LMFDB - Embedded newform 1044.1.o.a.463.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1044,1,Mod(115,1044)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1044, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("1044.115");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1044 = 2^{2} \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1044.o (of order $6$, degree $2$, 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:	$0.521023873189$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
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 9.1.96224799211776.1

Embedding invariants

Embedding label			463.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	1044.463
Dual form			1044.1.o.a.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.173648 + 0.300767i) q^{5} +(0.766044 + 0.642788i) q^{6} +1.00000 q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.173648 + 0.300767i) q^{5} +(0.766044 + 0.642788i) q^{6} +1.00000 q^{8} +(0.766044 - 0.642788i) q^{9} +0.347296 q^{10} +(-0.173648 - 0.300767i) q^{11} +(0.173648 - 0.984808i) q^{12} +(-0.766044 + 1.32683i) q^{13} +(0.0603074 - 0.342020i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.939693 - 0.342020i) q^{18} -1.00000 q^{19} +(-0.173648 - 0.300767i) q^{20} +(-0.173648 + 0.300767i) q^{22} +(-0.939693 + 0.342020i) q^{24} +(0.439693 + 0.761570i) q^{25} +1.53209 q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.500000 - 0.866025i) q^{29} +(-0.326352 + 0.118782i) q^{30} +(-0.766044 + 1.32683i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.266044 + 0.223238i) q^{33} +(0.173648 + 0.984808i) q^{36} +(0.500000 + 0.866025i) q^{38} +(0.266044 - 1.50881i) q^{39} +(-0.173648 + 0.300767i) q^{40} +(0.939693 + 1.62760i) q^{43} +0.347296 q^{44} +(0.0603074 + 0.342020i) q^{45} +(0.939693 + 1.62760i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.439693 - 0.761570i) q^{50} +(-0.766044 - 1.32683i) q^{52} -1.87939 q^{53} +1.00000 q^{54} +0.120615 q^{55} +(0.939693 - 0.342020i) q^{57} +(-0.500000 + 0.866025i) q^{58} +(0.266044 + 0.223238i) q^{60} +1.53209 q^{62} +1.00000 q^{64} +(-0.266044 - 0.460802i) q^{65} +(0.0603074 - 0.342020i) q^{66} +(0.766044 - 0.642788i) q^{72} +(-0.673648 - 0.565258i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-1.43969 + 0.524005i) q^{78} +(-0.766044 - 1.32683i) q^{79} +0.347296 q^{80} +(0.173648 - 0.984808i) q^{81} +(0.939693 - 1.62760i) q^{86} +(0.766044 + 0.642788i) q^{87} +(-0.173648 - 0.300767i) q^{88} +(0.266044 - 0.223238i) q^{90} +(0.266044 - 1.50881i) q^{93} +(0.939693 - 1.62760i) q^{94} +(0.173648 - 0.300767i) q^{95} +(0.173648 - 0.984808i) q^{96} +1.00000 q^{98} +(-0.326352 - 0.118782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 6 q^{8} + 6 q^{15} - 3 q^{16} - 6 q^{19} - 3 q^{25} - 3 q^{27} - 3 q^{29} - 3 q^{30} - 3 q^{32} - 3 q^{33} + 3 q^{38} - 3 q^{39} + 6 q^{45} - 3 q^{49} - 3 q^{50} + 6 q^{54} + 12 q^{55} - 3 q^{58} - 3 q^{60} + 6 q^{64} + 3 q^{65} + 6 q^{66} - 3 q^{75} + 3 q^{76} - 3 q^{78} - 3 q^{90} - 3 q^{93} + 6 q^{98} - 3 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^8 + 6 * q^15 - 3 * q^16 - 6 * q^19 - 3 * q^25 - 3 * q^27 - 3 * q^29 - 3 * q^30 - 3 * q^32 - 3 * q^33 + 3 * q^38 - 3 * q^39 + 6 * q^45 - 3 * q^49 - 3 * q^50 + 6 * q^54 + 12 * q^55 - 3 * q^58 - 3 * q^60 + 6 * q^64 + 3 * q^65 + 6 * q^66 - 3 * q^75 + 3 * q^76 - 3 * q^78 - 3 * q^90 - 3 * q^93 + 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times$.

$n$	$523$	$901$	$929$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$2$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$3$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$3$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$4$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$5$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$5$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$6$	0.766044	+	0.642788i	0.766044	+	0.642788i
$7$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$7$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$8$	1.00000			1.00000
$9$	0.766044	−	0.642788i	0.766044	−	0.642788i
$10$	0.347296			0.347296
$11$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$11$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$12$	0.173648	−	0.984808i	0.173648	−	0.984808i
$13$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$13$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$14$		0			0
$15$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$19$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$21$		0			0
$22$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$25$	0.439693	+	0.761570i	0.439693	+	0.761570i
$26$	1.53209			1.53209
$27$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$28$		0			0
$29$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$29$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$30$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$31$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$31$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$32$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$33$	0.266044	+	0.223238i	0.266044	+	0.223238i
$34$		0			0
$35$		0			0
$36$	0.173648	+	0.984808i	0.173648	+	0.984808i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.500000	+	0.866025i	0.500000	+	0.866025i
$39$	0.266044	−	1.50881i	0.266044	−	1.50881i
$40$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$41$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$41$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$42$		0			0
$43$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$43$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$44$	0.347296			0.347296
$45$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$46$		0			0
$47$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$47$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$48$	0.766044	+	0.642788i	0.766044	+	0.642788i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$	0.439693	−	0.761570i	0.439693	−	0.761570i
$51$		0			0
$52$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$53$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$53$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$54$	1.00000			1.00000
$55$	0.120615			0.120615
$56$		0			0
$57$	0.939693	−	0.342020i	0.939693	−	0.342020i
$58$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$	0.266044	+	0.223238i	0.266044	+	0.223238i
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$	1.53209			1.53209
$63$		0			0
$64$	1.00000			1.00000
$65$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$66$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.766044	−	0.642788i	0.766044	−	0.642788i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$76$	0.500000	−	0.866025i	0.500000	−	0.866025i
$77$		0			0
$78$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$79$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$79$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$80$	0.347296			0.347296
$81$	0.173648	−	0.984808i	0.173648	−	0.984808i
$82$		0			0
$83$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$83$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$84$		0			0
$85$		0			0
$86$	0.939693	−	1.62760i	0.939693	−	1.62760i
$87$	0.766044	+	0.642788i	0.766044	+	0.642788i
$88$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	0.266044	−	0.223238i	0.266044	−	0.223238i
$91$		0			0
$92$		0			0
$93$	0.266044	−	1.50881i	0.266044	−	1.50881i
$94$	0.939693	−	1.62760i	0.939693	−	1.62760i
$95$	0.173648	−	0.300767i	0.173648	−	0.300767i
$96$	0.173648	−	0.984808i	0.173648	−	0.984808i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	1.00000			1.00000
$99$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$100$	−0.879385			−0.879385
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$105$		0			0
$106$	0.939693	+	1.62760i	0.939693	+	1.62760i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$109$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$109$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$110$	−0.0603074	−	0.104455i	−0.0603074	−	0.104455i
$111$		0			0
$112$		0			0
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$115$		0			0
$116$	1.00000			1.00000
$117$	0.266044	+	1.50881i	0.266044	+	1.50881i
$118$		0			0
$119$		0			0
$120$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$121$	0.439693	−	0.761570i	0.439693	−	0.761570i
$122$		0			0
$123$		0			0
$124$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$125$	−0.652704			−0.652704
$126$		0			0
$127$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$127$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$128$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$129$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$130$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$132$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$133$		0			0
$134$		0			0
$135$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$136$		0			0
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$142$		0			0
$143$	0.532089			0.532089
$144$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$145$	0.347296			0.347296
$146$		0			0
$147$	0.173648	−	0.984808i	0.173648	−	0.984808i
$148$		0			0
$149$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$149$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$150$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$151$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$151$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$152$	−1.00000			−1.00000
$153$		0			0
$154$		0			0
$155$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$156$	1.17365	+	0.984808i	1.17365	+	0.984808i
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$159$	1.76604	−	0.642788i	1.76604	−	0.642788i
$160$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$161$		0			0
$162$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$163$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$163$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$164$		0			0
$165$	−0.113341	+	0.0412527i	−0.113341	+	0.0412527i
$166$		0			0
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$		0			0
$169$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$170$		0			0
$171$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$172$	−1.87939			−1.87939
$173$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$173$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$174$	0.173648	−	0.984808i	0.173648	−	0.984808i
$175$		0			0
$176$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$181$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$181$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$187$		0			0
$188$	−1.87939			−1.87939
$189$		0			0
$190$	−0.347296			−0.347296
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$	0.407604	+	0.342020i	0.407604	+	0.342020i
$196$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$197$	2.00000			2.00000			1.00000			$0$
$197$	2.00000			2.00000			1.00000			$0$
$198$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	0.439693	+	0.761570i	0.439693	+	0.761570i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	1.53209			1.53209
$209$	0.173648	+	0.300767i	0.173648	+	0.300767i
$210$		0			0
$211$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$211$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$212$	0.939693	−	1.62760i	0.939693	−	1.62760i
$213$		0			0
$214$		0			0
$215$	−0.652704			−0.652704
$216$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$217$		0			0
$218$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$219$		0			0
$220$	−0.0603074	+	0.104455i	−0.0603074	+	0.104455i
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$		0			0
$225$	0.826352	+	0.300767i	0.826352	+	0.300767i
$226$		0			0
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$		0			0
$231$		0			0
$232$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$233$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$233$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$234$	1.17365	−	0.984808i	1.17365	−	0.984808i
$235$	−0.652704			−0.652704
$236$		0			0
$237$	1.17365	+	0.984808i	1.17365	+	0.984808i
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$241$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$241$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$242$	−0.879385			−0.879385
$243$	0.173648	+	0.984808i	0.173648	+	0.984808i
$244$		0			0
$245$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$246$		0			0
$247$	0.766044	−	1.32683i	0.766044	−	1.32683i
$248$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$249$		0			0
$250$	0.326352	+	0.565258i	0.326352	+	0.565258i
$251$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$251$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$252$		0			0
$253$		0			0
$254$	0.500000	+	0.866025i	0.500000	+	0.866025i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$257$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$258$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$259$		0			0
$260$	0.532089			0.532089
$261$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$262$	−1.00000			−1.00000
$263$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$263$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$264$	0.266044	+	0.223238i	0.266044	+	0.223238i
$265$	0.326352	−	0.565258i	0.326352	−	0.565258i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$271$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$271$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.152704	−	0.264490i	0.152704	−	0.264490i
$276$		0			0
$277$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$277$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$	0.266044	+	1.50881i	0.266044	+	1.50881i
$280$		0			0
$281$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$281$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$282$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$283$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$283$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$284$		0			0
$285$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$286$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$287$		0			0
$288$	0.173648	+	0.984808i	0.173648	+	0.984808i
$289$	1.00000			1.00000
$290$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$291$		0			0
$292$		0			0
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$295$		0			0
$296$		0			0
$297$	0.347296			0.347296
$298$	1.53209			1.53209
$299$		0			0
$300$	0.826352	−	0.300767i	0.826352	−	0.300767i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.500000	+	0.866025i	0.500000	+	0.866025i
$305$		0			0
$306$		0			0
$307$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$307$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$308$		0			0
$309$		0			0
$310$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$311$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$311$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$312$	0.266044	−	1.50881i	0.266044	−	1.50881i
$313$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$313$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$314$		0			0
$315$		0			0
$316$	1.53209			1.53209
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$319$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$320$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.766044	+	0.642788i	0.766044	+	0.642788i
$325$	−1.34730			−1.34730
$326$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$327$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$328$		0			0
$329$		0			0
$330$	0.0923963	+	0.0775297i	0.0923963	+	0.0775297i
$331$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$331$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$337$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$338$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$339$		0			0
$340$		0			0
$341$	0.532089			0.532089
$342$	0.939693	+	0.342020i	0.939693	+	0.342020i
$343$		0			0
$344$	0.939693	+	1.62760i	0.939693	+	1.62760i
$345$		0			0
$346$	0.500000	−	0.866025i	0.500000	−	0.866025i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$349$	−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
$351$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$352$	0.347296			0.347296
$353$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$359$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$360$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$361$		0			0
$362$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$363$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$367$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	1.17365	+	0.984808i	1.17365	+	0.984808i
$373$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$373$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$374$		0			0
$375$	0.613341	−	0.223238i	0.613341	−	0.223238i
$376$	0.939693	+	1.62760i	0.939693	+	1.62760i
$377$	1.53209			1.53209
$378$		0			0
$379$	2.00000			2.00000			1.00000			$0$
$379$	2.00000			2.00000			1.00000			$0$
$380$	0.173648	+	0.300767i	0.173648	+	0.300767i
$381$	0.939693	−	0.342020i	0.939693	−	0.342020i
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$	0.766044	+	0.642788i	0.766044	+	0.642788i
$385$		0			0
$386$		0			0
$387$	1.76604	+	0.642788i	1.76604	+	0.642788i
$388$		0			0
$389$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$389$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$390$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$391$		0			0
$392$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$393$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$394$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$395$	0.532089			0.532089
$396$	0.266044	−	0.223238i	0.266044	−	0.223238i
$397$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$397$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$398$		0			0
$399$		0			0
$400$	0.439693	−	0.761570i	0.439693	−	0.761570i
$401$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$401$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$402$		0			0
$403$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$404$		0			0
$405$	0.266044	+	0.223238i	0.266044	+	0.223238i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$417$		0			0
$418$	0.173648	−	0.300767i	0.173648	−	0.300767i
$419$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$419$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$420$		0			0
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$	−1.87939			−1.87939
$423$	1.76604	+	0.642788i	1.76604	+	0.642788i
$424$	−1.87939			−1.87939
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$430$	0.326352	+	0.565258i	0.326352	+	0.565258i
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	1.00000			1.00000
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$436$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$	0.120615			0.120615
$441$	0.173648	+	0.984808i	0.173648	+	0.984808i
$442$		0			0
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$443$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.266044	−	1.50881i	0.266044	−	1.50881i
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	0.939693	−	0.342020i	0.939693	−	0.342020i
$457$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$457$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$465$	0.407604	+	0.342020i	0.407604	+	0.342020i
$466$	0.939693	+	1.62760i	0.939693	+	1.62760i
$467$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$467$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$468$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$469$		0			0
$470$	0.326352	+	0.565258i	0.326352	+	0.565258i
$471$		0			0
$472$		0			0
$473$	0.326352	−	0.565258i	0.326352	−	0.565258i
$474$	0.266044	−	1.50881i	0.266044	−	1.50881i
$475$	−0.439693	−	0.761570i	−0.439693	−	0.761570i
$476$		0			0
$477$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$478$		0			0
$479$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$479$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$480$	0.266044	+	0.223238i	0.266044	+	0.223238i
$481$		0			0
$482$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$483$		0			0
$484$	0.439693	+	0.761570i	0.439693	+	0.761570i
$485$		0			0
$486$	0.766044	−	0.642788i	0.766044	−	0.642788i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$490$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$491$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$491$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$492$		0			0
$493$		0			0
$494$	−1.53209			−1.53209
$495$	0.0923963	−	0.0775297i	0.0923963	−	0.0775297i
$496$	1.53209			1.53209
$497$		0			0
$498$		0			0
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	0.326352	−	0.565258i	0.326352	−	0.565258i
$501$		0			0
$502$	0.939693	+	1.62760i	0.939693	+	1.62760i
$503$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$503$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.03209	+	0.866025i	1.03209	+	0.866025i
$508$	0.500000	−	0.866025i	0.500000	−	0.866025i
$509$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$509$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$	0.500000	−	0.866025i	0.500000	−	0.866025i
$514$	−1.87939			−1.87939
$515$		0			0
$516$	1.76604	−	0.642788i	1.76604	−	0.642788i
$517$	0.326352	−	0.565258i	0.326352	−	0.565258i
$518$		0			0
$519$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$520$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$521$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$521$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$522$	0.173648	+	0.984808i	0.173648	+	0.984808i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	0.500000	+	0.866025i	0.500000	+	0.866025i
$525$		0			0
$526$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$527$		0			0
$528$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$529$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$530$	−0.652704			−0.652704
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.347296			0.347296
$540$	0.347296			0.347296
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$543$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$544$		0			0
$545$	−0.0603074	+	0.104455i	−0.0603074	+	0.104455i
$546$		0			0
$547$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$547$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$548$		0			0
$549$		0			0
$550$	−0.305407			−0.305407
$551$	0.500000	+	0.866025i	0.500000	+	0.866025i
$552$		0			0
$553$		0			0
$554$	0.500000	−	0.866025i	0.500000	−	0.866025i
$555$		0			0
$556$		0			0
$557$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$557$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$558$	1.17365	−	0.984808i	1.17365	−	0.984808i
$559$	−2.87939			−2.87939
$560$		0			0
$561$		0			0
$562$	0.939693	−	1.62760i	0.939693	−	1.62760i
$563$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$563$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$564$	1.76604	−	0.642788i	1.76604	−	0.642788i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$	0.326352	−	0.118782i	0.326352	−	0.118782i
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$573$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$574$		0			0
$575$		0			0
$576$	0.766044	−	0.642788i	0.766044	−	0.642788i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$579$		0			0
$580$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$581$		0			0
$582$		0			0
$583$	0.326352	+	0.565258i	0.326352	+	0.565258i
$584$		0			0
$585$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$586$		0			0
$587$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$587$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$588$	0.766044	+	0.642788i	0.766044	+	0.642788i
$589$	0.766044	−	1.32683i	0.766044	−	1.32683i
$590$		0			0
$591$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$592$		0			0
$593$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$593$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$594$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$595$		0			0
$596$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$597$		0			0
$598$		0			0
$599$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$599$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$600$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.152704	+	0.264490i	0.152704	+	0.264490i
$606$		0			0
$607$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$607$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$608$	0.500000	−	0.866025i	0.500000	−	0.866025i
$609$		0			0
$610$		0			0
$611$	−2.87939			−2.87939
$612$		0			0
$613$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$613$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$614$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$615$		0			0
$616$		0			0
$617$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$617$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$619$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$620$	0.532089			0.532089
$621$		0			0
$622$	−1.00000			−1.00000
$623$		0			0
$624$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$625$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$626$	0.939693	−	1.62760i	0.939693	−	1.62760i
$627$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$633$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$634$		0			0
$635$	0.173648	−	0.300767i	0.173648	−	0.300767i
$636$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$637$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$638$	0.347296			0.347296
$639$		0			0
$640$	0.347296			0.347296
$641$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$641$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$643$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$644$		0			0
$645$	0.613341	−	0.223238i	0.613341	−	0.223238i
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	0.173648	−	0.984808i	0.173648	−	0.984808i
$649$		0			0
$650$	0.673648	+	1.16679i	0.673648	+	1.16679i
$651$		0			0
$652$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	0.266044	+	0.223238i	0.266044	+	0.223238i
$655$	0.173648	+	0.300767i	0.173648	+	0.300767i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$659$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$660$	0.0209445	−	0.118782i	0.0209445	−	0.118782i
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$662$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$673$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$674$		0			0
$675$	−0.879385			−0.879385
$676$	1.34730			1.34730
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.939693	−	1.62760i	0.939693	−	1.62760i
$689$	1.43969	−	2.49362i	1.43969	−	2.49362i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$	−1.00000			−1.00000
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.766044	+	0.642788i	0.766044	+	0.642788i
$697$		0			0
$698$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$699$	1.76604	−	0.642788i	1.76604	−	0.642788i
$700$		0			0
$701$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$701$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$702$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$703$		0			0
$704$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$705$	0.613341	−	0.223238i	0.613341	−	0.223238i
$706$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$707$		0			0
$708$		0			0
$709$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$709$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$710$		0			0
$711$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−0.0923963	+	0.160035i	−0.0923963	+	0.160035i
$716$		0			0
$717$		0			0
$718$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$	0.266044	−	0.223238i	0.266044	−	0.223238i
$721$		0			0
$722$		0			0
$723$	1.17365	+	0.984808i	1.17365	+	0.984808i
$724$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$725$	0.439693	−	0.761570i	0.439693	−	0.761570i
$726$	0.826352	−	0.300767i	0.826352	−	0.300767i
$727$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$727$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$	0.500000	−	0.866025i	0.500000	−	0.866025i
$735$	0.266044	+	0.223238i	0.266044	+	0.223238i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$739$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$740$		0			0
$741$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$742$		0			0
$743$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$744$	0.266044	−	1.50881i	0.266044	−	1.50881i
$745$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$746$	1.53209			1.53209
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$751$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$751$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$752$	0.939693	−	1.62760i	0.939693	−	1.62760i
$753$	1.76604	−	0.642788i	1.76604	−	0.642788i
$754$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$759$		0			0
$760$	0.173648	−	0.300767i	0.173648	−	0.300767i
$761$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$762$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$763$		0			0
$764$	−1.00000			−1.00000
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.173648	−	0.984808i	0.173648	−	0.984808i
$769$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$769$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$775$	−1.34730			−1.34730
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$781$		0			0
$782$		0			0
$783$	1.00000			1.00000
$784$	1.00000			1.00000
$785$		0			0
$786$	0.939693	−	0.342020i	0.939693	−	0.342020i
$787$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$787$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$788$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$789$	1.17365	+	0.984808i	1.17365	+	0.984808i
$790$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$791$		0			0
$792$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$793$		0			0
$794$	0.939693	+	1.62760i	0.939693	+	1.62760i
$795$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$796$		0			0
$797$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$797$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$798$		0			0
$799$		0			0
$800$	−0.879385			−0.879385
$801$		0			0
$802$	1.53209			1.53209
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$807$		0			0
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$814$		0			0
$815$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$816$		0			0
$817$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$821$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$822$		0			0
$823$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$823$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$824$		0			0
$825$	−0.0530334	+	0.300767i	−0.0530334	+	0.300767i
$826$		0			0
$827$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$827$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$832$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−0.347296			−0.347296
$837$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$838$		0			0
$839$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$839$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$840$		0			0
$841$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$842$		0			0
$843$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$844$	0.939693	+	1.62760i	0.939693	+	1.62760i
$845$	0.467911			0.467911
$846$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$847$		0			0
$848$	0.939693	+	1.62760i	0.939693	+	1.62760i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$853$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$854$		0			0
$855$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$856$		0			0
$857$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$857$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$858$	0.407604	+	0.342020i	0.407604	+	0.342020i
$859$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$859$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$860$	0.326352	−	0.565258i	0.326352	−	0.565258i
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$865$	−0.347296			−0.347296
$866$		0			0
$867$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$868$		0			0
$869$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$870$	0.266044	+	0.223238i	0.266044	+	0.223238i
$871$		0			0
$872$	0.347296			0.347296
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$877$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$878$		0			0
$879$		0			0
$880$	−0.0603074	−	0.104455i	−0.0603074	−	0.104455i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	0.766044	−	0.642788i	0.766044	−	0.642788i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$	0.500000	−	0.866025i	0.500000	−	0.866025i
$887$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$887$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$892$		0			0
$893$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$894$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.53209			1.53209
$900$	−0.673648	+	0.565258i	−0.673648	+	0.565258i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$906$		0			0
$907$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$907$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$911$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$912$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$913$		0			0
$914$	0.500000	−	0.866025i	0.500000	−	0.866025i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$	1.00000			1.00000
$929$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$929$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$930$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$931$	0.500000	−	0.866025i	0.500000	−	0.866025i
$932$	0.939693	−	1.62760i	0.939693	−	1.62760i
$933$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$934$	0.939693	+	1.62760i	0.939693	+	1.62760i
$935$		0			0
$936$	0.266044	+	1.50881i	0.266044	+	1.50881i
$937$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$937$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$940$	0.326352	−	0.565258i	0.326352	−	0.565258i
$941$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$941$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.652704			−0.652704
$947$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$947$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$948$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$949$		0			0
$950$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$951$		0			0
$952$		0			0
$953$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$953$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$954$	1.76604	+	0.642788i	1.76604	+	0.642788i
$955$	−0.347296			−0.347296
$956$		0			0
$957$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$958$	0.939693	−	1.62760i	0.939693	−	1.62760i
$959$		0			0
$960$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$961$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$962$		0			0
$963$		0			0
$964$	1.53209			1.53209
$965$		0			0
$966$		0			0
$967$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$967$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$968$	0.439693	−	0.761570i	0.439693	−	0.761570i
$969$		0			0
$970$		0			0
$971$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$972$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$973$		0			0
$974$		0			0
$975$	1.26604	−	0.460802i	1.26604	−	0.460802i
$976$		0			0
$977$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$977$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$978$	1.17365	+	0.984808i	1.17365	+	0.984808i
$979$		0			0
$980$	0.347296			0.347296
$981$	0.266044	−	0.223238i	0.266044	−	0.223238i
$982$	−1.87939			−1.87939
$983$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$983$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$984$		0			0
$985$	−0.347296	+	0.601535i	−0.347296	+	0.601535i
$986$		0			0
$987$		0			0
$988$	0.766044	+	1.32683i	0.766044	+	1.32683i
$989$		0			0
$990$	−0.113341	−	0.0412527i	−0.113341	−	0.0412527i
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$993$	0.266044	+	0.223238i	0.266044	+	0.223238i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1044.1.o.a.463.1	yes	6
3.2	odd	2		3132.1.o.b.2899.2		6
4.3	odd	2		1044.1.o.b.463.3	yes	6
9.2	odd	6		3132.1.o.b.1855.2		6
9.7	even	3	inner	1044.1.o.a.115.1	✓	6
12.11	even	2		3132.1.o.a.2899.2		6
29.28	even	2		1044.1.o.b.463.3	yes	6
36.7	odd	6		1044.1.o.b.115.3	yes	6
36.11	even	6		3132.1.o.a.1855.2		6
87.86	odd	2		3132.1.o.a.2899.2		6
116.115	odd	2	CM	1044.1.o.a.463.1	yes	6
261.115	even	6		1044.1.o.b.115.3	yes	6
261.173	odd	6		3132.1.o.a.1855.2		6
348.347	even	2		3132.1.o.b.2899.2		6
1044.115	odd	6	inner	1044.1.o.a.115.1	✓	6
1044.695	even	6		3132.1.o.b.1855.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1044.1.o.a.115.1	✓	6	9.7	even	3	inner
1044.1.o.a.115.1	✓	6	1044.115	odd	6	inner
1044.1.o.a.463.1	yes	6	1.1	even	1	trivial
1044.1.o.a.463.1	yes	6	116.115	odd	2	CM
1044.1.o.b.115.3	yes	6	36.7	odd	6
1044.1.o.b.115.3	yes	6	261.115	even	6
1044.1.o.b.463.3	yes	6	4.3	odd	2
1044.1.o.b.463.3	yes	6	29.28	even	2
3132.1.o.a.1855.2		6	36.11	even	6
3132.1.o.a.1855.2		6	261.173	odd	6
3132.1.o.a.2899.2		6	12.11	even	2
3132.1.o.a.2899.2		6	87.86	odd	2
3132.1.o.b.1855.2		6	9.2	odd	6
3132.1.o.b.1855.2		6	1044.695	even	6
3132.1.o.b.2899.2		6	3.2	odd	2
3132.1.o.b.2899.2		6	348.347	even	2

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:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1044.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.173648 + 0.300767i) q^{5} +(0.766044 + 0.642788i) q^{6} +1.00000 q^{8} +(0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.173648 + 0.300767i) q^{5} +(0.766044 + 0.642788i) q^{6} +1.00000 q^{8} +(0.766044 - 0.642788i) q^{9} +0.347296 q^{10} +(-0.173648 - 0.300767i) q^{11} +(0.173648 - 0.984808i) q^{12} +(-0.766044 + 1.32683i) q^{13} +(0.0603074 - 0.342020i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.939693 - 0.342020i) q^{18} -1.00000 q^{19} +(-0.173648 - 0.300767i) q^{20} +(-0.173648 + 0.300767i) q^{22} +(-0.939693 + 0.342020i) q^{24} +(0.439693 + 0.761570i) q^{25} +1.53209 q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.500000 - 0.866025i) q^{29} +(-0.326352 + 0.118782i) q^{30} +(-0.766044 + 1.32683i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.266044 + 0.223238i) q^{33} +(0.173648 + 0.984808i) q^{36} +(0.500000 + 0.866025i) q^{38} +(0.266044 - 1.50881i) q^{39} +(-0.173648 + 0.300767i) q^{40} +(0.939693 + 1.62760i) q^{43} +0.347296 q^{44} +(0.0603074 + 0.342020i) q^{45} +(0.939693 + 1.62760i) q^{47} +(0.766044 + 0.642788i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.439693 - 0.761570i) q^{50} +(-0.766044 - 1.32683i) q^{52} -1.87939 q^{53} +1.00000 q^{54} +0.120615 q^{55} +(0.939693 - 0.342020i) q^{57} +(-0.500000 + 0.866025i) q^{58} +(0.266044 + 0.223238i) q^{60} +1.53209 q^{62} +1.00000 q^{64} +(-0.266044 - 0.460802i) q^{65} +(0.0603074 - 0.342020i) q^{66} +(0.766044 - 0.642788i) q^{72} +(-0.673648 - 0.565258i) q^{75} +(0.500000 - 0.866025i) q^{76} +(-1.43969 + 0.524005i) q^{78} +(-0.766044 - 1.32683i) q^{79} +0.347296 q^{80} +(0.173648 - 0.984808i) q^{81} +(0.939693 - 1.62760i) q^{86} +(0.766044 + 0.642788i) q^{87} +(-0.173648 - 0.300767i) q^{88} +(0.266044 - 0.223238i) q^{90} +(0.266044 - 1.50881i) q^{93} +(0.939693 - 1.62760i) q^{94} +(0.173648 - 0.300767i) q^{95} +(0.173648 - 0.984808i) q^{96} +1.00000 q^{98} +(-0.326352 - 0.118782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{8} + 6 q^{15} - 3 q^{16} - 6 q^{19} - 3 q^{25} - 3 q^{27} - 3 q^{29} - 3 q^{30} - 3 q^{32} - 3 q^{33} + 3 q^{38} - 3 q^{39} + 6 q^{45} - 3 q^{49} - 3 q^{50} + 6 q^{54} + 12 q^{55} - 3 q^{58} - 3 q^{60} + 6 q^{64} + 3 q^{65} + 6 q^{66} - 3 q^{75} + 3 q^{76} - 3 q^{78} - 3 q^{90} - 3 q^{93} + 6 q^{98} - 3 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^8 + 6 * q^15 - 3 * q^16 - 6 * q^19 - 3 * q^25 - 3 * q^27 - 3 * q^29 - 3 * q^30 - 3 * q^32 - 3 * q^33 + 3 * q^38 - 3 * q^39 + 6 * q^45 - 3 * q^49 - 3 * q^50 + 6 * q^54 + 12 * q^55 - 3 * q^58 - 3 * q^60 + 6 * q^64 + 3 * q^65 + 6 * q^66 - 3 * q^75 + 3 * q^76 - 3 * q^78 - 3 * q^90 - 3 * q^93 + 6 * q^98 - 3 * q^99

Introduction

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