LMFDB - Embedded newform 540.1.bf.b.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,1,Mod(79,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 10, 9]))

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

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

chi := DirichletCharacter("540.79");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	540.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.269495106822$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.5020969537440000.1

Embedding invariants

Embedding label			319.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	540.319
Dual form			540.1.bf.b.259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.326352 + 1.85083i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.326352 + 1.85083i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.173648 - 0.984808i) q^{12} +(-1.43969 - 1.20805i) q^{14} +(-0.766044 + 0.642788i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.173648 + 0.984808i) q^{18} +(0.173648 + 0.984808i) q^{20} +(0.939693 + 1.62760i) q^{21} +(-0.0603074 + 0.342020i) q^{23} +(0.766044 + 0.642788i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.500000 - 0.866025i) q^{27} +1.87939 q^{28} +(0.266044 - 0.223238i) q^{29} +(0.173648 - 0.984808i) q^{30} +(0.939693 - 0.342020i) q^{32} +(-0.939693 - 1.62760i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.766044 - 0.642788i) q^{40} +(1.17365 + 0.984808i) q^{41} +(-1.76604 - 0.642788i) q^{42} +(-0.939693 - 0.342020i) q^{43} +(-0.500000 + 0.866025i) q^{45} +(-0.173648 - 0.300767i) q^{46} +(-0.266044 - 1.50881i) q^{47} -1.00000 q^{48} +(-2.37939 + 0.866025i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(0.173648 + 0.984808i) q^{54} +(-1.43969 + 1.20805i) q^{56} +(-0.0603074 + 0.342020i) q^{58} +(0.500000 + 0.866025i) q^{60} +(-0.326352 - 1.85083i) q^{61} +(1.43969 + 1.20805i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.17365 - 0.984808i) q^{67} +(0.0603074 + 0.342020i) q^{69} +(1.76604 + 0.642788i) q^{70} +(0.939693 + 0.342020i) q^{72} +(0.500000 - 0.866025i) q^{75} +1.00000 q^{80} +(0.173648 - 0.984808i) q^{81} -1.53209 q^{82} +(-1.17365 + 0.984808i) q^{83} +(1.76604 - 0.642788i) q^{84} +(0.939693 - 0.342020i) q^{86} +(0.173648 - 0.300767i) q^{87} +(-0.766044 - 1.32683i) q^{89} +(-0.173648 - 0.984808i) q^{90} +(0.326352 + 0.118782i) q^{92} +(1.17365 + 0.984808i) q^{94} +(0.766044 - 0.642788i) q^{96} +(1.26604 - 2.19285i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^6 + 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{14} - 6 q^{23} + 3 q^{27} - 3 q^{29} - 3 q^{36} + 6 q^{41} - 6 q^{42} - 3 q^{45} + 3 q^{47} - 6 q^{48} - 3 q^{49} - 3 q^{56} - 6 q^{58} + 3 q^{60} - 3 q^{61} + 3 q^{63} - 3 q^{64} - 6 q^{67} + 6 q^{69} + 6 q^{70} + 3 q^{75} + 6 q^{80} - 6 q^{83} + 6 q^{84} + 3 q^{92} + 6 q^{94} + 3 q^{98}+O(q^{100}) $ 6 * q - 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^14 - 6 * q^23 + 3 * q^27 - 3 * q^29 - 3 * q^36 + 6 * q^41 - 6 * q^42 - 3 * q^45 + 3 * q^47 - 6 * q^48 - 3 * q^49 - 3 * q^56 - 6 * q^58 + 3 * q^60 - 3 * q^61 + 3 * q^63 - 3 * q^64 - 6 * q^67 + 6 * q^69 + 6 * q^70 + 3 * q^75 + 6 * q^80 - 6 * q^83 + 6 * q^84 + 3 * q^92 + 6 * q^94 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$2$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$3$	0.939693	−	0.342020i	0.939693	−	0.342020i
$3$	0.939693	−	0.342020i	0.939693	−	0.342020i
$4$	0.173648	−	0.984808i	0.173648	−	0.984808i
$5$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$5$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$6$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$7$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$7$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$8$	0.500000	+	0.866025i	0.500000	+	0.866025i
$9$	0.766044	−	0.642788i	0.766044	−	0.642788i
$10$	0.500000	−	0.866025i	0.500000	−	0.866025i
$11$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$11$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$12$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$13$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$13$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$14$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$15$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$16$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	0.173648	+	0.984808i	0.173648	+	0.984808i
$21$	0.939693	+	1.62760i	0.939693	+	1.62760i
$22$		0			0
$23$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$23$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$24$	0.766044	+	0.642788i	0.766044	+	0.642788i
$25$	0.766044	−	0.642788i	0.766044	−	0.642788i
$26$		0			0
$27$	0.500000	−	0.866025i	0.500000	−	0.866025i
$28$	1.87939			1.87939
$29$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$29$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$30$	0.173648	−	0.984808i	0.173648	−	0.984808i
$31$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$31$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$32$	0.939693	−	0.342020i	0.939693	−	0.342020i
$33$		0			0
$34$		0			0
$35$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$36$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$41$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$41$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$42$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$43$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$43$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$46$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$47$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$47$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$48$	−1.00000			−1.00000
$49$	−2.37939	+	0.866025i	−2.37939	+	0.866025i
$50$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.173648	+	0.984808i	0.173648	+	0.984808i
$55$		0			0
$56$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$57$		0			0
$58$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$	0.500000	+	0.866025i	0.500000	+	0.866025i
$61$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$61$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$62$		0			0
$63$	1.43969	+	1.20805i	1.43969	+	1.20805i
$64$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$65$		0			0
$66$		0			0
$67$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$67$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$68$		0			0
$69$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$70$	1.76604	+	0.642788i	1.76604	+	0.642788i
$71$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$71$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$72$	0.939693	+	0.342020i	0.939693	+	0.342020i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.500000	−	0.866025i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$	1.00000			1.00000
$81$	0.173648	−	0.984808i	0.173648	−	0.984808i
$82$	−1.53209			−1.53209
$83$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$83$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$84$	1.76604	−	0.642788i	1.76604	−	0.642788i
$85$		0			0
$86$	0.939693	−	0.342020i	0.939693	−	0.342020i
$87$	0.173648	−	0.300767i	0.173648	−	0.300767i
$88$		0			0
$89$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$89$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$90$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$91$		0			0
$92$	0.326352	+	0.118782i	0.326352	+	0.118782i
$93$		0			0
$94$	1.17365	+	0.984808i	1.17365	+	0.984808i
$95$		0			0
$96$	0.766044	−	0.642788i	0.766044	−	0.642788i
$97$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$97$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$98$	1.26604	−	2.19285i	1.26604	−	2.19285i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$101$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$101$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$102$		0			0
$103$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$103$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$104$		0			0
$105$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$106$		0			0
$107$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$107$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$108$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$109$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$109$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$110$		0			0
$111$		0			0
$112$	0.326352	−	1.85083i	0.326352	−	1.85083i
$113$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$113$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$114$		0			0
$115$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$116$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$121$	0.766044	+	0.642788i	0.766044	+	0.642788i
$122$	1.43969	+	1.20805i	1.43969	+	1.20805i
$123$	1.43969	+	0.524005i	1.43969	+	0.524005i
$124$		0			0
$125$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$126$	−1.87939			−1.87939
$127$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$127$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$128$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$129$	−1.00000			−1.00000
$130$		0			0
$131$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$131$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$132$		0			0
$133$		0			0
$134$	1.53209			1.53209
$135$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$136$		0			0
$137$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$137$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$138$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$139$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$139$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$140$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$141$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$142$		0			0
$143$		0			0
$144$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$145$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$146$		0			0
$147$	−1.93969	+	1.62760i	−1.93969	+	1.62760i
$148$		0			0
$149$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$149$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$150$	0.173648	+	0.984808i	0.173648	+	0.984808i
$151$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$151$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$157$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$158$		0			0
$159$		0			0
$160$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$161$	−0.652704			−0.652704
$162$	0.500000	+	0.866025i	0.500000	+	0.866025i
$163$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$163$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$164$	1.17365	−	0.984808i	1.17365	−	0.984808i
$165$		0			0
$166$	0.266044	−	1.50881i	0.266044	−	1.50881i
$167$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$167$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$168$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$169$	0.173648	+	0.984808i	0.173648	+	0.984808i
$170$		0			0
$171$		0			0
$172$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$173$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$173$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$174$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$175$	1.43969	+	1.20805i	1.43969	+	1.20805i
$176$		0			0
$177$		0			0
$178$	1.43969	+	0.524005i	1.43969	+	0.524005i
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	0.766044	+	0.642788i	0.766044	+	0.642788i
$181$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$181$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$182$		0			0
$183$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$184$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−1.53209			−1.53209
$189$	1.76604	+	0.642788i	1.76604	+	0.642788i
$190$		0			0
$191$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$191$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$192$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$193$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$193$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$194$		0			0
$195$		0			0
$196$	0.439693	+	2.49362i	0.439693	+	2.49362i
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	0.939693	+	0.342020i	0.939693	+	0.342020i
$201$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$202$	0.766044	+	0.642788i	0.766044	+	0.642788i
$203$	0.500000	+	0.419550i	0.500000	+	0.419550i
$204$		0			0
$205$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$206$	0.500000	−	0.866025i	0.500000	−	0.866025i
$207$	0.173648	+	0.300767i	0.173648	+	0.300767i
$208$		0			0
$209$		0			0
$210$	1.87939			1.87939
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$		0			0
$214$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$215$	1.00000			1.00000
$216$	1.00000			1.00000
$217$		0			0
$218$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$223$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$224$	0.939693	+	1.62760i	0.939693	+	1.62760i
$225$	0.173648	−	0.984808i	0.173648	−	0.984808i
$226$		0			0
$227$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$227$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$228$		0			0
$229$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$229$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$230$	0.266044	+	0.223238i	0.266044	+	0.223238i
$231$		0			0
$232$	0.326352	+	0.118782i	0.326352	+	0.118782i
$233$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$233$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$	0.766044	+	1.32683i	0.766044	+	1.32683i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$239$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$240$	0.939693	−	0.342020i	0.939693	−	0.342020i
$241$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$241$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$242$	−1.00000			−1.00000
$243$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$244$	−1.87939			−1.87939
$245$	1.93969	−	1.62760i	1.93969	−	1.62760i
$246$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$247$		0			0
$248$		0			0
$249$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$250$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$251$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$251$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$252$	1.43969	−	1.20805i	1.43969	−	1.20805i
$253$		0			0
$254$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$255$		0			0
$256$	0.766044	+	0.642788i	0.766044	+	0.642788i
$257$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$257$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$258$	0.766044	−	0.642788i	0.766044	−	0.642788i
$259$		0			0
$260$		0			0
$261$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$262$		0			0
$263$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$263$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$268$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$269$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$269$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$270$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	0.347296			0.347296
$277$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$277$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$278$		0			0
$279$		0			0
$280$	0.939693	−	1.62760i	0.939693	−	1.62760i
$281$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$281$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$282$	1.43969	+	0.524005i	1.43969	+	0.524005i
$283$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	0.500000	−	0.866025i	$-0.333333\pi$
$283$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$288$	0.500000	−	0.866025i	0.500000	−	0.866025i
$289$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$290$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$291$		0			0
$292$		0			0
$293$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$293$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$294$	0.439693	−	2.49362i	0.439693	−	2.49362i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−0.347296			−0.347296
$299$		0			0
$300$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$301$	0.326352	−	1.85083i	0.326352	−	1.85083i
$302$		0			0
$303$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$304$		0			0
$305$	0.939693	+	1.62760i	0.939693	+	1.62760i
$306$		0			0
$307$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$308$		0			0
$309$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$310$		0			0
$311$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$311$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$312$		0			0
$313$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$313$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$314$		0			0
$315$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$316$		0			0
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$		0			0
$319$		0			0
$320$	0.173648	−	0.984808i	0.173648	−	0.984808i
$321$	1.76604	−	0.642788i	1.76604	−	0.642788i
$322$	0.500000	−	0.419550i	0.500000	−	0.419550i
$323$		0			0
$324$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$325$		0			0
$326$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$327$	0.326352	−	0.118782i	0.326352	−	0.118782i
$328$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$329$	2.70574	−	0.984808i	2.70574	−	0.984808i
$330$		0			0
$331$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$331$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$332$	0.766044	+	1.32683i	0.766044	+	1.32683i
$333$		0			0
$334$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$335$	1.43969	+	0.524005i	1.43969	+	0.524005i
$336$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$344$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$345$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$346$		0			0
$347$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$347$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$348$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$349$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$349$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$350$	−1.87939			−1.87939
$351$		0			0
$352$		0			0
$353$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$353$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$354$		0			0
$355$		0			0
$356$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$357$		0			0
$358$		0			0
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$	−1.00000			−1.00000
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$363$	0.939693	+	0.342020i	0.939693	+	0.342020i
$364$		0			0
$365$		0			0
$366$	1.76604	+	0.642788i	1.76604	+	0.642788i
$367$	1.87939	+	0.684040i	1.87939	+	0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$367$	1.87939	+	0.684040i	1.87939	+	0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$368$	0.173648	−	0.300767i	0.173648	−	0.300767i
$369$	1.53209			1.53209
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$373$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$374$		0			0
$375$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$376$	1.17365	−	0.984808i	1.17365	−	0.984808i
$377$		0			0
$378$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.266044	+	0.223238i	0.266044	+	0.223238i
$382$		0			0
$383$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$383$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$384$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$385$		0			0
$386$		0			0
$387$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$388$		0			0
$389$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$389$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$		0			0
$399$		0			0
$400$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$401$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$401$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$402$	1.43969	−	0.524005i	1.43969	−	0.524005i
$403$		0			0
$404$	−1.00000			−1.00000
$405$	0.173648	+	0.984808i	0.173648	+	0.984808i
$406$	−0.652704			−0.652704
$407$		0			0
$408$		0			0
$409$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$409$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$410$	1.43969	−	0.524005i	1.43969	−	0.524005i
$411$		0			0
$412$	0.173648	+	0.984808i	0.173648	+	0.984808i
$413$		0			0
$414$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$415$	0.766044	−	1.32683i	0.766044	−	1.32683i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$419$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$420$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$421$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$421$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$422$		0			0
$423$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.31908	−	1.20805i	3.31908	−	1.20805i
$428$	0.326352	−	1.85083i	0.326352	−	1.85083i
$429$		0			0
$430$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$436$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$437$		0			0
$438$		0			0
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$442$		0			0
$443$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$443$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$444$		0			0
$445$	1.17365	+	0.984808i	1.17365	+	0.984808i
$446$	1.17365	+	0.984808i	1.17365	+	0.984808i
$447$	0.326352	+	0.118782i	0.326352	+	0.118782i
$448$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$449$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$449$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$450$	0.500000	+	0.866025i	0.500000	+	0.866025i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.939693	−	0.342020i	0.939693	−	0.342020i
$455$		0			0
$456$		0			0
$457$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$457$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$458$	−0.347296			−0.347296
$459$		0			0
$460$	−0.347296			−0.347296
$461$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$461$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$463$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$464$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$465$		0			0
$466$		0			0
$467$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$467$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$468$		0			0
$469$	1.43969	−	2.49362i	1.43969	−	2.49362i
$470$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$479$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$480$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$481$		0			0
$482$	0.326352	−	1.85083i	0.326352	−	1.85083i
$483$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$484$	0.766044	−	0.642788i	0.766044	−	0.642788i
$485$		0			0
$486$	0.766044	+	0.642788i	0.766044	+	0.642788i
$487$	−2.00000			−2.00000			−1.00000			$\pi$
$487$	−2.00000			−2.00000			−1.00000			$\pi$
$488$	1.43969	−	1.20805i	1.43969	−	1.20805i
$489$	0.939693	−	0.342020i	0.939693	−	0.342020i
$490$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$491$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$491$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$492$	0.766044	−	1.32683i	0.766044	−	1.32683i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$	0.766044	+	0.642788i	0.766044	+	0.642788i
$501$	0.266044	−	0.223238i	0.266044	−	0.223238i
$502$		0			0
$503$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$503$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$504$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$505$	0.500000	+	0.866025i	0.500000	+	0.866025i
$506$		0			0
$507$	0.500000	+	0.866025i	0.500000	+	0.866025i
$508$	0.326352	−	0.118782i	0.326352	−	0.118782i
$509$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$509$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$		0			0
$514$		0			0
$515$	0.766044	−	0.642788i	0.766044	−	0.642788i
$516$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$521$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$522$	0.173648	+	0.300767i	0.173648	+	0.300767i
$523$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$523$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$524$		0			0
$525$	1.76604	+	0.642788i	1.76604	+	0.642788i
$526$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$527$		0			0
$528$		0			0
$529$	0.826352	+	0.300767i	0.826352	+	0.300767i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.53209			1.53209
$535$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$536$	0.266044	−	1.50881i	0.266044	−	1.50881i
$537$		0			0
$538$	1.43969	−	1.20805i	1.43969	−	1.20805i
$539$		0			0
$540$	0.939693	+	0.342020i	0.939693	+	0.342020i
$541$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$541$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$542$		0			0
$543$	1.43969	+	1.20805i	1.43969	+	1.20805i
$544$		0			0
$545$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$546$		0			0
$547$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$547$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$548$		0			0
$549$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$550$		0			0
$551$		0			0
$552$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$	0.326352	+	1.85083i	0.326352	+	1.85083i
$561$		0			0
$562$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$563$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$563$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$564$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$565$		0			0
$566$	0.347296			0.347296
$567$	1.87939			1.87939
$568$		0			0
$569$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$569$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$570$		0			0
$571$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$571$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$572$		0			0
$573$		0			0
$574$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$575$	0.173648	+	0.300767i	0.173648	+	0.300767i
$576$	0.173648	+	0.984808i	0.173648	+	0.984808i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.939693	+	0.342020i	0.939693	+	0.342020i
$579$		0			0
$580$	0.266044	+	0.223238i	0.266044	+	0.223238i
$581$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$587$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$588$	1.26604	+	2.19285i	1.26604	+	2.19285i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$	0.266044	−	0.223238i	0.266044	−	0.223238i
$597$		0			0
$598$		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
$601$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$601$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$602$	0.939693	+	1.62760i	0.939693	+	1.62760i
$603$	−1.53209			−1.53209
$604$		0			0
$605$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$606$	0.939693	+	0.342020i	0.939693	+	0.342020i
$607$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$608$		0			0
$609$	0.613341	+	0.223238i	0.613341	+	0.223238i
$610$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$615$	−1.53209			−1.53209
$616$		0			0
$617$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$617$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$618$	0.173648	−	0.984808i	0.173648	−	0.984808i
$619$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$619$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$620$		0			0
$621$	0.266044	+	0.223238i	0.266044	+	0.223238i
$622$		0			0
$623$	2.20574	−	1.85083i	2.20574	−	1.85083i
$624$		0			0
$625$	0.173648	−	0.984808i	0.173648	−	0.984808i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.76604	−	0.642788i	1.76604	−	0.642788i
$631$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$631$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	+	0.866025i	0.500000	+	0.866025i
$641$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$642$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$643$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$643$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$644$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$645$	0.939693	−	0.342020i	0.939693	−	0.342020i
$646$		0			0
$647$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$647$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$648$	0.939693	−	0.342020i	0.939693	−	0.342020i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.173648	−	0.984808i	0.173648	−	0.984808i
$653$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$653$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$654$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$655$		0			0
$656$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$657$		0			0
$658$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$659$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$659$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$660$		0			0
$661$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$661$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$662$		0			0
$663$		0			0
$664$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$665$		0			0
$666$		0			0
$667$	0.0603074	+	0.104455i	0.0603074	+	0.104455i
$668$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$669$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$670$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$671$		0			0
$672$	1.43969	+	1.20805i	1.43969	+	1.20805i
$673$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$673$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$674$		0			0
$675$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$676$	1.00000			1.00000
$677$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$677$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.00000			−1.00000
$682$		0			0
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	2.70574	+	0.984808i	2.70574	+	0.984808i
$687$	0.326352	+	0.118782i	0.326352	+	0.118782i
$688$	0.766044	+	0.642788i	0.766044	+	0.642788i
$689$		0			0
$690$	0.326352	+	0.118782i	0.326352	+	0.118782i
$691$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$691$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$692$		0			0
$693$		0			0
$694$	0.500000	+	0.866025i	0.500000	+	0.866025i
$695$		0			0
$696$	0.347296			0.347296
$697$		0			0
$698$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$699$		0			0
$700$	1.43969	−	1.20805i	1.43969	−	1.20805i
$701$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$701$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.17365	+	0.984808i	1.17365	+	0.984808i
$706$		0			0
$707$	1.76604	−	0.642788i	1.76604	−	0.642788i
$708$		0			0
$709$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$709$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	0.766044	−	1.32683i	0.766044	−	1.32683i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	0.766044	−	0.642788i	0.766044	−	0.642788i
$721$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$722$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$723$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$724$	1.76604	−	0.642788i	1.76604	−	0.642788i
$725$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$726$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$727$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$727$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$730$		0			0
$731$		0			0
$732$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$733$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$733$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$734$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$735$	1.26604	−	2.19285i	1.26604	−	2.19285i
$736$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$737$		0			0
$738$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$743$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$744$		0			0
$745$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$746$		0			0
$747$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$748$		0			0
$749$	0.613341	+	3.47843i	0.613341	+	3.47843i
$750$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$751$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$751$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$752$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.939693	−	1.62760i	0.939693	−	1.62760i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$761$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$762$	−0.347296			−0.347296
$763$	0.113341	+	0.642788i	0.113341	+	0.642788i
$764$		0			0
$765$		0			0
$766$	0.500000	−	0.866025i	0.500000	−	0.866025i
$767$		0			0
$768$	0.939693	+	0.342020i	0.939693	+	0.342020i
$769$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$769$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$	0.500000	−	0.866025i	0.500000	−	0.866025i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.43969	−	0.524005i	1.43969	−	0.524005i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$784$	2.53209			2.53209
$785$		0			0
$786$		0			0
$787$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$787$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$788$		0			0
$789$	0.500000	+	0.866025i	0.500000	+	0.866025i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$797$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$798$		0			0
$799$		0			0
$800$	0.500000	−	0.866025i	0.500000	−	0.866025i
$801$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$802$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$803$		0			0
$804$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$805$	0.613341	−	0.223238i	0.613341	−	0.223238i
$806$		0			0
$807$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$808$	0.766044	−	0.642788i	0.766044	−	0.642788i
$809$	2.00000			2.00000			1.00000			$0$
$809$	2.00000			2.00000			1.00000			$0$
$810$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	0.500000	−	0.419550i	0.500000	−	0.419550i
$813$		0			0
$814$		0			0
$815$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$816$		0			0
$817$		0			0
$818$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$819$		0			0
$820$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$821$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$821$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$823$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$824$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$825$		0			0
$826$		0			0
$827$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$827$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$828$	0.326352	−	0.118782i	0.326352	−	0.118782i
$829$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$829$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$830$	0.266044	+	1.50881i	0.266044	+	1.50881i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$839$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$840$	0.326352	−	1.85083i	0.326352	−	1.85083i
$841$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$842$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$843$	1.87939			1.87939
$844$		0			0
$845$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$846$	1.53209			1.53209
$847$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$848$		0			0
$849$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$853$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$854$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$855$		0			0
$856$	0.939693	+	1.62760i	0.939693	+	1.62760i
$857$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$857$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$858$		0			0
$859$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$859$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$860$	0.173648	−	0.984808i	0.173648	−	0.984808i
$861$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$862$		0			0
$863$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$863$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$864$	0.173648	−	0.984808i	0.173648	−	0.984808i
$865$		0			0
$866$		0			0
$867$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$868$		0			0
$869$		0			0
$870$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$871$		0			0
$872$	0.173648	+	0.300767i	0.173648	+	0.300767i
$873$		0			0
$874$		0			0
$875$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$876$		0			0
$877$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$877$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$881$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$882$	−0.439693	−	2.49362i	−0.439693	−	2.49362i
$883$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$883$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$884$		0			0
$885$		0			0
$886$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$887$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$887$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$888$		0			0
$889$	−0.500000	+	0.419550i	−0.500000	+	0.419550i
$890$	−1.53209			−1.53209
$891$		0			0
$892$	−1.53209			−1.53209
$893$		0			0
$894$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$895$		0			0
$896$	1.76604	−	0.642788i	1.76604	−	0.642788i
$897$		0			0
$898$	0.173648	+	0.984808i	0.173648	+	0.984808i
$899$		0			0
$900$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$901$		0			0
$902$		0			0
$903$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$904$		0			0
$905$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$906$		0			0
$907$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$907$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$908$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$909$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$910$		0			0
$911$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$911$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.43969	+	1.20805i	1.43969	+	1.20805i
$916$	0.266044	−	0.223238i	0.266044	−	0.223238i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	0.266044	−	0.223238i	0.266044	−	0.223238i
$921$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$922$	0.326352	−	1.85083i	0.326352	−	1.85083i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.500000	+	0.866025i	0.500000	+	0.866025i
$927$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$928$	0.173648	−	0.300767i	0.173648	−	0.300767i
$929$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$929$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.939693	+	0.342020i	0.939693	+	0.342020i
$935$		0			0
$936$		0			0
$937$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$937$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$938$	0.500000	+	2.83564i	0.500000	+	2.83564i
$939$		0			0
$940$	1.43969	−	0.524005i	1.43969	−	0.524005i
$941$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$941$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$942$		0			0
$943$	−0.407604	+	0.342020i	−0.407604	+	0.342020i
$944$		0			0
$945$	−1.87939			−1.87939
$946$		0			0
$947$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$947$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$953$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$961$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$962$		0			0
$963$	1.43969	−	1.20805i	1.43969	−	1.20805i
$964$	0.939693	+	1.62760i	0.939693	+	1.62760i
$965$		0			0
$966$	0.326352	−	0.565258i	0.326352	−	0.565258i
$967$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$967$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$968$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$969$		0			0
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	−1.00000			−1.00000
$973$		0			0
$974$	1.53209	−	1.28558i	1.53209	−	1.28558i
$975$		0			0
$976$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$977$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$977$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$978$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$979$		0			0
$980$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$981$	0.266044	−	0.223238i	0.266044	−	0.223238i
$982$		0			0
$983$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$983$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$984$	0.266044	+	1.50881i	0.266044	+	1.50881i
$985$		0			0
$986$		0			0
$987$	2.20574	−	1.85083i	2.20574	−	1.85083i
$988$		0			0
$989$	0.173648	−	0.300767i	0.173648	−	0.300767i
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.17365	+	0.984808i	1.17365	+	0.984808i
$997$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$997$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.1.bf.b.319.1	yes	6
3.2	odd	2		1620.1.bf.b.199.1		6
4.3	odd	2		540.1.bf.a.319.1	yes	6
5.2	odd	4		2700.1.bj.a.751.1		12
5.3	odd	4		2700.1.bj.a.751.2		12
5.4	even	2		540.1.bf.a.319.1	yes	6
12.11	even	2		1620.1.bf.a.199.1		6
15.14	odd	2		1620.1.bf.a.199.1		6
20.3	even	4		2700.1.bj.a.751.1		12
20.7	even	4		2700.1.bj.a.751.2		12
20.19	odd	2	CM	540.1.bf.b.319.1	yes	6
27.11	odd	18		1620.1.bf.b.1099.1		6
27.16	even	9	inner	540.1.bf.b.259.1	yes	6
60.59	even	2		1620.1.bf.b.199.1		6
108.11	even	18		1620.1.bf.a.1099.1		6
108.43	odd	18		540.1.bf.a.259.1	✓	6
135.43	odd	36		2700.1.bj.a.151.1		12
135.97	odd	36		2700.1.bj.a.151.2		12
135.119	odd	18		1620.1.bf.a.1099.1		6
135.124	even	18		540.1.bf.a.259.1	✓	6
540.43	even	36		2700.1.bj.a.151.2		12
540.119	even	18		1620.1.bf.b.1099.1		6
540.259	odd	18	inner	540.1.bf.b.259.1	yes	6
540.367	even	36		2700.1.bj.a.151.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.1.bf.a.259.1	✓	6	108.43	odd	18
540.1.bf.a.259.1	✓	6	135.124	even	18
540.1.bf.a.319.1	yes	6	4.3	odd	2
540.1.bf.a.319.1	yes	6	5.4	even	2
540.1.bf.b.259.1	yes	6	27.16	even	9	inner
540.1.bf.b.259.1	yes	6	540.259	odd	18	inner
540.1.bf.b.319.1	yes	6	1.1	even	1	trivial
540.1.bf.b.319.1	yes	6	20.19	odd	2	CM
1620.1.bf.a.199.1		6	12.11	even	2
1620.1.bf.a.199.1		6	15.14	odd	2
1620.1.bf.a.1099.1		6	108.11	even	18
1620.1.bf.a.1099.1		6	135.119	odd	18
1620.1.bf.b.199.1		6	3.2	odd	2
1620.1.bf.b.199.1		6	60.59	even	2
1620.1.bf.b.1099.1		6	27.11	odd	18
1620.1.bf.b.1099.1		6	540.119	even	18
2700.1.bj.a.151.1		12	135.43	odd	36
2700.1.bj.a.151.1		12	540.367	even	36
2700.1.bj.a.151.2		12	135.97	odd	36
2700.1.bj.a.151.2		12	540.43	even	36
2700.1.bj.a.751.1		12	5.2	odd	4
2700.1.bj.a.751.1		12	20.3	even	4
2700.1.bj.a.751.2		12	5.3	odd	4
2700.1.bj.a.751.2		12	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	540.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.326352 + 1.85083i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.939693 + 0.342020i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.326352 + 1.85083i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.173648 - 0.984808i) q^{12} +(-1.43969 - 1.20805i) q^{14} +(-0.766044 + 0.642788i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.173648 + 0.984808i) q^{18} +(0.173648 + 0.984808i) q^{20} +(0.939693 + 1.62760i) q^{21} +(-0.0603074 + 0.342020i) q^{23} +(0.766044 + 0.642788i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.500000 - 0.866025i) q^{27} +1.87939 q^{28} +(0.266044 - 0.223238i) q^{29} +(0.173648 - 0.984808i) q^{30} +(0.939693 - 0.342020i) q^{32} +(-0.939693 - 1.62760i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-0.766044 - 0.642788i) q^{40} +(1.17365 + 0.984808i) q^{41} +(-1.76604 - 0.642788i) q^{42} +(-0.939693 - 0.342020i) q^{43} +(-0.500000 + 0.866025i) q^{45} +(-0.173648 - 0.300767i) q^{46} +(-0.266044 - 1.50881i) q^{47} -1.00000 q^{48} +(-2.37939 + 0.866025i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(0.173648 + 0.984808i) q^{54} +(-1.43969 + 1.20805i) q^{56} +(-0.0603074 + 0.342020i) q^{58} +(0.500000 + 0.866025i) q^{60} +(-0.326352 - 1.85083i) q^{61} +(1.43969 + 1.20805i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.17365 - 0.984808i) q^{67} +(0.0603074 + 0.342020i) q^{69} +(1.76604 + 0.642788i) q^{70} +(0.939693 + 0.342020i) q^{72} +(0.500000 - 0.866025i) q^{75} +1.00000 q^{80} +(0.173648 - 0.984808i) q^{81} -1.53209 q^{82} +(-1.17365 + 0.984808i) q^{83} +(1.76604 - 0.642788i) q^{84} +(0.939693 - 0.342020i) q^{86} +(0.173648 - 0.300767i) q^{87} +(-0.766044 - 1.32683i) q^{89} +(-0.173648 - 0.984808i) q^{90} +(0.326352 + 0.118782i) q^{92} +(1.17365 + 0.984808i) q^{94} +(0.766044 - 0.642788i) q^{96} +(1.26604 - 2.19285i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^6 + 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{14} - 6 q^{23} + 3 q^{27} - 3 q^{29} - 3 q^{36} + 6 q^{41} - 6 q^{42} - 3 q^{45} + 3 q^{47} - 6 q^{48} - 3 q^{49} - 3 q^{56} - 6 q^{58} + 3 q^{60} - 3 q^{61} + 3 q^{63} - 3 q^{64} - 6 q^{67} + 6 q^{69} + 6 q^{70} + 3 q^{75} + 6 q^{80} - 6 q^{83} + 6 q^{84} + 3 q^{92} + 6 q^{94} + 3 q^{98}+O(q^{100}) \) 6 * q - 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^14 - 6 * q^23 + 3 * q^27 - 3 * q^29 - 3 * q^36 + 6 * q^41 - 6 * q^42 - 3 * q^45 + 3 * q^47 - 6 * q^48 - 3 * q^49 - 3 * q^56 - 6 * q^58 + 3 * q^60 - 3 * q^61 + 3 * q^63 - 3 * q^64 - 6 * q^67 + 6 * q^69 + 6 * q^70 + 3 * q^75 + 6 * q^80 - 6 * q^83 + 6 * q^84 + 3 * q^92 + 6 * q^94 + 3 * q^98

Introduction

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