
$797$	1.87223	−	0.681437i	1.87223	−	0.681437i	0.906308	−	0.422618i	$-0.138889\pi$
$797$	1.87223	−	0.681437i	1.87223	−	0.681437i	0.965926	−	0.258819i	$-0.0833333\pi$
$798$		0			0
$799$		0			0
$800$	0.435862	−	0.754935i	0.435862	−	0.754935i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.86603	−	2.66496i	−1.86603	−	2.66496i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.82399	−	0.663878i	−1.82399	−	0.663878i
$809$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$809$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$810$	0.284489	+	1.61341i	0.284489	+	1.61341i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	1.41881	+	0.993464i	1.41881	+	0.993464i
$814$	−2.83564	−	2.37939i	−2.83564	−	2.37939i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$821$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$822$		0			0
$823$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$823$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$824$	−1.72527	+	0.627946i	−1.72527	+	0.627946i
$825$	1.39273	−	1.39273i	1.39273	−	1.39273i
$826$		0			0
$827$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$827$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$829$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$830$		0			0
$831$		0			0
$832$	0.231917	−	1.31527i	0.231917	−	1.31527i
$833$		0			0
$834$	−0.247315	+	2.82683i	−0.247315	+	2.82683i
$835$	1.70330	+	0.619951i	1.70330	+	0.619951i
$836$	3.31691			3.31691
$837$		0			0
$838$	−1.63830			−1.63830
$839$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$839$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$840$		0			0
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.142788	−	0.247315i	−0.142788	−	0.247315i
$846$		0			0
$847$		0			0
$848$	−0.00459940	−	0.0260845i	−0.00459940	−	0.0260845i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$853$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$854$		0			0
$855$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$856$	−1.11640	−	1.93366i	−1.11640	−	1.93366i
$857$	−1.25501	+	1.05308i	−1.25501	+	1.05308i	−0.258819	+	0.965926i	$0.583333\pi$
$857$	−1.25501	+	1.05308i	−1.25501	+	1.05308i	−0.996195	+	0.0871557i	$0.972222\pi$
$858$	1.15266	−	2.47189i	1.15266	−	2.47189i
$859$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$859$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.99239			−1.99239			−0.996195	−	0.0871557i	$-0.972222\pi$
$863$	−1.99239			−1.99239			−0.996195	+	0.0871557i	$0.972222\pi$
$864$	0.790050	+	0.368406i	0.790050	+	0.368406i
$865$	0.845237			0.845237
$866$	−0.796905	−	0.290050i	−0.796905	−	0.290050i
$867$	−0.0871557	+	0.996195i	−0.0871557	+	0.996195i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	1.25085	−	1.04959i	1.25085	−	1.04959i
$872$		0			0
$873$	0.448288	−	0.258819i	0.448288	−	0.258819i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.32893	−	0.483690i	1.32893	−	0.483690i	0.422618	−	0.906308i	$-0.361111\pi$
$877$	1.32893	−	0.483690i	1.32893	−	0.483690i	0.906308	+	0.422618i	$0.138889\pi$
$878$		0			0
$879$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$880$	0.0519704	+	0.294739i	0.0519704	+	0.294739i
$881$	0.342020	−	0.592396i	0.342020	−	0.592396i	−0.642788	−	0.766044i	$-0.722222\pi$
$881$	0.342020	−	0.592396i	0.342020	−	0.592396i	0.984808	+	0.173648i	$0.0555556\pi$
$882$	−1.61341	−	0.284489i	−1.61341	−	0.284489i
$883$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$883$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.47988	−	1.24177i	−1.47988	−	1.24177i	−0.906308	−	0.422618i	$-0.861111\pi$
$887$	−1.47988	−	1.24177i	−1.47988	−	1.24177i	−0.573576	−	0.819152i	$-0.694444\pi$
$888$	−1.05308	−	0.737376i	−1.05308	−	0.737376i
$889$		0			0
$890$		0			0
$891$	1.50881	+	1.26604i	1.50881	+	1.26604i
$892$	3.05252			3.05252
$893$		0			0
$894$	1.72527	+	1.20805i	1.72527	+	1.20805i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.08248	−	1.29005i	1.08248	−	1.29005i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	2.03440	−	0.740460i	2.03440	−	0.740460i
$905$		0			0
$906$		0			0
$907$	0.345975	+	1.96212i	0.345975	+	1.96212i	0.258819	+	0.965926i	$0.416667\pi$
$907$	0.345975	+	1.96212i	0.345975	+	1.96212i	0.0871557	+	0.996195i	$0.472222\pi$
$908$	−1.19080	+	2.06252i	−1.19080	+	2.06252i
$909$	1.50000	+	0.866025i	1.50000	+	0.866025i
$910$		0			0
$911$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$911$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$912$	0.151373	−	0.0132434i	0.151373	−	0.0132434i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.08248	+	0.393991i	1.08248	+	0.393991i
$917$		0			0
$918$		0			0
$919$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$919$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$920$		0			0
$921$	0.157980	−	0.0736672i	0.157980	−	0.0736672i
$922$	−1.25501	−	1.05308i	−1.25501	−	1.05308i
$923$		0			0
$924$		0			0
$925$	0.878770	−	0.737376i	0.878770	−	0.737376i
$926$		0			0
$927$	1.61341	−	0.284489i	1.61341	−	0.284489i
$928$		0			0
$929$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$929$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$930$		0			0
$931$	0.939693	−	0.342020i	0.939693	−	0.342020i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.323971	−	0.890103i	0.323971	−	0.890103i
$937$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$937$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$941$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$947$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$948$		0			0
$949$		0			0
$950$	−0.284489	+	1.61341i	−0.284489	+	1.61341i
$951$	−1.40883	+	0.123257i	−1.40883	+	0.123257i
$952$		0			0
$953$	−0.965926	−	1.67303i	−0.965926	−	1.67303i	−0.707107	−	0.707107i	$-0.750000\pi$
$953$	−0.965926	−	1.67303i	−0.965926	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$954$			0.285575i			0.285575i
$955$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$956$	0.448030	+	2.54090i	0.448030	+	2.54090i
$957$		0			0
$958$	1.97915	−	0.720350i	1.97915	−	0.720350i
$959$		0			0
$960$	−0.408960	−	1.52626i	−0.408960	−	1.52626i
$961$	0.173648	+	0.984808i	0.173648	+	0.984808i
$962$	0.794263	−	1.37570i	0.794263	−	1.37570i
$963$	0.681437	+	1.87223i	0.681437	+	1.87223i
$964$		0			0
$965$	0.133530	−	0.112045i	0.133530	−	0.112045i
$966$		0			0
$967$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$967$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$968$	2.47189	+	2.07417i	2.47189	+	2.07417i
$969$		0			0
$970$	−0.796905	−	0.290050i	−0.796905	−	0.290050i
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	1.37949	+	0.965926i	1.37949	+	0.965926i
$973$		0			0
$974$	−2.17718	−	0.792431i	−2.17718	−	0.792431i
$975$	0.692377	+	0.484808i	0.692377	+	0.484808i
$976$		0			0
$977$	−0.314757	+	1.78508i	−0.314757	+	1.78508i	0.258819	+	0.965926i	$0.416667\pi$
$977$	−0.314757	+	1.78508i	−0.314757	+	1.78508i	−0.573576	+	0.819152i	$0.694444\pi$
$978$		0			0
$979$		0			0
$980$	0.842020	+	1.45842i	0.842020	+	1.45842i
$981$		0			0
$982$	0.284489	−	0.492749i	0.284489	−	0.492749i
$983$	−0.314757	−	1.78508i	−0.314757	−	1.78508i	−0.573576	−	0.819152i	$-0.694444\pi$
$983$	−0.314757	−	1.78508i	−0.314757	−	1.78508i	0.258819	−	0.965926i	$-0.416667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.247173	+	1.40179i	0.247173	+	1.40179i
$989$		0			0
$990$		−	3.22683i		−	3.22683i
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.266044	+	0.223238i	0.266044	+	0.223238i
$996$		0			0
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$	2.10616			2.10616
$999$	0.811160	+	0.811160i	0.811160	+	0.811160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2565.1.dy.d.949.1	✓	24
5.4	even	2	inner	2565.1.dy.d.949.4	yes	24
19.18	odd	2	inner	2565.1.dy.d.949.4	yes	24
27.7	even	9	inner	2565.1.dy.d.1519.1	yes	24
95.94	odd	2	CM	2565.1.dy.d.949.1	✓	24
135.34	even	18	inner	2565.1.dy.d.1519.4	yes	24
513.493	odd	18	inner	2565.1.dy.d.1519.4	yes	24
2565.1519	odd	18	inner	2565.1.dy.d.1519.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2565.1.dy.d.949.1	✓	24	1.1	even	1	trivial
2565.1.dy.d.949.1	✓	24	95.94	odd	2	CM
2565.1.dy.d.949.4	yes	24	5.4	even	2	inner
2565.1.dy.d.949.4	yes	24	19.18	odd	2	inner
2565.1.dy.d.1519.1	yes	24	27.7	even	9	inner
2565.1.dy.d.1519.1	yes	24	2565.1519	odd	18	inner
2565.1.dy.d.1519.4	yes	24	135.34	even	18	inner
2565.1.dy.d.1519.4	yes	24	513.493	odd	18	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(-1.53950 - 0.560333i) q^{2} +(-0.819152 - 0.573576i) q^{3} +(1.29005 + 1.08248i) q^{4} +(-0.173648 + 0.984808i) q^{5} +(0.939693 + 1.34202i) q^{6} +(-0.560333 - 0.970525i) q^{8} +(0.342020 + 0.939693i) q^{9} +(0.819152 - 1.41881i) q^{10} +(-0.342020 - 1.93969i) q^{11} +(-0.435862 - 1.62666i) q^{12} +(0.794263 - 0.289088i) q^{13} +(0.707107 - 0.707107i) q^{15} +(0.0263861 + 0.149643i) q^{16} -1.63830i q^{18} +(0.500000 + 0.866025i) q^{19} +(-1.29005 + 1.08248i) q^{20} +(-0.560333 + 3.17781i) q^{22} +(-0.0976725 + 1.11640i) q^{24} +(-0.939693 - 0.342020i) q^{25} -1.38475 q^{26} +(0.258819 - 0.965926i) q^{27} +(-1.48481 + 0.692377i) q^{30} +(-0.151373 + 0.858480i) q^{32} +(-0.832395 + 1.78508i) q^{33} +(-0.575976 + 1.58248i) q^{36} +(-0.573576 + 0.993464i) q^{37} +(-0.284489 - 1.61341i) q^{38} +(-0.816436 - 0.218763i) q^{39} +(1.05308 - 0.383290i) q^{40} +(1.65846 - 2.87253i) q^{44} +(-0.984808 + 0.173648i) q^{45} +(0.0642174 - 0.137715i) q^{48} +(0.173648 - 0.984808i) q^{49} +(1.25501 + 1.05308i) q^{50} +(1.33757 + 0.486836i) q^{52} -0.174311 q^{53} +(-0.939693 + 1.34202i) q^{54} +1.96962 q^{55} +(0.0871557 - 0.996195i) q^{57} +(1.67763 - 0.146774i) q^{60} +(0.790050 - 1.36841i) q^{64} +(0.146774 + 0.832395i) q^{65} +(2.28171 - 2.28171i) q^{66} +(1.81535 - 0.660732i) q^{67} +(0.720350 - 0.858480i) q^{72} +(1.43969 - 1.20805i) q^{74} +(0.573576 + 0.819152i) q^{75} +(-0.292431 + 1.65846i) q^{76} +(1.13432 + 0.794263i) q^{78} -0.151951 q^{80} +(-0.766044 + 0.642788i) q^{81} +(-1.69088 + 1.41881i) q^{88} +(1.61341 + 0.284489i) q^{90} +(-0.939693 + 0.342020i) q^{95} +(0.616402 - 0.616402i) q^{96} +(-0.0898869 - 0.509774i) q^{97} +(-0.819152 + 1.41881i) q^{98} +(1.70574 - 0.984808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{16} + 12 q^{19} + 12 q^{24} - 12 q^{30} - 24 q^{36} + 12 q^{44} - 12 q^{64} + 24 q^{66} + 12 q^{74} - 24 q^{80} - 12 q^{96}+O(q^{100}) \) 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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