LMFDB - Embedded newform 2800.1.dc.c.851.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2800,1,Mod(51,2800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2800, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 4]))

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

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

chi := DirichletCharacter("2800.51");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2800 = 2^{4} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2800.dc (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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.0.2508800.2

Embedding invariants

Embedding label			851.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2800.851
Dual form			2800.1.dc.c.1451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.366025 - 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.00000i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.366025 - 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.00000i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.36603 - 0.366025i) q^{12} +(-0.866025 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.36603 + 0.366025i) q^{19} +(1.00000 - 1.00000i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(1.36603 - 0.366025i) q^{24} +1.00000 q^{28} +(0.866025 + 0.500000i) q^{31} +(0.866025 + 0.500000i) q^{32} -1.00000i q^{34} +1.00000i q^{36} +(-1.36603 + 0.366025i) q^{38} +1.00000i q^{41} +(-0.366025 + 1.36603i) q^{42} +(1.00000 + 1.00000i) q^{43} +(0.866025 + 0.500000i) q^{46} +(0.866025 - 0.500000i) q^{47} +(-1.00000 + 1.00000i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.36603 + 0.366025i) q^{51} +(0.366025 + 1.36603i) q^{53} +(-0.866025 + 0.500000i) q^{56} -2.00000i q^{57} +(1.36603 - 0.366025i) q^{59} +(0.366025 - 1.36603i) q^{61} -1.00000 q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{68} +(-1.00000 + 1.00000i) q^{69} -1.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.00000i) q^{76} +(-0.866025 + 0.500000i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} +(1.00000 - 1.00000i) q^{83} +(-0.366025 - 1.36603i) q^{84} +(-1.36603 - 0.366025i) q^{86} +(-0.866025 + 0.500000i) q^{89} -1.00000 q^{92} +(0.366025 - 1.36603i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(0.366025 - 1.36603i) q^{96} +1.00000 q^{97} -1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7	$ 4 q + 2 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7} - 2 q^{12} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{21} - 2 q^{23} + 2 q^{24} + 4 q^{28} - 2 q^{38} + 2 q^{42} + 4 q^{43} - 4 q^{48} - 2 q^{49} + 2 q^{51} - 2 q^{53} + 2 q^{59} - 2 q^{61} - 4 q^{62} - 4 q^{64} + 2 q^{68} - 4 q^{69} - 4 q^{71} - 2 q^{72} + 4 q^{76} - 2 q^{81} - 2 q^{82} + 4 q^{83} + 2 q^{84} - 2 q^{86} - 4 q^{92} - 2 q^{93} - 2 q^{94} - 2 q^{96} + 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7 - 2 * q^12 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^21 - 2 * q^23 + 2 * q^24 + 4 * q^28 - 2 * q^38 + 2 * q^42 + 4 * q^43 - 4 * q^48 - 2 * q^49 + 2 * q^51 - 2 * q^53 + 2 * q^59 - 2 * q^61 - 4 * q^62 - 4 * q^64 + 2 * q^68 - 4 * q^69 - 4 * q^71 - 2 * q^72 + 4 * q^76 - 2 * q^81 - 2 * q^82 + 4 * q^83 + 2 * q^84 - 2 * q^86 - 4 * q^92 - 2 * q^93 - 2 * q^94 - 2 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2800\mathbb{Z}\right)^\times$.

$n$	$351$	$801$	$2101$	$2577$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$2$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$3$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$	1.00000	+	1.00000i	1.00000	+	1.00000i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i
$8$			1.00000i			1.00000i
$9$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$10$		0			0
$11$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$11$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$12$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$13$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$13$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$14$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$18$	0.500000	−	0.866025i	0.500000	−	0.866025i
$19$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$19$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	1.00000	−	1.00000i	1.00000	−	1.00000i
$22$		0			0
$23$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$23$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$24$	1.36603	−	0.366025i	1.36603	−	0.366025i
$25$		0			0
$26$		0			0
$27$		0			0
$28$	1.00000			1.00000
$29$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$29$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$30$		0			0
$31$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$31$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$32$	0.866025	+	0.500000i	0.866025	+	0.500000i
$33$		0			0
$34$		−	1.00000i		−	1.00000i
$35$		0			0
$36$			1.00000i			1.00000i
$37$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$37$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$38$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$39$		0			0
$40$		0			0
$41$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$41$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$43$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$43$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$44$		0			0
$45$		0			0
$46$	0.866025	+	0.500000i	0.866025	+	0.500000i
$47$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$47$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$48$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$		0			0
$51$	1.36603	+	0.366025i	1.36603	+	0.366025i
$52$		0			0
$53$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$53$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$54$		0			0
$55$		0			0
$56$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$57$		−	2.00000i		−	2.00000i
$58$		0			0
$59$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$59$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$61$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$62$	−1.00000			−1.00000
$63$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$64$	−1.00000			−1.00000
$65$		0			0
$66$		0			0
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$	0.500000	+	0.866025i	0.500000	+	0.866025i
$69$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$70$		0			0
$71$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$72$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$		0			0
$76$	1.00000	−	1.00000i	1.00000	−	1.00000i
$77$		0			0
$78$		0			0
$79$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$79$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$82$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$83$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$83$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$84$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$85$		0			0
$86$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$87$		0			0
$88$		0			0
$89$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$89$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$90$		0			0
$91$		0			0
$92$	−1.00000			−1.00000
$93$	0.366025	−	1.36603i	0.366025	−	1.36603i
$94$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$95$		0			0
$96$	0.366025	−	1.36603i	0.366025	−	1.36603i
$97$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$97$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$98$		−	1.00000i		−	1.00000i
$99$		0			0
$100$		0			0
$101$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$102$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$103$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$103$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$		0			0
$106$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$107$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$108$		0			0
$109$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$109$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	−	0.866025i	0.500000	−	0.866025i
$113$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$113$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$114$	1.00000	+	1.73205i	1.00000	+	1.73205i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$119$	−1.00000			−1.00000
$120$		0			0
$121$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$122$	0.366025	+	1.36603i	0.366025	+	1.36603i
$123$	1.36603	−	0.366025i	1.36603	−	0.366025i
$124$	0.866025	−	0.500000i	0.866025	−	0.500000i
$125$		0			0
$126$	1.00000			1.00000
$127$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$127$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$128$	0.866025	−	0.500000i	0.866025	−	0.500000i
$129$	1.00000	−	1.73205i	1.00000	−	1.73205i
$130$		0			0
$131$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$131$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$132$		0			0
$133$	0.366025	+	1.36603i	0.366025	+	1.36603i
$134$		0			0
$135$		0			0
$136$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$137$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$137$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$138$	0.366025	−	1.36603i	0.366025	−	1.36603i
$139$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$139$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$140$		0			0
$141$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$142$	0.866025	−	0.500000i	0.866025	−	0.500000i
$143$		0			0
$144$	0.866025	+	0.500000i	0.866025	+	0.500000i
$145$		0			0
$146$		0			0
$147$	1.36603	+	0.366025i	1.36603	+	0.366025i
$148$		0			0
$149$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$151$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$152$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$153$		−	1.00000i		−	1.00000i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$157$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$158$	0.500000	−	0.866025i	0.500000	−	0.866025i
$159$	1.73205	−	1.00000i	1.73205	−	1.00000i
$160$		0			0
$161$	0.500000	−	0.866025i	0.500000	−	0.866025i
$162$		−	1.00000i		−	1.00000i
$163$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$163$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$164$	0.866025	+	0.500000i	0.866025	+	0.500000i
$165$		0			0
$166$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$	1.00000	+	1.00000i	1.00000	+	1.00000i
$169$		−	1.00000i		−	1.00000i
$170$		0			0
$171$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$172$	1.36603	−	0.366025i	1.36603	−	0.366025i
$173$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$173$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$178$	0.500000	−	0.866025i	0.500000	−	0.866025i
$179$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$179$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$180$		0			0
$181$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$181$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$182$		0			0
$183$	−2.00000			−2.00000
$184$	0.866025	−	0.500000i	0.866025	−	0.500000i
$185$		0			0
$186$	0.366025	+	1.36603i	0.366025	+	1.36603i
$187$		0			0
$188$		−	1.00000i		−	1.00000i
$189$		0			0
$190$		0			0
$191$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$191$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$192$	0.366025	+	1.36603i	0.366025	+	1.36603i
$193$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$193$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$194$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$195$		0			0
$196$	0.500000	+	0.866025i	0.500000	+	0.866025i
$197$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$197$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$198$		0			0
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$200$		0			0
$201$		0			0
$202$	1.00000	+	1.00000i	1.00000	+	1.00000i
$203$		0			0
$204$	1.00000	−	1.00000i	1.00000	−	1.00000i
$205$		0			0
$206$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$207$	0.866025	+	0.500000i	0.866025	+	0.500000i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$211$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$212$	1.36603	+	0.366025i	1.36603	+	0.366025i
$213$	0.366025	+	1.36603i	0.366025	+	1.36603i
$214$	0.366025	+	1.36603i	0.366025	+	1.36603i
$215$		0			0
$216$		0			0
$217$			1.00000i			1.00000i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$223$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$224$			1.00000i			1.00000i
$225$		0			0
$226$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$227$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$227$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$228$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$229$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$229$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$233$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$		0			0
$236$	0.366025	−	1.36603i	0.366025	−	1.36603i
$237$	1.00000	+	1.00000i	1.00000	+	1.00000i
$238$	0.866025	−	0.500000i	0.866025	−	0.500000i
$239$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$239$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$	0.500000	−	0.866025i	0.500000	−	0.866025i
$243$	1.36603	+	0.366025i	1.36603	+	0.366025i
$244$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$245$		0			0
$246$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$247$		0			0
$248$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$249$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$250$		0			0
$251$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$251$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$252$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$253$		0			0
$254$	1.00000	+	1.73205i	1.00000	+	1.73205i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$			2.00000i			2.00000i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$263$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$263$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$267$	1.00000	+	1.00000i	1.00000	+	1.00000i
$268$		0			0
$269$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$269$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$270$		0			0
$271$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$271$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$272$	1.00000			1.00000
$273$		0			0
$274$	1.00000			1.00000
$275$		0			0
$276$	0.366025	+	1.36603i	0.366025	+	1.36603i
$277$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$278$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$279$	−1.00000			−1.00000
$280$		0			0
$281$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$281$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$282$	1.36603	+	0.366025i	1.36603	+	0.366025i
$283$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$283$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$284$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$285$		0			0
$286$		0			0
$287$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$288$	−1.00000			−1.00000
$289$		0			0
$290$		0			0
$291$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$292$		0			0
$293$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$293$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$294$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.36603	−	0.366025i	1.36603	−	0.366025i
$299$		0			0
$300$		0			0
$301$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$302$			2.00000i			2.00000i
$303$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$304$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$305$		0			0
$306$	0.500000	+	0.866025i	0.500000	+	0.866025i
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$		0			0
$309$	1.00000	−	1.00000i	1.00000	−	1.00000i
$310$		0			0
$311$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$311$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$312$		0			0
$313$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$313$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$314$		0			0
$315$		0			0
$316$			1.00000i			1.00000i
$317$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$317$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$318$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$319$		0			0
$320$		0			0
$321$	−2.00000			−2.00000
$322$			1.00000i			1.00000i
$323$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$324$	0.500000	+	0.866025i	0.500000	+	0.866025i
$325$		0			0
$326$		0			0
$327$		0			0
$328$	−1.00000			−1.00000
$329$	0.866025	+	0.500000i	0.866025	+	0.500000i
$330$		0			0
$331$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$332$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$337$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$337$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$338$	0.500000	+	0.866025i	0.500000	+	0.866025i
$339$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$340$		0			0
$341$		0			0
$342$	1.00000	−	1.00000i	1.00000	−	1.00000i
$343$	−1.00000			−1.00000
$344$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$345$		0			0
$346$		0			0
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$		0			0
$349$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$349$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$354$	1.73205	+	1.00000i	1.73205	+	1.00000i
$355$		0			0
$356$			1.00000i			1.00000i
$357$	0.366025	+	1.36603i	0.366025	+	1.36603i
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$	0.866025	+	0.500000i	0.866025	+	0.500000i
$362$		0			0
$363$	1.00000	+	1.00000i	1.00000	+	1.00000i
$364$		0			0
$365$		0			0
$366$	1.73205	−	1.00000i	1.73205	−	1.00000i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$369$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$370$		0			0
$371$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$372$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$373$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$373$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$374$		0			0
$375$		0			0
$376$	0.500000	+	0.866025i	0.500000	+	0.866025i
$377$		0			0
$378$		0			0
$379$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$379$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$380$		0			0
$381$	−2.73205	+	0.732051i	−2.73205	+	0.732051i
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$383$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$384$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$385$		0			0
$386$		−	1.00000i		−	1.00000i
$387$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$388$	0.500000	−	0.866025i	0.500000	−	0.866025i
$389$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$389$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$390$		0			0
$391$	1.00000			1.00000
$392$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$393$		−	2.00000i		−	2.00000i
$394$	0.366025	−	1.36603i	0.366025	−	1.36603i
$395$		0			0
$396$		0			0
$397$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$397$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$398$		−	1.00000i		−	1.00000i
$399$	1.73205	−	1.00000i	1.73205	−	1.00000i
$400$		0			0
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$		0			0
$404$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$409$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$409$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$410$		0			0
$411$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$412$	1.00000			1.00000
$413$	1.00000	+	1.00000i	1.00000	+	1.00000i
$414$	−1.00000			−1.00000
$415$		0			0
$416$		0			0
$417$	1.00000	−	1.73205i	1.00000	−	1.73205i
$418$		0			0
$419$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$419$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$420$		0			0
$421$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$421$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$422$		0			0
$423$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$424$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$425$		0			0
$426$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$427$	1.36603	−	0.366025i	1.36603	−	0.366025i
$428$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$429$		0			0
$430$		0			0
$431$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$431$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$433$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$434$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$435$		0			0
$436$		0			0
$437$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$438$		0			0
$439$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$439$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$		−	1.00000i		−	1.00000i
$442$		0			0
$443$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$444$		0			0
$445$		0			0
$446$	0.500000	+	0.866025i	0.500000	+	0.866025i
$447$			2.00000i			2.00000i
$448$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$449$	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			0
$451$		0			0
$452$	0.500000	−	0.866025i	0.500000	−	0.866025i
$453$	−2.73205	−	0.732051i	−2.73205	−	0.732051i
$454$		0			0
$455$		0			0
$456$	2.00000			2.00000
$457$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$457$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$461$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$462$		0			0
$463$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$463$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$467$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.366025	+	1.36603i	0.366025	+	1.36603i
$473$		0			0
$474$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$475$		0			0
$476$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$477$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$478$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$479$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$479$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$484$			1.00000i			1.00000i
$485$		0			0
$486$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$487$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$487$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$488$	1.36603	+	0.366025i	1.36603	+	0.366025i
$489$		0			0
$490$		0			0
$491$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$491$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$492$	0.366025	−	1.36603i	0.366025	−	1.36603i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		−	1.00000i		−	1.00000i
$497$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$498$	2.00000			2.00000
$499$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$499$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	0.500000	−	0.866025i	0.500000	−	0.866025i
$505$		0			0
$506$		0			0
$507$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$508$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$509$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$509$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$521$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$522$		0			0
$523$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$523$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$524$	1.00000	−	1.00000i	1.00000	−	1.00000i
$525$		0			0
$526$		−	1.00000i		−	1.00000i
$527$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$528$		0			0
$529$		0			0
$530$		0			0
$531$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$532$	1.36603	+	0.366025i	1.36603	+	0.366025i
$533$		0			0
$534$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$541$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$542$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$543$		0			0
$544$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$545$		0			0
$546$		0			0
$547$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$547$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$548$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$549$	0.366025	+	1.36603i	0.366025	+	1.36603i
$550$		0			0
$551$		0			0
$552$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$553$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$554$	1.00000	+	1.00000i	1.00000	+	1.00000i
$555$		0			0
$556$	1.36603	−	0.366025i	1.36603	−	0.366025i
$557$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$557$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$558$	0.866025	−	0.500000i	0.866025	−	0.500000i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$563$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$563$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$564$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$565$		0			0
$566$	1.00000	−	1.00000i	1.00000	−	1.00000i
$567$	−1.00000			−1.00000
$568$		−	1.00000i		−	1.00000i
$569$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$569$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$571$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$572$		0			0
$573$	1.00000	+	1.00000i	1.00000	+	1.00000i
$574$	0.500000	−	0.866025i	0.500000	−	0.866025i
$575$		0			0
$576$	0.866025	−	0.500000i	0.866025	−	0.500000i
$577$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$577$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			0
$579$	1.36603	+	0.366025i	1.36603	+	0.366025i
$580$		0			0
$581$	1.36603	+	0.366025i	1.36603	+	0.366025i
$582$	1.00000	+	1.00000i	1.00000	+	1.00000i
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$587$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$587$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$588$	1.00000	−	1.00000i	1.00000	−	1.00000i
$589$	1.00000	+	1.00000i	1.00000	+	1.00000i
$590$		0			0
$591$	1.73205	+	1.00000i	1.73205	+	1.00000i
$592$		0			0
$593$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$593$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$597$	1.36603	+	0.366025i	1.36603	+	0.366025i
$598$		0			0
$599$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$599$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$603$		0			0
$604$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$605$		0			0
$606$	1.00000	−	1.73205i	1.00000	−	1.73205i
$607$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$607$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$608$	1.00000	+	1.00000i	1.00000	+	1.00000i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$613$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$613$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$617$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$618$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$619$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$619$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$620$		0			0
$621$		0			0
$622$		−	1.00000i		−	1.00000i
$623$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$624$		0			0
$625$		0			0
$626$	0.500000	−	0.866025i	0.500000	−	0.866025i
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$631$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$632$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$633$		0			0
$634$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$635$		0			0
$636$		−	2.00000i		−	2.00000i
$637$		0			0
$638$		0			0
$639$	0.866025	−	0.500000i	0.866025	−	0.500000i
$640$		0			0
$641$	−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			$\pi$
$642$	1.73205	−	1.00000i	1.73205	−	1.00000i
$643$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$643$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$644$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$645$		0			0
$646$	0.366025	−	1.36603i	0.366025	−	1.36603i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$649$		0			0
$650$		0			0
$651$	1.36603	−	0.366025i	1.36603	−	0.366025i
$652$		0			0
$653$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$653$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$654$		0			0
$655$		0			0
$656$	0.866025	−	0.500000i	0.866025	−	0.500000i
$657$		0			0
$658$	−1.00000			−1.00000
$659$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$659$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$660$		0			0
$661$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$661$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$662$	0.366025	+	1.36603i	0.366025	+	1.36603i
$663$		0			0
$664$	1.00000	+	1.00000i	1.00000	+	1.00000i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$670$		0			0
$671$		0			0
$672$	1.36603	−	0.366025i	1.36603	−	0.366025i
$673$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$673$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$674$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$675$		0			0
$676$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$677$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$677$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$678$	1.00000	+	1.00000i	1.00000	+	1.00000i
$679$	0.500000	+	0.866025i	0.500000	+	0.866025i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$683$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$684$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$685$		0			0
$686$	0.866025	−	0.500000i	0.866025	−	0.500000i
$687$		0			0
$688$	0.366025	−	1.36603i	0.366025	−	1.36603i
$689$		0			0
$690$		0			0
$691$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$701$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$			1.00000i			1.00000i
$707$	1.00000	−	1.00000i	1.00000	−	1.00000i
$708$	−2.00000			−2.00000
$709$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$709$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$710$		0			0
$711$	0.500000	−	0.866025i	0.500000	−	0.866025i
$712$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$713$		−	1.00000i		−	1.00000i
$714$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$715$		0			0
$716$		0			0
$717$	1.36603	−	0.366025i	1.36603	−	0.366025i
$718$		0			0
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$720$		0			0
$721$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$722$	−1.00000			−1.00000
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$727$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$727$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$		−	1.00000i		−	1.00000i
$730$		0			0
$731$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$732$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$733$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$733$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$734$		0			0
$735$		0			0
$736$		−	1.00000i		−	1.00000i
$737$		0			0
$738$	0.866025	+	0.500000i	0.866025	+	0.500000i
$739$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$739$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$740$		0			0
$741$		0			0
$742$	0.366025	−	1.36603i	0.366025	−	1.36603i
$743$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$744$	1.36603	+	0.366025i	1.36603	+	0.366025i
$745$		0			0
$746$		0			0
$747$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$748$		0			0
$749$	1.36603	−	0.366025i	1.36603	−	0.366025i
$750$		0			0
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$757$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$758$	1.36603	+	0.366025i	1.36603	+	0.366025i
$759$		0			0
$760$		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	$0.166667\pi$
$762$	2.00000	−	2.00000i	2.00000	−	2.00000i
$763$		0			0
$764$			1.00000i			1.00000i
$765$		0			0
$766$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$767$		0			0
$768$	1.36603	+	0.366025i	1.36603	+	0.366025i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$		0			0
$772$	0.500000	+	0.866025i	0.500000	+	0.866025i
$773$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$773$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$774$	1.36603	−	0.366025i	1.36603	−	0.366025i
$775$		0			0
$776$			1.00000i			1.00000i
$777$		0			0
$778$		0			0
$779$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$780$		0			0
$781$		0			0
$782$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$783$		0			0
$784$	1.00000			1.00000
$785$		0			0
$786$	1.00000	+	1.73205i	1.00000	+	1.73205i
$787$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$787$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$788$	0.366025	+	1.36603i	0.366025	+	1.36603i
$789$	1.36603	+	0.366025i	1.36603	+	0.366025i
$790$		0			0
$791$	0.500000	+	0.866025i	0.500000	+	0.866025i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.500000	+	0.866025i	0.500000	+	0.866025i
$797$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$797$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$798$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$799$			1.00000i			1.00000i
$800$		0			0
$801$	0.500000	−	0.866025i	0.500000	−	0.866025i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	1.36603	−	0.366025i	1.36603	−	0.366025i
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$811$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$814$		0			0
$815$		0			0
$816$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$817$	1.00000	+	1.73205i	1.00000	+	1.73205i
$818$	1.00000			1.00000
$819$		0			0
$820$		0			0
$821$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$821$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$822$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$825$		0			0
$826$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$827$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$827$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$828$	0.866025	−	0.500000i	0.866025	−	0.500000i
$829$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$829$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$832$		0			0
$833$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$834$			2.00000i			2.00000i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.366025	−	1.36603i	0.366025	−	1.36603i
$839$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$839$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$		−	1.00000i		−	1.00000i
$842$	0.366025	−	1.36603i	0.366025	−	1.36603i
$843$	1.36603	−	0.366025i	1.36603	−	0.366025i
$844$		0			0
$845$		0			0
$846$		−	1.00000i		−	1.00000i
$847$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$848$	1.00000	−	1.00000i	1.00000	−	1.00000i
$849$	1.00000	+	1.73205i	1.00000	+	1.73205i
$850$		0			0
$851$		0			0
$852$	1.36603	+	0.366025i	1.36603	+	0.366025i
$853$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$853$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$854$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$855$		0			0
$856$	1.36603	+	0.366025i	1.36603	+	0.366025i
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$860$		0			0
$861$	1.00000	+	1.00000i	1.00000	+	1.00000i
$862$	1.00000			1.00000
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$864$		0			0
$865$		0			0
$866$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$867$		0			0
$868$	0.866025	+	0.500000i	0.866025	+	0.500000i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$874$	1.00000	+	1.00000i	1.00000	+	1.00000i
$875$		0			0
$876$		0			0
$877$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$878$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$879$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$880$		0			0
$881$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$882$	0.500000	+	0.866025i	0.500000	+	0.866025i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$		0			0
$886$	0.366025	+	1.36603i	0.366025	+	1.36603i
$887$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$887$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$888$		0			0
$889$	1.73205	−	1.00000i	1.73205	−	1.00000i
$890$		0			0
$891$		0			0
$892$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$893$	1.36603	−	0.366025i	1.36603	−	0.366025i
$894$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$895$		0			0
$896$	0.866025	+	0.500000i	0.866025	+	0.500000i
$897$		0			0
$898$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$899$		0			0
$900$		0			0
$901$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$902$		0			0
$903$	2.00000			2.00000
$904$			1.00000i			1.00000i
$905$		0			0
$906$	2.73205	−	0.732051i	2.73205	−	0.732051i
$907$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$907$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$	1.00000	+	1.00000i	1.00000	+	1.00000i
$910$		0			0
$911$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$911$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$912$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.366025	+	1.36603i	0.366025	+	1.36603i
$918$		0			0
$919$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$919$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$927$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$932$		0			0
$933$	1.36603	+	0.366025i	1.36603	+	0.366025i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$937$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$938$		0			0
$939$	1.00000	+	1.00000i	1.00000	+	1.00000i
$940$		0			0
$941$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$941$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	0.866025	−	0.500000i	0.866025	−	0.500000i
$944$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$945$		0			0
$946$		0			0
$947$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$947$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$948$	1.36603	−	0.366025i	1.36603	−	0.366025i
$949$		0			0
$950$		0			0
$951$	2.00000			2.00000
$952$		−	1.00000i		−	1.00000i
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$	1.36603	+	0.366025i	1.36603	+	0.366025i
$955$		0			0
$956$	0.866025	+	0.500000i	0.866025	+	0.500000i
$957$		0			0
$958$	1.00000			1.00000
$959$		−	1.00000i		−	1.00000i
$960$		0			0
$961$		0			0
$962$		0			0
$963$	0.366025	+	1.36603i	0.366025	+	1.36603i
$964$		0			0
$965$		0			0
$966$	1.36603	−	0.366025i	1.36603	−	0.366025i
$967$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$967$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$968$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$969$	1.73205	+	1.00000i	1.73205	+	1.00000i
$970$		0			0
$971$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$971$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$972$	1.00000	−	1.00000i	1.00000	−	1.00000i
$973$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$974$		−	1.00000i		−	1.00000i
$975$		0			0
$976$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$977$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$977$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.36603	+	0.366025i	1.36603	+	0.366025i
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$	0.366025	+	1.36603i	0.366025	+	1.36603i
$985$		0			0
$986$		0			0
$987$	0.366025	−	1.36603i	0.366025	−	1.36603i
$988$		0			0
$989$	0.366025	−	1.36603i	0.366025	−	1.36603i
$990$		0			0
$991$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$991$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$992$	0.500000	+	0.866025i	0.500000	+	0.866025i
$993$	−2.00000			−2.00000
$994$	0.866025	+	0.500000i	0.866025	+	0.500000i
$995$		0			0
$996$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$997$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$997$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2800.1.dc.c.851.1	yes	4
5.2	odd	4		2800.1.di.a.1299.1		4
5.3	odd	4		2800.1.di.d.1299.1		4
5.4	even	2		2800.1.dc.b.851.1	yes	4
7.2	even	3	inner	2800.1.dc.c.51.1	yes	4
16.11	odd	4	inner	2800.1.dc.c.2251.1	yes	4
35.2	odd	12		2800.1.di.a.499.1		4
35.9	even	6		2800.1.dc.b.51.1	✓	4
35.23	odd	12		2800.1.di.d.499.1		4
80.27	even	4		2800.1.di.d.2699.1		4
80.43	even	4		2800.1.di.a.2699.1		4
80.59	odd	4		2800.1.dc.b.2251.1	yes	4
112.107	odd	12	inner	2800.1.dc.c.1451.1	yes	4
560.107	even	12		2800.1.di.d.1899.1		4
560.219	odd	12		2800.1.dc.b.1451.1	yes	4
560.443	even	12		2800.1.di.a.1899.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2800.1.dc.b.51.1	✓	4	35.9	even	6
2800.1.dc.b.851.1	yes	4	5.4	even	2
2800.1.dc.b.1451.1	yes	4	560.219	odd	12
2800.1.dc.b.2251.1	yes	4	80.59	odd	4
2800.1.dc.c.51.1	yes	4	7.2	even	3	inner
2800.1.dc.c.851.1	yes	4	1.1	even	1	trivial
2800.1.dc.c.1451.1	yes	4	112.107	odd	12	inner
2800.1.dc.c.2251.1	yes	4	16.11	odd	4	inner
2800.1.di.a.499.1		4	35.2	odd	12
2800.1.di.a.1299.1		4	5.2	odd	4
2800.1.di.a.1899.1		4	560.443	even	12
2800.1.di.a.2699.1		4	80.43	even	4
2800.1.di.d.499.1		4	35.23	odd	12
2800.1.di.d.1299.1		4	5.3	odd	4
2800.1.di.d.1899.1		4	560.107	even	12
2800.1.di.d.2699.1		4	80.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2800.dc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.366025 - 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.00000i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.366025 - 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 1.00000i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +(-1.36603 - 0.366025i) q^{12} +(-0.866025 - 0.500000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(0.500000 - 0.866025i) q^{18} +(1.36603 + 0.366025i) q^{19} +(1.00000 - 1.00000i) q^{21} +(-0.500000 - 0.866025i) q^{23} +(1.36603 - 0.366025i) q^{24} +1.00000 q^{28} +(0.866025 + 0.500000i) q^{31} +(0.866025 + 0.500000i) q^{32} -1.00000i q^{34} +1.00000i q^{36} +(-1.36603 + 0.366025i) q^{38} +1.00000i q^{41} +(-0.366025 + 1.36603i) q^{42} +(1.00000 + 1.00000i) q^{43} +(0.866025 + 0.500000i) q^{46} +(0.866025 - 0.500000i) q^{47} +(-1.00000 + 1.00000i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(1.36603 + 0.366025i) q^{51} +(0.366025 + 1.36603i) q^{53} +(-0.866025 + 0.500000i) q^{56} -2.00000i q^{57} +(1.36603 - 0.366025i) q^{59} +(0.366025 - 1.36603i) q^{61} -1.00000 q^{62} +(-0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(0.500000 + 0.866025i) q^{68} +(-1.00000 + 1.00000i) q^{69} -1.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.00000i) q^{76} +(-0.866025 + 0.500000i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} +(1.00000 - 1.00000i) q^{83} +(-0.366025 - 1.36603i) q^{84} +(-1.36603 - 0.366025i) q^{86} +(-0.866025 + 0.500000i) q^{89} -1.00000 q^{92} +(0.366025 - 1.36603i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(0.366025 - 1.36603i) q^{96} +1.00000 q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7	\( 4 q + 2 q^{3} + 2 q^{4} + 4 q^{6} + 2 q^{7} - 2 q^{12} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 2 q^{19} + 4 q^{21} - 2 q^{23} + 2 q^{24} + 4 q^{28} - 2 q^{38} + 2 q^{42} + 4 q^{43} - 4 q^{48} - 2 q^{49} + 2 q^{51} - 2 q^{53} + 2 q^{59} - 2 q^{61} - 4 q^{62} - 4 q^{64} + 2 q^{68} - 4 q^{69} - 4 q^{71} - 2 q^{72} + 4 q^{76} - 2 q^{81} - 2 q^{82} + 4 q^{83} + 2 q^{84} - 2 q^{86} - 4 q^{92} - 2 q^{93} - 2 q^{94} - 2 q^{96} + 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 4 * q^6 + 2 * q^7 - 2 * q^12 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 2 * q^19 + 4 * q^21 - 2 * q^23 + 2 * q^24 + 4 * q^28 - 2 * q^38 + 2 * q^42 + 4 * q^43 - 4 * q^48 - 2 * q^49 + 2 * q^51 - 2 * q^53 + 2 * q^59 - 2 * q^61 - 4 * q^62 - 4 * q^64 + 2 * q^68 - 4 * q^69 - 4 * q^71 - 2 * q^72 + 4 * q^76 - 2 * q^81 - 2 * q^82 + 4 * q^83 + 2 * q^84 - 2 * q^86 - 4 * q^92 - 2 * q^93 - 2 * q^94 - 2 * q^96 + 4 * q^97

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