LMFDB - Embedded newform 3640.1.lw.e.1077.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3640,1,Mod(1077,3640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3640, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 3, 6, 7]))

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

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

chi := DirichletCharacter("3640.1077");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3640.lw (of order $12$, degree $4$, 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:	$1.81659664598$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{12}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{12} - \cdots)$

Embedding invariants

Embedding label			1077.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3640.1077
Dual form			3640.1.lw.e.3373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-1.67303 + 0.448288i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(1.73205 + 1.00000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-1.67303 + 0.448288i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(1.73205 + 1.00000i) q^{9} +(-0.707107 - 0.707107i) q^{10} +(-1.22474 + 1.22474i) q^{12} +(0.258819 + 0.965926i) q^{13} +1.00000i q^{14} +1.73205i q^{15} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{18} +(0.517638 + 1.93185i) q^{19} +(-0.965926 - 0.258819i) q^{20} +(1.22474 - 1.22474i) q^{21} +(-0.500000 + 1.86603i) q^{23} +(-0.448288 + 1.67303i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(0.707107 + 0.707107i) q^{26} +(-1.22474 - 1.22474i) q^{27} +(0.500000 + 0.866025i) q^{28} +(0.866025 + 1.50000i) q^{30} +(-0.866025 - 0.500000i) q^{32} +(0.965926 + 0.258819i) q^{35} +(1.73205 - 1.00000i) q^{36} +(1.41421 + 1.41421i) q^{38} -1.73205i q^{39} +(-0.965926 + 0.258819i) q^{40} +(0.448288 - 1.67303i) q^{42} +(0.517638 - 1.93185i) q^{45} +(0.500000 + 1.86603i) q^{46} +(0.448288 + 1.67303i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.965926 + 0.258819i) q^{52} +(-1.67303 - 0.448288i) q^{54} +(0.866025 + 0.500000i) q^{56} -3.46410i q^{57} +(1.67303 - 0.448288i) q^{59} +(1.50000 + 0.866025i) q^{60} +(-0.965926 + 1.67303i) q^{61} +(-1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +(0.866025 - 0.500000i) q^{65} +(1.67303 - 2.89778i) q^{69} +(0.965926 - 0.258819i) q^{70} +(-0.500000 + 0.133975i) q^{71} +(1.00000 - 1.73205i) q^{72} +(1.67303 - 0.448288i) q^{75} +(1.93185 + 0.517638i) q^{76} +(-0.866025 - 1.50000i) q^{78} +(-0.707107 + 0.707107i) q^{80} +(0.500000 + 0.866025i) q^{81} -1.41421 q^{83} +(-0.448288 - 1.67303i) q^{84} +(-0.517638 - 1.93185i) q^{90} +(-0.965926 - 0.258819i) q^{91} +(1.36603 + 1.36603i) q^{92} +(1.73205 - 1.00000i) q^{95} +(1.22474 + 1.22474i) q^{96} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^7	$ 8 q + 4 q^{4} - 4 q^{7} - 4 q^{16} + 16 q^{18} - 4 q^{23} + 4 q^{28} + 4 q^{46} - 4 q^{49} - 4 q^{50} + 12 q^{60} - 8 q^{64} - 4 q^{71} + 8 q^{72} + 4 q^{81} + 4 q^{92}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^7 - 4 * q^16 + 16 * q^18 - 4 * q^23 + 4 * q^28 + 4 * q^46 - 4 * q^49 - 4 * q^50 + 12 * q^60 - 8 * q^64 - 4 * q^71 + 8 * q^72 + 4 * q^81 + 4 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3640\mathbb{Z}\right)^\times$.

$n$	$521$	$561$	$911$	$1457$	$1821$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.866025	−	0.500000i
$2$	0.866025	−	0.500000i	0.866025	−	0.500000i
$3$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$3$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.965926	+	0.258819i	$0.916667\pi$
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$5$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$6$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$7$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$7$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$8$		−	1.00000i		−	1.00000i
$9$	1.73205	+	1.00000i	1.73205	+	1.00000i
$10$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$11$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$11$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$12$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$13$	0.258819	+	0.965926i	0.258819	+	0.965926i
$13$	0.258819	+	0.965926i	0.258819	+	0.965926i
$14$			1.00000i			1.00000i
$15$			1.73205i			1.73205i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$17$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$18$	2.00000			2.00000
$19$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$19$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$20$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$21$	1.22474	−	1.22474i	1.22474	−	1.22474i
$22$		0			0
$23$	−0.500000	+	1.86603i	−0.500000	+	1.86603i			1.00000i	$0.5\pi$
$23$	−0.500000	+	1.86603i	−0.500000	+	1.86603i	−0.500000	+	0.866025i	$0.666667\pi$
$24$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$25$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$26$	0.707107	+	0.707107i	0.707107	+	0.707107i
$27$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$28$	0.500000	+	0.866025i	0.500000	+	0.866025i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	0.866025	+	1.50000i	0.866025	+	1.50000i
$31$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$31$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$32$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$33$		0			0
$34$		0			0
$35$	0.965926	+	0.258819i	0.965926	+	0.258819i
$36$	1.73205	−	1.00000i	1.73205	−	1.00000i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	1.41421	+	1.41421i	1.41421	+	1.41421i
$39$		−	1.73205i		−	1.73205i
$40$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$41$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$41$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$42$	0.448288	−	1.67303i	0.448288	−	1.67303i
$43$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$43$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$44$		0			0
$45$	0.517638	−	1.93185i	0.517638	−	1.93185i
$46$	0.500000	+	1.86603i	0.500000	+	1.86603i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.448288	+	1.67303i	0.448288	+	1.67303i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$51$		0			0
$52$	0.965926	+	0.258819i	0.965926	+	0.258819i
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$55$		0			0
$56$	0.866025	+	0.500000i	0.866025	+	0.500000i
$57$		−	3.46410i		−	3.46410i
$58$		0			0
$59$	1.67303	−	0.448288i	1.67303	−	0.448288i	0.707107	−	0.707107i	$-0.250000\pi$
$59$	1.67303	−	0.448288i	1.67303	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$60$	1.50000	+	0.866025i	1.50000	+	0.866025i
$61$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$61$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$62$		0			0
$63$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$64$	−1.00000			−1.00000
$65$	0.866025	−	0.500000i	0.866025	−	0.500000i
$66$		0			0
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	1.67303	−	2.89778i	1.67303	−	2.89778i
$70$	0.965926	−	0.258819i	0.965926	−	0.258819i
$71$	−0.500000	+	0.133975i	−0.500000	+	0.133975i	−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−0.500000	+	0.133975i	−0.500000	+	0.133975i			1.00000i	$0.5\pi$
$72$	1.00000	−	1.73205i	1.00000	−	1.73205i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$		0			0
$75$	1.67303	−	0.448288i	1.67303	−	0.448288i
$76$	1.93185	+	0.517638i	1.93185	+	0.517638i
$77$		0			0
$78$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$81$	0.500000	+	0.866025i	0.500000	+	0.866025i
$82$		0			0
$83$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$83$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$84$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$89$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$90$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$91$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$92$	1.36603	+	1.36603i	1.36603	+	1.36603i
$93$		0			0
$94$		0			0
$95$	1.73205	−	1.00000i	1.73205	−	1.00000i
$96$	1.22474	+	1.22474i	1.22474	+	1.22474i
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$99$		0			0
$100$			1.00000i			1.00000i
$101$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$101$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$102$		0			0
$103$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$103$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$104$	0.965926	−	0.258819i	0.965926	−	0.258819i
$105$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$106$		0			0
$107$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$107$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$108$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$		0			0
$111$		0			0
$112$	1.00000			1.00000
$113$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$113$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$114$	−1.73205	−	3.00000i	−1.73205	−	3.00000i
$115$	1.93185			1.93185
$116$		0			0
$117$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$118$	1.22474	−	1.22474i	1.22474	−	1.22474i
$119$		0			0
$120$	1.73205			1.73205
$121$	0.866025	+	0.500000i	0.866025	+	0.500000i
$122$			1.93185i			1.93185i
$123$		0			0
$124$		0			0
$125$	0.707107	+	0.707107i	0.707107	+	0.707107i
$126$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$127$	0.500000	+	0.133975i	0.500000	+	0.133975i	0.500000	−	0.866025i	$-0.333333\pi$
$127$	0.500000	+	0.133975i	0.500000	+	0.133975i			1.00000i	$0.5\pi$
$128$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$129$		0			0
$130$	0.500000	−	0.866025i	0.500000	−	0.866025i
$131$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$131$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$132$		0			0
$133$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$134$		0			0
$135$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$136$		0			0
$137$	0.866025	−	1.50000i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$137$	0.866025	−	1.50000i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$138$		−	3.34607i		−	3.34607i
$139$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$139$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$140$	0.707107	−	0.707107i	0.707107	−	0.707107i
$141$		0			0
$142$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$143$		0			0
$144$		−	2.00000i		−	2.00000i
$145$		0			0
$146$		0			0
$147$	0.448288	+	1.67303i	0.448288	+	1.67303i
$148$		0			0
$149$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$149$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$150$	1.22474	−	1.22474i	1.22474	−	1.22474i
$151$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$151$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$152$	1.93185	−	0.517638i	1.93185	−	0.517638i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$161$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$162$	0.866025	+	0.500000i	0.866025	+	0.500000i
$163$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$163$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$164$		0			0
$165$		0			0
$166$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$169$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$170$		0			0
$171$	−1.03528	+	3.86370i	−1.03528	+	3.86370i
$172$		0			0
$173$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$173$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$174$		0			0
$175$		−	1.00000i		−	1.00000i
$176$		0			0
$177$	−3.00000			−3.00000
$178$		0			0
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$181$			0.517638i			0.517638i	0.965926	+	0.258819i	$0.0833333\pi$
$181$			0.517638i			0.517638i	−0.965926	+	0.258819i	$0.916667\pi$
$182$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$183$	2.36603	−	2.36603i	2.36603	−	2.36603i
$184$	1.86603	+	0.500000i	1.86603	+	0.500000i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.67303	−	0.448288i	1.67303	−	0.448288i
$190$	1.00000	−	1.73205i	1.00000	−	1.73205i
$191$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$191$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$192$	1.67303	+	0.448288i	1.67303	+	0.448288i
$193$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$193$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−1.00000			$\pi$
$194$		0			0
$195$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$196$	−1.00000			−1.00000
$197$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$197$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$198$		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	+	0.866025i	0.500000	+	0.866025i
$201$		0			0
$202$	0.707107	−	1.22474i	0.707107	−	1.22474i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.73205	+	2.73205i	−2.73205	+	2.73205i
$208$	0.707107	−	0.707107i	0.707107	−	0.707107i
$209$		0			0
$210$	−1.73205			−1.73205
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	0.896575			0.896575
$214$		0			0
$215$		0			0
$216$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$	0.866025	−	0.500000i	0.866025	−	0.500000i
$225$	−2.00000			−2.00000
$226$	1.00000	+	1.00000i	1.00000	+	1.00000i
$227$	0.448288	+	0.258819i	0.448288	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$227$	0.448288	+	0.258819i	0.448288	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$228$	−3.00000	−	1.73205i	−3.00000	−	1.73205i
$229$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$229$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$230$	1.67303	−	0.965926i	1.67303	−	0.965926i
$231$		0			0
$232$		0			0
$233$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$233$	1.36603	+	1.36603i	1.36603	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$234$	0.517638	+	1.93185i	0.517638	+	1.93185i
$235$		0			0
$236$	0.448288	−	1.67303i	0.448288	−	1.67303i
$237$		0			0
$238$		0			0
$239$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$239$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$240$	1.50000	−	0.866025i	1.50000	−	0.866025i
$241$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$241$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$242$	1.00000			1.00000
$243$		0			0
$244$	0.965926	+	1.67303i	0.965926	+	1.67303i
$245$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$246$		0			0
$247$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$248$		0			0
$249$	2.36603	+	0.633975i	2.36603	+	0.633975i
$250$	0.965926	+	0.258819i	0.965926	+	0.258819i
$251$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$251$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$252$			2.00000i			2.00000i
$253$		0			0
$254$	0.500000	−	0.133975i	0.500000	−	0.133975i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$257$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$258$		0			0
$259$		0			0
$260$		−	1.00000i		−	1.00000i
$261$		0			0
$262$	0.448288	−	0.258819i	0.448288	−	0.258819i
$263$	−1.86603	−	0.500000i	−1.86603	−	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$263$	−1.86603	−	0.500000i	−1.86603	−	0.500000i	−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$267$		0			0
$268$		0			0
$269$	−1.67303	−	0.965926i	−1.67303	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$269$	−1.67303	−	0.965926i	−1.67303	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$270$			1.73205i			1.73205i
$271$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$271$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$272$		0			0
$273$	1.50000	+	0.866025i	1.50000	+	0.866025i
$274$		−	1.73205i		−	1.73205i
$275$		0			0
$276$	−1.67303	−	2.89778i	−1.67303	−	2.89778i
$277$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$277$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$278$	−1.41421			−1.41421
$279$		0			0
$280$	0.258819	−	0.965926i	0.258819	−	0.965926i
$281$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$281$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$282$		0			0
$283$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$283$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$284$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$285$	−3.34607	+	0.896575i	−3.34607	+	0.896575i
$286$		0			0
$287$		0			0
$288$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$289$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$293$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$294$	1.22474	+	1.22474i	1.22474	+	1.22474i
$295$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.93185			−1.93185
$300$	0.448288	−	1.67303i	0.448288	−	1.67303i
$301$		0			0
$302$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$303$	−2.36603	+	0.633975i	−2.36603	+	0.633975i
$304$	1.41421	−	1.41421i	1.41421	−	1.41421i
$305$	1.86603	+	0.500000i	1.86603	+	0.500000i
$306$		0			0
$307$	0.517638			0.517638			0.258819	−	0.965926i	$-0.416667\pi$
$307$	0.517638			0.517638			0.258819	+	0.965926i	$0.416667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−1.73205			−1.73205
$313$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$313$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$314$		0			0
$315$	1.41421	+	1.41421i	1.41421	+	1.41421i
$316$		0			0
$317$		0			0			−	1.00000i	$-0.5\pi$
$317$		0			0				1.00000i	$0.5\pi$
$318$		0			0
$319$		0			0
$320$	0.258819	+	0.965926i	0.258819	+	0.965926i
$321$		0			0
$322$	−1.86603	−	0.500000i	−1.86603	−	0.500000i
$323$		0			0
$324$	1.00000			1.00000
$325$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$331$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$332$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$337$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$337$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$338$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$339$		−	2.44949i		−	2.44949i
$340$		0			0
$341$		0			0
$342$	1.03528	+	3.86370i	1.03528	+	3.86370i
$343$	1.00000			1.00000
$344$		0			0
$345$	−3.23205	−	0.866025i	−3.23205	−	0.866025i
$346$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$347$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$347$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$348$		0			0
$349$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$349$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$350$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$351$	0.866025	−	1.50000i	0.866025	−	1.50000i
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$	−2.59808	+	1.50000i	−2.59808	+	1.50000i
$355$	0.258819	+	0.448288i	0.258819	+	0.448288i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.366025	+	0.366025i	0.366025	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$359$	0.366025	+	0.366025i	0.366025	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$360$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$361$	−2.59808	+	1.50000i	−2.59808	+	1.50000i
$362$	0.258819	+	0.448288i	0.258819	+	0.448288i
$363$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$364$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$365$		0			0
$366$	0.866025	−	3.23205i	0.866025	−	3.23205i
$367$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$367$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$368$	1.86603	−	0.500000i	1.86603	−	0.500000i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$373$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$374$		0			0
$375$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$376$		0			0
$377$		0			0
$378$	1.22474	−	1.22474i	1.22474	−	1.22474i
$379$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$379$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$380$		−	2.00000i		−	2.00000i
$381$	−0.776457	−	0.448288i	−0.776457	−	0.448288i
$382$		−	2.00000i		−	2.00000i
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$	1.67303	−	0.448288i	1.67303	−	0.448288i
$385$		0			0
$386$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$387$		0			0
$388$		0			0
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$391$		0			0
$392$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$393$	−0.866025	−	0.232051i	−0.866025	−	0.232051i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.258819	−	0.448288i	0.258819	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$397$	0.258819	−	0.448288i	0.258819	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$398$		0			0
$399$	3.00000	+	1.73205i	3.00000	+	1.73205i
$400$	0.866025	+	0.500000i	0.866025	+	0.500000i
$401$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$401$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$		0			0
$404$		−	1.41421i		−	1.41421i
$405$	0.707107	−	0.707107i	0.707107	−	0.707107i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$409$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$410$		0			0
$411$	−2.12132	+	2.12132i	−2.12132	+	2.12132i
$412$		0			0
$413$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$414$	−1.00000	+	3.73205i	−1.00000	+	3.73205i
$415$	0.366025	+	1.36603i	0.366025	+	1.36603i
$416$	0.258819	−	0.965926i	0.258819	−	0.965926i
$417$	1.73205	+	1.73205i	1.73205	+	1.73205i
$418$		0			0
$419$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$419$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$420$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	0.776457	−	0.448288i	0.776457	−	0.448288i
$427$	−0.965926	−	1.67303i	−0.965926	−	1.67303i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.500000	+	1.86603i	−0.500000	+	1.86603i			1.00000i	$0.5\pi$
$431$	−0.500000	+	1.86603i	−0.500000	+	1.86603i	−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$433$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$433$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.86370			−3.86370
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$		−	2.00000i		−	2.00000i
$442$		0			0
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.500000	−	0.866025i	0.500000	−	0.866025i
$449$	0.500000	−	0.133975i	0.500000	−	0.133975i		−	1.00000i	$-0.5\pi$
$449$	0.500000	−	0.133975i	0.500000	−	0.133975i	0.500000	+	0.866025i	$0.333333\pi$
$450$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$451$		0			0
$452$	1.36603	+	0.366025i	1.36603	+	0.366025i
$453$	0.776457	−	0.448288i	0.776457	−	0.448288i
$454$	0.517638			0.517638
$455$			1.00000i			1.00000i
$456$	−3.46410			−3.46410
$457$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$457$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$458$	1.93185	+	0.517638i	1.93185	+	0.517638i
$459$		0			0
$460$	0.965926	−	1.67303i	0.965926	−	1.67303i
$461$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$461$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$462$		0			0
$463$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$463$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$464$		0			0
$465$		0			0
$466$	1.86603	+	0.500000i	1.86603	+	0.500000i
$467$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$467$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$468$	1.41421	+	1.41421i	1.41421	+	1.41421i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$473$		0			0
$474$		0			0
$475$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$476$		0			0
$477$		0			0
$478$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$	0.866025	−	1.50000i	0.866025	−	1.50000i
$481$		0			0
$482$		0			0
$483$	1.67303	+	2.89778i	1.67303	+	2.89778i
$484$	0.866025	−	0.500000i	0.866025	−	0.500000i
$485$		0			0
$486$		0			0
$487$	1.50000	+	0.866025i	1.50000	+	0.866025i	1.00000			$0$
$487$	1.50000	+	0.866025i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$488$	1.67303	+	0.965926i	1.67303	+	0.965926i
$489$		0			0
$490$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$495$		0			0
$496$		0			0
$497$	0.133975	−	0.500000i	0.133975	−	0.500000i
$498$	2.36603	−	0.633975i	2.36603	−	0.633975i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	0.965926	−	0.258819i	0.965926	−	0.258819i
$501$		0			0
$502$	−0.517638			−0.517638
$503$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$503$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$504$	1.00000	+	1.73205i	1.00000	+	1.73205i
$505$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$506$		0			0
$507$	1.67303	−	0.448288i	1.67303	−	0.448288i
$508$	0.366025	−	0.366025i	0.366025	−	0.366025i
$509$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$509$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			1.00000i
$513$	1.73205	−	3.00000i	1.73205	−	3.00000i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.73205			1.73205
$520$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$523$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$524$	0.258819	−	0.448288i	0.258819	−	0.448288i
$525$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$526$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$527$		0			0
$528$		0			0
$529$	−2.36603	−	1.36603i	−2.36603	−	1.36603i
$530$		0			0
$531$	3.34607	+	0.896575i	3.34607	+	0.896575i
$532$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.93185			−1.93185
$539$		0			0
$540$	0.866025	+	1.50000i	0.866025	+	1.50000i
$541$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$541$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$542$		0			0
$543$	0.232051	−	0.866025i	0.232051	−	0.866025i
$544$		0			0
$545$		0			0
$546$	1.73205			1.73205
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$549$	−3.34607	+	1.93185i	−3.34607	+	1.93185i
$550$		0			0
$551$		0			0
$552$	−2.89778	−	1.67303i	−2.89778	−	1.67303i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$561$		0			0
$562$	0.366025	−	1.36603i	0.366025	−	1.36603i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	1.22474	−	0.707107i	1.22474	−	0.707107i
$566$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$567$	−1.00000			−1.00000
$568$	0.133975	+	0.500000i	0.133975	+	0.500000i
$569$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$569$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$570$	−2.44949	+	2.44949i	−2.44949	+	2.44949i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$		0			0
$573$	−2.44949	+	2.44949i	−2.44949	+	2.44949i
$574$		0			0
$575$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$576$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$577$		0			0			−	1.00000i	$-0.5\pi$
$577$		0			0				1.00000i	$0.5\pi$
$578$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$579$	2.89778	−	0.776457i	2.89778	−	0.776457i
$580$		0			0
$581$	0.707107	−	1.22474i	0.707107	−	1.22474i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	2.00000			2.00000
$586$	1.41421			1.41421
$587$	−0.448288	+	0.258819i	−0.448288	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$587$	−0.448288	+	0.258819i	−0.448288	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$588$	1.67303	+	0.448288i	1.67303	+	0.448288i
$589$		0			0
$590$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$599$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$599$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$600$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	0.133975	+	0.500000i	0.133975	+	0.500000i
$605$	0.258819	−	0.965926i	0.258819	−	0.965926i
$606$	−1.73205	+	1.73205i	−1.73205	+	1.73205i
$607$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$607$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$608$	0.517638	−	1.93185i	0.517638	−	1.93185i
$609$		0			0
$610$	1.86603	−	0.500000i	1.86603	−	0.500000i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	0.448288	−	0.258819i	0.448288	−	0.258819i
$615$		0			0
$616$		0			0
$617$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$617$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$618$		0			0
$619$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$619$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$620$		0			0
$621$	2.89778	−	1.67303i	2.89778	−	1.67303i
$622$		0			0
$623$		0			0
$624$	−1.50000	+	0.866025i	−1.50000	+	0.866025i
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	1.93185	+	0.517638i	1.93185	+	0.517638i
$631$	−0.133975	−	0.500000i	−0.133975	−	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$631$	−0.133975	−	0.500000i	−0.133975	−	0.500000i	−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		−	0.517638i		−	0.517638i
$636$		0			0
$637$	0.707107	−	0.707107i	0.707107	−	0.707107i
$638$		0			0
$639$	−1.00000	−	0.267949i	−1.00000	−	0.267949i
$640$	0.707107	+	0.707107i	0.707107	+	0.707107i
$641$	1.50000	+	0.866025i	1.50000	+	0.866025i	1.00000			$0$
$641$	1.50000	+	0.866025i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$642$		0			0
$643$	0.965926	−	1.67303i	0.965926	−	1.67303i	0.258819	−	0.965926i	$-0.416667\pi$
$643$	0.965926	−	1.67303i	0.965926	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$644$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$645$		0			0
$646$		0			0
$647$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$647$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$648$	0.866025	−	0.500000i	0.866025	−	0.500000i
$649$		0			0
$650$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$651$		0			0
$652$		0			0
$653$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$653$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$654$		0			0
$655$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$661$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$662$		0			0
$663$		0			0
$664$			1.41421i			1.41421i
$665$			2.00000i			2.00000i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$673$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$674$	0.366025	−	1.36603i	0.366025	−	1.36603i
$675$	1.67303	+	0.448288i	1.67303	+	0.448288i
$676$			1.00000i			1.00000i
$677$	−1.22474	−	1.22474i	−1.22474	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$677$	−1.22474	−	1.22474i	−1.22474	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$678$	−1.22474	−	2.12132i	−1.22474	−	2.12132i
$679$		0			0
$680$		0			0
$681$	−0.633975	−	0.633975i	−0.633975	−	0.633975i
$682$		0			0
$683$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$683$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$684$	2.82843	+	2.82843i	2.82843	+	2.82843i
$685$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$686$	0.866025	−	0.500000i	0.866025	−	0.500000i
$687$	−1.73205	−	3.00000i	−1.73205	−	3.00000i
$688$		0			0
$689$		0			0
$690$	−3.23205	+	0.866025i	−3.23205	+	0.866025i
$691$	0.448288	−	1.67303i	0.448288	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$691$	0.448288	−	1.67303i	0.448288	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$692$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$693$		0			0
$694$		0			0
$695$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$696$		0			0
$697$		0			0
$698$	0.258819	+	0.965926i	0.258819	+	0.965926i
$699$	−1.67303	−	2.89778i	−1.67303	−	2.89778i
$700$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		−	1.73205i		−	1.73205i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$			1.41421i			1.41421i
$708$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$709$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$709$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$710$	0.448288	+	0.258819i	0.448288	+	0.258819i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.89778	−	1.67303i	2.89778	−	1.67303i
$718$	0.500000	+	0.133975i	0.500000	+	0.133975i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$721$		0			0
$722$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$723$		0			0
$724$	0.448288	+	0.258819i	0.448288	+	0.258819i
$725$		0			0
$726$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$729$		−	1.00000i		−	1.00000i
$730$		0			0
$731$		0			0
$732$	−0.866025	−	3.23205i	−0.866025	−	3.23205i
$733$	−1.93185			−1.93185			−0.965926	−	0.258819i	$-0.916667\pi$
$733$	−1.93185			−1.93185			−0.965926	+	0.258819i	$0.916667\pi$
$734$		0			0
$735$	1.50000	−	0.866025i	1.50000	−	0.866025i
$736$	1.36603	−	1.36603i	1.36603	−	1.36603i
$737$		0			0
$738$		0			0
$739$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$739$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$740$		0			0
$741$	3.34607	−	0.896575i	3.34607	−	0.896575i
$742$		0			0
$743$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.44949	−	1.41421i	−2.44949	−	1.41421i
$748$		0			0
$749$		0			0
$750$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$752$		0			0
$753$	0.633975	+	0.633975i	0.633975	+	0.633975i
$754$		0			0
$755$	0.448288	+	0.258819i	0.448288	+	0.258819i
$756$	0.448288	−	1.67303i	0.448288	−	1.67303i
$757$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$757$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$758$		0			0
$759$		0			0
$760$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$761$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$761$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$762$	−0.896575			−0.896575
$763$		0			0
$764$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$765$		0			0
$766$		0			0
$767$	0.866025	+	1.50000i	0.866025	+	1.50000i
$768$	1.22474	−	1.22474i	1.22474	−	1.22474i
$769$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$769$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$770$		0			0
$771$		0			0
$772$			1.73205i			1.73205i
$773$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$773$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$		0			0
$786$	−0.866025	+	0.232051i	−0.866025	+	0.232051i
$787$	0.965926	−	1.67303i	0.965926	−	1.67303i	0.258819	−	0.965926i	$-0.416667\pi$
$787$	0.965926	−	1.67303i	0.965926	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$788$		0			0
$789$	2.89778	+	1.67303i	2.89778	+	1.67303i
$790$		0			0
$791$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$792$		0			0
$793$	−1.86603	−	0.500000i	−1.86603	−	0.500000i
$794$		−	0.517638i		−	0.517638i
$795$		0			0
$796$		0			0
$797$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$797$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$798$	3.46410			3.46410
$799$		0			0
$800$	1.00000			1.00000
$801$		0			0
$802$	1.36603	−	0.366025i	1.36603	−	0.366025i
$803$		0			0
$804$		0			0
$805$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$806$		0			0
$807$	2.36603	+	2.36603i	2.36603	+	2.36603i
$808$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$	0.258819	−	0.965926i	0.258819	−	0.965926i
$811$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$811$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$820$		0			0
$821$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$821$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$822$	−0.776457	+	2.89778i	−0.776457	+	2.89778i
$823$	0.500000	−	0.133975i	0.500000	−	0.133975i		−	1.00000i	$-0.5\pi$
$823$	0.500000	−	0.133975i	0.500000	−	0.133975i	0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$		0			0
$826$	0.448288	+	1.67303i	0.448288	+	1.67303i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	1.00000	+	3.73205i	1.00000	+	3.73205i
$829$	0.258819	+	0.448288i	0.258819	+	0.448288i	0.965926	−	0.258819i	$-0.0833333\pi$
$829$	0.258819	+	0.448288i	0.258819	+	0.448288i	−0.707107	+	0.707107i	$0.750000\pi$
$830$	1.00000	+	1.00000i	1.00000	+	1.00000i
$831$		0			0
$832$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$833$		0			0
$834$	2.36603	+	0.633975i	2.36603	+	0.633975i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.707107	−	1.22474i	0.707107	−	1.22474i
$839$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$839$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$840$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$841$	0.500000	−	0.866025i	0.500000	−	0.866025i
$842$		0			0
$843$	−2.12132	+	1.22474i	−2.12132	+	1.22474i
$844$		0			0
$845$	0.707107	+	0.707107i	0.707107	+	0.707107i
$846$		0			0
$847$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$848$		0			0
$849$	−0.866025	+	1.50000i	−0.866025	+	1.50000i
$850$		0			0
$851$		0			0
$852$	0.448288	−	0.776457i	0.448288	−	0.776457i
$853$			1.93185i			1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$853$			1.93185i			1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$854$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$855$	4.00000			4.00000
$856$		0			0
$857$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$857$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$858$		0			0
$859$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$859$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$860$		0			0
$861$		0			0
$862$	0.500000	+	1.86603i	0.500000	+	1.86603i
$863$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$863$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$864$	0.448288	+	1.67303i	0.448288	+	1.67303i
$865$	0.500000	+	0.866025i	0.500000	+	0.866025i
$866$		0			0
$867$	1.67303	−	0.448288i	1.67303	−	0.448288i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−3.34607	+	1.93185i	−3.34607	+	1.93185i
$875$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$876$		0			0
$877$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$877$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$878$		0			0
$879$	−1.73205	−	1.73205i	−1.73205	−	1.73205i
$880$		0			0
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$	0.776457	+	2.89778i	0.776457	+	2.89778i
$886$		0			0
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$		0			0
$889$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		−	1.00000i		−	1.00000i
$897$	3.23205	+	0.866025i	3.23205	+	0.866025i
$898$	0.366025	−	0.366025i	0.366025	−	0.366025i
$899$		0			0
$900$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.36603	−	0.366025i	1.36603	−	0.366025i
$905$	0.500000	−	0.133975i	0.500000	−	0.133975i
$906$	0.448288	−	0.776457i	0.448288	−	0.776457i
$907$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$907$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$908$	0.448288	−	0.258819i	0.448288	−	0.258819i
$909$	2.82843			2.82843
$910$	0.500000	+	0.866025i	0.500000	+	0.866025i
$911$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$911$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$912$	−3.00000	+	1.73205i	−3.00000	+	1.73205i
$913$		0			0
$914$	0.500000	−	0.866025i	0.500000	−	0.866025i
$915$	−2.89778	−	1.67303i	−2.89778	−	1.67303i
$916$	1.93185	−	0.517638i	1.93185	−	0.517638i
$917$	−0.258819	+	0.448288i	−0.258819	+	0.448288i
$918$		0			0
$919$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$919$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$920$		−	1.93185i		−	1.93185i
$921$	−0.866025	−	0.232051i	−0.866025	−	0.232051i
$922$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$923$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$924$		0			0
$925$		0			0
$926$	0.500000	+	0.866025i	0.500000	+	0.866025i
$927$		0			0
$928$		0			0
$929$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$929$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$930$		0			0
$931$	1.41421	−	1.41421i	1.41421	−	1.41421i
$932$	1.86603	−	0.500000i	1.86603	−	0.500000i
$933$		0			0
$934$	0.258819	−	0.965926i	0.258819	−	0.965926i
$935$		0			0
$936$	1.93185	+	0.517638i	1.93185	+	0.517638i
$937$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$941$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$942$		0			0
$943$		0			0
$944$	−1.22474	−	1.22474i	−1.22474	−	1.22474i
$945$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$		0			0
$950$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$951$		0			0
$952$		0			0
$953$	0.500000	−	0.133975i	0.500000	−	0.133975i		−	1.00000i	$-0.5\pi$
$953$	0.500000	−	0.133975i	0.500000	−	0.133975i	0.500000	+	0.866025i	$0.333333\pi$
$954$		0			0
$955$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$956$	0.500000	+	1.86603i	0.500000	+	1.86603i
$957$		0			0
$958$		0			0
$959$	0.866025	+	1.50000i	0.866025	+	1.50000i
$960$		−	1.73205i		−	1.73205i
$961$			1.00000i			1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.22474	+	1.22474i	1.22474	+	1.22474i
$966$	2.89778	+	1.67303i	2.89778	+	1.67303i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.500000	−	0.866025i	0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$	0.965926	−	1.67303i	0.965926	−	1.67303i	0.258819	−	0.965926i	$-0.416667\pi$
$971$	0.965926	−	1.67303i	0.965926	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$972$		0			0
$973$	1.22474	−	0.707107i	1.22474	−	0.707107i
$974$	1.73205			1.73205
$975$	0.866025	+	1.50000i	0.866025	+	1.50000i
$976$	1.93185			1.93185
$977$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$977$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$978$		0			0
$979$		0			0
$980$	0.258819	+	0.965926i	0.258819	+	0.965926i
$981$		0			0
$982$		0			0
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$			2.00000i			2.00000i
$989$		0			0
$990$		0			0
$991$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$991$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$992$		0			0
$993$		0			0
$994$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$995$		0			0
$996$	1.73205	−	1.73205i	1.73205	−	1.73205i
$997$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$997$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3640.1.lw.e.1077.1	✓	8
5.3	odd	4		3640.1.md.e.2533.2	yes	8
7.6	odd	2	inner	3640.1.lw.e.1077.2	yes	8
8.5	even	2	inner	3640.1.lw.e.1077.2	yes	8
13.6	odd	12		3640.1.md.e.1917.2	yes	8
35.13	even	4		3640.1.md.e.2533.1	yes	8
40.13	odd	4		3640.1.md.e.2533.1	yes	8
56.13	odd	2	CM	3640.1.lw.e.1077.1	✓	8
65.58	even	12	inner	3640.1.lw.e.3373.1	yes	8
91.6	even	12		3640.1.md.e.1917.1	yes	8
104.45	odd	12		3640.1.md.e.1917.1	yes	8
280.13	even	4		3640.1.md.e.2533.2	yes	8
455.188	odd	12	inner	3640.1.lw.e.3373.2	yes	8
520.253	even	12	inner	3640.1.lw.e.3373.2	yes	8
728.461	even	12		3640.1.md.e.1917.2	yes	8
3640.3373	odd	12	inner	3640.1.lw.e.3373.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3640.1.lw.e.1077.1	✓	8	1.1	even	1	trivial
3640.1.lw.e.1077.1	✓	8	56.13	odd	2	CM
3640.1.lw.e.1077.2	yes	8	7.6	odd	2	inner
3640.1.lw.e.1077.2	yes	8	8.5	even	2	inner
3640.1.lw.e.3373.1	yes	8	65.58	even	12	inner
3640.1.lw.e.3373.1	yes	8	3640.3373	odd	12	inner
3640.1.lw.e.3373.2	yes	8	455.188	odd	12	inner
3640.1.lw.e.3373.2	yes	8	520.253	even	12	inner
3640.1.md.e.1917.1	yes	8	91.6	even	12
3640.1.md.e.1917.1	yes	8	104.45	odd	12
3640.1.md.e.1917.2	yes	8	13.6	odd	12
3640.1.md.e.1917.2	yes	8	728.461	even	12
3640.1.md.e.2533.1	yes	8	35.13	even	4
3640.1.md.e.2533.1	yes	8	40.13	odd	4
3640.1.md.e.2533.2	yes	8	5.3	odd	4
3640.1.md.e.2533.2	yes	8	280.13	even	4

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:	\( N \)	\(=\)	\( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3640.lw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-1.67303 + 0.448288i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(1.73205 + 1.00000i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.258819 - 0.965926i) q^{5} +(-1.67303 + 0.448288i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000i q^{8} +(1.73205 + 1.00000i) q^{9} +(-0.707107 - 0.707107i) q^{10} +(-1.22474 + 1.22474i) q^{12} +(0.258819 + 0.965926i) q^{13} +1.00000i q^{14} +1.73205i q^{15} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{18} +(0.517638 + 1.93185i) q^{19} +(-0.965926 - 0.258819i) q^{20} +(1.22474 - 1.22474i) q^{21} +(-0.500000 + 1.86603i) q^{23} +(-0.448288 + 1.67303i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(0.707107 + 0.707107i) q^{26} +(-1.22474 - 1.22474i) q^{27} +(0.500000 + 0.866025i) q^{28} +(0.866025 + 1.50000i) q^{30} +(-0.866025 - 0.500000i) q^{32} +(0.965926 + 0.258819i) q^{35} +(1.73205 - 1.00000i) q^{36} +(1.41421 + 1.41421i) q^{38} -1.73205i q^{39} +(-0.965926 + 0.258819i) q^{40} +(0.448288 - 1.67303i) q^{42} +(0.517638 - 1.93185i) q^{45} +(0.500000 + 1.86603i) q^{46} +(0.448288 + 1.67303i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.965926 + 0.258819i) q^{52} +(-1.67303 - 0.448288i) q^{54} +(0.866025 + 0.500000i) q^{56} -3.46410i q^{57} +(1.67303 - 0.448288i) q^{59} +(1.50000 + 0.866025i) q^{60} +(-0.965926 + 1.67303i) q^{61} +(-1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +(0.866025 - 0.500000i) q^{65} +(1.67303 - 2.89778i) q^{69} +(0.965926 - 0.258819i) q^{70} +(-0.500000 + 0.133975i) q^{71} +(1.00000 - 1.73205i) q^{72} +(1.67303 - 0.448288i) q^{75} +(1.93185 + 0.517638i) q^{76} +(-0.866025 - 1.50000i) q^{78} +(-0.707107 + 0.707107i) q^{80} +(0.500000 + 0.866025i) q^{81} -1.41421 q^{83} +(-0.448288 - 1.67303i) q^{84} +(-0.517638 - 1.93185i) q^{90} +(-0.965926 - 0.258819i) q^{91} +(1.36603 + 1.36603i) q^{92} +(1.73205 - 1.00000i) q^{95} +(1.22474 + 1.22474i) q^{96} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^7	\( 8 q + 4 q^{4} - 4 q^{7} - 4 q^{16} + 16 q^{18} - 4 q^{23} + 4 q^{28} + 4 q^{46} - 4 q^{49} - 4 q^{50} + 12 q^{60} - 8 q^{64} - 4 q^{71} + 8 q^{72} + 4 q^{81} + 4 q^{92}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^7 - 4 * q^16 + 16 * q^18 - 4 * q^23 + 4 * q^28 + 4 * q^46 - 4 * q^49 - 4 * q^50 + 12 * q^60 - 8 * q^64 - 4 * q^71 + 8 * q^72 + 4 * q^81 + 4 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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