LMFDB - Embedded newform 2280.1.dj.a.1907.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2280,1,Mod(83,2280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 6, 9, 4]))

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

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

chi := DirichletCharacter("2280.83");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2280.dj (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:	$1.13786822880$
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 4.2.3249000.1

Embedding invariants

Embedding label			1907.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2280.1907
Dual form			2280.1.dj.a.923.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.866025 + 0.500000i) q^{10} -1.00000i q^{11} +1.00000i q^{12} +(0.500000 + 0.866025i) q^{14} +(0.965926 - 0.258819i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.36603 + 0.366025i) q^{17} +(0.707107 + 0.707107i) q^{18} +(0.866025 - 0.500000i) q^{19} +(0.707107 - 0.707107i) q^{20} +(0.965926 + 0.258819i) q^{21} +(-0.965926 - 0.258819i) q^{22} +(0.258819 + 0.965926i) q^{23} +(0.965926 + 0.258819i) q^{24} +(-0.866025 - 0.500000i) q^{25} +1.00000 q^{27} +(0.965926 - 0.258819i) q^{28} -1.00000i q^{30} -1.41421i q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.866025 + 0.500000i) q^{33} +(0.707107 - 1.22474i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.707107 - 0.707107i) q^{37} +(-0.258819 - 0.965926i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.866025 + 0.500000i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.36603 + 0.366025i) q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.707107 - 0.707107i) q^{45} +1.00000 q^{46} +(0.500000 - 0.866025i) q^{48} +(-0.707107 + 0.707107i) q^{50} +(-0.366025 - 1.36603i) q^{51} +(0.258819 + 0.965926i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.965926 + 0.258819i) q^{55} -1.00000i q^{56} +(-0.866025 - 0.500000i) q^{57} +(-1.00000 - 1.73205i) q^{59} +(-0.965926 - 0.258819i) q^{60} +(1.22474 + 0.707107i) q^{61} +(-1.36603 - 0.366025i) q^{62} +(-0.258819 - 0.965926i) q^{63} -1.00000i q^{64} +(0.258819 + 0.965926i) q^{66} +(-1.00000 - 1.00000i) q^{68} +(0.707107 - 0.707107i) q^{69} +(-0.965926 + 0.258819i) q^{70} +(0.707107 + 1.22474i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(1.36603 + 0.366025i) q^{73} +(-0.500000 - 0.866025i) q^{74} +1.00000i q^{75} -1.00000 q^{76} +(0.707107 + 0.707107i) q^{77} +(-0.965926 + 0.258819i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.258819 + 0.965926i) q^{82} +(1.00000 + 1.00000i) q^{83} +(-0.707107 - 0.707107i) q^{84} +(-0.707107 + 1.22474i) q^{85} +(0.707107 - 1.22474i) q^{86} +(0.707107 + 0.707107i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(-0.866025 + 0.500000i) q^{90} +(0.258819 - 0.965926i) q^{92} +(-1.22474 + 0.707107i) q^{93} +(0.258819 + 0.965926i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.866025 + 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 - 4 * q^9	$ 8 q - 4 q^{3} - 4 q^{9} + 4 q^{14} + 4 q^{16} + 4 q^{17} + 8 q^{27} - 4 q^{35} - 4 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 8 q^{46} + 4 q^{48} + 4 q^{51} - 8 q^{59} - 4 q^{62} - 8 q^{68} + 4 q^{73} - 4 q^{74} - 8 q^{76} - 4 q^{81} + 8 q^{83} - 4 q^{89}+O(q^{100}) $ 8 * q - 4 * q^3 - 4 * q^9 + 4 * q^14 + 4 * q^16 + 4 * q^17 + 8 * q^27 - 4 * q^35 - 4 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 8 * q^46 + 4 * q^48 + 4 * q^51 - 8 * q^59 - 4 * q^62 - 8 * q^68 + 4 * q^73 - 4 * q^74 - 8 * q^76 - 4 * q^81 + 8 * q^83 - 4 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2280\mathbb{Z}\right)^\times$.

$n$	$457$	$761$	$1141$	$1711$	$1921$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2280.1.dj.a.1907.2	yes	8
3.2	odd	2		2280.1.dj.b.1907.1	yes	8
5.3	odd	4		2280.1.dj.b.83.1	yes	8
8.3	odd	2	inner	2280.1.dj.a.1907.1	yes	8
15.8	even	4	inner	2280.1.dj.a.83.2	yes	8
19.11	even	3	inner	2280.1.dj.a.467.1	yes	8
24.11	even	2		2280.1.dj.b.1907.2	yes	8
40.3	even	4		2280.1.dj.b.83.2	yes	8
57.11	odd	6		2280.1.dj.b.467.2	yes	8
95.68	odd	12		2280.1.dj.b.923.2	yes	8
120.83	odd	4	inner	2280.1.dj.a.83.1	✓	8
152.11	odd	6	inner	2280.1.dj.a.467.2	yes	8
285.68	even	12	inner	2280.1.dj.a.923.1	yes	8
456.11	even	6		2280.1.dj.b.467.1	yes	8
760.163	even	12		2280.1.dj.b.923.1	yes	8
2280.923	odd	12	inner	2280.1.dj.a.923.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2280.1.dj.a.83.1	✓	8	120.83	odd	4	inner
2280.1.dj.a.83.2	yes	8	15.8	even	4	inner
2280.1.dj.a.467.1	yes	8	19.11	even	3	inner
2280.1.dj.a.467.2	yes	8	152.11	odd	6	inner
2280.1.dj.a.923.1	yes	8	285.68	even	12	inner
2280.1.dj.a.923.2	yes	8	2280.923	odd	12	inner
2280.1.dj.a.1907.1	yes	8	8.3	odd	2	inner
2280.1.dj.a.1907.2	yes	8	1.1	even	1	trivial
2280.1.dj.b.83.1	yes	8	5.3	odd	4
2280.1.dj.b.83.2	yes	8	40.3	even	4
2280.1.dj.b.467.1	yes	8	456.11	even	6
2280.1.dj.b.467.2	yes	8	57.11	odd	6
2280.1.dj.b.923.1	yes	8	760.163	even	12
2280.1.dj.b.923.2	yes	8	95.68	odd	12
2280.1.dj.b.1907.1	yes	8	3.2	odd	2
2280.1.dj.b.1907.2	yes	8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2280.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.258819 + 0.965926i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.866025 + 0.500000i) q^{10} -1.00000i q^{11} +1.00000i q^{12} +(0.500000 + 0.866025i) q^{14} +(0.965926 - 0.258819i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.36603 + 0.366025i) q^{17} +(0.707107 + 0.707107i) q^{18} +(0.866025 - 0.500000i) q^{19} +(0.707107 - 0.707107i) q^{20} +(0.965926 + 0.258819i) q^{21} +(-0.965926 - 0.258819i) q^{22} +(0.258819 + 0.965926i) q^{23} +(0.965926 + 0.258819i) q^{24} +(-0.866025 - 0.500000i) q^{25} +1.00000 q^{27} +(0.965926 - 0.258819i) q^{28} -1.00000i q^{30} -1.41421i q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.866025 + 0.500000i) q^{33} +(0.707107 - 1.22474i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.707107 - 0.707107i) q^{37} +(-0.258819 - 0.965926i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-0.866025 + 0.500000i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.36603 + 0.366025i) q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.707107 - 0.707107i) q^{45} +1.00000 q^{46} +(0.500000 - 0.866025i) q^{48} +(-0.707107 + 0.707107i) q^{50} +(-0.366025 - 1.36603i) q^{51} +(0.258819 + 0.965926i) q^{53} +(0.258819 - 0.965926i) q^{54} +(0.965926 + 0.258819i) q^{55} -1.00000i q^{56} +(-0.866025 - 0.500000i) q^{57} +(-1.00000 - 1.73205i) q^{59} +(-0.965926 - 0.258819i) q^{60} +(1.22474 + 0.707107i) q^{61} +(-1.36603 - 0.366025i) q^{62} +(-0.258819 - 0.965926i) q^{63} -1.00000i q^{64} +(0.258819 + 0.965926i) q^{66} +(-1.00000 - 1.00000i) q^{68} +(0.707107 - 0.707107i) q^{69} +(-0.965926 + 0.258819i) q^{70} +(0.707107 + 1.22474i) q^{71} +(-0.258819 - 0.965926i) q^{72} +(1.36603 + 0.366025i) q^{73} +(-0.500000 - 0.866025i) q^{74} +1.00000i q^{75} -1.00000 q^{76} +(0.707107 + 0.707107i) q^{77} +(-0.965926 + 0.258819i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.258819 + 0.965926i) q^{82} +(1.00000 + 1.00000i) q^{83} +(-0.707107 - 0.707107i) q^{84} +(-0.707107 + 1.22474i) q^{85} +(0.707107 - 1.22474i) q^{86} +(0.707107 + 0.707107i) q^{88} +(-0.500000 + 0.866025i) q^{89} +(-0.866025 + 0.500000i) q^{90} +(0.258819 - 0.965926i) q^{92} +(-1.22474 + 0.707107i) q^{93} +(0.258819 + 0.965926i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(0.866025 + 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 - 4 * q^9	\( 8 q - 4 q^{3} - 4 q^{9} + 4 q^{14} + 4 q^{16} + 4 q^{17} + 8 q^{27} - 4 q^{35} - 4 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 8 q^{46} + 4 q^{48} + 4 q^{51} - 8 q^{59} - 4 q^{62} - 8 q^{68} + 4 q^{73} - 4 q^{74} - 8 q^{76} - 4 q^{81} + 8 q^{83} - 4 q^{89}+O(q^{100}) \) 8 * q - 4 * q^3 - 4 * q^9 + 4 * q^14 + 4 * q^16 + 4 * q^17 + 8 * q^27 - 4 * q^35 - 4 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 8 * q^46 + 4 * q^48 + 4 * q^51 - 8 * q^59 - 4 * q^62 - 8 * q^68 + 4 * q^73 - 4 * q^74 - 8 * q^76 - 4 * q^81 + 8 * q^83 - 4 * q^89

Introduction

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