LMFDB - Embedded newform 2793.1.bf.c.638.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,1,Mod(197,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("2793.197");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2793.bf (of order $6$, degree $2$, 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:	$1.39388858028$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	no (minimal twist has level 399)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.159201.1

Embedding invariants

Embedding label			638.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2793.638
Dual form			2793.1.bf.c.197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.00000i q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{18} +(0.500000 + 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +1.00000i q^{26} -1.00000i q^{27} +(0.866025 - 0.500000i) q^{29} -1.00000i q^{30} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{33} -1.00000 q^{37} -1.00000i q^{38} +1.00000i q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{43} -1.00000i q^{45} +(1.73205 - 1.00000i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.866025 - 0.500000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{55} -1.00000i q^{57} -1.00000 q^{58} +(-0.866025 - 0.500000i) q^{62} -1.00000 q^{64} +1.00000i q^{65} +(-0.866025 + 0.500000i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(0.866025 + 0.500000i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(0.866025 + 0.500000i) q^{74} +(0.500000 - 0.866025i) q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +(0.866025 - 0.500000i) q^{86} -1.00000 q^{87} -1.00000 q^{88} +(-0.500000 + 0.866025i) q^{90} +(-0.866025 - 0.500000i) q^{93} -2.00000 q^{94} -1.00000i q^{95} +(-0.500000 + 0.866025i) q^{97} +(-0.866025 + 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{6} + 2 q^{9} + 2 q^{10} - 2 q^{13} + 2 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{22} + 2 q^{24} + 4 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{40} - 2 q^{43} - 2 q^{54} + 2 q^{55} - 4 q^{58} - 4 q^{64} - 2 q^{67} + 2 q^{78} + 2 q^{79} - 2 q^{81} + 2 q^{82} - 4 q^{87} - 4 q^{88} - 2 q^{90} - 8 q^{94} - 2 q^{97}+O(q^{100}) $ 4 * q + 2 * q^6 + 2 * q^9 + 2 * q^10 - 2 * q^13 + 2 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^22 + 2 * q^24 + 4 * q^31 + 2 * q^33 - 4 * q^37 + 2 * q^40 - 2 * q^43 - 2 * q^54 + 2 * q^55 - 4 * q^58 - 4 * q^64 - 2 * q^67 + 2 * q^78 + 2 * q^79 - 2 * q^81 + 2 * q^82 - 4 * q^87 - 4 * q^88 - 2 * q^90 - 8 * q^94 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2793\mathbb{Z}\right)^\times$.

$n$	$932$	$2110$	$2206$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.1.bf.c.638.1		4
3.2	odd	2	inner	2793.1.bf.c.638.2		4
7.2	even	3		399.1.n.a.11.2	yes	4
7.3	odd	6		2793.1.bi.c.1892.2		4
7.4	even	3		399.1.bi.a.296.2	yes	4
7.5	odd	6		2793.1.n.c.410.2		4
7.6	odd	2		2793.1.bf.b.638.1		4
19.7	even	3	inner	2793.1.bf.c.197.2		4
21.2	odd	6		399.1.n.a.11.1	✓	4
21.5	even	6		2793.1.n.c.410.1		4
21.11	odd	6		399.1.bi.a.296.1	yes	4
21.17	even	6		2793.1.bi.c.1892.1		4
21.20	even	2		2793.1.bf.b.638.2		4
57.26	odd	6	inner	2793.1.bf.c.197.1		4
133.26	odd	6		2793.1.bi.c.2762.1		4
133.45	odd	6		2793.1.n.c.1451.2		4
133.83	odd	6		2793.1.bf.b.197.2		4
133.102	even	3		399.1.n.a.254.2	yes	4
133.121	even	3		399.1.bi.a.368.1	yes	4
399.26	even	6		2793.1.bi.c.2762.2		4
399.83	even	6		2793.1.bf.b.197.1		4
399.254	odd	6		399.1.bi.a.368.2	yes	4
399.311	even	6		2793.1.n.c.1451.1		4
399.368	odd	6		399.1.n.a.254.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.1.n.a.11.1	✓	4	21.2	odd	6
399.1.n.a.11.2	yes	4	7.2	even	3
399.1.n.a.254.1	yes	4	399.368	odd	6
399.1.n.a.254.2	yes	4	133.102	even	3
399.1.bi.a.296.1	yes	4	21.11	odd	6
399.1.bi.a.296.2	yes	4	7.4	even	3
399.1.bi.a.368.1	yes	4	133.121	even	3
399.1.bi.a.368.2	yes	4	399.254	odd	6
2793.1.n.c.410.1		4	21.5	even	6
2793.1.n.c.410.2		4	7.5	odd	6
2793.1.n.c.1451.1		4	399.311	even	6
2793.1.n.c.1451.2		4	133.45	odd	6
2793.1.bf.b.197.1		4	399.83	even	6
2793.1.bf.b.197.2		4	133.83	odd	6
2793.1.bf.b.638.1		4	7.6	odd	2
2793.1.bf.b.638.2		4	21.20	even	2
2793.1.bf.c.197.1		4	57.26	odd	6	inner
2793.1.bf.c.197.2		4	19.7	even	3	inner
2793.1.bf.c.638.1		4	1.1	even	1	trivial
2793.1.bf.c.638.2		4	3.2	odd	2	inner
2793.1.bi.c.1892.1		4	21.17	even	6
2793.1.bi.c.1892.2		4	7.3	odd	6
2793.1.bi.c.2762.1		4	133.26	odd	6
2793.1.bi.c.2762.2		4	399.26	even	6

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:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2793.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{5} +(0.500000 + 0.866025i) q^{6} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +1.00000i q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.500000 + 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} -1.00000i q^{18} +(0.500000 + 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{24} +1.00000i q^{26} -1.00000i q^{27} +(0.866025 - 0.500000i) q^{29} -1.00000i q^{30} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{33} -1.00000 q^{37} -1.00000i q^{38} +1.00000i q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{43} -1.00000i q^{45} +(1.73205 - 1.00000i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(0.866025 - 0.500000i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{55} -1.00000i q^{57} -1.00000 q^{58} +(-0.866025 - 0.500000i) q^{62} -1.00000 q^{64} +1.00000i q^{65} +(-0.866025 + 0.500000i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(0.866025 + 0.500000i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(0.866025 + 0.500000i) q^{74} +(0.500000 - 0.866025i) q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +(0.866025 - 0.500000i) q^{86} -1.00000 q^{87} -1.00000 q^{88} +(-0.500000 + 0.866025i) q^{90} +(-0.866025 - 0.500000i) q^{93} -2.00000 q^{94} -1.00000i q^{95} +(-0.500000 + 0.866025i) q^{97} +(-0.866025 + 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{6} + 2 q^{9} + 2 q^{10} - 2 q^{13} + 2 q^{15} + 2 q^{16} + 2 q^{19} + 2 q^{22} + 2 q^{24} + 4 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{40} - 2 q^{43} - 2 q^{54} + 2 q^{55} - 4 q^{58} - 4 q^{64} - 2 q^{67} + 2 q^{78} + 2 q^{79} - 2 q^{81} + 2 q^{82} - 4 q^{87} - 4 q^{88} - 2 q^{90} - 8 q^{94} - 2 q^{97}+O(q^{100}) \) 4 * q + 2 * q^6 + 2 * q^9 + 2 * q^10 - 2 * q^13 + 2 * q^15 + 2 * q^16 + 2 * q^19 + 2 * q^22 + 2 * q^24 + 4 * q^31 + 2 * q^33 - 4 * q^37 + 2 * q^40 - 2 * q^43 - 2 * q^54 + 2 * q^55 - 4 * q^58 - 4 * q^64 - 2 * q^67 + 2 * q^78 + 2 * q^79 - 2 * q^81 + 2 * q^82 - 4 * q^87 - 4 * q^88 - 2 * q^90 - 8 * q^94 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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