LMFDB - Embedded newform 931.1.t.a.619.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,1,Mod(558,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("931.558");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	931.t (of order $6$, degree $2$, not 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:	$0.464629526761$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.17689.1

Embedding invariants

Embedding label			619.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	931.619
Dual form			931.1.t.a.558.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} -1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} -1.00000 q^{8} +1.00000i q^{10} +(-0.866025 + 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{15} -1.00000 q^{16} +(-0.866025 + 0.500000i) q^{17} +(0.866025 - 0.500000i) q^{19} +(-0.500000 + 0.866025i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(0.500000 + 0.866025i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.866025 + 0.500000i) q^{34} +(0.866025 - 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{39} -1.00000i q^{40} +(0.866025 + 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(-0.500000 + 0.866025i) q^{46} +(0.866025 + 0.500000i) q^{47} +(0.866025 - 0.500000i) q^{48} +(0.500000 - 0.866025i) q^{51} -1.00000 q^{53} -1.00000i q^{54} +(-0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} +(0.866025 - 0.500000i) q^{59} +(-0.866025 - 0.500000i) q^{61} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +1.00000 q^{67} -1.00000i q^{69} +(0.500000 - 0.866025i) q^{71} +(0.866025 - 0.500000i) q^{73} +(0.500000 - 0.866025i) q^{78} +1.00000 q^{79} -1.00000i q^{80} +(0.500000 + 0.866025i) q^{81} +(0.866025 + 0.500000i) q^{82} +(-0.500000 - 0.866025i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-0.866025 - 0.500000i) q^{87} +(-0.866025 - 0.500000i) q^{89} +(0.866025 + 0.500000i) q^{94} +(0.500000 + 0.866025i) q^{95} +(0.866025 + 0.500000i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^8	$ 4 q + 4 q^{2} - 4 q^{8} - 2 q^{15} - 4 q^{16} - 2 q^{23} + 2 q^{29} - 2 q^{30} + 2 q^{39} - 2 q^{43} - 2 q^{46} + 2 q^{51} - 4 q^{53} - 2 q^{57} + 2 q^{58} + 4 q^{64} - 2 q^{65} + 4 q^{67} + 2 q^{71} + 2 q^{78} + 4 q^{79} + 2 q^{81} - 2 q^{85} - 2 q^{86} + 2 q^{95}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^8 - 2 * q^15 - 4 * q^16 - 2 * q^23 + 2 * q^29 - 2 * q^30 + 2 * q^39 - 2 * q^43 - 2 * q^46 + 2 * q^51 - 4 * q^53 - 2 * q^57 + 2 * q^58 + 4 * q^64 - 2 * q^65 + 4 * q^67 + 2 * q^71 + 2 * q^78 + 4 * q^79 + 2 * q^81 - 2 * q^85 - 2 * q^86 + 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.1.t.a.619.1		4
7.2	even	3		931.1.k.a.68.1		4
7.3	odd	6		133.1.m.a.125.1	yes	4
7.4	even	3		133.1.m.a.125.2	yes	4
7.5	odd	6		931.1.k.a.68.2		4
7.6	odd	2	inner	931.1.t.a.619.2		4
19.7	even	3		931.1.k.a.178.1		4
21.11	odd	6		1197.1.ci.c.1189.2		4
21.17	even	6		1197.1.ci.c.1189.1		4
28.3	even	6		2128.1.cy.a.657.2		4
28.11	odd	6		2128.1.cy.a.657.1		4
35.3	even	12		3325.1.bi.b.524.2		4
35.4	even	6		3325.1.bc.a.3051.1		4
35.17	even	12		3325.1.bi.a.524.1		4
35.18	odd	12		3325.1.bi.a.524.2		4
35.24	odd	6		3325.1.bc.a.3051.2		4
35.32	odd	12		3325.1.bi.b.524.1		4
133.3	even	18		2527.1.y.d.1182.2		12
133.4	even	9		2527.1.y.e.62.1		12
133.10	even	18		2527.1.y.d.2050.2		12
133.11	even	3		2527.1.d.e.1084.1		2
133.17	odd	18		2527.1.y.e.2400.2		12
133.18	odd	6		2527.1.m.d.790.1		4
133.24	odd	18		2527.1.y.e.1833.2		12
133.25	even	9		2527.1.y.e.776.2		12
133.26	odd	6	inner	931.1.t.a.558.1		4
133.31	even	6		2527.1.m.d.1014.1		4
133.32	odd	18		2527.1.y.d.776.1		12
133.45	odd	6		133.1.m.a.83.2	yes	4
133.46	odd	6		2527.1.d.b.1084.2		2
133.52	even	18		2527.1.y.d.1833.1		12
133.53	odd	18		2527.1.y.d.62.2		12
133.59	even	18		2527.1.y.d.2400.1		12
133.60	odd	18		2527.1.y.d.1182.1		12
133.66	odd	18		2527.1.y.e.2050.1		12
133.67	odd	18		2527.1.y.d.2050.1		12
133.73	odd	18		2527.1.y.e.1182.1		12
133.74	even	9		2527.1.y.e.2400.1		12
133.80	odd	18		2527.1.y.e.62.2		12
133.81	even	9		2527.1.y.e.1833.1		12
133.83	odd	6		931.1.k.a.178.2		4
133.87	odd	6		2527.1.d.e.1084.2		2
133.88	odd	6		2527.1.m.d.1014.2		4
133.94	even	6		2527.1.m.d.790.2		4
133.101	odd	18		2527.1.y.e.776.1		12
133.102	even	3		133.1.m.a.83.1	✓	4
133.108	even	18		2527.1.y.d.776.2		12
133.109	odd	18		2527.1.y.d.1833.2		12
133.116	odd	18		2527.1.y.d.2400.2		12
133.121	even	3	inner	931.1.t.a.558.2		4
133.122	even	6		2527.1.d.b.1084.1		2
133.123	even	9		2527.1.y.e.2050.2		12
133.129	even	18		2527.1.y.d.62.1		12
133.130	even	9		2527.1.y.e.1182.2		12
399.311	even	6		1197.1.ci.c.748.2		4
399.368	odd	6		1197.1.ci.c.748.1		4
532.235	odd	6		2128.1.cy.a.881.2		4
532.311	even	6		2128.1.cy.a.881.1		4
665.102	odd	12		3325.1.bi.b.349.2		4
665.178	even	12		3325.1.bi.b.349.1		4
665.368	odd	12		3325.1.bi.a.349.1		4
665.444	odd	6		3325.1.bc.a.2876.1		4
665.577	even	12		3325.1.bi.a.349.2		4
665.634	even	6		3325.1.bc.a.2876.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.1.m.a.83.1	✓	4	133.102	even	3
133.1.m.a.83.2	yes	4	133.45	odd	6
133.1.m.a.125.1	yes	4	7.3	odd	6
133.1.m.a.125.2	yes	4	7.4	even	3
931.1.k.a.68.1		4	7.2	even	3
931.1.k.a.68.2		4	7.5	odd	6
931.1.k.a.178.1		4	19.7	even	3
931.1.k.a.178.2		4	133.83	odd	6
931.1.t.a.558.1		4	133.26	odd	6	inner
931.1.t.a.558.2		4	133.121	even	3	inner
931.1.t.a.619.1		4	1.1	even	1	trivial
931.1.t.a.619.2		4	7.6	odd	2	inner
1197.1.ci.c.748.1		4	399.368	odd	6
1197.1.ci.c.748.2		4	399.311	even	6
1197.1.ci.c.1189.1		4	21.17	even	6
1197.1.ci.c.1189.2		4	21.11	odd	6
2128.1.cy.a.657.1		4	28.11	odd	6
2128.1.cy.a.657.2		4	28.3	even	6
2128.1.cy.a.881.1		4	532.311	even	6
2128.1.cy.a.881.2		4	532.235	odd	6
2527.1.d.b.1084.1		2	133.122	even	6
2527.1.d.b.1084.2		2	133.46	odd	6
2527.1.d.e.1084.1		2	133.11	even	3
2527.1.d.e.1084.2		2	133.87	odd	6
2527.1.m.d.790.1		4	133.18	odd	6
2527.1.m.d.790.2		4	133.94	even	6
2527.1.m.d.1014.1		4	133.31	even	6
2527.1.m.d.1014.2		4	133.88	odd	6
2527.1.y.d.62.1		12	133.129	even	18
2527.1.y.d.62.2		12	133.53	odd	18
2527.1.y.d.776.1		12	133.32	odd	18
2527.1.y.d.776.2		12	133.108	even	18
2527.1.y.d.1182.1		12	133.60	odd	18
2527.1.y.d.1182.2		12	133.3	even	18
2527.1.y.d.1833.1		12	133.52	even	18
2527.1.y.d.1833.2		12	133.109	odd	18
2527.1.y.d.2050.1		12	133.67	odd	18
2527.1.y.d.2050.2		12	133.10	even	18
2527.1.y.d.2400.1		12	133.59	even	18
2527.1.y.d.2400.2		12	133.116	odd	18
2527.1.y.e.62.1		12	133.4	even	9
2527.1.y.e.62.2		12	133.80	odd	18
2527.1.y.e.776.1		12	133.101	odd	18
2527.1.y.e.776.2		12	133.25	even	9
2527.1.y.e.1182.1		12	133.73	odd	18
2527.1.y.e.1182.2		12	133.130	even	9
2527.1.y.e.1833.1		12	133.81	even	9
2527.1.y.e.1833.2		12	133.24	odd	18
2527.1.y.e.2050.1		12	133.66	odd	18
2527.1.y.e.2050.2		12	133.123	even	9
2527.1.y.e.2400.1		12	133.74	even	9
2527.1.y.e.2400.2		12	133.17	odd	18
3325.1.bc.a.2876.1		4	665.444	odd	6
3325.1.bc.a.2876.2		4	665.634	even	6
3325.1.bc.a.3051.1		4	35.4	even	6
3325.1.bc.a.3051.2		4	35.24	odd	6
3325.1.bi.a.349.1		4	665.368	odd	12
3325.1.bi.a.349.2		4	665.577	even	12
3325.1.bi.a.524.1		4	35.17	even	12
3325.1.bi.a.524.2		4	35.18	odd	12
3325.1.bi.b.349.1		4	665.178	even	12
3325.1.bi.b.349.2		4	665.102	odd	12
3325.1.bi.b.524.1		4	35.32	odd	12
3325.1.bi.b.524.2		4	35.3	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	931.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} -1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.866025 + 0.500000i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} -1.00000 q^{8} +1.00000i q^{10} +(-0.866025 + 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{15} -1.00000 q^{16} +(-0.866025 + 0.500000i) q^{17} +(0.866025 - 0.500000i) q^{19} +(-0.500000 + 0.866025i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(0.500000 + 0.866025i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-0.866025 + 0.500000i) q^{34} +(0.866025 - 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{39} -1.00000i q^{40} +(0.866025 + 0.500000i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(-0.500000 + 0.866025i) q^{46} +(0.866025 + 0.500000i) q^{47} +(0.866025 - 0.500000i) q^{48} +(0.500000 - 0.866025i) q^{51} -1.00000 q^{53} -1.00000i q^{54} +(-0.500000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} +(0.866025 - 0.500000i) q^{59} +(-0.866025 - 0.500000i) q^{61} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +1.00000 q^{67} -1.00000i q^{69} +(0.500000 - 0.866025i) q^{71} +(0.866025 - 0.500000i) q^{73} +(0.500000 - 0.866025i) q^{78} +1.00000 q^{79} -1.00000i q^{80} +(0.500000 + 0.866025i) q^{81} +(0.866025 + 0.500000i) q^{82} +(-0.500000 - 0.866025i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-0.866025 - 0.500000i) q^{87} +(-0.866025 - 0.500000i) q^{89} +(0.866025 + 0.500000i) q^{94} +(0.500000 + 0.866025i) q^{95} +(0.866025 + 0.500000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^8	\( 4 q + 4 q^{2} - 4 q^{8} - 2 q^{15} - 4 q^{16} - 2 q^{23} + 2 q^{29} - 2 q^{30} + 2 q^{39} - 2 q^{43} - 2 q^{46} + 2 q^{51} - 4 q^{53} - 2 q^{57} + 2 q^{58} + 4 q^{64} - 2 q^{65} + 4 q^{67} + 2 q^{71} + 2 q^{78} + 4 q^{79} + 2 q^{81} - 2 q^{85} - 2 q^{86} + 2 q^{95}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^8 - 2 * q^15 - 4 * q^16 - 2 * q^23 + 2 * q^29 - 2 * q^30 + 2 * q^39 - 2 * q^43 - 2 * q^46 + 2 * q^51 - 4 * q^53 - 2 * q^57 + 2 * q^58 + 4 * q^64 - 2 * q^65 + 4 * q^67 + 2 * q^71 + 2 * q^78 + 4 * q^79 + 2 * q^81 - 2 * q^85 - 2 * q^86 + 2 * q^95

Introduction

L-functions

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