LMFDB - Embedded newform 2664.1.cy.a.1675.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2664,1,Mod(1099,2664)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2664, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("2664.1099");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$2664 = 2^{3} \cdot 3^{2} \cdot 37$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2664.cy (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:	$1.32950919365$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{4} + 1$ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.262848.3

Embedding invariants

Embedding label			1675.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2664.1675
Dual form			2664.1.cy.a.1099.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-1.22474 + 0.707107i) q^{5} +(-0.866025 + 0.500000i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.00000 + 1.00000i) q^{10} -1.41421 q^{11} +(-0.866025 + 0.500000i) q^{13} +(-0.707107 + 0.707107i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(-1.00000 - 1.73205i) q^{19} +(-0.707107 + 1.22474i) q^{20} +(-1.36603 + 0.366025i) q^{22} +(0.500000 - 0.866025i) q^{25} +(-0.707107 + 0.707107i) q^{26} +(-0.500000 + 0.866025i) q^{28} +1.41421i q^{29} +1.00000i q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.366025 + 1.36603i) q^{34} +(0.707107 - 1.22474i) q^{35} -1.00000i q^{37} +(-1.41421 - 1.41421i) q^{38} +(-0.366025 + 1.36603i) q^{40} +1.00000 q^{43} +(-1.22474 + 0.707107i) q^{44} +(0.258819 - 0.965926i) q^{50} +(-0.500000 + 0.866025i) q^{52} +(-1.22474 - 0.707107i) q^{53} +(1.73205 - 1.00000i) q^{55} +(-0.258819 + 0.965926i) q^{56} +(0.366025 + 1.36603i) q^{58} +(0.258819 + 0.965926i) q^{62} -1.00000i q^{64} +(0.707107 - 1.22474i) q^{65} +(0.500000 + 0.866025i) q^{67} +1.41421i q^{68} +(0.366025 - 1.36603i) q^{70} +1.00000 q^{73} +(-0.258819 - 0.965926i) q^{74} +(-1.73205 - 1.00000i) q^{76} +(1.22474 - 0.707107i) q^{77} +(-0.866025 + 0.500000i) q^{79} +1.41421i q^{80} +(0.707107 - 1.22474i) q^{83} -2.00000i q^{85} +(0.965926 - 0.258819i) q^{86} +(-1.00000 + 1.00000i) q^{88} +(-0.707107 + 1.22474i) q^{89} +(0.500000 - 0.866025i) q^{91} +(2.44949 + 1.41421i) q^{95} -1.00000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 8 q^{10} + 4 q^{16} - 8 q^{19} - 4 q^{22} + 4 q^{25} - 4 q^{28} + 4 q^{34} + 4 q^{40} + 8 q^{43} - 4 q^{52} - 4 q^{58} + 4 q^{67} - 4 q^{70} + 8 q^{73} - 8 q^{88} + 4 q^{91} - 8 q^{97}+O(q^{100})$ 8 * q - 8 * q^10 + 4 * q^16 - 8 * q^19 - 4 * q^22 + 4 * q^25 - 4 * q^28 + 4 * q^34 + 4 * q^40 + 8 * q^43 - 4 * q^52 - 4 * q^58 + 4 * q^67 - 4 * q^70 + 8 * q^73 - 8 * q^88 + 4 * q^91 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2664\mathbb{Z}\right)^\times$ .

$n$	$1297$	$1333$	$1999$	$2369$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.965926	−	0.258819i	0.965926	−	0.258819i
$2$	0.965926	−	0.258819i	0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.866025	−	0.500000i
$5$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$5$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$	0.707107	−	0.707107i	0.707107	−	0.707107i
$9$		0			0
$10$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$11$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$11$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$12$		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	$0.5\pi$
$14$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$15$		0			0
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$17$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$18$		0			0
$19$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$20$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$21$		0			0
$22$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.500000	−	0.866025i
$26$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$27$		0			0
$28$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$29$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$29$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$30$		0			0
$31$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$31$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$32$	0.258819	−	0.965926i	0.258819	−	0.965926i
$33$		0			0
$34$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$35$	0.707107	−	1.22474i	0.707107	−	1.22474i
$36$		0			0
$37$		−	1.00000i		−	1.00000i
$37$		−	1.00000i		−	1.00000i
$38$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$39$		0			0
$40$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$43$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$44$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$		0			0
$50$	0.258819	−	0.965926i	0.258819	−	0.965926i
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$53$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$53$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$54$		0			0
$55$	1.73205	−	1.00000i	1.73205	−	1.00000i
$56$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$57$		0			0
$58$	0.366025	+	1.36603i	0.366025	+	1.36603i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$	0.258819	+	0.965926i	0.258819	+	0.965926i
$63$		0			0
$64$		−	1.00000i		−	1.00000i
$65$	0.707107	−	1.22474i	0.707107	−	1.22474i
$66$		0			0
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$68$			1.41421i			1.41421i
$69$		0			0
$70$	0.366025	−	1.36603i	0.366025	−	1.36603i
$71$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$71$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$72$		0			0
$73$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$73$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$74$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$75$		0			0
$76$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$77$	1.22474	−	0.707107i	1.22474	−	0.707107i
$78$		0			0
$79$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$79$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$80$			1.41421i			1.41421i
$81$		0			0
$82$		0			0
$83$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$83$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$84$		0			0
$85$		−	2.00000i		−	2.00000i
$86$	0.965926	−	0.258819i	0.965926	−	0.258819i
$87$		0			0
$88$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$89$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$89$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$90$		0			0
$91$	0.500000	−	0.866025i	0.500000	−	0.866025i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.44949	+	1.41421i	2.44949	+	1.41421i
$96$		0			0
$97$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$97$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$98$		0			0
$99$		0			0
$100$		−	1.00000i		−	1.00000i
$101$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$101$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$102$		0			0
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$105$		0			0
$106$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$109$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$110$	1.41421	−	1.41421i	1.41421	−	1.41421i
$111$		0			0
$112$			1.00000i			1.00000i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$		0			0
$115$		0			0
$116$	0.707107	+	1.22474i	0.707107	+	1.22474i
$117$		0			0
$118$		0			0
$119$		−	1.41421i		−	1.41421i
$120$		0			0
$121$	1.00000			1.00000
$122$		0			0
$123$		0			0
$124$	0.500000	+	0.866025i	0.500000	+	0.866025i
$125$		0			0
$126$		0			0
$127$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$127$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$128$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$129$		0			0
$130$	0.366025	−	1.36603i	0.366025	−	1.36603i
$131$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$131$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$132$		0			0
$133$	1.73205	+	1.00000i	1.73205	+	1.00000i
$134$	0.707107	+	0.707107i	0.707107	+	0.707107i
$135$		0			0
$136$	0.366025	+	1.36603i	0.366025	+	1.36603i
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				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			$\pi$
$140$		−	1.41421i		−	1.41421i
$141$		0			0
$142$		0			0
$143$	1.22474	−	0.707107i	1.22474	−	0.707107i
$144$		0			0
$145$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$146$	0.965926	−	0.258819i	0.965926	−	0.258819i
$147$		0			0
$148$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$		0			0
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$152$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$153$		0			0
$154$	1.00000	−	1.00000i	1.00000	−	1.00000i
$155$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$156$		0			0
$157$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$157$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$158$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$159$		0			0
$160$	0.366025	+	1.36603i	0.366025	+	1.36603i
$161$		0			0
$162$		0			0
$163$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$163$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$164$		0			0
$165$		0			0
$166$	0.366025	−	1.36603i	0.366025	−	1.36603i
$167$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$167$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$168$		0			0
$169$		0			0
$170$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$171$		0			0
$172$	0.866025	−	0.500000i	0.866025	−	0.500000i
$173$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$173$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$174$		0			0
$175$			1.00000i			1.00000i
$176$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$177$		0			0
$178$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		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	$0.5\pi$
$182$	0.258819	−	0.965926i	0.258819	−	0.965926i
$183$		0			0
$184$		0			0
$185$	0.707107	+	1.22474i	0.707107	+	1.22474i
$186$		0			0
$187$	1.00000	−	1.73205i	1.00000	−	1.73205i
$188$		0			0
$189$		0			0
$190$	2.73205	+	0.732051i	2.73205	+	0.732051i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$193$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$194$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$195$		0			0
$196$		0			0
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$199$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$200$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$201$		0			0
$202$	0.366025	+	1.36603i	0.366025	+	1.36603i
$203$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$			1.00000i			1.00000i
$209$	1.41421	+	2.44949i	1.41421	+	2.44949i
$210$		0			0
$211$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$211$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$212$	−1.41421			−1.41421
$213$		0			0
$214$		0			0
$215$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$216$		0			0
$217$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$218$	0.965926	+	0.258819i	0.965926	+	0.258819i
$219$		0			0
$220$	1.00000	−	1.73205i	1.00000	−	1.73205i
$221$		−	1.41421i		−	1.41421i
$222$		0			0
$223$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$223$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$224$	0.258819	+	0.965926i	0.258819	+	0.965926i
$225$		0			0
$226$		0			0
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$		0			0
$229$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$229$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$230$		0			0
$231$		0			0
$232$	1.00000	+	1.00000i	1.00000	+	1.00000i
$233$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$233$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$239$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$239$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$242$	0.965926	−	0.258819i	0.965926	−	0.258819i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.73205	+	1.00000i	1.73205	+	1.00000i
$248$	0.707107	+	0.707107i	0.707107	+	0.707107i
$249$		0			0
$250$		0			0
$251$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$251$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$252$		0			0
$253$		0			0
$254$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$	0.500000	+	0.866025i	0.500000	+	0.866025i
$260$		−	1.41421i		−	1.41421i
$261$		0			0
$262$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$	2.00000			2.00000
$266$	1.93185	+	0.517638i	1.93185	+	0.517638i
$267$		0			0
$268$	0.866025	+	0.500000i	0.866025	+	0.500000i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$271$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$272$	0.707107	+	1.22474i	0.707107	+	1.22474i
$273$		0			0
$274$		0			0
$275$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$279$		0			0
$280$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$281$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$281$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$282$		0			0
$283$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$283$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$284$		0			0
$285$		0			0
$286$	1.00000	−	1.00000i	1.00000	−	1.00000i
$287$		0			0
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$290$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$291$		0			0
$292$	0.866025	−	0.500000i	0.866025	−	0.500000i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$		0			0
$296$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$302$	0.707107	−	0.707107i	0.707107	−	0.707107i
$303$		0			0
$304$	−2.00000			−2.00000
$305$		0			0
$306$		0			0
$307$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$307$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$308$	0.707107	−	1.22474i	0.707107	−	1.22474i
$309$		0			0
$310$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$311$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$311$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$313$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$314$	0.965926	+	0.258819i	0.965926	+	0.258819i
$315$		0			0
$316$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$		−	2.00000i		−	2.00000i
$320$	0.707107	+	1.22474i	0.707107	+	1.22474i
$321$		0			0
$322$		0			0
$323$	2.82843			2.82843
$324$		0			0
$325$			1.00000i			1.00000i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$331$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$332$		−	1.41421i		−	1.41421i
$333$		0			0
$334$	1.00000	−	1.00000i	1.00000	−	1.00000i
$335$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$336$		0			0
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$338$		0			0
$339$		0			0
$340$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$341$		−	1.41421i		−	1.41421i
$342$		0			0
$343$		−	1.00000i		−	1.00000i
$344$	0.707107	−	0.707107i	0.707107	−	0.707107i
$345$		0			0
$346$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$		0			0
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	0.258819	+	0.965926i	0.258819	+	0.965926i
$351$		0			0
$352$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$		0			0
$356$			1.41421i			1.41421i
$357$		0			0
$358$		0			0
$359$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$359$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$360$		0			0
$361$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$362$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$363$		0			0
$364$		−	1.00000i		−	1.00000i
$365$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$366$		0			0
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$	1.00000	+	1.00000i	1.00000	+	1.00000i
$371$	1.41421			1.41421
$372$		0			0
$373$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$373$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$374$	0.517638	−	1.93185i	0.517638	−	1.93185i
$375$		0			0
$376$		0			0
$377$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$378$		0			0
$379$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$379$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$380$	2.82843			2.82843
$381$		0			0
$382$		0			0
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$386$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$387$		0			0
$388$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$389$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$389$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.707107	−	1.22474i	0.707107	−	1.22474i
$396$		0			0
$397$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$397$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$398$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$404$	0.707107	+	1.22474i	0.707107	+	1.22474i
$405$		0			0
$406$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$407$			1.41421i			1.41421i
$408$		0			0
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$			2.00000i			2.00000i
$416$	0.258819	+	0.965926i	0.258819	+	0.965926i
$417$		0			0
$418$	2.00000	+	2.00000i	2.00000	+	2.00000i
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$421$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$422$	0.965926	−	0.258819i	0.965926	−	0.258819i
$423$		0			0
$424$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$425$	0.707107	+	1.22474i	0.707107	+	1.22474i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$		0			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$435$		0			0
$436$	1.00000			1.00000
$437$		0			0
$438$		0			0
$439$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$439$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$440$	0.517638	−	1.93185i	0.517638	−	1.93185i
$441$		0			0
$442$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$443$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$443$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$		−	2.00000i		−	2.00000i
$446$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$447$		0			0
$448$	0.500000	+	0.866025i	0.500000	+	0.866025i
$449$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$449$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$			1.41421i			1.41421i
$456$		0			0
$457$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$457$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$458$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$459$		0			0
$460$		0			0
$461$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$461$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$463$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$464$	1.22474	+	0.707107i	1.22474	+	0.707107i
$465$		0			0
$466$	1.36603	−	0.366025i	1.36603	−	0.366025i
$467$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$467$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$468$		0			0
$469$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.41421			−1.41421
$474$		0			0
$475$	−2.00000			−2.00000
$476$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$477$		0			0
$478$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	0.500000	+	0.866025i	0.500000	+	0.866025i
$482$	0.707107	+	0.707107i	0.707107	+	0.707107i
$483$		0			0
$484$	0.866025	−	0.500000i	0.866025	−	0.500000i
$485$	1.22474	−	0.707107i	1.22474	−	0.707107i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$494$	1.93185	+	0.517638i	1.93185	+	0.517638i
$495$		0			0
$496$	0.866025	+	0.500000i	0.866025	+	0.500000i
$497$		0			0
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$		0			0
$501$		0			0
$502$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$503$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$503$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$504$		0			0
$505$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$506$		0			0
$507$		0			0
$508$	−1.00000			−1.00000
$509$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$509$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$512$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.707107	+	0.707107i	0.707107	+	0.707107i
$519$		0			0
$520$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$523$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$524$			1.41421i			1.41421i
$525$		0			0
$526$		0			0
$527$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$528$		0			0
$529$	1.00000			1.00000
$530$	1.93185	−	0.517638i	1.93185	−	0.517638i
$531$		0			0
$532$	2.00000			2.00000
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.965926	+	0.258819i	0.965926	+	0.258819i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$541$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$542$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$543$		0			0
$544$	1.00000	+	1.00000i	1.00000	+	1.00000i
$545$	−1.41421			−1.41421
$546$		0			0
$547$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$547$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$548$		0			0
$549$		0			0
$550$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$551$	2.44949	−	1.41421i	2.44949	−	1.41421i
$552$		0			0
$553$	0.500000	−	0.866025i	0.500000	−	0.866025i
$554$		0			0
$555$		0			0
$556$			1.00000i			1.00000i
$557$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$557$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$558$		0			0
$559$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$560$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$561$		0			0
$562$	0.366025	−	1.36603i	0.366025	−	1.36603i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$		0			0
$566$	0.707107	+	0.707107i	0.707107	+	0.707107i
$567$		0			0
$568$		0			0
$569$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$569$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$570$		0			0
$571$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$571$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$572$	0.707107	−	1.22474i	0.707107	−	1.22474i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$577$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$578$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$579$		0			0
$580$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$581$			1.41421i			1.41421i
$582$		0			0
$583$	1.73205	+	1.00000i	1.73205	+	1.00000i
$584$	0.707107	−	0.707107i	0.707107	−	0.707107i
$585$		0			0
$586$		0			0
$587$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$587$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$588$		0			0
$589$	1.73205	−	1.00000i	1.73205	−	1.00000i
$590$		0			0
$591$		0			0
$592$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$593$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$593$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$594$		0			0
$595$	1.00000	+	1.73205i	1.00000	+	1.73205i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$		0			0
$601$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$601$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$602$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$603$		0			0
$604$	0.500000	−	0.866025i	0.500000	−	0.866025i
$605$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$613$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$614$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$615$		0			0
$616$	0.366025	−	1.36603i	0.366025	−	1.36603i
$617$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$617$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$618$		0			0
$619$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$619$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$620$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$621$		0			0
$622$	1.36603	+	0.366025i	1.36603	+	0.366025i
$623$		−	1.41421i		−	1.41421i
$624$		0			0
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$627$		0			0
$628$	1.00000			1.00000
$629$	1.22474	+	0.707107i	1.22474	+	0.707107i
$630$		0			0
$631$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$631$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$632$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$633$		0			0
$634$		0			0
$635$	1.41421			1.41421
$636$		0			0
$637$		0			0
$638$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$639$		0			0
$640$	1.00000	+	1.00000i	1.00000	+	1.00000i
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$643$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$644$		0			0
$645$		0			0
$646$	2.73205	−	0.732051i	2.73205	−	0.732051i
$647$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$647$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$648$		0			0
$649$		0			0
$650$	0.258819	+	0.965926i	0.258819	+	0.965926i
$651$		0			0
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$		−	2.00000i		−	2.00000i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$661$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$662$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$663$		0			0
$664$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$665$	−2.82843			−2.82843
$666$		0			0
$667$		0			0
$668$	0.707107	−	1.22474i	0.707107	−	1.22474i
$669$		0			0
$670$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$671$		0			0
$672$		0			0
$673$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$673$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$674$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$675$		0			0
$676$		0			0
$677$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$677$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$678$		0			0
$679$	0.866025	−	0.500000i	0.866025	−	0.500000i
$680$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$681$		0			0
$682$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$683$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$683$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$684$		0			0
$685$		0			0
$686$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$687$		0			0
$688$	0.500000	−	0.866025i	0.500000	−	0.866025i
$689$	1.41421			1.41421
$690$		0			0
$691$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$691$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$692$	−1.41421			−1.41421
$693$		0			0
$694$		0			0
$695$		−	1.41421i		−	1.41421i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.500000	+	0.866025i	0.500000	+	0.866025i
$701$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$701$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$704$			1.41421i			1.41421i
$705$		0			0
$706$		0			0
$707$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$708$		0			0
$709$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$709$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$710$		0			0
$711$		0			0
$712$	0.366025	+	1.36603i	0.366025	+	1.36603i
$713$		0			0
$714$		0			0
$715$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$716$		0			0
$717$		0			0
$718$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$		0			0
$721$		0			0
$722$	−0.776457	+	2.89778i	−0.776457	+	2.89778i
$723$		0			0
$724$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$725$	1.22474	+	0.707107i	1.22474	+	0.707107i
$726$		0			0
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$728$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$729$		0			0
$730$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$731$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$732$		0			0
$733$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$733$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$734$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$735$		0			0
$736$		0			0
$737$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	1.22474	+	0.707107i	1.22474	+	0.707107i
$741$		0			0
$742$	1.36603	−	0.366025i	1.36603	−	0.366025i
$743$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$743$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$744$		0			0
$745$		0			0
$746$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$747$		0			0
$748$		−	2.00000i		−	2.00000i
$749$		0			0
$750$		0			0
$751$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$751$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$752$		0			0
$753$		0			0
$754$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$755$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$756$		0			0
$757$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$757$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$758$		0			0
$759$		0			0
$760$	2.73205	−	0.732051i	2.73205	−	0.732051i
$761$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$761$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$762$		0			0
$763$	−1.00000			−1.00000
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$769$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$770$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$771$		0			0
$772$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$		0			0
$775$	0.866025	+	0.500000i	0.866025	+	0.500000i
$776$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$777$		0			0
$778$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.41421			−1.41421
$786$		0			0
$787$	−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
$790$	0.366025	−	1.36603i	0.366025	−	1.36603i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$795$		0			0
$796$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$797$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$797$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$798$		0			0
$799$		0			0
$800$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$801$		0			0
$802$		0			0
$803$	−1.41421			−1.41421
$804$		0			0
$805$		0			0
$806$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$807$		0			0
$808$	1.00000	+	1.00000i	1.00000	+	1.00000i
$809$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$809$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$810$		0			0
$811$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$811$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$812$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$813$		0			0
$814$	0.366025	+	1.36603i	0.366025	+	1.36603i
$815$		0			0
$816$		0			0
$817$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$818$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$819$		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			0
$823$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$823$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$827$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$829$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$830$	0.517638	+	1.93185i	0.517638	+	1.93185i
$831$		0			0
$832$	0.500000	+	0.866025i	0.500000	+	0.866025i
$833$		0			0
$834$		0			0
$835$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$836$	2.44949	+	1.41421i	2.44949	+	1.41421i
$837$		0			0
$838$		0			0
$839$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$839$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$840$		0			0
$841$	−1.00000			−1.00000
$842$	0.517638	+	1.93185i	0.517638	+	1.93185i
$843$		0			0
$844$	0.866025	−	0.500000i	0.866025	−	0.500000i
$845$		0			0
$846$		0			0
$847$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$848$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$849$		0			0
$850$	1.00000	+	1.00000i	1.00000	+	1.00000i
$851$		0			0
$852$		0			0
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$859$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$860$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$	2.00000			2.00000
$866$		0			0
$867$		0			0
$868$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$869$	1.22474	−	0.707107i	1.22474	−	0.707107i
$870$		0			0
$871$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$872$	0.965926	−	0.258819i	0.965926	−	0.258819i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$877$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$878$	0.707107	−	0.707107i	0.707107	−	0.707107i
$879$		0			0
$880$		−	2.00000i		−	2.00000i
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$		0			0
$883$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$883$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$884$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$885$		0			0
$886$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$887$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$887$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$888$		0			0
$889$	1.00000			1.00000
$890$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$891$		0			0
$892$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.707107	+	0.707107i	0.707107	+	0.707107i
$897$		0			0
$898$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$899$	−1.41421			−1.41421
$900$		0			0
$901$	1.73205	−	1.00000i	1.73205	−	1.00000i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.707107	−	1.22474i	0.707107	−	1.22474i
$906$		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
$910$	0.366025	+	1.36603i	0.366025	+	1.36603i
$911$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$911$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$912$		0			0
$913$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$914$		0			0
$915$		0			0
$916$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$917$		−	1.41421i		−	1.41421i
$918$		0			0
$919$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$919$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$926$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$927$		0			0
$928$	1.36603	+	0.366025i	1.36603	+	0.366025i
$929$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$929$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$930$		0			0
$931$		0			0
$932$	1.22474	−	0.707107i	1.22474	−	0.707107i
$933$		0			0
$934$	1.36603	−	0.366025i	1.36603	−	0.366025i
$935$			2.82843i			2.82843i
$936$		0			0
$937$	−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			$\pi$
$938$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$939$		0			0
$940$		0			0
$941$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$941$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$947$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$947$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$948$		0			0
$949$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$950$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$951$		0			0
$952$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$953$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$953$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$954$		0			0
$955$		0			0
$956$	−1.41421			−1.41421
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$	0.707107	+	0.707107i	0.707107	+	0.707107i
$963$		0			0
$964$	0.866025	+	0.500000i	0.866025	+	0.500000i
$965$	1.22474	−	0.707107i	1.22474	−	0.707107i
$966$		0			0
$967$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$967$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$968$	0.707107	−	0.707107i	0.707107	−	0.707107i
$969$		0			0
$970$	1.00000	−	1.00000i	1.00000	−	1.00000i
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$		−	1.00000i		−	1.00000i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$977$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$978$		0			0
$979$	1.00000	−	1.73205i	1.00000	−	1.73205i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$983$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$984$		0			0
$985$		0			0
$986$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$987$		0			0
$988$	2.00000			2.00000
$989$		0			0
$990$		0			0
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$992$	0.965926	+	0.258819i	0.965926	+	0.258819i
$993$		0			0
$994$		0			0
$995$	0.707107	+	1.22474i	0.707107	+	1.22474i
$996$		0			0
$997$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$997$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2664.1.cy.a.1675.4	yes	8
3.2	odd	2	inner	2664.1.cy.a.1675.1	yes	8
8.3	odd	2	inner	2664.1.cy.a.1675.2	yes	8
24.11	even	2	inner	2664.1.cy.a.1675.3	yes	8
37.26	even	3	inner	2664.1.cy.a.1099.2	yes	8
111.26	odd	6	inner	2664.1.cy.a.1099.3	yes	8
296.211	odd	6	inner	2664.1.cy.a.1099.4	yes	8
888.803	even	6	inner	2664.1.cy.a.1099.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2664.1.cy.a.1099.1	✓	8	888.803	even	6	inner
2664.1.cy.a.1099.2	yes	8	37.26	even	3	inner
2664.1.cy.a.1099.3	yes	8	111.26	odd	6	inner
2664.1.cy.a.1099.4	yes	8	296.211	odd	6	inner
2664.1.cy.a.1675.1	yes	8	3.2	odd	2	inner
2664.1.cy.a.1675.2	yes	8	8.3	odd	2	inner
2664.1.cy.a.1675.3	yes	8	24.11	even	2	inner
2664.1.cy.a.1675.4	yes	8	1.1	even	1	trivial

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	2664.1.cy.a.1675.4

Level	$2664$
Weight	$1$
Character	2664.1675
Analytic conductor	$1.330$
Analytic rank	$0$
Dimension	$8$
Projective image	$S_{4}$
CM/RM	no
Inner twists	$8$