LMFDB - Embedded newform 2280.1.el.b.2189.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2280,1,Mod(149,2280)] 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("2280.149"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2280, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 9, 9, 4])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2280.el (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$1.13786822880$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{18}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{18} - \cdots)$

Embedding invariants

Embedding label			2189.1
Root			$-0.984808 - 0.173648i$ of defining polynomial
Character	$\chi$	$=$	2280.2189
Dual form			2280.1.el.b.1829.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.984808 - 0.173648i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.642788 + 0.766044i) q^{5} +(-0.766044 + 0.642788i) q^{6} +1.00000i q^{8} +(0.939693 - 0.342020i) q^{9} +(-0.939693 - 0.342020i) q^{10} +(0.342020 - 0.939693i) q^{12} +(0.766044 + 0.642788i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.642788 - 0.233956i) q^{17} +(-0.642788 + 0.766044i) q^{18} +(-0.173648 - 0.984808i) q^{19} +(0.984808 - 0.173648i) q^{20} +(1.32683 + 1.11334i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-0.173648 + 0.984808i) q^{25} +(0.866025 - 0.500000i) q^{27} +(-0.984808 - 0.173648i) q^{30} +(0.173648 - 0.300767i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.673648 - 0.118782i) q^{34} +(0.173648 - 0.984808i) q^{36} +(0.642788 + 0.766044i) q^{38} +(-0.766044 + 0.642788i) q^{40} +(0.866025 + 0.500000i) q^{45} +(-1.70574 - 0.300767i) q^{46} +(1.20805 - 0.439693i) q^{47} +(-0.642788 - 0.766044i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.342020 - 0.939693i) q^{50} +(-0.673648 - 0.118782i) q^{51} +(-1.20805 + 1.43969i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.342020 - 0.939693i) q^{57} +(0.939693 - 0.342020i) q^{60} +(-1.11334 + 1.32683i) q^{61} +0.347296i q^{62} -1.00000 q^{64} +(-0.524005 + 0.439693i) q^{68} +(1.50000 + 0.866025i) q^{69} +(0.342020 + 0.939693i) q^{72} +1.00000i q^{75} +(-0.939693 - 0.342020i) q^{76} +(-0.173648 - 0.984808i) q^{79} +(0.342020 - 0.939693i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.300767 - 0.173648i) q^{83} +(-0.233956 - 0.642788i) q^{85} -1.00000 q^{90} +(1.62760 - 0.592396i) q^{92} +(0.118782 - 0.326352i) q^{93} +(-0.826352 + 0.984808i) q^{94} +(0.642788 - 0.766044i) q^{95} +(0.939693 + 0.342020i) q^{96} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 6 q^{16} + 6 q^{34} - 6 q^{49} - 6 q^{51} - 6 q^{54} - 12 q^{64} + 18 q^{69} - 12 q^{85} - 12 q^{90} - 12 q^{94}+O(q^{100}) $ 12 * q + 6 * q^4 - 6 * q^16 + 6 * q^34 - 6 * q^49 - 6 * q^51 - 6 * q^54 - 12 * q^64 + 18 * q^69 - 12 * q^85 - 12 * q^90 - 12 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2280\mathbb{Z}\right)^\times$.

$n$	$457$	$761$	$1141$	$1711$	$1921$
$\chi(n)$	$-1$	$-1$	$-1$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$3$	0.984808	−	0.173648i	0.984808	−	0.173648i
$3$	0.984808	−	0.173648i	0.984808	−	0.173648i
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.642788	+	0.766044i	0.642788	+	0.766044i
$5$	0.642788	+	0.766044i	0.642788	+	0.766044i
$6$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$			1.00000i			1.00000i
$9$	0.939693	−	0.342020i	0.939693	−	0.342020i
$10$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	0.342020	−	0.939693i	0.342020	−	0.939693i
$13$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$13$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$14$		0			0
$15$	0.766044	+	0.642788i	0.766044	+	0.642788i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$	−0.642788	−	0.233956i	−0.642788	−	0.233956i		−	1.00000i	$-0.5\pi$
$17$	−0.642788	−	0.233956i	−0.642788	−	0.233956i	−0.642788	+	0.766044i	$0.722222\pi$
$18$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$19$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$19$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$20$	0.984808	−	0.173648i	0.984808	−	0.173648i
$21$		0			0
$22$		0			0
$23$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$23$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$24$	0.173648	+	0.984808i	0.173648	+	0.984808i
$25$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$26$		0			0
$27$	0.866025	−	0.500000i	0.866025	−	0.500000i
$28$		0			0
$29$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$29$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$30$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$31$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$31$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$32$	0.866025	+	0.500000i	0.866025	+	0.500000i
$33$		0			0
$34$	0.673648	−	0.118782i	0.673648	−	0.118782i
$35$		0			0
$36$	0.173648	−	0.984808i	0.173648	−	0.984808i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.642788	+	0.766044i	0.642788	+	0.766044i
$39$		0			0
$40$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$41$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$41$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$42$		0			0
$43$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$43$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$44$		0			0
$45$	0.866025	+	0.500000i	0.866025	+	0.500000i
$46$	−1.70574	−	0.300767i	−1.70574	−	0.300767i
$47$	1.20805	−	0.439693i	1.20805	−	0.439693i	0.342020	−	0.939693i	$-0.388889\pi$
$47$	1.20805	−	0.439693i	1.20805	−	0.439693i	0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$51$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$52$		0			0
$53$	−1.20805	+	1.43969i	−1.20805	+	1.43969i	−0.342020	+	0.939693i	$0.611111\pi$
$53$	−1.20805	+	1.43969i	−1.20805	+	1.43969i	−0.866025	+	0.500000i	$0.833333\pi$
$54$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$55$		0			0
$56$		0			0
$57$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$58$		0			0
$59$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$59$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$60$	0.939693	−	0.342020i	0.939693	−	0.342020i
$61$	−1.11334	+	1.32683i	−1.11334	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$61$	−1.11334	+	1.32683i	−1.11334	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$62$			0.347296i			0.347296i
$63$		0			0
$64$	−1.00000			−1.00000
$65$		0			0
$66$		0			0
$67$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$67$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$68$	−0.524005	+	0.439693i	−0.524005	+	0.439693i
$69$	1.50000	+	0.866025i	1.50000	+	0.866025i
$70$		0			0
$71$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$71$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$72$	0.342020	+	0.939693i	0.342020	+	0.939693i
$73$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$73$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$74$		0			0
$75$			1.00000i			1.00000i
$76$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$77$		0			0
$78$		0			0
$79$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$79$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$80$	0.342020	−	0.939693i	0.342020	−	0.939693i
$81$	0.766044	−	0.642788i	0.766044	−	0.642788i
$82$		0			0
$83$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$83$	−0.300767	−	0.173648i	−0.300767	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$84$		0			0
$85$	−0.233956	−	0.642788i	−0.233956	−	0.642788i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$89$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$90$	−1.00000			−1.00000
$91$		0			0
$92$	1.62760	−	0.592396i	1.62760	−	0.592396i
$93$	0.118782	−	0.326352i	0.118782	−	0.326352i
$94$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$95$	0.642788	−	0.766044i	0.642788	−	0.766044i
$96$	0.939693	+	0.342020i	0.939693	+	0.342020i
$97$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$97$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$98$	0.866025	+	0.500000i	0.866025	+	0.500000i
$99$		0			0
$100$	0.766044	+	0.642788i	0.766044	+	0.642788i
$101$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$101$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$102$	0.642788	−	0.233956i	0.642788	−	0.233956i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$	0.326352	−	1.85083i	0.326352	−	1.85083i
$107$	−1.62760	−	0.939693i	−1.62760	−	0.939693i	−0.984808	−	0.173648i	$-0.944444\pi$
$107$	−1.62760	−	0.939693i	−1.62760	−	0.939693i	−0.642788	−	0.766044i	$-0.722222\pi$
$108$		−	1.00000i		−	1.00000i
$109$	0.439693	+	0.524005i	0.439693	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$109$	0.439693	+	0.524005i	0.439693	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.96962			−1.96962			−0.984808	−	0.173648i	$-0.944444\pi$
$113$	−1.96962			−1.96962			−0.984808	+	0.173648i	$0.944444\pi$
$114$	0.766044	+	0.642788i	0.766044	+	0.642788i
$115$			1.73205i			1.73205i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$121$	0.500000	−	0.866025i	0.500000	−	0.866025i
$122$	0.300767	−	1.70574i	0.300767	−	1.70574i
$123$		0			0
$124$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$125$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$126$		0			0
$127$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$127$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$128$	0.866025	−	0.500000i	0.866025	−	0.500000i
$129$		0			0
$130$		0			0
$131$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$131$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.939693	+	0.342020i	0.939693	+	0.342020i
$136$	0.233956	−	0.642788i	0.233956	−	0.642788i
$137$	0.984808	+	0.826352i	0.984808	+	0.826352i	0.984808	−	0.173648i	$-0.0555556\pi$
$137$	0.984808	+	0.826352i	0.984808	+	0.826352i			1.00000i	$0.5\pi$
$138$	−1.73205			−1.73205
$139$	0.673648	+	0.118782i	0.673648	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$139$	0.673648	+	0.118782i	0.673648	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$	1.11334	−	0.642788i	1.11334	−	0.642788i
$142$		0			0
$143$		0			0
$144$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$145$		0			0
$146$		0			0
$147$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$148$		0			0
$149$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$149$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$150$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$151$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$151$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$152$	0.984808	−	0.173648i	0.984808	−	0.173648i
$153$	−0.684040			−0.684040
$154$		0			0
$155$	0.342020	−	0.0603074i	0.342020	−	0.0603074i
$156$		0			0
$157$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$157$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$158$	0.642788	+	0.766044i	0.642788	+	0.766044i
$159$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$160$	0.173648	+	0.984808i	0.173648	+	0.984808i
$161$		0			0
$162$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$163$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$163$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$164$		0			0
$165$		0			0
$166$	0.347296			0.347296
$167$	−1.50881	−	1.26604i	−1.50881	−	1.26604i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−1.50881	−	1.26604i	−1.50881	−	1.26604i	−0.642788	−	0.766044i	$-0.722222\pi$
$168$		0			0
$169$	0.939693	+	0.342020i	0.939693	+	0.342020i
$170$	0.524005	+	0.439693i	0.524005	+	0.439693i
$171$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$172$		0			0
$173$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	0.642788	+	0.766044i	$0.277778\pi$
$173$	−0.342020	+	0.939693i	−0.342020	+	0.939693i	−0.984808	+	0.173648i	$0.944444\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$	0.866025	−	0.500000i	0.866025	−	0.500000i
$181$	−0.673648	−	1.85083i	−0.673648	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−0.673648	−	1.85083i	−0.673648	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$182$		0			0
$183$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$184$	−1.11334	+	1.32683i	−1.11334	+	1.32683i
$185$		0			0
$186$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$187$		0			0
$188$	0.223238	−	1.26604i	0.223238	−	1.26604i
$189$		0			0
$190$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$193$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$193$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$194$		0			0
$195$		0			0
$196$	−1.00000			−1.00000
$197$	−1.32683	−	0.766044i	−1.32683	−	0.766044i	−0.342020	−	0.939693i	$-0.611111\pi$
$197$	−1.32683	−	0.766044i	−1.32683	−	0.766044i	−0.984808	+	0.173648i	$0.944444\pi$
$198$		0			0
$199$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$199$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$200$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$205$		0			0
$206$		0			0
$207$	1.62760	+	0.592396i	1.62760	+	0.592396i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.439693	+	1.20805i	−0.439693	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$211$	−0.439693	+	1.20805i	−0.439693	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$212$	0.642788	+	1.76604i	0.642788	+	1.76604i
$213$		0			0
$214$	1.87939			1.87939
$215$		0			0
$216$	0.500000	+	0.866025i	0.500000	+	0.866025i
$217$		0			0
$218$	−0.642788	−	0.233956i	−0.642788	−	0.233956i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$223$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$224$		0			0
$225$	0.173648	+	0.984808i	0.173648	+	0.984808i
$226$	1.70574	−	0.984808i	1.70574	−	0.984808i
$227$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$227$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$228$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$229$			1.28558i			1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$229$			1.28558i			1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$230$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$231$		0			0
$232$		0			0
$233$	1.50881	−	1.26604i	1.50881	−	1.26604i	0.642788	−	0.766044i	$-0.277778\pi$
$233$	1.50881	−	1.26604i	1.50881	−	1.26604i	0.866025	−	0.500000i	$-0.166667\pi$
$234$		0			0
$235$	1.11334	+	0.642788i	1.11334	+	0.642788i
$236$		0			0
$237$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	0.173648	−	0.984808i	0.173648	−	0.984808i
$241$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$241$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$242$			1.00000i			1.00000i
$243$	0.642788	−	0.766044i	0.642788	−	0.766044i
$244$	0.592396	+	1.62760i	0.592396	+	1.62760i
$245$	0.342020	−	0.939693i	0.342020	−	0.939693i
$246$		0			0
$247$		0			0
$248$	0.300767	+	0.173648i	0.300767	+	0.173648i
$249$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$251$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−0.342020	−	0.592396i	−0.342020	−	0.592396i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.984808	−	0.173648i	$-0.944444\pi$
$257$	−1.62760	+	0.592396i	−1.62760	+	0.592396i	−0.642788	+	0.766044i	$0.722222\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.342020	+	1.93969i	0.342020	+	1.93969i	0.342020	+	0.939693i	$0.388889\pi$
$263$	0.342020	+	1.93969i	0.342020	+	1.93969i			1.00000i	$0.500000\pi$
$264$		0			0
$265$	−1.87939			−1.87939
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$269$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$270$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$271$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$271$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$272$	0.118782	+	0.673648i	0.118782	+	0.673648i
$273$		0			0
$274$	−1.26604	−	0.223238i	−1.26604	−	0.223238i
$275$		0			0
$276$	1.50000	−	0.866025i	1.50000	−	0.866025i
$277$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$277$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$278$	−0.642788	+	0.233956i	−0.642788	+	0.233956i
$279$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$280$		0			0
$281$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$281$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$282$	−0.642788	+	1.11334i	−0.642788	+	1.11334i
$283$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$283$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$284$		0			0
$285$	0.500000	−	0.866025i	0.500000	−	0.866025i
$286$		0			0
$287$		0			0
$288$	0.984808	+	0.173648i	0.984808	+	0.173648i
$289$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.300767	+	0.173648i	−0.300767	+	0.173648i	−0.642788	−	0.766044i	$-0.722222\pi$
$293$	−0.300767	+	0.173648i	−0.300767	+	0.173648i	0.342020	+	0.939693i	$0.388889\pi$
$294$	0.939693	+	0.342020i	0.939693	+	0.342020i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.866025	+	0.500000i	0.866025	+	0.500000i
$301$		0			0
$302$	−1.32683	+	0.766044i	−1.32683	+	0.766044i
$303$		0			0
$304$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$305$	−1.73205			−1.73205
$306$	0.592396	−	0.342020i	0.592396	−	0.342020i
$307$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$307$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$308$		0			0
$309$		0			0
$310$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$		0			0
$313$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$313$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$314$		0			0
$315$		0			0
$316$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$317$	−0.342020	−	0.0603074i	−0.342020	−	0.0603074i		−	1.00000i	$-0.5\pi$
$317$	−0.342020	−	0.0603074i	−0.342020	−	0.0603074i	−0.342020	+	0.939693i	$0.611111\pi$
$318$		−	1.87939i		−	1.87939i
$319$		0			0
$320$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$321$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$322$		0			0
$323$	−0.118782	+	0.673648i	−0.118782	+	0.673648i
$324$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$325$		0			0
$326$		0			0
$327$	0.524005	+	0.439693i	0.524005	+	0.439693i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.50000	−	0.866025i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$331$	1.50000	−	0.866025i	1.50000	−	0.866025i	1.00000			$0$
$332$	−0.300767	+	0.173648i	−0.300767	+	0.173648i
$333$		0			0
$334$	1.93969	+	0.342020i	1.93969	+	0.342020i
$335$		0			0
$336$		0			0
$337$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$337$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$338$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$339$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$340$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$341$		0			0
$342$	0.866025	+	0.500000i	0.866025	+	0.500000i
$343$		0			0
$344$		0			0
$345$	0.300767	+	1.70574i	0.300767	+	1.70574i
$346$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$347$	−1.20805	−	1.43969i	−1.20805	−	1.43969i	−0.866025	−	0.500000i	$-0.833333\pi$
$347$	−1.20805	−	1.43969i	−1.20805	−	1.43969i	−0.342020	−	0.939693i	$-0.611111\pi$
$348$		0			0
$349$	−1.70574	−	0.984808i	−1.70574	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$349$	−1.70574	−	0.984808i	−1.70574	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$353$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$359$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$360$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$361$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$362$	1.50881	+	1.26604i	1.50881	+	1.26604i
$363$	0.342020	−	0.939693i	0.342020	−	0.939693i
$364$		0			0
$365$		0			0
$366$		−	1.73205i		−	1.73205i
$367$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$367$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$368$	0.300767	−	1.70574i	0.300767	−	1.70574i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.223238	−	0.266044i	−0.223238	−	0.266044i
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$		0			0
$375$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$376$	0.439693	+	1.20805i	0.439693	+	1.20805i
$377$		0			0
$378$		0			0
$379$		−	1.73205i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$379$		−	1.73205i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$380$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$381$		0			0
$382$		0			0
$383$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	−0.984808	−	0.173648i	$-0.944444\pi$
$383$	−0.118782	−	0.673648i	−0.118782	−	0.673648i	0.866025	−	0.500000i	$-0.166667\pi$
$384$	0.766044	−	0.642788i	0.766044	−	0.642788i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$389$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$390$		0			0
$391$	−0.592396	−	1.02606i	−0.592396	−	1.02606i
$392$	0.866025	−	0.500000i	0.866025	−	0.500000i
$393$		0			0
$394$	1.53209			1.53209
$395$	0.642788	−	0.766044i	0.642788	−	0.766044i
$396$		0			0
$397$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$397$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$398$	0.642788	−	0.766044i	0.642788	−	0.766044i
$399$		0			0
$400$	0.939693	−	0.342020i	0.939693	−	0.342020i
$401$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$401$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.984808	+	0.173648i	0.984808	+	0.173648i
$406$		0			0
$407$		0			0
$408$	0.118782	−	0.673648i	0.118782	−	0.673648i
$409$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$409$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$410$		0			0
$411$	1.11334	+	0.642788i	1.11334	+	0.642788i
$412$		0			0
$413$		0			0
$414$	−1.70574	+	0.300767i	−1.70574	+	0.300767i
$415$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$416$		0			0
$417$	0.684040			0.684040
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$421$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$422$	−0.223238	−	1.26604i	−0.223238	−	1.26604i
$423$	0.984808	−	0.826352i	0.984808	−	0.826352i
$424$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$425$	0.342020	−	0.592396i	0.342020	−	0.592396i
$426$		0			0
$427$		0			0
$428$	−1.62760	+	0.939693i	−1.62760	+	0.939693i
$429$		0			0
$430$		0			0
$431$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$431$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$432$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$433$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$433$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$434$		0			0
$435$		0			0
$436$	0.673648	−	0.118782i	0.673648	−	0.118782i
$437$	0.866025	−	1.50000i	0.866025	−	1.50000i
$438$		0			0
$439$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$439$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$440$		0			0
$441$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$442$		0			0
$443$	1.85083	+	0.326352i	1.85083	+	0.326352i	0.984808	−	0.173648i	$-0.0555556\pi$
$443$	1.85083	+	0.326352i	1.85083	+	0.326352i	0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$451$		0			0
$452$	−0.984808	+	1.70574i	−0.984808	+	1.70574i
$453$	1.50881	−	0.266044i	1.50881	−	0.266044i
$454$	0.500000	+	0.866025i	0.500000	+	0.866025i
$455$		0			0
$456$	0.939693	−	0.342020i	0.939693	−	0.342020i
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$459$	−0.673648	+	0.118782i	−0.673648	+	0.118782i
$460$	1.50000	+	0.866025i	1.50000	+	0.866025i
$461$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$461$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$	0.326352	−	0.118782i	0.326352	−	0.118782i
$466$	−0.673648	+	1.85083i	−0.673648	+	1.85083i
$467$	−1.32683	+	0.766044i	−1.32683	+	0.766044i	−0.984808	−	0.173648i	$-0.944444\pi$
$467$	−1.32683	+	0.766044i	−1.32683	+	0.766044i	−0.342020	+	0.939693i	$0.611111\pi$
$468$		0			0
$469$		0			0
$470$	−1.28558			−1.28558
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.766044	+	0.642788i	0.766044	+	0.642788i
$475$	1.00000			1.00000
$476$		0			0
$477$	−0.642788	+	1.76604i	−0.642788	+	1.76604i
$478$		0			0
$479$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$479$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$480$	0.342020	+	0.939693i	0.342020	+	0.939693i
$481$		0			0
$482$	−0.524005	−	1.43969i	−0.524005	−	1.43969i
$483$		0			0
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$		0			0
$486$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	−1.32683	−	1.11334i	−1.32683	−	1.11334i
$489$		0			0
$490$	0.173648	+	0.984808i	0.173648	+	0.984808i
$491$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$491$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.347296			−0.347296
$497$		0			0
$498$	0.342020	−	0.0603074i	0.342020	−	0.0603074i
$499$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$499$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	−1.00000			$\pi$
$500$			1.00000i			1.00000i
$501$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$502$		0			0
$503$	0.642788	−	0.233956i	0.642788	−	0.233956i		−	1.00000i	$-0.5\pi$
$503$	0.642788	−	0.233956i	0.642788	−	0.233956i	0.642788	+	0.766044i	$0.277778\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.984808	+	0.173648i	0.984808	+	0.173648i
$508$		0			0
$509$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$509$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$510$	0.592396	+	0.342020i	0.592396	+	0.342020i
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$514$	1.11334	−	1.32683i	1.11334	−	1.32683i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$523$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$524$		0			0
$525$		0			0
$526$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$527$	−0.181985	+	0.152704i	−0.181985	+	0.152704i
$528$		0			0
$529$	0.347296	+	1.96962i	0.347296	+	1.96962i
$530$	1.62760	−	0.939693i	1.62760	−	0.939693i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	0.766044	−	0.642788i	0.766044	−	0.642788i
$541$	−0.439693	−	1.20805i	−0.439693	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$541$	−0.439693	−	1.20805i	−0.439693	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$542$	−0.524005	+	1.43969i	−0.524005	+	1.43969i
$543$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$544$	−0.439693	−	0.524005i	−0.439693	−	0.524005i
$545$	−0.118782	+	0.673648i	−0.118782	+	0.673648i
$546$		0			0
$547$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$547$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$548$	1.20805	−	0.439693i	1.20805	−	0.439693i
$549$	−0.592396	+	1.62760i	−0.592396	+	1.62760i
$550$		0			0
$551$		0			0
$552$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.439693	−	0.524005i	0.439693	−	0.524005i
$557$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$557$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$558$	0.118782	+	0.326352i	0.118782	+	0.326352i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.300767	+	0.173648i	0.300767	+	0.173648i	0.642788	−	0.766044i	$-0.277778\pi$
$563$	0.300767	+	0.173648i	0.300767	+	0.173648i	−0.342020	+	0.939693i	$0.611111\pi$
$564$		−	1.28558i		−	1.28558i
$565$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$			1.00000i			1.00000i
$571$			1.96962i			1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$571$			1.96962i			1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.32683	+	1.11334i	−1.32683	+	1.11334i
$576$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.524005	+	0.0923963i	0.524005	+	0.0923963i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.173648	−	0.300767i	0.173648	−	0.300767i
$587$	−0.524005	+	1.43969i	−0.524005	+	1.43969i	0.342020	+	0.939693i	$0.388889\pi$
$587$	−0.524005	+	1.43969i	−0.524005	+	1.43969i	−0.866025	+	0.500000i	$0.833333\pi$
$588$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$589$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$590$		0			0
$591$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$592$		0			0
$593$	1.50881	+	1.26604i	1.50881	+	1.26604i	0.866025	+	0.500000i	$0.166667\pi$
$593$	1.50881	+	1.26604i	1.50881	+	1.26604i	0.642788	+	0.766044i	$0.277778\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$598$		0			0
$599$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$599$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$600$	−1.00000			−1.00000
$601$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$601$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$	0.766044	−	1.32683i	0.766044	−	1.32683i
$605$	0.984808	−	0.173648i	0.984808	−	0.173648i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	0.342020	−	0.939693i	0.342020	−	0.939693i
$609$		0			0
$610$	1.50000	−	0.866025i	1.50000	−	0.866025i
$611$		0			0
$612$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$613$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$613$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.85083	−	0.673648i	1.85083	−	0.673648i	0.866025	−	0.500000i	$-0.166667\pi$
$617$	1.85083	−	0.673648i	1.85083	−	0.673648i	0.984808	−	0.173648i	$-0.0555556\pi$
$618$		0			0
$619$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$619$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$620$	0.118782	−	0.326352i	0.118782	−	0.326352i
$621$	1.70574	+	0.300767i	1.70574	+	0.300767i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$631$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$632$	0.984808	−	0.173648i	0.984808	−	0.173648i
$633$	−0.223238	+	1.26604i	−0.223238	+	1.26604i
$634$	0.326352	−	0.118782i	0.326352	−	0.118782i
$635$		0			0
$636$	0.939693	+	1.62760i	0.939693	+	1.62760i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.939693	+	0.342020i	0.939693	+	0.342020i
$641$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$641$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$642$	1.85083	−	0.326352i	1.85083	−	0.326352i
$643$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$643$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$644$		0			0
$645$		0			0
$646$	−0.233956	−	0.642788i	−0.233956	−	0.642788i
$647$	−1.96962			−1.96962			−0.984808	−	0.173648i	$-0.944444\pi$
$647$	−1.96962			−1.96962			−0.984808	+	0.173648i	$0.944444\pi$
$648$	0.642788	+	0.766044i	0.642788	+	0.766044i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$653$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$654$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$659$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$660$		0			0
$661$	−0.826352	+	0.984808i	−0.826352	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$661$	−0.826352	+	0.984808i	−0.826352	+	0.984808i	−1.00000			$\pi$
$662$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$663$		0			0
$664$	0.173648	−	0.300767i	0.173648	−	0.300767i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.85083	+	0.673648i	−1.85083	+	0.673648i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	0.342020	+	0.939693i	0.342020	+	0.939693i
$676$	0.766044	−	0.642788i	0.766044	−	0.642788i
$677$	1.32683	+	0.766044i	1.32683	+	0.766044i	0.984808	−	0.173648i	$-0.0555556\pi$
$677$	1.32683	+	0.766044i	1.32683	+	0.766044i	0.342020	+	0.939693i	$0.388889\pi$
$678$	1.50881	−	1.26604i	1.50881	−	1.26604i
$679$		0			0
$680$	0.642788	−	0.233956i	0.642788	−	0.233956i
$681$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$682$		0			0
$683$			1.53209i			1.53209i	0.642788	+	0.766044i	$0.277778\pi$
$683$			1.53209i			1.53209i	−0.642788	+	0.766044i	$0.722222\pi$
$684$	−1.00000			−1.00000
$685$			1.28558i			1.28558i
$686$		0			0
$687$	0.223238	+	1.26604i	0.223238	+	1.26604i
$688$		0			0
$689$		0			0
$690$	−1.11334	−	1.32683i	−1.11334	−	1.32683i
$691$	−0.592396	−	0.342020i	−0.592396	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$691$	−0.592396	−	0.342020i	−0.592396	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$692$	0.642788	+	0.766044i	0.642788	+	0.766044i
$693$		0			0
$694$	1.76604	+	0.642788i	1.76604	+	0.642788i
$695$	0.342020	+	0.592396i	0.342020	+	0.592396i
$696$		0			0
$697$		0			0
$698$	1.96962			1.96962
$699$	1.26604	−	1.50881i	1.26604	−	1.50881i
$700$		0			0
$701$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$701$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.20805	+	0.439693i	1.20805	+	0.439693i
$706$	1.50000	+	0.866025i	1.50000	+	0.866025i
$707$		0			0
$708$		0			0
$709$	1.93969	+	0.342020i	1.93969	+	0.342020i	1.00000			$0$
$709$	1.93969	+	0.342020i	1.93969	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$710$		0			0
$711$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$712$		0			0
$713$	0.565258	−	0.205737i	0.565258	−	0.205737i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$719$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$720$		−	1.00000i		−	1.00000i
$721$		0			0
$722$	0.642788	−	0.766044i	0.642788	−	0.766044i
$723$			1.53209i			1.53209i
$724$	−1.93969	−	0.342020i	−1.93969	−	0.342020i
$725$		0			0
$726$	0.173648	+	0.984808i	0.173648	+	0.984808i
$727$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$727$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$728$		0			0
$729$	0.500000	−	0.866025i	0.500000	−	0.866025i
$730$		0			0
$731$		0			0
$732$	0.866025	+	1.50000i	0.866025	+	1.50000i
$733$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$733$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$734$		0			0
$735$	0.173648	−	0.984808i	0.173648	−	0.984808i
$736$	0.592396	+	1.62760i	0.592396	+	1.62760i
$737$		0			0
$738$		0			0
$739$	−0.439693	+	1.20805i	−0.439693	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$739$	−0.439693	+	1.20805i	−0.439693	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.20805	−	0.439693i	−1.20805	−	0.439693i	−0.342020	−	0.939693i	$-0.611111\pi$
$743$	−1.20805	−	0.439693i	−1.20805	−	0.439693i	−0.866025	+	0.500000i	$0.833333\pi$
$744$	0.326352	+	0.118782i	0.326352	+	0.118782i
$745$		0			0
$746$		0			0
$747$	−0.342020	−	0.0603074i	−0.342020	−	0.0603074i
$748$		0			0
$749$		0			0
$750$	0.342020	−	0.939693i	0.342020	−	0.939693i
$751$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$751$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$752$	−0.984808	−	0.826352i	−0.984808	−	0.826352i
$753$		0			0
$754$		0			0
$755$	0.984808	+	1.17365i	0.984808	+	1.17365i
$756$		0			0
$757$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$757$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$758$	0.866025	+	1.50000i	0.866025	+	1.50000i
$759$		0			0
$760$	0.766044	+	0.642788i	0.766044	+	0.642788i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.439693	−	0.524005i	−0.439693	−	0.524005i
$766$	0.439693	+	0.524005i	0.439693	+	0.524005i
$767$		0			0
$768$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$769$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$769$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$772$		0			0
$773$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.342020	−	0.939693i	$-0.611111\pi$
$773$	−0.984808	−	0.173648i	−0.984808	−	0.173648i	−0.642788	+	0.766044i	$0.722222\pi$
$774$		0			0
$775$	0.266044	+	0.223238i	0.266044	+	0.223238i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.02606	+	0.592396i	1.02606	+	0.592396i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$		0			0
$786$		0			0
$787$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$787$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$788$	−1.32683	+	0.766044i	−1.32683	+	0.766044i
$789$	0.673648	+	1.85083i	0.673648	+	1.85083i
$790$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−1.85083	+	0.326352i	−1.85083	+	0.326352i
$796$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$797$		−	1.53209i		−	1.53209i	−0.642788	−	0.766044i	$-0.722222\pi$
$797$		−	1.53209i		−	1.53209i	0.642788	−	0.766044i	$-0.277778\pi$
$798$		0			0
$799$	−0.879385			−0.879385
$800$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$811$	1.93969	+	0.342020i	1.93969	+	0.342020i	1.00000			$0$
$811$	1.93969	+	0.342020i	1.93969	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$812$		0			0
$813$	0.984808	−	1.17365i	0.984808	−	1.17365i
$814$		0			0
$815$		0			0
$816$	0.233956	+	0.642788i	0.233956	+	0.642788i
$817$		0			0
$818$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$819$		0			0
$820$		0			0
$821$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$821$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$822$	−1.28558			−1.28558
$823$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$823$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.642788	+	1.76604i	0.642788	+	1.76604i	0.642788	+	0.766044i	$0.277778\pi$
$827$	0.642788	+	1.76604i	0.642788	+	1.76604i			1.00000i	$0.5\pi$
$828$	1.32683	−	1.11334i	1.32683	−	1.11334i
$829$	0.592396	+	0.342020i	0.592396	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$829$	0.592396	+	0.342020i	0.592396	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$830$	0.223238	+	0.266044i	0.223238	+	0.266044i
$831$		0			0
$832$		0			0
$833$	0.118782	+	0.673648i	0.118782	+	0.673648i
$834$	−0.592396	+	0.342020i	−0.592396	+	0.342020i
$835$		−	1.96962i		−	1.96962i
$836$		0			0
$837$		−	0.347296i		−	0.347296i
$838$		0			0
$839$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$839$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$840$		0			0
$841$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$842$		0			0
$843$		0			0
$844$	0.826352	+	0.984808i	0.826352	+	0.984808i
$845$	0.342020	+	0.939693i	0.342020	+	0.939693i
$846$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$847$		0			0
$848$	1.85083	+	0.326352i	1.85083	+	0.326352i
$849$		0			0
$850$			0.684040i			0.684040i
$851$		0			0
$852$		0			0
$853$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$853$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$854$		0			0
$855$	0.342020	−	0.939693i	0.342020	−	0.939693i
$856$	0.939693	−	1.62760i	0.939693	−	1.62760i
$857$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$857$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	0.439693	−	0.524005i	0.439693	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.439693	−	0.524005i	0.439693	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$863$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$864$	1.00000			1.00000
$865$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$866$		0			0
$867$	−0.460802	−	0.266044i	−0.460802	−	0.266044i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.524005	+	0.439693i	−0.524005	+	0.439693i
$873$		0			0
$874$			1.73205i			1.73205i
$875$		0			0
$876$		0			0
$877$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$877$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$878$	1.85083	−	0.326352i	1.85083	−	0.326352i
$879$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$880$		0			0
$881$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$881$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$882$	0.984808	+	0.173648i	0.984808	+	0.173648i
$883$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$883$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$884$		0			0
$885$		0			0
$886$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$887$	0.223238	−	1.26604i	0.223238	−	1.26604i	−0.642788	−	0.766044i	$-0.722222\pi$
$887$	0.223238	−	1.26604i	0.223238	−	1.26604i	0.866025	−	0.500000i	$-0.166667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.939693	+	0.342020i	0.939693	+	0.342020i
$901$	1.11334	−	0.642788i	1.11334	−	0.642788i
$902$		0			0
$903$		0			0
$904$		−	1.96962i		−	1.96962i
$905$	0.984808	−	1.70574i	0.984808	−	1.70574i
$906$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$907$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$907$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$908$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$913$		0			0
$914$		0			0
$915$	−1.70574	+	0.300767i	−1.70574	+	0.300767i
$916$	1.11334	+	0.642788i	1.11334	+	0.642788i
$917$		0			0
$918$	0.524005	−	0.439693i	0.524005	−	0.439693i
$919$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$919$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$920$	−1.73205			−1.73205
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$929$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$930$	−0.223238	+	0.266044i	−0.223238	+	0.266044i
$931$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$932$	−0.342020	−	1.93969i	−0.342020	−	1.93969i
$933$		0			0
$934$	0.766044	−	1.32683i	0.766044	−	1.32683i
$935$		0			0
$936$		0			0
$937$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$937$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$938$		0			0
$939$		0			0
$940$	1.11334	−	0.642788i	1.11334	−	0.642788i
$941$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$941$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.342020	−	0.939693i	$-0.388889\pi$
$947$	0.984808	−	0.173648i	0.984808	−	0.173648i	0.642788	+	0.766044i	$0.277778\pi$
$948$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$949$		0			0
$950$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$951$	−0.347296			−0.347296
$952$		0			0
$953$	−0.223238	−	1.26604i	−0.223238	−	1.26604i	−0.866025	−	0.500000i	$-0.833333\pi$
$953$	−0.223238	−	1.26604i	−0.223238	−	1.26604i	0.642788	−	0.766044i	$-0.277778\pi$
$954$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$961$	0.439693	+	0.761570i	0.439693	+	0.761570i
$962$		0			0
$963$	−1.85083	−	0.326352i	−1.85083	−	0.326352i
$964$	1.17365	+	0.984808i	1.17365	+	0.984808i
$965$		0			0
$966$		0			0
$967$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$967$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$968$	0.866025	+	0.500000i	0.866025	+	0.500000i
$969$			0.684040i			0.684040i
$970$		0			0
$971$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$971$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$972$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.70574	+	0.300767i	1.70574	+	0.300767i
$977$	0.642788	+	1.11334i	0.642788	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$977$	0.642788	+	1.11334i	0.642788	+	1.11334i	−0.342020	+	0.939693i	$0.611111\pi$
$978$		0			0
$979$		0			0
$980$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$981$	0.592396	+	0.342020i	0.592396	+	0.342020i
$982$		0			0
$983$	0.524005	−	0.439693i	0.524005	−	0.439693i	−0.342020	−	0.939693i	$-0.611111\pi$
$983$	0.524005	−	0.439693i	0.524005	−	0.439693i	0.866025	+	0.500000i	$0.166667\pi$
$984$		0			0
$985$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$991$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$992$	0.300767	−	0.173648i	0.300767	−	0.173648i
$993$	1.32683	−	1.11334i	1.32683	−	1.11334i
$994$		0			0
$995$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$996$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$997$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$997$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$998$	1.20805	+	0.439693i	1.20805	+	0.439693i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2280.1.el.b.2189.1	yes	12
3.2	odd	2	inner	2280.1.el.b.2189.2	yes	12
5.4	even	2	inner	2280.1.el.b.2189.2	yes	12
8.5	even	2		2280.1.el.a.2189.1	yes	12
15.14	odd	2	CM	2280.1.el.b.2189.1	yes	12
19.5	even	9		2280.1.el.a.1829.1	✓	12
24.5	odd	2		2280.1.el.a.2189.2	yes	12
40.29	even	2		2280.1.el.a.2189.2	yes	12
57.5	odd	18		2280.1.el.a.1829.2	yes	12
95.24	even	18		2280.1.el.a.1829.2	yes	12
120.29	odd	2		2280.1.el.a.2189.1	yes	12
152.5	even	18	inner	2280.1.el.b.1829.1	yes	12
285.119	odd	18		2280.1.el.a.1829.1	✓	12
456.5	odd	18	inner	2280.1.el.b.1829.2	yes	12
760.309	even	18	inner	2280.1.el.b.1829.2	yes	12
2280.1829	odd	18	inner	2280.1.el.b.1829.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2280.1.el.a.1829.1	✓	12	19.5	even	9
2280.1.el.a.1829.1	✓	12	285.119	odd	18
2280.1.el.a.1829.2	yes	12	57.5	odd	18
2280.1.el.a.1829.2	yes	12	95.24	even	18
2280.1.el.a.2189.1	yes	12	8.5	even	2
2280.1.el.a.2189.1	yes	12	120.29	odd	2
2280.1.el.a.2189.2	yes	12	24.5	odd	2
2280.1.el.a.2189.2	yes	12	40.29	even	2
2280.1.el.b.1829.1	yes	12	152.5	even	18	inner
2280.1.el.b.1829.1	yes	12	2280.1829	odd	18	inner
2280.1.el.b.1829.2	yes	12	456.5	odd	18	inner
2280.1.el.b.1829.2	yes	12	760.309	even	18	inner
2280.1.el.b.2189.1	yes	12	1.1	even	1	trivial
2280.1.el.b.2189.1	yes	12	15.14	odd	2	CM
2280.1.el.b.2189.2	yes	12	3.2	odd	2	inner
2280.1.el.b.2189.2	yes	12	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2280.el (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.984808 - 0.173648i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.642788 + 0.766044i) q^{5} +(-0.766044 + 0.642788i) q^{6} +1.00000i q^{8} +(0.939693 - 0.342020i) q^{9} +(-0.939693 - 0.342020i) q^{10} +(0.342020 - 0.939693i) q^{12} +(0.766044 + 0.642788i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.642788 - 0.233956i) q^{17} +(-0.642788 + 0.766044i) q^{18} +(-0.173648 - 0.984808i) q^{19} +(0.984808 - 0.173648i) q^{20} +(1.32683 + 1.11334i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-0.173648 + 0.984808i) q^{25} +(0.866025 - 0.500000i) q^{27} +(-0.984808 - 0.173648i) q^{30} +(0.173648 - 0.300767i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.673648 - 0.118782i) q^{34} +(0.173648 - 0.984808i) q^{36} +(0.642788 + 0.766044i) q^{38} +(-0.766044 + 0.642788i) q^{40} +(0.866025 + 0.500000i) q^{45} +(-1.70574 - 0.300767i) q^{46} +(1.20805 - 0.439693i) q^{47} +(-0.642788 - 0.766044i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.342020 - 0.939693i) q^{50} +(-0.673648 - 0.118782i) q^{51} +(-1.20805 + 1.43969i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.342020 - 0.939693i) q^{57} +(0.939693 - 0.342020i) q^{60} +(-1.11334 + 1.32683i) q^{61} +0.347296i q^{62} -1.00000 q^{64} +(-0.524005 + 0.439693i) q^{68} +(1.50000 + 0.866025i) q^{69} +(0.342020 + 0.939693i) q^{72} +1.00000i q^{75} +(-0.939693 - 0.342020i) q^{76} +(-0.173648 - 0.984808i) q^{79} +(0.342020 - 0.939693i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.300767 - 0.173648i) q^{83} +(-0.233956 - 0.642788i) q^{85} -1.00000 q^{90} +(1.62760 - 0.592396i) q^{92} +(0.118782 - 0.326352i) q^{93} +(-0.826352 + 0.984808i) q^{94} +(0.642788 - 0.766044i) q^{95} +(0.939693 + 0.342020i) q^{96} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 6 q^{16} + 6 q^{34} - 6 q^{49} - 6 q^{51} - 6 q^{54} - 12 q^{64} + 18 q^{69} - 12 q^{85} - 12 q^{90} - 12 q^{94}+O(q^{100}) \) 12 * q + 6 * q^4 - 6 * q^16 + 6 * q^34 - 6 * q^49 - 6 * q^51 - 6 * q^54 - 12 * q^64 + 18 * q^69 - 12 * q^85 - 12 * q^90 - 12 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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