LMFDB - Embedded newform 1980.1.cf.b.967.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1980,1,Mod(43,1980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1980, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 9, 6]))

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

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

chi := DirichletCharacter("1980.43");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1980.cf (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:	$0.988148725013$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.4900500.1

Embedding invariants

Embedding label			967.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1980.967
Dual form			1980.1.cf.b.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000i q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000i q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.707107 + 0.707107i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(1.36603 - 0.366025i) q^{13} +(-0.866025 - 0.500000i) q^{14} +(-0.258819 + 0.965926i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.00000i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.866025 - 0.500000i) q^{20} -1.00000i q^{21} +(0.866025 + 0.500000i) q^{22} +(-0.965926 + 0.258819i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.41421i q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.707107 + 0.707107i) q^{28} +(-0.500000 - 0.866025i) q^{29} +(0.866025 + 0.500000i) q^{30} +(0.965926 - 0.258819i) q^{32} +1.00000i q^{33} +(-0.707107 - 1.22474i) q^{34} +(0.707107 + 0.707107i) q^{35} -1.00000 q^{36} +(1.00000 + 1.00000i) q^{37} +(1.22474 - 0.707107i) q^{39} +(-0.258819 - 0.965926i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.965926 - 0.258819i) q^{42} +(0.707107 - 0.707107i) q^{44} +1.00000i q^{45} +1.00000i q^{46} +(-0.965926 - 0.258819i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-0.965926 + 0.258819i) q^{50} +(0.707107 - 1.22474i) q^{51} +(-1.36603 - 0.366025i) q^{52} +(-0.500000 - 0.866025i) q^{54} +(-0.707107 - 0.707107i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.965926 + 0.258819i) q^{58} +(0.707107 - 0.707107i) q^{60} +(-0.866025 + 0.500000i) q^{61} +(-0.258819 - 0.965926i) q^{63} -1.00000i q^{64} +(-0.366025 + 1.36603i) q^{65} +(0.965926 + 0.258819i) q^{66} +(-0.258819 - 0.965926i) q^{67} +(-1.36603 + 0.366025i) q^{68} +(-0.866025 + 0.500000i) q^{69} +(0.866025 - 0.500000i) q^{70} +1.41421i q^{71} +(-0.258819 + 0.965926i) q^{72} +(1.22474 - 0.707107i) q^{74} +(-0.707107 - 0.707107i) q^{75} +(0.866025 + 0.500000i) q^{77} +(-0.366025 - 1.36603i) q^{78} +(-1.22474 + 0.707107i) q^{79} -1.00000 q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.707107 + 0.707107i) q^{82} +(0.965926 + 0.258819i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(0.366025 + 1.36603i) q^{85} +(-0.707107 - 0.707107i) q^{87} +(-0.500000 - 0.866025i) q^{88} +1.00000i q^{89} +(0.965926 + 0.258819i) q^{90} -1.41421i q^{91} +(0.965926 + 0.258819i) q^{92} +(-0.500000 + 0.866025i) q^{94} +(0.866025 - 0.500000i) q^{96} +(0.258819 + 0.965926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5}+O(q^{10}) $ 8 * q - 4 * q^5	$ 8 q - 4 q^{5} + 4 q^{13} + 4 q^{16} + 8 q^{17} - 4 q^{24} - 4 q^{25} - 4 q^{29} - 8 q^{36} + 8 q^{37} - 4 q^{52} - 4 q^{54} + 4 q^{56} + 4 q^{65} - 4 q^{68} + 4 q^{78} - 8 q^{80} + 4 q^{81} - 4 q^{84} - 4 q^{85} - 4 q^{88} - 4 q^{94}+O(q^{100}) $ 8 * q - 4 * q^5 + 4 * q^13 + 4 * q^16 + 8 * q^17 - 4 * q^24 - 4 * q^25 - 4 * q^29 - 8 * q^36 + 8 * q^37 - 4 * q^52 - 4 * q^54 + 4 * q^56 + 4 * q^65 - 4 * q^68 + 4 * q^78 - 8 * q^80 + 4 * q^81 - 4 * q^84 - 4 * q^85 - 4 * q^88 - 4 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1980\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$991$	$1541$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	−	0.965926i	0.258819	−	0.965926i
$2$	0.258819	−	0.965926i	0.258819	−	0.965926i
$3$	0.965926	−	0.258819i	0.965926	−	0.258819i
$3$	0.965926	−	0.258819i	0.965926	−	0.258819i
$4$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$5$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$5$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$6$		−	1.00000i		−	1.00000i
$7$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$7$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$8$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$9$	0.866025	−	0.500000i	0.866025	−	0.500000i
$10$	0.707107	+	0.707107i	0.707107	+	0.707107i
$11$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$11$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$12$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$13$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$13$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$14$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$15$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$16$	0.500000	+	0.866025i	0.500000	+	0.866025i
$17$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$17$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$18$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	0.866025	−	0.500000i	0.866025	−	0.500000i
$21$		−	1.00000i		−	1.00000i
$22$	0.866025	+	0.500000i	0.866025	+	0.500000i
$23$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$23$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$24$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$		−	1.41421i		−	1.41421i
$27$	0.707107	−	0.707107i	0.707107	−	0.707107i
$28$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$29$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$29$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$30$	0.866025	+	0.500000i	0.866025	+	0.500000i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.965926	−	0.258819i	0.965926	−	0.258819i
$33$			1.00000i			1.00000i
$34$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$35$	0.707107	+	0.707107i	0.707107	+	0.707107i
$36$	−1.00000			−1.00000
$37$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$37$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$38$		0			0
$39$	1.22474	−	0.707107i	1.22474	−	0.707107i
$40$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$43$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$43$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$44$	0.707107	−	0.707107i	0.707107	−	0.707107i
$45$			1.00000i			1.00000i
$46$			1.00000i			1.00000i
$47$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$47$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$48$	0.707107	+	0.707107i	0.707107	+	0.707107i
$49$		0			0
$50$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$51$	0.707107	−	1.22474i	0.707107	−	1.22474i
$52$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$55$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$56$	0.500000	+	0.866025i	0.500000	+	0.866025i
$57$		0			0
$58$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	0.707107	−	0.707107i	0.707107	−	0.707107i
$61$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$61$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$62$		0			0
$63$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$64$		−	1.00000i		−	1.00000i
$65$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$66$	0.965926	+	0.258819i	0.965926	+	0.258819i
$67$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$67$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$68$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$69$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$70$	0.866025	−	0.500000i	0.866025	−	0.500000i
$71$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$71$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$72$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$73$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$73$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$74$	1.22474	−	0.707107i	1.22474	−	0.707107i
$75$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$76$		0			0
$77$	0.866025	+	0.500000i	0.866025	+	0.500000i
$78$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$79$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$79$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$80$	−1.00000			−1.00000
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$83$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$83$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$84$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$85$	0.366025	+	1.36603i	0.366025	+	1.36603i
$86$		0			0
$87$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$88$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$89$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$89$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$90$	0.965926	+	0.258819i	0.965926	+	0.258819i
$91$		−	1.41421i		−	1.41421i
$92$	0.965926	+	0.258819i	0.965926	+	0.258819i
$93$		0			0
$94$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$95$		0			0
$96$	0.866025	−	0.500000i	0.866025	−	0.500000i
$97$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$97$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$98$		0			0
$99$	0.258819	+	0.965926i	0.258819	+	0.965926i
$100$			1.00000i			1.00000i
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$103$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$103$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$104$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$105$	0.866025	+	0.500000i	0.866025	+	0.500000i
$106$		0			0
$107$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$107$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$108$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$109$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$109$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$110$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$111$	1.22474	+	0.707107i	1.22474	+	0.707107i
$112$	0.965926	−	0.258819i	0.965926	−	0.258819i
$113$	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	$0.666667\pi$
$114$		0			0
$115$	0.258819	−	0.965926i	0.258819	−	0.965926i
$116$			1.00000i			1.00000i
$117$	1.00000	−	1.00000i	1.00000	−	1.00000i
$118$		0			0
$119$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$120$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$121$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$122$	0.258819	+	0.965926i	0.258819	+	0.965926i
$123$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$124$		0			0
$125$	1.00000			1.00000
$126$	−1.00000			−1.00000
$127$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$127$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$128$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$129$		0			0
$130$	1.22474	+	0.707107i	1.22474	+	0.707107i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	0.500000	−	0.866025i	0.500000	−	0.866025i
$133$		0			0
$134$	−1.00000			−1.00000
$135$	0.258819	+	0.965926i	0.258819	+	0.965926i
$136$			1.41421i			1.41421i
$137$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$137$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$138$	0.258819	+	0.965926i	0.258819	+	0.965926i
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$141$	−1.00000			−1.00000
$142$	1.36603	+	0.366025i	1.36603	+	0.366025i
$143$			1.41421i			1.41421i
$144$	0.866025	+	0.500000i	0.866025	+	0.500000i
$145$	1.00000			1.00000
$146$		0			0
$147$		0			0
$148$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$149$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$150$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$		0			0
$153$	0.366025	−	1.36603i	0.366025	−	1.36603i
$154$	0.707107	−	0.707107i	0.707107	−	0.707107i
$155$		0			0
$156$	−1.41421			−1.41421
$157$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$157$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$158$	0.366025	+	1.36603i	0.366025	+	1.36603i
$159$		0			0
$160$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$161$			1.00000i			1.00000i
$162$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$163$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$163$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$164$	0.500000	+	0.866025i	0.500000	+	0.866025i
$165$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$166$	0.500000	−	0.866025i	0.500000	−	0.866025i
$167$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$167$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$168$	0.707107	+	0.707107i	0.707107	+	0.707107i
$169$	0.866025	−	0.500000i	0.866025	−	0.500000i
$170$	1.41421			1.41421
$171$		0			0
$172$		0			0
$173$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$173$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$174$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$175$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$176$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$177$		0			0
$178$	0.965926	+	0.258819i	0.965926	+	0.258819i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	0.500000	−	0.866025i	0.500000	−	0.866025i
$181$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$182$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$183$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$184$	0.500000	−	0.866025i	0.500000	−	0.866025i
$185$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$186$		0			0
$187$	0.707107	+	1.22474i	0.707107	+	1.22474i
$188$	0.707107	+	0.707107i	0.707107	+	0.707107i
$189$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$190$		0			0
$191$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$191$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$192$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$193$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$193$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$194$		0			0
$195$			1.41421i			1.41421i
$196$		0			0
$197$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$197$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$198$	1.00000			1.00000
$199$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$199$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$200$	0.965926	+	0.258819i	0.965926	+	0.258819i
$201$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$202$		0			0
$203$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$204$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$205$	0.866025	−	0.500000i	0.866025	−	0.500000i
$206$		0			0
$207$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$208$	1.00000	+	1.00000i	1.00000	+	1.00000i
$209$		0			0
$210$	0.707107	−	0.707107i	0.707107	−	0.707107i
$211$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$211$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$212$		0			0
$213$	0.366025	+	1.36603i	0.366025	+	1.36603i
$214$	0.866025	−	0.500000i	0.866025	−	0.500000i
$215$		0			0
$216$			1.00000i			1.00000i
$217$		0			0
$218$	0.258819	−	0.965926i	0.258819	−	0.965926i
$219$		0			0
$220$	0.258819	+	0.965926i	0.258819	+	0.965926i
$221$	1.00000	−	1.73205i	1.00000	−	1.73205i
$222$	1.00000	−	1.00000i	1.00000	−	1.00000i
$223$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$223$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$224$		−	1.00000i		−	1.00000i
$225$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$226$	1.41421			1.41421
$227$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$227$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$228$		0			0
$229$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$229$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$230$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$231$	0.965926	+	0.258819i	0.965926	+	0.258819i
$232$	0.965926	+	0.258819i	0.965926	+	0.258819i
$233$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$233$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$234$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$235$	0.707107	−	0.707107i	0.707107	−	0.707107i
$236$		0			0
$237$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$238$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$239$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$239$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$240$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$241$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$241$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$242$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$243$	0.258819	−	0.965926i	0.258819	−	0.965926i
$244$	1.00000			1.00000
$245$		0			0
$246$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$247$		0			0
$248$		0			0
$249$	1.00000			1.00000
$250$	0.258819	−	0.965926i	0.258819	−	0.965926i
$251$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$251$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$252$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$253$		−	1.00000i		−	1.00000i
$254$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$255$	0.707107	+	1.22474i	0.707107	+	1.22474i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$257$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$258$		0			0
$259$	1.22474	−	0.707107i	1.22474	−	0.707107i
$260$	1.00000	−	1.00000i	1.00000	−	1.00000i
$261$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$262$		0			0
$263$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$263$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$264$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$265$		0			0
$266$		0			0
$267$	0.258819	+	0.965926i	0.258819	+	0.965926i
$268$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$269$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$269$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$270$	1.00000			1.00000
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	1.36603	+	0.366025i	1.36603	+	0.366025i
$273$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$274$		0			0
$275$	0.965926	−	0.258819i	0.965926	−	0.258819i
$276$	1.00000			1.00000
$277$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$277$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$278$		0			0
$279$		0			0
$280$	−1.00000			−1.00000
$281$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$281$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$282$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$283$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$283$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$284$	0.707107	−	1.22474i	0.707107	−	1.22474i
$285$		0			0
$286$	1.36603	+	0.366025i	1.36603	+	0.366025i
$287$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$288$	0.707107	−	0.707107i	0.707107	−	0.707107i
$289$		−	1.00000i		−	1.00000i
$290$	0.258819	−	0.965926i	0.258819	−	0.965926i
$291$		0			0
$292$		0			0
$293$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$293$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$		0			0
$296$	−1.41421			−1.41421
$297$	0.500000	+	0.866025i	0.500000	+	0.866025i
$298$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$299$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$300$	0.258819	+	0.965926i	0.258819	+	0.965926i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	1.00000i		−	1.00000i
$306$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$307$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$307$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$308$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$309$		0			0
$310$		0			0
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$313$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$313$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$314$			1.41421i			1.41421i
$315$	0.965926	+	0.258819i	0.965926	+	0.258819i
$316$	1.41421			1.41421
$317$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$317$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$318$		0			0
$319$	0.965926	−	0.258819i	0.965926	−	0.258819i
$320$	0.866025	+	0.500000i	0.866025	+	0.500000i
$321$	0.866025	+	0.500000i	0.866025	+	0.500000i
$322$	0.965926	+	0.258819i	0.965926	+	0.258819i
$323$		0			0
$324$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$325$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$326$	1.73205	−	1.00000i	1.73205	−	1.00000i
$327$	0.965926	−	0.258819i	0.965926	−	0.258819i
$328$	0.965926	−	0.258819i	0.965926	−	0.258819i
$329$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$330$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$331$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$331$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$332$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$333$	1.36603	+	0.366025i	1.36603	+	0.366025i
$334$			1.00000i			1.00000i
$335$	0.965926	+	0.258819i	0.965926	+	0.258819i
$336$	0.866025	−	0.500000i	0.866025	−	0.500000i
$337$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$337$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$338$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$339$	0.707107	+	1.22474i	0.707107	+	1.22474i
$340$	0.366025	−	1.36603i	0.366025	−	1.36603i
$341$		0			0
$342$		0			0
$343$	0.707107	−	0.707107i	0.707107	−	0.707107i
$344$		0			0
$345$		−	1.00000i		−	1.00000i
$346$	1.22474	+	0.707107i	1.22474	+	0.707107i
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$	0.258819	+	0.965926i	0.258819	+	0.965926i
$349$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$349$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$350$			1.00000i			1.00000i
$351$	0.707107	−	1.22474i	0.707107	−	1.22474i
$352$			1.00000i			1.00000i
$353$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$353$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$356$	0.500000	−	0.866025i	0.500000	−	0.866025i
$357$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$361$	1.00000			1.00000
$362$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$363$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$364$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$365$		0			0
$366$	0.500000	+	0.866025i	0.500000	+	0.866025i
$367$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$367$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$368$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$369$	−1.00000			−1.00000
$370$			1.41421i			1.41421i
$371$		0			0
$372$		0			0
$373$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$373$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$374$	1.36603	−	0.366025i	1.36603	−	0.366025i
$375$	0.965926	−	0.258819i	0.965926	−	0.258819i
$376$	0.866025	−	0.500000i	0.866025	−	0.500000i
$377$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$378$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$382$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$383$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$383$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$384$	−1.00000			−1.00000
$385$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$390$	1.36603	+	0.366025i	1.36603	+	0.366025i
$391$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$392$		0			0
$393$		0			0
$394$	0.707107	+	1.22474i	0.707107	+	1.22474i
$395$		−	1.41421i		−	1.41421i
$396$	0.258819	−	0.965926i	0.258819	−	0.965926i
$397$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$397$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$398$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$399$		0			0
$400$	0.500000	−	0.866025i	0.500000	−	0.866025i
$401$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$401$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$402$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$403$		0			0
$404$		0			0
$405$	0.500000	+	0.866025i	0.500000	+	0.866025i
$406$			1.00000i			1.00000i
$407$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$408$	0.366025	+	1.36603i	0.366025	+	1.36603i
$409$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$409$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$410$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.500000	+	0.866025i	0.500000	+	0.866025i
$415$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$416$	1.22474	−	0.707107i	1.22474	−	0.707107i
$417$		0			0
$418$		0			0
$419$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$419$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$420$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$421$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$421$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$422$	1.00000	+	1.00000i	1.00000	+	1.00000i
$423$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$424$		0			0
$425$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$426$	1.41421			1.41421
$427$	0.258819	+	0.965926i	0.258819	+	0.965926i
$428$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$429$	0.366025	+	1.36603i	0.366025	+	1.36603i
$430$		0			0
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	0.965926	+	0.258819i	0.965926	+	0.258819i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$	0.965926	−	0.258819i	0.965926	−	0.258819i
$436$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$437$		0			0
$438$		0			0
$439$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$439$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$440$	1.00000			1.00000
$441$		0			0
$442$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$443$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$443$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$444$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$445$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$446$	0.866025	+	0.500000i	0.866025	+	0.500000i
$447$	0.258819	−	0.965926i	0.258819	−	0.965926i
$448$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$451$	0.707107	−	0.707107i	0.707107	−	0.707107i
$452$	0.366025	−	1.36603i	0.366025	−	1.36603i
$453$		0			0
$454$		0			0
$455$	1.22474	+	0.707107i	1.22474	+	0.707107i
$456$		0			0
$457$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$457$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$458$	0.707107	−	0.707107i	0.707107	−	0.707107i
$459$		−	1.41421i		−	1.41421i
$460$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$461$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$461$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$462$	0.500000	−	0.866025i	0.500000	−	0.866025i
$463$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$463$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$464$	0.500000	−	0.866025i	0.500000	−	0.866025i
$465$		0			0
$466$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$467$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$469$	−1.00000			−1.00000
$470$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$471$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$472$		0			0
$473$		0			0
$474$	0.707107	+	1.22474i	0.707107	+	1.22474i
$475$		0			0
$476$			1.41421i			1.41421i
$477$		0			0
$478$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$479$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$479$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$480$			1.00000i			1.00000i
$481$	1.73205	+	1.00000i	1.73205	+	1.00000i
$482$	0.258819	+	0.965926i	0.258819	+	0.965926i
$483$	0.258819	+	0.965926i	0.258819	+	0.965926i
$484$	0.500000	+	0.866025i	0.500000	+	0.866025i
$485$		0			0
$486$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	0.258819	−	0.965926i	0.258819	−	0.965926i
$489$	1.73205	+	1.00000i	1.73205	+	1.00000i
$490$		0			0
$491$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$491$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$492$	0.707107	+	0.707107i	0.707107	+	0.707107i
$493$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$494$		0			0
$495$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$496$		0			0
$497$	1.36603	+	0.366025i	1.36603	+	0.366025i
$498$	0.258819	−	0.965926i	0.258819	−	0.965926i
$499$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$499$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$500$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$501$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$502$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$503$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$503$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$504$	0.866025	+	0.500000i	0.866025	+	0.500000i
$505$		0			0
$506$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$507$	0.707107	−	0.707107i	0.707107	−	0.707107i
$508$	0.258819	+	0.965926i	0.258819	+	0.965926i
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$510$	1.36603	−	0.366025i	1.36603	−	0.366025i
$511$		0			0
$512$	0.707107	+	0.707107i	0.707107	+	0.707107i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.500000	−	0.866025i	0.500000	−	0.866025i
$518$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$519$			1.41421i			1.41421i
$520$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$521$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$521$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$522$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$523$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$523$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$524$		0			0
$525$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$526$		0			0
$527$		0			0
$528$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$534$	1.00000			1.00000
$535$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$536$	0.866025	+	0.500000i	0.866025	+	0.500000i
$537$		0			0
$538$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$539$		0			0
$540$	0.258819	−	0.965926i	0.258819	−	0.965926i
$541$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$541$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$542$		0			0
$543$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$544$	0.707107	−	1.22474i	0.707107	−	1.22474i
$545$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$546$	−1.41421			−1.41421
$547$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$547$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$548$		0			0
$549$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$550$		−	1.00000i		−	1.00000i
$551$		0			0
$552$	0.258819	−	0.965926i	0.258819	−	0.965926i
$553$	0.366025	+	1.36603i	0.366025	+	1.36603i
$554$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$555$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$556$		0			0
$557$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$557$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$561$	1.00000	+	1.00000i	1.00000	+	1.00000i
$562$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$563$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$563$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$564$	0.866025	+	0.500000i	0.866025	+	0.500000i
$565$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$566$	−1.00000			−1.00000
$567$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$568$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$569$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$570$		0			0
$571$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$571$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$572$	0.707107	−	1.22474i	0.707107	−	1.22474i
$573$	1.00000	−	1.00000i	1.00000	−	1.00000i
$574$	0.500000	+	0.866025i	0.500000	+	0.866025i
$575$	0.707107	+	0.707107i	0.707107	+	0.707107i
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$579$		0			0
$580$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$581$	0.500000	−	0.866025i	0.500000	−	0.866025i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.366025	+	1.36603i	0.366025	+	1.36603i
$586$		−	1.41421i		−	1.41421i
$587$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$587$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$592$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$	0.965926	−	0.258819i	0.965926	−	0.258819i
$595$	1.41421			1.41421
$596$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$597$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$598$	0.366025	+	1.36603i	0.366025	+	1.36603i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	1.00000			1.00000
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$604$		0			0
$605$	0.866025	−	0.500000i	0.866025	−	0.500000i
$606$		0			0
$607$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$607$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$608$		0			0
$609$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$610$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$611$	−1.41421			−1.41421
$612$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$613$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$613$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$614$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$615$	0.707107	−	0.707107i	0.707107	−	0.707107i
$616$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$617$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$617$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$622$		0			0
$623$	0.965926	+	0.258819i	0.965926	+	0.258819i
$624$	1.22474	+	0.707107i	1.22474	+	0.707107i
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$	1.36603	+	0.366025i	1.36603	+	0.366025i
$629$	2.00000			2.00000
$630$	0.500000	−	0.866025i	0.500000	−	0.866025i
$631$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$631$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$632$	0.366025	−	1.36603i	0.366025	−	1.36603i
$633$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$634$		0			0
$635$	0.965926	−	0.258819i	0.965926	−	0.258819i
$636$		0			0
$637$		0			0
$638$		−	1.00000i		−	1.00000i
$639$	0.707107	+	1.22474i	0.707107	+	1.22474i
$640$	0.707107	−	0.707107i	0.707107	−	0.707107i
$641$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$641$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$642$	0.707107	−	0.707107i	0.707107	−	0.707107i
$643$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$643$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$644$	0.500000	−	0.866025i	0.500000	−	0.866025i
$645$		0			0
$646$		0			0
$647$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$647$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$648$	0.258819	+	0.965926i	0.258819	+	0.965926i
$649$		0			0
$650$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$651$		0			0
$652$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$653$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$653$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$654$		−	1.00000i		−	1.00000i
$655$		0			0
$656$		−	1.00000i		−	1.00000i
$657$		0			0
$658$	0.707107	+	0.707107i	0.707107	+	0.707107i
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$	0.500000	+	0.866025i	0.500000	+	0.866025i
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$	0.366025	+	1.36603i	0.366025	+	1.36603i
$663$	0.517638	−	1.93185i	0.517638	−	1.93185i
$664$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$665$		0			0
$666$	0.707107	−	1.22474i	0.707107	−	1.22474i
$667$	0.707107	+	0.707107i	0.707107	+	0.707107i
$668$	0.965926	+	0.258819i	0.965926	+	0.258819i
$669$			1.00000i			1.00000i
$670$	0.500000	−	0.866025i	0.500000	−	0.866025i
$671$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$672$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$673$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$673$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$674$	1.41421			1.41421
$675$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$676$	−1.00000			−1.00000
$677$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$677$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$678$	1.36603	−	0.366025i	1.36603	−	0.366025i
$679$		0			0
$680$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$681$		0			0
$682$		0			0
$683$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$683$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$684$		0			0
$685$		0			0
$686$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$687$	0.965926	+	0.258819i	0.965926	+	0.258819i
$688$		0			0
$689$		0			0
$690$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$	1.00000	−	1.00000i	1.00000	−	1.00000i
$693$	1.00000			1.00000
$694$		0			0
$695$		0			0
$696$	1.00000			1.00000
$697$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$698$	0.965926	−	0.258819i	0.965926	−	0.258819i
$699$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$700$	0.965926	+	0.258819i	0.965926	+	0.258819i
$701$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$701$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$702$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$703$		0			0
$704$	0.965926	+	0.258819i	0.965926	+	0.258819i
$705$	0.500000	−	0.866025i	0.500000	−	0.866025i
$706$	0.707107	−	1.22474i	0.707107	−	1.22474i
$707$		0			0
$708$		0			0
$709$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$709$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$710$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$711$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$712$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$713$		0			0
$714$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$715$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$716$		0			0
$717$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$721$		0			0
$722$	0.258819	−	0.965926i	0.258819	−	0.965926i
$723$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$724$	0.866025	+	0.500000i	0.866025	+	0.500000i
$725$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$726$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$727$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$727$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$728$	1.00000	+	1.00000i	1.00000	+	1.00000i
$729$		−	1.00000i		−	1.00000i
$730$		0			0
$731$		0			0
$732$	0.965926	−	0.258819i	0.965926	−	0.258819i
$733$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$733$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$734$		0			0
$735$		0			0
$736$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$737$	1.00000			1.00000
$738$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$739$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$739$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$740$	1.36603	+	0.366025i	1.36603	+	0.366025i
$741$		0			0
$742$		0			0
$743$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$743$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$744$		0			0
$745$	0.500000	+	0.866025i	0.500000	+	0.866025i
$746$		0			0
$747$	0.965926	−	0.258819i	0.965926	−	0.258819i
$748$		−	1.41421i		−	1.41421i
$749$	0.866025	−	0.500000i	0.866025	−	0.500000i
$750$		−	1.00000i		−	1.00000i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$753$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$754$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$755$		0			0
$756$			1.00000i			1.00000i
$757$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$757$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$758$		0			0
$759$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$760$		0			0
$761$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$761$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$762$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$763$	0.258819	−	0.965926i	0.258819	−	0.965926i
$764$	−1.41421			−1.41421
$765$	1.00000	+	1.00000i	1.00000	+	1.00000i
$766$		0			0
$767$		0			0
$768$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$770$	0.258819	+	0.965926i	0.258819	+	0.965926i
$771$		0			0
$772$		0			0
$773$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$773$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.00000	−	1.00000i	1.00000	−	1.00000i
$778$	0.258819	+	0.965926i	0.258819	+	0.965926i
$779$		0			0
$780$	0.707107	−	1.22474i	0.707107	−	1.22474i
$781$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$782$	1.00000	+	1.00000i	1.00000	+	1.00000i
$783$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$784$		0			0
$785$	0.366025	−	1.36603i	0.366025	−	1.36603i
$786$		0			0
$787$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$787$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$788$	1.36603	−	0.366025i	1.36603	−	0.366025i
$789$		0			0
$790$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$791$	1.41421			1.41421
$792$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$793$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$794$		0			0
$795$		0			0
$796$	1.22474	+	0.707107i	1.22474	+	0.707107i
$797$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$797$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$800$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$801$	0.500000	+	0.866025i	0.500000	+	0.866025i
$802$		0			0
$803$		0			0
$804$			1.00000i			1.00000i
$805$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$806$		0			0
$807$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$808$		0			0
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$	0.965926	−	0.258819i	0.965926	−	0.258819i
$811$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$811$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$812$	0.965926	+	0.258819i	0.965926	+	0.258819i
$813$		0			0
$814$	0.366025	+	1.36603i	0.366025	+	1.36603i
$815$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$816$	1.41421			1.41421
$817$		0			0
$818$		0			0
$819$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$820$	−1.00000			−1.00000
$821$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$821$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$822$		0			0
$823$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$823$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$824$		0			0
$825$	0.866025	−	0.500000i	0.866025	−	0.500000i
$826$		0			0
$827$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$827$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$828$	0.965926	−	0.258819i	0.965926	−	0.258819i
$829$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$829$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$830$	0.500000	+	0.866025i	0.500000	+	0.866025i
$831$	−1.41421			−1.41421
$832$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$833$		0			0
$834$		0			0
$835$	0.258819	−	0.965926i	0.258819	−	0.965926i
$836$		0			0
$837$		0			0
$838$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$841$		0			0
$842$		0			0
$843$	0.707107	−	0.707107i	0.707107	−	0.707107i
$844$	1.22474	−	0.707107i	1.22474	−	0.707107i
$845$			1.00000i			1.00000i
$846$			1.00000i			1.00000i
$847$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$848$		0			0
$849$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$850$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$851$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$852$	0.366025	−	1.36603i	0.366025	−	1.36603i
$853$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$853$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$854$	1.00000			1.00000
$855$		0			0
$856$	−1.00000			−1.00000
$857$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$858$	1.41421			1.41421
$859$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$859$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$860$		0			0
$861$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$862$		0			0
$863$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$863$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$864$	0.500000	−	0.866025i	0.500000	−	0.866025i
$865$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$866$		0			0
$867$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$868$		0			0
$869$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$870$		−	1.00000i		−	1.00000i
$871$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$872$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$873$		0			0
$874$		0			0
$875$	0.258819	−	0.965926i	0.258819	−	0.965926i
$876$		0			0
$877$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$877$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$878$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$879$	1.22474	−	0.707107i	1.22474	−	0.707107i
$880$	0.258819	−	0.965926i	0.258819	−	0.965926i
$881$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$882$		0			0
$883$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$883$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$884$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$885$		0			0
$886$	0.866025	+	0.500000i	0.866025	+	0.500000i
$887$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$887$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$888$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$889$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$890$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$891$	0.707107	+	0.707107i	0.707107	+	0.707107i
$892$	0.707107	−	0.707107i	0.707107	−	0.707107i
$893$		0			0
$894$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$895$		0			0
$896$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$897$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$898$		0			0
$899$		0			0
$900$	0.500000	+	0.866025i	0.500000	+	0.866025i
$901$		0			0
$902$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$903$		0			0
$904$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$905$	0.500000	−	0.866025i	0.500000	−	0.866025i
$906$		0			0
$907$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$907$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$908$		0			0
$909$		0			0
$910$	1.00000	−	1.00000i	1.00000	−	1.00000i
$911$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$911$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$912$		0			0
$913$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$914$		0			0
$915$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$916$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$917$		0			0
$918$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	0.500000	+	0.866025i	0.500000	+	0.866025i
$921$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$922$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$923$	0.517638	+	1.93185i	0.517638	+	1.93185i
$924$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$925$	0.366025	−	1.36603i	0.366025	−	1.36603i
$926$		0			0
$927$		0			0
$928$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$		0			0
$931$		0			0
$932$	0.366025	+	1.36603i	0.366025	+	1.36603i
$933$		0			0
$934$		0			0
$935$	−1.41421			−1.41421
$936$			1.41421i			1.41421i
$937$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$937$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$938$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$939$		0			0
$940$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$941$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$941$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$942$	0.366025	+	1.36603i	0.366025	+	1.36603i
$943$	0.965926	+	0.258819i	0.965926	+	0.258819i
$944$		0			0
$945$	1.00000			1.00000
$946$		0			0
$947$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$947$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$948$	1.36603	−	0.366025i	1.36603	−	0.366025i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	1.36603	+	0.366025i	1.36603	+	0.366025i
$953$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$953$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$954$		0			0
$955$			1.41421i			1.41421i
$956$	0.707107	+	1.22474i	0.707107	+	1.22474i
$957$	0.866025	−	0.500000i	0.866025	−	0.500000i
$958$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$959$		0			0
$960$	0.965926	+	0.258819i	0.965926	+	0.258819i
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$	1.41421	−	1.41421i	1.41421	−	1.41421i
$963$	0.965926	+	0.258819i	0.965926	+	0.258819i
$964$	1.00000			1.00000
$965$		0			0
$966$	1.00000			1.00000
$967$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$967$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$968$	0.965926	−	0.258819i	0.965926	−	0.258819i
$969$		0			0
$970$		0			0
$971$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$971$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$972$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$973$		0			0
$974$		0			0
$975$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$976$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$977$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$977$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$978$	1.41421	−	1.41421i	1.41421	−	1.41421i
$979$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$980$		0			0
$981$	0.866025	−	0.500000i	0.866025	−	0.500000i
$982$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$983$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$983$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$984$	0.866025	−	0.500000i	0.866025	−	0.500000i
$985$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$986$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$987$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$988$		0			0
$989$		0			0
$990$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$991$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$991$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$992$		0			0
$993$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$994$	0.707107	−	1.22474i	0.707107	−	1.22474i
$995$	0.707107	−	1.22474i	0.707107	−	1.22474i
$996$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$997$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$997$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$	1.41421			1.41421

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1980.1.cf.b.967.2	yes	8
4.3	odd	2	inner	1980.1.cf.b.967.1	yes	8
5.3	odd	4		1980.1.cf.a.1363.1	yes	8
9.7	even	3	inner	1980.1.cf.b.1627.1	yes	8
11.10	odd	2		1980.1.cf.a.967.1	yes	8
20.3	even	4		1980.1.cf.a.1363.2	yes	8
36.7	odd	6	inner	1980.1.cf.b.1627.2	yes	8
44.43	even	2		1980.1.cf.a.967.2	yes	8
45.43	odd	12		1980.1.cf.a.43.2	yes	8
55.43	even	4	inner	1980.1.cf.b.1363.2	yes	8
99.43	odd	6		1980.1.cf.a.1627.2	yes	8
180.43	even	12		1980.1.cf.a.43.1	✓	8
220.43	odd	4	inner	1980.1.cf.b.1363.1	yes	8
396.43	even	6		1980.1.cf.a.1627.1	yes	8
495.43	even	12	inner	1980.1.cf.b.43.1	yes	8
1980.43	odd	12	inner	1980.1.cf.b.43.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1980.1.cf.a.43.1	✓	8	180.43	even	12
1980.1.cf.a.43.2	yes	8	45.43	odd	12
1980.1.cf.a.967.1	yes	8	11.10	odd	2
1980.1.cf.a.967.2	yes	8	44.43	even	2
1980.1.cf.a.1363.1	yes	8	5.3	odd	4
1980.1.cf.a.1363.2	yes	8	20.3	even	4
1980.1.cf.a.1627.1	yes	8	396.43	even	6
1980.1.cf.a.1627.2	yes	8	99.43	odd	6
1980.1.cf.b.43.1	yes	8	495.43	even	12	inner
1980.1.cf.b.43.2	yes	8	1980.43	odd	12	inner
1980.1.cf.b.967.1	yes	8	4.3	odd	2	inner
1980.1.cf.b.967.2	yes	8	1.1	even	1	trivial
1980.1.cf.b.1363.1	yes	8	220.43	odd	4	inner
1980.1.cf.b.1363.2	yes	8	55.43	even	4	inner
1980.1.cf.b.1627.1	yes	8	9.7	even	3	inner
1980.1.cf.b.1627.2	yes	8	36.7	odd	6	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:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1980.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000i q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000i q^{6} +(0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(0.707107 + 0.707107i) q^{10} +(-0.258819 + 0.965926i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(1.36603 - 0.366025i) q^{13} +(-0.866025 - 0.500000i) q^{14} +(-0.258819 + 0.965926i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.00000i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(0.866025 - 0.500000i) q^{20} -1.00000i q^{21} +(0.866025 + 0.500000i) q^{22} +(-0.965926 + 0.258819i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.41421i q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.707107 + 0.707107i) q^{28} +(-0.500000 - 0.866025i) q^{29} +(0.866025 + 0.500000i) q^{30} +(0.965926 - 0.258819i) q^{32} +1.00000i q^{33} +(-0.707107 - 1.22474i) q^{34} +(0.707107 + 0.707107i) q^{35} -1.00000 q^{36} +(1.00000 + 1.00000i) q^{37} +(1.22474 - 0.707107i) q^{39} +(-0.258819 - 0.965926i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.965926 - 0.258819i) q^{42} +(0.707107 - 0.707107i) q^{44} +1.00000i q^{45} +1.00000i q^{46} +(-0.965926 - 0.258819i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-0.965926 + 0.258819i) q^{50} +(0.707107 - 1.22474i) q^{51} +(-1.36603 - 0.366025i) q^{52} +(-0.500000 - 0.866025i) q^{54} +(-0.707107 - 0.707107i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.965926 + 0.258819i) q^{58} +(0.707107 - 0.707107i) q^{60} +(-0.866025 + 0.500000i) q^{61} +(-0.258819 - 0.965926i) q^{63} -1.00000i q^{64} +(-0.366025 + 1.36603i) q^{65} +(0.965926 + 0.258819i) q^{66} +(-0.258819 - 0.965926i) q^{67} +(-1.36603 + 0.366025i) q^{68} +(-0.866025 + 0.500000i) q^{69} +(0.866025 - 0.500000i) q^{70} +1.41421i q^{71} +(-0.258819 + 0.965926i) q^{72} +(1.22474 - 0.707107i) q^{74} +(-0.707107 - 0.707107i) q^{75} +(0.866025 + 0.500000i) q^{77} +(-0.366025 - 1.36603i) q^{78} +(-1.22474 + 0.707107i) q^{79} -1.00000 q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.707107 + 0.707107i) q^{82} +(0.965926 + 0.258819i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(0.366025 + 1.36603i) q^{85} +(-0.707107 - 0.707107i) q^{87} +(-0.500000 - 0.866025i) q^{88} +1.00000i q^{89} +(0.965926 + 0.258819i) q^{90} -1.41421i q^{91} +(0.965926 + 0.258819i) q^{92} +(-0.500000 + 0.866025i) q^{94} +(0.866025 - 0.500000i) q^{96} +(0.258819 + 0.965926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5}+O(q^{10}) \) 8 * q - 4 * q^5	\( 8 q - 4 q^{5} + 4 q^{13} + 4 q^{16} + 8 q^{17} - 4 q^{24} - 4 q^{25} - 4 q^{29} - 8 q^{36} + 8 q^{37} - 4 q^{52} - 4 q^{54} + 4 q^{56} + 4 q^{65} - 4 q^{68} + 4 q^{78} - 8 q^{80} + 4 q^{81} - 4 q^{84} - 4 q^{85} - 4 q^{88} - 4 q^{94}+O(q^{100}) \) 8 * q - 4 * q^5 + 4 * q^13 + 4 * q^16 + 8 * q^17 - 4 * q^24 - 4 * q^25 - 4 * q^29 - 8 * q^36 + 8 * q^37 - 4 * q^52 - 4 * q^54 + 4 * q^56 + 4 * q^65 - 4 * q^68 + 4 * q^78 - 8 * q^80 + 4 * q^81 - 4 * q^84 - 4 * q^85 - 4 * q^88 - 4 * q^94

Introduction

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