LMFDB - Embedded newform 1260.1.cw.b.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,1,Mod(499,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1260.499");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1260.cw (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:	$0.628821915918$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.79380.1
Artin image:	$C_3^2\times D_6$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{36} - \cdots)$

Embedding invariants

Embedding label			499.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1260.499
Dual form			1260.1.cw.b.1159.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +1.00000 q^{16} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(0.500000 + 0.866025i) q^{29} +(-0.500000 + 0.866025i) q^{30} -1.00000 q^{32} +(0.500000 - 0.866025i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{40} +(0.500000 - 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{42} +(-0.500000 - 0.866025i) q^{43} +1.00000 q^{45} +(-1.00000 - 1.73205i) q^{46} +1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +1.00000 q^{54} +(-0.500000 - 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{58} +(0.500000 - 0.866025i) q^{60} +2.00000 q^{61} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{67} +(-1.00000 + 1.73205i) q^{69} +(-0.500000 + 0.866025i) q^{70} +(0.500000 - 0.866025i) q^{72} -1.00000 q^{75} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(-0.500000 - 0.866025i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(0.500000 + 0.866025i) q^{86} +(-0.500000 + 0.866025i) q^{87} +(-1.00000 + 1.73205i) q^{89} -1.00000 q^{90} +(1.00000 + 1.73205i) q^{92} -1.00000 q^{94} +(-0.500000 - 0.866025i) q^{96} +(0.500000 - 0.866025i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} - 2 q^{8} - q^{9} + q^{10} + q^{12} - q^{14} + q^{15} + 2 q^{16} + q^{18} - q^{20} - q^{21} + 2 q^{23} - q^{24} - q^{25} - 2 q^{27}+ \cdots + q^{98}+O(q^{100})$ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + q^7 - 2 * q^8 - q^9 + q^10 + q^12 - q^14 + q^15 + 2 * q^16 + q^18 - q^20 - q^21 + 2 * q^23 - q^24 - q^25 - 2 * q^27 + q^28 + q^29 - q^30 - 2 * q^32 + q^35 - q^36 + q^40 + q^41 + q^42 - q^43 + 2 * q^45 - 2 * q^46 + 2 * q^47 + q^48 - q^49 + q^50 + 2 * q^54 - q^56 - q^58 + q^60 + 4 * q^61 - 2 * q^63 + 2 * q^64 - 4 * q^67 - 2 * q^69 - q^70 + q^72 - 2 * q^75 - q^80 - q^81 - q^82 - q^83 - q^84 + q^86 - q^87 - 2 * q^89 - 2 * q^90 + 2 * q^92 - 2 * q^94 - q^96 + q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$ .

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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
$2$	−1.00000			−1.00000
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$3$	0.500000	+	0.866025i	0.500000	+	0.866025i
$4$	1.00000			1.00000
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$6$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i
$8$	−1.00000			−1.00000
$9$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$10$	0.500000	+	0.866025i	0.500000	+	0.866025i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	0.500000	+	0.866025i	0.500000	+	0.866025i
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$15$	0.500000	−	0.866025i	0.500000	−	0.866025i
$16$	1.00000			1.00000
$17$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$	0.500000	−	0.866025i	0.500000	−	0.866025i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$21$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$22$		0			0
$23$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$23$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	−1.00000			−1.00000
$28$	0.500000	+	0.866025i	0.500000	+	0.866025i
$29$	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		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$	−1.00000			−1.00000
$33$		0			0
$34$		0			0
$35$	0.500000	−	0.866025i	0.500000	−	0.866025i
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	0.500000	+	0.866025i	0.500000	+	0.866025i
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$42$	0.500000	−	0.866025i	0.500000	−	0.866025i
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$44$		0			0
$45$	1.00000			1.00000
$46$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$47$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$47$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$	0.500000	−	0.866025i	0.500000	−	0.866025i
$51$		0			0
$52$		0			0
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	1.00000			1.00000
$55$		0			0
$56$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$57$		0			0
$58$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$	0.500000	−	0.866025i	0.500000	−	0.866025i
$61$	2.00000			2.00000			1.00000			$0$
$61$	2.00000			2.00000			1.00000			$0$
$62$		0			0
$63$	−1.00000			−1.00000
$64$	1.00000			1.00000
$65$		0			0
$66$		0			0
$67$	−2.00000			−2.00000			−1.00000			$\pi$
$67$	−2.00000			−2.00000			−1.00000			$\pi$
$68$		0			0
$69$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$70$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.500000	−	0.866025i	0.500000	−	0.866025i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$	−1.00000			−1.00000
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$83$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$83$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$84$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$85$		0			0
$86$	0.500000	+	0.866025i	0.500000	+	0.866025i
$87$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$88$		0			0
$89$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$89$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$90$	−1.00000			−1.00000
$91$		0			0
$92$	1.00000	+	1.73205i	1.00000	+	1.73205i
$93$		0			0
$94$	−1.00000			−1.00000
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	0.500000	−	0.866025i	0.500000	−	0.866025i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$101$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$101$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$102$		0			0
$103$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$103$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$104$		0			0
$105$	1.00000			1.00000
$106$		0			0
$107$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$107$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$108$	−1.00000			−1.00000
$109$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$109$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$110$		0			0
$111$		0			0
$112$	0.500000	+	0.866025i	0.500000	+	0.866025i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$	1.00000	−	1.73205i	1.00000	−	1.73205i
$116$	0.500000	+	0.866025i	0.500000	+	0.866025i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$	−2.00000			−2.00000
$123$	1.00000			1.00000
$124$		0			0
$125$	1.00000			1.00000
$126$	1.00000			1.00000
$127$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$127$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$128$	−1.00000			−1.00000
$129$	0.500000	−	0.866025i	0.500000	−	0.866025i
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$		0			0
$133$		0			0
$134$	2.00000			2.00000
$135$	0.500000	+	0.866025i	0.500000	+	0.866025i
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	1.00000	−	1.73205i	1.00000	−	1.73205i
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$	0.500000	−	0.866025i	0.500000	−	0.866025i
$141$	0.500000	+	0.866025i	0.500000	+	0.866025i
$142$		0			0
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$145$	0.500000	−	0.866025i	0.500000	−	0.866025i
$146$		0			0
$147$	−1.00000			−1.00000
$148$		0			0
$149$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$150$	1.00000			1.00000
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		0			0
$159$		0			0
$160$	0.500000	+	0.866025i	0.500000	+	0.866025i
$161$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$162$	0.500000	+	0.866025i	0.500000	+	0.866025i
$163$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$163$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$164$	0.500000	−	0.866025i	0.500000	−	0.866025i
$165$		0			0
$166$	0.500000	+	0.866025i	0.500000	+	0.866025i
$167$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$167$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$168$	0.500000	−	0.866025i	0.500000	−	0.866025i
$169$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$170$		0			0
$171$		0			0
$172$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$	0.500000	−	0.866025i	0.500000	−	0.866025i
$175$	−1.00000			−1.00000
$176$		0			0
$177$		0			0
$178$	1.00000	−	1.73205i	1.00000	−	1.73205i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	1.00000			1.00000
$181$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$	1.00000	+	1.73205i	1.00000	+	1.73205i
$184$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.00000			1.00000
$189$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	0.500000	+	0.866025i	0.500000	+	0.866025i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	0.500000	−	0.866025i	0.500000	−	0.866025i
$201$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$202$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$203$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$204$		0			0
$205$	−1.00000			−1.00000
$206$	0.500000	+	0.866025i	0.500000	+	0.866025i
$207$	−2.00000			−2.00000
$208$		0			0
$209$		0			0
$210$	−1.00000			−1.00000
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$		0			0
$214$	0.500000	−	0.866025i	0.500000	−	0.866025i
$215$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$216$	1.00000			1.00000
$217$		0			0
$218$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$223$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$224$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$225$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$226$		0			0
$227$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$227$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$229$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$230$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$231$		0			0
$232$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$233$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$233$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	0.500000	−	0.866025i	0.500000	−	0.866025i
$241$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$241$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$242$	0.500000	+	0.866025i	0.500000	+	0.866025i
$243$	0.500000	−	0.866025i	0.500000	−	0.866025i
$244$	2.00000			2.00000
$245$	1.00000			1.00000
$246$	−1.00000			−1.00000
$247$		0			0
$248$		0			0
$249$	0.500000	−	0.866025i	0.500000	−	0.866025i
$250$	−1.00000			−1.00000
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	−1.00000			−1.00000
$253$		0			0
$254$	−1.00000			−1.00000
$255$		0			0
$256$	1.00000			1.00000
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$259$		0			0
$260$		0			0
$261$	−1.00000			−1.00000
$262$		0			0
$263$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$263$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.00000			−2.00000
$268$	−2.00000			−2.00000
$269$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$270$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$282$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$283$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$283$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.00000			1.00000
$288$	0.500000	−	0.866025i	0.500000	−	0.866025i
$289$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$290$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$291$		0			0
$292$		0			0
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$	1.00000			1.00000
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.00000	+	1.73205i	1.00000	+	1.73205i
$299$		0			0
$300$	−1.00000			−1.00000
$301$	0.500000	−	0.866025i	0.500000	−	0.866025i
$302$		0			0
$303$	1.00000			1.00000
$304$		0			0
$305$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$306$		0			0
$307$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$307$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$308$		0			0
$309$	0.500000	−	0.866025i	0.500000	−	0.866025i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$		0			0
$315$	0.500000	+	0.866025i	0.500000	+	0.866025i
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$321$	−1.00000			−1.00000
$322$	1.00000	−	1.73205i	1.00000	−	1.73205i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$325$		0			0
$326$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$327$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$328$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$329$	0.500000	+	0.866025i	0.500000	+	0.866025i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$333$		0			0
$334$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$335$	1.00000	+	1.73205i	1.00000	+	1.73205i
$336$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$337$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$337$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$338$	0.500000	+	0.866025i	0.500000	+	0.866025i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−1.00000			−1.00000
$344$	0.500000	+	0.866025i	0.500000	+	0.866025i
$345$	2.00000			2.00000
$346$		0			0
$347$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$347$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$348$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$349$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$350$	1.00000			1.00000
$351$		0			0
$352$		0			0
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$357$		0			0
$358$		0			0
$359$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$359$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$360$	−1.00000			−1.00000
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	1.00000			1.00000
$363$	0.500000	−	0.866025i	0.500000	−	0.866025i
$364$		0			0
$365$		0			0
$366$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$367$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$367$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$368$	1.00000	+	1.73205i	1.00000	+	1.73205i
$369$	0.500000	+	0.866025i	0.500000	+	0.866025i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.500000	+	0.866025i
$376$	−1.00000			−1.00000
$377$		0			0
$378$	0.500000	+	0.866025i	0.500000	+	0.866025i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.500000	+	0.866025i	0.500000	+	0.866025i
$382$		0			0
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$384$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$385$		0			0
$386$		0			0
$387$	1.00000			1.00000
$388$		0			0
$389$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$389$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$390$		0			0
$391$		0			0
$392$	0.500000	−	0.866025i	0.500000	−	0.866025i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$401$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	1.00000	+	1.73205i	1.00000	+	1.73205i
$403$		0			0
$404$	0.500000	−	0.866025i	0.500000	−	0.866025i
$405$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$406$	0.500000	−	0.866025i	0.500000	−	0.866025i
$407$		0			0
$408$		0			0
$409$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$409$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$410$	1.00000			1.00000
$411$		0			0
$412$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$413$		0			0
$414$	2.00000			2.00000
$415$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$419$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$420$	1.00000			1.00000
$421$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$421$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$422$		0			0
$423$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.00000	+	1.73205i	1.00000	+	1.73205i
$428$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$429$		0			0
$430$	0.500000	−	0.866025i	0.500000	−	0.866025i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	−1.00000			−1.00000
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	1.00000			1.00000
$436$	0.500000	+	0.866025i	0.500000	+	0.866025i
$437$		0			0
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$442$		0			0
$443$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$443$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$444$		0			0
$445$	2.00000			2.00000
$446$	0.500000	+	0.866025i	0.500000	+	0.866025i
$447$	1.00000	−	1.73205i	1.00000	−	1.73205i
$448$	0.500000	+	0.866025i	0.500000	+	0.866025i
$449$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$450$	0.500000	+	0.866025i	0.500000	+	0.866025i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$455$		0			0
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$459$		0			0
$460$	1.00000	−	1.73205i	1.00000	−	1.73205i
$461$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$461$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$463$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$464$	0.500000	+	0.866025i	0.500000	+	0.866025i
$465$		0			0
$466$		0			0
$467$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$467$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$468$		0			0
$469$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$470$	0.500000	+	0.866025i	0.500000	+	0.866025i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$481$		0			0
$482$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$483$	−2.00000			−2.00000
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$		0			0
$486$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$487$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$487$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$488$	−2.00000			−2.00000
$489$	2.00000			2.00000
$490$	−1.00000			−1.00000
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$	1.00000			1.00000
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	1.00000			1.00000
$501$	2.00000			2.00000
$502$		0			0
$503$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$503$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$504$	1.00000			1.00000
$505$	−1.00000			−1.00000
$506$		0			0
$507$	0.500000	−	0.866025i	0.500000	−	0.866025i
$508$	1.00000			1.00000
$509$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$509$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$		0			0
$514$		0			0
$515$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$516$	0.500000	−	0.866025i	0.500000	−	0.866025i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$522$	1.00000			1.00000
$523$	−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			$\pi$
$524$		0			0
$525$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$526$	0.500000	−	0.866025i	0.500000	−	0.866025i
$527$		0			0
$528$		0			0
$529$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	2.00000			2.00000
$535$	1.00000			1.00000
$536$	2.00000			2.00000
$537$		0			0
$538$	1.00000	+	1.73205i	1.00000	+	1.73205i
$539$		0			0
$540$	0.500000	+	0.866025i	0.500000	+	0.866025i
$541$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$541$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$544$		0			0
$545$	0.500000	−	0.866025i	0.500000	−	0.866025i
$546$		0			0
$547$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$547$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$550$		0			0
$551$		0			0
$552$	1.00000	−	1.73205i	1.00000	−	1.73205i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$	0.500000	−	0.866025i	0.500000	−	0.866025i
$561$		0			0
$562$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$563$	−2.00000			−2.00000			−1.00000			$\pi$
$563$	−2.00000			−2.00000			−1.00000			$\pi$
$564$	0.500000	+	0.866025i	0.500000	+	0.866025i
$565$		0			0
$566$	−1.00000			−1.00000
$567$	0.500000	−	0.866025i	0.500000	−	0.866025i
$568$		0			0
$569$	2.00000			2.00000			1.00000			$0$
$569$	2.00000			2.00000			1.00000			$0$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$	−1.00000			−1.00000
$575$	−2.00000			−2.00000
$576$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	0.500000	−	0.866025i	0.500000	−	0.866025i
$579$		0			0
$580$	0.500000	−	0.866025i	0.500000	−	0.866025i
$581$	0.500000	−	0.866025i	0.500000	−	0.866025i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$587$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$588$	−1.00000			−1.00000
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$593$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$594$		0			0
$595$		0			0
$596$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	1.00000			1.00000
$601$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$602$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$603$	1.00000	−	1.73205i	1.00000	−	1.73205i
$604$		0			0
$605$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$606$	−1.00000			−1.00000
$607$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$608$		0			0
$609$	−1.00000			−1.00000
$610$	1.00000	+	1.73205i	1.00000	+	1.73205i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	−1.00000			−1.00000
$615$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$616$		0			0
$617$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$617$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$618$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$622$		0			0
$623$	−2.00000			−2.00000
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	+	0.866025i	0.500000	+	0.866025i
$641$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$641$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	1.00000			1.00000
$643$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$643$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$644$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$645$	−1.00000			−1.00000
$646$		0			0
$647$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$647$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$648$	0.500000	+	0.866025i	0.500000	+	0.866025i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.00000	−	1.73205i	1.00000	−	1.73205i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	0.500000	−	0.866025i	0.500000	−	0.866025i
$655$		0			0
$656$	0.500000	−	0.866025i	0.500000	−	0.866025i
$657$		0			0
$658$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$661$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$662$		0			0
$663$		0			0
$664$	0.500000	+	0.866025i	0.500000	+	0.866025i
$665$		0			0
$666$		0			0
$667$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$668$	1.00000	−	1.73205i	1.00000	−	1.73205i
$669$	0.500000	−	0.866025i	0.500000	−	0.866025i
$670$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$671$		0			0
$672$	0.500000	−	0.866025i	0.500000	−	0.866025i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.500000	−	0.866025i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.00000			2.00000
$682$		0			0
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	1.00000			1.00000
$687$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$688$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$689$		0			0
$690$	−2.00000			−2.00000
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−1.00000			−1.00000
$695$		0			0
$696$	0.500000	−	0.866025i	0.500000	−	0.866025i
$697$		0			0
$698$	1.00000	+	1.73205i	1.00000	+	1.73205i
$699$		0			0
$700$	−1.00000			−1.00000
$701$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$701$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.500000	−	0.866025i	0.500000	−	0.866025i
$706$		0			0
$707$	1.00000			1.00000
$708$		0			0
$709$	2.00000			2.00000			1.00000			$0$
$709$	2.00000			2.00000			1.00000			$0$
$710$		0			0
$711$		0			0
$712$	1.00000	−	1.73205i	1.00000	−	1.73205i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	1.00000			1.00000
$721$	0.500000	−	0.866025i	0.500000	−	0.866025i
$722$	0.500000	+	0.866025i	0.500000	+	0.866025i
$723$	1.00000			1.00000
$724$	−1.00000			−1.00000
$725$	−1.00000			−1.00000
$726$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$727$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$727$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$		0			0
$731$		0			0
$732$	1.00000	+	1.73205i	1.00000	+	1.73205i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$	0.500000	−	0.866025i	0.500000	−	0.866025i
$735$	0.500000	+	0.866025i	0.500000	+	0.866025i
$736$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$737$		0			0
$738$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$743$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$744$		0			0
$745$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$746$		0			0
$747$	1.00000			1.00000
$748$		0			0
$749$	−1.00000			−1.00000
$750$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	1.00000			1.00000
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$761$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$762$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$763$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$764$		0			0
$765$		0			0
$766$	0.500000	+	0.866025i	0.500000	+	0.866025i
$767$		0			0
$768$	0.500000	+	0.866025i	0.500000	+	0.866025i
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$	−1.00000			−1.00000
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$784$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$785$		0			0
$786$		0			0
$787$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$787$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	−1.00000			−1.00000
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		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
$800$	0.500000	−	0.866025i	0.500000	−	0.866025i
$801$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$802$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$803$		0			0
$804$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$805$	2.00000			2.00000
$806$		0			0
$807$	1.00000	−	1.73205i	1.00000	−	1.73205i
$808$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$809$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$809$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$810$	0.500000	−	0.866025i	0.500000	−	0.866025i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$813$		0			0
$814$		0			0
$815$	−2.00000			−2.00000
$816$		0			0
$817$		0			0
$818$	1.00000			1.00000
$819$		0			0
$820$	−1.00000			−1.00000
$821$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$821$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$823$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$824$	0.500000	+	0.866025i	0.500000	+	0.866025i
$825$		0			0
$826$		0			0
$827$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$827$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$828$	−2.00000			−2.00000
$829$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$829$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$830$	0.500000	−	0.866025i	0.500000	−	0.866025i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−2.00000			−2.00000
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$	−1.00000			−1.00000
$841$		0			0
$842$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$843$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$844$		0			0
$845$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$846$	0.500000	−	0.866025i	0.500000	−	0.866025i
$847$	0.500000	−	0.866025i	0.500000	−	0.866025i
$848$		0			0
$849$	0.500000	+	0.866025i	0.500000	+	0.866025i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$853$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$854$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$855$		0			0
$856$	0.500000	−	0.866025i	0.500000	−	0.866025i
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$861$	0.500000	+	0.866025i	0.500000	+	0.866025i
$862$		0			0
$863$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$863$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$864$	1.00000			1.00000
$865$		0			0
$866$		0			0
$867$	−1.00000			−1.00000
$868$		0			0
$869$		0			0
$870$	−1.00000			−1.00000
$871$		0			0
$872$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$873$		0			0
$874$		0			0
$875$	0.500000	+	0.866025i	0.500000	+	0.866025i
$876$		0			0
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.00000			2.00000			1.00000			$0$
$881$	2.00000			2.00000			1.00000			$0$
$882$	0.500000	+	0.866025i	0.500000	+	0.866025i
$883$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$883$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$884$		0			0
$885$		0			0
$886$	−1.00000			−1.00000
$887$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$888$		0			0
$889$	0.500000	+	0.866025i	0.500000	+	0.866025i
$890$	−2.00000			−2.00000
$891$		0			0
$892$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$893$		0			0
$894$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$895$		0			0
$896$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$897$		0			0
$898$	1.00000			1.00000
$899$		0			0
$900$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$901$		0			0
$902$		0			0
$903$	1.00000			1.00000
$904$		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			$\pi$
$908$	1.00000	−	1.73205i	1.00000	−	1.73205i
$909$	0.500000	+	0.866025i	0.500000	+	0.866025i
$910$		0			0
$911$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$911$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	1.00000	−	1.73205i	1.00000	−	1.73205i
$916$	0.500000	+	0.866025i	0.500000	+	0.866025i
$917$		0			0
$918$		0			0
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$921$	0.500000	+	0.866025i	0.500000	+	0.866025i
$922$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.500000	−	0.866025i	0.500000	−	0.866025i
$927$	1.00000			1.00000
$928$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$929$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$929$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	0.500000	−	0.866025i	0.500000	−	0.866025i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	1.00000	+	1.73205i	1.00000	+	1.73205i
$939$		0			0
$940$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$941$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$941$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$942$		0			0
$943$	2.00000			2.00000
$944$		0			0
$945$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$946$		0			0
$947$	−2.00000			−2.00000			−1.00000			$\pi$
$947$	−2.00000			−2.00000			−1.00000			$\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.500000	−	0.866025i	0.500000	−	0.866025i
$961$	1.00000			1.00000
$962$		0			0
$963$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$964$	0.500000	−	0.866025i	0.500000	−	0.866025i
$965$		0			0
$966$	2.00000			2.00000
$967$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$968$	0.500000	+	0.866025i	0.500000	+	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$	0.500000	−	0.866025i	0.500000	−	0.866025i
$973$		0			0
$974$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$975$		0			0
$976$	2.00000			2.00000
$977$		0			0		1.00000			$0$
$977$		0			0		−1.00000			$\pi$
$978$	−2.00000			−2.00000
$979$		0			0
$980$	1.00000			1.00000
$981$	−1.00000			−1.00000
$982$		0			0
$983$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$983$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$984$	−1.00000			−1.00000
$985$		0			0
$986$		0			0
$987$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$988$		0			0
$989$	1.00000	−	1.73205i	1.00000	−	1.73205i
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.500000	−	0.866025i	0.500000	−	0.866025i
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		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	1260.1.cw.b.499.1	yes	2
3.2	odd	2		3780.1.cw.d.3439.1		2
4.3	odd	2		1260.1.cw.c.499.1	yes	2
5.4	even	2		1260.1.cw.c.499.1	yes	2
7.4	even	3		1260.1.bj.d.319.1	yes	2
9.2	odd	6		3780.1.bj.a.2179.1		2
9.7	even	3		1260.1.bj.d.79.1	yes	2
12.11	even	2		3780.1.cw.a.3439.1		2
15.14	odd	2		3780.1.cw.a.3439.1		2
20.19	odd	2	CM	1260.1.cw.b.499.1	yes	2
21.11	odd	6		3780.1.bj.a.739.1		2
28.11	odd	6		1260.1.bj.a.319.1	yes	2
35.4	even	6		1260.1.bj.a.319.1	yes	2
36.7	odd	6		1260.1.bj.a.79.1	✓	2
36.11	even	6		3780.1.bj.c.2179.1		2
45.29	odd	6		3780.1.bj.c.2179.1		2
45.34	even	6		1260.1.bj.a.79.1	✓	2
60.59	even	2		3780.1.cw.d.3439.1		2
63.11	odd	6		3780.1.cw.d.3259.1		2
63.25	even	3	inner	1260.1.cw.b.1159.1	yes	2
84.11	even	6		3780.1.bj.c.739.1		2
105.74	odd	6		3780.1.bj.c.739.1		2
140.39	odd	6		1260.1.bj.d.319.1	yes	2
180.79	odd	6		1260.1.bj.d.79.1	yes	2
180.119	even	6		3780.1.bj.a.2179.1		2
252.11	even	6		3780.1.cw.a.3259.1		2
252.151	odd	6		1260.1.cw.c.1159.1	yes	2
315.74	odd	6		3780.1.cw.a.3259.1		2
315.214	even	6		1260.1.cw.c.1159.1	yes	2
420.179	even	6		3780.1.bj.a.739.1		2
1260.1019	even	6		3780.1.cw.d.3259.1		2
1260.1159	odd	6	inner	1260.1.cw.b.1159.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.1.bj.a.79.1	✓	2	36.7	odd	6
1260.1.bj.a.79.1	✓	2	45.34	even	6
1260.1.bj.a.319.1	yes	2	28.11	odd	6
1260.1.bj.a.319.1	yes	2	35.4	even	6
1260.1.bj.d.79.1	yes	2	9.7	even	3
1260.1.bj.d.79.1	yes	2	180.79	odd	6
1260.1.bj.d.319.1	yes	2	7.4	even	3
1260.1.bj.d.319.1	yes	2	140.39	odd	6
1260.1.cw.b.499.1	yes	2	1.1	even	1	trivial
1260.1.cw.b.499.1	yes	2	20.19	odd	2	CM
1260.1.cw.b.1159.1	yes	2	63.25	even	3	inner
1260.1.cw.b.1159.1	yes	2	1260.1159	odd	6	inner
1260.1.cw.c.499.1	yes	2	4.3	odd	2
1260.1.cw.c.499.1	yes	2	5.4	even	2
1260.1.cw.c.1159.1	yes	2	252.151	odd	6
1260.1.cw.c.1159.1	yes	2	315.214	even	6
3780.1.bj.a.739.1		2	21.11	odd	6
3780.1.bj.a.739.1		2	420.179	even	6
3780.1.bj.a.2179.1		2	9.2	odd	6
3780.1.bj.a.2179.1		2	180.119	even	6
3780.1.bj.c.739.1		2	84.11	even	6
3780.1.bj.c.739.1		2	105.74	odd	6
3780.1.bj.c.2179.1		2	36.11	even	6
3780.1.bj.c.2179.1		2	45.29	odd	6
3780.1.cw.a.3259.1		2	252.11	even	6
3780.1.cw.a.3259.1		2	315.74	odd	6
3780.1.cw.a.3439.1		2	12.11	even	2
3780.1.cw.a.3439.1		2	15.14	odd	2
3780.1.cw.d.3259.1		2	63.11	odd	6
3780.1.cw.d.3259.1		2	1260.1019	even	6
3780.1.cw.d.3439.1		2	3.2	odd	2
3780.1.cw.d.3439.1		2	60.59	even	2

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	1260.1.cw.b.499.1

Level	$1260$
Weight	$1$
Character	1260.499
Analytic conductor	$0.629$
Analytic rank	$0$
Dimension	$2$
Projective image	$D_{3}$
CM discriminant	-20
Inner twists	$4$