LMFDB - Embedded newform 285.1.bd.b.119.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,1,Mod(44,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 14]))

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

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

chi := DirichletCharacter("285.44");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	285.bd (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:	$0.142233528600$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.859792878950625.1

Embedding invariants

Embedding label			119.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	285.119
Dual form			285.1.bd.b.194.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(1.03209 - 0.866025i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.266044 + 1.50881i) q^{6} +(0.266044 - 0.460802i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(1.03209 - 0.866025i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.266044 + 1.50881i) q^{6} +(0.266044 - 0.460802i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.43969 - 0.524005i) q^{10} +(0.673648 + 1.16679i) q^{12} +(0.766044 - 0.642788i) q^{15} +(-0.0923963 + 0.524005i) q^{16} +(-1.76604 + 0.642788i) q^{17} -1.53209 q^{18} +(0.173648 - 0.984808i) q^{19} -1.34730 q^{20} +(0.766044 - 0.642788i) q^{23} +(0.407604 + 0.342020i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.766044 - 1.32683i) q^{30} +(-0.173648 - 0.300767i) q^{31} +(0.233956 + 1.32683i) q^{32} +(-2.20574 + 1.85083i) q^{34} +(-1.26604 + 0.460802i) q^{36} +(-0.266044 - 1.50881i) q^{38} +(-0.500000 + 0.181985i) q^{40} +(0.500000 + 0.866025i) q^{45} +(0.766044 - 1.32683i) q^{46} +(1.43969 + 0.524005i) q^{47} +(-0.500000 - 0.181985i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.766044 + 1.32683i) q^{50} +(-0.326352 - 1.85083i) q^{51} +(1.43969 - 1.20805i) q^{53} +(0.266044 - 1.50881i) q^{54} +(0.939693 + 0.342020i) q^{57} +(0.233956 - 1.32683i) q^{60} +(-0.766044 + 0.642788i) q^{61} +(-0.407604 - 0.342020i) q^{62} +(0.766044 + 1.32683i) q^{64} +(-1.26604 + 2.19285i) q^{68} +(0.500000 + 0.866025i) q^{69} +(-0.407604 + 0.342020i) q^{72} -1.00000 q^{75} +(-0.673648 - 1.16679i) q^{76} +(-0.173648 + 0.984808i) q^{79} +(0.407604 - 0.342020i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.173648 + 0.300767i) q^{83} +(1.76604 + 0.642788i) q^{85} +(1.17365 + 0.984808i) q^{90} +(0.233956 - 1.32683i) q^{92} +(0.326352 - 0.118782i) q^{93} +2.34730 q^{94} +(-0.766044 + 0.642788i) q^{95} -1.34730 q^{96} +(-0.266044 + 1.50881i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{6} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^6 - 3 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 3 q^{6} - 3 q^{8} - 3 q^{10} + 3 q^{12} + 3 q^{16} - 6 q^{17} - 6 q^{20} + 6 q^{24} + 3 q^{27} + 6 q^{32} - 3 q^{34} - 3 q^{36} + 3 q^{38} - 3 q^{40} + 3 q^{45} + 3 q^{47} - 3 q^{48} - 3 q^{49} - 3 q^{51} + 3 q^{53} - 3 q^{54} + 6 q^{60} - 6 q^{62} - 3 q^{68} + 3 q^{69} - 6 q^{72} - 6 q^{75} - 3 q^{76} + 6 q^{80} + 6 q^{85} + 6 q^{90} + 6 q^{92} + 3 q^{93} + 12 q^{94} - 6 q^{96} + 3 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^6 - 3 * q^8 - 3 * q^10 + 3 * q^12 + 3 * q^16 - 6 * q^17 - 6 * q^20 + 6 * q^24 + 3 * q^27 + 6 * q^32 - 3 * q^34 - 3 * q^36 + 3 * q^38 - 3 * q^40 + 3 * q^45 + 3 * q^47 - 3 * q^48 - 3 * q^49 - 3 * q^51 + 3 * q^53 - 3 * q^54 + 6 * q^60 - 6 * q^62 - 3 * q^68 + 3 * q^69 - 6 * q^72 - 6 * q^75 - 3 * q^76 + 6 * q^80 + 6 * q^85 + 6 * q^90 + 6 * q^92 + 3 * q^93 + 12 * q^94 - 6 * q^96 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$3$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$3$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$4$	1.03209	−	0.866025i	1.03209	−	0.866025i
$5$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$5$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$6$	0.266044	+	1.50881i	0.266044	+	1.50881i
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$	0.266044	−	0.460802i	0.266044	−	0.460802i
$9$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$10$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.673648	+	1.16679i	0.673648	+	1.16679i
$13$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$13$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$14$		0			0
$15$	0.766044	−	0.642788i	0.766044	−	0.642788i
$16$	−0.0923963	+	0.524005i	−0.0923963	+	0.524005i
$17$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$17$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$18$	−1.53209			−1.53209
$19$	0.173648	−	0.984808i	0.173648	−	0.984808i
$19$	0.173648	−	0.984808i	0.173648	−	0.984808i
$20$	−1.34730			−1.34730
$21$		0			0
$22$		0			0
$23$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$23$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$24$	0.407604	+	0.342020i	0.407604	+	0.342020i
$25$	0.173648	+	0.984808i	0.173648	+	0.984808i
$26$		0			0
$27$	0.500000	−	0.866025i	0.500000	−	0.866025i
$28$		0			0
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$	0.766044	−	1.32683i	0.766044	−	1.32683i
$31$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$31$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$32$	0.233956	+	1.32683i	0.233956	+	1.32683i
$33$		0			0
$34$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$35$		0			0
$36$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$39$		0			0
$40$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$41$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$41$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$42$		0			0
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.500000	+	0.866025i
$46$	0.766044	−	1.32683i	0.766044	−	1.32683i
$47$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$47$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$48$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$	0.766044	+	1.32683i	0.766044	+	1.32683i
$51$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$52$		0			0
$53$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$53$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$54$	0.266044	−	1.50881i	0.266044	−	1.50881i
$55$		0			0
$56$		0			0
$57$	0.939693	+	0.342020i	0.939693	+	0.342020i
$58$		0			0
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$	0.233956	−	1.32683i	0.233956	−	1.32683i
$61$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$61$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$62$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$63$		0			0
$64$	0.766044	+	1.32683i	0.766044	+	1.32683i
$65$		0			0
$66$		0			0
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$69$	0.500000	+	0.866025i	0.500000	+	0.866025i
$70$		0			0
$71$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$71$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$72$	−0.407604	+	0.342020i	−0.407604	+	0.342020i
$73$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$73$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$74$		0			0
$75$	−1.00000			−1.00000
$76$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$77$		0			0
$78$		0			0
$79$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$79$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$80$	0.407604	−	0.342020i	0.407604	−	0.342020i
$81$	0.766044	+	0.642788i	0.766044	+	0.642788i
$82$		0			0
$83$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$83$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$84$		0			0
$85$	1.76604	+	0.642788i	1.76604	+	0.642788i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$89$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$90$	1.17365	+	0.984808i	1.17365	+	0.984808i
$91$		0			0
$92$	0.233956	−	1.32683i	0.233956	−	1.32683i
$93$	0.326352	−	0.118782i	0.326352	−	0.118782i
$94$	2.34730			2.34730
$95$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$96$	−1.34730			−1.34730
$97$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$97$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$98$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$99$		0			0
$100$	1.03209	+	0.866025i	1.03209	+	0.866025i
$101$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$101$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$102$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$		0			0
$106$	1.43969	−	2.49362i	1.43969	−	2.49362i
$107$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$107$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$108$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$109$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$109$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$113$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$114$	1.53209			1.53209
$115$	−1.00000			−1.00000
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.0923963	−	0.524005i	−0.0923963	−	0.524005i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$123$		0			0
$124$	−0.439693	−	0.160035i	−0.439693	−	0.160035i
$125$	0.500000	−	0.866025i	0.500000	−	0.866025i
$126$		0			0
$127$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$127$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$128$	0.766044	+	0.642788i	0.766044	+	0.642788i
$129$		0			0
$130$		0			0
$131$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$131$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$136$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$137$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$137$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$138$	1.17365	+	0.984808i	1.17365	+	0.984808i
$139$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$139$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$140$		0			0
$141$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$142$		0			0
$143$		0			0
$144$	0.266044	−	0.460802i	0.266044	−	0.460802i
$145$		0			0
$146$		0			0
$147$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$148$		0			0
$149$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$149$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$150$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$151$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$151$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$152$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$153$	1.87939			1.87939
$154$		0			0
$155$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$156$		0			0
$157$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$157$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$158$	0.266044	+	1.50881i	0.266044	+	1.50881i
$159$	0.939693	+	1.62760i	0.939693	+	1.62760i
$160$	0.673648	−	1.16679i	0.673648	−	1.16679i
$161$		0			0
$162$	1.43969	+	0.524005i	1.43969	+	0.524005i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$	0.407604	+	0.342020i	0.407604	+	0.342020i
$167$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	−0.766044	−	0.642788i	$-0.777778\pi$
$167$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	0.500000	+	0.866025i	$0.333333\pi$
$168$		0			0
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$	2.87939			2.87939
$171$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$172$		0			0
$173$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$173$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	1.26604	+	0.460802i	1.26604	+	0.460802i
$181$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$181$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$184$	−0.0923963	−	0.524005i	−0.0923963	−	0.524005i
$185$		0			0
$186$	0.407604	−	0.342020i	0.407604	−	0.342020i
$187$		0			0
$188$	1.93969	−	0.705990i	1.93969	−	0.705990i
$189$		0			0
$190$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$193$		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
$196$	0.233956	+	1.32683i	0.233956	+	1.32683i
$197$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$197$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$198$		0			0
$199$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$199$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$200$	0.500000	+	0.181985i	0.500000	+	0.181985i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$205$		0			0
$206$		0			0
$207$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$211$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$212$	0.439693	−	2.49362i	0.439693	−	2.49362i
$213$		0			0
$214$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$215$		0			0
$216$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$217$		0			0
$218$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$223$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$224$		0			0
$225$	0.173648	−	0.984808i	0.173648	−	0.984808i
$226$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$227$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$227$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$228$	1.26604	−	0.460802i	1.26604	−	0.460802i
$229$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$229$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$230$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$231$		0			0
$232$		0			0
$233$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	0.500000	−	0.866025i	$-0.333333\pi$
$233$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$234$		0			0
$235$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$236$		0			0
$237$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	0.266044	+	0.460802i	0.266044	+	0.460802i
$241$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$241$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$242$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$243$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$244$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$245$	0.939693	−	0.342020i	0.939693	−	0.342020i
$246$		0			0
$247$		0			0
$248$	−0.184793			−0.184793
$249$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$250$	0.266044	−	1.50881i	0.266044	−	1.50881i
$251$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$251$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$256$		0			0
$257$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$257$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$263$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$264$		0			0
$265$	−1.87939			−1.87939
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$269$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$270$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$271$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$271$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$272$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$273$		0			0
$274$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$275$		0			0
$276$	1.26604	+	0.460802i	1.26604	+	0.460802i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$279$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$280$		0			0
$281$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$281$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$282$	−0.407604	+	2.31164i	−0.407604	+	2.31164i
$283$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$283$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$284$		0			0
$285$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$286$		0			0
$287$		0			0
$288$	0.233956	−	1.32683i	0.233956	−	1.32683i
$289$	1.93969	−	1.62760i	1.93969	−	1.62760i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$293$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$294$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$301$		0			0
$302$	2.20574	−	0.802823i	2.20574	−	0.802823i
$303$		0			0
$304$	0.500000	+	0.181985i	0.500000	+	0.181985i
$305$	1.00000			1.00000
$306$	2.70574	−	0.984808i	2.70574	−	0.984808i
$307$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$307$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$308$		0			0
$309$		0			0
$310$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$		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
$315$		0			0
$316$	0.673648	+	1.16679i	0.673648	+	1.16679i
$317$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$317$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$318$	2.20574	+	1.85083i	2.20574	+	1.85083i
$319$		0			0
$320$	0.266044	−	1.50881i	0.266044	−	1.50881i
$321$	1.76604	−	0.642788i	1.76604	−	0.642788i
$322$		0			0
$323$	0.326352	+	1.85083i	0.326352	+	1.85083i
$324$	1.34730			1.34730
$325$		0			0
$326$		0			0
$327$	1.43969	−	1.20805i	1.43969	−	1.20805i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$332$	0.439693	+	0.160035i	0.439693	+	0.160035i
$333$		0			0
$334$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$335$		0			0
$336$		0			0
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$339$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$340$	2.37939	−	0.866025i	2.37939	−	0.866025i
$341$		0			0
$342$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$343$		0			0
$344$		0			0
$345$	0.173648	−	0.984808i	0.173648	−	0.984808i
$346$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$347$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$347$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$348$		0			0
$349$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$349$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$353$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$359$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$360$	0.532089			0.532089
$361$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$362$	−0.532089			−0.532089
$363$	0.939693	−	0.342020i	0.939693	−	0.342020i
$364$		0			0
$365$		0			0
$366$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$367$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$367$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$368$	0.266044	+	0.460802i	0.266044	+	0.460802i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.233956	−	0.405223i	0.233956	−	0.405223i
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	0.766044	+	0.642788i	0.766044	+	0.642788i
$376$	0.624485	−	0.524005i	0.624485	−	0.524005i
$377$		0			0
$378$		0			0
$379$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$379$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$380$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$381$		0			0
$382$		0			0
$383$	0.326352	−	1.85083i	0.326352	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$383$	0.326352	−	1.85083i	0.326352	−	1.85083i	0.500000	−	0.866025i	$-0.333333\pi$
$384$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$389$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$390$		0			0
$391$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$392$	0.266044	+	0.460802i	0.266044	+	0.460802i
$393$		0			0
$394$	1.79813	+	1.50881i	1.79813	+	1.50881i
$395$	0.766044	−	0.642788i	0.766044	−	0.642788i
$396$		0			0
$397$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$397$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$398$	1.53209			1.53209
$399$		0			0
$400$	−0.532089			−0.532089
$401$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$401$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$406$		0			0
$407$		0			0
$408$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$409$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$409$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$410$		0			0
$411$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$412$		0			0
$413$		0			0
$414$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$415$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$416$		0			0
$417$	1.87939			1.87939
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$421$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$422$	−1.79813	+	1.50881i	−1.79813	+	1.50881i
$423$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$424$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$425$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$426$		0			0
$427$		0			0
$428$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$429$		0			0
$430$		0			0
$431$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$431$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$432$	0.407604	+	0.342020i	0.407604	+	0.342020i
$433$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$433$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$434$		0			0
$435$		0			0
$436$	−2.53209			−2.53209
$437$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$438$		0			0
$439$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$439$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$440$		0			0
$441$	0.766044	−	0.642788i	0.766044	−	0.642788i
$442$		0			0
$443$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$443$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$451$		0			0
$452$	−0.358441	+	0.300767i	−0.358441	+	0.300767i
$453$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$454$	1.43969	−	0.524005i	1.43969	−	0.524005i
$455$		0			0
$456$	0.407604	−	0.342020i	0.407604	−	0.342020i
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	2.20574	−	0.802823i	2.20574	−	0.802823i
$459$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$460$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$461$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$461$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$462$		0			0
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$466$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$467$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$467$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$468$		0			0
$469$		0			0
$470$	−1.79813	−	1.50881i	−1.79813	−	1.50881i
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−1.53209			−1.53209
$475$	1.00000			1.00000
$476$		0			0
$477$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$478$		0			0
$479$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$479$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$480$	1.03209	+	0.866025i	1.03209	+	0.866025i
$481$		0			0
$482$	1.17365	+	2.03282i	1.17365	+	2.03282i
$483$		0			0
$484$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$485$		0			0
$486$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$489$		0			0
$490$	1.17365	−	0.984808i	1.17365	−	0.984808i
$491$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$491$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.173648	−	0.0632028i	0.173648	−	0.0632028i
$497$		0			0
$498$	−0.407604	+	0.342020i	−0.407604	+	0.342020i
$499$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$499$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$500$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$501$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$502$		0			0
$503$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$503$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$508$		0			0
$509$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$509$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$510$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$511$		0			0
$512$	−1.00000			−1.00000
$513$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$514$	−1.53209			−1.53209
$515$		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	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$523$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$524$		0			0
$525$		0			0
$526$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$527$	0.500000	+	0.419550i	0.500000	+	0.419550i
$528$		0			0
$529$		0			0
$530$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$531$		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
$540$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$541$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$541$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$542$	2.20574	+	0.802823i	2.20574	+	0.802823i
$543$	0.173648	−	0.300767i	0.173648	−	0.300767i
$544$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$545$	0.326352	+	1.85083i	0.326352	+	1.85083i
$546$		0			0
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$	−0.358441	+	2.03282i	−0.358441	+	2.03282i
$549$	0.939693	−	0.342020i	0.939693	−	0.342020i
$550$		0			0
$551$		0			0
$552$	0.532089			0.532089
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$557$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$557$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$558$	0.266044	+	0.460802i	0.266044	+	0.460802i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$563$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$564$	0.358441	+	2.03282i	0.358441	+	2.03282i
$565$	0.266044	+	0.223238i	0.266044	+	0.223238i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$571$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$571$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.766044	+	0.642788i	0.766044	+	0.642788i
$576$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	1.93969	−	3.35965i	1.93969	−	3.35965i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$587$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$587$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$588$	−1.34730			−1.34730
$589$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$590$		0			0
$591$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$592$		0			0
$593$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	−0.766044	−	0.642788i	$-0.777778\pi$
$593$	−0.266044	+	0.223238i	−0.266044	+	0.223238i	0.500000	+	0.866025i	$0.333333\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$598$		0			0
$599$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$599$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$600$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$601$	−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
$604$	1.58125	−	1.32683i	1.58125	−	1.32683i
$605$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	1.34730			1.34730
$609$		0			0
$610$	1.43969	−	0.524005i	1.43969	−	0.524005i
$611$		0			0
$612$	1.93969	−	1.62760i	1.93969	−	1.62760i
$613$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$613$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$617$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$618$		0			0
$619$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$619$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$620$	0.233956	+	0.405223i	0.233956	+	0.405223i
$621$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$622$		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	−0.500000	+	0.866025i	$0.666667\pi$
$631$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$632$	0.407604	+	0.342020i	0.407604	+	0.342020i
$633$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$634$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$635$		0			0
$636$	2.37939	+	0.866025i	2.37939	+	0.866025i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$641$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$641$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$642$	2.20574	−	1.85083i	2.20574	−	1.85083i
$643$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$643$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$644$		0			0
$645$		0			0
$646$	1.43969	+	2.49362i	1.43969	+	2.49362i
$647$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$647$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$648$	0.500000	−	0.181985i	0.500000	−	0.181985i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$653$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$654$	1.43969	−	2.49362i	1.43969	−	2.49362i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$659$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$660$		0			0
$661$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$661$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$662$	0.266044	−	1.50881i	0.266044	−	1.50881i
$663$		0			0
$664$	0.184793			0.184793
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.0812519	+	0.460802i	−0.0812519	+	0.460802i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	0.939693	+	0.342020i	0.939693	+	0.342020i
$676$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$677$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$677$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$678$	−0.0923963	−	0.524005i	−0.0923963	−	0.524005i
$679$		0			0
$680$	0.766044	−	0.642788i	0.766044	−	0.642788i
$681$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$682$		0			0
$683$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$683$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$684$	0.233956	+	1.32683i	0.233956	+	1.32683i
$685$	1.53209			1.53209
$686$		0			0
$687$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$688$		0			0
$689$		0			0
$690$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$691$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$691$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$692$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$693$		0			0
$694$	2.70574	+	0.984808i	2.70574	+	0.984808i
$695$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$696$		0			0
$697$		0			0
$698$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$699$	0.266044	−	0.223238i	0.266044	−	0.223238i
$700$		0			0
$701$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$701$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.43969	−	0.524005i	1.43969	−	0.524005i
$706$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$707$		0			0
$708$		0			0
$709$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$709$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$710$		0			0
$711$	0.500000	−	0.866025i	0.500000	−	0.866025i
$712$		0			0
$713$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$719$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$720$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$721$		0			0
$722$	−1.53209			−1.53209
$723$	−1.53209			−1.53209
$724$	−0.439693	+	0.160035i	−0.439693	+	0.160035i
$725$		0			0
$726$	1.17365	−	0.984808i	1.17365	−	0.984808i
$727$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$727$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$730$		0			0
$731$		0			0
$732$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$		0			0
$735$	0.173648	+	0.984808i	0.173648	+	0.984808i
$736$	1.03209	+	0.866025i	1.03209	+	0.866025i
$737$		0			0
$738$		0			0
$739$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$739$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$743$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$744$	0.0320889	−	0.181985i	0.0320889	−	0.181985i
$745$		0			0
$746$		0			0
$747$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$748$		0			0
$749$		0			0
$750$	1.43969	+	0.524005i	1.43969	+	0.524005i
$751$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$751$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$752$	−0.407604	+	0.705990i	−0.407604	+	0.705990i
$753$		0			0
$754$		0			0
$755$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$756$		0			0
$757$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$757$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$758$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$759$		0			0
$760$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$766$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$767$		0			0
$768$		0			0
$769$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$769$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	0.500000	−	0.866025i	0.500000	−	0.866025i
$772$		0			0
$773$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$773$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$774$		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
$782$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$783$		0			0
$784$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$785$		0			0
$786$		0			0
$787$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$787$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$788$	1.93969	+	0.705990i	1.93969	+	0.705990i
$789$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$790$	0.766044	−	1.32683i	0.766044	−	1.32683i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.326352	−	1.85083i	0.326352	−	1.85083i
$796$	1.26604	−	0.460802i	1.26604	−	0.460802i
$797$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$797$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$798$		0			0
$799$	−2.87939			−2.87939
$800$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$801$		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	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$811$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$811$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$812$		0			0
$813$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$814$		0			0
$815$		0			0
$816$	1.00000			1.00000
$817$		0			0
$818$	1.53209			1.53209
$819$		0			0
$820$		0			0
$821$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$821$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$822$	−1.79813	−	1.50881i	−1.79813	−	1.50881i
$823$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$823$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$827$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$828$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$829$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$829$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$830$	−0.0923963	−	0.524005i	−0.0923963	−	0.524005i
$831$		0			0
$832$		0			0
$833$	0.326352	−	1.85083i	0.326352	−	1.85083i
$834$	2.70574	−	0.984808i	2.70574	−	0.984808i
$835$	0.347296			0.347296
$836$		0			0
$837$	−0.347296			−0.347296
$838$		0			0
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$		0			0
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$	−0.532089	−	3.01763i	−0.532089	−	3.01763i
$843$		0			0
$844$	−1.03209	+	1.78763i	−1.03209	+	1.78763i
$845$	0.939693	+	0.342020i	0.939693	+	0.342020i
$846$	−2.20574	−	0.802823i	−2.20574	−	0.802823i
$847$		0			0
$848$	0.500000	+	0.866025i	0.500000	+	0.866025i
$849$		0			0
$850$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$851$		0			0
$852$		0			0
$853$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$853$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$854$		0			0
$855$	0.939693	−	0.342020i	0.939693	−	0.342020i
$856$	−1.00000			−1.00000
$857$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$857$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$859$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$863$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$864$	1.26604	+	0.460802i	1.26604	+	0.460802i
$865$	0.939693	+	0.342020i	0.939693	+	0.342020i
$866$		0			0
$867$	1.26604	+	2.19285i	1.26604	+	2.19285i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$873$		0			0
$874$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$875$		0			0
$876$		0			0
$877$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$877$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$878$	2.20574	−	1.85083i	2.20574	−	1.85083i
$879$	0.266044	+	0.223238i	0.266044	+	0.223238i
$880$		0			0
$881$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$881$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$882$	0.766044	−	1.32683i	0.766044	−	1.32683i
$883$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$883$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$884$		0			0
$885$		0			0
$886$	1.43969	+	2.49362i	1.43969	+	2.49362i
$887$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$887$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.766044	−	1.32683i	0.766044	−	1.32683i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$901$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$902$		0			0
$903$		0			0
$904$	−0.0923963	+	0.160035i	−0.0923963	+	0.160035i
$905$	0.173648	+	0.300767i	0.173648	+	0.300767i
$906$	0.407604	+	2.31164i	0.407604	+	2.31164i
$907$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$907$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$908$	1.03209	−	0.866025i	1.03209	−	0.866025i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$913$		0			0
$914$		0			0
$915$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$916$	1.58125	−	1.32683i	1.58125	−	1.32683i
$917$		0			0
$918$	0.500000	+	2.83564i	0.500000	+	2.83564i
$919$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$919$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$920$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$921$		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	$-0.111111\pi$
$929$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$930$	−0.532089			−0.532089
$931$	0.766044	+	0.642788i	0.766044	+	0.642788i
$932$	−0.467911			−0.467911
$933$		0			0
$934$	0.407604	−	2.31164i	0.407604	−	2.31164i
$935$		0			0
$936$		0			0
$937$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$937$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$938$		0			0
$939$		0			0
$940$	−1.93969	−	0.705990i	−1.93969	−	0.705990i
$941$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$941$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$947$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$948$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$949$		0			0
$950$	1.43969	−	0.524005i	1.43969	−	0.524005i
$951$	0.347296			0.347296
$952$		0			0
$953$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$953$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$954$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.43969	+	0.524005i	1.43969	+	0.524005i
$961$	0.439693	−	0.761570i	0.439693	−	0.761570i
$962$		0			0
$963$	0.326352	+	1.85083i	0.326352	+	1.85083i
$964$	1.58125	+	1.32683i	1.58125	+	1.32683i
$965$		0			0
$966$		0			0
$967$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$967$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$968$	−0.532089			−0.532089
$969$	−1.87939			−1.87939
$970$		0			0
$971$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$971$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$972$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$977$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$977$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$978$		0			0
$979$		0			0
$980$	0.673648	−	1.16679i	0.673648	−	1.16679i
$981$	0.939693	+	1.62760i	0.939693	+	1.62760i
$982$		0			0
$983$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$983$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$984$		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	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$992$	0.358441	−	0.300767i	0.358441	−	0.300767i
$993$	0.766044	+	0.642788i	0.766044	+	0.642788i
$994$		0			0
$995$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$996$	−0.233956	+	0.405223i	−0.233956	+	0.405223i
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$	2.20574	+	0.802823i	2.20574	+	0.802823i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.1.bd.b.119.1	yes	6
3.2	odd	2		285.1.bd.a.119.1	✓	6
5.2	odd	4		1425.1.bk.c.176.2		12
5.3	odd	4		1425.1.bk.c.176.1		12
5.4	even	2		285.1.bd.a.119.1	✓	6
15.2	even	4		1425.1.bk.c.176.1		12
15.8	even	4		1425.1.bk.c.176.2		12
15.14	odd	2	CM	285.1.bd.b.119.1	yes	6
19.4	even	9	inner	285.1.bd.b.194.1	yes	6
57.23	odd	18		285.1.bd.a.194.1	yes	6
95.4	even	18		285.1.bd.a.194.1	yes	6
95.23	odd	36		1425.1.bk.c.251.2		12
95.42	odd	36		1425.1.bk.c.251.1		12
285.23	even	36		1425.1.bk.c.251.1		12
285.137	even	36		1425.1.bk.c.251.2		12
285.194	odd	18	inner	285.1.bd.b.194.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.1.bd.a.119.1	✓	6	3.2	odd	2
285.1.bd.a.119.1	✓	6	5.4	even	2
285.1.bd.a.194.1	yes	6	57.23	odd	18
285.1.bd.a.194.1	yes	6	95.4	even	18
285.1.bd.b.119.1	yes	6	1.1	even	1	trivial
285.1.bd.b.119.1	yes	6	15.14	odd	2	CM
285.1.bd.b.194.1	yes	6	19.4	even	9	inner
285.1.bd.b.194.1	yes	6	285.194	odd	18	inner
1425.1.bk.c.176.1		12	5.3	odd	4
1425.1.bk.c.176.1		12	15.2	even	4
1425.1.bk.c.176.2		12	5.2	odd	4
1425.1.bk.c.176.2		12	15.8	even	4
1425.1.bk.c.251.1		12	95.42	odd	36
1425.1.bk.c.251.1		12	285.23	even	36
1425.1.bk.c.251.2		12	95.23	odd	36
1425.1.bk.c.251.2		12	285.137	even	36

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	285.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(1.03209 - 0.866025i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.266044 + 1.50881i) q^{6} +(0.266044 - 0.460802i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(1.43969 - 0.524005i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(1.03209 - 0.866025i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(0.266044 + 1.50881i) q^{6} +(0.266044 - 0.460802i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.43969 - 0.524005i) q^{10} +(0.673648 + 1.16679i) q^{12} +(0.766044 - 0.642788i) q^{15} +(-0.0923963 + 0.524005i) q^{16} +(-1.76604 + 0.642788i) q^{17} -1.53209 q^{18} +(0.173648 - 0.984808i) q^{19} -1.34730 q^{20} +(0.766044 - 0.642788i) q^{23} +(0.407604 + 0.342020i) q^{24} +(0.173648 + 0.984808i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.766044 - 1.32683i) q^{30} +(-0.173648 - 0.300767i) q^{31} +(0.233956 + 1.32683i) q^{32} +(-2.20574 + 1.85083i) q^{34} +(-1.26604 + 0.460802i) q^{36} +(-0.266044 - 1.50881i) q^{38} +(-0.500000 + 0.181985i) q^{40} +(0.500000 + 0.866025i) q^{45} +(0.766044 - 1.32683i) q^{46} +(1.43969 + 0.524005i) q^{47} +(-0.500000 - 0.181985i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.766044 + 1.32683i) q^{50} +(-0.326352 - 1.85083i) q^{51} +(1.43969 - 1.20805i) q^{53} +(0.266044 - 1.50881i) q^{54} +(0.939693 + 0.342020i) q^{57} +(0.233956 - 1.32683i) q^{60} +(-0.766044 + 0.642788i) q^{61} +(-0.407604 - 0.342020i) q^{62} +(0.766044 + 1.32683i) q^{64} +(-1.26604 + 2.19285i) q^{68} +(0.500000 + 0.866025i) q^{69} +(-0.407604 + 0.342020i) q^{72} -1.00000 q^{75} +(-0.673648 - 1.16679i) q^{76} +(-0.173648 + 0.984808i) q^{79} +(0.407604 - 0.342020i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.173648 + 0.300767i) q^{83} +(1.76604 + 0.642788i) q^{85} +(1.17365 + 0.984808i) q^{90} +(0.233956 - 1.32683i) q^{92} +(0.326352 - 0.118782i) q^{93} +2.34730 q^{94} +(-0.766044 + 0.642788i) q^{95} -1.34730 q^{96} +(-0.266044 + 1.50881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^6 - 3 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 3 q^{6} - 3 q^{8} - 3 q^{10} + 3 q^{12} + 3 q^{16} - 6 q^{17} - 6 q^{20} + 6 q^{24} + 3 q^{27} + 6 q^{32} - 3 q^{34} - 3 q^{36} + 3 q^{38} - 3 q^{40} + 3 q^{45} + 3 q^{47} - 3 q^{48} - 3 q^{49} - 3 q^{51} + 3 q^{53} - 3 q^{54} + 6 q^{60} - 6 q^{62} - 3 q^{68} + 3 q^{69} - 6 q^{72} - 6 q^{75} - 3 q^{76} + 6 q^{80} + 6 q^{85} + 6 q^{90} + 6 q^{92} + 3 q^{93} + 12 q^{94} - 6 q^{96} + 3 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 3 * q^6 - 3 * q^8 - 3 * q^10 + 3 * q^12 + 3 * q^16 - 6 * q^17 - 6 * q^20 + 6 * q^24 + 3 * q^27 + 6 * q^32 - 3 * q^34 - 3 * q^36 + 3 * q^38 - 3 * q^40 + 3 * q^45 + 3 * q^47 - 3 * q^48 - 3 * q^49 - 3 * q^51 + 3 * q^53 - 3 * q^54 + 6 * q^60 - 6 * q^62 - 3 * q^68 + 3 * q^69 - 6 * q^72 - 6 * q^75 - 3 * q^76 + 6 * q^80 + 6 * q^85 + 6 * q^90 + 6 * q^92 + 3 * q^93 + 12 * q^94 - 6 * q^96 + 3 * q^98

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