LMFDB - Embedded newform 3192.1.hj.b.2309.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3192,1,Mod(629,3192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3192, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 9, 9, 1]))

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

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

chi := DirichletCharacter("3192.629");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3192.hj (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:	$1.59301552032$
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:	$D_{18}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{18} - \cdots)$

Embedding invariants

Embedding label			2309.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	3192.2309
Dual form			3192.1.hj.b.629.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(0.173648 + 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.673648 + 1.85083i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(1.93969 + 0.342020i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(-0.439693 + 0.524005i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(-1.93969 - 0.342020i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.500000 + 0.866025i) q^{18} +(0.173648 + 0.984808i) q^{19} -1.96962i q^{20} +(0.939693 + 0.342020i) q^{21} +(0.673648 + 1.85083i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-2.20574 - 1.85083i) q^{25} +(0.592396 + 0.342020i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.173648 + 0.984808i) q^{28} +1.96962i q^{30} +(-0.766044 - 0.642788i) q^{32} +(1.26604 + 1.50881i) q^{35} +(0.766044 - 0.642788i) q^{36} +(0.939693 - 0.342020i) q^{38} +(-0.592396 - 0.342020i) q^{39} +(-1.93969 + 0.342020i) q^{40} +(0.173648 - 0.984808i) q^{42} -1.96962i q^{45} +(1.70574 - 0.984808i) q^{46} +(0.766044 + 0.642788i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.43969 + 2.49362i) q^{50} +(0.233956 - 0.642788i) q^{52} +(-0.766044 + 0.642788i) q^{54} +1.00000 q^{56} +(-0.939693 + 0.342020i) q^{57} +(-0.266044 - 1.50881i) q^{59} +(1.93969 - 0.342020i) q^{60} +(-1.43969 + 0.524005i) q^{61} +(-0.173648 + 0.984808i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.673648 - 1.16679i) q^{65} +(-1.70574 + 0.984808i) q^{69} +(1.26604 - 1.50881i) q^{70} +(-1.43969 - 0.524005i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(1.43969 - 2.49362i) q^{75} +(-0.500000 - 0.866025i) q^{76} +(-0.233956 + 0.642788i) q^{78} +(1.11334 + 1.32683i) q^{79} +(0.673648 + 1.85083i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.11334 - 0.642788i) q^{83} -1.00000 q^{84} +(-1.93969 + 0.342020i) q^{90} +(0.233956 + 0.642788i) q^{91} +(-1.26604 - 1.50881i) q^{92} +(-1.93969 - 0.342020i) q^{95} +(0.500000 - 0.866025i) q^{96} +(-0.766044 + 0.642788i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 3 q^{12} + 3 q^{13} - 6 q^{15} + 3 q^{18} + 3 q^{23} - 3 q^{25} - 3 q^{27} + 3 q^{35} - 6 q^{40} - 3 q^{49} - 3 q^{50} + 6 q^{52} + 6 q^{56} + 3 q^{59} + 6 q^{60}+ \cdots + 3 q^{96}+O(q^{100}) $ 6 * q - 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 3 * q^12 + 3 * q^13 - 6 * q^15 + 3 * q^18 + 3 * q^23 - 3 * q^25 - 3 * q^27 + 3 * q^35 - 6 * q^40 - 3 * q^49 - 3 * q^50 + 6 * q^52 + 6 * q^56 + 3 * q^59 + 6 * q^60 - 3 * q^61 - 3 * q^64 - 3 * q^65 + 3 * q^70 - 3 * q^71 + 3 * q^75 - 3 * q^76 - 6 * q^78 + 3 * q^80 - 6 * q^84 - 6 * q^90 + 6 * q^91 - 3 * q^92 - 6 * q^95 + 3 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3192\mathbb{Z}\right)^\times$.

$n$	$799$	$913$	$1009$	$1597$	$2129$
$\chi(n)$	$1$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$	$-1$

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 $

$2$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$2$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$3$	0.173648	+	0.984808i	0.173648	+	0.984808i
$3$	0.173648	+	0.984808i	0.173648	+	0.984808i
$4$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$5$	−0.673648	+	1.85083i	−0.673648	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$5$	−0.673648	+	1.85083i	−0.673648	+	1.85083i	−0.500000	+	0.866025i	$0.666667\pi$
$6$	0.939693	−	0.342020i	0.939693	−	0.342020i
$7$	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
$10$	1.93969	+	0.342020i	1.93969	+	0.342020i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$13$	−0.439693	+	0.524005i	−0.439693	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$13$	−0.439693	+	0.524005i	−0.439693	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$14$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$15$	−1.93969	−	0.342020i	−1.93969	−	0.342020i
$16$	0.766044	−	0.642788i	0.766044	−	0.642788i
$17$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$17$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$18$	0.500000	+	0.866025i	0.500000	+	0.866025i
$19$	0.173648	+	0.984808i	0.173648	+	0.984808i
$19$	0.173648	+	0.984808i	0.173648	+	0.984808i
$20$		−	1.96962i		−	1.96962i
$21$	0.939693	+	0.342020i	0.939693	+	0.342020i
$22$		0			0
$23$	0.673648	+	1.85083i	0.673648	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$23$	0.673648	+	1.85083i	0.673648	+	1.85083i	0.173648	+	0.984808i	$0.444444\pi$
$24$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$25$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$26$	0.592396	+	0.342020i	0.592396	+	0.342020i
$27$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$28$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$29$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$29$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$30$			1.96962i			1.96962i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$33$		0			0
$34$		0			0
$35$	1.26604	+	1.50881i	1.26604	+	1.50881i
$36$	0.766044	−	0.642788i	0.766044	−	0.642788i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	0.939693	−	0.342020i	0.939693	−	0.342020i
$39$	−0.592396	−	0.342020i	−0.592396	−	0.342020i
$40$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$41$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$41$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$42$	0.173648	−	0.984808i	0.173648	−	0.984808i
$43$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$43$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$44$		0			0
$45$		−	1.96962i		−	1.96962i
$46$	1.70574	−	0.984808i	1.70574	−	0.984808i
$47$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$47$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$48$	0.766044	+	0.642788i	0.766044	+	0.642788i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$51$		0			0
$52$	0.233956	−	0.642788i	0.233956	−	0.642788i
$53$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$53$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$54$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$55$		0			0
$56$	1.00000			1.00000
$57$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$58$		0			0
$59$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$59$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$60$	1.93969	−	0.342020i	1.93969	−	0.342020i
$61$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$61$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$64$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$65$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$66$		0			0
$67$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$67$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$68$		0			0
$69$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$70$	1.26604	−	1.50881i	1.26604	−	1.50881i
$71$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$72$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$73$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$73$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$74$		0			0
$75$	1.43969	−	2.49362i	1.43969	−	2.49362i
$76$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$77$		0			0
$78$	−0.233956	+	0.642788i	−0.233956	+	0.642788i
$79$	1.11334	+	1.32683i	1.11334	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$79$	1.11334	+	1.32683i	1.11334	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$80$	0.673648	+	1.85083i	0.673648	+	1.85083i
$81$	0.766044	−	0.642788i	0.766044	−	0.642788i
$82$		0			0
$83$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$83$	−1.11334	−	0.642788i	−1.11334	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$84$	−1.00000			−1.00000
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$89$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$90$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$91$	0.233956	+	0.642788i	0.233956	+	0.642788i
$92$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$93$		0			0
$94$		0			0
$95$	−1.93969	−	0.342020i	−1.93969	−	0.342020i
$96$	0.500000	−	0.866025i	0.500000	−	0.866025i
$97$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$97$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$98$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$99$		0			0
$100$	2.70574	+	0.984808i	2.70574	+	0.984808i
$101$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$101$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$105$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$106$		0			0
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	0.766044	+	0.642788i	0.766044	+	0.642788i
$109$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$109$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$110$		0			0
$111$		0			0
$112$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$113$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$113$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$114$	0.500000	+	0.866025i	0.500000	+	0.866025i
$115$	−3.87939			−3.87939
$116$		0			0
$117$	0.233956	−	0.642788i	0.233956	−	0.642788i
$118$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$119$		0			0
$120$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$121$	0.500000	−	0.866025i	0.500000	−	0.866025i
$122$	0.766044	+	1.32683i	0.766044	+	1.32683i
$123$		0			0
$124$		0			0
$125$	3.20574	−	1.85083i	3.20574	−	1.85083i
$126$	1.00000			1.00000
$127$	−0.439693	+	0.524005i	−0.439693	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$127$	−0.439693	+	0.524005i	−0.439693	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$128$	0.939693	+	0.342020i	0.939693	+	0.342020i
$129$		0			0
$130$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$131$	−1.26604	+	0.223238i	−1.26604	+	0.223238i	−0.766044	−	0.642788i	$-0.777778\pi$
$131$	−1.26604	+	0.223238i	−1.26604	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$132$		0			0
$133$	0.939693	+	0.342020i	0.939693	+	0.342020i
$134$		0			0
$135$	1.93969	−	0.342020i	1.93969	−	0.342020i
$136$		0			0
$137$	0.439693	+	1.20805i	0.439693	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$137$	0.439693	+	1.20805i	0.439693	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$138$	1.26604	+	1.50881i	1.26604	+	1.50881i
$139$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$139$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$140$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$141$		0			0
$142$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$143$		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
$148$		0			0
$149$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$149$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$150$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$151$			1.96962i			1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$151$			1.96962i			1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$152$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.673648	+	0.118782i	0.673648	+	0.118782i
$157$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$157$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$158$	1.11334	−	1.32683i	1.11334	−	1.32683i
$159$		0			0
$160$	1.70574	−	0.984808i	1.70574	−	0.984808i
$161$	1.93969	+	0.342020i	1.93969	+	0.342020i
$162$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$163$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$163$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$164$		0			0
$165$		0			0
$166$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$167$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$167$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$168$	0.173648	+	0.984808i	0.173648	+	0.984808i
$169$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$172$		0			0
$173$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$173$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$174$		0			0
$175$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$176$		0			0
$177$	1.43969	−	0.524005i	1.43969	−	0.524005i
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	0.673648	+	1.85083i	0.673648	+	1.85083i
$181$	−1.26604	−	0.223238i	−1.26604	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.26604	−	0.223238i	−1.26604	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$182$	0.592396	−	0.342020i	0.592396	−	0.342020i
$183$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$184$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.00000			−1.00000
$190$			1.96962i			1.96962i
$191$			1.28558i			1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$191$			1.28558i			1.28558i	−0.766044	+	0.642788i	$0.777778\pi$
$192$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$193$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$193$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	−1.00000			$\pi$
$194$		0			0
$195$	1.03209	−	0.866025i	1.03209	−	0.866025i
$196$	0.766044	+	0.642788i	0.766044	+	0.642788i
$197$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$197$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$198$		0			0
$199$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$199$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$200$	0.500000	−	2.83564i	0.500000	−	2.83564i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$208$			0.684040i			0.684040i
$209$		0			0
$210$	1.70574	+	0.984808i	1.70574	+	0.984808i
$211$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$211$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$212$		0			0
$213$	0.266044	−	1.50881i	0.266044	−	1.50881i
$214$		0			0
$215$		0			0
$216$	0.500000	−	0.866025i	0.500000	−	0.866025i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$223$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$224$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$225$	2.70574	+	0.984808i	2.70574	+	0.984808i
$226$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$227$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$227$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$228$	0.766044	−	0.642788i	0.766044	−	0.642788i
$229$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$229$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$230$	0.673648	+	3.82045i	0.673648	+	3.82045i
$231$		0			0
$232$		0			0
$233$	0.233956	−	0.642788i	0.233956	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$233$	0.233956	−	0.642788i	0.233956	−	0.642788i	1.00000			$0$
$234$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$235$		0			0
$236$	0.766044	+	1.32683i	0.766044	+	1.32683i
$237$	−1.11334	+	1.32683i	−1.11334	+	1.32683i
$238$		0			0
$239$	0.592396	−	0.342020i	0.592396	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$239$	0.592396	−	0.342020i	0.592396	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$240$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$241$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$241$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$242$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$243$	0.766044	+	0.642788i	0.766044	+	0.642788i
$244$	1.17365	−	0.984808i	1.17365	−	0.984808i
$245$	1.93969	−	0.342020i	1.93969	−	0.342020i
$246$		0			0
$247$	−0.592396	−	0.342020i	−0.592396	−	0.342020i
$248$		0			0
$249$	0.439693	−	1.20805i	0.439693	−	1.20805i
$250$	−2.37939	−	2.83564i	−2.37939	−	2.83564i
$251$	0.233956	+	0.642788i	0.233956	+	0.642788i	1.00000			$0$
$251$	0.233956	+	0.642788i	0.233956	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$252$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$253$		0			0
$254$	0.592396	+	0.342020i	0.592396	+	0.342020i
$255$		0			0
$256$	0.173648	−	0.984808i	0.173648	−	0.984808i
$257$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$257$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$258$		0			0
$259$		0			0
$260$	1.03209	+	0.866025i	1.03209	+	0.866025i
$261$		0			0
$262$	0.439693	+	1.20805i	0.439693	+	1.20805i
$263$	0.439693	+	0.524005i	0.439693	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$263$	0.439693	+	0.524005i	0.439693	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$	0.173648	−	0.984808i	0.173648	−	0.984808i
$267$		0			0
$268$		0			0
$269$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$269$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$270$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$271$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$271$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$272$		0			0
$273$	−0.592396	+	0.342020i	−0.592396	+	0.342020i
$274$	1.11334	−	0.642788i	1.11334	−	0.642788i
$275$		0			0
$276$	1.26604	−	1.50881i	1.26604	−	1.50881i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$	0.500000	−	0.866025i	0.500000	−	0.866025i
$279$		0			0
$280$	−0.673648	+	1.85083i	−0.673648	+	1.85083i
$281$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$281$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$282$		0			0
$283$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$283$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$284$	1.53209			1.53209
$285$		−	1.96962i		−	1.96962i
$286$		0			0
$287$		0			0
$288$	0.939693	+	0.342020i	0.939693	+	0.342020i
$289$	0.939693	−	0.342020i	0.939693	−	0.342020i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$293$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$294$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$295$	2.97178	+	0.524005i	2.97178	+	0.524005i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$300$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$301$		0			0
$302$	1.93969	−	0.342020i	1.93969	−	0.342020i
$303$		0			0
$304$	0.766044	+	0.642788i	0.766044	+	0.642788i
$305$		−	3.01763i		−	3.01763i
$306$		0			0
$307$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$307$	−0.826352	−	0.984808i	−0.826352	−	0.984808i	−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		−	0.684040i		−	0.684040i
$313$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$313$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$314$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$315$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$316$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$317$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$317$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$318$		0			0
$319$		0			0
$320$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$321$		0			0
$322$		−	1.96962i		−	1.96962i
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$325$	1.93969	−	0.342020i	1.93969	−	0.342020i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$331$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$332$	1.26604	+	0.223238i	1.26604	+	0.223238i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.939693	−	0.342020i	0.939693	−	0.342020i
$337$	0.233956	−	0.642788i	0.233956	−	0.642788i	−0.766044	−	0.642788i	$-0.777778\pi$
$337$	0.233956	−	0.642788i	0.233956	−	0.642788i	1.00000			$0$
$338$	0.500000	−	0.181985i	0.500000	−	0.181985i
$339$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$340$		0			0
$341$		0			0
$342$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$343$	−1.00000			−1.00000
$344$		0			0
$345$	−0.673648	−	3.82045i	−0.673648	−	3.82045i
$346$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$347$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$347$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$348$		0			0
$349$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$349$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$350$	1.43969	+	2.49362i	1.43969	+	2.49362i
$351$	0.673648	+	0.118782i	0.673648	+	0.118782i
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$355$	1.93969	−	2.31164i	1.93969	−	2.31164i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.70574	+	0.300767i	−1.70574	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$359$	−1.70574	+	0.300767i	−1.70574	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$360$	1.70574	−	0.984808i	1.70574	−	0.984808i
$361$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$362$			1.28558i			1.28558i
$363$	0.939693	+	0.342020i	0.939693	+	0.342020i
$364$	−0.439693	−	0.524005i	−0.439693	−	0.524005i
$365$		0			0
$366$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$367$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$367$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$368$	1.70574	+	0.984808i	1.70574	+	0.984808i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$		0			0
$375$	2.37939	+	2.83564i	2.37939	+	2.83564i
$376$		0			0
$377$		0			0
$378$	0.173648	+	0.984808i	0.173648	+	0.984808i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	1.93969	−	0.342020i	1.93969	−	0.342020i
$381$	−0.592396	−	0.342020i	−0.592396	−	0.342020i
$382$	1.26604	−	0.223238i	1.26604	−	0.223238i
$383$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$383$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$384$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$385$		0			0
$386$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$387$		0			0
$388$		0			0
$389$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$389$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$390$	−1.03209	−	0.866025i	−1.03209	−	0.866025i
$391$		0			0
$392$	0.500000	−	0.866025i	0.500000	−	0.866025i
$393$	−0.439693	−	1.20805i	−0.439693	−	1.20805i
$394$		0			0
$395$	−3.20574	+	1.16679i	−3.20574	+	1.16679i
$396$		0			0
$397$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$397$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$398$		0			0
$399$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$400$	−2.87939			−2.87939
$401$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$401$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.673648	+	1.85083i	0.673648	+	1.85083i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$409$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$410$		0			0
$411$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$412$		0			0
$413$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$414$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$415$	1.93969	−	1.62760i	1.93969	−	1.62760i
$416$	0.673648	−	0.118782i	0.673648	−	0.118782i
$417$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$418$		0			0
$419$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$419$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$420$	0.673648	−	1.85083i	0.673648	−	1.85083i
$421$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$421$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−1.53209			−1.53209
$427$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$431$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$432$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$433$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$433$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$438$		0			0
$439$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$439$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$440$		0			0
$441$	0.766044	+	0.642788i	0.766044	+	0.642788i
$442$		0			0
$443$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$443$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.500000	+	0.866025i	0.500000	+	0.866025i
$449$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$449$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$450$	0.500000	−	2.83564i	0.500000	−	2.83564i
$451$		0			0
$452$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$453$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$454$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$455$	−1.34730			−1.34730
$456$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$457$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$457$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$458$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$459$		0			0
$460$	3.64543	−	1.32683i	3.64543	−	1.32683i
$461$	−0.233956	+	0.642788i	−0.233956	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$461$	−0.233956	+	0.642788i	−0.233956	+	0.642788i	−1.00000			$\pi$
$462$		0			0
$463$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$463$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$464$		0			0
$465$		0			0
$466$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$			0.684040i			0.684040i
$469$		0			0
$470$		0			0
$471$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$472$	1.17365	−	0.984808i	1.17365	−	0.984808i
$473$		0			0
$474$	1.50000	+	0.866025i	1.50000	+	0.866025i
$475$	1.43969	−	2.49362i	1.43969	−	2.49362i
$476$		0			0
$477$		0			0
$478$	−0.439693	−	0.524005i	−0.439693	−	0.524005i
$479$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$479$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$480$	1.26604	+	1.50881i	1.26604	+	1.50881i
$481$		0			0
$482$		0			0
$483$			1.96962i			1.96962i
$484$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$485$		0			0
$486$	0.500000	−	0.866025i	0.500000	−	0.866025i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$489$		0			0
$490$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$491$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$491$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$492$		0			0
$493$		0			0
$494$	−0.233956	+	0.642788i	−0.233956	+	0.642788i
$495$		0			0
$496$		0			0
$497$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$498$	−1.26604	−	0.223238i	−1.26604	−	0.223238i
$499$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$499$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$500$	−2.37939	+	2.83564i	−2.37939	+	2.83564i
$501$		0			0
$502$	0.592396	−	0.342020i	0.592396	−	0.342020i
$503$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$503$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$504$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$505$		0			0
$506$		0			0
$507$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$508$	0.233956	−	0.642788i	0.233956	−	0.642788i
$509$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$509$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$	0.766044	−	0.642788i	0.766044	−	0.642788i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.326352	−	0.118782i	0.326352	−	0.118782i
$520$	0.673648	−	1.16679i	0.673648	−	1.16679i
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$	1.70574	+	0.300767i	1.70574	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$523$	1.70574	+	0.300767i	1.70574	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$524$	1.11334	−	0.642788i	1.11334	−	0.642788i
$525$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$526$	0.439693	−	0.524005i	0.439693	−	0.524005i
$527$		0			0
$528$		0			0
$529$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$530$		0			0
$531$	0.766044	+	1.32683i	0.766044	+	1.32683i
$532$	−1.00000			−1.00000
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$539$		0			0
$540$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$541$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$541$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$542$		0			0
$543$		−	1.28558i		−	1.28558i
$544$		0			0
$545$		0			0
$546$	0.439693	+	0.524005i	0.439693	+	0.524005i
$547$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$547$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$548$	−0.826352	−	0.984808i	−0.826352	−	0.984808i
$549$	1.17365	−	0.984808i	1.17365	−	0.984808i
$550$		0			0
$551$		0			0
$552$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$553$	1.70574	−	0.300767i	1.70574	−	0.300767i
$554$		0			0
$555$		0			0
$556$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$557$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$557$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$558$		0			0
$559$		0			0
$560$	1.93969	+	0.342020i	1.93969	+	0.342020i
$561$		0			0
$562$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$563$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$563$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$564$		0			0
$565$	−0.233956	+	0.642788i	−0.233956	+	0.642788i
$566$	1.76604	−	0.642788i	1.76604	−	0.642788i
$567$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$568$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$569$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$569$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$570$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−1.26604	+	0.223238i	−1.26604	+	0.223238i
$574$		0			0
$575$	1.93969	−	5.32926i	1.93969	−	5.32926i
$576$	0.173648	−	0.984808i	0.173648	−	0.984808i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$579$	0.826352	−	0.984808i	0.826352	−	0.984808i
$580$		0			0
$581$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.03209	+	0.866025i	1.03209	+	0.866025i
$586$	1.43969	−	1.20805i	1.43969	−	1.20805i
$587$	1.70574	−	0.300767i	1.70574	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$587$	1.70574	−	0.300767i	1.70574	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$588$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$589$		0			0
$590$		−	3.01763i		−	3.01763i
$591$		0			0
$592$		0			0
$593$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$593$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$599$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	0.939693	+	0.342020i	$0.111111\pi$
$599$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i	−1.00000			$\pi$
$600$	2.87939			2.87939
$601$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$601$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$602$		0			0
$603$		0			0
$604$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$605$	1.26604	+	1.50881i	1.26604	+	1.50881i
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	0.500000	−	0.866025i	0.500000	−	0.866025i
$609$		0			0
$610$	−2.97178	+	0.524005i	−2.97178	+	0.524005i
$611$		0			0
$612$		0			0
$613$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$613$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$614$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$615$		0			0
$616$		0			0
$617$	−1.26604	−	0.223238i	−1.26604	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	−1.26604	−	0.223238i	−1.26604	−	0.223238i	−0.766044	+	0.642788i	$0.777778\pi$
$618$		0			0
$619$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$619$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$620$		0			0
$621$	1.26604	−	1.50881i	1.26604	−	1.50881i
$622$		0			0
$623$		0			0
$624$	−0.673648	+	0.118782i	−0.673648	+	0.118782i
$625$	0.766044	+	4.34445i	0.766044	+	4.34445i
$626$		0			0
$627$		0			0
$628$	−0.347296			−0.347296
$629$		0			0
$630$	−0.673648	+	1.85083i	−0.673648	+	1.85083i
$631$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$631$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$632$	−0.592396	+	1.62760i	−0.592396	+	1.62760i
$633$		0			0
$634$		0			0
$635$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$636$		0			0
$637$	0.673648	+	0.118782i	0.673648	+	0.118782i
$638$		0			0
$639$	1.53209			1.53209
$640$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$641$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.939693	−	0.342020i	$-0.111111\pi$
$641$	1.43969	+	0.524005i	1.43969	+	0.524005i	0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$643$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$644$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$645$		0			0
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	0.939693	+	0.342020i	0.939693	+	0.342020i
$649$		0			0
$650$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$651$		0			0
$652$		0			0
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$	0.439693	−	2.49362i	0.439693	−	2.49362i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$659$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$660$		0			0
$661$	−0.673648	−	1.85083i	−0.673648	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$661$	−0.673648	−	1.85083i	−0.673648	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$662$		0			0
$663$		0			0
$664$		−	1.28558i		−	1.28558i
$665$	−1.26604	+	1.50881i	−1.26604	+	1.50881i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$673$	1.11334	−	0.642788i	1.11334	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$673$	1.11334	−	0.642788i	1.11334	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$674$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$675$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$676$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$677$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$677$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$678$	0.326352	−	0.118782i	0.326352	−	0.118782i
$679$		0			0
$680$		0			0
$681$	0.326352	+	1.85083i	0.326352	+	1.85083i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.766044	+	0.642788i	0.766044	+	0.642788i
$685$	−2.53209			−2.53209
$686$	0.173648	+	0.984808i	0.173648	+	0.984808i
$687$	0.326352	+	1.85083i	0.326352	+	1.85083i
$688$		0			0
$689$		0			0
$690$	−3.64543	+	1.32683i	−3.64543	+	1.32683i
$691$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$691$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$692$	0.173648	+	0.300767i	0.173648	+	0.300767i
$693$		0			0
$694$		0			0
$695$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$696$		0			0
$697$		0			0
$698$	0.939693	+	0.342020i	0.939693	+	0.342020i
$699$	0.673648	+	0.118782i	0.673648	+	0.118782i
$700$	2.20574	−	1.85083i	2.20574	−	1.85083i
$701$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$701$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$702$		−	0.684040i		−	0.684040i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$709$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$709$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$710$	−2.61334	−	1.50881i	−2.61334	−	1.50881i
$711$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.439693	+	0.524005i	0.439693	+	0.524005i
$718$	0.592396	+	1.62760i	0.592396	+	1.62760i
$719$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$719$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$720$	−1.26604	−	1.50881i	−1.26604	−	1.50881i
$721$		0			0
$722$	0.500000	+	0.866025i	0.500000	+	0.866025i
$723$		0			0
$724$	1.26604	−	0.223238i	1.26604	−	0.223238i
$725$		0			0
$726$	0.173648	−	0.984808i	0.173648	−	0.984808i
$727$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$727$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$728$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$729$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$730$		0			0
$731$		0			0
$732$	1.17365	+	0.984808i	1.17365	+	0.984808i
$733$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$733$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$734$		0			0
$735$	0.673648	+	1.85083i	0.673648	+	1.85083i
$736$	0.673648	−	1.85083i	0.673648	−	1.85083i
$737$		0			0
$738$		0			0
$739$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$739$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$740$		0			0
$741$	0.233956	−	0.642788i	0.233956	−	0.642788i
$742$		0			0
$743$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$743$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.26604	+	0.223238i	1.26604	+	0.223238i
$748$		0			0
$749$		0			0
$750$	2.37939	−	2.83564i	2.37939	−	2.83564i
$751$	−1.70574	−	0.300767i	−1.70574	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$751$	−1.70574	−	0.300767i	−1.70574	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$752$		0			0
$753$	−0.592396	+	0.342020i	−0.592396	+	0.342020i
$754$		0			0
$755$	−3.64543	−	1.32683i	−3.64543	−	1.32683i
$756$	0.939693	−	0.342020i	0.939693	−	0.342020i
$757$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$757$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$758$		0			0
$759$		0			0
$760$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$	−0.233956	+	0.642788i	−0.233956	+	0.642788i
$763$		0			0
$764$	−0.439693	−	1.20805i	−0.439693	−	1.20805i
$765$		0			0
$766$		0			0
$767$	0.907604	+	0.524005i	0.907604	+	0.524005i
$768$	1.00000			1.00000
$769$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$769$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$770$		0			0
$771$		0			0
$772$	1.11334	+	0.642788i	1.11334	+	0.642788i
$773$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$773$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$785$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$786$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$787$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$787$	1.70574	−	0.984808i	1.70574	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$788$		0			0
$789$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$790$	1.70574	+	2.95442i	1.70574	+	2.95442i
$791$	0.173648	−	0.300767i	0.173648	−	0.300767i
$792$		0			0
$793$	0.358441	−	0.984808i	0.358441	−	0.984808i
$794$	1.87939	−	0.684040i	1.87939	−	0.684040i
$795$		0			0
$796$		0			0
$797$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$797$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$798$	1.00000			1.00000
$799$		0			0
$800$	0.500000	+	2.83564i	0.500000	+	2.83564i
$801$		0			0
$802$	1.76604	−	0.642788i	1.76604	−	0.642788i
$803$		0			0
$804$		0			0
$805$	−1.93969	+	3.35965i	−1.93969	+	3.35965i
$806$		0			0
$807$	1.53209	+	1.28558i	1.53209	+	1.28558i
$808$		0			0
$809$	0.592396	−	0.342020i	0.592396	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$809$	0.592396	−	0.342020i	0.592396	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$810$	1.70574	−	0.984808i	1.70574	−	0.984808i
$811$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$811$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−0.439693	−	0.524005i	−0.439693	−	0.524005i
$820$		0			0
$821$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$821$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$822$	0.826352	+	0.984808i	0.826352	+	0.984808i
$823$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$823$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$827$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$827$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$828$	1.70574	+	0.984808i	1.70574	+	0.984808i
$829$	−1.70574	−	0.984808i	−1.70574	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$829$	−1.70574	−	0.984808i	−1.70574	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$830$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$831$		0			0
$832$	−0.233956	−	0.642788i	−0.233956	−	0.642788i
$833$		0			0
$834$	0.939693	+	0.342020i	0.939693	+	0.342020i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	1.70574	−	0.300767i	1.70574	−	0.300767i
$839$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$839$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$840$	−1.93969	−	0.342020i	−1.93969	−	0.342020i
$841$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$842$		0			0
$843$	0.500000	+	0.866025i	0.500000	+	0.866025i
$844$		0			0
$845$	−1.03209	−	0.181985i	−1.03209	−	0.181985i
$846$		0			0
$847$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$848$		0			0
$849$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$850$		0			0
$851$		0			0
$852$	0.266044	+	1.50881i	0.266044	+	1.50881i
$853$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$853$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$854$	1.53209			1.53209
$855$	1.93969	−	0.342020i	1.93969	−	0.342020i
$856$		0			0
$857$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$857$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$858$		0			0
$859$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$859$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$860$		0			0
$861$		0			0
$862$	0.500000	−	0.866025i	0.500000	−	0.866025i
$863$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$863$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$864$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$865$	0.673648	+	0.118782i	0.673648	+	0.118782i
$866$		0			0
$867$	0.500000	+	0.866025i	0.500000	+	0.866025i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	1.26604	+	1.50881i	1.26604	+	1.50881i
$875$		−	3.70167i		−	3.70167i
$876$		0			0
$877$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$877$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$878$		0			0
$879$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$880$		0			0
$881$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$881$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$882$	0.500000	−	0.866025i	0.500000	−	0.866025i
$883$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$883$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$884$		0			0
$885$			3.01763i			3.01763i
$886$		0			0
$887$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$887$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$888$		0			0
$889$	0.233956	+	0.642788i	0.233956	+	0.642788i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.766044	−	0.642788i	0.766044	−	0.642788i
$897$	0.233956	−	1.32683i	0.233956	−	1.32683i
$898$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$899$		0			0
$900$	−2.87939			−2.87939
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.173648	+	0.300767i	0.173648	+	0.300767i
$905$	1.26604	−	2.19285i	1.26604	−	2.19285i
$906$	0.673648	+	1.85083i	0.673648	+	1.85083i
$907$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$907$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$908$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$909$		0			0
$910$	0.233956	+	1.32683i	0.233956	+	1.32683i
$911$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$911$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$912$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$913$		0			0
$914$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$915$	2.97178	−	0.524005i	2.97178	−	0.524005i
$916$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$917$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$918$		0			0
$919$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$919$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$920$	−1.93969	−	3.35965i	−1.93969	−	3.35965i
$921$	0.826352	−	0.984808i	0.826352	−	0.984808i
$922$	0.673648	+	0.118782i	0.673648	+	0.118782i
$923$	0.907604	−	0.524005i	0.907604	−	0.524005i
$924$		0			0
$925$		0			0
$926$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$927$		0			0
$928$		0			0
$929$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$929$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$930$		0			0
$931$	0.766044	−	0.642788i	0.766044	−	0.642788i
$932$			0.684040i			0.684040i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.673648	−	0.118782i	0.673648	−	0.118782i
$937$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$937$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$941$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$942$	0.347296			0.347296
$943$		0			0
$944$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$945$	0.673648	−	1.85083i	0.673648	−	1.85083i
$946$		0			0
$947$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$947$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$948$	0.592396	−	1.62760i	0.592396	−	1.62760i
$949$		0			0
$950$	−2.70574	−	0.984808i	−2.70574	−	0.984808i
$951$		0			0
$952$		0			0
$953$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$953$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$954$		0			0
$955$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$956$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$957$		0			0
$958$		0			0
$959$	1.26604	+	0.223238i	1.26604	+	0.223238i
$960$	1.26604	−	1.50881i	1.26604	−	1.50881i
$961$	0.500000	+	0.866025i	0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.37939	−	0.866025i	2.37939	−	0.866025i
$966$	1.93969	−	0.342020i	1.93969	−	0.342020i
$967$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$967$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$968$	1.00000			1.00000
$969$		0			0
$970$		0			0
$971$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$971$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$972$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$973$	0.939693	−	0.342020i	0.939693	−	0.342020i
$974$		0			0
$975$	0.673648	+	1.85083i	0.673648	+	1.85083i
$976$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$977$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$977$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$978$		0			0
$979$		0			0
$980$	−1.70574	+	0.984808i	−1.70574	+	0.984808i
$981$		0			0
$982$		0			0
$983$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$983$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.673648	+	0.118782i	0.673648	+	0.118782i
$989$		0			0
$990$		0			0
$991$	1.26604	+	1.50881i	1.26604	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$991$	1.26604	+	1.50881i	1.26604	+	1.50881i	0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$	1.17365	+	0.984808i	1.17365	+	0.984808i
$995$		0			0
$996$			1.28558i			1.28558i
$997$	0.326352	−	1.85083i	0.326352	−	1.85083i	−0.173648	−	0.984808i	$-0.555556\pi$
$997$	0.326352	−	1.85083i	0.326352	−	1.85083i	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	3192.1.hj.b.2309.1	yes	6
3.2	odd	2		3192.1.hj.c.2309.1	yes	6
7.6	odd	2		3192.1.hj.d.2309.1	yes	6
8.5	even	2		3192.1.hj.d.2309.1	yes	6
19.2	odd	18		3192.1.hj.c.629.1	yes	6
21.20	even	2		3192.1.hj.a.2309.1	yes	6
24.5	odd	2		3192.1.hj.a.2309.1	yes	6
56.13	odd	2	CM	3192.1.hj.b.2309.1	yes	6
57.2	even	18	inner	3192.1.hj.b.629.1	yes	6
133.97	even	18		3192.1.hj.a.629.1	✓	6
152.21	odd	18		3192.1.hj.a.629.1	✓	6
168.125	even	2		3192.1.hj.c.2309.1	yes	6
399.230	odd	18		3192.1.hj.d.629.1	yes	6
456.173	even	18		3192.1.hj.d.629.1	yes	6
1064.629	even	18		3192.1.hj.c.629.1	yes	6
3192.629	odd	18	inner	3192.1.hj.b.629.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3192.1.hj.a.629.1	✓	6	133.97	even	18
3192.1.hj.a.629.1	✓	6	152.21	odd	18
3192.1.hj.a.2309.1	yes	6	21.20	even	2
3192.1.hj.a.2309.1	yes	6	24.5	odd	2
3192.1.hj.b.629.1	yes	6	57.2	even	18	inner
3192.1.hj.b.629.1	yes	6	3192.629	odd	18	inner
3192.1.hj.b.2309.1	yes	6	1.1	even	1	trivial
3192.1.hj.b.2309.1	yes	6	56.13	odd	2	CM
3192.1.hj.c.629.1	yes	6	19.2	odd	18
3192.1.hj.c.629.1	yes	6	1064.629	even	18
3192.1.hj.c.2309.1	yes	6	3.2	odd	2
3192.1.hj.c.2309.1	yes	6	168.125	even	2
3192.1.hj.d.629.1	yes	6	399.230	odd	18
3192.1.hj.d.629.1	yes	6	456.173	even	18
3192.1.hj.d.2309.1	yes	6	7.6	odd	2
3192.1.hj.d.2309.1	yes	6	8.5	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:	\( N \)	\(=\)	\( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3192.hj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(0.173648 + 0.984808i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.673648 + 1.85083i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(1.93969 + 0.342020i) q^{10} +(-0.500000 - 0.866025i) q^{12} +(-0.439693 + 0.524005i) q^{13} +(-0.939693 - 0.342020i) q^{14} +(-1.93969 - 0.342020i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.500000 + 0.866025i) q^{18} +(0.173648 + 0.984808i) q^{19} -1.96962i q^{20} +(0.939693 + 0.342020i) q^{21} +(0.673648 + 1.85083i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(-2.20574 - 1.85083i) q^{25} +(0.592396 + 0.342020i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.173648 + 0.984808i) q^{28} +1.96962i q^{30} +(-0.766044 - 0.642788i) q^{32} +(1.26604 + 1.50881i) q^{35} +(0.766044 - 0.642788i) q^{36} +(0.939693 - 0.342020i) q^{38} +(-0.592396 - 0.342020i) q^{39} +(-1.93969 + 0.342020i) q^{40} +(0.173648 - 0.984808i) q^{42} -1.96962i q^{45} +(1.70574 - 0.984808i) q^{46} +(0.766044 + 0.642788i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.43969 + 2.49362i) q^{50} +(0.233956 - 0.642788i) q^{52} +(-0.766044 + 0.642788i) q^{54} +1.00000 q^{56} +(-0.939693 + 0.342020i) q^{57} +(-0.266044 - 1.50881i) q^{59} +(1.93969 - 0.342020i) q^{60} +(-1.43969 + 0.524005i) q^{61} +(-0.173648 + 0.984808i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.673648 - 1.16679i) q^{65} +(-1.70574 + 0.984808i) q^{69} +(1.26604 - 1.50881i) q^{70} +(-1.43969 - 0.524005i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(1.43969 - 2.49362i) q^{75} +(-0.500000 - 0.866025i) q^{76} +(-0.233956 + 0.642788i) q^{78} +(1.11334 + 1.32683i) q^{79} +(0.673648 + 1.85083i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.11334 - 0.642788i) q^{83} -1.00000 q^{84} +(-1.93969 + 0.342020i) q^{90} +(0.233956 + 0.642788i) q^{91} +(-1.26604 - 1.50881i) q^{92} +(-1.93969 - 0.342020i) q^{95} +(0.500000 - 0.866025i) q^{96} +(-0.766044 + 0.642788i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} + 3 q^{7} + 3 q^{8} + 6 q^{10} - 3 q^{12} + 3 q^{13} - 6 q^{15} + 3 q^{18} + 3 q^{23} - 3 q^{25} - 3 q^{27} + 3 q^{35} - 6 q^{40} - 3 q^{49} - 3 q^{50} + 6 q^{52} + 6 q^{56} + 3 q^{59} + 6 q^{60}+ \cdots + 3 q^{96}+O(q^{100}) \) 6 * q - 3 * q^5 + 3 * q^7 + 3 * q^8 + 6 * q^10 - 3 * q^12 + 3 * q^13 - 6 * q^15 + 3 * q^18 + 3 * q^23 - 3 * q^25 - 3 * q^27 + 3 * q^35 - 6 * q^40 - 3 * q^49 - 3 * q^50 + 6 * q^52 + 6 * q^56 + 3 * q^59 + 6 * q^60 - 3 * q^61 - 3 * q^64 - 3 * q^65 + 3 * q^70 - 3 * q^71 + 3 * q^75 - 3 * q^76 - 6 * q^78 + 3 * q^80 - 6 * q^84 - 6 * q^90 + 6 * q^91 - 3 * q^92 - 6 * q^95 + 3 * q^96

Introduction

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