LMFDB - Embedded newform 840.1.dh.a.437.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,1,Mod(173,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 6, 9, 10]))

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

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

chi := DirichletCharacter("840.173");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	840.dh (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.419214610612$
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:	$D_{12}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{12} - \cdots)$

Embedding invariants

Embedding label			437.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	840.437
Dual form			840.1.dh.a.173.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.258819 - 0.448288i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.707107 - 0.707107i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.258819 - 0.965926i) q^{18} +(-0.965926 + 0.258819i) q^{20} +(-0.965926 - 0.258819i) q^{21} +(-0.366025 - 0.366025i) q^{22} +(0.500000 - 0.866025i) q^{24} -1.00000i q^{25} +(-0.707107 + 0.707107i) q^{27} +(-0.500000 - 0.866025i) q^{28} -1.93185i q^{29} +(0.707107 + 0.707107i) q^{30} +(-0.866025 - 0.500000i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.133975 + 0.500000i) q^{33} +(0.965926 - 0.258819i) q^{35} -1.00000 q^{36} +1.00000i q^{40} +(-0.500000 + 0.866025i) q^{42} +(-0.448288 + 0.258819i) q^{44} +(0.258819 - 0.965926i) q^{45} +(-0.707107 - 0.707107i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(0.448288 + 1.67303i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.133975 - 0.500000i) q^{55} +(-0.965926 + 0.258819i) q^{56} +(-1.86603 - 0.500000i) q^{58} +(-0.965926 + 1.67303i) q^{59} +(0.866025 - 0.500000i) q^{60} +(-0.707107 + 0.707107i) q^{62} +1.00000 q^{63} -1.00000i q^{64} +(0.448288 + 0.258819i) q^{66} -1.00000i q^{70} +(-0.258819 + 0.965926i) q^{72} +(-1.36603 + 0.366025i) q^{73} +(0.258819 + 0.965926i) q^{75} +(0.448288 - 0.258819i) q^{77} +(1.50000 - 0.866025i) q^{79} +(0.965926 + 0.258819i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.22474 + 1.22474i) q^{83} +(0.707107 + 0.707107i) q^{84} +(0.500000 + 1.86603i) q^{87} +(0.133975 + 0.500000i) q^{88} +(-0.866025 - 0.500000i) q^{90} +(0.965926 + 0.258819i) q^{93} +(-0.866025 + 0.500000i) q^{96} +(-1.36603 + 1.36603i) q^{97} +(0.965926 - 0.258819i) q^{98} -0.517638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 4 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{22} + 4 q^{24} - 4 q^{28} - 8 q^{33} - 8 q^{36} - 4 q^{42} + 4 q^{49} + 4 q^{54} - 8 q^{55} - 8 q^{58} + 8 q^{63} - 4 q^{73} + 12 q^{79} + 4 q^{81} + 4 q^{87} + 8 q^{88} - 4 q^{97}+O(q^{100}) $ 8 * q - 4 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^22 + 4 * q^24 - 4 * q^28 - 8 * q^33 - 8 * q^36 - 4 * q^42 + 4 * q^49 + 4 * q^54 - 8 * q^55 - 8 * q^58 + 8 * q^63 - 4 * q^73 + 12 * q^79 + 4 * q^81 + 4 * q^87 + 8 * q^88 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.258819	−	0.965926i
$2$	0.258819	−	0.965926i	0.258819	−	0.965926i
$3$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$3$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$4$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$5$	0.707107	−	0.707107i	0.707107	−	0.707107i
$5$	0.707107	−	0.707107i	0.707107	−	0.707107i
$6$			1.00000i			1.00000i
$7$	0.866025	+	0.500000i	0.866025	+	0.500000i
$7$	0.866025	+	0.500000i	0.866025	+	0.500000i
$8$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$9$	0.866025	−	0.500000i	0.866025	−	0.500000i
$10$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$11$	0.258819	−	0.448288i	0.258819	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$11$	0.258819	−	0.448288i	0.258819	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$12$	0.965926	+	0.258819i	0.965926	+	0.258819i
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$	0.707107	−	0.707107i	0.707107	−	0.707107i
$15$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$16$	0.500000	+	0.866025i	0.500000	+	0.866025i
$17$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$17$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$18$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$21$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$22$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$	0.500000	−	0.866025i	0.500000	−	0.866025i
$25$		−	1.00000i		−	1.00000i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$28$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$29$		−	1.93185i		−	1.93185i	−0.258819	−	0.965926i	$-0.583333\pi$
$29$		−	1.93185i		−	1.93185i	0.258819	−	0.965926i	$-0.416667\pi$
$30$	0.707107	+	0.707107i	0.707107	+	0.707107i
$31$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$31$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$32$	0.965926	−	0.258819i	0.965926	−	0.258819i
$33$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$34$		0			0
$35$	0.965926	−	0.258819i	0.965926	−	0.258819i
$36$	−1.00000			−1.00000
$37$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$37$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$38$		0			0
$39$		0			0
$40$			1.00000i			1.00000i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$45$	0.258819	−	0.965926i	0.258819	−	0.965926i
$46$		0			0
$47$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$47$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$48$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$49$	0.500000	+	0.866025i	0.500000	+	0.866025i
$50$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$51$		0			0
$52$		0			0
$53$	0.448288	+	1.67303i	0.448288	+	1.67303i	0.707107	+	0.707107i	$0.250000\pi$
$53$	0.448288	+	1.67303i	0.448288	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$54$	0.500000	+	0.866025i	0.500000	+	0.866025i
$55$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$56$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$57$		0			0
$58$	−1.86603	−	0.500000i	−1.86603	−	0.500000i
$59$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$59$	−0.965926	+	1.67303i	−0.965926	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$60$	0.866025	−	0.500000i	0.866025	−	0.500000i
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$63$	1.00000			1.00000
$64$		−	1.00000i		−	1.00000i
$65$		0			0
$66$	0.448288	+	0.258819i	0.448288	+	0.258819i
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$		0			0
$69$		0			0
$70$		−	1.00000i		−	1.00000i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$73$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$73$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$	0.258819	+	0.965926i	0.258819	+	0.965926i
$76$		0			0
$77$	0.448288	−	0.258819i	0.448288	−	0.258819i
$78$		0			0
$79$	1.50000	−	0.866025i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$79$	1.50000	−	0.866025i	1.50000	−	0.866025i	1.00000			$0$
$80$	0.965926	+	0.258819i	0.965926	+	0.258819i
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$		0			0
$83$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$83$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$84$	0.707107	+	0.707107i	0.707107	+	0.707107i
$85$		0			0
$86$		0			0
$87$	0.500000	+	1.86603i	0.500000	+	1.86603i
$88$	0.133975	+	0.500000i	0.133975	+	0.500000i
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$91$		0			0
$92$		0			0
$93$	0.965926	+	0.258819i	0.965926	+	0.258819i
$94$		0			0
$95$		0			0
$96$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$97$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$97$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$98$	0.965926	−	0.258819i	0.965926	−	0.258819i
$99$		−	0.517638i		−	0.517638i
$100$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$101$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$101$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$102$		0			0
$103$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$103$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$104$		0			0
$105$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$106$	1.73205			1.73205
$107$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$107$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$108$	0.965926	−	0.258819i	0.965926	−	0.258819i
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$	−0.517638			−0.517638
$111$		0			0
$112$			1.00000i			1.00000i
$113$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$113$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$114$		0			0
$115$		0			0
$116$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$117$		0			0
$118$	1.36603	+	1.36603i	1.36603	+	1.36603i
$119$		0			0
$120$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$121$	0.366025	+	0.633975i	0.366025	+	0.633975i
$122$		0			0
$123$		0			0
$124$	0.500000	+	0.866025i	0.500000	+	0.866025i
$125$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$126$	0.258819	−	0.965926i	0.258819	−	0.965926i
$127$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$127$	−1.36603	−	1.36603i	−1.36603	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$128$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$129$		0			0
$130$		0			0
$131$	0.448288	−	0.258819i	0.448288	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$131$	0.448288	−	0.258819i	0.448288	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$132$	0.366025	−	0.366025i	0.366025	−	0.366025i
$133$		0			0
$134$		0			0
$135$			1.00000i			1.00000i
$136$		0			0
$137$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$137$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.866025	+	0.500000i	0.866025	+	0.500000i
$145$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$146$			1.41421i			1.41421i
$147$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$148$		0			0
$149$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$149$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$150$	1.00000			1.00000
$151$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$151$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$155$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$156$		0			0
$157$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$157$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$158$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$159$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$160$	0.500000	−	0.866025i	0.500000	−	0.866025i
$161$		0			0
$162$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$163$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$163$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$164$		0			0
$165$	0.258819	+	0.448288i	0.258819	+	0.448288i
$166$	1.50000	−	0.866025i	1.50000	−	0.866025i
$167$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$167$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$168$	0.866025	−	0.500000i	0.866025	−	0.500000i
$169$			1.00000i			1.00000i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$173$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$174$	1.93185			1.93185
$175$	0.500000	−	0.866025i	0.500000	−	0.866025i
$176$	0.517638			0.517638
$177$	0.500000	−	1.86603i	0.500000	−	1.86603i
$178$		0			0
$179$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$179$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$180$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	0.500000	−	0.866025i	0.500000	−	0.866025i
$187$		0			0
$188$		0			0
$189$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$	0.258819	+	0.965926i	0.258819	+	0.965926i
$193$	0.500000	+	1.86603i	0.500000	+	1.86603i	0.500000	+	0.866025i	$0.333333\pi$
$193$	0.500000	+	1.86603i	0.500000	+	1.86603i			1.00000i	$0.5\pi$
$194$	0.965926	+	1.67303i	0.965926	+	1.67303i
$195$		0			0
$196$		−	1.00000i		−	1.00000i
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$	−0.500000	−	0.133975i	−0.500000	−	0.133975i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	0.707107	+	0.707107i	0.707107	+	0.707107i
$201$		0			0
$202$	1.00000	−	1.00000i	1.00000	−	1.00000i
$203$	0.965926	−	1.67303i	0.965926	−	1.67303i
$204$		0			0
$205$		0			0
$206$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	0.258819	+	0.965926i	0.258819	+	0.965926i
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$	0.448288	−	1.67303i	0.448288	−	1.67303i
$213$		0			0
$214$	0.866025	+	0.500000i	0.866025	+	0.500000i
$215$		0			0
$216$		−	1.00000i		−	1.00000i
$217$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$218$		0			0
$219$	1.22474	−	0.707107i	1.22474	−	0.707107i
$220$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$221$		0			0
$222$		0			0
$223$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$223$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$224$	0.965926	+	0.258819i	0.965926	+	0.258819i
$225$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$226$		0			0
$227$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$227$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$232$	1.36603	+	1.36603i	1.36603	+	1.36603i
$233$		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
$236$	1.67303	−	0.965926i	1.67303	−	0.965926i
$237$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−1.00000			−1.00000
$241$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$241$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$242$	0.707107	−	0.189469i	0.707107	−	0.189469i
$243$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$244$		0			0
$245$	0.965926	+	0.258819i	0.965926	+	0.258819i
$246$		0			0
$247$		0			0
$248$	0.965926	−	0.258819i	0.965926	−	0.258819i
$249$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$250$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$251$		−	0.517638i		−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$251$		−	0.517638i		−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$252$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$253$		0			0
$254$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$257$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.965926	−	1.67303i	−0.965926	−	1.67303i
$262$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$263$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$263$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$264$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$265$	1.50000	+	0.866025i	1.50000	+	0.866025i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	0.258819	−	0.448288i	0.258819	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$269$	0.258819	−	0.448288i	0.258819	−	0.448288i	0.965926	+	0.258819i	$0.0833333\pi$
$270$	0.965926	+	0.258819i	0.965926	+	0.258819i
$271$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$271$	−1.50000	+	0.866025i	−1.50000	+	0.866025i	−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$276$		0			0
$277$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$277$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$278$		0			0
$279$	−1.00000			−1.00000
$280$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$283$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.707107	−	0.707107i	0.707107	−	0.707107i
$289$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$290$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$291$	0.965926	−	1.67303i	0.965926	−	1.67303i
$292$	1.36603	+	0.366025i	1.36603	+	0.366025i
$293$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$293$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$294$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$295$	0.500000	+	1.86603i	0.500000	+	1.86603i
$296$		0			0
$297$	0.133975	+	0.500000i	0.133975	+	0.500000i
$298$	0.366025	+	1.36603i	0.366025	+	1.36603i
$299$		0			0
$300$	0.258819	−	0.965926i	0.258819	−	0.965926i
$301$		0			0
$302$	0.707107	+	0.707107i	0.707107	+	0.707107i
$303$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	−0.517638			−0.517638
$309$			1.41421i			1.41421i
$310$			1.00000i			1.00000i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	0.500000	−	1.86603i	0.500000	−	1.86603i		−	1.00000i	$-0.5\pi$
$313$	0.500000	−	1.86603i	0.500000	−	1.86603i	0.500000	−	0.866025i	$-0.333333\pi$
$314$		0			0
$315$	0.707107	−	0.707107i	0.707107	−	0.707107i
$316$	−1.73205			−1.73205
$317$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$317$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$318$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$319$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$320$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$321$		−	1.00000i		−	1.00000i
$322$		0			0
$323$		0			0
$324$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$	0.500000	−	0.133975i	0.500000	−	0.133975i
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	−0.448288	−	1.67303i	−0.448288	−	1.67303i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$337$	0.366025	+	0.366025i	0.366025	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$337$	0.366025	+	0.366025i	0.366025	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$338$	0.965926	+	0.258819i	0.965926	+	0.258819i
$339$		0			0
$340$		0			0
$341$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$342$		0			0
$343$			1.00000i			1.00000i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$	0.500000	−	1.86603i	0.500000	−	1.86603i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$351$		0			0
$352$	0.133975	−	0.500000i	0.133975	−	0.500000i
$353$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$353$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$354$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	0.500000	+	0.866025i	0.500000	+	0.866025i
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	−0.517638	−	0.517638i	−0.517638	−	0.517638i
$364$		0			0
$365$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$366$		0			0
$367$	−0.133975	−	0.500000i	−0.133975	−	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$367$	−0.133975	−	0.500000i	−0.133975	−	0.500000i	−1.00000			$\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$372$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$373$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$373$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$374$		0			0
$375$	0.866025	+	0.500000i	0.866025	+	0.500000i
$376$		0			0
$377$		0			0
$378$			1.00000i			1.00000i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$	1.67303	+	0.965926i	1.67303	+	0.965926i
$382$		0			0
$383$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$383$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$384$	1.00000			1.00000
$385$	0.133975	−	0.500000i	0.133975	−	0.500000i
$386$	1.93185			1.93185
$387$		0			0
$388$	1.86603	−	0.500000i	1.86603	−	0.500000i
$389$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$389$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$390$		0			0
$391$		0			0
$392$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$393$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$394$		0			0
$395$	0.448288	−	1.67303i	0.448288	−	1.67303i
$396$	−0.258819	+	0.448288i	−0.258819	+	0.448288i
$397$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$397$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$398$		0			0
$399$		0			0
$400$	0.866025	−	0.500000i	0.866025	−	0.500000i
$401$		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
$404$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$405$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$406$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$407$		0			0
$408$		0			0
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$413$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$414$		0			0
$415$	1.73205			1.73205
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$419$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$420$	1.00000			1.00000
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$		0			0
$423$		0			0
$424$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.707107	−	0.707107i	0.707107	−	0.707107i
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$433$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$433$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$434$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$435$	1.67303	+	0.965926i	1.67303	+	0.965926i
$436$		0			0
$437$		0			0
$438$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$439$	0.866025	+	1.50000i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$439$	0.866025	+	1.50000i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$440$	0.448288	+	0.258819i	0.448288	+	0.258819i
$441$	0.866025	+	0.500000i	0.866025	+	0.500000i
$442$		0			0
$443$	1.67303	+	0.448288i	1.67303	+	0.448288i	0.965926	−	0.258819i	$-0.0833333\pi$
$443$	1.67303	+	0.448288i	1.67303	+	0.448288i	0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$		0			0
$446$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$447$	1.00000	−	1.00000i	1.00000	−	1.00000i
$448$	0.500000	−	0.866025i	0.500000	−	0.866025i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$451$		0			0
$452$		0			0
$453$	0.258819	−	0.965926i	0.258819	−	0.965926i
$454$	−1.00000			−1.00000
$455$		0			0
$456$		0			0
$457$	0.133975	−	0.500000i	0.133975	−	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$457$	0.133975	−	0.500000i	0.133975	−	0.500000i	1.00000			$0$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$461$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$462$	0.258819	+	0.448288i	0.258819	+	0.448288i
$463$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$463$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$464$	1.67303	−	0.965926i	1.67303	−	0.965926i
$465$	0.866025	−	0.500000i	0.866025	−	0.500000i
$466$		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
$472$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$473$		0			0
$474$	0.866025	+	1.50000i	0.866025	+	1.50000i
$475$		0			0
$476$		0			0
$477$	1.22474	+	1.22474i	1.22474	+	1.22474i
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$481$		0			0
$482$	0.707107	−	0.707107i	0.707107	−	0.707107i
$483$		0			0
$484$		−	0.732051i		−	0.732051i
$485$			1.93185i			1.93185i
$486$	0.866025	+	0.500000i	0.866025	+	0.500000i
$487$	−0.500000	+	0.133975i	−0.500000	+	0.133975i	−0.500000	−	0.866025i	$-0.666667\pi$
$487$	−0.500000	+	0.133975i	−0.500000	+	0.133975i			1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$	0.500000	−	0.866025i	0.500000	−	0.866025i
$491$	−1.93185			−1.93185			−0.965926	−	0.258819i	$-0.916667\pi$
$491$	−1.93185			−1.93185			−0.965926	+	0.258819i	$0.916667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$496$		−	1.00000i		−	1.00000i
$497$		0			0
$498$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	0.258819	+	0.965926i	0.258819	+	0.965926i
$501$		0			0
$502$	−0.500000	−	0.133975i	−0.500000	−	0.133975i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$505$	1.36603	−	0.366025i	1.36603	−	0.366025i
$506$		0			0
$507$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$508$	0.500000	+	1.86603i	0.500000	+	1.86603i
$509$	0.258819	+	0.448288i	0.258819	+	0.448288i	0.965926	−	0.258819i	$-0.0833333\pi$
$509$	0.258819	+	0.448288i	0.258819	+	0.448288i	−0.707107	+	0.707107i	$0.750000\pi$
$510$		0			0
$511$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$512$	0.707107	+	0.707107i	0.707107	+	0.707107i
$513$		0			0
$514$		0			0
$515$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$523$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$523$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$524$	−0.517638			−0.517638
$525$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$526$		0			0
$527$		0			0
$528$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$529$	0.866025	+	0.500000i	0.866025	+	0.500000i
$530$	1.22474	−	1.22474i	1.22474	−	1.22474i
$531$			1.93185i			1.93185i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.500000	+	0.866025i	0.500000	+	0.866025i
$536$		0			0
$537$	1.36603	+	0.366025i	1.36603	+	0.366025i
$538$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$539$	0.517638			0.517638
$540$	0.500000	−	0.866025i	0.500000	−	0.866025i
$541$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$541$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$542$	0.448288	+	1.67303i	0.448288	+	1.67303i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$		0			0
$549$		0			0
$550$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$551$		0			0
$552$		0			0
$553$	1.73205			1.73205
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.67303	+	0.448288i	−1.67303	+	0.448288i	−0.965926	−	0.258819i	$-0.916667\pi$
$557$	−1.67303	+	0.448288i	−1.67303	+	0.448288i	−0.707107	+	0.707107i	$0.750000\pi$
$558$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$559$		0			0
$560$	0.707107	+	0.707107i	0.707107	+	0.707107i
$561$		0			0
$562$		0			0
$563$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$563$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.866025	−	0.500000i	0.866025	−	0.500000i
$568$		0			0
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$577$	−0.500000	−	1.86603i	−0.500000	−	1.86603i	−0.500000	−	0.866025i	$-0.666667\pi$
$577$	−0.500000	−	1.86603i	−0.500000	−	1.86603i		−	1.00000i	$-0.5\pi$
$578$	0.258819	+	0.965926i	0.258819	+	0.965926i
$579$	−0.965926	−	1.67303i	−0.965926	−	1.67303i
$580$	0.500000	+	1.86603i	0.500000	+	1.86603i
$581$	0.448288	+	1.67303i	0.448288	+	1.67303i
$582$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$583$	0.866025	+	0.232051i	0.866025	+	0.232051i
$584$	0.707107	−	1.22474i	0.707107	−	1.22474i
$585$		0			0
$586$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$587$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$587$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$588$	0.258819	+	0.965926i	0.258819	+	0.965926i
$589$		0			0
$590$	1.93185			1.93185
$591$		0			0
$592$		0			0
$593$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$593$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$594$	0.517638			0.517638
$595$		0			0
$596$	1.41421			1.41421
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$601$		−	1.73205i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$		−	1.73205i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$602$		0			0
$603$		0			0
$604$	0.866025	−	0.500000i	0.866025	−	0.500000i
$605$	0.707107	+	0.189469i	0.707107	+	0.189469i
$606$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$607$	1.86603	+	0.500000i	1.86603	+	0.500000i	1.00000			$0$
$607$	1.86603	+	0.500000i	1.86603	+	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$608$		0			0
$609$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$613$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$614$		0			0
$615$		0			0
$616$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$617$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$617$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$618$	1.36603	+	0.366025i	1.36603	+	0.366025i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$	0.965926	+	0.258819i	0.965926	+	0.258819i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−1.00000			−1.00000
$626$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$631$	1.73205			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$631$	1.73205			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$632$	−0.448288	+	1.67303i	−0.448288	+	1.67303i
$633$		0			0
$634$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$635$	−1.93185			−1.93185
$636$			1.73205i			1.73205i
$637$		0			0
$638$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$643$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$643$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$647$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$648$	0.258819	+	0.965926i	0.258819	+	0.965926i
$649$	0.500000	+	0.866025i	0.500000	+	0.866025i
$650$		0			0
$651$	0.707107	+	0.707107i	0.707107	+	0.707107i
$652$		0			0
$653$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$653$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$654$		0			0
$655$	0.133975	−	0.500000i	0.133975	−	0.500000i
$656$		0			0
$657$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$658$		0			0
$659$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$659$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$660$		−	0.517638i		−	0.517638i
$661$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$661$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$662$		0			0
$663$		0			0
$664$	−1.73205			−1.73205
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	0.448288	+	0.258819i	0.448288	+	0.258819i
$670$		0			0
$671$		0			0
$672$	−1.00000			−1.00000
$673$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$673$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$674$	0.448288	−	0.258819i	0.448288	−	0.258819i
$675$	0.707107	+	0.707107i	0.707107	+	0.707107i
$676$	0.500000	−	0.866025i	0.500000	−	0.866025i
$677$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$677$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.965926	+	0.258819i	$0.916667\pi$
$678$		0			0
$679$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$680$		0			0
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$	0.133975	+	0.500000i	0.133975	+	0.500000i
$683$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$683$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$684$		0			0
$685$		0			0
$686$	0.965926	+	0.258819i	0.965926	+	0.258819i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$691$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$692$		0			0
$693$	0.258819	−	0.448288i	0.258819	−	0.448288i
$694$		0			0
$695$		0			0
$696$	−1.67303	−	0.965926i	−1.67303	−	0.965926i
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$701$	−0.517638			−0.517638			−0.258819	−	0.965926i	$-0.583333\pi$
$701$	−0.517638			−0.517638			−0.258819	+	0.965926i	$0.583333\pi$
$702$		0			0
$703$		0			0
$704$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$705$		0			0
$706$		0			0
$707$	0.707107	+	1.22474i	0.707107	+	1.22474i
$708$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$709$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$709$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$710$		0			0
$711$	0.866025	−	1.50000i	0.866025	−	1.50000i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.707107	+	1.22474i	0.707107	+	1.22474i
$717$		0			0
$718$		0			0
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	0.965926	−	0.258819i	0.965926	−	0.258819i
$721$	1.00000	−	1.00000i	1.00000	−	1.00000i
$722$	0.707107	+	0.707107i	0.707107	+	0.707107i
$723$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$724$		0			0
$725$	−1.93185			−1.93185
$726$	−0.633975	+	0.366025i	−0.633975	+	0.366025i
$727$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$727$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$		−	1.00000i		−	1.00000i
$730$	1.00000	+	1.00000i	1.00000	+	1.00000i
$731$		0			0
$732$		0			0
$733$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$733$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$734$	−0.517638			−0.517638
$735$	−1.00000			−1.00000
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$739$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$740$		0			0
$741$		0			0
$742$	1.50000	+	0.866025i	1.50000	+	0.866025i
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$745$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$746$		0			0
$747$	1.67303	+	0.448288i	1.67303	+	0.448288i
$748$		0			0
$749$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$750$	0.707107	−	0.707107i	0.707107	−	0.707107i
$751$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$751$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$752$		0			0
$753$	0.133975	+	0.500000i	0.133975	+	0.500000i
$754$		0			0
$755$	0.258819	+	0.965926i	0.258819	+	0.965926i
$756$	0.965926	+	0.258819i	0.965926	+	0.258819i
$757$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$757$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$	1.36603	−	1.36603i	1.36603	−	1.36603i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.258819	−	0.965926i	0.258819	−	0.965926i
$769$	1.73205			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$769$	1.73205			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$770$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$771$		0			0
$772$	0.500000	−	1.86603i	0.500000	−	1.86603i
$773$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$773$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$774$		0			0
$775$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$776$		−	1.93185i		−	1.93185i
$777$		0			0
$778$	1.00000	−	1.00000i	1.00000	−	1.00000i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	1.36603	+	1.36603i	1.36603	+	1.36603i
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$		0			0
$786$	0.258819	+	0.448288i	0.258819	+	0.448288i
$787$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$787$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$788$		0			0
$789$		0			0
$790$	−1.50000	−	0.866025i	−1.50000	−	0.866025i
$791$		0			0
$792$	0.366025	+	0.366025i	0.366025	+	0.366025i
$793$		0			0
$794$		0			0
$795$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$796$		0			0
$797$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$797$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$798$		0			0
$799$		0			0
$800$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$801$		0			0
$802$		0			0
$803$	−0.189469	+	0.707107i	−0.189469	+	0.707107i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$808$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$	−1.00000			−1.00000
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$813$	1.22474	−	1.22474i	1.22474	−	1.22474i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.707107	+	0.707107i	0.707107	+	0.707107i
$819$		0			0
$820$		0			0
$821$	−0.258819	−	0.448288i	−0.258819	−	0.448288i	0.707107	−	0.707107i	$-0.250000\pi$
$821$	−0.258819	−	0.448288i	−0.258819	−	0.448288i	−0.965926	+	0.258819i	$0.916667\pi$
$822$		0			0
$823$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$824$	0.707107	+	1.22474i	0.707107	+	1.22474i
$825$	0.500000	+	0.133975i	0.500000	+	0.133975i
$826$	0.500000	+	1.86603i	0.500000	+	1.86603i
$827$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$827$	1.22474	+	1.22474i	1.22474	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$	0.448288	−	1.67303i	0.448288	−	1.67303i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.965926	−	0.258819i	0.965926	−	0.258819i
$838$	0.366025	−	1.36603i	0.366025	−	1.36603i
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$	0.258819	−	0.965926i	0.258819	−	0.965926i
$841$	−2.73205			−2.73205
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.707107	+	0.707107i	0.707107	+	0.707107i
$846$		0			0
$847$			0.732051i			0.732051i
$848$	−1.22474	+	1.22474i	−1.22474	+	1.22474i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$		0			0
$855$		0			0
$856$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$857$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$857$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$863$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$864$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$865$		0			0
$866$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$867$	0.707107	−	0.707107i	0.707107	−	0.707107i
$868$			1.00000i			1.00000i
$869$		−	0.896575i		−	0.896575i
$870$	1.36603	−	1.36603i	1.36603	−	1.36603i
$871$		0			0
$872$		0			0
$873$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$874$		0			0
$875$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$876$	−1.41421			−1.41421
$877$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$877$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$878$	1.67303	−	0.448288i	1.67303	−	0.448288i
$879$	0.866025	+	0.500000i	0.866025	+	0.500000i
$880$	0.366025	−	0.366025i	0.366025	−	0.366025i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	0.707107	−	0.707107i	0.707107	−	0.707107i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$		0			0
$885$	−0.965926	−	1.67303i	−0.965926	−	1.67303i
$886$	0.866025	−	1.50000i	0.866025	−	1.50000i
$887$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$887$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$888$		0			0
$889$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$890$		0			0
$891$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$892$	0.133975	+	0.500000i	0.133975	+	0.500000i
$893$		0			0
$894$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$895$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$896$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$897$		0			0
$898$		0			0
$899$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$900$			1.00000i			1.00000i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$907$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$907$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$908$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$909$	1.41421			1.41421
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	0.866025	−	0.232051i	0.866025	−	0.232051i
$914$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$915$		0			0
$916$		0			0
$917$	0.517638			0.517638
$918$		0			0
$919$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$919$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$920$		0			0
$921$		0			0
$922$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$923$		0			0
$924$	0.500000	−	0.133975i	0.500000	−	0.133975i
$925$		0			0
$926$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$927$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$928$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.366025	−	0.366025i	0.366025	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$937$	0.366025	−	0.366025i	0.366025	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$938$		0			0
$939$			1.93185i			1.93185i
$940$		0			0
$941$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$941$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$942$		0			0
$943$		0			0
$944$	−1.93185			−1.93185
$945$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$946$		0			0
$947$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$947$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$948$	1.67303	−	0.448288i	1.67303	−	0.448288i
$949$		0			0
$950$		0			0
$951$			1.00000i			1.00000i
$952$		0			0
$953$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$953$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$954$	1.50000	−	0.866025i	1.50000	−	0.866025i
$955$		0			0
$956$		0			0
$957$	0.965926	+	0.258819i	0.965926	+	0.258819i
$958$		0			0
$959$		0			0
$960$	0.866025	+	0.500000i	0.866025	+	0.500000i
$961$		0			0
$962$		0			0
$963$	0.258819	+	0.965926i	0.258819	+	0.965926i
$964$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$965$	1.67303	+	0.965926i	1.67303	+	0.965926i
$966$		0			0
$967$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	−0.366025	−	0.366025i	−0.366025	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$968$	−0.707107	−	0.189469i	−0.707107	−	0.189469i
$969$		0			0
$970$	1.86603	+	0.500000i	1.86603	+	0.500000i
$971$	−1.67303	+	0.965926i	−1.67303	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$971$	−1.67303	+	0.965926i	−1.67303	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$972$	0.707107	−	0.707107i	0.707107	−	0.707107i
$973$		0			0
$974$			0.517638i			0.517638i
$975$		0			0
$976$		0			0
$977$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$977$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$978$		0			0
$979$		0			0
$980$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$981$		0			0
$982$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$983$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$983$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$991$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$992$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.866025	+	1.50000i	0.866025	+	1.50000i
$997$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$997$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.1.dh.a.437.2	yes	8
3.2	odd	2	inner	840.1.dh.a.437.1	yes	8
4.3	odd	2		3360.1.ft.b.17.2		8
5.3	odd	4		840.1.dh.b.773.1	yes	8
7.5	odd	6		840.1.dh.b.677.1	yes	8
8.3	odd	2		3360.1.ft.b.17.1		8
8.5	even	2	inner	840.1.dh.a.437.1	yes	8
12.11	even	2		3360.1.ft.b.17.1		8
15.8	even	4		840.1.dh.b.773.2	yes	8
20.3	even	4		3360.1.ft.a.2033.2		8
21.5	even	6		840.1.dh.b.677.2	yes	8
24.5	odd	2	CM	840.1.dh.a.437.2	yes	8
24.11	even	2		3360.1.ft.b.17.2		8
28.19	even	6		3360.1.ft.a.1937.2		8
35.33	even	12	inner	840.1.dh.a.173.2	yes	8
40.3	even	4		3360.1.ft.a.2033.1		8
40.13	odd	4		840.1.dh.b.773.2	yes	8
56.5	odd	6		840.1.dh.b.677.2	yes	8
56.19	even	6		3360.1.ft.a.1937.1		8
60.23	odd	4		3360.1.ft.a.2033.1		8
84.47	odd	6		3360.1.ft.a.1937.1		8
105.68	odd	12	inner	840.1.dh.a.173.1	✓	8
120.53	even	4		840.1.dh.b.773.1	yes	8
120.83	odd	4		3360.1.ft.a.2033.2		8
140.103	odd	12		3360.1.ft.b.593.2		8
168.5	even	6		840.1.dh.b.677.1	yes	8
168.131	odd	6		3360.1.ft.a.1937.2		8
280.173	even	12	inner	840.1.dh.a.173.1	✓	8
280.243	odd	12		3360.1.ft.b.593.1		8
420.383	even	12		3360.1.ft.b.593.1		8
840.173	odd	12	inner	840.1.dh.a.173.2	yes	8
840.803	even	12		3360.1.ft.b.593.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.1.dh.a.173.1	✓	8	105.68	odd	12	inner
840.1.dh.a.173.1	✓	8	280.173	even	12	inner
840.1.dh.a.173.2	yes	8	35.33	even	12	inner
840.1.dh.a.173.2	yes	8	840.173	odd	12	inner
840.1.dh.a.437.1	yes	8	3.2	odd	2	inner
840.1.dh.a.437.1	yes	8	8.5	even	2	inner
840.1.dh.a.437.2	yes	8	1.1	even	1	trivial
840.1.dh.a.437.2	yes	8	24.5	odd	2	CM
840.1.dh.b.677.1	yes	8	7.5	odd	6
840.1.dh.b.677.1	yes	8	168.5	even	6
840.1.dh.b.677.2	yes	8	21.5	even	6
840.1.dh.b.677.2	yes	8	56.5	odd	6
840.1.dh.b.773.1	yes	8	5.3	odd	4
840.1.dh.b.773.1	yes	8	120.53	even	4
840.1.dh.b.773.2	yes	8	15.8	even	4
840.1.dh.b.773.2	yes	8	40.13	odd	4
3360.1.ft.a.1937.1		8	56.19	even	6
3360.1.ft.a.1937.1		8	84.47	odd	6
3360.1.ft.a.1937.2		8	28.19	even	6
3360.1.ft.a.1937.2		8	168.131	odd	6
3360.1.ft.a.2033.1		8	40.3	even	4
3360.1.ft.a.2033.1		8	60.23	odd	4
3360.1.ft.a.2033.2		8	20.3	even	4
3360.1.ft.a.2033.2		8	120.83	odd	4
3360.1.ft.b.17.1		8	8.3	odd	2
3360.1.ft.b.17.1		8	12.11	even	2
3360.1.ft.b.17.2		8	4.3	odd	2
3360.1.ft.b.17.2		8	24.11	even	2
3360.1.ft.b.593.1		8	280.243	odd	12
3360.1.ft.b.593.1		8	420.383	even	12
3360.1.ft.b.593.2		8	140.103	odd	12
3360.1.ft.b.593.2		8	840.803	even	12

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	840.dh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +1.00000i q^{6} +(0.866025 + 0.500000i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.258819 - 0.448288i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.707107 - 0.707107i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.258819 - 0.965926i) q^{18} +(-0.965926 + 0.258819i) q^{20} +(-0.965926 - 0.258819i) q^{21} +(-0.366025 - 0.366025i) q^{22} +(0.500000 - 0.866025i) q^{24} -1.00000i q^{25} +(-0.707107 + 0.707107i) q^{27} +(-0.500000 - 0.866025i) q^{28} -1.93185i q^{29} +(0.707107 + 0.707107i) q^{30} +(-0.866025 - 0.500000i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.133975 + 0.500000i) q^{33} +(0.965926 - 0.258819i) q^{35} -1.00000 q^{36} +1.00000i q^{40} +(-0.500000 + 0.866025i) q^{42} +(-0.448288 + 0.258819i) q^{44} +(0.258819 - 0.965926i) q^{45} +(-0.707107 - 0.707107i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(0.448288 + 1.67303i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.133975 - 0.500000i) q^{55} +(-0.965926 + 0.258819i) q^{56} +(-1.86603 - 0.500000i) q^{58} +(-0.965926 + 1.67303i) q^{59} +(0.866025 - 0.500000i) q^{60} +(-0.707107 + 0.707107i) q^{62} +1.00000 q^{63} -1.00000i q^{64} +(0.448288 + 0.258819i) q^{66} -1.00000i q^{70} +(-0.258819 + 0.965926i) q^{72} +(-1.36603 + 0.366025i) q^{73} +(0.258819 + 0.965926i) q^{75} +(0.448288 - 0.258819i) q^{77} +(1.50000 - 0.866025i) q^{79} +(0.965926 + 0.258819i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.22474 + 1.22474i) q^{83} +(0.707107 + 0.707107i) q^{84} +(0.500000 + 1.86603i) q^{87} +(0.133975 + 0.500000i) q^{88} +(-0.866025 - 0.500000i) q^{90} +(0.965926 + 0.258819i) q^{93} +(-0.866025 + 0.500000i) q^{96} +(-1.36603 + 1.36603i) q^{97} +(0.965926 - 0.258819i) q^{98} -0.517638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 4 q^{10} - 4 q^{15} + 4 q^{16} + 4 q^{22} + 4 q^{24} - 4 q^{28} - 8 q^{33} - 8 q^{36} - 4 q^{42} + 4 q^{49} + 4 q^{54} - 8 q^{55} - 8 q^{58} + 8 q^{63} - 4 q^{73} + 12 q^{79} + 4 q^{81} + 4 q^{87} + 8 q^{88} - 4 q^{97}+O(q^{100}) \) 8 * q - 4 * q^10 - 4 * q^15 + 4 * q^16 + 4 * q^22 + 4 * q^24 - 4 * q^28 - 8 * q^33 - 8 * q^36 - 4 * q^42 + 4 * q^49 + 4 * q^54 - 8 * q^55 - 8 * q^58 + 8 * q^63 - 4 * q^73 + 12 * q^79 + 4 * q^81 + 4 * q^87 + 8 * q^88 - 4 * q^97

Introduction

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