LMFDB - Embedded newform 1596.1.dt.d.1259.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1596,1,Mod(251,1596)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1596, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 9, 2]))

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

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

chi := DirichletCharacter("1596.251");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1596.dt (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:	$0.796507760162$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{9} - \cdots)$

Embedding invariants

Embedding label			1259.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	1596.1259
Dual form			1596.1.dt.d.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.326352 + 0.118782i) q^{10} +(0.939693 - 1.62760i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.766044 - 0.642788i) q^{14} +(0.266044 - 0.223238i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.43969 - 0.524005i) q^{17} +1.00000 q^{18} +(0.939693 + 0.342020i) q^{19} -0.347296 q^{20} +(-0.939693 + 0.342020i) q^{21} +(-0.326352 + 1.85083i) q^{22} +(-0.766044 + 0.642788i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(-0.152704 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.939693 + 0.342020i) q^{28} +(-0.173648 + 0.300767i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(0.173648 + 0.984808i) q^{32} +(1.43969 + 1.20805i) q^{33} +(-1.17365 + 0.984808i) q^{34} +(0.0603074 - 0.342020i) q^{35} +(-0.939693 + 0.342020i) q^{36} +1.53209 q^{37} -1.00000 q^{38} +(0.326352 - 0.118782i) q^{40} +(-0.266044 + 1.50881i) q^{41} +(0.766044 - 0.642788i) q^{42} +(-0.326352 - 1.85083i) q^{44} +(0.173648 + 0.300767i) q^{45} +(0.500000 - 0.866025i) q^{46} +(0.939693 + 0.342020i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.439693 + 0.761570i) q^{50} +(0.266044 + 1.50881i) q^{51} +(-0.173648 + 0.984808i) q^{54} +(-0.613341 + 0.223238i) q^{55} -1.00000 q^{56} +(-0.500000 + 0.866025i) q^{57} +(0.0603074 - 0.342020i) q^{60} +(0.766044 + 0.642788i) q^{62} +(-0.173648 - 0.984808i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.76604 - 0.642788i) q^{66} +(0.766044 - 1.32683i) q^{68} +(-0.500000 - 0.866025i) q^{69} +(0.0603074 + 0.342020i) q^{70} +(-0.766044 - 0.642788i) q^{71} +(0.766044 - 0.642788i) q^{72} +(-1.43969 + 0.524005i) q^{74} +0.879385 q^{75} +(0.939693 - 0.342020i) q^{76} +1.87939 q^{77} +(-0.266044 + 0.223238i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-0.266044 - 1.50881i) q^{82} +(-0.500000 + 0.866025i) q^{84} +(-0.500000 - 0.181985i) q^{85} +(0.939693 + 1.62760i) q^{88} +(-0.0603074 - 0.342020i) q^{89} +(-0.266044 - 0.223238i) q^{90} +(-0.173648 + 0.984808i) q^{92} +(0.939693 - 0.342020i) q^{93} +(-0.173648 - 0.300767i) q^{95} -1.00000 q^{96} +(0.173648 - 0.984808i) q^{98} +(-1.43969 + 1.20805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{12} - 3 q^{15} + 3 q^{17} + 6 q^{18} - 3 q^{22} - 3 q^{25} + 3 q^{27} - 3 q^{31} + 3 q^{33} - 6 q^{34} + 6 q^{35} - 6 q^{38} + 3 q^{40} + 3 q^{41} - 3 q^{44}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^12 - 3 * q^15 + 3 * q^17 + 6 * q^18 - 3 * q^22 - 3 * q^25 + 3 * q^27 - 3 * q^31 + 3 * q^33 - 6 * q^34 + 6 * q^35 - 6 * q^38 + 3 * q^40 + 3 * q^41 - 3 * q^44 + 3 * q^46 - 3 * q^49 - 3 * q^50 - 3 * q^51 + 3 * q^55 - 6 * q^56 - 3 * q^57 + 6 * q^60 - 3 * q^64 - 6 * q^66 - 3 * q^69 + 6 * q^70 - 3 * q^74 - 6 * q^75 + 3 * q^80 + 3 * q^82 - 3 * q^84 - 3 * q^85 - 6 * q^89 + 3 * q^90 - 6 * q^96 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1596\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$2$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$3$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$3$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$4$	0.766044	−	0.642788i	0.766044	−	0.642788i
$5$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	0.500000	−	0.866025i	$-0.333333\pi$
$5$	−0.266044	−	0.223238i	−0.266044	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$6$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i
$8$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$9$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$10$	0.326352	+	0.118782i	0.326352	+	0.118782i
$11$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$11$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$12$	0.500000	+	0.866025i	0.500000	+	0.866025i
$13$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$13$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$14$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$15$	0.266044	−	0.223238i	0.266044	−	0.223238i
$16$	0.173648	−	0.984808i	0.173648	−	0.984808i
$17$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$17$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$18$	1.00000			1.00000
$19$	0.939693	+	0.342020i	0.939693	+	0.342020i
$19$	0.939693	+	0.342020i	0.939693	+	0.342020i
$20$	−0.347296			−0.347296
$21$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$22$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$23$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$23$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$24$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$25$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$26$		0			0
$27$	0.500000	−	0.866025i	0.500000	−	0.866025i
$28$	0.939693	+	0.342020i	0.939693	+	0.342020i
$29$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$29$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$30$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$32$	0.173648	+	0.984808i	0.173648	+	0.984808i
$33$	1.43969	+	1.20805i	1.43969	+	1.20805i
$34$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$35$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$36$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$37$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$37$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$38$	−1.00000			−1.00000
$39$		0			0
$40$	0.326352	−	0.118782i	0.326352	−	0.118782i
$41$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$41$	−0.266044	+	1.50881i	−0.266044	+	1.50881i	−0.766044	+	0.642788i	$0.777778\pi$
$42$	0.766044	−	0.642788i	0.766044	−	0.642788i
$43$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$43$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$44$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$45$	0.173648	+	0.300767i	0.173648	+	0.300767i
$46$	0.500000	−	0.866025i	0.500000	−	0.866025i
$47$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$47$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$48$	0.939693	+	0.342020i	0.939693	+	0.342020i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$	0.439693	+	0.761570i	0.439693	+	0.761570i
$51$	0.266044	+	1.50881i	0.266044	+	1.50881i
$52$		0			0
$53$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$53$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$54$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$55$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$56$	−1.00000			−1.00000
$57$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$58$		0			0
$59$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$59$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$60$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$61$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$61$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$62$	0.766044	+	0.642788i	0.766044	+	0.642788i
$63$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$64$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$65$		0			0
$66$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$	0.766044	−	1.32683i	0.766044	−	1.32683i
$69$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$70$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$71$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$71$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$72$	0.766044	−	0.642788i	0.766044	−	0.642788i
$73$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$73$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$74$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$75$	0.879385			0.879385
$76$	0.939693	−	0.342020i	0.939693	−	0.342020i
$77$	1.87939			1.87939
$78$		0			0
$79$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$79$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$80$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$81$	0.766044	+	0.642788i	0.766044	+	0.642788i
$82$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$83$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$83$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$84$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$85$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$86$		0			0
$87$		0			0
$88$	0.939693	+	1.62760i	0.939693	+	1.62760i
$89$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$89$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$90$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$91$		0			0
$92$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$93$	0.939693	−	0.342020i	0.939693	−	0.342020i
$94$		0			0
$95$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$96$	−1.00000			−1.00000
$97$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$97$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$98$	0.173648	−	0.984808i	0.173648	−	0.984808i
$99$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$100$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$101$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$101$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$102$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$103$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$103$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$104$		0			0
$105$	0.326352	+	0.118782i	0.326352	+	0.118782i
$106$		0			0
$107$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$107$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$108$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$109$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$109$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$110$	0.500000	−	0.419550i	0.500000	−	0.419550i
$111$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$112$	0.939693	−	0.342020i	0.939693	−	0.342020i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	0.173648	−	0.984808i	0.173648	−	0.984808i
$115$	0.347296			0.347296
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.17365	+	0.984808i	1.17365	+	0.984808i
$120$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$121$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$122$		0			0
$123$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$124$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$125$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$126$	0.500000	+	0.866025i	0.500000	+	0.866025i
$127$		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	$0.888889\pi$
$132$	1.87939			1.87939
$133$	0.173648	+	0.984808i	0.173648	+	0.984808i
$134$		0			0
$135$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$136$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$137$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$137$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$138$	0.766044	+	0.642788i	0.766044	+	0.642788i
$139$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$139$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$140$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$141$		0			0
$142$	0.939693	+	0.342020i	0.939693	+	0.342020i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$145$		0			0
$146$		0			0
$147$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$148$	1.17365	−	0.984808i	1.17365	−	0.984808i
$149$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$149$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$150$	−0.826352	+	0.300767i	−0.826352	+	0.300767i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$153$	−1.53209			−1.53209
$154$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$155$	−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			0
$159$		0			0
$160$	0.173648	−	0.300767i	0.173648	−	0.300767i
$161$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$162$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	0.766044	+	1.32683i	0.766044	+	1.32683i
$165$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$166$		0			0
$167$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$167$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$168$	0.173648	−	0.984808i	0.173648	−	0.984808i
$169$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$170$	0.532089			0.532089
$171$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$172$		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
$175$	0.673648	−	0.565258i	0.673648	−	0.565258i
$176$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$177$		0			0
$178$	0.173648	+	0.300767i	0.173648	+	0.300767i
$179$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$179$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$180$	0.326352	+	0.118782i	0.326352	+	0.118782i
$181$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$181$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$182$		0			0
$183$		0			0
$184$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$185$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$186$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$187$	0.500000	−	2.83564i	0.500000	−	2.83564i
$188$		0			0
$189$	1.00000			1.00000
$190$	0.266044	+	0.223238i	0.266044	+	0.223238i
$191$	2.00000			2.00000			1.00000			$0$
$191$	2.00000			2.00000			1.00000			$0$
$192$	0.939693	−	0.342020i	0.939693	−	0.342020i
$193$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$193$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$194$		0			0
$195$		0			0
$196$	0.173648	+	0.984808i	0.173648	+	0.984808i
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$	0.939693	−	1.62760i	0.939693	−	1.62760i
$199$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$199$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$200$	0.826352	+	0.300767i	0.826352	+	0.300767i
$201$		0			0
$202$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$203$		0			0
$204$	1.17365	+	0.984808i	1.17365	+	0.984808i
$205$	0.407604	−	0.342020i	0.407604	−	0.342020i
$206$	0.326352	−	1.85083i	0.326352	−	1.85083i
$207$	0.939693	−	0.342020i	0.939693	−	0.342020i
$208$		0			0
$209$	1.43969	−	1.20805i	1.43969	−	1.20805i
$210$	−0.347296			−0.347296
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$	0.766044	−	0.642788i	0.766044	−	0.642788i
$214$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$215$		0			0
$216$	0.500000	+	0.866025i	0.500000	+	0.866025i
$217$	0.500000	−	0.866025i	0.500000	−	0.866025i
$218$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$219$		0			0
$220$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$221$		0			0
$222$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$223$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$223$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$224$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$225$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$	0.173648	+	0.984808i	0.173648	+	0.984808i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$231$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$232$		0			0
$233$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$233$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$239$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$239$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$240$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$241$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$241$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$242$	1.93969	+	1.62760i	1.93969	+	1.62760i
$243$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$244$		0			0
$245$	0.326352	−	0.118782i	0.326352	−	0.118782i
$246$	1.53209			1.53209
$247$		0			0
$248$	1.00000			1.00000
$249$		0			0
$250$	0.113341	−	0.642788i	0.113341	−	0.642788i
$251$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$251$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$252$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$253$	0.326352	+	1.85083i	0.326352	+	1.85083i
$254$		0			0
$255$	0.266044	−	0.460802i	0.266044	−	0.460802i
$256$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$257$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$257$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$258$		0			0
$259$	0.766044	+	1.32683i	0.766044	+	1.32683i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$264$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$265$		0			0
$266$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$267$	0.347296			0.347296
$268$		0			0
$269$	0.326352	−	1.85083i	0.326352	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$269$	0.326352	−	1.85083i	0.326352	−	1.85083i	0.500000	−	0.866025i	$-0.333333\pi$
$270$	0.266044	−	0.223238i	0.266044	−	0.223238i
$271$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$271$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$272$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$273$		0			0
$274$		0			0
$275$	−1.55303	−	0.565258i	−1.55303	−	0.565258i
$276$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$277$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$277$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$278$	0.173648	+	0.300767i	0.173648	+	0.300767i
$279$	0.173648	+	0.984808i	0.173648	+	0.984808i
$280$	0.266044	+	0.223238i	0.266044	+	0.223238i
$281$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$281$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$282$		0			0
$283$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$283$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$284$	−1.00000			−1.00000
$285$	0.326352	−	0.118782i	0.326352	−	0.118782i
$286$		0			0
$287$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$288$	0.173648	−	0.984808i	0.173648	−	0.984808i
$289$	1.03209	−	0.866025i	1.03209	−	0.866025i
$290$		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	$0.111111\pi$
$294$	0.939693	+	0.342020i	0.939693	+	0.342020i
$295$		0			0
$296$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$297$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$298$		0			0
$299$		0			0
$300$	0.673648	−	0.565258i	0.673648	−	0.565258i
$301$		0			0
$302$		0			0
$303$	−1.87939			−1.87939
$304$	0.500000	−	0.866025i	0.500000	−	0.866025i
$305$		0			0
$306$	1.43969	−	0.524005i	1.43969	−	0.524005i
$307$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$308$	1.43969	−	1.20805i	1.43969	−	1.20805i
$309$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$310$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$311$		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
$315$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$316$		0			0
$317$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$317$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$318$		0			0
$319$		0			0
$320$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$321$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$322$	1.00000			1.00000
$323$	1.53209			1.53209
$324$	1.00000			1.00000
$325$		0			0
$326$		0			0
$327$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$328$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$329$		0			0
$330$	0.326352	+	0.565258i	0.326352	+	0.565258i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$334$		0			0
$335$		0			0
$336$	0.173648	+	0.984808i	0.173648	+	0.984808i
$337$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$337$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$338$	0.766044	−	0.642788i	0.766044	−	0.642788i
$339$		0			0
$340$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$341$	−1.87939			−1.87939
$342$	0.939693	+	0.342020i	0.939693	+	0.342020i
$343$	−1.00000			−1.00000
$344$		0			0
$345$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$346$	0.766044	−	0.642788i	0.766044	−	0.642788i
$347$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$347$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$348$		0			0
$349$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$349$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$350$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$351$		0			0
$352$	1.76604	+	0.642788i	1.76604	+	0.642788i
$353$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$353$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$354$		0			0
$355$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$356$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$357$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$358$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$359$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$359$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$360$	−0.347296			−0.347296
$361$	0.766044	+	0.642788i	0.766044	+	0.642788i
$362$		0			0
$363$	2.37939	−	0.866025i	2.37939	−	0.866025i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$367$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$368$	0.500000	+	0.866025i	0.500000	+	0.866025i
$369$	0.766044	−	1.32683i	0.766044	−	1.32683i
$370$	0.500000	+	0.181985i	0.500000	+	0.181985i
$371$		0			0
$372$	0.500000	−	0.866025i	0.500000	−	0.866025i
$373$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$373$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$374$	0.500000	+	2.83564i	0.500000	+	2.83564i
$375$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$376$		0			0
$377$		0			0
$378$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$381$		0			0
$382$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$383$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$383$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$384$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$385$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$386$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$387$		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
$391$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$392$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$397$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$397$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$398$	1.00000			1.00000
$399$	−1.00000			−1.00000
$400$	−0.879385			−0.879385
$401$		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
$404$	1.43969	+	1.20805i	1.43969	+	1.20805i
$405$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$406$		0			0
$407$	1.43969	−	2.49362i	1.43969	−	2.49362i
$408$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$409$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$409$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$410$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$411$		0			0
$412$	0.326352	+	1.85083i	0.326352	+	1.85083i
$413$		0			0
$414$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$415$		0			0
$416$		0			0
$417$	0.347296			0.347296
$418$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$	0.326352	−	0.118782i	0.326352	−	0.118782i
$421$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$421$	−0.326352	+	1.85083i	−0.326352	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$426$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$427$		0			0
$428$	0.939693	+	0.342020i	0.939693	+	0.342020i
$429$		0			0
$430$		0			0
$431$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$431$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$433$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$433$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$434$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$435$		0			0
$436$	0.347296			0.347296
$437$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$438$		0			0
$439$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$439$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$440$	0.113341	−	0.642788i	0.113341	−	0.642788i
$441$	0.766044	−	0.642788i	0.766044	−	0.642788i
$442$		0			0
$443$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$443$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$444$	0.766044	+	1.32683i	0.766044	+	1.32683i
$445$	−0.0603074	+	0.104455i	−0.0603074	+	0.104455i
$446$	1.43969	+	0.524005i	1.43969	+	0.524005i
$447$		0			0
$448$	0.500000	−	0.866025i	0.500000	−	0.866025i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$451$	2.20574	+	1.85083i	2.20574	+	1.85083i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$457$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$457$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$458$		0			0
$459$	0.266044	−	1.50881i	0.266044	−	1.50881i
$460$	0.266044	−	0.223238i	0.266044	−	0.223238i
$461$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−0.173648	−	0.984808i	$-0.555556\pi$
$461$	−1.17365	−	0.984808i	−1.17365	−	0.984808i	−1.00000			$\pi$
$462$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$463$		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			0
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.152704	−	0.866025i	0.152704	−	0.866025i
$476$	1.53209			1.53209
$477$		0			0
$478$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$479$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$479$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$480$	0.266044	+	0.223238i	0.266044	+	0.223238i
$481$		0			0
$482$		0			0
$483$	0.500000	−	0.866025i	0.500000	−	0.866025i
$484$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$485$		0			0
$486$	0.500000	−	0.866025i	0.500000	−	0.866025i
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$491$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$491$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$492$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$493$		0			0
$494$		0			0
$495$	0.652704			0.652704
$496$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$497$	0.173648	−	0.984808i	0.173648	−	0.984808i
$498$		0			0
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$	0.113341	+	0.642788i	0.113341	+	0.642788i
$501$		0			0
$502$		0			0
$503$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$503$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$504$	0.939693	+	0.342020i	0.939693	+	0.342020i
$505$	0.326352	−	0.565258i	0.326352	−	0.565258i
$506$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$507$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$508$		0			0
$509$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	1.43969	−	1.20805i	1.43969	−	1.20805i	0.939693	−	0.342020i	$-0.111111\pi$
$510$	−0.0923963	+	0.524005i	−0.0923963	+	0.524005i
$511$		0			0
$512$	1.00000			1.00000
$513$	0.766044	−	0.642788i	0.766044	−	0.642788i
$514$	1.87939			1.87939
$515$	0.613341	−	0.223238i	0.613341	−	0.223238i
$516$		0			0
$517$		0			0
$518$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$519$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$520$		0			0
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$522$		0			0
$523$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$523$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$524$		0			0
$525$	0.439693	+	0.761570i	0.439693	+	0.761570i
$526$	0.266044	+	1.50881i	0.266044	+	1.50881i
$527$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$528$	1.43969	−	1.20805i	1.43969	−	1.20805i
$529$		0			0
$530$		0			0
$531$		0			0
$532$	0.766044	+	0.642788i	0.766044	+	0.642788i
$533$		0			0
$534$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$535$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$536$		0			0
$537$	1.43969	+	1.20805i	1.43969	+	1.20805i
$538$	0.326352	+	1.85083i	0.326352	+	1.85083i
$539$	0.939693	+	1.62760i	0.939693	+	1.62760i
$540$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$541$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$541$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$542$	1.43969	+	0.524005i	1.43969	+	0.524005i
$543$		0			0
$544$	0.766044	+	1.32683i	0.766044	+	1.32683i
$545$	−0.0209445	−	0.118782i	−0.0209445	−	0.118782i
$546$		0			0
$547$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$547$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$548$		0			0
$549$		0			0
$550$	1.65270			1.65270
$551$		0			0
$552$	1.00000			1.00000
$553$		0			0
$554$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$555$	0.407604	−	0.342020i	0.407604	−	0.342020i
$556$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$557$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$557$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$558$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$559$		0			0
$560$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$561$	2.70574	+	0.984808i	2.70574	+	0.984808i
$562$		0			0
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$567$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$568$	0.939693	−	0.342020i	0.939693	−	0.342020i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$574$	1.17365	−	0.984808i	1.17365	−	0.984808i
$575$	0.673648	+	0.565258i	0.673648	+	0.565258i
$576$	0.173648	+	0.984808i	0.173648	+	0.984808i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$579$	0.326352	+	0.118782i	0.326352	+	0.118782i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$587$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$587$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$588$	−1.00000			−1.00000
$589$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$590$		0			0
$591$		0			0
$592$	0.266044	−	1.50881i	0.266044	−	1.50881i
$593$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$593$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$594$	1.43969	+	1.20805i	1.43969	+	1.20805i
$595$	−0.0923963	−	0.524005i	−0.0923963	−	0.524005i
$596$		0			0
$597$	0.500000	−	0.866025i	0.500000	−	0.866025i
$598$		0			0
$599$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$599$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$600$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$601$		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	+	0.866025i	−0.152704	+	0.866025i
$606$	1.76604	−	0.642788i	1.76604	−	0.642788i
$607$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$608$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$613$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$613$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$614$	0.173648	+	0.984808i	0.173648	+	0.984808i
$615$	0.266044	+	0.460802i	0.266044	+	0.460802i
$616$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$617$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$617$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$618$	1.76604	+	0.642788i	1.76604	+	0.642788i
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$620$	0.173648	+	0.300767i	0.173648	+	0.300767i
$621$	0.173648	+	0.984808i	0.173648	+	0.984808i
$622$		0			0
$623$	0.266044	−	0.223238i	0.266044	−	0.223238i
$624$		0			0
$625$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$626$		0			0
$627$	0.939693	+	1.62760i	0.939693	+	1.62760i
$628$		0			0
$629$	2.20574	−	0.802823i	2.20574	−	0.802823i
$630$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$631$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$631$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.500000	+	0.866025i	0.500000	+	0.866025i
$640$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$641$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$641$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$642$	0.766044	−	0.642788i	0.766044	−	0.642788i
$643$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$643$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$644$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$645$		0			0
$646$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$649$		0			0
$650$		0			0
$651$	0.766044	+	0.642788i	0.766044	+	0.642788i
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	0.173648	−	0.300767i	0.173648	−	0.300767i
$655$		0			0
$656$	1.43969	+	0.524005i	1.43969	+	0.524005i
$657$		0			0
$658$		0			0
$659$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$659$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$660$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.173648	−	0.300767i	0.173648	−	0.300767i
$666$	1.53209			1.53209
$667$		0			0
$668$		0			0
$669$	1.17365	−	0.984808i	1.17365	−	0.984808i
$670$		0			0
$671$		0			0
$672$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$673$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$673$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$674$	0.939693	+	0.342020i	0.939693	+	0.342020i
$675$	−0.826352	−	0.300767i	−0.826352	−	0.300767i
$676$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$677$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$677$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$678$		0			0
$679$		0			0
$680$	0.407604	−	0.342020i	0.407604	−	0.342020i
$681$		0			0
$682$	1.76604	−	0.642788i	1.76604	−	0.642788i
$683$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$683$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$684$	−1.00000			−1.00000
$685$		0			0
$686$	0.939693	−	0.342020i	0.939693	−	0.342020i
$687$		0			0
$688$		0			0
$689$		0			0
$690$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$691$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$691$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$692$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$693$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$694$	0.939693	+	0.342020i	0.939693	+	0.342020i
$695$	−0.0603074	+	0.104455i	−0.0603074	+	0.104455i
$696$		0			0
$697$	0.407604	+	2.31164i	0.407604	+	2.31164i
$698$		0			0
$699$		0			0
$700$	0.152704	−	0.866025i	0.152704	−	0.866025i
$701$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$701$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$702$		0			0
$703$	1.43969	+	0.524005i	1.43969	+	0.524005i
$704$	−1.87939			−1.87939
$705$		0			0
$706$	0.326352	−	1.85083i	0.326352	−	1.85083i
$707$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$708$		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	$0.888889\pi$
$710$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$711$		0			0
$712$	0.326352	+	0.118782i	0.326352	+	0.118782i
$713$	0.939693	+	0.342020i	0.939693	+	0.342020i
$714$	0.766044	−	1.32683i	0.766044	−	1.32683i
$715$		0			0
$716$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$717$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$718$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$719$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$719$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$720$	0.326352	−	0.118782i	0.326352	−	0.118782i
$721$	−1.87939			−1.87939
$722$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−1.93969	+	1.62760i	−1.93969	+	1.62760i
$727$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$727$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$728$		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	$0.666667\pi$
$734$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$735$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$736$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$737$		0			0
$738$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$739$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$739$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$740$	−0.532089			−0.532089
$741$		0			0
$742$		0			0
$743$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$743$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$744$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$745$		0			0
$746$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$747$		0			0
$748$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$749$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$750$	0.613341	+	0.223238i	0.613341	+	0.223238i
$751$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$751$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.766044	−	0.642788i	0.766044	−	0.642788i
$757$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$757$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$758$		0			0
$759$	−1.87939			−1.87939
$760$	0.347296			0.347296
$761$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$761$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$762$		0			0
$763$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$764$	1.53209	−	1.28558i	1.53209	−	1.28558i
$765$	0.407604	+	0.342020i	0.407604	+	0.342020i
$766$		0			0
$767$		0			0
$768$	0.500000	−	0.866025i	0.500000	−	0.866025i
$769$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$769$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$770$	0.613341	+	0.223238i	0.613341	+	0.223238i
$771$	0.939693	−	1.62760i	0.939693	−	1.62760i
$772$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$773$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$773$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$774$		0			0
$775$	−0.673648	+	0.565258i	−0.673648	+	0.565258i
$776$		0			0
$777$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$778$		0			0
$779$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$780$		0			0
$781$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$782$	0.266044	−	1.50881i	0.266044	−	1.50881i
$783$		0			0
$784$	0.766044	+	0.642788i	0.766044	+	0.642788i
$785$		0			0
$786$		0			0
$787$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$787$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$788$		0			0
$789$	1.43969	+	0.524005i	1.43969	+	0.524005i
$790$		0			0
$791$		0			0
$792$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$797$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$797$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$798$	0.939693	−	0.342020i	0.939693	−	0.342020i
$799$		0			0
$800$	0.826352	−	0.300767i	0.826352	−	0.300767i
$801$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	0.173648	+	0.300767i	0.173648	+	0.300767i
$806$		0			0
$807$	1.76604	+	0.642788i	1.76604	+	0.642788i
$808$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$	0.173648	+	0.300767i	0.173648	+	0.300767i
$811$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$811$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$812$		0			0
$813$	1.17365	−	0.984808i	1.17365	−	0.984808i
$814$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$815$		0			0
$816$	1.53209			1.53209
$817$		0			0
$818$		0			0
$819$		0			0
$820$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$821$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$821$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$822$		0			0
$823$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$823$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$824$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$825$	0.826352	−	1.43128i	0.826352	−	1.43128i
$826$		0			0
$827$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$827$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$828$	0.500000	−	0.866025i	0.500000	−	0.866025i
$829$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$829$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$830$		0			0
$831$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$832$		0			0
$833$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$834$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$835$		0			0
$836$	0.326352	−	1.85083i	0.326352	−	1.85083i
$837$	−1.00000			−1.00000
$838$		0			0
$839$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$839$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$840$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$841$	0.766044	+	0.642788i	0.766044	+	0.642788i
$842$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$843$		0			0
$844$		0			0
$845$	0.326352	+	0.118782i	0.326352	+	0.118782i
$846$		0			0
$847$	1.26604	−	2.19285i	1.26604	−	2.19285i
$848$		0			0
$849$	0.266044	+	1.50881i	0.266044	+	1.50881i
$850$	1.03209	+	0.866025i	1.03209	+	0.866025i
$851$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$852$	0.173648	−	0.984808i	0.173648	−	0.984808i
$853$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$853$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$854$		0			0
$855$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$856$	−1.00000			−1.00000
$857$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.500000	−	0.866025i	$-0.333333\pi$
$857$	1.43969	−	0.524005i	1.43969	−	0.524005i	0.939693	+	0.342020i	$0.111111\pi$
$858$		0			0
$859$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−0.173648	+	0.984808i	$0.555556\pi$
$859$	−1.17365	+	0.984808i	−1.17365	+	0.984808i	−1.00000			$\pi$
$860$		0			0
$861$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$862$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$863$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$863$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$864$	0.939693	+	0.342020i	0.939693	+	0.342020i
$865$	0.326352	+	0.118782i	0.326352	+	0.118782i
$866$		0			0
$867$	0.673648	+	1.16679i	0.673648	+	1.16679i
$868$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$873$		0			0
$874$	0.766044	−	0.642788i	0.766044	−	0.642788i
$875$	−0.652704			−0.652704
$876$		0			0
$877$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$877$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$878$	1.43969	−	1.20805i	1.43969	−	1.20805i
$879$	0.266044	+	0.223238i	0.266044	+	0.223238i
$880$	0.113341	+	0.642788i	0.113341	+	0.642788i
$881$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$881$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$882$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$883$		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
$886$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$887$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$887$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$888$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$889$		0			0
$890$	0.0209445	−	0.118782i	0.0209445	−	0.118782i
$891$	1.76604	−	0.642788i	1.76604	−	0.642788i
$892$	−1.53209			−1.53209
$893$		0			0
$894$		0			0
$895$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$896$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.439693	+	0.761570i	0.439693	+	0.761570i
$901$		0			0
$902$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$907$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$908$		0			0
$909$	0.326352	−	1.85083i	0.326352	−	1.85083i
$910$		0			0
$911$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$911$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$912$	0.766044	+	0.642788i	0.766044	+	0.642788i
$913$		0			0
$914$	1.76604	−	0.642788i	1.76604	−	0.642788i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.266044	+	1.50881i	0.266044	+	1.50881i
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$921$	0.939693	+	0.342020i	0.939693	+	0.342020i
$922$	1.43969	+	0.524005i	1.43969	+	0.524005i
$923$		0			0
$924$	0.939693	+	1.62760i	0.939693	+	1.62760i
$925$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$926$		0			0
$927$	1.43969	−	1.20805i	1.43969	−	1.20805i
$928$		0			0
$929$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$929$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$930$	0.347296			0.347296
$931$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$936$		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
$940$		0			0
$941$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$941$	−1.76604	−	0.642788i	−1.76604	−	0.642788i	−1.00000			$\pi$
$942$		0			0
$943$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$944$		0			0
$945$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$946$		0			0
$947$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$948$		0			0
$949$		0			0
$950$	0.152704	+	0.866025i	0.152704	+	0.866025i
$951$		0			0
$952$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$953$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$953$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$954$		0			0
$955$	−0.532089	−	0.446476i	−0.532089	−	0.446476i
$956$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$961$		0			0
$962$		0			0
$963$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$964$		0			0
$965$	−0.0923963	+	0.0775297i	−0.0923963	+	0.0775297i
$966$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$967$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$967$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$968$	2.53209			2.53209
$969$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$970$		0			0
$971$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$971$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$972$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$973$	0.266044	−	0.223238i	0.266044	−	0.223238i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$	−0.613341	−	0.223238i	−0.613341	−	0.223238i
$980$	0.173648	−	0.300767i	0.173648	−	0.300767i
$981$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$982$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$983$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$983$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$984$	1.17365	−	0.984808i	1.17365	−	0.984808i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$991$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$991$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$992$	0.766044	−	0.642788i	0.766044	−	0.642788i
$993$		0			0
$994$	0.173648	+	0.984808i	0.173648	+	0.984808i
$995$	0.173648	+	0.300767i	0.173648	+	0.300767i
$996$		0			0
$997$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$997$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$998$		0			0
$999$	0.766044	−	1.32683i	0.766044	−	1.32683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1596.1.dt.d.1259.1	yes	6
3.2	odd	2		1596.1.dt.b.1259.1	yes	6
4.3	odd	2		1596.1.dt.c.1259.1	yes	6
7.6	odd	2		1596.1.dt.a.1259.1	yes	6
12.11	even	2		1596.1.dt.a.1259.1	yes	6
19.4	even	9	inner	1596.1.dt.d.251.1	yes	6
21.20	even	2		1596.1.dt.c.1259.1	yes	6
28.27	even	2		1596.1.dt.b.1259.1	yes	6
57.23	odd	18		1596.1.dt.b.251.1	yes	6
76.23	odd	18		1596.1.dt.c.251.1	yes	6
84.83	odd	2	CM	1596.1.dt.d.1259.1	yes	6
133.118	odd	18		1596.1.dt.a.251.1	✓	6
228.23	even	18		1596.1.dt.a.251.1	✓	6
399.251	even	18		1596.1.dt.c.251.1	yes	6
532.251	even	18		1596.1.dt.b.251.1	yes	6
1596.251	odd	18	inner	1596.1.dt.d.251.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1596.1.dt.a.251.1	✓	6	133.118	odd	18
1596.1.dt.a.251.1	✓	6	228.23	even	18
1596.1.dt.a.1259.1	yes	6	7.6	odd	2
1596.1.dt.a.1259.1	yes	6	12.11	even	2
1596.1.dt.b.251.1	yes	6	57.23	odd	18
1596.1.dt.b.251.1	yes	6	532.251	even	18
1596.1.dt.b.1259.1	yes	6	3.2	odd	2
1596.1.dt.b.1259.1	yes	6	28.27	even	2
1596.1.dt.c.251.1	yes	6	76.23	odd	18
1596.1.dt.c.251.1	yes	6	399.251	even	18
1596.1.dt.c.1259.1	yes	6	4.3	odd	2
1596.1.dt.c.1259.1	yes	6	21.20	even	2
1596.1.dt.d.251.1	yes	6	19.4	even	9	inner
1596.1.dt.d.251.1	yes	6	1596.251	odd	18	inner
1596.1.dt.d.1259.1	yes	6	1.1	even	1	trivial
1596.1.dt.d.1259.1	yes	6	84.83	odd	2	CM

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:	\( N \)	\(=\)	\( 1596 = 2^{2} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1596.dt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.326352 + 0.118782i) q^{10} +(0.939693 - 1.62760i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.766044 - 0.642788i) q^{14} +(0.266044 - 0.223238i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.43969 - 0.524005i) q^{17} +1.00000 q^{18} +(0.939693 + 0.342020i) q^{19} -0.347296 q^{20} +(-0.939693 + 0.342020i) q^{21} +(-0.326352 + 1.85083i) q^{22} +(-0.766044 + 0.642788i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(-0.152704 - 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{27} +(0.939693 + 0.342020i) q^{28} +(-0.173648 + 0.300767i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(0.173648 + 0.984808i) q^{32} +(1.43969 + 1.20805i) q^{33} +(-1.17365 + 0.984808i) q^{34} +(0.0603074 - 0.342020i) q^{35} +(-0.939693 + 0.342020i) q^{36} +1.53209 q^{37} -1.00000 q^{38} +(0.326352 - 0.118782i) q^{40} +(-0.266044 + 1.50881i) q^{41} +(0.766044 - 0.642788i) q^{42} +(-0.326352 - 1.85083i) q^{44} +(0.173648 + 0.300767i) q^{45} +(0.500000 - 0.866025i) q^{46} +(0.939693 + 0.342020i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.439693 + 0.761570i) q^{50} +(0.266044 + 1.50881i) q^{51} +(-0.173648 + 0.984808i) q^{54} +(-0.613341 + 0.223238i) q^{55} -1.00000 q^{56} +(-0.500000 + 0.866025i) q^{57} +(0.0603074 - 0.342020i) q^{60} +(0.766044 + 0.642788i) q^{62} +(-0.173648 - 0.984808i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.76604 - 0.642788i) q^{66} +(0.766044 - 1.32683i) q^{68} +(-0.500000 - 0.866025i) q^{69} +(0.0603074 + 0.342020i) q^{70} +(-0.766044 - 0.642788i) q^{71} +(0.766044 - 0.642788i) q^{72} +(-1.43969 + 0.524005i) q^{74} +0.879385 q^{75} +(0.939693 - 0.342020i) q^{76} +1.87939 q^{77} +(-0.266044 + 0.223238i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-0.266044 - 1.50881i) q^{82} +(-0.500000 + 0.866025i) q^{84} +(-0.500000 - 0.181985i) q^{85} +(0.939693 + 1.62760i) q^{88} +(-0.0603074 - 0.342020i) q^{89} +(-0.266044 - 0.223238i) q^{90} +(-0.173648 + 0.984808i) q^{92} +(0.939693 - 0.342020i) q^{93} +(-0.173648 - 0.300767i) q^{95} -1.00000 q^{96} +(0.173648 - 0.984808i) q^{98} +(-1.43969 + 1.20805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{12} - 3 q^{15} + 3 q^{17} + 6 q^{18} - 3 q^{22} - 3 q^{25} + 3 q^{27} - 3 q^{31} + 3 q^{33} - 6 q^{34} + 6 q^{35} - 6 q^{38} + 3 q^{40} + 3 q^{41} - 3 q^{44}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^12 - 3 * q^15 + 3 * q^17 + 6 * q^18 - 3 * q^22 - 3 * q^25 + 3 * q^27 - 3 * q^31 + 3 * q^33 - 6 * q^34 + 6 * q^35 - 6 * q^38 + 3 * q^40 + 3 * q^41 - 3 * q^44 + 3 * q^46 - 3 * q^49 - 3 * q^50 - 3 * q^51 + 3 * q^55 - 6 * q^56 - 3 * q^57 + 6 * q^60 - 3 * q^64 - 6 * q^66 - 3 * q^69 + 6 * q^70 - 3 * q^74 - 6 * q^75 + 3 * q^80 + 3 * q^82 - 3 * q^84 - 3 * q^85 - 6 * q^89 + 3 * q^90 - 6 * q^96 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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