LMFDB - Embedded newform 1512.1.ef.c.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,1,Mod(13,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8, 9]))

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

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

chi := DirichletCharacter("1512.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1512.ef (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:	$0.754586299101$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			13.1
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	1512.13
Dual form			1512.1.ef.c.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.984808 + 0.826352i) q^{5} +(0.642788 + 0.766044i) q^{6} +(0.939693 + 0.342020i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.642788 - 1.11334i) q^{10} +(0.642788 - 0.766044i) q^{12} +(-0.300767 + 1.70574i) q^{13} +(0.173648 - 0.984808i) q^{14} +(-1.26604 - 0.223238i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.939693 - 0.342020i) q^{18} +(-0.342020 - 0.592396i) q^{19} +(-1.20805 - 0.439693i) q^{20} +(-0.984808 + 0.173648i) q^{21} +(-1.43969 + 0.524005i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.113341 + 0.642788i) q^{25} +1.73205 q^{26} +1.00000i q^{27} -1.00000 q^{28} +1.28558i q^{30} +(-0.766044 - 0.642788i) q^{32} +(0.642788 + 1.11334i) q^{35} +(-0.173648 + 0.984808i) q^{36} +(-0.524005 + 0.439693i) q^{38} +(-0.592396 - 1.62760i) q^{39} +(-0.223238 + 1.26604i) q^{40} +(0.342020 + 0.939693i) q^{42} +(1.20805 - 0.439693i) q^{45} +(0.766044 + 1.32683i) q^{46} +(-0.342020 + 0.939693i) q^{48} +(0.766044 + 0.642788i) q^{49} +(0.613341 - 0.223238i) q^{50} +(-0.300767 - 1.70574i) q^{52} +(0.984808 - 0.173648i) q^{54} +(0.173648 + 0.984808i) q^{56} +(0.592396 + 0.342020i) q^{57} +(1.26604 - 0.223238i) q^{60} +(1.85083 + 0.673648i) q^{61} +(0.766044 - 0.642788i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.70574 + 1.43128i) q^{65} +(0.984808 - 1.17365i) q^{69} +(0.984808 - 0.826352i) q^{70} +(0.766044 - 1.32683i) q^{71} +1.00000 q^{72} +(-0.419550 - 0.500000i) q^{75} +(0.524005 + 0.439693i) q^{76} +(-1.50000 + 0.866025i) q^{78} +(0.326352 + 1.85083i) q^{79} +1.28558 q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.300767 - 1.70574i) q^{83} +(0.866025 - 0.500000i) q^{84} +(-0.642788 - 1.11334i) q^{90} +(-0.866025 + 1.50000i) q^{91} +(1.17365 - 0.984808i) q^{92} +(0.152704 - 0.866025i) q^{95} +(0.984808 + 0.173648i) q^{96} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{8} + 6 q^{9} - 6 q^{15} - 6 q^{23} - 12 q^{25} - 12 q^{28} - 6 q^{50} + 6 q^{60} - 6 q^{64} + 12 q^{72} - 18 q^{78} + 6 q^{79} - 6 q^{81} + 12 q^{92} + 6 q^{95} + 6 q^{98}+O(q^{100}) $ 12 * q + 6 * q^8 + 6 * q^9 - 6 * q^15 - 6 * q^23 - 12 * q^25 - 12 * q^28 - 6 * q^50 + 6 * q^60 - 6 * q^64 + 12 * q^72 - 18 * q^78 + 6 * q^79 - 6 * q^81 + 12 * q^92 + 6 * q^95 + 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$-1$	$1$

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
$3$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$3$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$4$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$5$	0.984808	+	0.826352i	0.984808	+	0.826352i	0.984808	−	0.173648i	$-0.0555556\pi$
$5$	0.984808	+	0.826352i	0.984808	+	0.826352i			1.00000i	$0.5\pi$
$6$	0.642788	+	0.766044i	0.642788	+	0.766044i
$7$	0.939693	+	0.342020i	0.939693	+	0.342020i
$7$	0.939693	+	0.342020i	0.939693	+	0.342020i
$8$	0.500000	+	0.866025i	0.500000	+	0.866025i
$9$	0.500000	−	0.866025i	0.500000	−	0.866025i
$10$	0.642788	−	1.11334i	0.642788	−	1.11334i
$11$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$11$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$12$	0.642788	−	0.766044i	0.642788	−	0.766044i
$13$	−0.300767	+	1.70574i	−0.300767	+	1.70574i	0.342020	+	0.939693i	$0.388889\pi$
$13$	−0.300767	+	1.70574i	−0.300767	+	1.70574i	−0.642788	+	0.766044i	$0.722222\pi$
$14$	0.173648	−	0.984808i	0.173648	−	0.984808i
$15$	−1.26604	−	0.223238i	−1.26604	−	0.223238i
$16$	0.766044	−	0.642788i	0.766044	−	0.642788i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$19$	−0.342020	−	0.592396i	−0.342020	−	0.592396i	0.642788	−	0.766044i	$-0.277778\pi$
$19$	−0.342020	−	0.592396i	−0.342020	−	0.592396i	−0.984808	+	0.173648i	$0.944444\pi$
$20$	−1.20805	−	0.439693i	−1.20805	−	0.439693i
$21$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$22$		0			0
$23$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$23$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$25$	0.113341	+	0.642788i	0.113341	+	0.642788i
$26$	1.73205			1.73205
$27$			1.00000i			1.00000i
$28$	−1.00000			−1.00000
$29$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$29$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$30$			1.28558i			1.28558i
$31$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$31$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$32$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$33$		0			0
$34$		0			0
$35$	0.642788	+	1.11334i	0.642788	+	1.11334i
$36$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	−0.524005	+	0.439693i	−0.524005	+	0.439693i
$39$	−0.592396	−	1.62760i	−0.592396	−	1.62760i
$40$	−0.223238	+	1.26604i	−0.223238	+	1.26604i
$41$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$41$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$42$	0.342020	+	0.939693i	0.342020	+	0.939693i
$43$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$43$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$44$		0			0
$45$	1.20805	−	0.439693i	1.20805	−	0.439693i
$46$	0.766044	+	1.32683i	0.766044	+	1.32683i
$47$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$47$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$48$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$49$	0.766044	+	0.642788i	0.766044	+	0.642788i
$50$	0.613341	−	0.223238i	0.613341	−	0.223238i
$51$		0			0
$52$	−0.300767	−	1.70574i	−0.300767	−	1.70574i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.984808	−	0.173648i	0.984808	−	0.173648i
$55$		0			0
$56$	0.173648	+	0.984808i	0.173648	+	0.984808i
$57$	0.592396	+	0.342020i	0.592396	+	0.342020i
$58$		0			0
$59$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$59$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$60$	1.26604	−	0.223238i	1.26604	−	0.223238i
$61$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.984808	+	0.173648i	$0.0555556\pi$
$61$	1.85083	+	0.673648i	1.85083	+	0.673648i	0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$	0.766044	−	0.642788i	0.766044	−	0.642788i
$64$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$65$	−1.70574	+	1.43128i	−1.70574	+	1.43128i
$66$		0			0
$67$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$67$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$68$		0			0
$69$	0.984808	−	1.17365i	0.984808	−	1.17365i
$70$	0.984808	−	0.826352i	0.984808	−	0.826352i
$71$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$71$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$72$	1.00000			1.00000
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$	−0.419550	−	0.500000i	−0.419550	−	0.500000i
$76$	0.524005	+	0.439693i	0.524005	+	0.439693i
$77$		0			0
$78$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$79$	0.326352	+	1.85083i	0.326352	+	1.85083i	0.500000	+	0.866025i	$0.333333\pi$
$79$	0.326352	+	1.85083i	0.326352	+	1.85083i	−0.173648	+	0.984808i	$0.555556\pi$
$80$	1.28558			1.28558
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$		0			0
$83$	−0.300767	−	1.70574i	−0.300767	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$83$	−0.300767	−	1.70574i	−0.300767	−	1.70574i	0.342020	−	0.939693i	$-0.388889\pi$
$84$	0.866025	−	0.500000i	0.866025	−	0.500000i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$91$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$92$	1.17365	−	0.984808i	1.17365	−	0.984808i
$93$		0			0
$94$		0			0
$95$	0.152704	−	0.866025i	0.152704	−	0.866025i
$96$	0.984808	+	0.173648i	0.984808	+	0.173648i
$97$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$97$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$98$	0.500000	−	0.866025i	0.500000	−	0.866025i
$99$		0			0
$100$	−0.326352	−	0.565258i	−0.326352	−	0.565258i
$101$	−1.85083	−	0.673648i	−1.85083	−	0.673648i	−0.984808	−	0.173648i	$-0.944444\pi$
$101$	−1.85083	−	0.673648i	−1.85083	−	0.673648i	−0.866025	−	0.500000i	$-0.833333\pi$
$102$		0			0
$103$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$103$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$104$	−1.62760	+	0.592396i	−1.62760	+	0.592396i
$105$	−1.11334	−	0.642788i	−1.11334	−	0.642788i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−0.342020	−	0.939693i	−0.342020	−	0.939693i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	0.939693	−	0.342020i	0.939693	−	0.342020i
$113$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.939693	+	0.342020i	$0.111111\pi$
$113$	1.43969	+	1.20805i	1.43969	+	1.20805i	0.500000	+	0.866025i	$0.333333\pi$
$114$	0.233956	−	0.642788i	0.233956	−	0.642788i
$115$	−1.85083	−	0.673648i	−1.85083	−	0.673648i
$116$		0			0
$117$	1.32683	+	1.11334i	1.32683	+	1.11334i
$118$		0			0
$119$		0			0
$120$	−0.439693	−	1.20805i	−0.439693	−	1.20805i
$121$	0.173648	−	0.984808i	0.173648	−	0.984808i
$122$	0.342020	−	1.93969i	0.342020	−	1.93969i
$123$		0			0
$124$		0			0
$125$	0.223238	−	0.386659i	0.223238	−	0.386659i
$126$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$127$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$127$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$128$	0.939693	+	0.342020i	0.939693	+	0.342020i
$129$		0			0
$130$	1.70574	+	1.43128i	1.70574	+	1.43128i
$131$	−1.85083	+	0.673648i	−1.85083	+	0.673648i	−0.866025	+	0.500000i	$0.833333\pi$
$131$	−1.85083	+	0.673648i	−1.85083	+	0.673648i	−0.984808	+	0.173648i	$0.944444\pi$
$132$		0			0
$133$	−0.118782	−	0.673648i	−0.118782	−	0.673648i
$134$		0			0
$135$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$136$		0			0
$137$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$137$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$138$	−1.32683	−	0.766044i	−1.32683	−	0.766044i
$139$	0.642788	−	0.233956i	0.642788	−	0.233956i		−	1.00000i	$-0.5\pi$
$139$	0.642788	−	0.233956i	0.642788	−	0.233956i	0.642788	+	0.766044i	$0.277778\pi$
$140$	−0.984808	−	0.826352i	−0.984808	−	0.826352i
$141$		0			0
$142$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$143$		0			0
$144$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$145$		0			0
$146$		0			0
$147$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$148$		0			0
$149$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$149$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$150$	−0.419550	+	0.500000i	−0.419550	+	0.500000i
$151$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$151$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$152$	0.342020	−	0.592396i	0.342020	−	0.592396i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	1.11334	+	1.32683i	1.11334	+	1.32683i
$157$	0.984808	+	0.826352i	0.984808	+	0.826352i	0.984808	−	0.173648i	$-0.0555556\pi$
$157$	0.984808	+	0.826352i	0.984808	+	0.826352i			1.00000i	$0.5\pi$
$158$	1.76604	−	0.642788i	1.76604	−	0.642788i
$159$		0			0
$160$	−0.223238	−	1.26604i	−0.223238	−	1.26604i
$161$	−1.53209			−1.53209
$162$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	−1.62760	+	0.592396i	−1.62760	+	0.592396i
$167$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$167$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$168$	−0.642788	−	0.766044i	−0.642788	−	0.766044i
$169$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$170$		0			0
$171$	−0.684040			−0.684040
$172$		0			0
$173$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$173$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$174$		0			0
$175$	−0.113341	+	0.642788i	−0.113341	+	0.642788i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$179$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$180$	−0.984808	+	0.826352i	−0.984808	+	0.826352i
$181$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.642788	−	0.766044i	$-0.722222\pi$
$181$	−0.984808	−	1.70574i	−0.984808	−	1.70574i	−0.342020	−	0.939693i	$-0.611111\pi$
$182$	1.62760	+	0.592396i	1.62760	+	0.592396i
$183$	−1.93969	+	0.342020i	−1.93969	+	0.342020i
$184$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.342020	+	0.939693i	−0.342020	+	0.939693i
$190$	−0.879385			−0.879385
$191$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	0.939693	−	0.342020i	$-0.111111\pi$
$191$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i	−1.00000			$\pi$
$192$		−	1.00000i		−	1.00000i
$193$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$193$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$194$		0			0
$195$	0.761570	−	2.09240i	0.761570	−	2.09240i
$196$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−0.500000	+	0.419550i	−0.500000	+	0.419550i
$201$		0			0
$202$	−0.342020	+	1.93969i	−0.342020	+	1.93969i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$208$	0.866025	+	1.50000i	0.866025	+	1.50000i
$209$		0			0
$210$	−0.439693	+	1.20805i	−0.439693	+	1.20805i
$211$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$211$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$212$		0			0
$213$			1.53209i			1.53209i
$214$		0			0
$215$		0			0
$216$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$223$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$224$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$225$	0.613341	+	0.223238i	0.613341	+	0.223238i
$226$	0.939693	−	1.62760i	0.939693	−	1.62760i
$227$	0.524005	−	0.439693i	0.524005	−	0.439693i	−0.342020	−	0.939693i	$-0.611111\pi$
$227$	0.524005	−	0.439693i	0.524005	−	0.439693i	0.866025	+	0.500000i	$0.166667\pi$
$228$	−0.673648	−	0.118782i	−0.673648	−	0.118782i
$229$	0.342020	−	1.93969i	0.342020	−	1.93969i		−	1.00000i	$-0.5\pi$
$229$	0.342020	−	1.93969i	0.342020	−	1.93969i	0.342020	−	0.939693i	$-0.388889\pi$
$230$	−0.342020	+	1.93969i	−0.342020	+	1.93969i
$231$		0			0
$232$		0			0
$233$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$233$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$234$	0.866025	−	1.50000i	0.866025	−	1.50000i
$235$		0			0
$236$		0			0
$237$	−1.20805	−	1.43969i	−1.20805	−	1.43969i
$238$		0			0
$239$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$239$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$240$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$241$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$241$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$242$	−1.00000			−1.00000
$243$	0.866025	+	0.500000i	0.866025	+	0.500000i
$244$	−1.96962			−1.96962
$245$	0.223238	+	1.26604i	0.223238	+	1.26604i
$246$		0			0
$247$	1.11334	−	0.405223i	1.11334	−	0.405223i
$248$		0			0
$249$	1.11334	+	1.32683i	1.11334	+	1.32683i
$250$	−0.419550	−	0.152704i	−0.419550	−	0.152704i
$251$	0.984808	+	1.70574i	0.984808	+	1.70574i	0.642788	+	0.766044i	$0.277778\pi$
$251$	0.984808	+	1.70574i	0.984808	+	1.70574i	0.342020	+	0.939693i	$0.388889\pi$
$252$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$253$		0			0
$254$	1.43969	−	1.20805i	1.43969	−	1.20805i
$255$		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
$260$	1.11334	−	1.92836i	1.11334	−	1.92836i
$261$		0			0
$262$	0.984808	+	1.70574i	0.984808	+	1.70574i
$263$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$263$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$264$		0			0
$265$		0			0
$266$	−0.642788	+	0.233956i	−0.642788	+	0.233956i
$267$		0			0
$268$		0			0
$269$	−0.684040			−0.684040			−0.342020	−	0.939693i	$-0.611111\pi$
$269$	−0.684040			−0.684040			−0.342020	+	0.939693i	$0.611111\pi$
$270$	1.11334	+	0.642788i	1.11334	+	0.642788i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		−	1.73205i		−	1.73205i
$274$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$275$		0			0
$276$	−0.524005	+	1.43969i	−0.524005	+	1.43969i
$277$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$277$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$278$	−0.342020	−	0.592396i	−0.342020	−	0.592396i
$279$		0			0
$280$	−0.642788	+	1.11334i	−0.642788	+	1.11334i
$281$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$281$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$282$		0			0
$283$	0.223238	−	1.26604i	0.223238	−	1.26604i	−0.642788	−	0.766044i	$-0.722222\pi$
$283$	0.223238	−	1.26604i	0.223238	−	1.26604i	0.866025	−	0.500000i	$-0.166667\pi$
$284$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$285$	0.300767	+	0.826352i	0.300767	+	0.826352i
$286$		0			0
$287$		0			0
$288$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$289$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.20805	−	0.439693i	1.20805	−	0.439693i	0.342020	−	0.939693i	$-0.388889\pi$
$293$	1.20805	−	0.439693i	1.20805	−	0.439693i	0.866025	+	0.500000i	$0.166667\pi$
$294$			1.00000i			1.00000i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.460802	−	2.61334i	−0.460802	−	2.61334i
$300$	0.565258	+	0.326352i	0.565258	+	0.326352i
$301$		0			0
$302$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$303$	1.93969	−	0.342020i	1.93969	−	0.342020i
$304$	−0.642788	−	0.233956i	−0.642788	−	0.233956i
$305$	1.26604	+	2.19285i	1.26604	+	2.19285i
$306$		0			0
$307$	0.342020	−	0.592396i	0.342020	−	0.592396i	−0.642788	−	0.766044i	$-0.722222\pi$
$307$	0.342020	−	0.592396i	0.342020	−	0.592396i	0.984808	+	0.173648i	$0.0555556\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$311$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$312$	1.11334	−	1.32683i	1.11334	−	1.32683i
$313$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$313$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$314$	0.642788	−	1.11334i	0.642788	−	1.11334i
$315$	1.28558			1.28558
$316$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$317$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$317$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$318$		0			0
$319$		0			0
$320$	−1.20805	+	0.439693i	−1.20805	+	0.439693i
$321$		0			0
$322$	0.266044	+	1.50881i	0.266044	+	1.50881i
$323$		0			0
$324$	0.766044	+	0.642788i	0.766044	+	0.642788i
$325$	−1.13052			−1.13052
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$331$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$332$	0.866025	+	1.50000i	0.866025	+	1.50000i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.642788	+	0.766044i	−0.642788	+	0.766044i
$337$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$337$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$338$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$339$	−1.85083	−	0.326352i	−1.85083	−	0.326352i
$340$		0			0
$341$		0			0
$342$	0.118782	+	0.673648i	0.118782	+	0.673648i
$343$	0.500000	+	0.866025i	0.500000	+	0.866025i
$344$		0			0
$345$	1.93969	−	0.342020i	1.93969	−	0.342020i
$346$		0			0
$347$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$347$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$348$		0			0
$349$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$349$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$350$	0.652704			0.652704
$351$	−1.70574	−	0.300767i	−1.70574	−	0.300767i
$352$		0			0
$353$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$353$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$354$		0			0
$355$	1.85083	−	0.673648i	1.85083	−	0.673648i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$359$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$360$	0.984808	+	0.826352i	0.984808	+	0.826352i
$361$	0.266044	−	0.460802i	0.266044	−	0.460802i
$362$	−1.50881	+	1.26604i	−1.50881	+	1.26604i
$363$	0.342020	+	0.939693i	0.342020	+	0.939693i
$364$	0.300767	−	1.70574i	0.300767	−	1.70574i
$365$		0			0
$366$	0.673648	+	1.85083i	0.673648	+	1.85083i
$367$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$367$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$368$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$373$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$374$		0			0
$375$			0.446476i			0.446476i
$376$		0			0
$377$		0			0
$378$	0.984808	+	0.173648i	0.984808	+	0.173648i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	0.152704	+	0.866025i	0.152704	+	0.866025i
$381$	−1.62760	−	0.939693i	−1.62760	−	0.939693i
$382$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$383$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$383$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$384$	−0.984808	+	0.173648i	−0.984808	+	0.173648i
$385$		0			0
$386$	0.939693	+	1.62760i	0.939693	+	1.62760i
$387$		0			0
$388$		0			0
$389$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$389$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$390$	−2.19285	−	0.386659i	−2.19285	−	0.386659i
$391$		0			0
$392$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$393$	1.26604	−	1.50881i	1.26604	−	1.50881i
$394$		0			0
$395$	−1.20805	+	2.09240i	−1.20805	+	2.09240i
$396$		0			0
$397$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$397$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$398$		0			0
$399$	0.439693	+	0.524005i	0.439693	+	0.524005i
$400$	0.500000	+	0.419550i	0.500000	+	0.419550i
$401$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−0.766044	+	0.642788i	$0.777778\pi$
$401$	−1.76604	+	0.642788i	−1.76604	+	0.642788i	−1.00000			$1.00000\pi$
$402$		0			0
$403$		0			0
$404$	1.96962			1.96962
$405$	0.223238	−	1.26604i	0.223238	−	1.26604i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$409$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$410$		0			0
$411$	0.642788	+	0.766044i	0.642788	+	0.766044i
$412$		0			0
$413$		0			0
$414$	1.53209			1.53209
$415$	1.11334	−	1.92836i	1.11334	−	1.92836i
$416$	1.32683	−	1.11334i	1.32683	−	1.11334i
$417$	−0.439693	+	0.524005i	−0.439693	+	0.524005i
$418$		0			0
$419$	0.118782	−	0.673648i	0.118782	−	0.673648i	−0.866025	−	0.500000i	$-0.833333\pi$
$419$	0.118782	−	0.673648i	0.118782	−	0.673648i	0.984808	−	0.173648i	$-0.0555556\pi$
$420$	1.26604	+	0.223238i	1.26604	+	0.223238i
$421$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$421$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	1.50881	−	0.266044i	1.50881	−	0.266044i
$427$	1.50881	+	1.26604i	1.50881	+	1.26604i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$431$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$432$	0.642788	+	0.766044i	0.642788	+	0.766044i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.802823	+	0.673648i	0.802823	+	0.673648i
$438$		0			0
$439$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$439$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$440$		0			0
$441$	0.939693	−	0.342020i	0.939693	−	0.342020i
$442$		0			0
$443$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$443$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$449$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$449$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$450$	0.113341	−	0.642788i	0.113341	−	0.642788i
$451$		0			0
$452$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$453$	−0.524005	+	1.43969i	−0.524005	+	1.43969i
$454$	−0.524005	−	0.439693i	−0.524005	−	0.439693i
$455$	−2.09240	+	0.761570i	−2.09240	+	0.761570i
$456$			0.684040i			0.684040i
$457$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	−0.766044	−	0.642788i	$-0.777778\pi$
$457$	−0.266044	−	1.50881i	−0.266044	−	1.50881i	0.500000	−	0.866025i	$-0.333333\pi$
$458$	−1.96962			−1.96962
$459$		0			0
$460$	1.96962			1.96962
$461$	−0.223238	−	1.26604i	−0.223238	−	1.26604i	−0.866025	−	0.500000i	$-0.833333\pi$
$461$	−0.223238	−	1.26604i	−0.223238	−	1.26604i	0.642788	−	0.766044i	$-0.277778\pi$
$462$		0			0
$463$	0.326352	−	0.118782i	0.326352	−	0.118782i	−0.173648	−	0.984808i	$-0.555556\pi$
$463$	0.326352	−	0.118782i	0.326352	−	0.118782i	0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$		0			0
$466$	0.326352	+	0.118782i	0.326352	+	0.118782i
$467$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$467$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$468$	−1.62760	−	0.592396i	−1.62760	−	0.592396i
$469$		0			0
$470$		0			0
$471$	−1.26604	−	0.223238i	−1.26604	−	0.223238i
$472$		0			0
$473$		0			0
$474$	−1.20805	+	1.43969i	−1.20805	+	1.43969i
$475$	0.342020	−	0.286989i	0.342020	−	0.286989i
$476$		0			0
$477$		0			0
$478$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$479$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$479$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$480$	0.826352	+	0.984808i	0.826352	+	0.984808i
$481$		0			0
$482$		0			0
$483$	1.32683	−	0.766044i	1.32683	−	0.766044i
$484$	0.173648	+	0.984808i	0.173648	+	0.984808i
$485$		0			0
$486$	0.342020	−	0.939693i	0.342020	−	0.939693i
$487$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$487$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$488$	0.342020	+	1.93969i	0.342020	+	1.93969i
$489$		0			0
$490$	1.20805	−	0.439693i	1.20805	−	0.439693i
$491$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$491$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$492$		0			0
$493$		0			0
$494$	−0.592396	−	1.02606i	−0.592396	−	1.02606i
$495$		0			0
$496$		0			0
$497$	1.17365	−	0.984808i	1.17365	−	0.984808i
$498$	1.11334	−	1.32683i	1.11334	−	1.32683i
$499$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$499$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$500$	−0.0775297	+	0.439693i	−0.0775297	+	0.439693i
$501$		0			0
$502$	1.50881	−	1.26604i	1.50881	−	1.26604i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$	0.939693	+	0.342020i	0.939693	+	0.342020i
$505$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$506$		0			0
$507$	1.96962	−	0.347296i	1.96962	−	0.347296i
$508$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$509$	1.62760	−	0.592396i	1.62760	−	0.592396i	0.642788	−	0.766044i	$-0.277778\pi$
$509$	1.62760	−	0.592396i	1.62760	−	0.592396i	0.984808	+	0.173648i	$0.0555556\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$	0.592396	−	0.342020i	0.592396	−	0.342020i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−2.09240	−	0.761570i	−2.09240	−	0.761570i
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$		0			0
$523$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.342020	+	0.939693i	$0.611111\pi$
$523$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.642788	+	0.766044i	$0.722222\pi$
$524$	1.50881	−	1.26604i	1.50881	−	1.26604i
$525$	−0.223238	−	0.613341i	−0.223238	−	0.613341i
$526$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$527$		0			0
$528$		0			0
$529$	1.03209	−	0.866025i	1.03209	−	0.866025i
$530$		0			0
$531$		0			0
$532$	0.342020	+	0.592396i	0.342020	+	0.592396i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.118782	+	0.673648i	0.118782	+	0.673648i
$539$		0			0
$540$	0.439693	−	1.20805i	0.439693	−	1.20805i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	1.70574	+	0.984808i	1.70574	+	0.984808i
$544$		0			0
$545$		0			0
$546$	−1.70574	+	0.300767i	−1.70574	+	0.300767i
$547$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$547$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$548$	0.500000	+	0.866025i	0.500000	+	0.866025i
$549$	1.50881	−	1.26604i	1.50881	−	1.26604i
$550$		0			0
$551$		0			0
$552$	1.50881	+	0.266044i	1.50881	+	0.266044i
$553$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$554$		0			0
$555$		0			0
$556$	−0.524005	+	0.439693i	−0.524005	+	0.439693i
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$	1.20805	+	0.439693i	1.20805	+	0.439693i
$561$		0			0
$562$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$563$	1.85083	−	0.673648i	1.85083	−	0.673648i	0.866025	−	0.500000i	$-0.166667\pi$
$563$	1.85083	−	0.673648i	1.85083	−	0.673648i	0.984808	−	0.173648i	$-0.0555556\pi$
$564$		0			0
$565$	0.419550	+	2.37939i	0.419550	+	2.37939i
$566$	−1.28558			−1.28558
$567$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$568$	1.53209			1.53209
$569$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$569$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$570$	0.761570	−	0.439693i	0.761570	−	0.439693i
$571$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$571$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$572$		0			0
$573$	0.223238	+	0.266044i	0.223238	+	0.266044i
$574$		0			0
$575$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$576$	0.500000	+	0.866025i	0.500000	+	0.866025i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$579$	1.20805	−	1.43969i	1.20805	−	1.43969i
$580$		0			0
$581$	0.300767	−	1.70574i	0.300767	−	1.70574i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.386659	+	2.19285i	0.386659	+	2.19285i
$586$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$587$	0.642788	+	0.233956i	0.642788	+	0.233956i	0.642788	−	0.766044i	$-0.277778\pi$
$587$	0.642788	+	0.233956i	0.642788	+	0.233956i			1.00000i	$0.5\pi$
$588$	0.984808	−	0.173648i	0.984808	−	0.173648i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−2.49362	+	0.907604i	−2.49362	+	0.907604i
$599$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$599$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$600$	0.223238	−	0.613341i	0.223238	−	0.613341i
$601$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$601$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$602$		0			0
$603$		0			0
$604$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$605$	0.984808	−	0.826352i	0.984808	−	0.826352i
$606$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$607$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$607$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$608$	−0.118782	+	0.673648i	−0.118782	+	0.673648i
$609$		0			0
$610$	1.93969	−	1.62760i	1.93969	−	1.62760i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	−0.642788	−	0.233956i	−0.642788	−	0.233956i
$615$		0			0
$616$		0			0
$617$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$617$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$618$		0			0
$619$	0.223238	+	1.26604i	0.223238	+	1.26604i	0.866025	+	0.500000i	$0.166667\pi$
$619$	0.223238	+	1.26604i	0.223238	+	1.26604i	−0.642788	+	0.766044i	$0.722222\pi$
$620$		0			0
$621$	−0.524005	−	1.43969i	−0.524005	−	1.43969i
$622$		0			0
$623$		0			0
$624$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$625$	1.15270	−	0.419550i	1.15270	−	0.419550i
$626$		0			0
$627$		0			0
$628$	−1.20805	−	0.439693i	−1.20805	−	0.439693i
$629$		0			0
$630$	−0.223238	−	1.26604i	−0.223238	−	1.26604i
$631$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$631$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$632$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$633$		0			0
$634$		0			0
$635$	−0.419550	+	2.37939i	−0.419550	+	2.37939i
$636$		0			0
$637$	−1.32683	+	1.11334i	−1.32683	+	1.11334i
$638$		0			0
$639$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$640$	0.642788	+	1.11334i	0.642788	+	1.11334i
$641$	0.326352	+	0.118782i	0.326352	+	0.118782i	0.500000	−	0.866025i	$-0.333333\pi$
$641$	0.326352	+	0.118782i	0.326352	+	0.118782i	−0.173648	+	0.984808i	$0.555556\pi$
$642$		0			0
$643$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.984808	+	0.173648i	$0.0555556\pi$
$643$	1.32683	+	1.11334i	1.32683	+	1.11334i	0.342020	+	0.939693i	$0.388889\pi$
$644$	1.43969	−	0.524005i	1.43969	−	0.524005i
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	0.500000	−	0.866025i	0.500000	−	0.866025i
$649$		0			0
$650$	0.196312	+	1.11334i	0.196312	+	1.11334i
$651$		0			0
$652$		0			0
$653$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$653$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$654$		0			0
$655$	−2.37939	−	0.866025i	−2.37939	−	0.866025i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$659$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$660$		0			0
$661$	−0.118782	+	0.673648i	−0.118782	+	0.673648i	0.866025	+	0.500000i	$0.166667\pi$
$661$	−0.118782	+	0.673648i	−0.118782	+	0.673648i	−0.984808	+	0.173648i	$0.944444\pi$
$662$		0			0
$663$		0			0
$664$	1.32683	−	1.11334i	1.32683	−	1.11334i
$665$	0.439693	−	0.761570i	0.439693	−	0.761570i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.866025	+	0.500000i	0.866025	+	0.500000i
$673$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$673$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$674$	−1.00000			−1.00000
$675$	−0.642788	+	0.113341i	−0.642788	+	0.113341i
$676$	2.00000			2.00000
$677$	0.300767	+	1.70574i	0.300767	+	1.70574i	0.642788	+	0.766044i	$0.277778\pi$
$677$	0.300767	+	1.70574i	0.300767	+	1.70574i	−0.342020	+	0.939693i	$0.611111\pi$
$678$			1.87939i			1.87939i
$679$		0			0
$680$		0			0
$681$	−0.233956	+	0.642788i	−0.233956	+	0.642788i
$682$		0			0
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$	0.642788	−	0.233956i	0.642788	−	0.233956i
$685$	0.642788	−	1.11334i	0.642788	−	1.11334i
$686$	0.766044	−	0.642788i	0.766044	−	0.642788i
$687$	0.673648	+	1.85083i	0.673648	+	1.85083i
$688$		0			0
$689$		0			0
$690$	−0.673648	−	1.85083i	−0.673648	−	1.85083i
$691$	−0.524005	+	0.439693i	−0.524005	+	0.439693i	−0.866025	−	0.500000i	$-0.833333\pi$
$691$	−0.524005	+	0.439693i	−0.524005	+	0.439693i	0.342020	+	0.939693i	$0.388889\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.826352	+	0.300767i	0.826352	+	0.300767i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	0.347296i		−	0.347296i
$700$	−0.113341	−	0.642788i	−0.113341	−	0.642788i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$			1.73205i			1.73205i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.50881	−	1.26604i	−1.50881	−	1.26604i
$708$		0			0
$709$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$709$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$710$	−0.984808	−	1.70574i	−0.984808	−	1.70574i
$711$	1.76604	+	0.642788i	1.76604	+	0.642788i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−1.20805	+	1.43969i	−1.20805	+	1.43969i
$718$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	0.642788	−	1.11334i	0.642788	−	1.11334i
$721$		0			0
$722$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$723$		0			0
$724$	1.50881	+	1.26604i	1.50881	+	1.26604i
$725$		0			0
$726$	0.866025	−	0.500000i	0.866025	−	0.500000i
$727$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$727$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$728$	−1.73205			−1.73205
$729$	−1.00000			−1.00000
$730$		0			0
$731$		0			0
$732$	1.70574	−	0.984808i	1.70574	−	0.984808i
$733$	−0.642788	+	0.233956i	−0.642788	+	0.233956i	−0.642788	−	0.766044i	$-0.722222\pi$
$733$	−0.642788	+	0.233956i	−0.642788	+	0.233956i			1.00000i	$0.5\pi$
$734$		0			0
$735$	−0.826352	−	0.984808i	−0.826352	−	0.984808i
$736$	1.43969	+	0.524005i	1.43969	+	0.524005i
$737$		0			0
$738$		0			0
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$	−0.761570	+	0.907604i	−0.761570	+	0.907604i
$742$		0			0
$743$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$743$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.62760	−	0.592396i	−1.62760	−	0.592396i
$748$		0			0
$749$		0			0
$750$	0.439693	−	0.0775297i	0.439693	−	0.0775297i
$751$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$751$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$754$		0			0
$755$	1.96962			1.96962
$756$		−	1.00000i		−	1.00000i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	0.826352	−	0.300767i	0.826352	−	0.300767i
$761$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$761$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$762$	−0.642788	+	1.76604i	−0.642788	+	1.76604i
$763$		0			0
$764$	0.173648	+	0.300767i	0.173648	+	0.300767i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.342020	+	0.939693i	0.342020	+	0.939693i
$769$		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
$772$	1.43969	−	1.20805i	1.43969	−	1.20805i
$773$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.342020	+	0.939693i	$0.611111\pi$
$773$	−0.984808	+	1.70574i	−0.984808	+	1.70574i	−0.642788	+	0.766044i	$0.722222\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$			2.22668i			2.22668i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$	0.286989	+	1.62760i	0.286989	+	1.62760i
$786$	−1.70574	−	0.984808i	−1.70574	−	0.984808i
$787$	1.62760	−	0.592396i	1.62760	−	0.592396i	0.642788	−	0.766044i	$-0.277778\pi$
$787$	1.62760	−	0.592396i	1.62760	−	0.592396i	0.984808	+	0.173648i	$0.0555556\pi$
$788$		0			0
$789$	−0.342020	+	0.0603074i	−0.342020	+	0.0603074i
$790$	2.27038	+	0.826352i	2.27038	+	0.826352i
$791$	0.939693	+	1.62760i	0.939693	+	1.62760i
$792$		0			0
$793$	−1.70574	+	2.95442i	−1.70574	+	2.95442i
$794$	−1.32683	+	1.11334i	−1.32683	+	1.11334i
$795$		0			0
$796$		0			0
$797$	−0.223238	+	1.26604i	−0.223238	+	1.26604i	0.642788	+	0.766044i	$0.277778\pi$
$797$	−0.223238	+	1.26604i	−0.223238	+	1.26604i	−0.866025	+	0.500000i	$0.833333\pi$
$798$	0.439693	−	0.524005i	0.439693	−	0.524005i
$799$		0			0
$800$	0.326352	−	0.565258i	0.326352	−	0.565258i
$801$		0			0
$802$	0.939693	+	1.62760i	0.939693	+	1.62760i
$803$		0			0
$804$		0			0
$805$	−1.50881	−	1.26604i	−1.50881	−	1.26604i
$806$		0			0
$807$	0.592396	−	0.342020i	0.592396	−	0.342020i
$808$	−0.342020	−	1.93969i	−0.342020	−	1.93969i
$809$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$809$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$810$	−1.28558			−1.28558
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.866025	+	1.50000i	0.866025	+	1.50000i
$820$		0			0
$821$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$821$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$822$	0.642788	−	0.766044i	0.642788	−	0.766044i
$823$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$823$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$827$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$828$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$829$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$829$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$830$	−2.09240	−	0.761570i	−2.09240	−	0.761570i
$831$		0			0
$832$	−1.32683	−	1.11334i	−1.32683	−	1.11334i
$833$		0			0
$834$	0.592396	+	0.342020i	0.592396	+	0.342020i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−0.684040			−0.684040
$839$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$839$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$840$		−	1.28558i		−	1.28558i
$841$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$842$		0			0
$843$	−0.118782	+	0.326352i	−0.118782	+	0.326352i
$844$		0			0
$845$	−1.28558	−	2.22668i	−1.28558	−	2.22668i
$846$		0			0
$847$	0.500000	−	0.866025i	0.500000	−	0.866025i
$848$		0			0
$849$	0.439693	+	1.20805i	0.439693	+	1.20805i
$850$		0			0
$851$		0			0
$852$	−0.524005	−	1.43969i	−0.524005	−	1.43969i
$853$	1.50881	−	1.26604i	1.50881	−	1.26604i	0.642788	−	0.766044i	$-0.277778\pi$
$853$	1.50881	−	1.26604i	1.50881	−	1.26604i	0.866025	−	0.500000i	$-0.166667\pi$
$854$	0.984808	−	1.70574i	0.984808	−	1.70574i
$855$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$856$		0			0
$857$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$857$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$858$		0			0
$859$	−1.32683	−	1.11334i	−1.32683	−	1.11334i	−0.984808	−	0.173648i	$-0.944444\pi$
$859$	−1.32683	−	1.11334i	−1.32683	−	1.11334i	−0.342020	−	0.939693i	$-0.611111\pi$
$860$		0			0
$861$		0			0
$862$	0.173648	+	0.984808i	0.173648	+	0.984808i
$863$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$863$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$864$	0.642788	−	0.766044i	0.642788	−	0.766044i
$865$		0			0
$866$		0			0
$867$	0.866025	+	0.500000i	0.866025	+	0.500000i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	0.524005	−	0.907604i	0.524005	−	0.907604i
$875$	0.342020	−	0.286989i	0.342020	−	0.286989i
$876$		0			0
$877$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$877$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$878$		0			0
$879$	−0.826352	+	0.984808i	−0.826352	+	0.984808i
$880$		0			0
$881$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$881$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$882$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$883$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$883$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$887$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$888$		0			0
$889$	0.326352	+	1.85083i	0.326352	+	1.85083i
$890$		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
$897$	1.70574	+	2.03282i	1.70574	+	2.03282i
$898$	1.43969	+	0.524005i	1.43969	+	0.524005i
$899$		0			0
$900$	−0.652704			−0.652704
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$905$	0.439693	−	2.49362i	0.439693	−	2.49362i
$906$	1.50881	+	0.266044i	1.50881	+	0.266044i
$907$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$907$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$908$	−0.342020	+	0.592396i	−0.342020	+	0.592396i
$909$	−1.50881	+	1.26604i	−1.50881	+	1.26604i
$910$	1.11334	+	1.92836i	1.11334	+	1.92836i
$911$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$911$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$912$	0.673648	−	0.118782i	0.673648	−	0.118782i
$913$		0			0
$914$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$915$	−2.19285	−	1.26604i	−2.19285	−	1.26604i
$916$	0.342020	+	1.93969i	0.342020	+	1.93969i
$917$	−1.96962			−1.96962
$918$		0			0
$919$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$919$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$920$	−0.342020	−	1.93969i	−0.342020	−	1.93969i
$921$			0.684040i			0.684040i
$922$	−1.20805	+	0.439693i	−1.20805	+	0.439693i
$923$	2.03282	+	1.70574i	2.03282	+	1.70574i
$924$		0			0
$925$		0			0
$926$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$927$		0			0
$928$		0			0
$929$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$929$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$930$		0			0
$931$	0.118782	−	0.673648i	0.118782	−	0.673648i
$932$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$933$		0			0
$934$	−1.32683	+	1.11334i	−1.32683	+	1.11334i
$935$		0			0
$936$	−0.300767	+	1.70574i	−0.300767	+	1.70574i
$937$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$937$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.642788	+	0.233956i	−0.642788	+	0.233956i	−0.642788	−	0.766044i	$-0.722222\pi$
$941$	−0.642788	+	0.233956i	−0.642788	+	0.233956i			1.00000i	$0.5\pi$
$942$			1.28558i			1.28558i
$943$		0			0
$944$		0			0
$945$	−1.11334	+	0.642788i	−1.11334	+	0.642788i
$946$		0			0
$947$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$947$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$948$	1.62760	+	0.939693i	1.62760	+	0.939693i
$949$		0			0
$950$	−0.342020	−	0.286989i	−0.342020	−	0.286989i
$951$		0			0
$952$		0			0
$953$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$954$		0			0
$955$	0.223238	−	0.386659i	0.223238	−	0.386659i
$956$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$957$		0			0
$958$		0			0
$959$	0.173648	−	0.984808i	0.173648	−	0.984808i
$960$	0.826352	−	0.984808i	0.826352	−	0.984808i
$961$	0.766044	−	0.642788i	0.766044	−	0.642788i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.27038	−	0.826352i	−2.27038	−	0.826352i
$966$	−0.984808	−	1.17365i	−0.984808	−	1.17365i
$967$	0.266044	+	0.223238i	0.266044	+	0.223238i	0.766044	−	0.642788i	$-0.222222\pi$
$967$	0.266044	+	0.223238i	0.266044	+	0.223238i	−0.500000	+	0.866025i	$0.666667\pi$
$968$	0.939693	−	0.342020i	0.939693	−	0.342020i
$969$		0			0
$970$		0			0
$971$	0.684040			0.684040			0.342020	−	0.939693i	$-0.388889\pi$
$971$	0.684040			0.684040			0.342020	+	0.939693i	$0.388889\pi$
$972$	−0.984808	−	0.173648i	−0.984808	−	0.173648i
$973$	0.684040			0.684040
$974$	0.326352	+	1.85083i	0.326352	+	1.85083i
$975$	0.979055	−	0.565258i	0.979055	−	0.565258i
$976$	1.85083	−	0.673648i	1.85083	−	0.673648i
$977$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$977$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$978$		0			0
$979$		0			0
$980$	−0.642788	−	1.11334i	−0.642788	−	1.11334i
$981$		0			0
$982$		0			0
$983$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$983$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−0.907604	+	0.761570i	−0.907604	+	0.761570i
$989$		0			0
$990$		0			0
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$995$		0			0
$996$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$997$	0.342020	+	1.93969i	0.342020	+	1.93969i	0.342020	+	0.939693i	$0.388889\pi$
$997$	0.342020	+	1.93969i	0.342020	+	1.93969i			1.00000i	$0.500000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.1.ef.c.13.1	✓	12
7.6	odd	2	inner	1512.1.ef.c.13.2	yes	12
8.5	even	2	inner	1512.1.ef.c.13.2	yes	12
27.25	even	9	inner	1512.1.ef.c.349.1	yes	12
56.13	odd	2	CM	1512.1.ef.c.13.1	✓	12
189.160	odd	18	inner	1512.1.ef.c.349.2	yes	12
216.133	even	18	inner	1512.1.ef.c.349.2	yes	12
1512.349	odd	18	inner	1512.1.ef.c.349.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.1.ef.c.13.1	✓	12	1.1	even	1	trivial
1512.1.ef.c.13.1	✓	12	56.13	odd	2	CM
1512.1.ef.c.13.2	yes	12	7.6	odd	2	inner
1512.1.ef.c.13.2	yes	12	8.5	even	2	inner
1512.1.ef.c.349.1	yes	12	27.25	even	9	inner
1512.1.ef.c.349.1	yes	12	1512.349	odd	18	inner
1512.1.ef.c.349.2	yes	12	189.160	odd	18	inner
1512.1.ef.c.349.2	yes	12	216.133	even	18	inner

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1512.ef (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.984808 + 0.826352i) q^{5} +(0.642788 + 0.766044i) q^{6} +(0.939693 + 0.342020i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.642788 - 1.11334i) q^{10} +(0.642788 - 0.766044i) q^{12} +(-0.300767 + 1.70574i) q^{13} +(0.173648 - 0.984808i) q^{14} +(-1.26604 - 0.223238i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.939693 - 0.342020i) q^{18} +(-0.342020 - 0.592396i) q^{19} +(-1.20805 - 0.439693i) q^{20} +(-0.984808 + 0.173648i) q^{21} +(-1.43969 + 0.524005i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.113341 + 0.642788i) q^{25} +1.73205 q^{26} +1.00000i q^{27} -1.00000 q^{28} +1.28558i q^{30} +(-0.766044 - 0.642788i) q^{32} +(0.642788 + 1.11334i) q^{35} +(-0.173648 + 0.984808i) q^{36} +(-0.524005 + 0.439693i) q^{38} +(-0.592396 - 1.62760i) q^{39} +(-0.223238 + 1.26604i) q^{40} +(0.342020 + 0.939693i) q^{42} +(1.20805 - 0.439693i) q^{45} +(0.766044 + 1.32683i) q^{46} +(-0.342020 + 0.939693i) q^{48} +(0.766044 + 0.642788i) q^{49} +(0.613341 - 0.223238i) q^{50} +(-0.300767 - 1.70574i) q^{52} +(0.984808 - 0.173648i) q^{54} +(0.173648 + 0.984808i) q^{56} +(0.592396 + 0.342020i) q^{57} +(1.26604 - 0.223238i) q^{60} +(1.85083 + 0.673648i) q^{61} +(0.766044 - 0.642788i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-1.70574 + 1.43128i) q^{65} +(0.984808 - 1.17365i) q^{69} +(0.984808 - 0.826352i) q^{70} +(0.766044 - 1.32683i) q^{71} +1.00000 q^{72} +(-0.419550 - 0.500000i) q^{75} +(0.524005 + 0.439693i) q^{76} +(-1.50000 + 0.866025i) q^{78} +(0.326352 + 1.85083i) q^{79} +1.28558 q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.300767 - 1.70574i) q^{83} +(0.866025 - 0.500000i) q^{84} +(-0.642788 - 1.11334i) q^{90} +(-0.866025 + 1.50000i) q^{91} +(1.17365 - 0.984808i) q^{92} +(0.152704 - 0.866025i) q^{95} +(0.984808 + 0.173648i) q^{96} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{8} + 6 q^{9} - 6 q^{15} - 6 q^{23} - 12 q^{25} - 12 q^{28} - 6 q^{50} + 6 q^{60} - 6 q^{64} + 12 q^{72} - 18 q^{78} + 6 q^{79} - 6 q^{81} + 12 q^{92} + 6 q^{95} + 6 q^{98}+O(q^{100}) \) 12 * q + 6 * q^8 + 6 * q^9 - 6 * q^15 - 6 * q^23 - 12 * q^25 - 12 * q^28 - 6 * q^50 + 6 * q^60 - 6 * q^64 + 12 * q^72 - 18 * q^78 + 6 * q^79 - 6 * q^81 + 12 * q^92 + 6 * q^95 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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