LMFDB - Embedded newform 2808.1.fi.b.2131.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2808,1,Mod(259,2808)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2808.259"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2808, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 4, 9])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 2808 = 2^{3} \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2808.fi (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,0,0,0,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$1.40137455547$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{54})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{9} + 1 $ x^18 - x^9 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{27}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{27} + \cdots)$

Embedding invariants

Embedding label			2131.2
Root			$0.0581448 + 0.998308i$ of defining polynomial
Character	$\chi$	$=$	2808.2131
Dual form			2808.1.fi.b.2443.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.396080 + 0.918216i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.914900 + 0.767692i) q^{5} +(-0.973045 + 0.230616i) q^{6} +(-1.28971 + 0.469417i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.686242 + 0.727374i) q^{9} +(-0.597159 - 1.03431i) q^{10} +(-0.0581448 - 0.998308i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(-0.238329 - 1.35163i) q^{14} +(-1.06728 - 0.536009i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.0581448 + 0.100710i) q^{17} +(-0.597159 - 0.802123i) q^{18} +(1.12229 - 0.408481i) q^{20} +(-0.941855 - 0.998308i) q^{21} +(0.993238 + 0.116093i) q^{24} +(0.0740425 - 0.419916i) q^{25} +1.00000 q^{26} +(-0.939693 - 0.342020i) q^{27} +1.37248 q^{28} +(0.713197 - 0.957990i) q^{30} +(-1.76604 - 0.642788i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.109277 + 0.0397734i) q^{34} +(0.819590 - 1.41957i) q^{35} +(0.893633 - 0.448799i) q^{36} +(0.396080 + 0.686030i) q^{37} +(0.835488 - 0.549509i) q^{39} +(0.207391 + 1.17617i) q^{40} +(1.14669 - 0.754192i) q^{42} +(-1.28004 - 1.07408i) q^{43} +(0.0694434 - 1.19230i) q^{45} +(1.67948 - 0.611281i) q^{47} +(-0.286803 + 0.957990i) q^{48} +(0.676961 - 0.568038i) q^{49} +(0.400679 + 0.145835i) q^{50} +(-0.0694434 + 0.0932786i) q^{51} +(-0.173648 + 0.984808i) q^{52} +(0.500000 - 0.866025i) q^{54} +(-0.238329 + 1.35163i) q^{56} +(0.819590 + 0.868715i) q^{60} +(0.939693 - 1.62760i) q^{62} +(0.543613 - 1.26024i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.914900 + 0.767692i) q^{65} +(-0.0201935 - 0.114523i) q^{68} +(1.25569 + 1.05364i) q^{70} +(0.973045 + 1.68536i) q^{71} +(0.286803 + 0.957990i) q^{72} +(-0.744386 + 0.270935i) q^{74} +(0.414900 - 0.0983331i) q^{75} +(0.396080 + 0.918216i) q^{78} -1.19432 q^{80} +(-0.0581448 - 0.998308i) q^{81} +(0.543613 + 1.26024i) q^{84} +(-0.130511 - 0.0475021i) q^{85} +(1.28004 - 1.07408i) q^{86} +(1.16212 + 0.275428i) q^{90} +(0.686242 + 1.18861i) q^{91} +(-0.109277 - 1.87621i) q^{93} +(0.310355 + 1.76011i) q^{94} +(-0.893633 - 0.448799i) q^{96} +(0.441855 + 0.765316i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{8} - 18 q^{21} + 18 q^{26} + 18 q^{30} - 18 q^{31} + 9 q^{54} - 9 q^{64} + 9 q^{70} - 9 q^{75} + 9 q^{85} + 9 q^{98}+O(q^{100}) $ 18 * q + 9 * q^8 - 18 * q^21 + 18 * q^26 + 18 * q^30 - 18 * q^31 + 9 * q^54 - 9 * q^64 + 9 * q^70 - 9 * q^75 + 9 * q^85 + 9 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2808\mathbb{Z}\right)^\times$.

$n$	$703$	$1081$	$1405$	$2081$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$2$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$3$	0.396080	+	0.918216i	0.396080	+	0.918216i
$3$	0.396080	+	0.918216i	0.396080	+	0.918216i
$4$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$5$	−0.914900	+	0.767692i	−0.914900	+	0.767692i	−0.973045	−	0.230616i	$-0.925926\pi$
$5$	−0.914900	+	0.767692i	−0.914900	+	0.767692i	0.0581448	+	0.998308i	$0.481481\pi$
$6$	−0.973045	+	0.230616i	−0.973045	+	0.230616i
$7$	−1.28971	+	0.469417i	−1.28971	+	0.469417i	−0.893633	−	0.448799i	$-0.851852\pi$
$7$	−1.28971	+	0.469417i	−1.28971	+	0.469417i	−0.396080	+	0.918216i	$0.629630\pi$
$8$	0.500000	−	0.866025i	0.500000	−	0.866025i
$9$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$10$	−0.597159	−	1.03431i	−0.597159	−	1.03431i
$11$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$11$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$12$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$13$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$14$	−0.238329	−	1.35163i	−0.238329	−	1.35163i
$15$	−1.06728	−	0.536009i	−1.06728	−	0.536009i
$16$	0.766044	+	0.642788i	0.766044	+	0.642788i
$17$	0.0581448	+	0.100710i	0.0581448	+	0.100710i	0.893633	−	0.448799i	$-0.148148\pi$
$17$	0.0581448	+	0.100710i	0.0581448	+	0.100710i	−0.835488	+	0.549509i	$0.814815\pi$
$18$	−0.597159	−	0.802123i	−0.597159	−	0.802123i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	1.12229	−	0.408481i	1.12229	−	0.408481i
$21$	−0.941855	−	0.998308i	−0.941855	−	0.998308i
$22$		0			0
$23$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$23$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$24$	0.993238	+	0.116093i	0.993238	+	0.116093i
$25$	0.0740425	−	0.419916i	0.0740425	−	0.419916i
$26$	1.00000			1.00000
$27$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$28$	1.37248			1.37248
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$	0.713197	−	0.957990i	0.713197	−	0.957990i
$31$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$31$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$32$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$33$		0			0
$34$	−0.109277	+	0.0397734i	−0.109277	+	0.0397734i
$35$	0.819590	−	1.41957i	0.819590	−	1.41957i
$36$	0.893633	−	0.448799i	0.893633	−	0.448799i
$37$	0.396080	+	0.686030i	0.396080	+	0.686030i	0.993238	−	0.116093i	$-0.0370370\pi$
$37$	0.396080	+	0.686030i	0.396080	+	0.686030i	−0.597159	+	0.802123i	$0.703704\pi$
$38$		0			0
$39$	0.835488	−	0.549509i	0.835488	−	0.549509i
$40$	0.207391	+	1.17617i	0.207391	+	1.17617i
$41$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$41$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$42$	1.14669	−	0.754192i	1.14669	−	0.754192i
$43$	−1.28004	−	1.07408i	−1.28004	−	1.07408i	−0.993238	−	0.116093i	$-0.962963\pi$
$43$	−1.28004	−	1.07408i	−1.28004	−	1.07408i	−0.286803	−	0.957990i	$-0.592593\pi$
$44$		0			0
$45$	0.0694434	−	1.19230i	0.0694434	−	1.19230i
$46$		0			0
$47$	1.67948	−	0.611281i	1.67948	−	0.611281i	0.686242	−	0.727374i	$-0.259259\pi$
$47$	1.67948	−	0.611281i	1.67948	−	0.611281i	0.993238	+	0.116093i	$0.0370370\pi$
$48$	−0.286803	+	0.957990i	−0.286803	+	0.957990i
$49$	0.676961	−	0.568038i	0.676961	−	0.568038i
$50$	0.400679	+	0.145835i	0.400679	+	0.145835i
$51$	−0.0694434	+	0.0932786i	−0.0694434	+	0.0932786i
$52$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.500000	−	0.866025i	0.500000	−	0.866025i
$55$		0			0
$56$	−0.238329	+	1.35163i	−0.238329	+	1.35163i
$57$		0			0
$58$		0			0
$59$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$59$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$60$	0.819590	+	0.868715i	0.819590	+	0.868715i
$61$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$61$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$62$	0.939693	−	1.62760i	0.939693	−	1.62760i
$63$	0.543613	−	1.26024i	0.543613	−	1.26024i
$64$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$65$	0.914900	+	0.767692i	0.914900	+	0.767692i
$66$		0			0
$67$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$67$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$68$	−0.0201935	−	0.114523i	−0.0201935	−	0.114523i
$69$		0			0
$70$	1.25569	+	1.05364i	1.25569	+	1.05364i
$71$	0.973045	+	1.68536i	0.973045	+	1.68536i	0.686242	+	0.727374i	$0.259259\pi$
$71$	0.973045	+	1.68536i	0.973045	+	1.68536i	0.286803	+	0.957990i	$0.407407\pi$
$72$	0.286803	+	0.957990i	0.286803	+	0.957990i
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$	−0.744386	+	0.270935i	−0.744386	+	0.270935i
$75$	0.414900	−	0.0983331i	0.414900	−	0.0983331i
$76$		0			0
$77$		0			0
$78$	0.396080	+	0.918216i	0.396080	+	0.918216i
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$	−1.19432			−1.19432
$81$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$82$		0			0
$83$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$83$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$84$	0.543613	+	1.26024i	0.543613	+	1.26024i
$85$	−0.130511	−	0.0475021i	−0.130511	−	0.0475021i
$86$	1.28004	−	1.07408i	1.28004	−	1.07408i
$87$		0			0
$88$		0			0
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$	1.16212	+	0.275428i	1.16212	+	0.275428i
$91$	0.686242	+	1.18861i	0.686242	+	1.18861i
$92$		0			0
$93$	−0.109277	−	1.87621i	−0.109277	−	1.87621i
$94$	0.310355	+	1.76011i	0.310355	+	1.76011i
$95$		0			0
$96$	−0.893633	−	0.448799i	−0.893633	−	0.448799i
$97$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$97$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$98$	0.441855	+	0.765316i	0.441855	+	0.765316i
$99$		0			0
$100$	−0.213197	+	0.369268i	−0.213197	+	0.369268i
$101$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$101$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$102$	−0.0798028	−	0.0845860i	−0.0798028	−	0.0845860i
$103$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$103$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$104$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$105$	1.62810	+	0.190297i	1.62810	+	0.190297i
$106$		0			0
$107$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$107$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.766044	+	0.642788i	0.766044	+	0.642788i
$109$	−1.78727			−1.78727			−0.893633	−	0.448799i	$-0.851852\pi$
$109$	−1.78727			−1.78727			−0.893633	+	0.448799i	$0.851852\pi$
$110$		0			0
$111$	−0.473045	+	0.635410i	−0.473045	+	0.635410i
$112$	−1.28971	−	0.469417i	−1.28971	−	0.469417i
$113$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$113$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.835488	+	0.549509i	0.835488	+	0.549509i
$118$		0			0
$119$	−0.122265	−	0.102593i	−0.122265	−	0.102593i
$120$	−0.997837	+	0.656288i	−0.997837	+	0.656288i
$121$	0.173648	+	0.984808i	0.173648	+	0.984808i
$122$		0			0
$123$		0			0
$124$	1.43969	+	1.20805i	1.43969	+	1.20805i
$125$	−0.342534	−	0.593286i	−0.342534	−	0.593286i
$126$	1.14669	+	0.754192i	1.14669	+	0.754192i
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$	0.939693	−	0.342020i	0.939693	−	0.342020i
$129$	0.479241	−	1.60078i	0.479241	−	1.60078i
$130$	−0.914900	+	0.767692i	−0.914900	+	0.767692i
$131$	−1.67948	−	0.611281i	−1.67948	−	0.611281i	−0.686242	−	0.727374i	$-0.740741\pi$
$131$	−1.67948	−	0.611281i	−1.67948	−	0.611281i	−0.993238	+	0.116093i	$0.962963\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.12229	−	0.408481i	1.12229	−	0.408481i
$136$	0.116290			0.116290
$137$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$137$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$138$		0			0
$139$	−1.82873	−	0.665602i	−1.82873	−	0.665602i	−0.993238	−	0.116093i	$-0.962963\pi$
$139$	−1.82873	−	0.665602i	−1.82873	−	0.665602i	−0.835488	−	0.549509i	$-0.814815\pi$
$140$	−1.25569	+	1.05364i	−1.25569	+	1.05364i
$141$	1.22650	+	1.30001i	1.22650	+	1.30001i
$142$	−1.82873	+	0.665602i	−1.82873	+	0.665602i
$143$		0			0
$144$	−0.993238	+	0.116093i	−0.993238	+	0.116093i
$145$		0			0
$146$		0			0
$147$	0.789712	+	0.396608i	0.789712	+	0.396608i
$148$	−0.137557	−	0.780125i	−0.137557	−	0.780125i
$149$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$149$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$150$	0.0247926	+	0.425672i	0.0247926	+	0.425672i
$151$	−0.914900	−	0.767692i	−0.914900	−	0.767692i	0.0581448	−	0.998308i	$-0.481481\pi$
$151$	−0.914900	−	0.767692i	−0.914900	−	0.767692i	−0.973045	+	0.230616i	$0.925926\pi$
$152$		0			0
$153$	−0.113155	−	0.0268182i	−0.113155	−	0.0268182i
$154$		0			0
$155$	2.10922	−	0.767692i	2.10922	−	0.767692i
$156$	−0.973045	+	0.230616i	−0.973045	+	0.230616i
$157$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$157$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$158$		0			0
$159$		0			0
$160$	0.207391	−	1.17617i	0.207391	−	1.17617i
$161$		0			0
$162$	0.993238	+	0.116093i	0.993238	+	0.116093i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	−0.766044	−	0.642788i	$-0.777778\pi$
$167$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	0.500000	+	0.866025i	$0.333333\pi$
$168$	−1.33549	+	0.316516i	−1.33549	+	0.316516i
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$	0.0694434	−	0.120279i	0.0694434	−	0.120279i
$171$		0			0
$172$	0.835488	+	1.44711i	0.835488	+	1.44711i
$173$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$173$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$174$		0			0
$175$	0.101622	+	0.576327i	0.101622	+	0.576327i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.973045	−	1.68536i	−0.973045	−	1.68536i	−0.686242	−	0.727374i	$-0.740741\pi$
$179$	−0.973045	−	1.68536i	−0.973045	−	1.68536i	−0.286803	−	0.957990i	$-0.592593\pi$
$180$	−0.473045	+	1.09664i	−0.473045	+	1.09664i
$181$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$181$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$182$	−1.28971	+	0.469417i	−1.28971	+	0.469417i
$183$		0			0
$184$		0			0
$185$	−0.889034	−	0.323582i	−0.889034	−	0.323582i
$186$	1.86668	+	0.218183i	1.86668	+	0.218183i
$187$		0			0
$188$	−1.78727			−1.78727
$189$	1.37248			1.37248
$190$		0			0
$191$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$191$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$192$	0.597159	−	0.802123i	0.597159	−	0.802123i
$193$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$193$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$194$		0			0
$195$	−0.342534	+	1.14414i	−0.342534	+	1.14414i
$196$	−0.830416	+	0.302247i	−0.830416	+	0.302247i
$197$	−0.686242	+	1.18861i	−0.686242	+	1.18861i	0.286803	+	0.957990i	$0.407407\pi$
$197$	−0.686242	+	1.18861i	−0.686242	+	1.18861i	−0.973045	+	0.230616i	$0.925926\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	−0.326636	−	0.274080i	−0.326636	−	0.274080i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.0971586	−	0.0639022i	0.0971586	−	0.0639022i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.500000	−	0.866025i	0.500000	−	0.866025i
$209$		0			0
$210$	−0.470122	+	1.57032i	−0.470122	+	1.57032i
$211$	−1.52173	+	1.27688i	−1.52173	+	1.27688i	−0.686242	+	0.727374i	$0.740741\pi$
$211$	−1.52173	+	1.27688i	−1.52173	+	1.27688i	−0.835488	+	0.549509i	$0.814815\pi$
$212$		0			0
$213$	−1.16212	+	1.56100i	−1.16212	+	1.56100i
$214$	0.173648	−	0.984808i	0.173648	−	0.984808i
$215$	1.99567			1.99567
$216$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$217$	2.57942			2.57942
$218$	0.310355	−	1.76011i	0.310355	−	1.76011i
$219$		0			0
$220$		0			0
$221$	0.0890830	−	0.0747496i	0.0890830	−	0.0747496i
$222$	−0.543613	−	0.576196i	−0.543613	−	0.576196i
$223$	−1.57020	+	0.571507i	−1.57020	+	0.571507i	−0.973045	−	0.230616i	$-0.925926\pi$
$223$	−1.57020	+	0.571507i	−1.57020	+	0.571507i	−0.597159	+	0.802123i	$0.703704\pi$
$224$	0.686242	−	1.18861i	0.686242	−	1.18861i
$225$	0.254625	+	0.342020i	0.254625	+	0.342020i
$226$	0.766044	+	1.32683i	0.766044	+	1.32683i
$227$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$227$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$228$		0			0
$229$	−0.207391	−	1.17617i	−0.207391	−	1.17617i	−0.893633	−	0.448799i	$-0.851852\pi$
$229$	−0.207391	−	1.17617i	−0.207391	−	1.17617i	0.686242	−	0.727374i	$-0.259259\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.286803	+	0.496758i	0.286803	+	0.496758i	0.973045	−	0.230616i	$-0.0740741\pi$
$233$	0.286803	+	0.496758i	0.286803	+	0.496758i	−0.686242	+	0.727374i	$0.740741\pi$
$234$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$235$	−1.06728	+	1.84858i	−1.06728	+	1.84858i
$236$		0			0
$237$		0			0
$238$	0.122265	−	0.102593i	0.122265	−	0.102593i
$239$	−1.57020	−	0.571507i	−1.57020	−	0.571507i	−0.597159	−	0.802123i	$-0.703704\pi$
$239$	−1.57020	−	0.571507i	−1.57020	−	0.571507i	−0.973045	+	0.230616i	$0.925926\pi$
$240$	−0.473045	−	1.09664i	−0.473045	−	1.09664i
$241$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$241$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$242$	−1.00000			−1.00000
$243$	0.893633	−	0.448799i	0.893633	−	0.448799i
$244$		0			0
$245$	−0.183274	+	1.03940i	−0.183274	+	1.03940i
$246$		0			0
$247$		0			0
$248$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$249$		0			0
$250$	0.643753	−	0.234307i	0.643753	−	0.234307i
$251$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$251$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$252$	−0.941855	+	0.998308i	−0.941855	+	0.998308i
$253$		0			0
$254$		0			0
$255$	−0.00807555	−	0.138652i	−0.00807555	−	0.138652i
$256$	0.173648	+	0.984808i	0.173648	+	0.984808i
$257$	0.137557	+	0.780125i	0.137557	+	0.780125i	0.973045	+	0.230616i	$0.0740741\pi$
$257$	0.137557	+	0.780125i	0.137557	+	0.780125i	−0.835488	+	0.549509i	$0.814815\pi$
$258$	1.49324	+	0.749932i	1.49324	+	0.749932i
$259$	−0.832863	−	0.698855i	−0.832863	−	0.698855i
$260$	−0.597159	−	1.03431i	−0.597159	−	1.03431i
$261$		0			0
$262$	0.893633	−	1.54782i	0.893633	−	1.54782i
$263$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$263$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	0.207391	+	1.17617i	0.207391	+	1.17617i
$271$	1.98648			1.98648			0.993238	−	0.116093i	$-0.0370370\pi$
$271$	1.98648			1.98648			0.993238	+	0.116093i	$0.0370370\pi$
$272$	−0.0201935	+	0.114523i	−0.0201935	+	0.114523i
$273$	−0.819590	+	1.10090i	−0.819590	+	1.10090i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$277$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$278$	0.973045	−	1.68536i	0.973045	−	1.68536i
$279$	1.67948	−	0.843467i	1.67948	−	0.843467i
$280$	−0.819590	−	1.41957i	−0.819590	−	1.41957i
$281$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$281$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$282$	−1.49324	+	0.982118i	−1.49324	+	0.982118i
$283$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$283$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$284$	−0.337935	−	1.91652i	−0.337935	−	1.91652i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0581448	−	0.998308i	0.0581448	−	0.998308i
$289$	0.493238	−	0.854314i	0.493238	−	0.854314i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.82873	+	0.665602i	1.82873	+	0.665602i	0.993238	+	0.116093i	$0.0370370\pi$
$293$	1.82873	+	0.665602i	1.82873	+	0.665602i	0.835488	+	0.549509i	$0.185185\pi$
$294$	−0.527715	+	0.708845i	−0.527715	+	0.708845i
$295$		0			0
$296$	0.792160			0.792160
$297$		0			0
$298$	0.347296			0.347296
$299$		0			0
$300$	−0.423510	−	0.0495013i	−0.423510	−	0.0495013i
$301$	2.15508	+	0.784384i	2.15508	+	0.784384i
$302$	0.914900	−	0.767692i	0.914900	−	0.767692i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	0.0460600	−	0.106779i	0.0460600	−	0.106779i
$307$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$307$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$		0			0
$310$	0.389768	+	2.21048i	0.389768	+	2.21048i
$311$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$311$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$312$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$313$	−1.52173	−	1.27688i	−1.52173	−	1.27688i	−0.835488	−	0.549509i	$-0.814815\pi$
$313$	−1.52173	−	1.27688i	−1.52173	−	1.27688i	−0.686242	−	0.727374i	$-0.740741\pi$
$314$		0			0
$315$	0.470122	+	1.57032i	0.470122	+	1.57032i
$316$		0			0
$317$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$317$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$318$		0			0
$319$		0			0
$320$	1.12229	+	0.408481i	1.12229	+	0.408481i
$321$	−0.396080	−	0.918216i	−0.396080	−	0.918216i
$322$		0			0
$323$		0			0
$324$	−0.286803	+	0.957990i	−0.286803	+	0.957990i
$325$	−0.426394			−0.426394
$326$		0			0
$327$	−0.707900	−	1.64110i	−0.707900	−	1.64110i
$328$		0			0
$329$	−1.87910	+	1.57675i	−1.87910	+	1.57675i
$330$		0			0
$331$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$331$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$332$		0			0
$333$	−0.770807	−	0.182685i	−0.770807	−	0.182685i
$334$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$335$		0			0
$336$	−0.0798028	−	1.37016i	−0.0798028	−	1.37016i
$337$	0.337935	+	1.91652i	0.337935	+	1.91652i	0.396080	+	0.918216i	$0.370370\pi$
$337$	0.337935	+	1.91652i	0.337935	+	1.91652i	−0.0581448	+	0.998308i	$0.518519\pi$
$338$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$339$	1.36912	+	0.687600i	1.36912	+	0.687600i
$340$	0.106393	+	0.0892747i	0.106393	+	0.0892747i
$341$		0			0
$342$		0			0
$343$	0.0798028	−	0.138223i	0.0798028	−	0.138223i
$344$	−1.57020	+	0.571507i	−1.57020	+	0.571507i
$345$		0			0
$346$		0			0
$347$	−0.744386	−	0.270935i	−0.744386	−	0.270935i	−0.0581448	−	0.998308i	$-0.518519\pi$
$347$	−0.744386	−	0.270935i	−0.744386	−	0.270935i	−0.686242	+	0.727374i	$0.740741\pi$
$348$		0			0
$349$	0.344948	−	1.95630i	0.344948	−	1.95630i	0.0581448	−	0.998308i	$-0.481481\pi$
$349$	0.344948	−	1.95630i	0.344948	−	1.95630i	0.286803	−	0.957990i	$-0.407407\pi$
$350$	−0.585218			−0.585218
$351$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$352$		0			0
$353$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$353$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$354$		0			0
$355$	−2.18408	−	0.794940i	−2.18408	−	0.794940i
$356$		0			0
$357$	0.0457754	−	0.152901i	0.0457754	−	0.152901i
$358$	1.82873	−	0.665602i	1.82873	−	0.665602i
$359$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$359$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$360$	−0.997837	−	0.656288i	−0.997837	−	0.656288i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$364$	−0.238329	−	1.35163i	−0.238329	−	1.35163i
$365$		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
$370$	0.473045	−	0.819338i	0.473045	−	0.819338i
$371$		0			0
$372$	−0.539014	+	1.80043i	−0.539014	+	1.80043i
$373$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$373$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$374$		0			0
$375$	0.409094	−	0.549509i	0.409094	−	0.549509i
$376$	0.310355	−	1.76011i	0.310355	−	1.76011i
$377$		0			0
$378$	−0.238329	+	1.35163i	−0.238329	+	1.35163i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.439408	−	0.368707i	0.439408	−	0.368707i	−0.396080	−	0.918216i	$-0.629630\pi$
$383$	0.439408	−	0.368707i	0.439408	−	0.368707i	0.835488	+	0.549509i	$0.185185\pi$
$384$	0.686242	+	0.727374i	0.686242	+	0.727374i
$385$		0			0
$386$		0			0
$387$	1.65968	−	0.193988i	1.65968	−	0.193988i
$388$		0			0
$389$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$389$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$390$	−1.06728	−	0.536009i	−1.06728	−	0.536009i
$391$		0			0
$392$	−0.153455	−	0.870285i	−0.153455	−	0.870285i
$393$	−0.103920	−	1.78424i	−0.103920	−	1.78424i
$394$	−1.05138	−	0.882215i	−1.05138	−	0.882215i
$395$		0			0
$396$		0			0
$397$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$397$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$398$		0			0
$399$		0			0
$400$	0.326636	−	0.274080i	0.326636	−	0.274080i
$401$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$401$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$402$		0			0
$403$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$404$		0			0
$405$	0.819590	+	0.868715i	0.819590	+	0.868715i
$406$		0			0
$407$		0			0
$408$	0.0460600	+	0.106779i	0.0460600	+	0.106779i
$409$		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
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.766044	+	0.642788i	0.766044	+	0.642788i
$417$	−0.113155	−	1.94280i	−0.113155	−	1.94280i
$418$		0			0
$419$	0.207391	+	1.17617i	0.207391	+	1.17617i	0.893633	+	0.448799i	$0.148148\pi$
$419$	0.207391	+	1.17617i	0.207391	+	1.17617i	−0.686242	+	0.727374i	$0.740741\pi$
$420$	−1.46483	−	0.735663i	−1.46483	−	0.735663i
$421$	0.439408	+	0.368707i	0.439408	+	0.368707i	0.835488	−	0.549509i	$-0.185185\pi$
$421$	0.439408	+	0.368707i	0.439408	+	0.368707i	−0.396080	+	0.918216i	$0.629630\pi$
$422$	−0.993238	−	1.72034i	−0.993238	−	1.72034i
$423$	−0.707900	+	1.64110i	−0.707900	+	1.64110i
$424$		0			0
$425$	0.0465948	−	0.0169591i	0.0465948	−	0.0169591i
$426$	−1.33549	−	1.41553i	−1.33549	−	1.41553i
$427$		0			0
$428$	0.939693	+	0.342020i	0.939693	+	0.342020i
$429$		0			0
$430$	−0.346545	+	1.96536i	−0.346545	+	1.96536i
$431$	−0.792160			−0.792160			−0.396080	−	0.918216i	$-0.629630\pi$
$431$	−0.792160			−0.792160			−0.396080	+	0.918216i	$0.629630\pi$
$432$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$433$	−1.37248			−1.37248			−0.686242	−	0.727374i	$-0.740741\pi$
$433$	−1.37248			−1.37248			−0.686242	+	0.727374i	$0.740741\pi$
$434$	−0.447912	+	2.54024i	−0.447912	+	2.54024i
$435$		0			0
$436$	1.67948	+	0.611281i	1.67948	+	0.611281i
$437$		0			0
$438$		0			0
$439$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$439$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$440$		0			0
$441$	−0.0513832	+	0.882215i	−0.0513832	+	0.882215i
$442$	0.0581448	+	0.100710i	0.0581448	+	0.100710i
$443$	1.49079	+	1.25092i	1.49079	+	1.25092i	0.893633	+	0.448799i	$0.148148\pi$
$443$	1.49079	+	1.25092i	1.49079	+	1.25092i	0.597159	+	0.802123i	$0.296296\pi$
$444$	0.661840	−	0.435299i	0.661840	−	0.435299i
$445$		0			0
$446$	−0.290162	−	1.64559i	−0.290162	−	1.64559i
$447$	0.290162	−	0.190842i	0.290162	−	0.190842i
$448$	1.05138	+	0.882215i	1.05138	+	0.882215i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	−0.381039	+	0.191365i	−0.381039	+	0.191365i
$451$		0			0
$452$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$453$	0.342534	−	1.14414i	0.342534	−	1.14414i
$454$		0			0
$455$	−1.54033	−	0.560633i	−1.54033	−	0.560633i
$456$		0			0
$457$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$457$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$458$	1.19432			1.19432
$459$	−0.0201935	−	0.114523i	−0.0201935	−	0.114523i
$460$		0			0
$461$	0.0996057	−	0.564892i	0.0996057	−	0.564892i	−0.893633	−	0.448799i	$-0.851852\pi$
$461$	0.0996057	−	0.564892i	0.0996057	−	0.564892i	0.993238	−	0.116093i	$-0.0370370\pi$
$462$		0			0
$463$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$463$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$464$		0			0
$465$	1.54033	+	1.63265i	1.54033	+	1.63265i
$466$	−0.539014	+	0.196185i	−0.539014	+	0.196185i
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$467$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$468$	−0.597159	−	0.802123i	−0.597159	−	0.802123i
$469$		0			0
$470$	−1.63517	−	1.37207i	−1.63517	−	1.37207i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	0.0798028	+	0.138223i	0.0798028	+	0.138223i
$477$		0			0
$478$	0.835488	−	1.44711i	0.835488	−	1.44711i
$479$	−1.86668	+	0.679415i	−1.86668	+	0.679415i	−0.893633	+	0.448799i	$0.851852\pi$
$479$	−1.86668	+	0.679415i	−1.86668	+	0.679415i	−0.973045	+	0.230616i	$0.925926\pi$
$480$	1.16212	−	0.275428i	1.16212	−	0.275428i
$481$	0.606829	−	0.509190i	0.606829	−	0.509190i
$482$		0			0
$483$		0			0
$484$	0.173648	−	0.984808i	0.173648	−	0.984808i
$485$		0			0
$486$	0.286803	+	0.957990i	0.286803	+	0.957990i
$487$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$487$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$	−0.991780	−	0.360978i	−0.991780	−	0.360978i
$491$	−1.28004	+	1.07408i	−1.28004	+	1.07408i	−0.286803	+	0.957990i	$0.592593\pi$
$491$	−1.28004	+	1.07408i	−1.28004	+	1.07408i	−0.993238	+	0.116093i	$0.962963\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$497$	−2.04609	−	1.71687i	−2.04609	−	1.71687i
$498$		0			0
$499$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$499$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$500$	0.118961	+	0.674660i	0.118961	+	0.674660i
$501$	−0.310355	−	0.155866i	−0.310355	−	0.155866i
$502$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$503$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$503$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$504$	−0.819590	−	1.10090i	−0.819590	−	1.10090i
$505$		0			0
$506$		0			0
$507$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$508$		0			0
$509$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$510$	0.137948	+	0.0161238i	0.137948	+	0.0161238i
$511$		0			0
$512$	−1.00000			−1.00000
$513$		0			0
$514$	−0.792160			−0.792160
$515$		0			0
$516$	−0.997837	+	1.34033i	−0.997837	+	1.34033i
$517$		0			0
$518$	0.832863	−	0.698855i	0.832863	−	0.698855i
$519$		0			0
$520$	1.12229	−	0.408481i	1.12229	−	0.408481i
$521$	−0.396080	+	0.686030i	−0.396080	+	0.686030i	−0.993238	−	0.116093i	$-0.962963\pi$
$521$	−0.396080	+	0.686030i	−0.396080	+	0.686030i	0.597159	+	0.802123i	$0.296296\pi$
$522$		0			0
$523$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$523$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$524$	1.36912	+	1.14883i	1.36912	+	1.14883i
$525$	−0.488943	+	0.321583i	−0.488943	+	0.321583i
$526$		0			0
$527$	−0.0379513	−	0.215233i	−0.0379513	−	0.215233i
$528$		0			0
$529$	0.766044	+	0.642788i	0.766044	+	0.642788i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.914900	−	0.767692i	0.914900	−	0.767692i
$536$		0			0
$537$	1.16212	−	1.56100i	1.16212	−	1.56100i
$538$		0			0
$539$		0			0
$540$	−1.19432			−1.19432
$541$	−1.94609			−1.94609			−0.973045	−	0.230616i	$-0.925926\pi$
$541$	−1.94609			−1.94609			−0.973045	+	0.230616i	$0.925926\pi$
$542$	−0.344948	+	1.95630i	−0.344948	+	1.95630i
$543$		0			0
$544$	−0.109277	−	0.0397734i	−0.109277	−	0.0397734i
$545$	1.63517	−	1.37207i	1.63517	−	1.37207i
$546$	−0.941855	−	0.998308i	−0.941855	−	0.998308i
$547$	1.86668	−	0.679415i	1.86668	−	0.679415i	0.893633	−	0.448799i	$-0.148148\pi$
$547$	1.86668	−	0.679415i	1.86668	−	0.679415i	0.973045	−	0.230616i	$-0.0740741\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.0550102	−	0.944489i	−0.0550102	−	0.944489i
$556$	1.49079	+	1.25092i	1.49079	+	1.25092i
$557$	0.893633	+	1.54782i	0.893633	+	1.54782i	0.835488	+	0.549509i	$0.185185\pi$
$557$	0.893633	+	1.54782i	0.893633	+	1.54782i	0.0581448	+	0.998308i	$0.481481\pi$
$558$	0.539014	+	1.80043i	0.539014	+	1.80043i
$559$	−0.835488	+	1.44711i	−0.835488	+	1.44711i
$560$	1.54033	−	0.560633i	1.54033	−	0.560633i
$561$		0			0
$562$		0			0
$563$	0.539014	+	0.196185i	0.539014	+	0.196185i	0.597159	−	0.802123i	$-0.296296\pi$
$563$	0.539014	+	0.196185i	0.539014	+	0.196185i	−0.0581448	+	0.998308i	$0.518519\pi$
$564$	−0.707900	−	1.64110i	−0.707900	−	1.64110i
$565$	−0.317741	+	1.80200i	−0.317741	+	1.80200i
$566$	−1.53209			−1.53209
$567$	0.543613	+	1.26024i	0.543613	+	1.26024i
$568$	1.94609			1.94609
$569$	−0.344948	+	1.95630i	−0.344948	+	1.95630i	−0.0581448	+	0.998308i	$0.518519\pi$
$569$	−0.344948	+	1.95630i	−0.344948	+	1.95630i	−0.286803	+	0.957990i	$0.592593\pi$
$570$		0			0
$571$	0.109277	+	0.0397734i	0.109277	+	0.0397734i	0.396080	−	0.918216i	$-0.370370\pi$
$571$	0.109277	+	0.0397734i	0.109277	+	0.0397734i	−0.286803	+	0.957990i	$0.592593\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.973045	+	0.230616i	0.973045	+	0.230616i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	0.755685	+	0.634095i	0.755685	+	0.634095i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−1.18624	+	0.138652i	−1.18624	+	0.138652i
$586$	−0.973045	+	1.68536i	−0.973045	+	1.68536i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	−0.606439	−	0.642788i	−0.606439	−	0.642788i
$589$		0			0
$590$		0			0
$591$	−1.36320	−	0.159336i	−1.36320	−	0.159336i
$592$	−0.137557	+	0.780125i	−0.137557	+	0.780125i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$	0.190620			0.190620
$596$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$597$		0			0
$598$		0			0
$599$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$599$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$600$	0.122291	−	0.408481i	0.122291	−	0.408481i
$601$	1.57020	−	0.571507i	1.57020	−	0.571507i	0.597159	−	0.802123i	$-0.296296\pi$
$601$	1.57020	−	0.571507i	1.57020	−	0.571507i	0.973045	+	0.230616i	$0.0740741\pi$
$602$	−1.14669	+	1.98613i	−1.14669	+	1.98613i
$603$		0			0
$604$	0.597159	+	1.03431i	0.597159	+	1.03431i
$605$	−0.914900	−	0.767692i	−0.914900	−	0.767692i
$606$		0			0
$607$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$607$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.893633	−	1.54782i	−0.893633	−	1.54782i
$612$	0.0971586	+	0.0639022i	0.0971586	+	0.0639022i
$613$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$613$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$		0			0
$619$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$619$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$620$	−2.24458			−2.24458
$621$		0			0
$622$		0			0
$623$		0			0
$624$	0.993238	+	0.116093i	0.993238	+	0.116093i
$625$	1.16952	+	0.425672i	1.16952	+	0.425672i
$626$	1.52173	−	1.27688i	1.52173	−	1.27688i
$627$		0			0
$628$		0			0
$629$	−0.0460600	+	0.0797782i	−0.0460600	+	0.0797782i
$630$	−1.62810	+	0.190297i	−1.62810	+	0.190297i
$631$	−0.0581448	−	0.100710i	−0.0581448	−	0.100710i	0.835488	−	0.549509i	$-0.185185\pi$
$631$	−0.0581448	−	0.100710i	−0.0581448	−	0.100710i	−0.893633	+	0.448799i	$0.851852\pi$
$632$		0			0
$633$	−1.77518	−	0.891529i	−1.77518	−	0.891529i
$634$	0.266044	+	1.50881i	0.266044	+	1.50881i
$635$		0			0
$636$		0			0
$637$	−0.676961	−	0.568038i	−0.676961	−	0.568038i
$638$		0			0
$639$	−1.89363	−	0.448799i	−1.89363	−	0.448799i
$640$	−0.597159	+	1.03431i	−0.597159	+	1.03431i
$641$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$642$	0.973045	−	0.230616i	0.973045	−	0.230616i
$643$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$643$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$644$		0			0
$645$	0.790446	+	1.83246i	0.790446	+	1.83246i
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−0.893633	−	0.448799i	−0.893633	−	0.448799i
$649$		0			0
$650$	0.0740425	−	0.419916i	0.0740425	−	0.419916i
$651$	1.02166	+	2.36847i	1.02166	+	2.36847i
$652$		0			0
$653$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$653$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$654$	1.73909	−	0.412172i	1.73909	−	0.412172i
$655$	2.00583	−	0.730063i	2.00583	−	0.730063i
$656$		0			0
$657$		0			0
$658$	−1.22650	−	2.12435i	−1.22650	−	2.12435i
$659$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$659$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$660$		0			0
$661$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$661$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$	0.103920	+	0.0521907i	0.103920	+	0.0521907i
$664$		0			0
$665$		0			0
$666$	0.313758	−	0.727374i	0.313758	−	0.727374i
$667$		0			0
$668$	0.326352	−	0.118782i	0.326352	−	0.118782i
$669$	−1.14669	−	1.21542i	−1.14669	−	1.21542i
$670$		0			0
$671$		0			0
$672$	1.36320	+	0.159336i	1.36320	+	0.159336i
$673$	0.137557	−	0.780125i	0.137557	−	0.780125i	−0.835488	−	0.549509i	$-0.814815\pi$
$673$	0.137557	−	0.780125i	0.137557	−	0.780125i	0.973045	−	0.230616i	$-0.0740741\pi$
$674$	−1.94609			−1.94609
$675$	−0.213197	+	0.369268i	−0.213197	+	0.369268i
$676$	1.00000			1.00000
$677$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$677$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$678$	−0.914900	+	1.22892i	−0.914900	+	1.22892i
$679$		0			0
$680$	−0.106393	+	0.0892747i	−0.106393	+	0.0892747i
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$	0.122265	+	0.102593i	0.122265	+	0.102593i
$687$	0.997837	−	0.656288i	0.997837	−	0.656288i
$688$	−0.290162	−	1.64559i	−0.290162	−	1.64559i
$689$		0			0
$690$		0			0
$691$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$691$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$692$		0			0
$693$		0			0
$694$	0.396080	−	0.686030i	0.396080	−	0.686030i
$695$	2.18408	−	0.794940i	2.18408	−	0.794940i
$696$		0			0
$697$		0			0
$698$	1.86668	+	0.679415i	1.86668	+	0.679415i
$699$	−0.342534	+	0.460103i	−0.342534	+	0.460103i
$700$	0.101622	−	0.576327i	0.101622	−	0.576327i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$703$		0			0
$704$		0			0
$705$	−2.12013	−	0.247807i	−2.12013	−	0.247807i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$709$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$710$	1.16212	−	2.01286i	1.16212	−	2.01286i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	0.142629	+	0.0716309i	0.142629	+	0.0716309i
$715$		0			0
$716$	0.337935	+	1.91652i	0.337935	+	1.91652i
$717$	−0.0971586	−	1.66815i	−0.0971586	−	1.66815i
$718$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	0.819590	−	0.868715i	0.819590	−	0.868715i
$721$		0			0
$722$	0.939693	−	0.342020i	0.939693	−	0.342020i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.396080	−	0.918216i	−0.396080	−	0.918216i
$727$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$727$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$728$	1.37248			1.37248
$729$	0.766044	+	0.642788i	0.766044	+	0.642788i
$730$		0			0
$731$	0.0337428	−	0.191365i	0.0337428	−	0.191365i
$732$		0			0
$733$	−0.539014	−	0.196185i	−0.539014	−	0.196185i	0.0581448	−	0.998308i	$-0.481481\pi$
$733$	−0.539014	−	0.196185i	−0.539014	−	0.196185i	−0.597159	+	0.802123i	$0.703704\pi$
$734$		0			0
$735$	−1.02698	+	0.243399i	−1.02698	+	0.243399i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	0.724747	+	0.608135i	0.724747	+	0.608135i
$741$		0			0
$742$		0			0
$743$	0.290162	+	1.64559i	0.290162	+	1.64559i	0.686242	+	0.727374i	$0.259259\pi$
$743$	0.290162	+	1.64559i	0.290162	+	1.64559i	−0.396080	+	0.918216i	$0.629630\pi$
$744$	−1.67948	−	0.843467i	−1.67948	−	0.843467i
$745$	0.317741	+	0.266617i	0.317741	+	0.266617i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.28971	−	0.469417i	1.28971	−	0.469417i
$750$	0.470122	+	0.498300i	0.470122	+	0.498300i
$751$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$751$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$752$	1.67948	+	0.611281i	1.67948	+	0.611281i
$753$	−1.52173	−	0.177865i	−1.52173	−	0.177865i
$754$		0			0
$755$	1.42639			1.42639
$756$	−1.28971	−	0.469417i	−1.28971	−	0.469417i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$761$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$762$		0			0
$763$	2.30506	−	0.838973i	2.30506	−	0.838973i
$764$		0			0
$765$	0.124114	−	0.0623323i	0.124114	−	0.0623323i
$766$	0.286803	+	0.496758i	0.286803	+	0.496758i
$767$		0			0
$768$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$769$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$769$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$770$		0			0
$771$	−0.661840	+	0.435299i	−0.661840	+	0.435299i
$772$		0			0
$773$	−0.835488	−	1.44711i	−0.835488	−	1.44711i	−0.893633	−	0.448799i	$-0.851852\pi$
$773$	−0.835488	−	1.44711i	−0.835488	−	1.44711i	0.0581448	−	0.998308i	$-0.481481\pi$
$774$	−0.0971586	+	1.66815i	−0.0971586	+	1.66815i
$775$	−0.400679	+	0.693996i	−0.400679	+	0.693996i
$776$		0			0
$777$	0.311820	−	1.04155i	0.311820	−	1.04155i
$778$		0			0
$779$		0			0
$780$	0.713197	−	0.957990i	0.713197	−	0.957990i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.883710			0.883710
$785$		0			0
$786$	1.77518	+	0.207489i	1.77518	+	0.207489i
$787$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$787$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$788$	1.05138	−	0.882215i	1.05138	−	0.882215i
$789$		0			0
$790$		0			0
$791$	−1.05138	+	1.82105i	−1.05138	+	1.82105i
$792$		0			0
$793$		0			0
$794$	0.266044	+	0.223238i	0.266044	+	0.223238i
$795$		0			0
$796$		0			0
$797$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$797$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$798$		0			0
$799$	0.159215	+	0.133597i	0.159215	+	0.133597i
$800$	0.213197	+	0.369268i	0.213197	+	0.369268i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$807$		0			0
$808$		0			0
$809$	1.78727			1.78727			0.893633	−	0.448799i	$-0.148148\pi$
$809$	1.78727			1.78727			0.893633	+	0.448799i	$0.148148\pi$
$810$	−0.997837	+	0.656288i	−0.997837	+	0.656288i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	0.786803	+	1.82401i	0.786803	+	1.82401i
$814$		0			0
$815$		0			0
$816$	−0.113155	+	0.0268182i	−0.113155	+	0.0268182i
$817$		0			0
$818$		0			0
$819$	−1.33549	−	0.316516i	−1.33549	−	0.316516i
$820$		0			0
$821$	0.0890830	+	0.0747496i	0.0890830	+	0.0747496i	0.686242	−	0.727374i	$-0.259259\pi$
$821$	0.0890830	+	0.0747496i	0.0890830	+	0.0747496i	−0.597159	+	0.802123i	$0.703704\pi$
$822$		0			0
$823$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$823$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$827$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$828$		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
$832$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$833$	0.0965688	+	0.0351482i	0.0965688	+	0.0351482i
$834$	1.93293	+	0.225927i	1.93293	+	0.225927i
$835$	0.0720261	−	0.408481i	0.0720261	−	0.408481i
$836$		0			0
$837$	1.43969	+	1.20805i	1.43969	+	1.20805i
$838$	−1.19432			−1.19432
$839$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$839$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$840$	0.978851	−	1.31482i	0.978851	−	1.31482i
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$	−0.439408	+	0.368707i	−0.439408	+	0.368707i
$843$		0			0
$844$	1.86668	−	0.679415i	1.86668	−	0.679415i
$845$	0.597159	−	1.03431i	0.597159	−	1.03431i
$846$	−1.49324	−	0.982118i	−1.49324	−	0.982118i
$847$	−0.686242	−	1.18861i	−0.686242	−	1.18861i
$848$		0			0
$849$	−1.28004	+	0.841897i	−1.28004	+	0.841897i
$850$	0.00861037	+	0.0488318i	0.00861037	+	0.0488318i
$851$		0			0
$852$	1.62593	−	1.06939i	1.62593	−	1.06939i
$853$	−1.36912	−	1.14883i	−1.36912	−	1.14883i	−0.973045	−	0.230616i	$-0.925926\pi$
$853$	−1.36912	−	1.14883i	−1.36912	−	1.14883i	−0.396080	−	0.918216i	$-0.629630\pi$
$854$		0			0
$855$		0			0
$856$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$857$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$857$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$859$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$860$	−1.87532	−	0.682561i	−1.87532	−	0.682561i
$861$		0			0
$862$	0.137557	−	0.780125i	0.137557	−	0.780125i
$863$	1.98648			1.98648			0.993238	−	0.116093i	$-0.0370370\pi$
$863$	1.98648			1.98648			0.993238	+	0.116093i	$0.0370370\pi$
$864$	0.939693	−	0.342020i	0.939693	−	0.342020i
$865$		0			0
$866$	0.238329	−	1.35163i	0.238329	−	1.35163i
$867$	0.979807	+	0.114523i	0.979807	+	0.114523i
$868$	−2.42387	−	0.882215i	−2.42387	−	0.882215i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.893633	+	1.54782i	−0.893633	+	1.54782i
$873$		0			0
$874$		0			0
$875$	0.720269	+	0.604377i	0.720269	+	0.604377i
$876$		0			0
$877$	0.344948	+	1.95630i	0.344948	+	1.95630i	0.286803	+	0.957990i	$0.407407\pi$
$877$	0.344948	+	1.95630i	0.344948	+	1.95630i	0.0581448	+	0.998308i	$0.481481\pi$
$878$		0			0
$879$	0.113155	+	1.94280i	0.113155	+	1.94280i
$880$		0			0
$881$	0.993238	+	1.72034i	0.993238	+	1.72034i	0.597159	+	0.802123i	$0.296296\pi$
$881$	0.993238	+	1.72034i	0.993238	+	1.72034i	0.396080	+	0.918216i	$0.370370\pi$
$882$	−0.859890	−	0.203798i	−0.859890	−	0.203798i
$883$	−0.396080	+	0.686030i	−0.396080	+	0.686030i	−0.993238	−	0.116093i	$-0.962963\pi$
$883$	−0.396080	+	0.686030i	−0.396080	+	0.686030i	0.597159	+	0.802123i	$0.296296\pi$
$884$	−0.109277	+	0.0397734i	−0.109277	+	0.0397734i
$885$		0			0
$886$	−1.49079	+	1.25092i	−1.49079	+	1.25092i
$887$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$887$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$888$	0.313758	+	0.727374i	0.313758	+	0.727374i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	1.67098			1.67098
$893$		0			0
$894$	0.137557	+	0.318893i	0.137557	+	0.318893i
$895$	2.18408	+	0.794940i	2.18408	+	0.794940i
$896$	−1.05138	+	0.882215i	−1.05138	+	0.882215i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.122291	−	0.408481i	−0.122291	−	0.408481i
$901$		0			0
$902$		0			0
$903$	0.133349	+	2.28951i	0.133349	+	2.28951i
$904$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$905$		0			0
$906$	1.06728	+	0.536009i	1.06728	+	0.536009i
$907$	−0.439408	−	0.368707i	−0.439408	−	0.368707i	0.396080	−	0.918216i	$-0.370370\pi$
$907$	−0.439408	−	0.368707i	−0.439408	−	0.368707i	−0.835488	+	0.549509i	$0.814815\pi$
$908$		0			0
$909$		0			0
$910$	0.819590	−	1.41957i	0.819590	−	1.41957i
$911$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$911$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.207391	+	1.17617i	−0.207391	+	1.17617i
$917$	2.45299			2.45299
$918$	0.116290			0.116290
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	0.539014	+	0.196185i	0.539014	+	0.196185i
$923$	1.49079	−	1.25092i	1.49079	−	1.25092i
$924$		0			0
$925$	0.317402	−	0.115525i	0.317402	−	0.115525i
$926$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$927$		0			0
$928$		0			0
$929$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$929$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$930$	−1.87532	+	1.23342i	−1.87532	+	1.23342i
$931$		0			0
$932$	−0.0996057	−	0.564892i	−0.0996057	−	0.564892i
$933$		0			0
$934$	1.43969	+	1.20805i	1.43969	+	1.20805i
$935$		0			0
$936$	0.893633	−	0.448799i	0.893633	−	0.448799i
$937$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$937$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$938$		0			0
$939$	0.569728	−	1.90302i	0.569728	−	1.90302i
$940$	1.63517	−	1.37207i	1.63517	−	1.37207i
$941$	−1.28971	−	0.469417i	−1.28971	−	0.469417i	−0.396080	−	0.918216i	$-0.629630\pi$
$941$	−1.28971	−	0.469417i	−1.28971	−	0.469417i	−0.893633	+	0.448799i	$0.851852\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−1.25569	+	1.05364i	−1.25569	+	1.05364i
$946$		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
$950$		0			0
$951$	1.05138	+	1.11440i	1.05138	+	1.11440i
$952$	−0.149980	+	0.0545883i	−0.149980	+	0.0545883i
$953$	−0.973045	+	1.68536i	−0.973045	+	1.68536i	−0.286803	+	0.957990i	$0.592593\pi$
$953$	−0.973045	+	1.68536i	−0.973045	+	1.68536i	−0.686242	+	0.727374i	$0.740741\pi$
$954$		0			0
$955$		0			0
$956$	1.28004	+	1.07408i	1.28004	+	1.07408i
$957$		0			0
$958$	−0.344948	−	1.95630i	−0.344948	−	1.95630i
$959$		0			0
$960$	0.0694434	+	1.19230i	0.0694434	+	1.19230i
$961$	1.93969	+	1.62760i	1.93969	+	1.62760i
$962$	0.396080	+	0.686030i	0.396080	+	0.686030i
$963$	0.686242	−	0.727374i	0.686242	−	0.727374i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.0890830	−	0.0747496i	0.0890830	−	0.0747496i	−0.597159	−	0.802123i	$-0.703704\pi$
$967$	0.0890830	−	0.0747496i	0.0890830	−	0.0747496i	0.686242	+	0.727374i	$0.259259\pi$
$968$	0.939693	+	0.342020i	0.939693	+	0.342020i
$969$		0			0
$970$		0			0
$971$	0.792160			0.792160			0.396080	−	0.918216i	$-0.370370\pi$
$971$	0.792160			0.792160			0.396080	+	0.918216i	$0.370370\pi$
$972$	−0.993238	+	0.116093i	−0.993238	+	0.116093i
$973$	2.67098			2.67098
$974$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$975$	−0.168886	−	0.391521i	−0.168886	−	0.391521i
$976$		0			0
$977$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$977$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$978$		0			0
$979$		0			0
$980$	0.527715	−	0.914030i	0.527715	−	0.914030i
$981$	1.22650	−	1.30001i	1.22650	−	1.30001i
$982$	−0.835488	−	1.44711i	−0.835488	−	1.44711i
$983$	−0.606829	−	0.509190i	−0.606829	−	0.509190i	0.286803	−	0.957990i	$-0.407407\pi$
$983$	−0.606829	−	0.509190i	−0.606829	−	0.509190i	−0.893633	+	0.448799i	$0.851852\pi$
$984$		0			0
$985$	−0.284641	−	1.61428i	−0.284641	−	1.61428i
$986$		0			0
$987$	−2.19207	−	1.10090i	−2.19207	−	1.10090i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$	1.76604	−	0.642788i	1.76604	−	0.642788i
$993$		0			0
$994$	2.04609	−	1.71687i	2.04609	−	1.71687i
$995$		0			0
$996$		0			0
$997$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$997$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$998$		0			0
$999$	−0.137557	−	0.780125i	−0.137557	−	0.780125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2808.1.fi.b.2131.2	yes	18
8.3	odd	2		2808.1.fi.a.2131.2	✓	18
13.12	even	2		2808.1.fi.a.2131.2	✓	18
27.13	even	9	inner	2808.1.fi.b.2443.2	yes	18
104.51	odd	2	CM	2808.1.fi.b.2131.2	yes	18
216.67	odd	18		2808.1.fi.a.2443.2	yes	18
351.337	even	18		2808.1.fi.a.2443.2	yes	18
2808.2443	odd	18	inner	2808.1.fi.b.2443.2	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2808.1.fi.a.2131.2	✓	18	8.3	odd	2
2808.1.fi.a.2131.2	✓	18	13.12	even	2
2808.1.fi.a.2443.2	yes	18	216.67	odd	18
2808.1.fi.a.2443.2	yes	18	351.337	even	18
2808.1.fi.b.2131.2	yes	18	1.1	even	1	trivial
2808.1.fi.b.2131.2	yes	18	104.51	odd	2	CM
2808.1.fi.b.2443.2	yes	18	27.13	even	9	inner
2808.1.fi.b.2443.2	yes	18	2808.2443	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:	\( N \)	\(=\)	\( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2808.fi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.396080 + 0.918216i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.914900 + 0.767692i) q^{5} +(-0.973045 + 0.230616i) q^{6} +(-1.28971 + 0.469417i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.686242 + 0.727374i) q^{9} +(-0.597159 - 1.03431i) q^{10} +(-0.0581448 - 0.998308i) q^{12} +(-0.173648 - 0.984808i) q^{13} +(-0.238329 - 1.35163i) q^{14} +(-1.06728 - 0.536009i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.0581448 + 0.100710i) q^{17} +(-0.597159 - 0.802123i) q^{18} +(1.12229 - 0.408481i) q^{20} +(-0.941855 - 0.998308i) q^{21} +(0.993238 + 0.116093i) q^{24} +(0.0740425 - 0.419916i) q^{25} +1.00000 q^{26} +(-0.939693 - 0.342020i) q^{27} +1.37248 q^{28} +(0.713197 - 0.957990i) q^{30} +(-1.76604 - 0.642788i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.109277 + 0.0397734i) q^{34} +(0.819590 - 1.41957i) q^{35} +(0.893633 - 0.448799i) q^{36} +(0.396080 + 0.686030i) q^{37} +(0.835488 - 0.549509i) q^{39} +(0.207391 + 1.17617i) q^{40} +(1.14669 - 0.754192i) q^{42} +(-1.28004 - 1.07408i) q^{43} +(0.0694434 - 1.19230i) q^{45} +(1.67948 - 0.611281i) q^{47} +(-0.286803 + 0.957990i) q^{48} +(0.676961 - 0.568038i) q^{49} +(0.400679 + 0.145835i) q^{50} +(-0.0694434 + 0.0932786i) q^{51} +(-0.173648 + 0.984808i) q^{52} +(0.500000 - 0.866025i) q^{54} +(-0.238329 + 1.35163i) q^{56} +(0.819590 + 0.868715i) q^{60} +(0.939693 - 1.62760i) q^{62} +(0.543613 - 1.26024i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.914900 + 0.767692i) q^{65} +(-0.0201935 - 0.114523i) q^{68} +(1.25569 + 1.05364i) q^{70} +(0.973045 + 1.68536i) q^{71} +(0.286803 + 0.957990i) q^{72} +(-0.744386 + 0.270935i) q^{74} +(0.414900 - 0.0983331i) q^{75} +(0.396080 + 0.918216i) q^{78} -1.19432 q^{80} +(-0.0581448 - 0.998308i) q^{81} +(0.543613 + 1.26024i) q^{84} +(-0.130511 - 0.0475021i) q^{85} +(1.28004 - 1.07408i) q^{86} +(1.16212 + 0.275428i) q^{90} +(0.686242 + 1.18861i) q^{91} +(-0.109277 - 1.87621i) q^{93} +(0.310355 + 1.76011i) q^{94} +(-0.893633 - 0.448799i) q^{96} +(0.441855 + 0.765316i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{8} - 18 q^{21} + 18 q^{26} + 18 q^{30} - 18 q^{31} + 9 q^{54} - 9 q^{64} + 9 q^{70} - 9 q^{75} + 9 q^{85} + 9 q^{98}+O(q^{100}) \) 18 * q + 9 * q^8 - 18 * q^21 + 18 * q^26 + 18 * q^30 - 18 * q^31 + 9 * q^54 - 9 * q^64 + 9 * q^70 - 9 * q^75 + 9 * q^85 + 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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